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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A textbook store sold a combined total of 429 chemistry and biology textbooks in a week. The number of chemistry textbooks sold was 51 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Using system of linear equation, the store sold 240 chemistry books and 189 biology books
System of Linear EquationA system of equations is a set or collection of equations that you deal with all together at once. The general representation of linear equations are given as y = mx + c
m = slopec = y-interceptLet set our variables as;
chemistry = x biology = yx + y = 429 ...eq(i)
x = 51 + y ...eq(ii)
Put eq(ii) into (i)
(51 + y) + y = 429
51 + 2y = 429
2y = 429
y = 189
x = 51 + 189
x = 240
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5+5p=5p +5 is what property
Answer:
Commutative Property Addition
how many 3/4 cups serving aare in 5 1/2 cups of yogurt
Answer:
Below
Step-by-step explanation:
5 1/2 = 11 / 2
11/2 ÷ 3/4 = 11/2 x 4/3 = 44/6 = 7 1/3
A player spins two spinners. The outcome of each spinner is 1, 2, or 3. Each outcome is
equally likely. Define the random variable X to be the maximum of the two numbers on the
spinners. What is E[X]?
I can ride my bike 8 miles in 2 hours. How many feet can I ride per minute?
At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 inches with his second jump. If the distances form a geometric sequence, what is the total distance Mr. Meyering jumps if he completes infinitely many jumps?
Hint: Use S = a1/ 1-r and remember that |r| must be less than 1.
If the distances form a geometric sequence, the total distance Mr. Meyering jumps if he completes infinitely many jumps is equal to 40 inches.
What is a geometric sequence?In Mathematics, a geometric sequence can be defined as a series of real and natural numbers that are calculated by multiplying the next number by the same number (common ratio) each time.
Mathematically, the sum of an infinite geometric sequence can be calculated by using this mathematical expression:
S = a₁/(1 - r)
Where:
S represents the sum of an infinite geometric sequence.r represents the common ratio or constant ratio.a is the first term of a geometric sequence.How to determine the total distance Mr. Meyering jumps?First of all, we would determine the common ratio between the distances he jumped as follows;
Common ratio, r = a₂/a₁
Common ratio, r = 10/20
Common ratio, r = 0.5.
For the total distance, we have;
S = a₁/(1 - r)
S = 20/(1 - 0.5)
S = 20/0.5
S = 40 inches.
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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.
7. The population of Ludwigville has been steadily declining by 15% each year. If this trend continues, and the population is now 5,000 , what will the population be 12 years from now?
A. 711
B. 0
C. 4250
D. 4289
8. Evaluate e⁵, Round to the nearest ten thousandth.
A. 147.9068
B. 148.1236
C. 149.4200
D. 148.4132
9. Simplify 6e⁴ (8e⁵)/12e⁷
A. 4e²
B. 4e¹³
C. 36e⁹
D. 2e²
The population be 12 years from now is 6.612.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.
Aloud to yourself as you read the issueCreate a DrawingAsk yourself, "What am I looking for?"Describe what has been presented.Locate the key phrasesSolveVerify your work.Population after n years = Present Population = (1 + (r/n))ⁿ
Population after 12 years = 5000 ( 1 + (15/100))²
= 5000(115/100)²
= 5000 (115/100)*(115/100)
= 6.612.5
Hence, the population be 12 years from now is 6.612.
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Determine whether the following graph is a direct variation. Explain how you came to your conclusion. PLEASE I REALLY NEED IT DONE ILL GIVE YOU
BRAINLIEST!!!!!! and pls give me a real answer!!
The graph in the figure is not a direct variation
How to determine the category of the graphFrom the question, we have the graph that represents the given parameters that can be used in our computation
By definition, the graph of a direct variation represents a straight line that passes through the origin
Also, from the graph, we can see that:
The line on the graph is not a straight line. In fact, the line is a curve
A curve does not represent any type of variation
Hence. the graph is not a direct variation
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Joshua earns $.50 for each delivery he makes plus an additional $10.00 per day. Write and solve an inequality to represent the number of packages Joshua has to deliver so that he can make more than $20.00 each day.
To express the amount of parcels Joshua must transport in order to earn more than $20 per day, we can use the inequality 5x + 10 > 20.
What is Inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1]
The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.
There are two form of inequality relations that are not strict, in contrast to strict inequalities:
The indication of an or b denotes that.
According to our question-
x stands for every delivery he makes:
.5x + 10 > 20
This demonstrates that in order for the inequality to exist, it must exceed $20.
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limit. There are 25 question
The median monthly rent in 1987 was $399 and $523 in 1995. What was the percent increase in the median monthly rent
prices from 1987 to 1995? Round to the nearest tenth of a percent.
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Using the percentage increase formula, we know that the median monthly rent increase from 1987 to 1995 is 31%.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, we know that:
The median monthly rent in 1987 was $399.
The median monthly rent in 1995 was $523.
Percentage increase formula: C = x2 - x1/x1 * 100
Where c is the relative change, x1 is the initial value and x2 is the final value.
