MATHEMATICS
MIDDLE SCHOOL

Answer:

the square root of 37 is the answer

MIDDLE SCHOOL

A proportional relationship is formed when y=16 and x=-4 what is the value of x when y=4?

Answer:

-1

Step-by-step explanation:

The correct model to use for a proportional relationship is y = kx, where k is the constant of proportionality.

If y = 16 when x = -4, then this model becomes 16 = k(-4). Solving for k, we get k = -16/4, or k = -4.

Thus, the specific formula to use here is y = -4x.

Now if y = 4, 4 = -4x, and x must therefore be x = -1.

COLLEGE

If a 4000 watt oven is on for 5 hours, then how many kilowatt-hours (kw-hrs) of energy are used?

If a 4000 watt oven is on for 5 hours, then how many kilowatt-hours (kw-hrs) of energy are used?

Solution: We are given that the oven is 4000 watt and it is on for 5 hours.

We have to find the how many kilowatt-hours (Kw-hrs) of energy are used by the oven.

We first need to convert watts into kilowatt's. We know that:

Therefore, 4000 Watts

Now, we can find how many kilowatt-hours (Kw-hrs) of energy are used by the oven.

Energy used by the oven Kw-hrs

Therefore, 20 kilowatt-hours (kw-hrs) of energy are used by the oven.

MIDDLE SCHOOL

Which of the following demonstrates the Distributive Property? 2(3a + 4) = 6a + 4

2(3a + 4) = 3a + 8

2(3a + 4) = 6a + 8

2(3a + 4) = 5a + 6

2(3a + 4) = 2 * 3a + 2 * 4 = 6a + 8

answer choice 3 is the correct answer

answer choice 3 is the correct answer

2(3a+4) 6a+8=6a+8.....

MIDDLE SCHOOL

The planet neptune orbits the sun. its orbital radius is 30.1 astronomical units (AU). assuming neptunes orbit is circular, what is the distance it travels in a single orbit around the sun? Solve in terms of pi.

Answer:

The distance it travels in a single orbit around the sun is

Step-by-step explanation:

Given : The planet Neptune orbits the sun. its orbital radius is 30.1 astronomical units (AU). Assuming Neptune orbit is circular.

To find : What is the distance it travels in a single orbit around the sun?

Solution :

The radius of the orbital is 30.1 AU.

We have given that assume orbit is circular.

So, distance travels in a single orbit is circumference of the orbit.

Circumference is

r=30.1 AU

Therefore, The distance it travels in a single orbit around the sun is

Answer:

circumference = radius * 2 * PI

circumference = 189.12 astronomical units

Step-by-step explanation:

MIDDLE SCHOOL

The cost of renting a car for a day is $0.70 per mile plus a $20 flat fee (a) write an equation to represent this relationship. Let x be the number of miles driven and y be the total cost for the day.

(b) what does the graph of this equation form on a coordinate plain.

(c) what is the slope and the y-intercept of the graph of the relationship? explain.

Answer:

a) y = .70x + 20

-To find this, use the rate as x since it will change based on the number of miles. Since 20 is a flat fee, it can be added at the end as a constant.

b) This graph forms a straight line.

-This is because the answer in a is a linear equation.

c) The slope is .70 and the y-intercept is 20.

-For this one, the y-intercept is always the constant at the end of the equation and the slope is the coefficient of x.

HIGH SCHOOL

A company is setting up offices in two different cities. The number of employees hired by the company for its office in city A over x months is given by the function f(x) = 9x. The number of employees hired by the company for its office in city B over x months is given by the function g(x) = 3(2)x.

Which function best describes the total number of employees in the company over x months, and after how many months will the total number of employees be 141?

h(x) = 3(3x + (2)x); 5 months

h(x) = 3(2x + (3)x); 2 months

h(x) = 2(3x + 3(2)x); 4 months

h(x) = 3x + (2)x; 6 months

For this case we have the following functions:

City A:

f (x) = 9x

City B:

g (x) = 3 (2) ^ x

The total number of employees will be:

h (x) = f (x) + g (x)

Substituting we have:

h (x) = 9x + 3 (2) ^ x

Rewriting we have:

h (x) = 3 (3x + (2) ^ x)

For 5 months we have:

h (5) = 3 * (3 * (5) + (2) ^ 5)

h (5) = 141

Answer:

the total number of employees in the company over x months and the total number of employees will be 141 when the function is:

h (x) = 3 (3x + (2)^x); 5 months

City A:

f (x) = 9x

City B:

g (x) = 3 (2) ^ x

The total number of employees will be:

h (x) = f (x) + g (x)

Substituting we have:

h (x) = 9x + 3 (2) ^ x

Rewriting we have:

h (x) = 3 (3x + (2) ^ x)

For 5 months we have:

h (5) = 3 * (3 * (5) + (2) ^ 5)

h (5) = 141

Answer:

the total number of employees in the company over x months and the total number of employees will be 141 when the function is:

h (x) = 3 (3x + (2)^x); 5 months

The funcyion for the problem is

h(x) = 3(3x + (2)x);

5 months

h(x) = 3(3x + (2)x);

5 months

COLLEGE

One day a king left his castle with a bag of silver coins to wander his kingdom. To the first peasant he met, he gave half his coins plus two more. A little later, he met another peasant to whom he also gave half his coins plus two more. Walking on, he met a third peasant and again gave half his coins plus two more. Finally, the king went home with two coins left in his bag. (a) How many coins did he have to begin with?

(b) What if he was left with "n" amount of coins?

(c) What if he gave away any unit fraction (1/a) each time?

(d) What if he gave away any unit fraction (1/a) each time and was left with any amount of coins (d)?

Answer:

Step-by-step explanation:

Let us assume the king before leaving his castle had x silver coins.

For the first peasant he met he gave

Now he is left with

Next peasant he gave half of what he had and two more

Hence next peasant got

Balance left =

Third peasant got half + 2 more

Hence third peasant got

Balance he had

HIGH SCHOOL

What is the probability of getting either a sum of 5 or at least one 4 in the roll of a pair of dice?

The answer should be 2/12

MIDDLE SCHOOL

You spin a spinner with five equal sections a number of times. You record your results in the table. Find the experimental probability of spinning 3.

Answer:

The experimental probability of spinning 3 = .

Step-by-step explanation:

Number of sections in the spinner = 5

Number of sections that show number 3 = 1

Let us recall the definition of probability.

probability of an event =

Here, the number of favorable events is the number of sections that show number 3 which is equal to 1.

Total number of events is the total number of sections that is equal to 5.

Hence, the experimental probability of spinning 3 = .