Suppose fhat F(x) = x^2 and G(x) = -1/4 (x+7)^2 . Which statement best compares the graph of G(x) with the graph if F(x)?
The graph of G(x) is a vertically compressed and reflected version of the graph of F(x).
What is a graph?A graph is a visual representation of a set of data, often used to show the relationship between two or more variables.
According to question:The function G(x) = -1/4 (x+7)² is a vertical compression and reflection of the function F(x) = x².
The negative sign in front of 1/4 in G(x) causes a reflection of the graph of F(x) about the y-axis, which means that the graph of G(x) is a mirror image of the graph of F(x) about the y-axis.
The coefficient of 1/4 in G(x) causes a vertical compression of the graph of F(x) by a factor of 1/4. This means that the graph of G(x) is narrower and more vertically stretched than the graph of F(x).
Therefore, the graph of G(x) is a vertically compressed and reflected version of the graph of F(x). In other words, G(x) is a transformation of F(x).
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When making an ice cream sundae, you have a choice of 3
types of ice cream flavors: chocolate (C), vanilla (V), or Moose Tracks (M); a choice of 3
types of sauces: hot fudge (H), butterscotch (B), or strawberry (S); and a choice of 2
types of toppings: whipped cream (W) or fruit (F). If you are choosing only one of each, list the sample space in regard to the sundaes (combinations of ice cream flavors, sauces, and toppings) you could pick from.
Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }
Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}
find the general antiderivative of (((7/ (x^(1/3))) - 4 (x^2)^(1/3)
Answer:[tex]\frac{21}{2} x^{2/3} - \frac{12}{5}x^{\frac{5}{3} } + C[/tex]
Step-by-step explanation:
[tex]\int {\frac{7}{x^{1/3} }-4x^{2/3} } \, dx \\\int {7x^{-1/3}} - 4x^{2/3}\, dx \\= 7*\frac{3}{2}x^{2/3} - 4*\frac{3}{5}x^{\frac{5}{3} } + C\\ =\frac{21}{2} x^{2/3} + \frac{12}{5}x^{\frac{5}{3} } + C\\\\\\ Assuming: (x^{2})^\frac{1}{3}[/tex]
I need help with Question 15 of my homework.
The probability of exactly 3 successes in 15 trials with a probability of success on a single trial of 0.77 is approximately 0.1648.
What is probability of exactly 3 successes in 15 trials?To find the probability of exactly 3 successes in a binomial distribution with n=15 trials and a probability of success on a single trial q=0.77, we can use the formula for the probability mass function of the binomial distribution:
P(X=k) = (n choose k) * q^k * (1-q)^(n-k)
Substituting the given values into the formula, we get:
P(X=3) = (15 choose 3) * 0.77^3 * (1-0.77)^(15-3)
P(X=3) = (15!/((15-3)!3!)) * 0.77^3 * 0.23^12
P(X=3) = 0.1648.
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pls solve asap ..... for 15 points
tysm
as will mark brainlist
Answer:
a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.
b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.
The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.
How to find the time taken ?The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:
= 200 / 80
= 2.5 hours
He arrived at :
= 10 + 2.5 hours
= 12 : 30 am
The difference was :
= 13: 50 arrival of Karen - 12 : 30
= 1 hour 20 minutes
To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.
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PLEASE HELP QUICK IM CONFUSEDDD
Answer:
x = 2.16228, -4.16228
Step-by-step explanation:
(2x² - 2x) - 5 = (x - 2)²
2x² - 2x - 5 = x² - 4x + 4
x² + 2x - 9 = 0
Use quadradic equation to find the roots of x: a=1 , b=2, c=-9
x = 1 ± √10
x = 2.16228, -4.16228
Kate watered all the flowers at a business park. While watering, she noticed the daisies had
been planted in groups of 3 and the lilies had been planted in groups of 12. If Kate watered
the same number of each flower, what is the minimum number of each that she must have
watered?
Katemust have watered at least 12 daisies (in groups of 3) and 12 lilies (in groups of 12).
What is the minimum number of each that she must have watered?To determine the minimum number of each flower Kate must have watered, we need to find the least common multiple (LCM) of 3 and 12.
