Answer:
1.
Monomial
A monomial is a single term algebraic expression. e.g.
4xy-3x^25y^3Binomial
A binomial is a two-term algebraic expression. e.g.
2x + 5-3y + 74x^2 - 2xTrinomial
trinomial is a three-term algebraic expression.
e.g.
x^3 - 2x^2 + 3x2x^2 + 4xy - 6y^23x^3 + 4x^2 - 5xPolynomial
A polynomial is a sum of one or more monomials.
e.g.
4x^3 - 3x^2 + 2x + 12x^4 + 3x^3 - 4x^2 + 5x - 66x^2 + 4xy - 2y^2Degree of a polynomial
the degree of a polynomial is the highest power of the variable in any of the terms.
e.g.
3x^4 + 2x^3 - 5x^2 + x - 7 (degree = 4)-2x^3 + 5x^2 - 3x + 1 (degree = 3)4x^5 - 2x^2 + 7 (degree = 5)2.
2x² - 4x + 3
The collection of algebra tiles includes 2 blue tiles with x², 4 red tiles with -x, and 3 yellow tiles with constant 1. By interpreting the tiles as algebraic terms, we can form the expression 2x² - 4x + 3, which combines the terms to represent the tiles' arrangement. The expression can be simplified or manipulated further using algebraic operations.
3.
algebra tiles to model the expression 3x²-4x+7.
I can only give sample:
3 red tiles containing x²
4 blue tiles containing -x.
7 white tiles containing 1.
The above drawing is the answer to no. 3 you can see the explaination in no.3 below.
Monomial
My Understanding of this term
Monomial, where only one term is there. We use no addition and subtraction sign to separate the variables.
An example that illustrates this term
5xy
Binomial
My understanding of this term
Binomial, where two terms are there. We use either addition or subtraction but separate only two variables.
An example that illustrates this term
4xy+ 2xya
Trinomial
My understanding of this term
Trinomial, where three terms are there. We use either both addition and subtraction sign or only subtraction or only addition. But we separate only three variables.
An example that illustrates this term
4xy+2ca+asd
Polynomial
My understanding of this term
Polynomial, where four or more than four terms.We use either both addition and subtraction sign or only subtraction or only addition. But we separate four or more than four variables.
An example that illustrates this term
4xy+2ca+asd+4xzy+10axy
Degree of a Polynomial
My understanding of this term
Degree of Polynomial is the highest of the degrees of the polynomial's Monomial's with non zero polynomial.
An example that illustrates this term
[tex]2 {x}^{2} + 5x {y}^{6} =6[/tex]
6 is the degree of polynomial as it is the highest.
2.
[tex]2 {x}^{2} - 4x + 3[/tex]
3.
[tex]3 {x}^{2} - 4x + 7[/tex]
The above drawing is the answer to the question. As it is a bit dirty I will explain it
as in no. 2 question you have to do the same way
the blue colour type should be 3 tiles of x^2. Then the red one should be same as no. 2. Then the yellow one we should write 7 ones.
ie
1 1 1 1 1 1 1
In yellow tyles
I hope it helped you.
find the equation that is parallel to the line y=x+9 and passes through the point (-6,7).Write the equation in slope intercept form
Answer: -1
Step-by-step explanation:
First, determine your slope from the given equation y = x - 6
In slope intercept form: y = mx + b, the value for m is the slope.
By looking at "x", there is a coefficient of 1 and therefore 1 is the slope.
Since parallel lines have the same slope, use the slope 1 to rewrite a second eqaution using
the point-slope formula: y - y1 = m(x - x1) and the given point (-6,7)
y - y1 = m(x - x1)
y - (7) = 1 (x - (-6)) (Plug in values)
y -7 = 1(x +-6) (Distribute negatives)
y -7 = -1x -6 (Distribute 1 to both terms in the parentheses)
+ 6 +6 (add 6 from both sides)
y = 1x - 1 OR y = x - 1
Check your work by plugging in the given point to your equation:
y = x - 1
6 = 7 - 1 (Plug in values)
7 = 7
which of the following is true with regards to statistical analysis? which of the following is true with regards to statistical analysis? bivariate analysis is a special form of multivariate analysis. it examines the relation between two or more variables. regression analysis is a univariate analysis. multivariate analysis examines the relationship between one, two or more variables. univariate analysis involves the analysis of a single variable.
