we know that
the solution process between step 1 and step 2 is
Adds 5x both sides
The town of Simpsonville has two tow truck companies. Company A charges an initial fee of $30 plus $2 per mile. Company B charges an initial fee of $20 plus $4 per mile. Use the graph to determine when it's cheaper to use Company B instead of Company A.
Using the graph, it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.
How to interpret Linear equation graphs?For us to solve this question, we need to first create an equation;
If A company initially supplies $30 and then $2 per mile, then the equation here is:
y = 2x + 30
If B company initially supplies $20 and then $4 per mile, then the equation is expressed as:
y = 4x + 20
Due to the fact that the two wages are asked to be equalized, we equate these two equations with each other and find the result.
2x + 30 = 4x + 20
2x = 10
x = 10/2
x = 5
This is the number of miles that both companies will charge a customer the same amount.
Then the time for which it is cheaper to use company B is when number of miles is less than 5.
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Integers greater than -6 and less than 2
IN OTHER WORDS WE ARE LOOKING FOR WHOLE NUMBERS BETWEEN -6 AND 2
\( - 5 \\ - 4 \\ - 3 \\ - 2 \\ - 1 \\ 0 \\ 1\)
ATTACHED IS THE SOLUTION
Answer:
1,0,-1,-2,-3,-4,-5
Step-by-step explanation:
6 2/5 subtract 2 9/10
Answer: 9 3/10
Step-by-step explanation:
6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1 3/10= 8 + 1 + 3/10= 9 3/10
The formula is T = L/S, where T is the time in seconds, L is the length of the tape in inches, and S is the operating speed in inches per second. How long a tape does a police officer need to record a 2-minute confession at an operating speed of 3 1/2 inches per second?
Answer:
im not sure im sorry
Step-by-step explanation:
not sure
99x76 using an over strategy
Multiplication means the repeated addition of groups of equal sizes. When 99 and 76 are multiplied we get the value 7524.
What is Multiplication?Multiplication means the repeated addition of groups of equal sizes.
The given two numbers are 99 and 76.
Set up your multiplication problem like this:
99
*76
______
9 x 6 = 54. Put 4 below the line and 5 as a reminder on top:
99
*76
______
4
6 x 9 = 54. Take 54 and add 5 from the previous step to get 59. Enter 59 at the bottom
99
*76
______
594
Enter a 0 at the bottom right as a place holder, because you now move over one digit:
99
*76
______
594
+ 0
7 x 9 = 63. Put 3 below the line and 6 as a reminder on top:
99
*76
______
594
+ 30
7 x 9 = 63. Take 63 and add 6 from the previous step to get 69. Enter 69 at the bottom:
99
*76
______
594
+6930
Add up the bottom two numbers (594 + 6930 = 7524) to get the answer:
99
*76
______
594
+6930
________
7524
Therefore Multiplication of 99 and 76 is 7524.
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A line passes through the points(-2,-6) and has a slope of - 5/2write an equation in slope intercept from for this line
We need to find the equation of the line passes through the points(-2,-6) and has a slope of - 5/2
The general equation of the line in slope - intercept form is :
\(y=m\cdot x+b\)Where m is the slope and b is y - intercept
Given the slope = -5/2
so,
\(m=-\frac{5}{2}\)We will find the value of b using the given point ( -2 , -6 )
so, the equation will be:
when x = -2 , y = -6
\(\begin{gathered} -6=-\frac{5}{2}\cdot-2+b \\ \\ -6=5+b \\ b=-6-5 \\ \\ b=-11 \end{gathered}\)so, the equation of the line is:
\(y=-\frac{5}{2}x-11\)
help please i dont know the answer explain if you want
please mark me as brainlist..
Find a, b, c if a(1,3,2) + b(1,-5,6) + c(2,1,-2) =(4,10,-8).
The coefficients of the linear combination a · (1, 3, 2) + b · (1, - 5, 6) + c · (2, 1, - 2) = (4, 10, - 8) are a = 1, b = - 1 and c = 2.
How to determine the values of all coefficients of a linear combinationVectors can generated by combining vectors by means of fundamental operations in real fields (vector sum, multiplication of a vector by a scalar).
