Answer: The area of the floor can be found by multiplying the width and the length.
Area of the floor = (6x - 9)(6x + 9) = 36x^2 - 63x - 81
The area of each tile can be found by evaluating the expression 24x^2 - 12x - 36.
Area of each tile = 24x^2 - 12x - 36
To find out how many tiles are needed to cover the floor we need to divide the area of the floor by the area of each tile.
Number of tiles needed = (36x^2 - 63x - 81) / (24x^2 - 12x - 36)
The division is simplified by canceling out common factors between the numerator and denominator, the number of tiles is a fraction that can't be simplified any further.
So the answer is (36x^2 - 63x - 81) / (24x^2 - 12x - 36) tiles are needed to cover the floor.
Step-by-step explanation:
If you do a report on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, are you using a sample
or population?
Answer: If you are reporting on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, you are using a population.
A population is a complete set of all the individuals or elements that share a common characteristic, such as all breast cancer patients seen at a hospital in a given year. A sample, on the other hand, is a subset of a population that is selected for analysis or study.
In this case, since you are reporting on all breast cancer patients seen at the hospital last year, you are using the entire population of breast cancer patients, rather than just a sample of them.
Step-by-step explanation:
Evaluate. Write your answer as a fraction in simplest form.
Answer: 16/81
Step-by-step explanation:
To do this you have to do 2^4 which is 16.
Next, you have to do 3^4 which is 81
This gives you 16/81.
Now check if you can simplify it.
You can't so this is your answer :D
I hope this was able to help you :D
question the height of 3-year-old boys is approximately normally distributed. duncan and shane are 3-year-old boys.duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. shane is 34.0 inches tall and is at the 62nd percentile of the distribution. which of the following is closest to the mean of the height distribution?
Duncan's height is closest to the mean.
Duncan (32nd percentile) has a z-score of z = 0.4677 and Shane (62nd percentile) has a z-score of z = 0.3055 when using "Table A" or "normalcy" on a TI calculator. Now that we have the z-score formula, we can create
−0.4677 = (32 − μ)/σ
and
Duncan and Shane are 3-year-old boys. Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. shane is 34.0 inches tall and is at the 62nd percentile of the distribution.
0.3055 = (34 − μ)/σ
Since the boys' heights fall under the same distribution, it should be noted that and will have the same values in each equation. Consequently, this is a set of linear equations.
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Graph the line
y=-1/3x-6
Answer:
the slope is -1/3 and the coordinates are (0,-6) and (3,-7). Below is a picture of the equation graphed.
Step-by-step explanation:
Having alot of trouble figuring this out! 100pts to anyone that can help!
help pls i need the answer and fast !!!
Answer: The slope of the line is 2/3.
The line is not solid, it is dashed.
The area below the line is shaded.
A solution to the inequality is (2,3).
The x-intercept of the boundary line is (-3/2,0)
All the statements except the first one are true about the graph of y< 2/3 x +1.
Step-by-step explanation:
What’s the answer I’m so confused!!!
Answer: C
If you leave behind 0.5 then instead of 24 the correct answer would be 22.
Quincy and Celine have to move 16 small boxes and 10 large boxes. the chart indicates the time that each person takes to move each type of box. they start moving the boxes at 9.00 a.m. the earliest time at which they can be finished moving all of the boxes is:
a. 9:41 a.m
b. 9:42 a.m
c. 9:43 a.m
d. 9:44 a.m
e. 9:45 a.m
The earliest time at which they can be finished moving all of the boxes is: d. 9:44 a.m
Quincy and Celine the earliest timeTo determine the earliest time at which Quincy and Celine can finish moving all of the boxes, we need to determine the maximum amount of time it will take for them to move all of the boxes. We can do this by calculating the time it will take for each person to move each type of box individually, and then adding those times together.
Quincy takes 1 minute to move a small box and 2 minutes to move a large box. Celine takes 2 minutes to move a small box and 3 minutes to move a large box.