The correct option is: "Univariate analysis involves the analysis of a single variable."
The following statement is true with regards to statistical analysis:
Univariate analysis involves the analysis of a single variable.
The other statements are not entirely accurate:
Bivariate analysis is a form of multivariate analysis that examines the relationship between two variables, but multivariate analysis can involve more than two variables.
Regression analysis is a multivariate analysis technique that examines the relationship between one dependent variable and one or more independent variables.
Multivariate analysis involves the examination of the relationship between two or more variables, not necessarily one, two, or more.
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a scientist claims that the mean gestation period for a fox is more than 48.9 weeks. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g
The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.
If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.
The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.
Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.
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if nurse susan jones day includes seven trips from the nursing pod to each of the 12 rooms back and forth, 20 trips to the central medical supply, six trips to the break room, and 12 trips to the pod linen supply, how many miles does she walk during her shift? what are the differences in the travel times between the two nurses for the random day?
Nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.
Without knowing the travel times of the two nurses, it is not possible to determine the differences in their travel times for a random day.
Assuming that each trip from the nursing pod to a room and back is approximately 50 feet and each trip to the central medical supply, break room, and linen supply is approximately 100 feet, nurse Susan Jones would walk a total of:
- 7 trips to each of the 12 rooms = 7 x 12 x 2 x 50 feet = 8,400 feet
- 20 trips to the central medical supply = 20 x 2 x 100 feet = 4,000 feet
- 6 trips to the break room = 6 x 2 x 100 feet = 1,200 feet
- 12 trips to the pod linen supply = 12 x 2 x 100 feet = 2,400 feet
Therefore, nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.
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Nurse Susan Jones would walk nearly 34.4 miles during her shift.
Assuming that Nurse Susan Jones walks an average of 0.2 miles per round trip, she would walk approximately 34.4 miles during her shift (7 trips x 12 rooms x 2 round trips x 0.2 miles per round trip + 20 trips x 2 round trips x 0.2 miles per round trip + 6 trips x 2 round trips x 0.2 miles per round trip + 12 trips x 2 round trips x 0.2 miles per round trip).
Unfortunately, there is not enough information provided to calculate the differences in travel times between two nurses on a random day. It would depend on factors such as the number and location of rooms each nurse is responsible for, the location of the medical supply and break room, and any additional tasks or responsibilities each nurse has during their shift.
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in the faculty lecture, dr. salon mentioned a survey that was taken in the slums in nairobi. from this survey, how long did the average person live in the slums?
Without specific data from the survey, I cannot provide the exact average length of time a person lived in the slums. I can be found by collecting data and finding average.
In general, surveys can be used to gather information on a population's characteristics and experiences, including their life expectancy. If the survey conducted in the slums of Nairobi included questions about life expectancy or mortality rates, the average lifespan of the individuals surveyed could be calculated using the data collected. It's important to note that the average lifespan in the slums may differ from that of other areas in Nairobi or other regions of the world.
Based on the information provided, Dr. Salon mentioned a survey conducted in the slums of Nairobi. To determine how long the average person lived in the slums, we would follow these steps:
1. Collect the data: The survey would gather information about the length of time people lived in the slums.
2. Calculate the average: Add up the total number of years all respondents lived in the slums and divide by the total number of respondents.
Without specific data from the survey, can't provide the exact average length of time a person lived in the slums. Please provide more information or refer back to Dr. Salon's lecture for the results of the survey.
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FINANCE Rawan deposits $13,000 into an account that pays 2.6% annual interest
compounded every 6 months.
a. Write a function to represent the balance A in the account after t years.
b. What will be the balance after 4 years?
c. What will be the balance after 7.5 years?
a) Required function is [tex]A(t) = 13,000 \times (1.013)^{2t}[/tex]
b) The balance after 4 years is $15,182.51.
c)The balance after 7.5 years is $16,802.59
a. What is the function represent the balance A in the account after t years?