A vector is a linear combination of a given set of vectors when not all scalar coefficients are zero, at least one of them must not be zero. Herein we find a linear combination of vectors, that is, a vector composition of the form:
U = Σ αₙ · Vₙ, for n = {1, 2, 3, ..., m - 1, m}
Where:
U - Resulting linear combination.Vₙ - n-th Vector generator.αₙ - n-th Coefficientm - Number of vector generators.Now we proceed to solve the linear combination. First, determine the vector generators and coefficients:
V₁ = (1, 3, 2), V₂ = (1, - 5, 6), V₃ = (2, 1, - 2)
α₁ = a, α₂ = b, α₃ = c
Second, create the equation of linear combination and simplify by real field operations:
U = α₁ · V₁ + α₂ · V₂ + α₃ · V₃
a · (1, 3, 2) + b · (1, - 5, 6) + c · (2, 1, - 2) = (4, 10, - 8)
(a, 3 · a, 2 · a) + (b, - 5 · b, 6 · b) + (2 · c, c, - 2 · c) = (4, 10, - 8)
(a + b + 2 · c, 3 · a - 5 · b + c, 2 · a + 6 · b - 2 · c) = (4, 10, - 8)
Where a, b, c are real coefficients (scalars).
Third, derive the resulting system of linear equations:
a + b + 2 · c = 4
3 · a - 5 · b + c = 10
2 · a + 6 · b - 2 · c = - 8
Fourth, find the solution to the system by means of numerical methods:
(a, b, c) = (1, - 1, 2)
The coefficients associated to the linear combination are (a, b, c) = (1, - 1, 2).
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The ratio of girls to boys in a class is 4 to 1. There are 24 girls in the class. How many students are in the class?
Answer:
a
Step-by-step explanation:
Answer:
The answer is
A ) 30
Step-by-step explanation:
For every 4 girls in the class, there is 1 boy.
24/4 = 6
24 + 6 = 30
I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)
write an equation in point-slope form for the line through the given point with the given slope
(10,-9)m is -2
Answer:
Step-by-step explanation:
Point: 10,-9
k=-2
y=-2x+b
So: 9, -7
8,-5
7,-3
6,-1
5,1
4,3
3,5
2,7
1,9
0,11
y=-2x+11
Answer:
y + 9 = - 2(x - 10)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 2 and (a, b ) = (10, - 9 ) , then
y - (- 9) = - 2(x - 10) , that is
y + 9 = - 2(x - 10)
Evaluate the piecewise function
The solution of the composite function fog(x) = 3x + 3 at x > 2.
What is composite function?Let the two function f(x) and g(x) generate a new function h(x) using an operation.
The operation is composition of functions and h(x) is a composite function.
We have three piecewise function.
First we have to show that,
the composite function,
fog(x) at x > 2.
For that,
g(x) at x > 2 is,
g(x) = 3x.
Now, f(g(x)),
= f(3x)
= 3x + 3 at x > 2.
Therefore, the function is fog(x) = 3x + 3.
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The complete question:
Find the fog(x) at x > 2
A company created a new container in the shape of a
triangular prism that will hold sunflower seeds. A three-
dimensional image of the container is shown below, as
well as a two-dimensional image of the base.
6 in.
3.2 in.
2 in.
3.2 in.
1 in.
square inches
1 in.
The container will be made from cardboard. How many
square inches of cardboard are needed to make one
container? Assume there are no overlapping areas.
The number of square inches of cardboard that are needed to make one
the container is 18.
We have,
The volume of the triangular prism.
= Area of the triangle x height
Now,
Height = 6 in
And,
To find the area of a triangle, we can use Heron's formula.
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.
Let's calculate the area using Heron's formula:
s = (3.2 + 3.2 + 2) / 2 = 4.2
A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))
A = √(4.2 x 1 x 1 x 2.2)
A = √(9.24)
A ≈ 3.04 square inches
Now,
The volume of the triangular prism.
= Area of the triangle x height
= 3.04 x 6
= 18.24 in²
Now,
Area of one cardboard.
= 1² in²
= 1 in²
Now,
The number of square inches of cardboard that are needed to make one
container.
= The volume of the triangular prism / Area of one cardboard
= 18.24 in² / 1 in²
= 18.24
= 18
Therefore,
The number of square inches of cardboard that are needed to make one
the container is 18.
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In a class test, +4 marks were awarded for the correct answers and -1 mark for the wrong answers. Student scores 40 marks. If his correct answers were 11, find his wrong answers.
Step-by-step explanation:
Let y the number of wrong answers got.
\(11( + 4) + ( - 1)y = 40 \\ 44 - y = 40 \\ - y = - 4 \\ y = 4\)
∴ He got 4 wrong answers.
Can someone help me? I’ll reward points + brainalist
Answer:
Step-by-step explanation:
The given box in both questions are cuboid.
Question 3:
Volume of cuboid = length * width * height
= 3 * 3 * 5 = 45 units.
Question 4:
Volume of cuboid = length * width * height
= 4 * 2 * 6 = 48 units
Select all lengths that are equal to 3 yards 16 inches.
The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).
