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tensa zangetsu [6.8K]

3 years ago

9

Daniela and her friends are going on a road trip that is 517.74 miles long. If they have 312.03 miles until their destination, h

ow far have they already traveled?

1 answer:

jarptica [38.1K]3 years ago

8 0

Answer:

205.71 miles

Step-by-step explanation:

you take the miles they are going to travel minus the miles you have been given.In this case you are going to take 517.74-312.03

You might be interested in

Two trains leave stations 256 miles apart at the same time and travel toward each other. one train travels at 70 miles per hour

Leya [2.2K]

Answer:

1.6 hours

Step-by-step explanation:

The 2 trains together are going 160 mph.

256 / 160 = 1.6 hours

7 0

2 years ago

examine the graph below. select the solutions to the graph from the following points. select three that apply.

vova2212 [387]

Answer:

Options (1), (2), (3)

Step-by-step explanation:

Let the equation of the line is,

y = mx + b

Here m = slope of the line

b = y-intercept

Given line on the graph is passing through two points (-3, 0) and (0, 1).

Slope of this line will be,

m = $\frac{y_2-y_1}{x_2-x_1}$

= $\frac{1-0}{0+3}$

= $\frac{1}{3}$

y-intercept of the line 'b' = 1

Equation of the line will be,

y = $\frac{1}{3}x+1$

If the points given in the options satisfy the equation, they will be the solution of the line.

Option (1),

For (3, 2),

2 = $\frac{3}{3}+1$

2 = 2

True.

(3, 2) is the solution.

Option (2)

For (21, 8),

8 = $\frac{21}{3}+1$

8 = 8

True.

(21, 8) is the solution.

Option(3)

For (-15, -4),

-4 = $\frac{-15}{3}+1$

-4 = -4

True.

(-15, -4) is the solution.

Option (4)

For (12, 9)

9 = $\frac{12}{3}+1$

9 = 5

False

(12, 9) is not the solution.

Option (5)

For (-6, 1)

1 = $\frac{-6}{3}+1$

1 = -1

False

(-6, 1) is not the solution.

Therefore, Options (1), (2), (3) are the solutions.

5 0

3 years ago

Factor the greatest common factor (GCF) from each polynomial. - 12y + 48x

IRISSAK [1]

Answer:

-12(y-4x)

Step-by-step explanation:

-12y+48x=-12(y-4x)

3 0

2 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Find the 61st term of the arithmetic sequence<br> 8, 7, 6, ...

Lesechka [4]

Answer:

The 61st term is -52

Step-by-step explanation:

5 0

3 years ago