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3 years ago

1 Pete owed each of his three sisters $10. Which statement accurately represents how much Pete owes in total?

Mathematics

1 answer:

Kaylis [27]3 years ago

5 0

Answer:

$30 in total.

Step-by-step explanation:

Since he owes 3 people 10 dollars each, you simply need to multiply:

10×3= $30 dollars in total.

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team rise over run finished the last 12 miles in 1/2 an hour what was their average speed in miles per hour

saveliy_v [14]

Answer:

Step-by-step explanation: it’s been half an hour and they ran the 12 miles so in an hour which is double half an hour they ran two times what they did in half an hour

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3 years ago

Read 2 more answers

If n(A) =15 n (B) = 9 n(A∩B) =4 <br> find n(A U B)

Xelga [282]

Answer:

Step-by-step explanation:

n(A) only =15-4=11

n(B) only=9-4=5

n(A n B)=4

n(A U B)=11+5+4=20

5 0

3 years ago

From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. Wha

Helga [31]

Answer:

The correct option is D. 2/7

Step-by-step explanation:

Consider the provided information.

There are 8 volunteers including Andrew and Karen, 4 people are to be selected at random to organize a charity event.

We need to determine the probability Andrew will be among the 4 volunteers selected and Karen will not.

We want to select Andrew and 3 others but not Karen in the group.

Thus, the number of ways to select 3 member out of 8-2=6

(We subtract 2 from 8 because Andrew is already selected and we don't want Karen to be selected, so subtract 2 from 8.)

The required probability is:

$\dfrac{^6C_3}{^8C_4}=\dfrac{\frac{6!}{3!3!}}{\frac{8!}{4!4!}}\\\\\\\dfrac{^6C_3}{^8C_4}=\frac{20}{70}\\\\\\\dfrac{^6C_3}{^8C_4}=\dfrac{2}{7}$

Hence, the correct option is D. 2/7

6 0

4 years ago

Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

7 0

4 years ago

URGENT!!!!!! Find the value of q in the following system so that the solution to the system is——

valkas [14]

<h3>Answer: Q = 8</h3>

====================================================

Explanation:

The left hand side of the first equation is x-3y

The left hand side of the second equation is 2x-6y = 2(x-3y). Note how it's simply double of the first expression x-3y

If we multiply both sides of the first equation by 2, we get

x-3y = 4

2(x-3y) = 2*4

2x-6y = 8

Meaning that 2x-6y = 8 is equivalent to x-3y = 4. Both produce the same line leading to infinitely many solutions. Each solution will lay along the line x-3y = 4.

We can say each solution is in the set {(x,y): x-3y = 4}

Which is the same as saying each solution is of the form (3y+4,y)

4 0

4 years ago