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3 years ago

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1 Jessie’s bus ride to school is 5 minutes more than 23 the time of Robert’s bus ride. Which graph shows the possible times of J

essie’s and Robert’s bus rides?

1 answer:

Lunna [17]3 years ago

7 0

Which graph are you supposed to pick?

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Company A charges a base rate of $5 per month, plus 4 cents per minute that you are on the phone. Company B charges a base rate

Afina-wow [57]

...........................

4 0

3 years ago

Line E passes through the points (2, 3) and (4, -3). What is the slope of a line perpendicular to line E?

lilavasa [31]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 2 &,& 3~) 
% (c,d)
&&(~ 4 &,& -3~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-3}{4-2}\implies \cfrac{-6}{2}\implies \cfrac{-3}{1}$

now, a line perpendicular to that one, will have a "negative reciprocal" slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for}\quad \cfrac{-3}{1}\\\\
negative\implies +\cfrac{3}{ 1}\qquad reciprocal\implies +\cfrac{ 1}{3}\implies \cfrac{1}{3}$

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

3 years ago

Choose the pair of events that is mutually exclusive.

barxatty [35]

Answer:

even numbers greater than 50 and prime numbers greater than 50

Step-by-step explanation:

An event can be considered as mutually exclusive in probability and statistics when two sample propositions cannot be held as true by any means. Therefore, the pair that clearly illustrates a mutually exclusive event would be "even numbers greater than 50 and prime numbers greater than 50."

The only prime number that is even is 2, so even numbers over 50 would be divisible by 2, and then not prime.

5 0

3 years ago

Coach Williams bought trophies for his players at the end of the season. Each trophy is packed in a cube-shaped box that has a v

Diano4ka-milaya [45]

Answer:

The volume of the cart will be 24 ft^3

Step-by-step explanation:

The first thing we need to calculate for this question is the number of boxes that fill the entire cart.

A layer of boxes consists of 8 boxes.

The cart holds a maximum of 3 layers of boxes.

So, the total number of boxes held by the cart are:

Total boxes = number of layers * boxes per layer

Total boxes = 3 * 8

Total boxes = 24

Since each box has a volume of one cubic foot, the total volume of the cart will be:

Volume of cart = number of boxes * volume of each box

Volume of cart = 24 * 1

Volume of cart = 24 ft^3

5 0

3 years ago