Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
What is composite function?
Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x
Main body:
according to question;
f(x) = 2x³
g(x) = 3x³ -2
we need to find composite function:
f o g (x) = 2(3x³-2)
{to find composite function , we replace one function as value of x in another}
f o g(x) = 6x³ -4
= 6x³ -4
f o g(1) = 6*1 -
= 2
g o f(x) = 3(2x³)-2
g o f(x) = 6x³ -2
= 6x -2
g o f(1) = 6*1 -2
= 5
Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
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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]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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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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What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?
y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)
Answer:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given points:
(-3, -1)(2, 9)Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point (-3, -1) into the point-slope formula:
[tex]\implies y-(-1)=2(x-(-3))[/tex]
[tex]\implies y+1=2(x+3)[/tex]
Substitute the found slope and point (2, 9) into the point-slope formula:
[tex]\implies y-9=2(x-2)[/tex]
Therefore, the correct answer option is:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
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.
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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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 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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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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$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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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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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:
i’ll give brainliest!!!!
Answer:
Lyric ran faster.
Step-by-step explanation:
When you plot y = 5x, you can trace a certain point to see which value is higher. When I plotted y = 5x and chose the point when x = 8, y = 40 for Kira, and for Lyric, at x = 8, y = 80. Since the y coordinate (distance) is higher, Lyric ran faster.
Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.
Step-by-step explanation:You may use the following logic to analyze this situation. Theoretically, the faster runner will have traveled a longer distance at any given point in time different than 0 when comparing to the other runner. Therefore, let's randomly pick a point in time to see who had traveled the longer distance.
The time we'll evaluate will be 4 seconds.
1. Evaluating the function to find Kira's traveled distance at 4 seconds.
For this, simply substitute the "x" by the number "4" in the given equation for Kira:
[tex]y=5(4)\\ \\y=20[/tex]
Conclusion: Kira had traveled a total distance of 20 yards, 4 seconds after starting the race.
2. Evaluating the function to find Lyric's traveled distance at 4 seconds.
To evaluate the graph, we'll have to draw a line where x=4 sits and then find the value of "y" the function returns. Check the attached images in order to see this process.
Conclusion: Lyric had traveled a total distance of 40 yards, 4 seconds after starting the race.
3. General conclusion.
After 4 seconds Kira traveled 20 yards;
After 4 seconds Lyric traveled 40 yards.
Conclusion: Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.
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]?
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
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)
Fill in the blanks. (Enter the domain in interval notation.) Function Alternative Notation Domain Range 2. -12 points LarPCakcCC3 4.7002 Fill in the blanks. (Enter the range in interval notation.) Function Alternative Notation Domain Range y cos-1x -1 s x s 1 3. -3 points LarPCakcc3 4.7.003 Fill in the blanks. (Enter the domain and the range in interval notation.) Function Alternative Notation Domain Range y-arctan x y-
The interval notation of domain and range is (-∞, ∞).
Interval notation:
In algebra, interval notation refers the way to describe continuous sets of real numbers by the numbers that bound them.
Given,
Here we need to write the interval notation of domain and range.
In order to find the interval notation, first we have to know the definition of domain and range.
In math domain refers the domain of a function is the set of values that we are allowed to plug into our function. Basically, this set is the x values in a function such as f(x).
And where as the range of a function is the set of values that the function assumes. And it is the values that the function shoots out after we plug an x value in.
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I can ride my bike 8 miles in 2 hours. How many feet can I ride per minute?
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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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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If my math teacher asked me what's 5÷10+2-9 what would the answer be ??
Answer:-6.5
Step-by-step explanation:
Answer:
Step-by-step explanation
Use pemdas.
P- Parenthesis
e- Exponents
m- Multiplication
d- Division
a- Additon
s-Subtraction
5÷10+2-9
=5÷12-9
=5÷3
=1.666666666667
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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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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Why were goods planned to become obsolete?
A. So that the company would become known for quality goods
B. So that people would keep buying new things
C. So that companies could protect their brand
D. So that people could save as much money as possible
Answer: B
Step-by-step explanation: B. So that people would keep buying new things
Goods are often planned to become obsolete in order to encourage people to continue buying new things. This can be done by intentionally designing products with a limited lifespan or by using materials that are prone to wear and tear. Companies may also release new versions of products or discontinue support for older models in order to encourage consumers to upgrade to the latest version. By making their products become obsolete, companies can create a sense of urgency for consumers to keep buying new things and maintain their sales.
5+5p=5p +5 is what property
Answer:
Commutative Property Addition
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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help please and thanks so much
Answer:
Option 2
Step-by-step explanation:
The greater than sign with the line under it means greater than/less than or equal to. So -2.4 is less than or equal to -2.40.
-Hope this helped
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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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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What is the sum? 8 + (negative 12) Group of answer choices –4 20 4 –20