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The multiples of 12 are: 12, 24, 36, 48, 60, ...
We can see that the least common multiple of 3 and 12 is 12, as it is the smallest number that appears in both lists. Therefore, she must have watered at least 12 daisies (in groups of 3) and 12 lilies (in groups of 12).
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Problem 3: Find the diameter of a semicircle with an area of 76.97 square yards.
The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.
What is the diameter of a semicircle with an area of 76.97Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²
Where r radius and π is constant pi.
Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:
76.97 = 1/2 × (πr²)
Multiplying both sides by 2, we get:
153.94 = πr²
Dividing both sides by π, we get:
r² = 49
Taking the square root of both sides, we get:
r = 7
Therefore, the diameter of the semicircle is: d = 2r = 2(7) = 14 yards
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if g(x)= 3x²+7x-1, then f'(x)=?
Answer:
Step-by-step explanation:
Answer: The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.
To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).
Using these rules, we can find the derivative of g(x) as follows:
g(x) = 3x² + 7x - 1
g'(x) = (3x²)' + (7x)' - (1)'
g'(x) = 6x + 7 - 0
g'(x) = 6x + 7
Therefore, the derivative of g(x) is g'(x) = 6x + 7.
Step-by-step explanation:
You may need to use the appropriate technology to answer this question.
The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.
Company A
34 59 43 30 3
32 42 85 30 48
110 50 10 26 70
52 83 78 27 70
27 90 38 52 76
Company B
45 63 42 32 67
104 45 27 38 84
75 46 32 50 64
41 36 33 65 64
(a)
Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let 1 = population mean minutes late for delayed Company A flights and 2 = population mean minutes late for delayed Company B flights.)
H0: 1 − 2 < 0
Ha: 1 − 2 = 0
H0: 1 − 2 ≤ 0
Ha: 1 − 2 > 0
H0: 1 − 2 ≥ 0
Ha: 1 − 2 < 0
H0: 1 − 2 ≠ 0
Ha: 1 − 2 = 0
H0: 1 − 2 = 0
Ha: 1 − 2 ≠ 0
(b)
What is the sample mean number of minutes late for delayed flights for each of these two airlines?
Company A
min
Company B
min
(c)
Calculate the test statistic. (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
Using a 0.05 level of significance, what is your conclusion?
Do not Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0
(b) Means: Company A___50.6___ min.; Company B___52.75___ min.
c)The t-value is -0.30107., The p-value is 0 .764815.
What is a Hypothesis?A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon
A)H0: μ1 − μ2 = 0
i.e there is no difference between the means of delayed flight for two different airlines
Ha: μ1 − μ2 ≠ 0
i.e there is a difference between the means of delayed flight for two different airlines
(b)
Company A___50.6___ min.
Company B___52.75___ min.
Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25
= 1265/25= 50.6
Mean of Company B = x`2= ∑x/n =
=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20
= 1055/20= 52.75
Difference Scores Calculations
Company A
Sample size for Company A= n1= 25
Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24
Mean for Company A= x`1= 50.6
Total Squared Difference (x-x`1) for Company A= SS1: 16938
s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75
Company B
Sample size for Company B= n1= 20
Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19
Mean for Company B= x`2= 52.75
Total Squared Difference (x-x`2) for Company B= SS2=7427.75
s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93
T-value Calculation
Pooled Variance= Sp²
Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)
Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65
s2x`1 = s2p/n1 = 566.65/25 = 22.67
s2x`2 = s2p/n2 = 566.65/20 = 28.33
t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3
The t-value is -0.30107.
The total degrees of freedom is = n1+n2- 2= 25+20-2=43
The critical region for two tailed test at significance level ∝ =0.05 is
t(0.025) (43) = t > ±2.017
Since the calculated value of t= -0.30107. does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.
The p-value is 0 .764815. The result is not significant at p < 0.05.
C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
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6. Which transformation(s) must be applied to object A to place it in the position of object B?
rotation, reflection, and translation
reflection and translation
rotation and reflection
rotation and translation
The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).
