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djverab [1.8K]
3 years ago
5

Five friends are leaving a bar for home. Aside from the owner of the car, one other person is deemed able to operate the vehicle

. In how many ways can these five friends be seated for the ride home?
Mathematics
1 answer:
erastova [34]3 years ago
3 0

Answer:

4

Step-by-step explanation:

one person is deemed to drive and that person is fixed on the driver's seat no mater which arrangement.

we have now 2 more seats one adjacent to the driver and one rear (two combined).

so the total ways in which all five can be arranged is as follows.

driver, adjacent to him(1)  and three back.

driver adjacent to him (different person) and three back.

see the driver is always fixed so we can ignore him.

thus we when driver set fixed , on two remaining seats (adjacent to driver and the back )there can be 4 different combinations.

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The volume of triangular prism V = A * h.
So, V = 3.5*5 = 17.5 cubic inches
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Solve the question and check the solution. Express numbers as integers or simplified fractions. 5(m+5)=7m+9
Yanka [14]

Answer:

m = 8

Step-by-step explanation:

5(m+5)=7m+9   (distribute & evaluate parenthesis)

5(m)+5(5)=7m+9

5m + 25 = 7m + 9  (move all m-terms to one side and constants to the other)

5m - 7m = 9 - 25  (evaluate both sides)

-2m = -16 (divide both sides by -2)

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7 0
3 years ago
In 1987, the population of country A was estimated at 87 million people, with an annual growth rate of 3.5%. The 1987 population
KATRIN_1 [288]

Answer:

Step-by-step explanation:

Given that in 1987, the population of country A was estimated at 87 million people, with an annual growth rate of 3.5%

Thus the equation for population for country A would be

P(A) = 87e^{0.035t}

The 1987 population of country B was estimated at 243 million with an annual growth rate of 0.6%.

So equation for population for country B would be

P(B) = 243e^{0.006t} where t = time in years and P in millions

a) P(A) = 2*87 when

2=e^{0.035t}

Take log and solve

ln 2 = 0.005 t

t = 138.63

Thus after 138 years population will double for A

b) P(A) = P(B) when

P(A) = 87e^{0.035t}=P(B) = 243e^{0.006t}\\e^{0.035t-0.006t}=\frac{243}{87} =2.793\\0.029t = 1.027\\t= 35.42

Approximately after 35.5 years the populations of both countries would be equal.

7 0
3 years ago
Read 2 more answers
HELP IM FAILING MATH OOOOFFFF
meriva

The point-slope form:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (-4,\ -1) and \left(\dfrac{1}{2},\ 3\right).

Substitute:

m=\dfrac{3-(-1)}{\frac{1}{2}-(-4)}=\dfrac{4}{4\frac{1}{2}}=\dfrac{4}{\frac{9}{2}}=4\cdot\dfrac{2}{9}=\dfrac{8}{9}\\\\y-(-1)=\dfrac{8}{9}(x-(-4))\\\\y+1=\dfrac{8}{9}(x+4)

The standard form: Ax + By = C

y+1=\dfrac{8}{9}(x+4)\qquad\text{multiply both sides by 9}\\\\9y+9=8(x+4)\qquad\text{use distributive property}\\\\9y+9=8x+32\qquad\text{subtract 9 from both sides}\\\\9y=8x+23\qquad\text{subtract 8x from both sides}\\\\-8x+9y=23\qquad\text{change the signs}\\\\\boxed{8x-9y=23}

4 0
3 years ago
Aubrey invested $61,000 in an account paying an interest rate of 1.9% compounded continuously. Assuming no deposits or withdrawa
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Answer: 9.9 years.

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If interest is compounded continuously, then formula to compute final amount A = Pe^{rt}, where P =initial amount, r= rate of interest , t=time.

Given: P= $61,000, r= 1.9% =0.019  , A = $ 73600

Substitute all values in formula

73600=61000e^{0.019t}\\\\\Rightarrow\ \dfrac{73600}{61000}=e^{0.019t}\\\\\Rightarrow\ 1.20655738=e^{0.019t}

Taking natural log on both sides

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Hence, the required time = 9.9 years.

4 0
3 years ago
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