Your friend, Margret, needs your help in solving a math problem that she got from her math teacher.
This was the problem:

What number can be put where the question mark is?
Justify your answer.
? =

Answer:

the answer is smallest to biggest

Step-by-step explanation:

Answer:

1) dA/dt = -21 cm²/s and Area is decreasing

2)dP/dt = 0 and perimeter is constant

3) dD/dt = 21/13 cm/s and diagonal is increasing

Step-by-step explanation:

We are given that;

length l of a rectangle is decreasing at a rate of 3 cm/sec.

Thus, dl/dt = -3 cm/sec

Also, the width w is increasing at a rate of 3 cm/sec. Thus;

dw/dt = 3 cm/sec

When l=5 cm and w=12 cm;

A) Area is given by the formula;

A = lw

The rate at which area is increasing is;

dA/dt = l(dw/dt) + w(dl/dt)

Plugging in the relevant values;

dA/dt = 5(3) + 12(-3)

dA/dt = 15 - 36

dA/dt = -21 cm²/s

This is less than 0.thus, A is decreasing.

B) Formula for perimeter is;

P = 2l + 2w

rate of change of perimeter is;

dP/dt = 2(dw/dt) + 2(dl/dt)

Plugging in the relevant values, we have;

dP/dt = 2(-3) + 2(3)

dP/dt = 0

Thus,Perimeter is constant

C) the length of the diagonal of a rectangle is given by;

D = √(w² + l²)

Rate of change of diagonal is;

dD/dt = [2w(dw/dt) + 2l(dl/dt)]/(2√(w² + l²))

2 will cancel out in numerator and denominator to give;

dD/dt = [w(dw/dt) + l(dl/dt)]/(√(w² + l²))

Plugging in the relevant values gives;

dD/dt = [12(3) + 5(-3)]/(√(12² + 5²))

dD/dt = (36 - 15)/13

dD/dt = 21/13 cm/s

This is greater than 0.

Thus, diagonal is increasing.

Answer:

disproportionate stratified sample

Step-by-step explanation:

Based on the given information we can say that Abel's sample is a disproportionate stratified sample. This is the case mainly because the department worker population ranges from 40 to 120 workers. This changing population makes the 10 workers that were chosen for the sample not proportionate to the entire population. Therefore, under different population sizes workers have different chances of getting selected for the study which ultimately creates different results.

Answer:

[tex] \huge \frac{7}{8} \\ [/tex]

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

From the question we have

[tex]m = \frac{ - 9 - - 2}{ - 10 - - 2} = \frac{ - 9 + 2}{ - 10 + 2} = \frac{ - 7}{ - 8} = \frac{7}{8} \\ [/tex]

We have the final answer as

[tex] \frac{7}{8} \\ [/tex]

Hope this helps you

Answer:

7/8

Step-by-step explanation:

She needs to score AT LEAST 19 points

Step-by-step explanation:

24 + 21 + 20 + 19 = 84

84 ÷ 2 = 21

Answer:

510

Step-by-step explanation:

Answer:

The answer is 14

Step-by-step explanation:

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

Complete the multiplication and the equation becomes

The two fractions now have like denominators so you can add the numerators.

there....

The solution of the expression ''2 divided by 1/7'' is 14.

Used the concept of the divide that states,

The division method is used to distribute a group of things into equal parts. The division is just the opposite of multiplications.

Given that,

2 divided by 1/7

Now it can be written as,

2 divided by 1/7

[tex]2 \div \dfrac{1}{7}[/tex]

[tex]2 \times 7[/tex]

[tex]14[/tex]

Therefore, the solution of the expression is 14.

To learn more about the divide visit:

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Answer:

55860

Step-by-step explanation:

This way super dupper easy

Answer:

V is approximately 11.81

Step-by-step explanation:

We use the sine rule

V/sin 98 = 10/sin 57

Cross multiply

V * sin 57 = 9.90268068

V = 9.90268068/sin 57

V= 11.80759295

V ~ 11.81

Answer:

Your dead meat then...

