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2 years ago

Andy and Donald are both running toward the soccer ball during a game.

Mathematics

1 answer:

zavuch27 [327]2 years ago

6 0

Answer:

Correct option: second one -> Andy and Donald do not collide.

Step-by-step explanation:

To find if the boys collide, we need to find if there is a common value of t where the their x position are equal and their y position are equal. To do this, we make x(t) of Andy equal to x(t) of Donald, , then if there is a value for t, we do the same for y(t) and check if the values of t are equal:

24 + 23t = 12 + t

22t = -12

t = -0.5455 seconds

As the time is negative, it will not occur, so the boys will never collide.

Correct option: second one

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37 For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottl

Pavel [41]

Answer:

Step-by-step explanation:

Let j represent the cost of a juice box.

Let w represent the cost of a bottle of water.

One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92.. This means that

18j + 32w = 19.92 - - - - - - - - - - - - 1

The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. This means that

14j + 26w = 15.76- - - - - - - - - - - - 2

Multiplying equation 1 by 14 and equation 2 by 18, it becomes

252j + 448w = 278.88

252j + 468w = 283.68

Subtracting, it becomes

- 20j = - 4.8

j = - 4.8/- 20 = 0.24

Substituting j = 0.24 into equation 1, it becomes

18 × 0.24 + 32w = 19.92

4.32 + 32w = 19.92

32w = 19.92 - 4.32 = 15.6

w = 15.6/32 = 0.4875

Kara's prices are incorrect.

the cost of a juice box is $0.24

the cost of a bottle of water is $0.4875

7 0

2 years ago

Suppose that a company's sales were $1,000,000 6 years ago and are $9,000,000 at the end of the 6 years. Find the geometric mean

Dmitriy789 [7]

Answer:

The geometric mean growth rate of sales is 1.4422.

Step-by-step explanation:

We have two sales values, one from 6 years ago and the other from now.

We have to calculate the geometric growth rate of sales.

We have:

$y(-6)=1,000,000\\\\y(0)=9,000,000$

We can write the relation between these two values as:

$y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422$

The geometric mean growth rate of sales is 1.4422.

6 0

2 years ago

An airliner carries 150 passengers and has doors with a height of 78 in. Heights of men are normally distributed with a mean of

iogann1982 [59]

Answer:

Step-by-step explanation:

x, height of men is N(69, 2.8)

Sample size n =150

Hence sample std dev = $\frac{2.8}{\sqrt{150} } =0.229$

Hence Z score = $\frac{x-69}{0.229}$

A) Prob that a random man from 150 can fit without bending

= P(X<78) = P(Z<3.214)=1.0000

B) n =75

Sample std dev = $\frac{2.8}{\sqrt{75} } =0.3233$

P(X bar <72) = P(Z<9.28) = 1.00

C) Prob of B is more relevent because average male passengers would be more relevant than a single person

(D) The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

3 0

2 years ago

On a backpacking trip through Europe, Troy spent 20 Swiss francs to stay one night in a youth hostel. If the foreign exchange ra

Vlad [161]

He spent 9 dollars and 9 cents so $9.09

5 0

2 years ago

Read 2 more answers

At 11:00 a.M., there are 400 members and 150 non-members visiting a museum. After 11:00 a.M., 10 members leave every five minute

alexdok [17]

Answer:

$16:27$

Step-by-step explanation:

GIVEN: At $11:00\text{ A.M.}$ , there are $400$ members and $150$ non-members visiting a museum. After $11:00\text{ A.M.}$ , $10$ members leave every five minutes and $5$ non-members arrive every five minutes.