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Answer:
b. reflection and translation
Step-by-step explanation:
how do i do this. please help thank you
Answer:
[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]
find g(x+4): g(x)=-5+2x/1+x
2x + 3/x + 5 is the value of expression .
What is an expression in mathematics?
A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:
The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.
g(x) = -5+2x/1+x
g(x+4) = -5+2(x + 4)/1+(x + 4 )
= -5 + 2X + 8/1 + X + 4
= 2x + 3/x + 5
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The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25
The answer is $359.25, which is closest to option A: $363.75.
What is multiplication?Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:
$75 × $4.79 = $359.25
Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.
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Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment. A 5-column table with 2 rows. Column 1 is labeled Bond with entries A B C 7 and one-half 15, X Y Z 7 and three-fourths 15. Column 2 is labeled current yield with entries 7.5, 8.4. Column 3 is labeled volume with entries 128, 17. Column 4 is labeled Close with entries 104 and three-fourths, 100 and one-half. Column 5 is labeled Net change with entries blank, + one-fourth. If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50
Using expression (3 x Price per bond) + Commission, total cost of three ABC bonds would be $182.70.
What exactly are expressions?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated or simplified to produce a value. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions.
Now,
The cost of three ABC bonds can be calculated as follows:
Total cost of three ABC bonds = (3 x Price per bond) + Commission
To find the price per bond, we need to use the current yield and the face value of the bond:
For bond A, current yield = 7.5, face value = 100, so price per bond = 100 x (7.5/100) = 7.50
For bond B, current yield = 8.4, face value = 100, so price per bond = 100 x (8.4/100) = 8.40
For bond C, current yield = 7.75, face value = 100, so price per bond = 100 x (7.75/100) = 7.75
So the total cost of three ABC bonds would be:
(3 x 7.50) + (3 x 8.40) + (3 x 7.75) + (3 x 10) = $104.25 + $25.20 + $23.25 + $30 = $182.70
Therefore, the correct answer is not listed.
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The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.
Predict the number of households with cable television in year 10.
A) 8.5 million
B) 10.8 million
C) 12.4 million
D) 14.1 milion
In scatter plot, 12 .4 million is the number of households with cable television in year 10.
What is scatter plot?
A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they may display the degree of connection, if any, between the values of observable quantities or events (referred to as variables).
slope = 9 - 5/7 - 1 = 4/6 = 2/3
N - 5 = 2/3 (T - 1 )
N(t) = 2/3 T + 13/3
when t = 11
N(11) = 2/3 * 11 + 13/3
= 35/3
= 12.4
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Select the point on the number line that best approximates the location of √14
Answer:
To approximate the location of the square root of 14 on a number line, we can first find the two integers that √14 is between. We know that:
3^2 = 9 < 14 < 16 = 4^2
So √14 is between 3 and 4. We can divide the distance between 3 and 4 into equal parts and estimate the location of √14 based on where it falls in that interval.
Dividing the interval into 10 equal parts, we get:
3.0 - 3.1 - 3.2 - 3.3 - 3.4 - 3.5 - 3.6 - 3.7 - 3.8 - 3.9 - 4.0
Since √14 is closer to 3 than to 4, we can estimate its location as being closer to 3.4 than to 3.5. Therefore, a good approximation for the location of √14 on the number line is 3.7.
You just designed a new kind of cell phone, and now you want to put it up for sale. Each phone costs you
$100 to produce.
Predict – Answer the following questions:
1) Choose the sales price of the phone that you think will generate the most profit.
2) What could happen if you set the price too low?
3) What could happen if you set the price too high?
Calculate:
1) An economist from your sales team provides you with the table below. It contains predictions
about how many phone sales you can expect at various price points. Complete the other columns.
Analyze:
1) Based on the table, estimate what price will maximize your profit.
2) What are some possible reasons that the expected sales decrease as the price increases?
3) What is the x-intercept? What does that point represent?
Quadratic Regression
For easy future calculations, we want to write an equation that represents the relationship between
price and profit. Enter your data for x and y into a calculator. Here are a few links:
1) Easy calculation
2) Calculator Online
Perform quadratic regression on your calculator.
