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Dahasolnce [82]
3 years ago
10

A High School soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on the

highway of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high schoold and the stadium\
Mathematics
1 answer:
finlep [7]3 years ago
4 0

Answer: The coordinate are

( 5 , 2.5 )

Distance = 5

Step-by-step explanation:

The coordinates of the rest stop will be the mid point between the high school is at point (3, 4) and the stadium in Columbus at point (7, 1).

Mid point = (X1 +X2)/2 , (Y1+Y2)/2

(3+7)/2 , (4+1)/2 = ( 5 , 2.5 )

The approximate distance between the high school and the stadium will be

D^2 = (7-3)^2 +( 4-1)^2

Where D = distance

D^2 = 4^2 + 3^2

D = 5

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ch4aika [34]

Answer:

6-pack for 3.12

Step-by-step explanation:

Find unit price

2.24/4=0.56

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7 0
3 years ago
Read 2 more answers
A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective
andriy [413]

Answer:

(a) P(X \leq 20) = 0.9319

(b) Expected number of defective light bulbs = 15

(c) Standard deviation of defective light bulbs = 3.67

Step-by-step explanation:

We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.

Firstly, the above situation can be represented through binomial distribution, i.e.;

P(X=r) = \binom{n}{r} p^{r} (1-p)^{2} ;x=0,1,2,3,....

where, n = number of samples taken = 150

            r = number of success

           p = probability of success which in our question is % of bulbs that

                  are defective, i.e. 10%

<em>Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.</em>

So, Let X = No. of defective bulbs in a box

<u>Mean of X</u>, \mu = n \times p = 150 \times 0.10 = 15

<u>Standard deviation of X</u>, \sigma = \sqrt{np(1-p)} = \sqrt{150 \times 0.10 \times (1-0.10)} = 3.7

So, X ~ N(\mu = 15, \sigma^{2} = 3.7^{2})

Now, the z score probability distribution is given by;

                Z = \frac{X-\mu}{\sigma} ~ N(0,1)

(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X \leq 20) = P(X < 20.5)  ---- using continuity correction

    P(X < 20.5) = P( \frac{X-\mu}{\sigma} < \frac{20.5-15}{3.7} ) = P(Z < 1.49) = 0.9319

(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = n \times p = 150 \times 0.10 = 15.

Standard deviation of defective light bulbs is given by = S.D. = \sqrt{np(1-p)} = \sqrt{150 \times 0.10 \times (1-0.10)} = 3.67

8 0
3 years ago
Carolyn has $2.55 in her purse in nickels and dimes. The number of nickels is nine less than three times the number of dimes. Fi
Flauer [41]

Hi, the answer is ;

Answer:

12 dimes and 27 nickels

Step-by-step explanation:

.05N + .1d = 2.55

N= 3d - 9

0.05 (3d-9) + 0.1d = 2.55

0.15d - 0.45 + 0.1d = 2.55

0.25d = 2.55 + 0.45

0.25d = 3

D = 12

N = 3 (12) - 9

N = 36 - 9

N = 27

5 0
3 years ago
Emily has nickels and quarters. She has 3 fewer
lawyer [7]

Answer:

Step-by-step explanation:

she has 3 quarters

4 0
3 years ago
Which of the following is equal to 5 4/9? The answers are:
madam [21]

Answer:

5.4

Step-by-step explanation:

First work out 4/9 this is the same thing as 4 ÷ 9 which equals 0.44444

and then add the whole number 5 so,

5 + 0.44444 = 5.44444

3 0
3 years ago
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