The function to represent the balance A in the account after t years can be given by:
[tex]A(t) = P \times (1 + \frac{r}{n})^{(nt)}[/tex]
where P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = $13,000, r = 2.6%, n = 2 (interest is compounded every 6 months), and t is the time in years.
Substituting these values into the formula,
[tex]A(t) = 13,000 \times (1 + \frac{ 0.026}{2})^{(2t)}[/tex]
Simplifying the expression,
[tex]A(t) = 13,000 \times (1.013)^{2t}[/tex]
b. To find the balance after 4 years, we can substitute t = 4 into the formula we derived above:
[tex]A(4) = 13,000 \times (1.013)^{(2 \times 4)} \\ = 13,000 \times (1.013)^8 \\ = 15,182.51[/tex]
Therefore, the balance after 4 years is $15,182.51.
c. To find the balance after 7.5 years, we can substitute t = 7.5 into the formula we derived above:
A(t) = 13,000 × (1.013)¹⁵ = 16,802.59
Therefore, the balance after 7.5 years is $16,802.59.
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Janelle opened a savings account with $500 that earns 0.3% simple interest annually. After how many years will the balance in the account be $510.50?
It will take 7 years for Janelle's savings account balance to reach $510.50 at an annual interest rate of 0.3%.
What is simple interest?The interest rate on a loan or investment is calculated using the original principal amount. It does not take into account the effects of compounding, hence the interest charge or payment does not alter over time. Simple interest can be applied to several sorts of loans or savings accounts. It is computed only on the basis of the principal.
We can use the formula for simple interest to solve this problem:
Simple Interest = Principal * Rate * Time
where Principal is the initial amount in the account, Rate is the annual interest rate, and Time is the number of years.
Let's use the given information to find the time it takes to reach a balance of $510.50:
Simple Interest = $510.50 - $500 = $10.50
Principal = $500
Rate = 0.3% = 0.003 (since the rate is given as a percentage, we need to divide by 100 to get the decimal equivalent)
Substituting these values into the formula, we get:
$10.50 = $500 * 0.003 * Time
Simplifying this equation, we get:
Time = $10.50 / ($500 * 0.003) = 7 years
Therefore, it will take 7 years for Janelle's savings account balance to reach $510.50 at an annual interest rate of 0.3%.
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The figure shows the dimensions of two city parks, where RST is congruent to XYZ and YX is congruent to XYZ. A city
employee wants to order new fences to surround both parks. What is the total length of the fences
required to surround the parks?
The total length of fences needed to surround the parks is ______
feet.
The total length of fences needed to surround the parks is 1500 feet. The length is calculated by adding up the lengths of all sides of both parks.
To find the total length of fences needed to surround the parks, we need to add up the lengths of all the sides of both parks.
For park RST, the total length of the fences needed is
RS + ST + RT = 230 + 350 + 230 = 810 ft
For park XYZ, since YX is congruent to XYZ, we can label YX as YZ for simplicity. The total length of the fences needed for park XYZ is
XY + YZ + XZ = YZ + YZ + 230 = 2YZ + 230
To find YZ, we can use the fact that park RST is congruent to park XYZ, so the corresponding sides are equal in length. This means YZ = RT = 230 ft.
Substituting this value, we get
2YZ + 230 = 2(230) + 230 = 690 ft
Therefore, the total length of fences needs to surround two parks with dimensions ARST XYZ and YX YZ is
810 + 690 = 1500 ft.
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--The given question is incomplete, the complete question is given
" The figure shows the dimensions of two city parks, where RST is congruent to XYZ and YX is congruent to XYZ. A city
employee wants to order new fences to surround both parks. What is the total length of the fences
required to surround the parks?
ST is 350 ft., XZ is 230 ft.
The total length of fences needed to surround the parks is ______
feet."--
dean halverson recently read that full-time college students study 20 hours each week. she decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. a random sample of 33 students were asked to keep a diary of their activities over a period of several weeks. it was found that the average number of hours that the 33 students studied each week was 22.2 hours. the sample standard deviation of 3.9 hours. find the p -value. the p -value should be rounded to 4-decimal places.
The p-value is 0.0001, indicating strong evidence that college students study more than 20 hours per week based on the sample data.
