A child was born exactly y years ago. How many years old will the child be exactly f years from now?

The volume of a cone varies jointly as the square of its radius and its height. if the volume of a cone is 99piπ cubic inches wh

tatyana61 [14]

Any answer choices ?

7 0

3 years ago

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology ex

Nataly [62]

Answer:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

Step-by-step explanation:

Previous concepts

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".

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".

$p_A$ represent the real population proportion female for Biology

$\hat p_A =\frac{84199}{144796}=0.582$ represent the estimated proportion female for biology

$n_A=144796$ is the sample size for A

$p_B$ represent the real population proportion female for calculus AB

$\hat p_B =\frac{102598}{211693}=0.485$ represent the estimated proportion female for Calculus AB

$n_B=211693$ is the sample size required for B

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

5 0

4 years ago

What are the values for matrix A?: 1 2 3 4 1 3 4 5 6 7 8 Noo 4 1 0 0 9 6 7 8 10 12 14 15 16 13 14 14 15 16

Gala2k [10]

Since the values are the same on both sides the matrix value is a=1

7 0

3 years ago

a rectangular garden is 47 ft longer than it is wide. its perimeter is 314 ft. what is the equation to describe the width and le

Ronch [10]

The perimeter = 2 length + 2 width

the length = the width +47

314 = 2*(w+47) +2w

314 = 2w +94 +2w

220 =4w

w= 220/4 = 55

l = 55+47 = 102

the length = 102 ft

the width = 55 ft

hope helped

3 0

4 years ago

Given f(x) = -* -<br> - 5, solve for x when f(x) = -3.

Ne4ueva [31]

Answer:

x = -2

Step-by-step explanation:

Step 1: Define

f(x) = -x - 5

f(x) = -3

Step 2: Substitute and Evaluate

-3 = -x - 5

2 = -x

x = -2

7 0

3 years ago

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