Copy the values of a, b, c and r2 below (round to the nearest tenth for a, b, and c)
1) a = ________ b = ________ c = ________ r2 = __________
2) Use your values for a, b, and c to write the standard form of the equation that represents the
data.
a. f(x) = ax2 + bx + c f(x) = x2 + x +
3) What is r2
, and what does it say about your equation?
4) Sketch a graph of your equation on the coordinate plane below. Make sure to label:
a. The axes and what they represent
b. The zero(s)
c. The maximum
Evaluate:
1) Explain why profit, as a function of sales price, follows a quadratic curve
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Predict:
Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).
If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.
If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.
Calculate:
See the table below.
Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)
100 20 2,000 2,000 0
120 18 2,160 1,800 360
140 16 2,240 1,600 640
160 14 2,240 1,400 840
180 12 2,160 1,200 960
200 10 2,000 1,000 1,000
Analyze:
Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.
As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.
The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.
Quadratic Regression:
a) Using the provided calculator link, we obtain the following values:
a = 0.05
b = -10
c = 500
r2 = 0.9
b) The standard form of the equation that represents the data is:
f(x) = 0.05x2 - 10x + 500
c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.
d) See graph below.
Graph of quadratic equation
Evaluate:
Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these
The sum of a number and 2 is 6 less than twice that number.
Answer:
8
Step-by-step explanation:
Let's use algebra to solve the problem.
Let x be the number we're looking for.
The problem states that "the sum of a number and 2 is 6 less than twice that number", which can be written as:
x + 2 = 2x - 6
To solve for x, we need to isolate it on one side of the equation. We can start by subtracting x from both sides:
x + 2 - x = 2x - 6 - x
Simplifying:
2 = x - 6
Now we can isolate x by adding 6 to both sides:
2 + 6 = x - 6 + 6
Simplifying:
8 = x
Therefore, the number we're looking for is 8.
Answer:
8
Step-by-step explanation:
A new theater is being built for the city ballet. The balcony has 90 seats. The
floor has 15 rows with x seats in each row. The number of people in the
theater must be under 240 to meet fire safety regulations.
What is the solution of this inequality, and what is its meaning?
The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.
What is inequality?
In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.
To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.
Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)
Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240
Now we can solve for x by first subtracting 90 from both sides of the inequality,
15 × x ≤ 150
Next, we can divide both sides of the inequality by 15,
x ≤ 10
Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.
To check this solution, we can plug x = 10 into our expression for the total number of seats,
Total number of seats = 90 + (15 × 10) = 240
This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.
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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ
=
40.3
. You would like to be 90% confident that your esimate is within 2 of the true population mean. How large of a sample size is required?
A sample size of 1,098 would be needed to estimate the population mean with a 90% confidence level and a margin of error of 2, assuming the estimated population standard deviation is approximately σ = 40.3.
How large of a sample size is required?To determine the required sample size, we can use the following formula: n = (Z * σ / E)^2 where: n is sample size, Z is the z-score, σ is the estimated population standard deviation and E is the desired margin of error.
Note that 90% confidence corresponds to a z-score of 1.645.
Plugging in the given values, we get:
n = (1.645 * 40.3 / 2)^2
n = 33.14675^2
n = 1098.70703556
n ≈ 1,098.
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A family has a gross income of $95,000.00 a year and pays a federal tax rate of 18%.
What is their net income after taxes?
Answer and Step-by-step explanation: To calculate the net income of the family after taxes, we need to first determine the amount of taxes they will pay.
The federal tax rate of 18% means that the family will pay 18 cents in taxes for every dollar of gross income they earn.
So, the amount of federal taxes the family will pay can be calculated as:
Federal taxes = Gross income x Tax rate
Federal taxes = $95,000.00 x 0.18
Federal taxes = $17,100.00
Now that we know the amount of federal taxes the family will pay, we can calculate their net income by subtracting the federal taxes from their gross income:
Net income = Gross income - Federal taxes
Net income = $95,000.00 - $17,100.00
Net income = $77,900.00
Therefore, the family's net income after paying federal taxes is $77,900.00.
Determine the amount of taxes owed on a taxable income of $51, 100.