How to calculate the p-value?To test the hypothesis that the average number of hours that college students study per week is greater than 20, we can use a one-sample t-test.
The null hypothesis is that the population mean is equal to 20 hours per week, while the alternative hypothesis is that the population mean is greater than 20 hours per week.
Let's calculate the t-value:
t = (sample mean - hypothesized population mean) / (sample standard deviation / √(sample size))
t = (22.2 - 20) / (3.9 / √(33))
t = 4.49
The degrees of freedom for the t-test is 33 - 1 = 32.
Using a t-table or calculator, we can find the p-value associated with a t-value of 4.49 and 32 degrees of freedom. The p-value is less than 0.0001 (it is actually very close to 0), which means that there is very strong evidence to reject the null hypothesis and conclude that college students study more than 20 hours per week.
Therefore, the p-value is 0.0001 (rounded to 4 decimal places).
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During a snowstorm, Annabelle tracked the amount of snow on the ground. When
the storm began, there were 3 inches of snow on the ground. Snow fell at a constant
rate of 1 inch per hour until another 4 inches had fallen. The storm then stopped for 6
hours and then started again at a constant rate of 2 inches per hour for the next 5
hours. As soon as the storm stopped again, the sun came out and melted the snow for
the next 7 hours at a constant rate of 2 inches per hour. Make a graph showing the
inches of snow on the ground over time using the data that Annabelle collected.
The graph will have a horizontal line from 4 to 15 hours (since there is no change in snow depth during that time) and two downward sloping lines from 0 to 4 hours and from 15 to 22 hours (representing snowfall and snow melt, respectively)
How to draw a graph?To make a graph of the inches of snow on the ground over time, we can use the following steps:
We can divide the time into different intervals based on the snowfall, the break in the storm, and the snow melt. We have:
Snowfall for the first 4 hours (at a rate of 1 inch per hour).Break in the storm for 6 hours.Snowfall for the next 5 hours (at a rate of 2 inches per hour).Snow melt for the next 7 hours (at a rate of 2 inches per hour).We can then calculate the inches of snow on the ground at the end of each interval, starting with the initial 3 inches of snow. We have:
After 4 hours of snowfall: 3 + 4(1) = 7 inches of snow on the ground.After 10 hours (4 hours of snowfall + 6 hours of break): 7 inches of snow on the ground.After 15 hours (10 hours + 5 hours of snowfall): 7 + 5(2) = 17 inches of snow on the ground.After 22 hours (15 hours + 7 hours of snow melt): 17 - 7(2) = 3 inches of snow on the ground.We can now plot these points on a graph with time (in hours) on the x-axis and inches of snow on the y-axis. The graph will have four points: (0,3), (4,7), (15,17), and (22,3).
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Convert the polar coordinates (6, -π/3) to Cartesian coordinates. Leave answers in fractional form. Use the "/" key as the fraction bar.
the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).
What is a fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:
x = r cos(θ)
y = r sin(θ)
Substituting the given values, we get:
x = 6 cos(-π/3) = 6 × (1/2) = 3
y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3
Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).
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4negative slope equations, 2undefined slope equations, and 2zero slope equations (y=mx+b)
Answer:
negative
y=-x
y=-2x+6
y=(-1/2)x+1
y=-5x+20
undefined
x=4
x=-3
zero slope
y=2
y=-100
Write down the equations of six lines that increase in steepness
Answer:
Step-by-step explanation:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Solve the system using linear combination. Show all work.
{3x+4y=21
{5x+4y=11
Therefore, the solution to the system of equation is (x, y) = (-5, 9).
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, the left-hand side and the right-hand side, separated by an equals sign (=). An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
To solve the system using linear combination, we want to eliminate one of the variables by adding the two equations together.
{3x + 4y = 21
{5x + 4y = 11
Notice that if we subtract the first equation from the second, we get:
(5x + 4y) - (3x + 4y) = 11 - 21
2x = -10
x = -5
Now we can substitute x = -5 into either of the original equations and solve for y:
3x + 4y = 21
3(-5) + 4y = 21
-15 + 4y = 21
4y = 36
y = 9
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Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations. A. 5 × 3 = 15 B. 1 5 × 1 3 = 1 15 C. 1 5 × 3 = 3 5 D. 5 ÷ 1 3 = 15 E. 1 3 ÷ 5 = 1 15
Answer: a and d
Step-by-step explanation:
1 pear = 3 slices
5 pears = 15 slices
5x3=15
OR
5/1/3=15
Equation A and Equation D are the two equations that Kylie can use to solve the problem.
