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The ratio of trucks to cars in a parking lot was 5 to 2. How many trucks were in the lot if there where 18 cars?

Elena L [17]

90 trucks- for every 2 cars there are 5 trucks

6 0

3 years ago

Find c. Round to the nearest tenth

sergeinik [125]

Answer:

c = <u>0.5 cm</u>

Step-by-step explanation:

Using the Sine rule in the triangle, then

= ( cross- multiply )

c × sin105° = 2 × sin15° ( divide both sides by sin105°

c = ≈ 0.5 cm ( to the nearest tenth )

8 0

3 years ago

Please explain how you got your answers! (: Solve the problem by using the counting principle.

Natasha2012 [34]

A. The number of fabric-pattern-color combinations is 4 * 13 * 9 = 468

B. P(1st choice) = no of novels / total books = 3/6 = 1/2
    P(2nd choice) = no of remaining novels/ total remaining books = 2/5
    P(both novels) = 1/2 * 2/5 = 1/5 (without replacement assumed)

C. P(1st choice) = no of biographies / total books = 2/6 = 1/3
    P(2nd choice) = no of remaining biographies/ total remaining books = 1/5
    P(both biographies) = 1/3 * 1/5 = 1/15 (without replacement assumed)

D. P(1st choice) = no of history books / total books = 1/6
    P(2nd choice) = no of novels/ total remaining books = 3/5
    P(a history, then a novel) = 1/6 * 3/5 = 1/10 (without replacement assumed)

7 0

3 years ago

A rectangle has a perimeter of 30 ft. Find a function that models its area A in terms of the length x of one of its sides. What

Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

Let the other side of the rectangle be y. The perimeter of the rectangle is expressed as P = 2(x+y)

Given P = 30ft, on substituting P = 30 into the expression;

30 = 2(x+y)

x+y = 15

y = 15-x

Also since the area of the rectangle is xy;

A = xy

Substitute y = 15-x into the area;

A = x(15-x)

A = 15x-x²

The function that models its area A in terms of the length x of one of its sides is A = 15x-x²

The side of length x yields the greatest area when dA/dx = 0

dA/dx = 15-2x

15-2x = 0

-2x = -15

x = -15/-2

x = 7.5 ft

Hence the side length, x that yields the greatest area is 7.5ft.

Since y = 15-x

y = 15-7.5

y = 7.5

Area of the rectangle = 7.5*7.5

Area of the rectangle = 56.25ft²

6 0

3 years ago

Three people spend $22.50 on large popcorns and soft drinks. They go back the next week and each pay $8.00 for each ticket, they

kakasveta [241]

Answer:

Cost of each large soft drink is $3.00 and Cost of each Large bucket of popcorn is $4.50.

Step-by-step explanation:

Let the Cost of each large soft drink be x.

Also Let the Cost of each Large bucket of popcorn be y.

Number of people = 3

Money Spend on popcorn and soft drink = $22.50

Hence we can say that;

$3x+3y=22.50 \ \ \ \ equation \ 1$

Next week three people traveled again.

Each ticket was bought = $8.00

Number of tickets bought = 3

Money spend on tickets = $8\times3 = \$24$

Total return trip = $37.50

Also they each get a large soft drink, but they share one large bucket of popcorn

Cost of Soft drink = 3x

Cost of popcorn = y

Now Total return trip is equal to sum of Money spend on tickets and Cost of soft drink and Cost of popcorn.

Hence equation can be framed as;

$24+3x+y=37.50\\3x+y=37.50-24\\3x+y = 13.50 \ \ \ \ eqaution \ 2$

Now Subtracting equation 2 from equation 1 we get;

$(3x+3y)-(3x+y)=22.50-13.50\\\\3x+3y-3x-y=9\\\\2y= 9\\\\y=\frac{9}{2}=\$4.50$

Now substituting the value of y in equation 1 we get;

$3x+3y=22.50\\\\3x+3\times4.50=22.50\\\\3x+13.50=22.50\\\\3x=22.50-13.50\\\\3x= 9\\\\x=\frac{9}{3}=\$3.00$

Hence Cost of each large soft drink is $3.00 and Cost of each Large bucket of popcorn is $4.50.

7 0

3 years ago