To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.
1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).
Therefore, 3 yards is equal to 3 * 36 = 108 inches.
Now, we can compare 108 inches to 3 yards 16 inches.
108 inches is equal to 3 yards, so it matches the given length.
To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.
Therefore, 3 yards 16 inches is equivalent to:
3 yards
108 inches
3 yards 0.44 yards (or approximately 3.44 yards)
108 inches 0.44 yards (or approximately 108.44 inches)
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the temperatures at midday on march 1st in five cities are shown in the bar chart below. What is the difference in temperature between rome and munich?
The difference in temperature between Rome and Munich is given as follows:
6ºC.
How to obtain the difference in temperatures?The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.
The bar graph in the context of this problem gives the temperature for each town.
From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:
Rome: 11 ºC.Munich: 5 ºC.Hence the difference in temperature between Rome and Munich is given as follows:
11 - 5 = 6ºC.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Find the MAD of the data below; 65 52 43 51 Round your answer to the nearest hundredths. MAD: type your answer...
Solution
MAD: Mean Absolute Deviation
The given Data are : 65, 52,43,51
\(\text{Mean(m) = }\frac{65+52+43+51}{4}\text{ = }\frac{211}{4}\text{ = 52.75}\)\(\begin{gathered} M.A.D=\frac{\sum ^{}_{}|x\text{ -m| }}{n} \\ \text{ =}\frac{|65-52.75|+|52-52.75|+|43-52.75|+|51-52.75|}{4} \\ =\frac{12.25+0.75+9.75+1.75}{4} \\ =\frac{24.5}{4} \\ =\text{ 6.125} \end{gathered}\)
Consider the following random experiment. First, roll a die and observe the number of dots facing up; then, toss a coin the number of times that the die shows and observe the total number of heads. For example, if the die shows three dots facing up and the coin (which is then tossed three times) comes up heads exactly twice, then the outcome of the experiment can be represented as (3, 2).
a. Determine a sample space for this experiment.
b. Determine the event that the total number of heads is even.
Answer:
{(1, 0), (1, 1), (2,0), (2,1), (2, 2), (3,0), (3,1), (3,2), (3,3), (4, 0), (4,1), (4,2), (4,3), (4,4), (5,0), (5,1),(5,2), (5,3), (5,4), (5,5), (6,0), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)}
B.)
{(2,2), (3,2), (4,2), (4,4), (5,2), (5,4), (6,2), (6,4), (6,6)}
Step-by-step explanation:
Sample space :
Die roll, then number of coin tosses based on the outcome of the die roll, then number of heada from the toss(es) is recorded along with the outcome of the die roll.
{(1, 0), (1, 1), (2,0), (2,1), (2, 2), (3,0), (3,1), (3,2), (3,3), (4, 0), (4,1), (4,2), (4,3), (4,4), (5,0), (5,1),(5,2), (5,3), (5,4), (5,5), (6,0), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)}
Event that the total number of head is even:
{(2,2), (3,2), (4,2), (4,4), (5,2), (5,4), (6,2), (6,4), (6,6)}
Marta conducts emissions inspections on cars. She finds that 8 % 8%8, percent of the cars fail the inspection. Let X XX be the number of cars Marta inspects until a car fails an inspection. Assume that the results of each inspection are independent. Find the mean and standard deviation of X XX. Round your answers to one decimal place.
There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.
What connection exists between the mean and the standard deviation?First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:
The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.
What is the standard deviation and mean formula?The mean is calculated as follows:
Mean = (all data values added together) / (number of data values)
However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.
The standard deviation equation is as follows:
Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":
No of the size of the data collection, the mean rises by precisely K.
No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.
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Sara is packing for vacation. She is taking three shirts: yellow (Y), white (W), , and green (G). She is also taking a pair of jeans (J), a pair of black pants , and a pair of shorts (S). For shoes, she is packing tennis shoes (T) and a pair of dress shoes (D). Each outfit will be made of shirt, pair of pants, and pair of shoes. Which list shows all possible outfits that Sara can create from these options?A. YJ,YB,YS,WJ,WB,WS,GJ,GB GS,TDB. YJ,YB,YS,YT,YD,WJ,WB,WS,WT,WD,GJ,GB,GS,GT,GDC. YBT,YBD,YST,YSD,WBT,WBD,WST,WSD,GBT,GBD,GST,GSDD. YJT,YJD,YBT,YBD,YST,YSD,WJT,WJD,WBT,WBD,WST,WSD,GJT,GJD,GBT,GBD,GST, GSD
Rewrite in the simplest form 7(−8f−2)+10(−5f+7)
Answer:
-106f+56
Step-by-step explanation:
7(-8f-2)= -56f-14
10(-5f+7)= -50f+70
-56f-14. +. 50f+70
=-106f+56
Answer:
-2(53f-28)
Step-by-step explanation:
Distribute7(−8f−2)+10(−5f+7)
7x-8f=-56f 7x-2=-14
10x-5f=-50f 10x7=70
-56f-14+-50f+70 Adding a negative to something means to subtract. Like right here at -14 + -50 is the same as -14 - 50
2. Add the numbers
-56f-14+-50f+70 -14+70=56
-56f+56-50f
3. Combine like terms
-56f+56-50f -56+ -50= -106
-106f +56
4. Common Factor
-106f + 56
-2(53f-28)
consider the verizon data. find a 95% ci for the ratio of medians. estimate the percent bias (relative to the standard error) and compare with the results for the ratio of means
95% confidence interval for the ratio of medians is a range of values that we are confident contains the true population ratio, with a specified level of confidence.