This is a simple mathematics problem.
Kylie has five pears. She cuts each of her pears into thirds, i.e., three slices of each pear.
So, now Kylie will do the same for each pear she has:
Total Slices with Kylie = 5 x 3
Total Slices with Kylie = 15
Equation D can also be used to define the situation of Kylie. Total pears with her are five and each pear is divided into thirds, i.e., 1/3
Total Slices with Kylie = 5 ÷ 1/3
Total Slices with Kylie = 15
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Chase is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2.50 per mile driven. Make a table of values and then write an equation for C,C, in terms of m,m, representing the total cost of renting the truck if Chase were to drive m miles.
The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
What is the equation?Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
The equation would be:
C is the total cost and m is the miles driven.
We know that:
Charge of the truck: $35
Charge per mile: $2.50
Then, form the equation as follows:
C = 35 + 2.50m
Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
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#15 Please HELP!!!!!!!!!!!!!!!
The calculated measure of the arc PM is 19 degrees
Calculating the measures of the arc PMFrom the question, we have the following parameters that can be used in our computation:
The circle
The angles created by secants and tangents that intersect outside a circle, which states that
The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.
So, we have
PM = 1/2 * (59 - 21)
Evaluate
PM = 19
Hence, the measure of the arc is 19 degrees
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o bill starts riding his bike towards town at a constant rate of 8 mph. then, 30 minutes later, his wife starts driving on the same path at a constant average of 30 mph. how long will it take her to catch up to bill?
So, it will take approximately 0.1818 hours (around 11 minutes) for Bill's wife to catch up to him.
To determine how long it will take Bill's wife to catch up to him, we can use the concept of relative speed.
First, let's calculate the distance Bill covers in 30 minutes (0.5 hours) before his wife starts driving:
Distance = Speed × Time
Distance = 8 mph × 0.5 hours = 4 miles
Now, let's calculate the relative speed between Bill and his wife:
Relative Speed = Wife's Speed - Bill's Speed
Relative Speed = 30 mph - 8 mph = 22 mph
Now, we can calculate the time it will take for Bill's wife to catch up to him:
Time = Distance / Relative Speed
Time = 4 miles / 22 mph ≈ 0.1818 hours
So, it will take approximately 0.1818 hours (around 11 minutes) for Bill's wife to catch up to him.
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It will take his wife 2/11 hours (approximately 0.18 hours or about 11 minutes) to catch up to Bill.
Let's use the terms rate, time, and distance in our explanation.
Bill's rate is 8 mph.
His wife's rate is 30 mph.
The time Bill has ridden before his wife starts is 0.5 hours (30 minutes).
Calculate the distance Bill has ridden before his wife starts: distance = rate × time
distance = 8 mph × 0.5 hours
distance = 4 miles
Set up the equation to find the time it takes for his wife to catch up to Bill:
(rate of Bill) × (time for wife) = (rate of wife) × (time for wife) - 4 miles
Solve for the time for his wife:
8 × (time for wife) = 30 × (time for wife) - 4
8 × (time for wife) = 30 × (time for wife) - 4
8 × (time for wife) - 30 × (time for wife) = -4
-22 × (time for wife) = -4
time for wife = 4/22 = 2/11 hours.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru typically has less wait time, and why?
Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean
The correct answer is: Super Fast Food, because it has a smaller median.
What is the median?
The median is a measure of central tendency that represents the middle value in a set of data when the data is arranged in ascending or descending order.
Based on the given information, Super Fast Food typically has less wait time compared to Fast Chicken.
The median is the middle value in a set of data, and it is often used as a measure of central tendency in box plots. In this case, the median for Super Fast Food is 12, while the median for Fast Chicken is 12.5. Since the median for Super Fast Food is smaller than the median for Fast Chicken, it suggests that the wait times at Super Fast Food are generally lower than those at Fast Chicken.
