A rectangular living room measures 6 by 12 feet. At $36 per square yard, how much will it cost to carpet the room?

Answers

Answer 1
First, we need to determine the area of the living room in square feet, which can be calculated by multiplying the length by the width:

Area = length x width = 6 feet x 12 feet = 72 square feet

Since carpet is usually priced by the square yard, we need to convert the area from square feet to square yards. There are 9 square feet in 1 square yard, so:

Area in square yards = 72 square feet / 9 = 8 square yards

Now, we can calculate the total cost of carpeting the living room by multiplying the area in square yards by the price per square yard:

Cost = area in square yards x price per square yard = 8 square yards x $36 per square yard = $288

Therefore, it would cost $288 to carpet the living room.
Answer 2

Answer:

It will cost $288 to carpet the living room at $36 per square yard.

Step-by-step explanation:

First, we need to convert the room dimensions to square yards, since the carpet price is given in square yards.

The area of the living room is:

[tex]\sf:\implies 6\: ft \times 12\: ft = 72\: ft^2[/tex]

To convert this to square yards, we divide by 9 (since there are 9 square feet in a square yard):

[tex]\sf:\implies \dfrac{72\: ft^2}{9} = 8\: yards^2[/tex]

So the living room is 8 square yards in area.

To find the cost of carpeting the room, we multiply the area by the cost per square yard:

[tex]\sf:\implies 8\: yards^2 \times \$36/square\: yard = \boxed{\bold{\:\:\$288\:\:}}\:\:\:\green{\checkmark}[/tex]

Therefore, it will cost $288 to carpet the living room at $36 per square yard.


Related Questions

Cuál es el valor de la razón del cambio cuando metemos un vaso de agua al tiempo al congelador por 15 minutos?

Answers

The value of the rate of change when we put a glass of water at room temperature is 1/3.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another.

The connection defining how one quantity changes in response to the change in another quantity is given by the rate of change formula. The formula for calculating the rate of change from y coordinates to x coordinates is y/x = (y2 - y1)/. (x2 - x1 ).

Rate of change  = change in temperature / time

= 10-5/15

=5 / 15

= 1/3

Therefore, the Rate of change is 1/3.

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Complete question;

What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes.

Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1. 05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.


WILL GIVE BRANLIEST

Answers

The total amount of money Victoria will have in her bank account after x years can be modeled by the function f(x) = 200 * (1.05)ˣ.

How can we model Victoria's bank account growth over time?

To model the total amount of money Victoria will have in her bank account after depositing her $200 and accruing interest over time, we can combine the two functions h(x) and s(x).

We can use the following formula to represent the total amount of money Victoria will have in her bank account after x years:

f(x) = h(x) + h(x) * s(x)

where h(x) represents the $200 that Victoria has saved at home, and h(x) * s(x) represents the amount of interest accrued on that $200 in x years according to the function s(x).

The justification for this formula is that the total amount of money Victoria will have in her bank account after x years is the sum of the initial amount of $200 and the interest accrued on that amount over x years.

The interest accrued can be calculated by multiplying the initial amount by the interest rate function s(x).

For example, if Victoria leaves her $200 in the bank for 5 years, the total amount of money she will have in her account can be calculated using the formula:

f(5) = h(5) + h(5) * s(5) = 200 + 200 * (1.05)⁴ ≈ $273.04

Therefore, the total amount of money Victoria will have in her bank account after x years can be modeled using the function f(x) = h(x) + h(x) * s(x).

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Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of
12
1212 draws, Romain didn't get picked even once.
Let's test the hypothesis that each brother has an equal chance of
1
3
3
1

start fraction, 1, divided by, 3, end fraction of getting picked in each draw versus the alternative that Romain's probability is lower.
Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of
12
1212 times? Round your answer, if necessary, to the nearest tenth of a percent.

Answers

Based on the observed outcome, it is therefore very or highly unlikely that Romain's probability is equal to that of the other brothers, and thus  it is possible that Romain is cheating.

What is the probability?

Beneath the assumption that each brother has an break even with chance of getting picked in each draw, the likelihood of Romain not getting picked indeed once out of 12 times is:

P(Romain not picked) = (2/3)¹²

                                  = 0.0077

This is one that is less than 1%, which suggests that the observed result is made up of a likelihood less than 1% beneath the given speculation. Therefore, we need to reject the hypothesis that each brother has an equal chance of getting picked in all of the draw.