So, for Quincy:Time to move 16 small boxes: 16 boxes * 1 minute/box = 16 minutes
Time to move 10 large boxes: 10 boxes * 2 minutes/box = 20 minutes
Total time for Quincy: 16 minutes + 20 minutes = 36 minutes
For Celine:Time to move 16 small boxes: 16 boxes * 2 minutes/box = 32 minutes
Time to move 10 large boxes: 10 boxes * 3 minutes/box = 30 minutes
Total time for Celine: 32 minutes + 30 minutes = 62 minutes
To get the earliest time they can finish moving all the boxes, we take the maximum of the two times:
Max(36 minutes, 62 minutes) = 62 minutes
Start time: 9:00 a.m.
End time: 9:00 a.m. + 62 minutes = 9:62 a.m.
So the earliest time they can finish moving all the boxes is 9:62 a.m.
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Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?
answer choices
The correlation must be 0.
The correlation must be positive.
A straight line is not a good model for the data.
The regression line might or might not be a good model for the data, depending on the extent of the curve.
If a plot of the residuals shows a curved pattern, it indicates that a straight line is not a good model for the data. This does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve.
When a least-squares regression line is fit to a set of data, it is used to determine the linear relationship between two variables. If a plot of the residuals (the difference between the observed values and the predicted values from the regression line) shows a curved pattern, it indicates that a straight line is not a good model for the data. This could mean that there is a nonlinear relationship between the two variables or that the data contains outliers that are not accounted for by the regression line. However, it does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve. To determine if the regression line is an accurate model for the data, it is important to visually inspect the plot of the residuals and assess whether the pattern is random or systematic. If the pattern is random, it indicates that the regression line is a good model for the data. If the pattern is systematic, it indicates that the regression line is not a good model for the data and alternative models should be considered.
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14. A brand-new school district needs to generate ID numbers for its student body. The district anticipates a total
enrollment of 75,000 students within the next ten years. Will a five-digit ID number using the symbols 0, 1,…, 9
be enough? Explain your reasoning using logarithms
The different combinations of the five-digit number formed are enough to create ID numbers.
What is meant by combinations?
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant.
We first find the total number of 5-digit enrollment IDs that can be created using all possible combinations of numbers possible.
Since each digit of the five-digit number can be from 0-9, there are ten possible values for each digit.
So the total number of ways a five-digit number can be formed
= 10*10*10*10*10 = 100,000
For the given question, it is mentioned that only 75,000 students are expected to be enrolled in the next ten years,
Since 100,000 is greater than 75,000 the five-digit ID number will be enough.
But if the school is to last longer than ten years, it is safe to use a six or seven-digit ID number.
Therefore a five-digit Id number using symbols from 0-9 will be enough.
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6/10 Darlene runs kilometer in the morning and 1 2/5 kilometers in
About how many kilometers does Darlene run?
the afternoon.
The number of kilometers that Darlene runs is given as follows:
2.4 kilometers.
How to obtain the distance that Darlene runs?The distance that Darlene runs is obtained applying the proportions in the context of the problem.
The proportion is applied to convert the mixed number to decimal, adding the integer part to the division of the numerator by the denominator.
The distances are given as follows:
Morning: 1 km.Afternoon: 1 + 2/5 = 1 + 0.4 = 1.4 km.Hence the total distance is of:
1 + 1.4 = 2.4 km.
Missing InformationShe ran 1 km in the morning.
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Which is greater -6, 6, or -2
For what positive integers $c$, with $c < 100$, does the following quadratic have rational roots?
\[ 3x^2 + 20x + c \]
If you find more than one, then list the values separated by commas.
Answer: A quadratic of the form $ax^2 + bx + c$ has rational roots if and only if its discriminant, $b^2 - 4ac$, is a perfect square. In this case, the discriminant is $(20)^2 - 4(3)(c) = 400 - 12c$. So, we need to find the positive integers $c < 100$ that make $12c$ a perfect square.
The perfect squares that are less than $100$ are $1,4,9,16,25,36,49,64,81$, so the possible values for $c$ are $33,44,55,66,77,88$.
So, the positive integers $c$, with $c < 100$, that make the quadratic have rational roots are $33,44,55,66,77,88$
Step-by-step explanation:
Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km². This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.
The area of the glacier at the start of last year was 56.31 km², based on a percentage reduction of 0.2%.
