MATHEMATICS MIDDLE SCHOOL

Carla and Frank can each wash a car and clean the interior in 2 hours, but Missy needs 3 hours to do the work. If the three work together, how long will it take to clean 7 cars?

Answers

Answer 1

Answer:

Remark

Start by figuring this out for 1 car. Worry about the 7 part when you find 1.

This problem is used quite frequently in physics. For example resistors in parallel use the same equation.

Formula

1/frank + 1/carla + 1/missy = 1/ time taken to do 1 mar.

Givens

Frank = 2 hours

Carla = 2 hours

Missy = 3 hours.

Substitute and Solve

1/2 + 1/2 + 1/3 = 1/Three_together.

3/6 + 3/6 + 2/6 = 1/Three_together.

8/6 = 1/Three_together. Cross multiply

8 * Three_Together = 6*1

8 * Three_Together = 6 Divide by 8

Three_Together = 6/8 = 3/4 = 0.75 hours. or 45 minutes for 1 car

Seven Cars

For 7 cars multiply 0.75 by 7

7 * 0.75 = 5.25 hours. <<<< Answer

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the area of a square floor on a scale drawing is 100 square centimeters and the scale of the drawing is cm : 2 ft what is the area of the actual floor what is the ratio of the area in the drawing to the actual area

Answers

The actual floor is 200 square feet and the ratio is 100 square centimeters: 200 square feet

the ratio would be 50:1 because you would have to simplify the ratio 100:2

Four different sets of objects contain 4, 5, 6, and 8 objects, respectively. Howmany unique combinations can be formed by picking one object from each
set?

Answers

Answer:

960

Step-by-step explanation:

We can find the number of unique combinations by

Multiplying 4*5*6*8

960

There are 960 possible choices by picking 1 from each group

Solve by using the quadratic formula.
3psquared+7p+2=0

Answers

Answer:

-1/3,-2

Step-by-step explanation:

The quadratic formula is [-b±√(b^2-4ac)]/2a. In this equations 3p^2 is a, 7p is b, and 2 is c.

Then just plug in the numbers.

[-7±√((-7^2)-4(3)(2)]/2(3)

[-7±√(25)]/6

(-7+5)/6 and (-7-5)/6

-1/3 and -2 are the answers, if you plug these numbers into the original equation, you find that they equal 0 which means that they work.

Answer:

$\large\boxed{x=-2\ or\ x=-(1)/(3)}$

Step-by-step explanation:

The quadratic formula of a quadratic equation

$ax^2+bx+c=0\n\nx=(-b\pm√(b^2-4ac))/(2a)$

We have the equation:

$3p^2+7p+2=0\to a=3,\ b=7,\ c=2$

Substitute:

$b^2-4ac=7^2-4(3)(2)=49-24=25\n\n√(b^2-4ac)=√(25)=5\n\nx_1=(-7-5)/(2(3))=(-12)/(6)=-2\n\nx_2=(-7+5)/(2(3))=(-2)/(6)=-(1)/(3)$

Loren compares the fractions 2/3 and 5/8 by first rewriting them using a common numerator. He does everything correctly. Which shows Loren’s comparison?A. 5/6 > 5/8
B. 10/3 < 10/8
C 10/15 < 10/16
D 10/15 >10/16

Answers

Answer:

D 10/15 > 10/16

Step-by-step explanation:

The least common multiple of 2 and 5 is 10.

2/3 = 10/15

5/8 = 10/16

10/15 > 10/16

Answer: D.

After sitting in a refrigerator for a while, a turkey at a temperature of 34 degrees F is placed on the counter and slowly warms closer to room temperature 72 degrees f. The turkey reaches the temperature of 41 degrees F after 35 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 80 minutes.

Answers

Answer:

k = 0.006
T = 48 °F

Step-by-step explanation:

The initial temperature difference of 72 -34 = 38 °F is reduced to a difference of 72 -41 = 31 °F after 35 minutes. The exponential term in the temperature expression could have the factor ...

(31/38)^(t/35) = e^(-kt)

Taking the natural log, we find ...

(t/35)ln(31/38) = -kt

k = ln(38/31)/35 ≈ 0.00581711

To the nearest thousandth, this is ...

k ≈ 0.006

Using this in the equation for temperature, we have ...

T = 72 -38e^(-0.006t)

Filling in the desired value for t (80), we find the turkey temperature after 80 minutes to be about

T = 72 -38e^(-.006×80) = 72 -38e^-.48 ≈ 48.49

T ≈ 48 °F

The value of k is about 0.006, and the turkey temperature is about 48 °F.