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See text below

Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of 12 draws, Romain didn't get picked even once. 1 Let's test the hypothesis that each brother has an equal chance of of getting picked in each draw versus 3 the alternative that Romain's probability is lower. Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of 12 times? Round your answer, if necessary, to the nearest tenth of a percent. Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis. What should we conclude regarding the hypothesis? Choose 1 answer: We cannot reject the hypothesis. B We should reject the hypothesis.

HELP
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair.

Function 1

graph of function f of x equals negative x squared plus 8 multiplied by x minus 15

Function 2

f(x) = −x2 + 2x − 15

Function 1 has the larger maximum at (4, 1).
Function 1 has the larger maximum at (1, 4).
Function 2 has the larger maximum at (−14, 1).
Function 2 has the larger maximum at (1, −14).

Answers

The correct statement regarding the maximum values of the quadratic functions is given as follows:

Function 1 has the larger maximum at (4, 1).

How to obtain the maximum values?

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The x-coordinate of the vertex of a quadratic function is given as follows:

x = -b/2a.

Hence, for each function, the x-coordinate of the vertex is given as follows:

Function 1: x = -8/-2 = 4.Function 2: x = -2/-2 = 1.

Each function has a negative leading coefficient, hence the vertex represents a maximum value, and the y-coordinate is given as follows:

Function 1: f(4) = -(4)² + 8(4) - 15 = 1.Function 2: f(1) = -(1)² + 2(1) - 15 = -14.

1 > -14, hence the correct statement is given as follows:

Function 1 has the larger maximum at (4, 1).

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At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 800 vines are planted per acre. for each additional vine that is planted, the production of each vine decreases by about 1 percent. so the number of pounds of grapes produced per acre is modeled by
a(n) = (800 + n)(10 − 0.01n)
where n is the number of additional vines planted. find the number of vines that should be planted to maximize grape production.

Answers

Planting an additional 210 vines will maximize grape production.

How to maximize grape production?

To find the number of vines that should be planted to maximize grape production, we need to find the maximum value of the function A(n) = (800 + n)(10 - 0.01n), which represents the number of pounds of grapes produced per acre as a function of the number of additional vines planted. To find the maximum value, we can take the derivative of A(n) with respect to n and set it equal to zero.

A'(n) = -0.01n² + 2.1n + 800

Setting A'(n) = 0, we get

-0.01n²+ 2.1n + 800 = 0

Solving for n using the quadratic formula, we get

n ≈ 210

Therefore, planting an additional 210 vines will maximize grape production.

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At midnight, the temperature in a city was 5 degrees celsius. the temperature was dropping at a steady rate of 1 degrees celsius per hour.

a. write an inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees celsius.

b. explain or show your reasoning.

Answers

The inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees Celsius is t > 8.

The inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees Celsius is t > 8.

When the temperature drops at a steady rate of 1 degree Celsius per hour, it will take 8 hours to reach -3 degrees Celsius from the initial temperature of 5 degrees Celsius.

Therefore, any time past 8 hours after midnight will result in a temperature colder than -3 degrees Celsius.

Thus, the inequality t > 8 represents the number of hours past midnight when the temperature was colder than -3 degrees Celsius.

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Scientists estimate that the mass of the sun is 1. 9891 x 10 kg. How many zeros are in this


number when it is written in standard notation?


A 26


B 30


C 35


D 25

Answers

There are 30 zeros in the mass of the sun which is 1.9891 x 10³⁰ kg when it is written in standard notation. The correct answer is option B.

To determine how many zeros are in the mass of the sun (1.9891 x 10³⁰ kg) when it is written in standard notation, you first need to recognize that the provided mass is not written correctly. It should be written as 1.9891 x 10^n kg, where n is an integer representing the exponent.

The actual mass of the sun is 1.9891 x 10³⁰ kg. When written in standard notation, this number would be:

1,989,100,000,000,000,000,000,000,000,000 kg

There are 30 zeros in this number when written in standard notation.

So, the correct answer is B) 30.

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HELP NEEDED ASAP!!!!
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:

High Low Q1 Q3 IQR Median Mean σ
Rome 18 1 3 7 4 6.5 6.4 4.3
New York 14 1 4.5 8.5 4 5.5 6.1 3.2


Which of the choices below best describes how to measure the center of these data?
a.Both centers are best described by the mean.
b.Both centers are best described by the median.
c.The Rome data center is best described by the mean. The New York data center is best described by the median.
d.The Rome data center is best described by the median. The New York data center is best described by the mean.