Now, insert the values in the formula as follows:
C = x2 - x1/x1 * 100
C = 523 - 399/399 * 100
C = 124/399 * 100
C = 31.07
Round off: 31%
Therefore, using the percentage increase formula, we know that the median monthly rent increase from 1987 to 1995 is 31%.
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What is the sum? 8 + (negative 12) Group of answer choices –4 20 4 –20
Which of the following is a parametric equation?
Answer:
[tex]x=5t-3[/tex]
[tex]y=3t^2-5[/tex]
Step-by-step explanation:
[tex]x=5t-3[/tex][tex]y=3t^2-5[/tex]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
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:
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. What is the probability that a. At most 6 of the calls involve a fax message? b. Exactly 6 of the calls involve a fax message? c. At least 6 of the calls involve a fax message? d. More than 6 of the calls involve a fax message?
Step 1
The distribution given is a binomial distribution with following data:
[tex]n=25, \quad p=0.25[/tex]
Step 2:
(a) Probability of at most 6 calls involving a fax message:
We have to add probabilities for x=0 to x=6
[tex]\begin{aligned}& P(X \leq 6)=\sum_{x=0}^6{ }^{25} C_x(0.25)^x(1-0.25)^{25-x} \\& =\left(\begin{array}{l}{ }^{25} C_0(0.25)^0(1-0.25)^{25-0}+{ }^{25} C_1(0.25)^1(1-0.25)^{25-1} \\+{ }^{25} C_2(0.25)^2(1-0.25)^{25-2}+{ }^{25} C_3(0.25)^3(1-0.25)^{25-3} \\+{ }^{25} C_4(0.25)^4(1-0.25)^{25-4}+{ }^{25} C_{5 x}(0.25)^5(1-0.25)^{25-5} \\+{ }^{25} C_6(0.25)^6(1-0.25)^{25-6}\end{array}\right)\end{aligned}[/tex]
[tex]\begin{aligned}& =\left(\begin{array}{l}{ }^{25} C_0(0.25)^0(0.75)^{25-0}+{ }^{25} C_1(0.25)^1(0.75)^{24} \\+{ }^{25} C_2(0.25)^2(0.75)^{23}+{ }^{25} C_3(0.25)^3(0.75)^{22} \\+{ }^{25} C_4(0.25)^4(0.75)^{21}+{ }^{25} C_{5 x}(0.25)^5(0.75)^{20} \\+{ }^{25} C_6(0.25)^6(0.75)^{19}\end{array}\right) \\& =\left(\begin{array}{l}0.0007525+0.006271+0.02508+0.06410 \\+0.1175+0.003171+0.182819\end{array}\right) \\& =0.5611\end{aligned}[/tex]
Therefore,
[tex]P(X \leq 6)=0.5611[/tex]
Step 3:
(b) Probability of exactly 6 calls involving a fax message:
We have to find probabilities for x=6[tex]\begin{aligned}& P(X=6)={ }^{25} C_6(0.25)^6(1-0.25)^{25-6} \\& ={ }^{25} C_6(0.25)^6(0.75)^{19} \\& =0.182819\end{aligned}[/tex]
Therefore,
P(X=6)=0.182819
Step 4:
(c) Probability of at least 6 calls involving a fax message:
We have to add probabilities for x=0 to x=5 and subtract from 1[tex]\begin{aligned}& P(X \geq 6)=1-(P(X < 6)) \\& =1-(P(X \leq 6)-P(X=6)) \\& =1-(0.5611-0.1828) \\& =0.6217\end{aligned}[/tex]
Therefore,[tex]P(X \geq 6)=0.6217[/tex]
Step 5:
(d) Probability of more than 6 calls involving a fax message:
We have to add probabilities for x=0 to x=6 and subtract from 1[tex]\begin{aligned}& P(X \geq 6)=1-(P(X \leq 6)) \\& =1-(0.5611) \\& =0.4389\end{aligned}[/tex]
Therefore,
[tex]P(X \geq 6)=0.4389[/tex]
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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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I’m needing some help with this
Answer: place points at (0,3) and (5,5)
Step-by-step explanation: the formula for a line is y = mx + b, where m is the slope and b is the y-intercept (the point where the line meets the y-axis). Since b is positive 3, place a point at (0,3).
m = 2/5, and since slope is rise over run (distance traveled in y axis over distance traveled in x axis) and it is positive, your next point is 2 up and 5 right, which is (5,5). You could also place a point at (-2,-2).
Answer:
Step-by-step explanation:
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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My past due bill is $585.00, and I just made payment arrangements for the next 3 months to keep my account from being suspended. My normal monthly bill is $50.00 per month. How much will I need to pay each month
He need to pay $245 per month .
How is the amount of interest you will pay calculated?
Subtract the number of payments you'll be making that year from the interest rate. You would divide 0.06 by 12 to get 0.005 if you had a monthly payment schedule and an interest rate of 6%. To calculate the amount of interest you will be required to pay that month, multiply that amount by the outstanding loan balance.Past due bill = $585
Now just made payment arrangements for the next 3 months to keep my account from being suspended
So, Payment each month of past bill = 585/3 = 195
His normal monthly bill is $50.00 per month.