Hence, the correct answer is: Super Fast Food, because it has a smaller median.
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Restaurant Revenue
In this activity, you will create quadratic inequalities in one variable and use them to solve problems. Read this scenario, and then use the information to answer the questions that follow.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
Part A
Question
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
Enter the correct answer in the box. Type the cost expression on the first line and the customer expression on the second line
The cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x). Also the inequality equation is 160 - 4x -2[tex]x^{2}[/tex] [tex]\geq[/tex] 130 to maintain minimum revenue of $130 after rising price by x number of times by $1 as 2 customers leave on average per hour.
Let x represents the number of $1 increases in the cost of the buffet.
Noah manages a buffet at a local restaurant and charges $10 for the buffet.
On average, 16 customers choose the buffet as their meal every hour.
That is, the average revenue from 16 customers is = $(10*16)= $160
After surveying Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour.
That is, as cost of buffet for every hour rises by $x from $10 we get, $ (10+x) , and the average number of customers who select the buffet will decrease by 2 per hour.
The new average number of customers per hour after rise in cost of buffet by $x is (16 -2x).
This implies, the revenue earned now is = $(16- 2x)(10 + x) = $(160 + 16x - 20x -2[tex]x^{2}[/tex] ) = $ (160 - 4x -2[tex]x^{2}[/tex] )
The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Thus, after the increase in price by $x per hour , the inequality equation that helps Noah to pick best pricing decisions will be ,
160 - 4x -2[tex]x^{2}[/tex] [tex]\geq[/tex] 130
Here, cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x).
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Solve the right triangle. 5
6
F
E
D
30°
Write your answers in simplified, rationalized form. Do not round. DF =
DE =
10
m∠D =
60
°
The length of the other leg is 8 cm, and the measures of the two acute angles are approximately 36.87° and 53.13°.
To solve the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
[tex]10^2 = 6^2 + x^2 \\x = sqrt(10^2 - 6^2) = 8 cm[/tex]
So the length of the other leg is 8 cm.
Let θ be one of the acute angles:
sin(θ) = opposite/hypotenuse = 6/10 = 0.6
cos(θ) = adjacent/hypotenuse = x/10 = 8/10 = 0.8
θ ≈ 36.87°.
Since the other acute angle is complementary to θ, its measure is 90° - 36.87° = 53.13°.
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--The complete Question is, A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Solve the right triangle, finding the length of the other leg and the measures of the two acute angles. --
what is the range and domain of y = 3x^2 + 2?
The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
Define range!In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).
According to question:The given function is y = 3x² + 2.
The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.
Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.
The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).
Since the minimum value of the function is 2, the range of the function is [2, ∞).
Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
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Amy is sewing some pants for herself. This is the rule for how much fabric she needs to buy. • Measure from your waist to the finished length of thepants • Double this measurement • Add 8inches 1. Amy’s measurement from her waist to the finished length of the pants is 35inches. How many inches of fabric does sheneed?
Amy needs 78 inches of fabric for her pants if she follows the given rule.
Define inches ?
An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.
To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.
Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.
Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.
Therefore, Amy needs 78 inches of fabric for her pants.
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Consider w1 = 4 + 2i and w2 = –1 – 3i. Which graph represents the sum w1 + w2? On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (3, negative 5). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (3, negative 1). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (5, 5). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line goes from (0, 0) to point (5, 1).
The graph that represents the sum w1 + w2 is: b. A line goes from (0, 0) to point (3, negative 1). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real.
What graph represents the sum w1 + w2?To find the sum of w1 and w2, we simply add their real and imaginary parts separately:
w1 + w2 = (4 + 2i) + (-1 - 3i) = 3 - i
So the real part of the sum is 3, and the imaginary part is -1. Therefore, the sum w1 + w2 corresponds to the point (3, -1) on the coordinate plane.
The graph that represents this point is option (b), where a line goes from (0, 0) to point (3, -1) on a coordinate plane with the y-axis labeled imaginary and the x-axis labeled real. The other options do not represent the correct point or are not lines passing through the origin.