Answers

The choice which best describes the measure of center of these data is (d) Rome data center is "best-described" by median and  data center of "New-York" is "best-described" by mean.

In the table provided below, we see that the "IQR" for Rome is relatively large compared to the IQR for New York, which suggests that that there may be some skewness in the distribution of the Rome data. So, the median would be a better-measure of center than the mean.

On the other hand, the IQR for "New-York" is relatively small, which indicates that the data is more symmetric and the mean would be a better measure of center.

Therefore, the correct answer is (d).

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The given question is incomplete, the complete question is

The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:

                    High   Low    Q1     Q3    IQR    Median    Mean    σ

Rome              18       1         3       7        4         6.5          6.4    4.3

New York       14       1        4.5    8.5     4          5.5          6.1     3.2

Which of the choices below best describes how to measure the center of these data?

(a) Both centers are best described by the mean.

(b) Both centers are best described by the median.

(c) The Rome data center is best described by the mean. The New York data center is best described by the median.

(d) The Rome data center is best described by the median. The New York data center is best described by the mean.

In a random sample of 74 homeowners in a city, 22 homeowners said they would


support a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The sampling


method had a margin of error of ±3. 1%.



A) Find the point estimate.



B) Find the lower and upper limits and state the interval

Answers

Point estimate is 29.7%.

The confidence interval for the proportion of homeowners who support the ban on nonnatural lawn fertilizers is (26.6%, 32.8%).

A) The point estimate is the proportion of homeowners who support the ban on nonnatural lawn fertilizers.

In this case, 22 out of 74 homeowners support the ban. To find the point estimate, divide the number of supporters (22) by the total number of homeowners in the sample (74):
Point estimate = 22 / 74 ≈ 0.297 or 29.7%

B) To find the lower and upper limits, we need to consider the margin of error (±3.1%). Subtract the margin of error from the point estimate for the lower limit, and add the margin of error to the point estimate for the upper limit:
Lower limit = 29.7% - 3.1% = 26.6%
Upper limit = 29.7% + 3.1% = 32.8%

The confidence interval for the proportion of homeowners who support the ban on nonnatural lawn fertilizers is (26.6%, 32.8%).

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This ladder is extended to a length of 18 feet. The bottom of the ladder is 4. 5 feet from the base of the building. What angle does the ladder make with the ground?

Answers

The ladder makes an angle of approximately 82 degrees with the ground when it is extended to a length of 18 feet and the bottom of the ladder is 4.5 feet from the base of the building.

To determine the angle that the ladder makes with the ground, we can use trigonometry. Let x be the height of the ladder when it is leaned against the building. Then, using the Pythagorean theorem, we have: [tex]x^{2}[/tex] + [tex]4.5^{2}[/tex] = [tex]18^{2}[/tex]

Solving for x, we get: x = sqrt([tex]18^{2}[/tex] - [tex]4.5^{2}[/tex]), x ≈ 17.29

Therefore, the ladder makes an angle θ with the ground such that: sin θ = opposite/hypotenuse = x/18, θ = arcsin(x/18)

Substituting x ≈ 17.29, we get: θ ≈ 81.99 degrees

Therefore, the ladder makes an angle of approximately 82 degrees with the ground when it is extended to a length of 18 feet and the bottom of the ladder is 4.5 feet from the base of the building.

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Which equations will find the distance between the lions and giraffes? Select all that apply. 11+16 = c 112+ 162 = c2 c2+ 162 = 112 121+ 256 = c2 11(2)+16(2) = 2c

Answers

The equations that will find the distance between the lions and giraffes include the following:

B. 11² + 16² = c².

D. 11(2) + 16(2) = 2.

What is distance?

In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:

11² + 16² = c²

Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:

11(2) + 16(2) = c

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A positive integer k is such that k(k + 2013) is a perfect square. Show that k cannot be prime and

find the correct value of k​

Answers

The only possible value of k is k = 336675.

What is the correct value of K ?

