Cathy cakes read 22 pages during a 30 minute study hall. How many pages would she read in 45 minutes

A rectangle is a quadrilateral (has four sides and four angle) with two pairs of parallel sides. Opposite sides of a rectangle are equal to each other. Also all the angles of a rectangle are 90° each.

The area of a rectangle = length * width

For rectangle 1, length = 12 m, width = 3 m

Therefore area of rectangle 1 = length * width = 12 m * 3 m = 36 m²

For rectangle 2, length =(12 m - 3 m - 3 m) = 6 m, width =(15 m - 10 m) =5 m

Therefore area of rectangle 2 = length * width = 6 m * 5 m = 30 m²

For rectangle 3, length = 15 m, width = 3 m

Therefore area of rectangle 3 = length * width = 15 m * 3 m = 45 m²

Area of composite shape = Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3

Area of composite shape = 36 m² + 30 m² + 45 m² = 111 m²

3 0

3 years ago

The mean time required to repair breakdowns of a certain copying machine is 93 minutes. The company which manufactures the machi

Sonja [21]

Answer:

$t=\frac{88.8-93}{\frac{26.6}{\sqrt{73}}}=-1.349$

$p_v =P(t_{(72)}$

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 reject the null hypothesis, and we can't concluce that the true mean is less than 93 min at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=88.8$ represent the sample mean

$s=26.6$ represent the sample standard deviation for the sample

$n=73$ sample size

$\mu_o =93$ 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 i lower than 93 min, the system of hypothesis would be:

Null hypothesis: $\mu \geq 93$

Alternative hypothesis: $\mu < 93$

If we analyze the size for the sample is > 30 but we don't know the population deviation so 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:

$t=\frac{88.8-93}{\frac{26.6}{\sqrt{73}}}=-1.349$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=73-1=72$

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

$p_v =P(t_{(72)}$

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 reject the null hypothesis, and we can't concluce that the true mean is less than 93 min at 5% of signficance.

5 0

3 years ago

PLEASE HELP ME AS SOON AS POSSIBLE!

mestny [16]

Answer:

2(c - 8) = 3

Hope this helps, thank you :) !!

4 0

3 years ago

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