What is a percentage decrease?A percentage decrease represents the difference between the starting and ending values, expressed as a percentage of the starting value.
In working out the percentage reduction, we determine the difference between the ending and starting values. This difference is divided by the starting value and multiplied by 100.
The current area of the glacier = 56.20 km²
The percentage reduction = 0.2%
Proportionately, the current area, in percentage terms = 99.8% (1 - 0.2%)
99.8% = 56.20 km²
100% = 56.31 km²
Thus, to 2 decimal points, the area of the glacier at the start of last year was 56.31 km².
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Which verbal expression best represents the equation 2(n - 7) = -14
a) twice a number less than seven is equal to negative fourteen
b) the product of two and seven less than a number is equal to negative fourteen
c) seven less than twice a number is equal to negative fourteen
d) negative seven minus twice a number is negative fourteen
The verbal expression that best represents the equation 2(n - 7) = -14 is: c) seven less than twice a number is equal to negative fourteen.
What is verbal expression?Verbal expression can be defined as the way of writing mathematical expression into words or translating equation into words.
Now let interpret this equation 2(n - 7) = -14 into verbal expression.
n = a number
2n = twice a number
2n - 7 = seven less than twice a number
-14 = negative fourteen
Therefore we can conclude that the correct option is C.
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4y=12x=3 and let y+3x+1 a solution
The system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 has the following solution: (x, y) = (1 / 24, 7 / 8)
How to solve a system of linear equations
In this question we find the case of a system of two linear equations with two variables, this case may have an unique solution. This system can be solved by algebraic properties.
First, write the system of linear equations:
4 · y - 12 · x = 3
y + 3 · x = 1
Second, clear y in the second equation:
y = 1 - 3 · x
Third, substitute in the first equation:
4 · (1 - 3 · x) - 12 · x = 3
Fourth, expand the expression and clear variable x:
4 - 12 · x - 12 · x = 3
4 - 24 · x = 3
24 · x = 4 - 3
24 · x = 1
x = 1 / 24
Fifth, determine the value of variable y:
y = 1 - 3 · (1 / 24)
y = 1 - 1 / 8
y = 7 / 8
The solution to the system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 is (x, y) = (1 / 24, 7 / 8).
RemarkThe statement reports several typing mistakes. The system of linear equations is shown below:
4 · y - 12 · x = 3
y + 3 · x = 1
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a picture is enlarged by keeping its width the same and increasing its length. the scatter plot shows the perimeter of the picture (y) for different lengths (x):plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140which function best represents the data in the scatter plot?
The function best represents the data in the scatter plot is y = 2x + 20.
The function of the straight line has the general formula: y = mx + c
where m is the slope of the line, and c is the y-intercept
So first, we will need to find the slope (m):
The slope can be calculated with the points (x₁, y₁) and (x₂, y₂) as follows:
m = (y₂ - y₁)/(x₂ - x₁)
= 120 - 60/50 - 20
= 60/30
= 2/1
So, now we have the slope of our equation y = 2x + b but we still need to find b (or where the y intersects.)
Now, consider the ordered pair (20, 60)
y = 2x + b
60 = 2 × 20 + b
b = 60 - 40
b = 20
Now, put the value of b in y = 2x + b, and we get
y = 2x + 20
Also, b can not be -20 because this is a positive y-intercept, and we know it has a slope of 2.
Therefore the function is y = 2x + 20
--The given question is incomplete; the complete question is
"A picture is enlarged by keeping its width the same and increasing its length. The scatter plot below shows the perimeter of the picture (y) for different lengths (x):
Plot the ordered pairs 20, 60 and 30, 80 and 40, 100 and 50, 120 and 60, 140
Which function best represents the data in the scatter plot?
y = 2x − 20
y = 2x + 20
y = x − 20
y = x + 20"--
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Insurance cost is to be distributed among manufacturing, selling and administration in the ratio of 1/10 to 1/3 to 1/9. If the total cost was $12,005 how should it be distributed to these departments
Manufacturing should pay $2206.80, Selling should pay $7356.0and Administration should pay $2452.00
What is the distribution?Generally, To find out how much each department should pay, you can use the proportion of the cost that corresponds to their respective ratio.