Suppose, for the sake of contradiction, that k is a prime such that k(k+2013) is a perfect square. Let's denote the perfect square as m^2, where m is a positive integer. Then we can write:

k(k+2013) = m^2

Expanding the left-hand side, we get:

k^2 + 2013k = m^2

Moving all the terms to one side, we get:

k^2 - m^2 + 2013k = 0

Using the difference of squares, we can factor this as:

(k - m)(k + m) + 2013k = 0

Since k is a prime, it must be greater than 1. Thus, k + m and k - m are both integers greater than 1 whose product is divisible by k. This means that at least one of them is divisible by k. Since k is prime, this can only happen if either k + m or km is equal to k. Thus, we have two cases to consider:

Case 1: k + m = k, which implies m = 0. But m is a positive integer, so this is impossible.

Case 2: k - m = k, which implies m = 0. But again, m is a positive integer, so this is impossible.

Therefore, our assumption that k is prime leads to a contradiction, and we conclude that k cannot be prime.

To find the correct value of k, note that k and k+2013 share a common factor of 3. Thus, we can write k = 3n and k+2013 = 3m for some integers n and m. Substituting these expressions into the equation k(k+2013) = m^2 and simplifying, we get:

3n(3n+2013) = m^2

n(3n+2013/3) = m^2/3

n(n+671) = m^2/3

Since n and n+671 are relatively prime, both n and n+671 must be perfect squares. Let's write n = p^2 and n+671 = q^2 for some integers p and q. Then we have:

q^2 - p^2 = 671

Using the difference of squares again, we can factor this as:

(q + p)(q - p) = 671

Since 671 is a prime, its only factors are 1 and 671. Therefore, we have two possibilities:

q + p = 671, q - p = 1, which implies q = 336, p = 335, n = p^2 = 112225, k = 3n = 336675

q + p = 671, q - p = 671, which implies q = 336 + 335 = 671, p = 0, which is not a valid solution since n cannot be negative.

k = 336675. is the best possible answer.

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find a constant b so that y(t) = e^2t [1 4 b] is a solution of y′ = [4 1 3 2 3 3 −2 −1 −1]y.

Answers

We have found a value of b that makes y(t) = [tex]e^2t[/tex] [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y. To check if y(t) is a solution of y′ = Ay, we need to substitute it into the differential equation and see if it holds.

Let's start by finding y′:

y′(t) = [[tex]2e^2t, 8e^2t, 4be^2t[/tex]]

Now, let's find Ay:

Ay = [4 1 3; 2 3 3; −2 −1 −1] [1; 4; b] = [4+4b; 14; -5-b]

We want y(t) = e^2t [1; 4; b] to satisfy y′ = Ay, so we set them equal:

y′ = Ay

[[tex]2e^2t; 8e^2t; 4be^2t] = [4+4b; 14; -5-b] e^2t[/tex] [1; 4; b]

Expanding this equation, we get:

[tex]2e^2t[/tex]= (4+4b)[tex]e^2t[/tex]

[tex]8e^2t[/tex] = 14 [tex]e^2t[/tex]

[tex]4be^2t[/tex]= (-5-b) [tex]e^2t[/tex]

The second equation is always true, so we can ignore it. For the first equation, we can cancel out [tex]e^2t[/tex] on both sides to get:

2 = 4+4b

Solving for b, we get:

b = -1/2

Finally, we can substitute b = -1/2 back into the third equation to check if it holds:

4be^2t = (-5-b) [tex]e^2t[/tex]

-2e^2t = (-5 + 1/2)[tex]e^2t[/tex]

This equation is true, so we have found a value of b that makes y(t) = [tex]e^2t[/tex] [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y.

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Which scatter plot below would best be modeled by using linear regression?

Answers

Answer:

Top

Step-by-step explanation:

The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. Therefore, the top option has the most closest lines to a linear function.

(Ex. 1) Y=4x-2

This example shows the corresponding possibilities of a linear regression because of the way the line is represented as graphed, making a straight line as similar to the top option

(Ex. 2) f(x) = x^2-5+15

This example dialates to a similar option like the third option, which isnt linear regression because of it being a quadratic function.

In a nut shell, all data plotted on the graph that are formed closer together and corresponds to a linear equation is a linear regression

Part 3
sales tax is 8%
basketballs are 20% off
you have two customers john and david. john has $250 and
david has $150. john is coaching a baseball team and wants
to buy 10 baseball bats for his team. david wants to buy 3
pairs of running shoes for his kids. will each person be able
to buy the items that they want? explain.
baseball bats are 5% off
running shoes are 15% off
i
tax
with
discount
total
cost
john
david

Answers

John will be able to buy the 10 baseball bats for his team with some money left over is -$6.50 and David will be able to buy the 3 pairs of running shoes for his kids with some money left over is $12.30.

