All categories

1 month ago

1. A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles.

1 answer:

6 0

Every square meter of ceiling needs 10.75 tiles. To calculate the number of tiles needed for various ceiling areas: For a ceiling area of 1, it requires 10.75 tiles. For a ceiling area of 10, it requires 10.75 × 10, which equals 107.5 tiles. For an area of 100, it needs 10.75 × 100, totaling 1075 tiles. Consequently, that represents the necessary solution.

You might be interested in

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn w

Zina [12379]

Answer:

The number of standard deviations above the mean is $z_o = 1.4607$

Step-by-step explanation:

The question indicates that:

The average weight of the corn ears from each farm is $\mu=1.26$

The standard deviation for the corn ears from Iowa is $\sigma_1$

The standard deviation for the corn ears from Ohio is

$\sigma_2= 0.01 + \sigma_1$

A randomly chosen ear of corn from Iowa weighs x = 1.39 pounds

The standardized score is z = 1.645

The weight of a randomly chosen ear of corn from Ohio measures $x_1 = 1.39\ pound$

In general, the standardized score of corn weight from Iowa can be mathematically defined as:

$z = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $\sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}$

=> $\sigma_1 = 0.0790$

Conversely, the standardized score of corn weight from Ohio is expressed as:

$z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }$

=> $z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }$

=> $z_o = \frac{ 1.39 - 1.26 }{ 0.089}$

=> $z_o = 1.4607$

A positive value indicates this quantity represents the number of standard deviations above the mean.

4 0

3 months ago

Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy

tester [12383]

Answer:

1. 3.767

2. 0.145

Step-by-step explanation:

Define X as the exam scores and Y as the number of drinks.

X Y X-Xbar Y-Ybar (X-Xbar)(Y-Ybar) (X-Xbar)² (Y-Ybar)²

75 5 -2.3 2.3 -5.29 5.29 5.29

92 3 14.7 0.3 4.41 216.09 0.09

84 2 6.7 -0.7 -4.69 44.89 0.49

64 4 -13.3 1.3 -17.29 176.89 1.69

64 2 -13.3 -0.7 9.31 176.89 0.49

86 7 8.7 4.3 37.41 75.69 18.49

81 3 3.7 0.3 1.11 13.69 0.09

61 0 -16.3 -2.7 44.01 265.69 7.29

73 1 -4.3 -1.7 7.31 18.49 2.89

93 0 15.7 -2.7 -42.39 246.49 7.29

sumx=773, sumy=27, sum(x-xbar)(y-ybar)= 33.9, sum(X-Xbar)²= 1240.1,sum(Y-Ybar)²= 44.1

Xbar=sumx/n=773/10=77.3

Ybar=sumy/n=27/10=2.7

$Cov(x,y)=sxy=\frac{Sum(X-Xbar)(Y-Ybar)}{n-1}$

Cov(x,y)=33.9/9

Cov(x,y)=3.76667

Thus, the sample covariance of exam scores and energy drink consumption is 3.767

$Cor(x,y)=r=\frac{Sum(X-Xbar)(Y-Ybar)}{\sqrt{Sum(X-Xbar)^2sum(Y-Ybar)^2} }$

$Cor(x,y)=r=\frac{33.9}{\sqrt{(1240.1)(44.1)} }$

Cor(x,y)=r=33.9/233.85553

Cor(x,y)=r=0.14496

The sample correlation coefficient for the relationship between exam scores and energy drink consumption is 0.145.

7 0

2 months ago

Noah drew a scaled copy of Polygon P and labeled it Polygon Q. If the area of Polygon P is 5 square units, what scale factor did

babunello [11817]

Answer:

The scale factor equates to 3.

Detailed explanation:

Please refer to the provided image for clarity regarding this issue.

We know that

If two shapes are similar, then the ratio of their areas corresponds to the square of the scale factor.

Let

z -----> scale factor

x -----> area of polygon Q

y ----> area of polygon P

Thus, we have

$z^{2}=\frac{x}{y}$

so, we proceed with

$y=5\ units^2$

Determining the area of polygon Q

The polygon Q can be divided into five distinct squares.

Refer to the additional figure N 2.

The area of polygon Q, which represents the total area of the five squares, is

$x=5(3^2)=45\ units^2$

Calculating the scale factor

$z^{2}=\frac{x}{y}$

Thus, we derive

$x=45\ units^2$

$y=5\ units^2$

By substituting the values, we find

$z^{2}=\frac{45}{5}$

$z^{2}=9$

Taking the square root of both sides results in

$z=3$

Thus,

The scale factor resolves to 3.

8 0

3 months ago

Read 2 more answers

Tesla wanted to determine the average miles per kWh that their vehicles get across all models and variations. They took a sample

lawyer [12517]

Answer:

$\mu_{\bar x} = \mu = E(X) =30KWh$

$\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{100}}=0.3$

Step-by-step explanation:

Previous concepts

Normal distribution, is defined as a symmetric "probability distribution centered around the mean, indicating that values near the mean are more common than those further away".

The Z-score measures a value's relation to the mean of a set of values, displayed in terms of how many standard deviations away it is from that mean.

According to the central limit theorem, "with a population having mean μ and standard deviation σ, if we draw sufficient random samples from this population with replacement, the means of those samples will resemble a normal distribution, regardless of the original population's shape, as long as the sample size is large enough".

Solution to the problem

In this scenario, we select a sample size of n = 100

The central limit theorem informs us that the distribution of the sample mean $\bar X$ is defined by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Thus, the mean for the sample would be:

$\mu_{\bar x} = \mu = E(X) =30KWh$

And the standard deviation would be:

$\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{100}}=0.3$

6 0

2 months ago

The triangles below are similar. Triangle S R P. Angle S is 54 degrees, R is 41 degrees, P is 85 degrees. Triangle X Y Z. Angle

Inessa [12570]

The similarity statements that illustrate the relationship between the two triangles include Triangle S R P being similar to triangle X Z Y, Triangle R S P corresponding to triangle Z X Y, and Triangle R P S matching triangle Z Y X.

3 0

2 months ago

Read 2 more answers