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2 years ago

Solid A and Solid B are similar. The surface area of Solid A is 675 m² and the surface area of

Mathematics

1 answer:

kirill115 [55]2 years ago

8 0

The Volume of solid A that is similar to solid B is: 960 × 1.25 = 1,200 m³.

<h3>What is the Surface Area and Volume of Similar Shapes?</h3>

If two solids, A and B, are given and have corresponding dimensions as a and b respectively, we would have the following:

Surface area of solid A/Surface area of solid B = a²/b²

Volume of solid A/Volume of solid B = a³/b³

Given that solid A and solid B are similar, and:

Surface area of solid A = 675 m²
Surface area of solid B = 432 m²
Volume of solid B = 960 m³.

Find their corresponding dimensions, a and b:

Surface area of solid A/Surface area of solid B = a²/b²

Substitute

675/432 = a²/b²

√(675/432) = a/b

1.25 = a/b

Scale factor of Solid A to Solid B is 1.25.

Multiply 1.25 by 960 to get the volume of solid A.

Volume of solid A = 960 × 1.25 = 1,200 m³.

Learn more about area and volume of similar shapes on:

brainly.com/question/12580764

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SashulF [63]

Answer:

a)For this case the best estimator for the true mean is the sample mean $\hat \mu =\bar X$ because:

$E(\bar X)= \frac{\sum_{i=1}^n E(X_i)}{n}$

And if we assume that each observation $X_1 , X_2,...,X_n$ follows a normal distribution $X_i \sim N(\mu,\sigma)$ then we have:

$E(\bar X)=\frac{1}{n} n\mu =\mu$

So then yes the $\bar X[/tex[ is a unbiased estimator for the true mean. b) [tex]z_{\alpha/2}=1.96$

c) $ME= 1.96 \frac{0.4}{\sqrt{50}}=0.1109$

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

$\bar X=4.1$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=0.4$ represent the population standard deviation

n=50 represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=0.4$

The sample mean $\bar X$ is distributed on this way:

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

A. What is the point estimate in this scenario? Is it an unbiased estimator?

For this case the best estimator for the true mean is the sample mean $\hat \mu =\bar X$ because:

$E(\bar X)= \frac{\sum_{i=1}^n E(X_i)}{n}$

And if we assume that each observation $X_1 , X_2,...,X_n$ follows a normal distribution $X_i \sim N(\mu,\sigma)$ then we have:

$E(\bar X)=\frac{1}{n} n\mu =\mu$

So then yes the $\bar X[/tex[ is a unbiased estimator for the true mean. B. What is the critical z-value for a 95% interval?
The next step would be find the value of [tex]\z_{\alpha/2}$ , $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=1.96$

C. What is the margin of error for a 95% interval in this scenario? Show your work.

The margin of error is given by:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

If we replace the values that we have we got:

$ME= 1.96 \frac{0.4}{\sqrt{50}}=0.1109$

The confidence interval on this case is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since we have all the values we can replace:

$4.1 - 1.96\frac{0.4}{\sqrt{50}}=3.989$

$4.1 + 1.96\frac{0.4}{\sqrt{50}}=4.211$

So on this case the 95% confidence interval would be given by (3.989;4.211)

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3 years ago

Mya applied the distributive property to write the equivalent expressions below.

Fynjy0 [20]

Maya wrote two expressions that are not equivalent.
Here is how she should have factored:

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3 years ago

Read 2 more answers

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Answer: 3y - x - 42 = 0

Step-by-step explanation:

The equation y + 1 = -3(x - 5)

Now expand the expression by opening the brackets

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Recall,

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rearranging the equation above in order to determine the ( m)

y = -3x -1 + 15

y = -3x + 14

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From the equation given, m₁ = -3, therefore , to get m₂

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m₂ = 1/3

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Just replaced the -3 in the equation above by m₂ = 1/3 in

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y = x/3 + 14

Now , multiply both the RHS and LHS of the equation by 3, to make it a linear.

3y = x + 3 x 14

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