Based on the given information, we can calculate the total cost for each customer after factoring in the sales tax and discounts.

For John:
The cost of 10 baseball bats without any discounts or tax would be 10 * $25 = $250.
Since baseball bats are 5% off, John will get a discount of 0.05 * $250 = $12.50.
So, the cost of 10 baseball bats after discount is $250 - $12.50 = $237.50.
Adding 8% sales tax to this amount, the total cost for John will be $237.50 + (0.08 * $237.50) = $256.50.

For David:
The cost of 3 pairs of running shoes without any discounts or tax would be 3 * $50 = $150.
Since running shoes are 15% off, David will get a discount of 0.15 * $150 = $22.50.
So, the cost of 3 pairs of running shoes after discount is $150 - $22.50 = $127.50.
Adding 8% sales tax to this amount, the total cost for David will be $127.50 + (0.08 * $127.50) = $137.70.

Therefore, John will be able to buy the 10 baseball bats for his team with some money left over ($250 - $256.50 = -$6.50) and David will be able to buy the 3 pairs of running shoes for his kids with some money left over ($150 - $137.70 = $12.30).

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Twenty students in A and 20 students in class B were asked how many hours they took to prepare for an exam. The data sets represents their answers

Answers

The data sets represent the answers of twenty students in Class A and twenty students in Class B regarding the number of hours they took to prepare for an exam. These data sets are important because they help us understand the study habits and time allocation of the students in each class.


To analyze the data sets, first, collect the data from each student in both classes. Record the number of hours they took to prepare for the exam, ensuring you have 20 responses from Class A and 20 from Class B. Then, you can compute the average, or mean, time spent for each class by summing up the hours reported by all students in each class and dividing by 20.


Next, compare the averages for Class A and Class B to determine if there is a significant difference in the time spent preparing for the exam. Additionally, you can calculate other statistical measures such as median and mode to gain further insight into the data sets.


Furthermore, analyzing the distribution of the data, such as the range, will provide information on the variability of the time spent studying in each class. This can help identify any trends or patterns in the students' preparation time.


In conclusion, the data sets representing the number of hours spent by students in Class A and Class B to prepare for an exam can provide valuable insights into their study habits, the effectiveness of their preparation, and any possible correlations between time spent studying and exam performance.

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A contractor is building a set of stairs out of concrete. Each stair is exactly the same length, width, and height.
(a) Which solid figures can the stairs be broken into? What are the dimensions of each solid figure?
(b) How much concrete will be needed to form the stairs?

Answers

The stairs can be broken up into three rectangular prisms

The concrete that will be needed to form the stairs is 9.72 m ^3

How to solve for the amount of concrete

To get the volume of concrete

Since they are 3

2.7 / 3

= 0.9

1.5 / 3

= 0.5

0.5 + 0.5

= 1

each width is 3.6m

The volume of each = 0.9 x 1.5 x 3.6 = 4.86

Volume 2 = 0.9 x 1.0 x 3.6 = 3.24

Volume 3 = 0.9 x 0.5 x 3.6 = 1.62

amount of concrete = 1.62 + 3.24 + 4.86

= 9.72 m ^3

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Exercise 11. 3. 1: Applying the pigeonhole principle - heights and times. About Apply the pigeonhole principle to answer the following questions. If the pigeonhole principle can not be applied, give a specific counterexample. (a) A team of three high jumpers all have a personal record that is at least 6 feet and less than 7 feet. Is it necessarily true that two of the team members must have personal records that are within four inches of each other

Answers

To apply the pigeonhole principle, we need to determine the number of pigeonholes and the number of pigeons. The pigeonhole principle cannot be applied to this question.

In this case, the"  holes" are the high minidresses and the" lockers" are the ranges of  particular records. Let's assume that the range of  particular records is from 6  bases( 72  elevation) to 7  bases( 84  elevation).   The difference between the upper and lower bounds of the range is

84- 72 =  12  elevation.

We can divide this range into five subintervals of length2.4  elevation( 72,74.4),(74.4,76.8),(76.8,79.2),(79.2,81.6), and(81.6, 84).  

