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3 years ago

What is a rational number?

1 answer:

8 0

Any number that can be rewritten as a simple fraction is a rational number. This means that natural numbers, whole numbers and integers, like 5, are all part of the set of rational numbers as well because they can be written as fractions, as are mixed numbers like 1 ½.

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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

3 years ago

Round your answer to the nearest hundredth AC=

KatRina [158]

Answer:

AC ≈ 2.96

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos65° = $\frac{adjacent}{hypotenuse}$ = $\frac{AC}{AB}$ = $\frac{AC}{7}$

Multiply both sides by 7

7 × cos65° = AC , thus

AC ≈ 2.96 ( to the nearest hundredth )

7 0

3 years ago

What is the value of the expression below?<br> -4(5 - 10)' +36

Levart [38]

Answer:

Step-by-step explanation:

-4 x (-5) = 20

4 0

3 years ago

Describe the square roots of numbers using 2 sentences.

slava [35]

Answer:

Square roots of numbers less than 1 are between 0 and 1, while square roots of numbers greater than 1 are greater than 1. For numbers between 0 and 1, the square root is greater than the number; for numbers larger than 1, the square root is less than the number.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

75% of b is 12. What is b?

Juli2301 [7.4K]

Answer:

b=16

Step-by-step explanation:

75%=75/100=3/4

3/4*b=12

b=12/1*4/3

b=16

5 0

3 years ago

Read 2 more answers