100 POINTS URGENT!
Simplify the expression.

fraction with negative 7 times the quantity 2 minus the cube root of 64 times 3 end quantity as the numerator and 5 as the denominator

Group of answer choices

−14

negative twelve sevenths

twelve sevenths

14

The system has one solution. Option A

The substitution method of solving simultaneous equations involving substituting the value of one variable I to a given equation.

Given the equation;

10x - y = 1    (1)

5x -4y = -3   (2)

Make 'y' the subject from equation (1)

-y = 1 - 10x

y = -1 + 10x

Substitute the value into equation(2)

5x - 4(-1 + 10x) = -3

expand the bracket

5x + 4 - 40x = -3

collect like terms

-35x = -7

x = 1/5

Now, substitute the value of x as 1/5

y = -1 + 10(1/5)

y = -1 + 2

y = 1

Hence, the values are 1/5 and 1

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Independent Variable: 30 pieces of gum

Dependent Variable: 2 pieces of gum

We predict that independent variables will affect dependent variables. What transpires as a result of the independent variable is known as a dependent variable.

The variable you change or manipulate in an experimental study to examine its effects is known as an independent variable. Because it is unaffected by any other study variables, it is referred to as being "independent."

The variable that alters as a result of the modification of the independent variable is known as a dependent variable. The result that interests you is what you're measuring, and it "depends" on your independent variable.

He has 30 pieces of gum which is the independent, 2 would be the dependent.

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The equation of the line of best fit, rounded to the nearest integer, is y = 381x - 566.

What does "Line of Best Fit" mean?

The trend line sometimes referred to as the line of best fit in statistics, uses a straight line on the scatter plot to best depicts the given data points. All of the points, part of the points, or none may be traversed by a straight line. In the statistical approach, it is regarded as one of the significant results of regression analysis.

Given values of x and y, we will use the graphing calculator to find the line of Best Fit, we will get an equation in linear form as:

or, y = 381x - 566

Hence, the equation of the line is y = 381x - 566.

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The  samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center are:

Sample can be defined as the way  of randomly collecting data or information from a group of population so as to draw or reach a conclusion.

Most researcher tend to collect sample when carrying out a survey in which they will then examine, analyze and evaluate the sample they collected before reaching a conclusion.

When a researcher want to carryout survey so as to know how the  resident of a city feel about building a new youth center. The researcher has to collect the survey sample from :

Therefore the correct option is B,D,E.

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The complete question is:

Which are samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center? Select all that apply.

10 names selected from the city phone book.

100 residents who live near the proposed site for the youth center.

100 tourists at the city park last Friday.

50 children at each of the city’s four elementary schools.

100 parents of children at each of the city’s four elementary schools.

The required rate of change is given as [tex]C=\frac{-2t^4-2t^3+200t+50}{\left(t^3+50\right)^2}[/tex].

Given that,
To determine the rate of change in the function of the bloodstream,

C(t) = [tex]\left(\frac{\left[2t^{2\:}\:+\:t\right]}{\left[t^{3\:}\:+\:50\right]}\right)[/tex]

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

Here,
C(t) = [tex]\left(\frac{\left[2t^{2\:}\:+\:t\right]}{\left[t^{3\:}\:+\:50\right]}\right)[/tex]

Apply the rule of ,[tex]\left(\frac{f}{g}\right)'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]
[tex]dC/dt=\frac{\frac{d}{dt}\left(\left[2t^2+t\right]\right)\left[t^3+50\right]-\frac{d}{dt}\left(\left[t^3+50\right]\right)\left[2t^2+t\right]}{\left[t^3+50\right]^2}[/tex]

[tex]C =\frac{-2t^4-2t^3+200t+50}{\left(t^3+50\right)^2}[/tex]
For the value so of the t substitute t in the above expression,

Thus, the required rate of change is given as [tex]C=\frac{-2t^4-2t^3+200t+50}{\left(t^3+50\right)^2}[/tex].

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The forecast for the first week of June is 206.40.

The forecast for for the first week of June will be based on the five-week moving average.

Five-week moving average: (applications of (week 1 + week 2 + week 3 + week 4 +week 5)) / 5

For first 5 week: (238 + 199 +215 +212 +207)/5 = 214.20

For second 5 week: (199 + 215+ 212+ 207+ 211)/5 = 208.80

For third 5 week : (215 + 212 + 207 + 211 + 196)/5 = 208.20

For the fourth 5 week or the first week of June:

(212 + 207 + 211+ 196 + 206)/5 = 206.40

The question is incomplete, the complete question is:

Exhibit 17-5 State Division of Motor Vehicles (DMV) statistics show the rate of new driver's license applications to be as shown below.

Month  Week Application

April  

               1       238

               2        199

               3        215

               4        212

May         1         207

               2         211

               3          196

               4          206

Refer to Exhibit 17-5. Using a five-week moving average, what is the forecast for the first week in June?

a. 198.45

b. 202.83

C. 206.40

d. 200.20

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The amount will be $1,730.21 in the account after 11 years if  quarterly payments of $ 650 into an annuity paying 9% interest compounded.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

P = 650

r = 9% = 0.09

t = 11 years

n = 4

Plug all the values in the formula, we get:

A = $1,730.21

Thus, the amount will be $1,730.21 in the account after 11 years if  quarterly payments of $ 650 into an annuity paying 9% interest compounded.

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