Since there are only five subintervals, but we've three high minidresses, it isn't  inescapably true that two of the  platoon members must have  particular records that are within four  elevation of each other. For  illustration, if the three high minidresses have  particular records of 6  bases 3  elevation( 75  elevation), 6  bases 7  elevation( 79  elevation), and 7  bases( 84  elevation),  also none of them have  particular records within four  elevation of each other.

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Zola wrote the area of the rectangle as `2a+3a+4a`.



amir wrote the area as `(2+3+4) a.





explain why they are both correct


please help as quickly as possible


assp

Answers

Both Zola and Amir are correct in writing the area of the rectangle. They have simply used different ways of expressing the same value.

Zola and Amir have both written the area of a rectangle using different algebraic expressions.

Zola wrote the area of the rectangle as `2a + 3a + 4a`, which can be simplified using the distributive property of multiplication:

2a + 3a + 4a = (2 + 3 + 4)a

Therefore, Zola's expression simplifies to `(2 + 3 + 4)a`, which is the same as Amir's expression.

Amir wrote the area of the rectangle as `(2 + 3 + 4) a`, which can also be simplified:

(2 + 3 + 4) a = 9a

Therefore, Amir's expression simplifies to `9a`, which is the same as the sum of the terms in Zola's expression.

Therefore, both Zola and Amir are correct in writing the area of the rectangle. They have simply used different ways of expressing the same value.

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Michael had 8/9 of a spool of yarn. He used 2/5 of his yarn for a project. What fraction of the spool was used for the project?

Answers

Answer:16/45 of his yarn

Step-by-step explanation:

8/9 x 2/5 = 16/45

In a study of the relationship between birth order and college success, an investigator found that 126 in a sample of 180 college graduates were firstborn or only children; in a sample of 100 nongraduates of comparable age and socioeconomic background, the number of firstborn or only children was 54. estimate the difference in the proportions of firstborn or only children for the two populations from which these samples were drawn. give a bound for the error of estimation.

Answers

The difference in the proportions of firstborn or only children for the two populations from which these samples were drawn is 0.16.The bound for the error of estimation is 95% confidence that the true difference in proportions of firstborn or only children for the two populations is between 0.058 and 0.262.

To estimate the difference in the proportions of firstborn or only children for the two populations, we can use the sample proportions and apply the formula:

p1 - p2 = (x1/n1) - (x2/n2)

where p1 and p2 are the true population proportions, x1 and x2 are the numbers of firstborn or only children in the samples, and n1 and n2 are the sample sizes.

Sample of college graduates: x1 = 126, n1 = 180Sample of non-graduates: x2 = 54, n2 = 100

The sample proportions,

p1 = x1/n1 = 0.7

p2 = x2/n2 = 0.54

Substituting these values into the formula,

p1 - p2 = (x1/n1) - (x2/n2) = 0.7 - 0.54 = 0.16

Therefore, we estimate that the difference in the proportions of firstborn or only children for the two populations is 0.16.

To find a bound for the error of estimation, we can use the formula:

E = z sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2)

where E is the margin of error, z is the critical value for the desired level of confidence (we'll use z = 1.96 for a 95% confidence interval), and p1 and p2 are the sample proportions.

Substituting the given values, we get:

E = 1.96sqrt(0.7(1-0.7)/180 + 0.54*(1-0.54)/100) ≈ 0.102

Therefore, we can say with 95% confidence that the true difference in proportions of firstborn or only children for the two populations is between 0.058 and 0.262

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pls solve this asap ​

Answers

Step-by-step explanation:

perimeter of triangle=22 cm

AB+BC+CA=22cm

AB+4+AB =22cm (given,AB=AC)

2AB+4cm=22cm

2AB=22-4cm

2AB=18

AB=18÷2

AB=9cm

A savings account balance is compounded annually. if the interest rate is 2% per year and the current balance is $1430.00 what will the balance be 8 years from now

Answers

Answer:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the present balance ($1430.00)

r = the annual interest rate (2% or 0.02)

n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)

t = the number of years (8 years in this case)

Plugging in the values into the formula:

A = 1430(1 + 0.02/1)^(1*8)

Simplifying the equation:

A = 1430(1.02)^8

Using a calculator or performing the calculations manually:

A ≈ 1430(1.171661)

A ≈ 1674.02

the balance after 8 years will be approximately $1674.02.

The balance of the savings account 8 years from now, with an annual interest rate of 2% and an initial balance of $1430.00, will be approximately $1708.26.

