You paint 1313 of a wall in 1414 hour. At that rate, how long will it take you to paint one wall?

Express 9-y^2 as the product of two binomial factors.

matrenka [14]

3^2-y^2

then apply formula (a-b)(a+b)=a^2-b^2

so,,
(3-y)(3+y)

4 0

4 years ago

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105 in radiu is equa to answer fast

Dafna1 [17]

Answer: I would assume you mean 105 in radius to diameter which would be 210 since diameter is just radius times 2. <u>Otherwise, explain the question more since it's barely legible.</u>

7 0

3 years ago

3) A particular motorcycle is 9 ft long. A

Shalnov [3]

The model is 3 inches, since 3 times 3 is 9 and 1 times 3 is 3.

5 0

3 years ago

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin(x

V125BC [204]

Answer with explanation:

The equation of two curves are

y=8 sin x

y=8 cos x

The point of intersection of two curves are

→8 sin x=8 cos x

sinx = cos x

$x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}$

When you will look between points , 0 and $x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}$ ,the curve obtained is right angled triangle.

Now, rotate the curve that is right angled triangle along the line , y= -1, to obtain a shape similar or resembling with Right triangular prism.

Draw a circular disc in the right triangular prism , having radius =x,and small part on the triangle having length dx.dx varies from 0 to $\frac{\pi}{4}$ .

Required volume of solid obtained

$=\int\limits^{\frac{\pi}{4}}_0 {8 \sin x} \, dx \\\\=|-8\cos x|\left \{ {{x=\frac{\pi}{4}}} \atop {x=0}} \right.\\\\=8-4\sqrt{2}$

=8-4√2 cubic units

5 0

3 years ago

According to the norms established for a reading comprehension test, eighth-graders should average 83.2 with a standard deviatio

joja [24]

Answer:

$t=\frac{86.7-83.2}{\frac{8.6}{\sqrt{45}}}=2.73$

$p_v =P(t_{44}>2.73)=0.0045$

If we compare the p value and a significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is signficantly higher than 83.2 at 1% of significance.

Step-by-step explanation:

Data given and notation

$\bar X=86.7$ represent the average life for the sample

$s=8.6$ represent the population standard deviation

$n=45$ sample size

$\mu_o =83.2$ represent the value that we want to test

$\alpha=0.01$ 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 apply a two tailed test.

What are H0 and Ha for this study?

Null hypothesis: $\mu \leq 83.2$

Alternative hypothesis : $\mu > 83.2$

Compute the test statistic

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (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:

$t=\frac{86.7-83.2}{\frac{8.6}{\sqrt{45}}}=2.73$

Give the appropriate conclusion for the test

First we need to calculate the degrees of freedom given by:

$df=n-1=45-1=44$

Since is a one side right tailed test the p value would be:

$p_v =P(t_{44}>2.73)=0.0045$

Conclusion

If we compare the p value and a significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is signficantly higher than 83.2 at 1% of significance.

8 0

3 years ago