Step-by-step explanation:

But I’m pretty sure its b?

sorry if it’s wrong

Answer:

the answer is c took this before

Answer:

175

Step-by-step explanation:

A deposit is adding money to the bank, so the integer will be positive.

That makes our integer: 175

Answer:

45

Step-by-step explanation:

45 > 42 but < 47 and it's a multiple of 3 and 5

Answer:

you make 20 dollars in a month

Step-by-step explanation:

15 is 3/4 a month, unit rate would be 5 dollars a week so therefore a whole month would be 20

Answer:

6

Step-by-step explanation:

6 is the slope of the function

Answer:

The system that could be used find the price in dollars of each large candle, x, and each small candle, Y is given as:

5x + 7y = 96...... Equation 1

4x + 8y = 88..... Equation 2

Step-by-step explanation:

From the question:

Let cost of:

large candles = x

Small candles = y

A customer at a store paid $96 for 5 large candles and 7 small candles.

Hence:

5x + 7y = 96...... Equation 1

At the same store a second customer paid $8 less than the first customer for 4 large candles and 8 smal candies

Hence:

4x + 8y = $96 - $8

4x + 8y = 88..... Equation 2

The system that could be used find the price in dollars of each large candle, x, and each small candle, Y is given as:

5x + 7y = 96...... Equation 1

4x + 8y = 88..... Equation 2

Answer:

y = x - 5

Step-by-step explanation:

Comparing the given y = x - 7 to y = mx + b, we see that the slope is +1.

In y = x + b we replace y with -11 and x with -6 to determine the y-intercept, b:

-11 = -6  + b

Then b must be -5, and so the desired new equation is

y = x - 5

Answer:

2L + 24 = 72

2L = 72-24

L = 48 ÷ 2

= 24 feet

Answer:

5 times

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

Set of data in terms of ordered pairs represents a function when output value of each input value is different.

Option A

Since, for every value of x there is a different value of y, it's a function.

Option B

In each ordered pair, for every value of x there is a different value of y.

Therefore, it's a function.

Option C

From the given graph, for every value of x there is a different value of y.

Therefore, it's a function.

Option D

From the given set of ordered pairs we find for x = 1 there are two values of y (y = 4 and 3).

Therefore, the given set of ordered pairs doesn't represent a function.

Option D is the answer.

Answer:

well 5% of 600 is 30. so if you make 600 phone calls and an average of 5% of those calls are people signing up, then that would be 30.

Answer:

The alternative hypothesis is

      [tex]H_a : p_1 \ne \ p_2[/tex]

The rejection region is the region outside the interval

         [tex]-1.96 < z_{critical} < 1.96[/tex]

Step-by-step explanation:

From the question we are told that

    The significance level is  [tex]\alpha = 0.05[/tex]

     The null hypothesis is  [tex]H_o : p_1 = p_2[/tex]

      The  alternative hypothesis is  [tex]H_a : p_1 \ne \ p_2[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Hence the rejection region is the region outside the interval [tex]-1.96 < z_{critical} < 1.96[/tex]

The alternative hypothesis is, [tex]H _a; \ P_1\neq P_2[/tex] .

And the rejection region is the region outside the interval is [tex]-1.96< Z_c_r_i_t_i_c_a_l <1.96[/tex] .

Given that,

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance.

We have to determine,

What is the alternative hypothesis and rejection region?

According to the question,

The significance level is,  [tex]\alpha = 5 \ percent = 0.05[/tex]

The null hypothesis is [tex]H_0 ; P_1 = P_2[/tex]

The alternative hypothesis is, [tex]H _a; \ P_1\neq P_2[/tex]

In the normal distribution table, the critical value [tex]\dfrac{\alpha}{2}[/tex] is,

[tex]Z _\frac{\alpha}{2} = 1.96[/tex]

Hence, the rejection region is the region outside the interval is [tex]-1.96< Z_c_r_i_t_i_c_a_l <1.96[/tex] .

To know more about the Hypothesis click the link given below.

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