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tell whether the ordered pair is a solution of the inequality. 2z less than 15; z =11
The ordered pair (z, 11) is not a solution of the inequality.
Explain inequality
An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.
According to the given information
To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:
2z < 15
2(11) < 15
22 < 15 (this is false)
Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.
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(Score for Question 3: of 12 points) 3. What is the surface area of this composite solid? Show your work.
The surface area of this solid would be; 127.
To Find the surface area of the composite solid, we have;
Sides (a) area
4 * 3 = 12
12 * 2 = 24
Now Sides (b) area
7 * 3 = 21
21 * 3 = 63
Then Face (c) area
3 * 4 / 2 = 6
6 * 2 = 12
Base area
4 * 7 = 28
Total surface area
To calculate the total surface area we have to add the value of each face :
28 + 12 + 63 + 24 = 127
Thus, the surface area of this solid is 127.
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the mean life of a television set is 97 months with a variance of 169 . if a sample of 59 televisions is randomly selected, what is the probability that the sample mean would be less than 100.9 months? round your answer to four decimal places.
The probability that the sample mean would be less than 100.9 months is approximately 0.9600.
We can use the central limit theorem to approximate the sampling distribution of the sample mean as a normal distribution with a mean of 97 months (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.
The standard deviation of the sampling distribution can be calculated as follows
σ/√n = √(169)/√59 = 2.065
Therefore, the z-score corresponding to a sample mean of 100.9 months is
z = (100.9 - 97) / 2.065 = 1.75
Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score less than 1.75 is approximately 0.9599.
Therefore, the probability that the sample mean would be less than 100.9 months is approximately 0.9599.
Rounding this to four decimal places, we get
P(x < 100.9) ≈ 0.9600
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How many pair of numbers (x;y) that satisfy
log₃ (x² + y² + x) + log₂ (x² + y²) ≤ log₃ (x) + log₂ (x² + y² + 24x)
Answer:
We can simplify the given inequality using the properties of logarithms:
log₃ (x² + y² + x) + log₂ (x² + y²) ≤ log₃ (x) + log₂ (x² + y² + 24x)
log₃ [(x² + y² + x) / x] + log₂ [(x² + y²) / (x² + y² + 24x)] ≤ 0
log₃ [(x + y²) / x] + log₂ [(1 - 24x / (x² + y² + 24x))] ≤ 0
log₃ [(x + y²) / x] + log₂ [(x² + y² + 24x - 24x) / (x² + y² + 24x))] ≤ 0
log₃ [(x + y²) / x] + log₂ [(x² + y²) / (x² + y² + 24x))] ≤ 0
log₃ [(x + y²) / x] - log₂ [(x² + y² + 24x) / (x² + y²))] ≥ 0
log₃ [(x + y²) / x] - log₂ [(x + 24) / x] ≥ 0
log₃ [(x + y²) / x] ≥ log₂ [(x + 24) / x]
(x + y²) / x ≥ (x + 24) / x^2
x + y² ≥ x + 24
y² ≥ 24
y ≤ ± 2√6
Therefore, the system of inequalities that satisfies the given inequality is:
y ≤ 2√6, y ≥ -2√6
For each value of y between -2√6 and 2√6, there is a corresponding range of x values that satisfies the inequality.
For example, if y = 0, then the inequality simplifies to:
log₃ (x) + log₂ (x²) ≤ 0
log₃ x + 2 log₂ x ≤ 0
log₃ x + log₂ x² ≤ 0
log₆ x³ ≤ 0
x³ ≤ 1
x ≤ 1
So, if y = 0, then the possible values of x are:
0 < x ≤ 1
Thus, for each value of y between -2√6 and 2√6, there is a corresponding range of x values that satisfies the inequality.
Therefore, the total number of pairs (x,y) that satisfy the inequality is infinite, since there are infinitely many real numbers between -2√6 and 2√6, and each of these corresponds to a range of x values that satisfies the inequality.