So, I need to pay per month = $50+$195
= $245
Hence ,He need to pay $245 per month .
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when an article is sold for 1200 there is 10% profit at what price should it be sold to gain 20%
Step-by-step explanation:
When an article is sold for 1200 there is 10% profit at what price should it be sold to gain 20%.
find the base price without any profit:
$1,200/1.1 = $1,090.9090901
to gain 20%:
$1,090.9090901 * 1.2 = $1,309.09 (rounded)
If 3x – y = 5 and 2x + y = 15, evaluate x^2 + 2y
If 3x – y = 5 and 2x + y = 15 then evaluation of x^2 + 2y is equal to 72.
What is evaluation ?
Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.
3x-y=5 and 2x+y= 15
Add the two equations together to eliminate y
3x-y=5
2x+y= 15
---------------------
5x = 20
Divide by 5
5x/5 = 20/5
x = 4
Now we can find y
2x+y = 15
2(4) +y = 15
8+y =15
Subtract 8 from each side
8+y-8 = 15-8
y =7
We want to find
x^2+2xy
(4)^2 +2(4)(7)
16+56
72
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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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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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$2, 900 is invested in an account earning 6.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
PLEASE HELP
The Principal when calculated quarterly will give a sum of 2900 + (2.525)^4t at a rate of 6.1% interest
What is Compound Interest?
Compound interest is usually referred to as "interest on interest." Compound interest can work in your favour as your assets increase over time, but it can also work against you if you're paying off debt, such as credit cards. A calculator can assist in estimating how much money compound interest will generate over time.
Given that the Principal amount is $2900
and the Rate of Interest is 6.1%
Since, the interest is calculated quarterly
Amount = Principal * (1 + Rate/4)^4*Time
Amount = 2900 + (1 + 6.1/4)^4t
Amount = 2900 + (10.1/4)^4t
Amount = 2900 + (2.525)^4t
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Determine the number of imaginary zeros of the function with the given degree and graph. Explain your reasoning.
Answer:
1
Step-by-step explanation:
Number of roots = number of real roots + number of non-real roots
The graph intersects the x-axis 3 times
4 = 3 + x
x = 1
A person earned $44 a day for babysitting 6 hours. How much can the person earn by babysitting 9 hours a day, at the same hourly rate?
Answer:
The babysitter earns $66 babysitting for 9 hours a day.
Step-by-step explanation:
1. First, you need to find the amount of money they make babysitting for 3 hours, since 9 and 6 are divisible by 3.
2. Then you divide $44 by 2, to find that they make $22 babysitting for 3 hours.
3. Then you multiply $22 by 3 to get your answer of $66.
Find the value of the polynomial x2–3xy+ 1/2 y2 if x= 1/2 and y= 2/3 .
The value of the given polynomial x² - 3xy + 1/2y² if x = 12 and y = 2/3 is; -19 / 36.
What is the value of the polynomial for the given variable values?It follows from the task content that the value of the polynomial be determined for the given polynomial expression.
As evident in the task content; the given expression is;
x² - 3xy + 1/2 y².
Hence, since the given values of x and y are: 1/2 and 2/3 respectively.
On this note, we have that;
( 1/2 )² - ( 3 × 1 / 2 × 2 / 3 ) + ( 1 / 2 × (2 / 3)² )
= 1/4 - 1 + ( 2 / 9 )
= -3 / 4 + 2 / 9
= -19 / 36
On this note, the value of the given polynomial is; -19 / 36.
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Which of the following rational functions has a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = –3?
The rational function that has a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = -3 is:
f(x) = 3 / (x - 4)(x + 3)
What is horizontal asymptote?
A horizontal asymptote is a horizontal line that a graph approaches as the independent variable (x) becomes very large or very small. A vertical asymptote is a vertical line that a graph approaches but does not cross as the independent variable becomes very large or very small.A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph moves closer to the line as the inputs get closer to 0 or -1. A graph's slant asymptote is a slanted line with the equation y = mx + b, where the graph moves closer to the line as the inputs go toward + or -.To learn more about horizontal asymptote
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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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Casey inherited $70000, and decided to invest some of the money in a savings account earning 1% interest per year, and the rest in a certificate of deposit earning 2% interest per year. If the interest from the certificate of deposit was $800 more than the interest from the savings account, how much did Casey invest in each account?
Savings:
Certificate of Deposit:
The amount that Casey invested in the savings account is $10,000 and the amount Casey invested in the certificate of deposit is $60,000.
How much was invested in the savings account and the certificate of deposit?0.01c - 0.02s = $800 equation 1
c + s = $70,000 equation 2
Where:
c = amount invested in the certificate of deposit s = amount invested in the savings accountMultiply equation 2 by 0.01:
0.01c + 0.01s = 700 equation 3
Subtract equation 3 from equation 1:
0.01s = 100
Divide both sides of the equation by 0.01:
s = 100 / 0.01
s = 10,000
Substitute for s in equation 2:
c + 10,000 = 70,000
c = 70,000 - 10,000
c = 60,000
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