A confidence interval is a range of values that we are confident contains the true population parameter, with a specified level of confidence. In this case, we are looking at the ratio of medians in the Verizon data and finding a 95% confidence interval for the ratio.
Let's say the sample median for the first data set is M1 and the sample median for the second data set is M2. The standard error for M1 and M2 can be calculated using the formula for the standard error of the median.
Next, we use the formula for a confidence interval for the ratio of medians:
=> (M1/M2) +/- (Z * SE(M1/M2)),
where Z is the critical value from a standard normal distribution for a 95% confidence level.
The percent bias is the difference between the estimated value and the true value, divided by the true value and expressed as a percentage. In this case, we will calculate the percent bias of the confidence interval for the ratio of medians relative to the standard error.
Finally, we compare the results for the ratio of medians with the results for the ratio of means. This comparison can give us an idea of the difference in the level of accuracy and precision between the two estimates.
Complete Question:
Consider the Verizon data. find a 95% confidence interval for the ratio of medians. estimate the percent bias (relative to the standard error) and compare with the results for the ratio of means
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Find the standard form of the equation of the parabola with the given characteristics. focus: (6, 6) directrix: x = −6
The standard form of the equation of the parabola is \(y=-(\frac{x^2-12x+36}{24})\)
The general form of a parabola is (x-h)=4p(y-k)
Where, (h,k) is vertex, (h,k+p) is the focus, and y=k-p is directrix.
The focus of the parabola is (6,6).
comparing the values with (h,k+p)=(6,6)
h=6
k+p=-6.... (1)
Directrix of the parabola is
k-p=-6.... (2)
On adding (1) and (2) we get
2k=0
k=0
Put this value in equation (1).
0+p=-6
The value of p= -6.
Substituent h=6,k=0, and p=-6 in the general form of a parabola, we get
(x-h)^2=4p(y-k)
(x-6)^2=4(-6)(y-0)
x^2-12x+36=-24y
Divide both sides by 24.
y=(x^2-12x+36/24)
Therefore the standard form of the equation of the parabola is
y=-(x^2-12x+36/24)
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A study of adult males found their head circumferences to be Normally distributed, with a mean of 57.5 centimeters and a standard deviation of 1.5 centimeters.
Jack’s head has a circumference in the 16th percentile. How many centimeters is his head circumference? Give your answer to the nearest tenth.
Answer:
56.0 on edge
Step-by-step explanation:
Since Jack’s head has a circumference in the 16th percentile, his head circumference is 56.0 centimeters.
What is percentile?We know that In a normal distribution, a percentile is a value that has a certain percentage of observations below it.
The Z score is defined as "a numerical measurement used in statistics to determine a value's relationship to the mean (average) of a group of values, expressed in standard deviations from the mean."
Z score can be calculated as
Z = (x - μ)/σ
How to solve it?Here, mean = μ = 57.5 centimeters
standard deviation = σ = 1.5 centimeters
Let the circumference of Jack’s head = x centimeters
The percentile = 16
Z value for 16 percentile = - 0.994
So, (x - 57.5)/1.5 = - 0.994
i.e. x - 57.5 = - 0.994*1.5 = - 1.491
i.e. x = - 1.491 + 57.5 = 56.009
The nearest tenth value for 56.009 is 56.0
Then Jack's head circumference is 56.0 centimeters.