4) Your phone needs to be charged every other day and your tablet needs to be charged every third day. If you charge both today, how many days will it be until you need to charge both on the same day?​

Answers

To solve this problem, we need to find the least common multiple (LCM) of 2 and 3, which is the smallest number that is a multiple of both 2 and 3.

The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ...

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

The smallest number that appears in both lists is 6, which is the LCM of 2 and 3. Therefore, you will need to charge both your phone and tablet on the same day again in 6 days.

Answer:

If they were both charged today, it would be on the sixth day that they were actually charging at the same time

what principal will earn $67.14 interest at 6.25% for 82 days?​

Answers

Answer: attach an image

Step-by-step explanation:

To find the principal, we can use the formula for simple interest:

I = P*r*t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

We need to convert 82 days to years by dividing it by 365 (the number of days in a year):

t = 82/365

t = 0.2247

Now we can plug in the values we know and solve for P:

67.14 = P*0.0625*0.2247

P = 67.14/(0.0625*0.2247)

P = 1900

Therefore, the principal is $1900.

Prove that the triangle FGH is right-angle des at F

Answers

The Pythagorean Theorem is used to prove that triangle FGH is a right triangle at angle F.

What are similar triangles?

Similar triangles are triangles that share these two features listed as follows:

Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.

Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:

4/4.8 = FH/3.6 = 5/6.

Hence the length FH is given as follows:

4/4.8 = FH/3.6

FH = 3.6 x 4/4.8

FH = 3.

If the Pythagorean Theorem is respected, the triangle is a right triangle, hence:

3² + 4² = 5²

9 + 16 = 25

25 = 25. -> right trianglge.

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evaluate : 20-[5+(9-6]​

Answers

Answer:

12

Step-by-step explanation:

20-(5+(9-6)) = 20-(5+(3)) = 20-(8) = 12.

Alternatively, rewrite the question without parenthesis.

20-(5+(9-6)) = 20-(5+9-6) = 20-5-9+6 = 12.

BODMAS rule is used here
Soooo…
20-(5+(3)
20-(8)
=12
Hope it helps

The length of human hair is proportional to the number of months it has grown.



a. what is the hair length in centimeters after 6 months? round your answer to the nearest hundredth.



the hair length is about blank


centimeters.



question 2


b. how long does it take hair to grow 8 inches?



it takes blank


months.



question 3


c. use a different method than the one in part (b) to find how long it takes hair to grow 20 inches.



it takes blank


months.

Answers

human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.

First, let's establish the proportionality constant, which is the average rate at which human hair grows. On average, human hair grows approximately 0.5 inches per month.

Now, let's find out how many months it takes for hair to grow 20 inches. We can set up a proportion equation as follows:

Length of hair (in inches) / Number of months = Proportionality constant
Let "x" be the number of months it takes for hair to grow 20 inches. We can write the equation as:
20 inches / x months = 0.5 inches/month

To solve for x, we can multiply both sides by x months, which gives us:
20 inches = 0.5 inches/month * x months
Now, we can divide both sides by 0.5 inches/month:

x months = 20 inches / 0.5 inches/month
x months = 40 months

So, it takes 40 months for human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.

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A track has the dimensions shown.
36.5 m
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SAMANT
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84.4 m
Ta
inside of track
outside of track
. The track has 8 lanes
• Each lane is 2.1 meters wide
36.5 m
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16. To the nearest tenth of a meter, what is
the perimeter of the outside of the
track?
Byp
*REQUIRED
ANA
1
√x
Sign out

Answers

Answer:

Step-by-step explanation:

What rate of interest compounded annually is required to double an investment in 29 years? Round your answer to two decimal places

Answers

An interest rate of approximately 2.40% per annum, compounded annually, is required to double an investment in 29 years.

Let "r" be the annual interest rate, then the investment will double after 29 years if (1 + r)^29 = 2. Solving this equation, we get r ≈ 0.0240 or 2.40% (rounded to two decimal places) as the required annual interest rate. This means that if the investment is compounded annually at this rate, it will double after 29 years.

Alternatively, we can use the formula for compound interest, A = P(1 + r/n)^(nt), where A is the future value, P is the present value, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

We want to find the interest rate, r, that will double the investment, so we can set A = 2P, t = 29, n = 1 (compounded annually), and solve for r. This gives us r ≈ 0.0240 or 2.40%.

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