Answer:
x
Step-by-step explanation:
To solve this inequality, we can use the properties of logarithms to simplify it. First, we can combine the two logarithms on the left side of the inequality using the product rule:
log₃[(x² + y² + x)(x² + y²)] ≤ log₃(x) + log₂(x² + y² + 24x)
Next, we can use the fact that logₐ(b) ≤ logₐ© if b ≤ c to simplify the right side of the inequality:
log₃[(x² + y² + x)(x² + y²)] ≤ log₃(x(x² + y² + 24x))
Now we can expand both sides of the inequality and simplify:
log₃(x⁴ + 2x³y² + x²y⁴ + x³ + xy²) ≤ log₃(x⁴ + 24x³)
Subtracting log₃(x⁴ + 24x³) from both sides gives:
log₃(x⁴ + 2x³y² + x²y⁴ + x³ + xy²) - log₃(x⁴ + 24x³) ≤ 0
Using the quotient rule for logarithms gives:
log₃[(x⁴ + 2x³y² + x²y⁴ + x³ + xy²)/(x⁴ + 24x³)] ≤ 0
Finally, we can use the fact that logₐ(b) ≤ 0 if and only if b ≤ 1 to solve for x and y:
(x⁴ + 2x³y² + x²y⁴ + x³ + xy²)/(x⁴ + 24x³) ≤ 1
Multiplying both sides by (x⁴ + 24x³) gives:
x⁴ + 2x³y² + x²y⁴ + x³ + xy² ≤ x⁴ + 24x³
Simplifying gives:
2x³y² + x²y⁴ + x³ - 24x³ ≤ -xy²
Rearranging terms gives:
xy² - 2x³y² - x²y⁴ - x³ + 24x³ ≥ 0
Factoring out an xy term gives:
xy(y - (2x)^(3/2))(y + (2x)^(3/2)) ≥ 0
This inequality holds when either y ≥ (2x)^(3/2) or y ≤ -(2x)^(3/2). Therefore, there are two pairs of numbers that satisfy this inequality for any given value of x.
I hope this helps!
On a trip, you had to change your money from dollars to euros.
You got 450
euros for 600
dollars.
What is a unit rate that describes the exchange?
Answer: 0.75 euros = 1 dollar
Step-by-step explanation:
Unit rate
450 euros ----> 600 dollars
450/600 = 0.75
0.75 euros = 1 dollar
Uni rate for the exchange of dollars to euros is 0.75 euros/dollars.
Explanation :[tex]\implies[/tex] To find the unit rate of exchange from dollars to euros, divide the amount of euros Monica received by the amount of dollars she paid:
[tex]\largearrow{\sf{\boxd{\boxed{Unit \ change = \dfrac{Number \ of \ euros \ you \got}{Number \ of \ dollars \ you \ have} }}}}[/tex]
[tex]\implies{\sf{Unit \ change = \dfrac{\cancel{450}}{\cancel{600}} }}[/tex]
[tex]\implies{\sf{Unit \ change = 0.75 }}[/tex]
As a result, the unit rate for the exchange of dollars to euros is 0.75 euros/dollar.
In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 4.5 inches. Out of the 1912 boys who go to that school, how many would be expected to be between 61 and 70 inches tall, to the nearest whole number?
The range of heights between 66 inches and 76 inches indicates the center 95% of males' heights from this school.
What do we mean by interval?All the numbers between two specific integers are referred to as an interval.
All actual values between those two are included in this range.
The class interval is calculated by deducting the upper limit from the class' lower limit.
The following is the formula for the class interval: Upper limit - Lower limit equals the class interval.
Let x represent the heights of the male students at this institution.
The Empirical Rule states that given the mean and standard deviation:
1) Approximately 68% of the x values fall within the range of the mean plus or minus one standard deviation.
2) Nearly 95% of the x values fall within the range of the mean plus or minus two standard deviations.
3) Nearly 99.7% of the x values fall within a range of 3 standard deviations either above or below the mean.
Considering the data provided:
mean = 71 inches
Standard deviation = 2.5 inches
We want to know where 95% of the x values fall. The variation from the mean is 2 standard deviations. Therefore,
2 standard deviations = 2 × 2.5 = 5 inches
Heights:
71 - 5 = 66 inches and
71 + 5 = 76 inches
Therefore, the range of heights between 66 inches and 76 inches indicates the center 95% of males' heights from this school.
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Complete question:
In an all-boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 2.5 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.