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4 years ago

Simplify the expression.

Mathematics

1 answer:

lesantik [10]4 years ago

4 0

Break it down into steps, so like this:

3*3= 3^2 and 3*3*3*3*3* = 3^5

solve: solve:

multiple the two answers

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A school wants 2 chaperones for every 25 students. There are 100 students going on the field trip. How many chaperones does the

d1i1m1o1n [39]

The answer is 8. because 100/25=4 and 4x2=8

5 0

4 years ago

Read 2 more answers

4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

Ivan

Question:

The quantities x and y are in proportion

x y

4 6

30 45

8 b

a 15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

$a = 10$ and $b = 12$

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

$(x_1,y_1) = (4,6)$

$(x_2,y_2) = (30,45)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{45 - 6}{30 -4}$

$m = \frac{39}{26}$

$m = 1.5$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

This gives:

$y - 6 = 1.5(x - 4)$

$y - 6 = 1.5x - 6$

$y = 1.5x$

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in $y = 1.5x$

$b = 1.5 * 8$

$b = 12$

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in $y = 1.5x$

$15 = 1.5 * a$

Solve for a

$a = \frac{15}{1.5}$

$a = 10$

Solving (b): The constant of variation.

This has been solved in (a) above as:

$m = 1.5$

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

This shows direct variation

3 0

3 years ago

10. A cube has faces numbered 1 to 6. If you roll this cube 4 times, how many different outcomes are possible?

Georgia [21]

Answer: If we throw 4 cubes, there are 1296 different outcomes are possible.

Step-by-step explanation:

Given : A cube has faces numbered 1 to 6.

So the number of outcomes for throwing one die = 6

If we throw 4 cubes , then

According to the Fundamental counting principle,

The total number of different outcomes are possible = $(\text{Number of outcomes for throwing one die})^4$

Therefore , The total number of different outcomes are possible $=6^4=1296$

Hence, there are 1296 different outcomes are possible.

8 0

4 years ago

A phone company offers to monthly plans. Plan a cost $23 plus an additional $.08 for each minute of calls. Plan B cost $19 an ad

Anettt [7]

Answer:

The indifference point is 100 minutes.

Step-by-step explanation:

Giving the following information:

Plan a cost $23 plus an additional $.08 for each minute of calls.

Plan B cost $19 an additional $.12 for each minute of calls.

First, we need to establish the total cost formula for each plan:

Plan A= 23 + 0.08*x

Plan B= 19 + 0.12*x

x= number of minutes

Now, to calculate the indifference point, we equal both formulas and isolate x:

23 + 0.08x = 19 + 0.12x

4 = 0.04x

100= x

The indifference point is 100 minutes.

Prove:

Plan A= 23 + 0.08*100= $31

Plan B= 19 + 0.12*100= $31

5 0

3 years ago

Phil bought 700 shares of a company’s stock for $9.29/share. He pays a broker a commission of $18 to buy and sell stock. After o

Lelechka [254]

+ $0.61

Have a nice day.

5 0

4 years ago