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3 years ago

Given square WXYZ. If ZY = 20, find WV. Write your response in the form WV=_____.

Mathematics

1 answer:

Citrus2011 [14]3 years ago

6 0

Answer:

14.14

Step-by-step explanation:

Recall :

The sides of a square are always equal ;

Since all sides are equal, the the diagonal of the square will be :

XZ² = XY² + WX²

XZ² = 20² + 20²

XZ² = 400 + 400

XZ² = 800

XZ = √800

XZ = 28.28

WY = XZ

WV = 1/2 WY

WV = 1/2 * 28.28

WV = 14.14

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Why does the expression i to the power 4n+2 is always equal to -1

Alexandra [31]

Answer:

See Below.

Step-by-step explanation:

We are given:

$i^{4n+2}$

Using exponent properties:

$=i^{4n}\cdot i^2$

Rewriting:

$=(i^4)^n\cdot i^2$

Since i⁴ = 1 and i² = -1:

$=(1)^n\cdot -1$

1 to any power is still 1:

$=1\cdot -1 = -1$

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3 years ago

Solve for the missing side labeled "x."

agasfer [191]

Answer:

x = 6.3375

Step-by-step explanation:

sin53 = 4/5 (roughly) = 5.07/x

=> 4x = 25.35

=> x = 6.3375

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3 years ago

In science class we discovered that 7/8 of an apple is water.What fraction of the apple is not water?

nevsk [136]

Answer:

1/8

Hope this helps

4 0

3 years ago

Read 2 more answers

An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry ou

Katyanochek1 [597]

Answer:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

$p_v =P(t_{(5)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

Step-by-step explanation:

Data given and notation

The mean and sample deviation can be calculated from the following formulas:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)}{n-1}}$

$\bar X=29.35$ represent the sample mean

$s=1.365$ represent the sample standard deviation

$n=6$ sample size

$\mu_o =30$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 30 or no, the system of hypothesis are :

Null hypothesis: $\mu \geq 30$

Alternative hypothesis: $\mu < 30$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=6-1=5$

Since is a one-side left tailed test the p value would given by:

$p_v =P(t_{(5)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

5 0

3 years ago

A cuboid with dimensions 45 cm by 16 cm by 12 cm is cut to form smaller cubes of

LenKa [72]

Answer:

<u>135 cubes</u>

Step-by-step explanation:

Volume of cuboid :

45 x 16 x 12
720 x 12
8,640 cm³

Volume of a small cube :

(4)³
64 cm³

Number of cubes :

n = 8,640/64
n = <u>135 cubes</u>

4 0

2 years ago