First, calculate the total ratio by adding the three ratios together:
1/10 + 1/3 + 1/9 = 0.544
Then, divide the total cost by the total ratio to find the unit cost:
$12,005 / 0.544 = $22068.01
Next, multiply the unit cost by the ratio for each department to find out how much they should pay:
Manufacturing: $22068.01 x 1/10 = $2206.80
Selling: $22068.01 x 1/3 = $7356.0
Administration: $22068.01 x 1/9 = $2452.00
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Please help
Fill in each answer box so that the resulting statement is true
View image
Answer and Explain PLease
A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.
The square has four sides, hence:
360/4 = 90º.
The other figure has three sides, which are similar, hence:
360/3 = 120º.
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If 4 -letter "words" are formed using the letters A, B, C, D, E, F, G, how many such words are possible for each of the following conditions: (a) No condition is imposed. Your answer is : (b) No letter can be repeated in a word. Your answer is : (c) Each word must begin with the letter A and letters can be repeated. Your answer is : (d) The letter C must be at the end and letters can be repeated. Your answer is : (e) The second letter must be a vowel and letters can be repeated. Your answer is :
In this case, there are 8 letters, so the total number of 4-letter words possible is 8^4 = 4096.
(b) In this case, each letter can be used only once, so we must choose 4 different letters out of 8 letters. This can be done using the combination formula C(8,4) = 70.
(c) Since each word must begin with the letter A, the remaining 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(d) The letter C must be at the end, so the first 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(e) The second letter must be a vowel, so the first letter can be chosen out of 4 letters (A, E, I, O). The remaining 3 letters can be chosen out of 7 letters. This can be done using the combination formula C(4,1) x C(7,3) = 140.
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In a cash drawer, there is $125 in $5 and $10 bills. The number of $10 bills is twice the number of $5 bills. How many of each type of bill is in the drawer?
Answer:
Step-by-step explanation:
You can use the equations:
x = 2y
where x is the number of $10 bills and y the number of $5 bills and:
10x+5y = 125
Solving gives x=10 and y = 5, or in other words there are 10 $10 bills and 5 $5 bills
i need help me alot plss
Find the area of the following composite figure.
Is this correct?
Step-by-step explanation:
the sum of the area of the inner rectangle and the area of the 2 outer half-circles (that together are the area of one full circle).
the radius of the circles is 10 ft.
so, the diameter (= the width of the inner rectangle) = 2×10 = 20 ft.
so, the area of the inner rectangle is
30×20 = 600 ft²
the area of the combined full circle is
pi×r² = pi×10² = 100pi = 314.1592654... ft²
together that is
914.1592654... ft²
Find the area of the figure.
Answer: 38
Step-by-step explanation:
You can split this shape into 2 rectangles. The area of the two rectangles = 5 * 4 + 6 * 3
= 20 + 18
= 38
It would take Jack $4$ hours to mow the lawn if he works alone. Fortunately, after he mows for $2$ hours, Jill joins him. They finish mowing $90$ minutes later. How many minutes would it have taken for Jill to mow the entire lawn alone?
Answer: 720
Step-by-step explanation:
using the basic definition show that {3n-2/n}n=1 converges
The sequence (3n-2/n)n=1 converges to 1.
How to determine if the series convergesTo show that (3n-2/n)n=1 converges, we need to find the limit as n approaches infinity.
Using algebraic manipulation, we have the following steps
lim (3n-2/n)n = lim (3-2/n)^n
lim (3n-2/n)n = (3-2/∞)^∞
lim (3n-2/n)n = 1^∞
lim (3n-2/n)n = 1
The basic definition of convergence states that a sequence converges if the limit of the sequence as n approaches infinity is equal to a finite number
Since the limit of (3n-2/n)n as n approaches infinity is 1, we can conclude that the sequence converges to 1.
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1. A 1992 poll conducted by the University of Montana classified respondents by sex and political
party, as shown in the picture.
a) What is the probability of selecting a Democrat?
b) What is the probability of selecting a respondent that is Independent and Female?
c) What is the probability of selecting a respondent that is Republican given that is Male?
d) What is the probability of selecting a respondent that is Republican or Female?
e) Are the events being a Republican independent of being a Male? Justify and explain
A: The probability of selecting a Democrat is 84/212 = 0.3968 or 39.68%.
