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3 years ago

Find the distance between (-8,7) and (13,-1)

Mathematics

1 answer:

grin007 [14]3 years ago

6 0

Answer:

22.4722

Step-by-step explanation:

To answer this question we need to use the distance formula. The distance formula is as follows:

$d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}$

Now, let's identify what each variable is:

x2 = 13

x1 = -8

y2 = -1

y1 = 7

Next, let's put these into the equation:

$d = \sqrt{(13 - (-8))^2 + (-1 -7)^2}$

Time to solve the equation:

$d = \sqrt{(21)^2+(-8)^2} \\d = \sqrt{441 + 64} \\d = \sqrt{505} \\d = 22.4722$

Therefore, the distance between the points of (-8,7) and (13,1) is 22.4722.

I hope this helps!!

- Kay :)

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Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 64% of vehi

ira [324]

Answer:

a) 0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

b) 0.996 is the probability that more than half of the vehicles carry just one person.

Step-by-step explanation:

We are given the following information:

A) Binomial distribution

We treat vehicle on road with one passenger as a success.

P(success) = 64% = 0.64

Then the number of vehicles follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

$P(x \geq 6) = P(x =6) +...+ P(x = 10) \\= \binom{10}{6}(0.64)^6(1-0.64)^4 +...+ \binom{10}{10}(0.64)^{10}(1-0.79)^0\\=0.7291$

0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

B) By normal approximation

Sample size, n = 92

p = 0.64

$\mu = np = 92(0.64) = 58.88$

$\sigma = \sqrt{np(1-p)} = \sqrt{92(0.64)(1-0.64)} = 4.60$

We have to evaluate the probability that more than 47 cars carry just one person.

$P(x \geq 47)$

After continuity correction, we will evaluate

$P( x \geq 46.5) = P( z > \displaystyle\frac{46.5 - 58.88}{4.60}) = P(z > -2.6913)$

$= 1 - P(z \leq -2.6913)$

Calculation the value from standard normal z table, we have,

$P(x > 46.5) = 1 - 0.004 = 0.996 = 99.6\%$

0.996 is the probability that more than half out of 92 vehicles carry just one person.

5 0

2 years ago

Lopez’s mailing bill is automatically deducting $19 from his bank account every month. How much will the deductions total for th

MakcuM [25]

If Lopez's mailing bill continues to deduct 19$ from his bank account every month for a year, then in total, the deductions total for the year would be $228.00.

Why?

$19.00 is being taken away each month. There are 12 months in a year.

$19.00 x 12 months = the total of $228.00 a year.

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2 years ago

Find the area of each triangle.

lord [1]

Hi there!

We can find the area of a triangle with the formula:
$area = 0.5 \times base \times height$

Filling in this formula gives us the following answers.

Triangle 1
$area = 0.5 \times 5 \times 8 = 20$

Triangle 2
$area = 0.5 \times 7 \times 9 = 31.5$

Triangle 3
$area = 0.5 \times 16 \times 12 = 96$

8 0

3 years ago

Read 2 more answers

Trigonometry Reference Angles and Triangles Find the exact value of sin 135*

Tomtit [17]

Answer:

sqrt(2)/2

Step-by-step explanation:

Sin(135) = sin(180-135) = sin(45)

= 1/sqrt(2) or sqrt(2)/2

sqrt: square root

4 0

3 years ago

In a equation below, for what value of c does x=4? 1/2(2x+4)=3x-c

oksano4ka [1.4K]

Answer:

c = 6

Step-by-step explanation:

1/2 (2(4) + 4) = 3(4) - c

1/2 (8 + 4) = 12 - c

1/2 (12) = 12 - c

6 = 12 - c

-6 = -c

c = 6

5 0

2 years ago

Find the distance between (-8,7) and (13,-1)​

Find the distance between (-8,7) and (13,-1)