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3 years ago

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Carrie ran some of the miles and walked some of the miles in a 10-mile race. Each mile she ran took 9 minutes, and each mile she

walked took
16 minutes. She finished the race in 120 minutes.
Which system of equations can be used to determine the number of miles Carrie ran, r, and walked, W?
r+9 = 10
ОА.
W + 16 = 120
B.
r = 10w
9r + 16w = 120
OC.
r+w = 10
9r + 16w = 120
D.
r+w = 10
16r + 9w = 120

2 answers:

natka813 [3]3 years ago

6 0

You can use y=Mx+b or you can use ride over run because all you need to do is find which number you would like to use for your x and y and you can figure it out easy

Hunter-Best [27]3 years ago

5 0

9514 1404 393

Answer:

C. r+w = 10; 9r + 16w = 120

Step-by-step explanation:

The problem statement describes two relationships. Each of these gives rise to an equation.

total miles: r + w = 10

total time: 9r +16w = 120

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What value of x is in the solution set of 2(3x-1) ≥ 4x-6?

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2 years ago

Write an exponential function to represent a person consuming a bag of candy in which the initial value in an is 175 pieces and

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We will see that the exponential decay function is:

f(x) = 175*(0.8)^x

<h3>How to find the exponential decay?</h3>

The general exponential decay is:

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Where:

A is the initial value.
r is the rate of decay in decimal form.
x is the variable, in this case is the time.

Here we know that the initial value is 175, and the rate of decay is 20%. To get this in decimal form, we just divide it by 100%.

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Replacing that in the exponential function, we get:

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If you want to learn more about exponential functions, you can read:

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2 years ago

Three people spend $22.50 on large popcorns and soft drinks. They go back the next week and each pay $8.00 for each ticket, they

kakasveta [241]

Answer:

Cost of each large soft drink is $3.00 and Cost of each Large bucket of popcorn is $4.50.

Step-by-step explanation:

Let the Cost of each large soft drink be x.

Also Let the Cost of each Large bucket of popcorn be y.

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Hence we can say that;

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Total return trip = $37.50

Also they each get a large soft drink, but they share one large bucket of popcorn

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Cost of popcorn = y

Now Total return trip is equal to sum of Money spend on tickets and Cost of soft drink and Cost of popcorn.

Hence equation can be framed as;

$24+3x+y=37.50\\3x+y=37.50-24\\3x+y = 13.50 \ \ \ \ eqaution \ 2$

Now Subtracting equation 2 from equation 1 we get;

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Now substituting the value of y in equation 1 we get;

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3 years ago

A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian

Minchanka [31]

Answer:

Question 1:

(b) 4,445

Question 2:

(c) 2.1%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Question 1:

We have no previous estimate for the population proportion, so we use $\pi = 0.5$ .

The sample size is n for which M = 0.015. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.015 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.015\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.015}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.015})^2$

$n = 4268$

Samples above this value should be used, and the smaller sample above this value is of 4445, so the answer is given by option b.

Question 2:

Now we find M for which $n = 2222$ .

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 1.96\sqrt{\frac{0.5*0.5}{2222}}$

$M = 0.021$

So 2.1%, and the correct answer is given by option c.

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