Alfred made 21 goals in 3.5 minutes. What is Alfred’s unit rate?

Maria created a graph of B(t), the temperature over time. For the interval between t = 3 and t = 7, the average rate of change i

LuckyWell [14K]

What are the statements?

4 0

2 years ago

Read 2 more answers

Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they canno

tensa zangetsu [6.8K]

<h2>Answer with explanation:</h2>

As per given , we have

$\hat{p}=0.48$ , n=331

Critical value for 90% Confidence interval : $z_{\alpha/2}=1.645$

a) Confidence interval :

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.48\pm (1.645)\sqrt{\dfrac{0.48(1-0.48)}{331}}\\\\\approx 0.48\pm0.02746\\\\=(0.48-0.02746,\ 0.48+0.02746)\\\\=(0.45254,\ 0.50746)$

Hence, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot a ord it : $(0.45254,\ 0.50746)$

b) Margin of error : E=1.5%=0.015

Formula for sample size : $n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

For p =0.48 , we have

$n=0.48(1-0.48)(\dfrac{1.645}{0.015})^2=3001.88373333\approx3002$

Hence, the required sample size to survey = 3002

6 0

2 years ago

A certain ferry moves up and down a river between Town A and B. It takes the ferry two hours to travel to Town A and only an hou

Y_Kistochka [10]

Answer:

The distance between two cities is <em>60 miles.</em>

Step-by-step explanation:

Time taken to travel from B to A = 2 hours

Time taken to travel from A to B = 1.5 hours

Current speed = 5 mph

Let the speed of ferry in still water = <em>u</em> mph

When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).

Let the distance between the two cities A and B = D miles

While moving with the current, speed = $(u+5)\ mph$

While moving against the current, speed = $(u-5)\ mph$

Formula for Distance = Speed $\times$ Time

Distance traveled in each case is same i.e. D.

So,

$D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph$

Now,

$D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}$

So, the distance between two cities is <em>60 miles.</em>

6 0

2 years ago

A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a blue marble randomly from the box, replaces it, and th

allochka39001 [22]

Answer:

$\dfrac{9}{64}$

Step-by-step explanation:

Sampling with replacement means that we choose a marble, note its colour, put it back and shake the box, then choose a marble again.

There are $1+3+4=8$ marbles in total. The probability that the first chosen marble is blue is $\dfrac{3}{8}.$ then Maya replaces this marble and the probability of choosing the second blue marble is the same. Using the product rule, the probability of drawing 2 blue marbles in a row is