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Complete each statement explaining what the slope and the y-intercept tell Jeremy about the trip he’s planning. Select the correct answer from each drop-down menu. 1: The slope of the line tells Jeremy: A (the time it takes the team to climb the rock formation) B(the steepness of the rock formation) C (the average rate at which people climb the rock formation) D (the maximum height the team will climb) E(the initial height where the team starts climbing).......2: The y-intercept of the line tells Jeremy A(the time it takes the team to climb the rock formation) B(the average rate at which people climb the rock formation) C (the initial height where the team starts climbing) D (the steepness of the rock formation) E (the maximum height the team will climb)
Answer:
C and CStep-by-step explanation:
The slope-intercept form:
y = mx + b, where m is a slope and b is a y-interceptThe slope refers to the steepness of the line and is same as the rate of change.
The y- intercept is the starting point or the point of the intersection of the line with the y- axis.
1: The slope of the line tells Jeremy: A (the time it takes the team to climb the rock formation), noB (the steepness of the rock formation), noC (the average rate at which people climb the rock formation) D (the maximum height the team will climb), no E (the initial height where the team starts climbing), no 2: The y-intercept of the line tells Jeremy A (the time it takes the team to climb the rock formation), noB (the average rate at which people climb the rock formation), no C (the initial height where the team starts climbing) D (the steepness of the rock formation), no E (the maximum height the team will climb), noAnswer:
Check the screenshot
Step-by-step explanation:
The _ function calculates the repayment for a loan; the _ function calculates the interest portion of the loan repayment
Part 1:
The PMT Function in Excel is used to calculate the repayment of a loan. The PMT Function calculates the amount of loan repayment.
The generic formula for PMT Function is as follows:
=PMT(rate,nper, pv,[fv],[type])
Now let us understand each of the components of the PMT Function:
rate: The interest rate for the loan
per: Total number of payments of the loan repayment.
PV: Present Value of a series of Future Payments ie. the Principal of the Loan
VF: The future value of the loan or the cash balance that an individual wants to obtain after the loan is paid. This can be omitted, if omitted its value will be taken as zero ie the value of the loan in the future will be zero.
Type: The numbers 0 and 1 indicate when the payment of the loan is due. This is optional and can be omitted If it is 0 or omitted then payments are considered to be due at the end of the period(ie. end of month or quarter or end of year as the case may be). If it is 1 then payments are considered to be due at the beginning of the period((ie. beginning of month or quarter or end of the year as the case may be)
Part 2:
The Excel IPMT Function can be used to calculate the interest portion of loan repayment for a given period.
The generic formula for Excel IPMT Function is as follows:
=IPMT(rate,per,nper,pv,fv,[type])
Now let us understand each of the components of the IPMT Function:
rate: The interest rate for the loan
per: The period for which the interest payment has to be determined and should range between 1 and per
per: Total number of payments of the loan
PV: Present Value of a series of Future Payments ie. the Principal of the Loan
VF: The future value of the loan repayment or the cash balance that an individual wants to obtain after the loan is paid . This can be omitted, if omitted its value will be taken as zero ie the value of the loan in the future will be zero.
Type: The numbers 0 and 1 indicate when the loan repayment is due. This is optional and can be omitted If it is 0 or omitted then payments are considered to be due at the end of the period(ie. end of month or quarter or end of year as the case may be). If it is 1 then payments are considered to be due at the beginning of the period((ie. beginning of the month or quarter or end of the year as the case may be).
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NEED PLS THANK YOU DUE TODAY
Now , to find the area
Total area of figure = Area of first Triangle + Area of second triangle
The area of the triangle = ( 1/2 ) x Length x Base
Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )
= ( 1/2 ) x 540 + ( 1/2 ) x 120
= 270 + 60
= 330 inches²
Therefore , the value is 330 inches²
Hence , The area of the figure is 330 inches²
Find a and b using the factor theorem.
\(f(x)=x^3+ax^2+bx-12\) has factor \((x-1), (x+1)\)
The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.
To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.
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simplify the expression -2m-6(m+1)
Answer:
-8m - 6
Step-by-step explanation:
-2m -6( m + 1 )
Distributive property (multiply what is in the parenthesis by what is out of it)
-2m -6 * m + -6 * 1
-2m -6m - 6
Combine like terms
-2m + -6m = -8m (remember 2 negatives numbers added will give you a bigger negative number so think of it as adding 2 numbers and then putting the negative sign in front of it)
-8m - 6
You cannot simplify it anymore, since it's not like terms
Hope this helped!
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A normal distribution (X) has a mean of 100 and a standard deviation of 10.
What is the x value that is the third quartile for this distribution?
Round your answer to the first decimal position.
The x value for the third quartile for this distribution is 106.8
Z score
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
where μ is the mean, x = raw score and σ is the standard deviation.
Given μ = 100, σ = 10.
The third quartile correspond with a z score of 0.675, hence:
0.675 = (x - 100) / 10
x = 106.8
The x value for the third quartile for this distribution is 106.8
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