B: The probability of selecting an Independent and Female respondent is 16/212 = 0.075 or 7.5%.
C: The probability of selecting a Republican given that the respondent is Male is 45/69 = 0.6522 or 65.22%.
D: The probability of selecting a Republican or Female respondent is 126/212 = 0.5962 or 59.62%.
E: The events being a Republican independent of being a Male, P(Republican/Male) = P(Republican) which means these events are independent.
What is the probability?
Probability is a mathematical concept that quantifies the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
a) To find the probability of selecting a Democrat, we need to add up the number of Democratic respondents and divide by the total number of respondents. In this case, the number of Democratic respondents is 36 + 48 = 84. The total number of respondents is 84 + 45 + 24 + 33 + 16 = 212. So the probability of selecting a Democrat is 84/212 = 0.3968 or 39.68%.
b) To find the probability of selecting an Independent and Female respondent, we need to find the number of Independent and Female respondents, and divide by the total number of respondents. In this case, the number of Independent and Female respondents is 16. The total number of respondents is 212, so the probability of selecting an Independent and Female respondent is 16/212 = 0.075 or 7.5%.
c) To find the probability of selecting a Republican given that the respondent is Male, we need to use conditional probability formula. P(Republican/Male) = P(Republican and Male) / P(Male)
In this case, the number of Republican and Male respondents is 45. The number of Male respondents is 45+24 = 69
So the probability of selecting a Republican given that the respondent is Male is 45/69 = 0.6522 or 65.22%.
d) To find the probability of selecting a respondent that is Republican or Female, we need to find the number of Republican or Female respondents and divide by the total number of respondents. In this case, the number of Republican or Female respondents is 45 + 33 + 48 = 126. The total number of respondents is 212, so the probability of selecting a Republican or Female respondent is 126/212 = 0.5962 or 59.62%.
e) To answer whether the events being a Republican independent of being a Male or not, we need to check the independence of the events. Events A and B are independent if and only if P(A/B) = P(A) = P(B)
In this case, P(Republican/Male) = 0.6522 and P(Republican) = (45+33)/212 = 0.4906
So the events being a Republican independent of being a Male, P(Republican/Male) = P(Republican) which means these events are independent.
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twenty-four workers were surveyed and asked how long it takes them to travel to work each day. the data below are given in minutes. 20 35 42 52 65 20 60 49 24 37 23 24 22 20 41 25 28 27 50 47 58 30 32 48 which of the following shows the data in a stem-and-leaf plot?
Use the data to create a stemplot.
Twenty-four workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes.
20 35 42 52 65 20 60 49 24 37 23 24
22 20 41 25 28 27 50 47 58 30 32 48
The data in a stem-and-leaf plot:
3/0257
2/0002344578
4/12789
5/028
6/05
Stemplots (Stem-and-Leaf Plots)Another presentation that is similar to a histogram is a stemplot. In statistics, a stemplot is a tool for presenting quantitative data in a graphical format, similar to a histogram, namely to assist in visualizing the shape of the data distribution which is often used in exploratory analysis. Stemplots were introduced by Arthur Bowley in the early 1900's. However, its general use only began in 1980 after John Tukey's published Exploratory Data Analysis in 1977.
Stem-and-leaf plots provide more information about true values than histograms. As in a histogram, the length of each bar corresponds to the number of events that fall into a given interval. On Histograms. we can only see the frequency value of the data but we don't know what the actual number value is. In contrast to the histogram, in SLP besides we can know the frequency value, we can also know what the actual data value is. This is done by dividing the observed values into two components, stem and leaf.
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determine if (x-3) is a factor of (x^4-13x^2+36) using synthetic division
Answer:
Yes, (x-3) is a factor of (x^4-13x^2+36) using synthetic division.
Synthetic division:
| x -3 |
x^4 -13x^2+36
x^3 -10x^2+27x-108
The remainder is zero, so (x-3) is a factor of the polynomial (x^4-13x^2+36).
Step-by-step explanation: