To evaluate: the proportions $\frac{60}{15}=\frac{12}{y}$ by cross products property.

Tobias Ali
2021-08-15
Answered

To evaluate: the proportions $\frac{60}{15}=\frac{12}{y}$ by cross products property.

You can still ask an expert for help

joshyoung05M

Answered 2021-08-16
Author has **97** answers

Calculation:

The product of the numerator of the ratio and of the denominator of the other is known as a cross product. Cross products can be used to determine whether the ratios form a proportion or not. If the cross products are equal, then the ratios form a proportion.

$\frac{60}{15}=\frac{12}{y}$ [Write the proportion.]

$60\times y=15\times 12$ [Apply cross products property.]

$60y=180$ [Multiply.]

$\frac{60y}{60}=\frac{180}{60}$ [Divide each side by 24 to place the variable on one side of the equation]

$y=3$ [Simplify.]

Hence, the solution of the proportions$\frac{60}{15}=\frac{12}{y}$ is $y=3$ .

The product of the numerator of the ratio and of the denominator of the other is known as a cross product. Cross products can be used to determine whether the ratios form a proportion or not. If the cross products are equal, then the ratios form a proportion.

Hence, the solution of the proportions

Jeffrey Jordon

Answered 2021-12-17
Author has **2027** answers

Answer is given below (on video)

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Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

$\begin{array}{|ccccccc|}\hline 11.8& 7.7& 6.5& 6.8& 9.7& 6.8& 7.3\\ 7.9& 9.7& 8.7& 8.1& 8.5& 6.3& 7.0\\ 7.3& 7.4& 5.3& 9.0& 8.1& 11.3& 6.3\\ 7.2& 7.7& 7.8& 11.6& 10.7& 7.0\\ \hline\end{array}$

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion.$[Hint.\text{}?{x}_{j}=219.5.]$ (Round your answer to three decimal places.)

MPa

State which estimator you used.

$x$

$p?$

$\frac{s}{x}$

$s$

$\stackrel{~}{\chi}$

b) Calculate a point estimate of the strength value that separates the weakest$50\mathrm{\%}$ of all such beams from the strongest $50\mathrm{\%}$ .

MPa

State which estimator you used.

$s$

$x$

$p?$

$\stackrel{~}{\chi}$

$\frac{s}{x}$

c) Calculate a point estimate of the population standard deviation ?.$[Hint:\text{}?{x}_{i}2=1859.53.]$ (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

$\stackrel{~}{\chi}$

$x$

$s$

$\frac{s}{x}$

$p?$

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation$\frac{?}{?}$ . (Round your answer to four decimal places.)

State which estimator you used.

$p?$

$\stackrel{~}{\chi}$

$s$

$\frac{s}{x}$

$x$

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion.

MPa

State which estimator you used.

b) Calculate a point estimate of the strength value that separates the weakest

MPa

State which estimator you used.

c) Calculate a point estimate of the population standard deviation ?.

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation

State which estimator you used.

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