Answer:
the simplified expression is negative twelve sevenths
Step-by-step explanation:
To simplify the expression, we can start by applying the rules for combining like terms:
(-7) * 2 - (3 * sqrt(64)) = (-14) - (3 * sqrt(64))
Next, we can use the fact that the square root of 64 is 8 to simplify the expression further:
(-14) - (3 * sqrt(64)) = (-14) - (3 * 8) = (-14) - 24 = -38
Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor:
-38 / 5 = (-38 / 2) / (5 / 2) = -19 / 2 = negative twelve sevenths
Therefore, the simplified expression is negative twelve sevenths.
Answer:
the simplified expression is negative twelve sevenths
Step-by-step explanation:
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.
The samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center are:
100 residents who live near the proposed site for the youth center.50 children at each of the city’s four elementary schools.100 parents of children at each of the city’s four elementary schools.What is sample?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 :
100 residents who live near the proposed site for the youth center.50 children at each of the city’s four elementary schools.100 parents of children at each of the city’s four elementary schools.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.
terry has 30 piecies of gum and guves 2 peaices to each of his friends. identify the independednt and dependednt variables. write a rule in functionnotation for each situation
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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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 April Week1 1 Application 238 199 Nm 215 212 207 211 May nm 196 206 Refer to Exhibit 17-5. Using a five-week moving average, what is the forecast for the first week in April? a. 198.45 Ob. 202.83 C. 206.40 d. 200.20
Previous question
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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MODELING WITH MATHEMATICS The table shows the total numbers y of people who reported an earthquake x minutes after it ended.
a. Use a graphing calculator to find the equation of the line of best fit. Round all values to the nearest integer.
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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Assume that you make quarterly payments of $ 650 into an annuity paying 9% interest compounded quarterly. How much will be in the account after 11 years?
Amount =
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.
What is compound interest?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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Question 3 (10 marks). The concentration of antibiotic in the bloodstream t hours after
being injected is given by the function
C(t) = [tex]\frac{2t^{2} + t }{t^{3} + 50}[/tex]
where C is measured in milligrams per liter of blood.
a. Find the rate of change of C(t).
b. Determine the rate of change for t = 8, 12, 24, and 36.
c. Briefly describe what seems to be occurring as the number of hours increases.
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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Solve the system using the substitution method. If the system does not have one unique solution, also state the number of solutions and whether the system is
inconsistent or the equations are dependent. Express numbers as integers or simplified fractions.
10x-y-1
5x-4y=-3
The system has one solution.
The solution set is
{0}.
O The system has no solution ().
The system is inconsistent.
The equations are dependent.
O The system has infinitely many solutions.
The solution set is
The system is inconsistent.
The equations are dependent.
X
0-0
The system has one solution. Option A
How to solve the system of equationsThe 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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