A) $5,310.00
B) $6,919.00
C) $11,682.00
D) $12,744.40
The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.
What is the taxable amount?To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.
For the tax year 2021, the federal income tax brackets and rates for single filers are:
10% on taxable income from $0 to $9,950
12% on taxable income from $9,951 to $40,525
22% on taxable income from $40,526 to $86,375
24% on taxable income from $86,376 to $164,925
32% on taxable income from $164,926 to $209,425
35% on taxable income from $209,426 to $523,600
37% on taxable income over $523,600
To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.
Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.
Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.
Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.
Adding these three amounts together, we get the total tax owed:
$995 + $3,384.48 + $2,312.72 = $6,692.20
Therefore, the closest answer choice is B) $6,919.00.
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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).
What is an income?An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.
Define tax?Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.
=$51100* 22/100
=$11242
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multiply (3+8i)(2-13i) and write in standard form
Answer:
the answer is 110-23i
1) What is the equation of the trend line in the scatter plot?
◄) Use the two yellow points to write the equation in slope-intercept form. Write any
coefficients as integers, proper fractions, or improper fractions in simplest form.
8 9 10
X
An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 9)/(9 - 0)
Slope (m) = -4/9
At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9 = -4/9(x - 0)
y - 9 = -4x/9
y = -4x/9 + 9
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DeShawn and Ndiba each improved their yards by planting daylilies and ornamental grass. They
bought their supplies from the same store. DeShawn spent $80 on 1 daylily and 12 bunches of
ornamental grass. Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass. What is
the cost of one daylily and the cost of one bunch of ornamental grass?
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
System of the equations :A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.
Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.
Here we have
DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.
Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.
Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.
From the problem,
We can set up a system of equations based on the information given:
DeShawn's purchase: 1d + 12g = 80 ---- (1)
Ndiba's purchase: 5d + 2g = 52 --- (2)
We can solve this system of equations using substitution or elimination.
Here, we will use substitution:
Solving for d in terms of g from Deshawn's equation:
1d = 80 - 12g --- (3)
Substituting into Ndiba's equation:
=> 5(80 - 12g) + 2g = 52
=> 400 - 60g + 2g = 52
=> - 58g = - 348
=> g = 6
From (3)
1d = 80 - 12(6)
1d = 80 - 72
d = 8
Therefore,
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
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Finding Side Lengths in a Right Triangle
A
Intro
8
B
00
S
5
15
C
D
What is the value of s?
units
The caculated value of the length of the leg s is approximately 9.95 units.
Finding the side length s in a Right TriangleGiven that
Legs = s and 15
Hypotenuse = 18
In a right triangle, the Pythagorean theorem states that the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
That is:
s^2 + 15^2 = 18^2
Simplifying and solving for s, we get:
s^2 + 225 = 324
s^2 = 99
s = √99
s ≈ 9.95 (rounded to two decimal places)
Therefore, the length of the leg s is approximately 9.95 units.
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A pipe is made of 1cm thick, has a radius of 11cm. Find the volume of the metal used in making 2.4cm of pipe
Over the last year, customers who have phoned their cable company for technical support have had to wait for a customer service representative an average of 28 minutes, with a standard deviation of 5.5 minutes. Company records have shown wait times to be normally distributed. What is the likelihood that a person phones the cable company and waits between 10 to 20 minutes for service?
The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
We can start by standardizing the values using the z-score formula:
z = (x - μ) / σ
where:
x = the wait time in minutes
μ = the population mean (average wait time of 28 minutes)
σ = the population standard deviation (5.5 minutes)
For x = 10 minutes:
z = (10 - 28) / 5.5 = -3.27
For x = 20 minutes:
z = (20 - 28) / 5.5 = -1.45
Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.
Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:
0.0735 - 0.0006 = 0.0729
Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
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A farmer counted the number of apples on each tree in his orchard. How many trees have at least 21 apples but fewer than 80 apples?
Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.
Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:
n1 - n2
To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.
Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:
- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.
- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.
- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.
Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:
The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.
The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.
Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:
n1 - n2 = 0.16T - 0.025T = 0.135T
Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.
Step-by-step explanation: