Step-by-step explanation:
In statistics, linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. ... Linear regression has many practical uses.
Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be
retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into
a retirement savings account that will earn 12% compounded monthly. Then one year after
making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after
he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum
worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12%
compounded monthly. How much should the monthly deposits be for his retirement plan?
Answer:
Step-by-step explanation:
Today's Age = 30
Retirement Age = 64
Total Monthly Deposits = ( 64 - 30 ) * 12 = 408
In case of 12% Compounded Monthly , Interest Rate per month = ( 12% / 12 ) = 1%
Effective Interest Rate per year = ( 1 + 0.12/12 )12 - 1 = 1.1268 - 1 = 0.1268 = 12.68%
Present value of Annual 25 Years withdrawal of $100,000 at time of Retirement = $100,000 * PVAF ( 12.68% , 25 )
= $100,000 * 7.4864
= $748,642.20
Present Value of Money for nephew at time of Retirement = $1,000,000 * PVF ( 12.68% , 25 )
= $1,000,000 * 0.050535
= $50,534.52
Now the Present Value of total Amount Required at time of Retirement = $748,642.20 + $50,534.52
= $799,176.70
Now the monthly deposit be X
= X * FVAF ( 408 , 1% ) = $799,176.70
= X * 5752.85 = $799,176.70
X = $138.918
Therefore Monthly Deposit = $138.92
How do you determine similarities in shapes?
Answer:
Step-by-step explanation:
. if every corresponding internal angles in both shapes are equal
. if all corresponding sides are equal or have same ratio.
more rules but depends on the shape also ( triangle, rectangle, hexagon,...)
Solve 20x = 10 for x. A. x = 1/2 B. x = 1.5 C. x = 2 D. x = 10
Answer:
A. 1/2
Step-by-step explanation:
20x=10
Divide 20 on both sides of the equation to get x by itself
20x=10
___. __
20. 20
x =1/2
Answer:
A) x= 1/2
Step-by-step explanation:
20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!
The area of a round table in Kim’s living room is 201 square inches. What is the circumference of the round table, to the nearest hundredth of an inch? A.100.49 inchesC.50.24 inchesB.89.03 inchesD.25.12 inches
Answer:
C. 50.24 inches
Step-by-step explanation:
The area of a circle can be represented by [tex]\pi r^{2}[/tex]. To find the circumference, all we need to do is know the radius, and then we can plug that value into the circumference formula [tex]2\pi r[/tex]. So, to find the radius we see that:
[tex]\pi r^{2} = 201[/tex]
[tex]r = \sqrt{\frac{201}{\pi } }[/tex]
So, the circumference is:
[tex]2\pi (\sqrt{\frac{201}{\pi } })[/tex], which is closest to the answer C) 50.24 inches.
Hope this helped! :)
4. The Gold family sold their house for $450,000. They paid a realty
company 6% for selling the house. How much money did they pay the
company? *
Answer:
27,000
Step-by-step explanation:
$450,000 x 0.06= $27,000
0.06 is the 6% that you multiply by the total amount they earned to see how much they paid the realty company.
If
f(x) = -4x + 8 and
g(x) = √ x – 1, which statement is true?
Answer:
-3 is not in the domain of f°g
Step-by-step explanation:
f°g=f(g(x))
f(x) = -4(√x-1)+8
*Remember that √x-1 has to be larger than 0
since √-3-1 = √-4, -3 is not in the domain of f°g
Multiply (2m+3)(m^2-2m+2)
A) 2m^3-m^2-8m+3
B) 2m^3-m^2-10m+3
C)2m^3-m^2-4m+3
D)2m^37m^2-4m+2
Answer:
Step-by-step explanation:
The first step is to distribute the 2m and 3 to ([tex]m^2-2m+2[/tex]), like so:
[tex](2m+3)(m^2-2m+2)[/tex]
[tex]2m^3-4m^2+4m+3m^2-6m+6[/tex]
Then, add like terms:
[tex]2m^3 -m^2 -2m + 6[/tex]
Study the example shown below:
Which expression should replace the word "numerator" in the work shown?
2x-8 x-3
x2 - 7x+10 x2- 7x+10
2x-8-(x-3)
x2 - 7x+10
numerator
(x-2)(x-5)
Answer:
x-5
Step-by-step explanation:
got it right
The expression to replace the numerator is (x - 5).
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(2x - 8 - (x - 3)) / (x² - 7x + 10)
= (2x - x - 8 + 3) / (x - 2) (x - 5)
= (x - 5) / (x - 2) (x - 5)
Thus,
The numerator is (x - 5).
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
PLEASE HELP WITH THIS EASY MATH QUESTION!! it’s down below!!!!
Answer:
22
Step-by-step explanation:
=x(x+22)
Answer:
The answer is 22
What’s the correct answer for this?
Answer:
perpendicular linesssssssss
The answer is B. perpendicular lines. This is because only perpendicular lines can form 4 congruent angles when they intersect (all 4 angles will be 90 degrees).
(1 point) The volume of the solid obtained by rotating the region enclosed by x=2y,y3=x(with y≥0) about the y-axis can be computed using the method of disks or washers via an integral V=∫ba ? with limits of integration a= and b= . The volume is V= cubic units. Note: You can earn full credit if the last question is correct and all other questions are either blank or correct.
[tex]x=2y[/tex] and [tex]x=y^3[/tex] intersect when
[tex]2y=y^3\implies y^3-2y=y(y^2-2)=y(y-\sqrt2)(y+\sqrt2)=0[/tex]
[tex]\implies y=0\text{ or }y=\sqrt2\text{ or }y=-\sqrt2[/tex]
We omit the negative root, since we only care for [tex]y\ge0[/tex].
In the interval (0, √2), we have [tex]y^3<2y[/tex]. Then the volume is given by the integral
[tex]\displaystyle\pi\int_0^{\sqrt2}(2y)^2-(y^3)^2\,\mathrm dy=\pi\int_0^{\sqrt2}4y^2-y^6\,\mathrm dy[/tex]
and so the volume is (32√2)/21 π.
a line is perpendicular to y=-4x-2 and intersects the point (0,9). what is the equation for this perpendicular line?
Answer:
y=(1/4)x + 9 OR y=x/4 +9
Step-by-step explanation:
Perpendicular lines have a slope/gradient of -1/n
Because the slope of this line is -4, the slope of a line perpendicular to it would be 1/4.
y=(1/4)x+b
(0,9) is the y-intercept, so b = 9
y=(1/4)x + 9 OR y=x/4 +9
On the first day of school, each student is given $0.50 to attend. On day two, each student earns $1.00. on day 3, $2.00, etc. How much do students earn on the 9th day
Answer:
255.50
Step-by-step explanation:
If each day the number is doubled, then all you must do is keep on doubling to the ninth day and then add it all together
How many solutions does the equation -2a + 2a + 7 = 8 have
Step-by-step explanation:
-2a + 2a + 7 = 8
Solving like terms
7 = 8
= 8 - 7 = 1
Has one solution
A box below needs to be painted.
How many square inches of paint will be needed to cover the entire surface?
A
80/12 in2
B
61/9 in2
C
49/5 in2
D
77/55 in2
Answer: c
Step-by-step explanation:
Answer:B
Step-by-step explanation:
please help Jacqueline is a teacher in Alaska, where she contributes 9% of her earnings to her pension. If her earnings for a school year were $42,000, what did she contribute to her pension?
a.) $3,250
b.) $3,560
c.) $3,780
d.) $3,890
will give brainliest
Answer:
c.) $3,780
Step-by-step explanation:
9/100 × $42,000
= 9 × $420
= $3,780
Two datasets arranged in descending order are: {8, x, 4,1) and (9. y, 5,2). If the medians of
the two given datasets are equal, what is the value of (y – x)??
Answer
Answer:
Legon fo)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Dataset 1 (in increasing order)
{1, 4, x, 8}
Dataset 2 (in increasing order)
{2, 5, y, 9}
Median of dataset 1
[4 + x] / [2]
Median of dataset 2
[5 + y] / [2]
since the medians of the two given sets of data are the same,
=> [4 + x] / [2] = [5 + y] / [2]
=> 2(5 + y) = 2(4 + x)
=> 10 + 2y = 8 + 2x
=> 2y - 2x = 8 - 10
=> 2y - 2x = - 2
=> 2(y - x) = - 2
=> [2(y - x)] / [2] = [- 2] / [2]
denominators and numerators cancel out
=> (y - x) = - 1
Therefore, (y - x) ² = (-1)²
=> (y - x) ² = 1
If the fish tanks dimension are 60 by 15 by 34 and its is completely empty, what volume of water is needed to fill three fourths of the aquarium? Please help
Answer:
22,950 units³
Step-by-step explanation:
All you have to do is:
[tex]\frac{3}{4} *60*15*34=\\45*15*34=\\675*34=\\\\22,950[/tex]
Easy math, but not sure what I did wrong.
Alex took 31 exams during 5 years studying at the MaPhAs University. Each year, he took more exams than the previous year. During his 5th year, he took three times as many exams as in the 1st year. How many exams did Alex take during his 4th year at the university?
Answer:
8
Step-by-step explanation:
In his 5th year, he took 3 times as many exams as the first year. So the number of exams taken in the 5th year must be a multiple of 3.
If a₁ = 1, then a₅ = 3. However, this isn't possible because we need 4 integers between them, and a sum of 31.
If a₁ = 2, then a₅ = 6. Same problem as before.
If a₁ = 3, then a₅ = 9. This is a possible solution.
If a₁ = 4, then a₅ = 12. If we assume a₂ = 5, a₃ = 6, and a₄ = 7, then the sum is 34, so this is not a possible solution.
Therefore, Alex took 3 exams in his first year and 9 exams in his fifth year. So he took 19 exams total in his second, third, and fourth years.
3 < a₂ < a₃ < a₄ < 9
If a₂ = 4, then a₃ = 7 and a₄ = 8.
If a₂ = 5, then a₃ = 6 and a₄ = 8.
If a₂ = 6, then there's no solution.
So Alex must have taken 8 exams in his fourth year.
Not sure on how to do these questions
Answer:f(8)=g(8)
Step-by-step explanation:
So in these problems f(8) means that you look at the f(x) function (function 1) and plug in 8 for x. Then since it says g(8), you look at the g(x) function and substitute x for 8. If we do that, f(x)=2(8)-3 which is 13. g(x)=3/2x+1=13. The two of them are equal when x=8. So the answer is the third choice
Answer:
f(8)=g(8)
Step-by-step explanation:
Just put the values of given functions in the equation
What is the axis of symmetry for the graph of y – 4x = 7 – x2 ?
Answer:
x = 2
Step-by-step explanation:
A graph shows the axis of symmetry easily. It is the x-coordinate of the vertex.
x = 2
__
You can rearrange the equation to ...
y -7 = 4x -x^2
y -7 = x(4 -x)
The axis of symmetry is halfway between x-values that give the same y-value. Here, y=7 for x=0 and for x=4. That is, the right side of this equation is zero at those x-values. The axis of symmetry is halfway between, at x = (0+4)/2 = 2
The axis of symmetry is x=2.
_____
Alternate solutions
In standard form,
ax^2 +bx +c = y
the axis of symmetry is ...
x = -b/(2a)
Putting this equation into that form, we have ...
-x^2 +4x +7 = y
x = -(4)/(2(-1))
x = 2 . . . . axis of symmetry
__
We can rearrange the equation to vertex form.
y -7 = -x^2 +4x
y -7 -4 = -(x^2 -4x +4) . . . . . add the square of half the x-coefficient inside parentheses. Add an equal amount to the other side of the equation.
y -11 = -(x -2)^2
This tells us the vertex of the graph is (2, 11), so the axis of symmetry is x=2.
Describe each pattern formed. Find the next three terms. 4,8,16,32
Answer:
The pattern is multiplying by 2.
Next three terms: 64,128,256
Step-by-step explanation:
4,8,16,32
To get from 4 to 8 we can multiply by 2.
To get from 8 to 16 we can multiply by 2.
To get from 16 to 32 we can multiply by 2.
So the pattern is multiplying by 2.
To find the next three terms:
32*2=64
64*2=128
128*2=256
What is the number of possible permutations of 5 objects taken 2 at a time? A. 10 B. 20 C. 60 D. 120
Answer:
B. 20
Step-by-step explanation:
5P2 is equal to 20 using the permutation formula.
2. Heather made 35
cookies for a party. Ted
made 30 cookies. At
the party 47 cookies
were eaten. How many
cookies are left?
Answer:
18
Step-by-step explanation:
The total number of cookies that were made
35+30 = 65
The cookies that were eaten is 47
65-47 =18
There were 18 cookies left
Answer:
$18
Step-by-step explanation:
35+30=65
65-47=18
Steve believes that it takes more meters than centimeters to measure the length of his desk. It is right?
Answer:
No he is not right because his desk is not that big, and with centimeters it's possible because the centimeters are like more little
answer : D
Anyone knows the answer?
Answer:
E
Step-by-step explanation:
so you put the square root of 10 and then it will give you a decimal
Answer:
F
Step-by-step explanation:
when you put in 10 you get
3.16227766017 to the nearest number is 3.2
Approximate the 5839 to the nearest
1:Ten
2:hundred
Thousand 3:
Answer:
(1): nearest ten is 5840
(2):nearest hundred is 5800
(3):nearest thousand is 6000
Step-by-step explanation:
For nearest ten we get 5840
For nearest hundred we get 5800
For nearest thousand we get 6000
I have the brainy app on my phone, and I have plus on my phone, but when I try to log in on my computer< it says I still need to upgrade, how do I use brainy plus on my computer?
to use brainy plus on your computer you need to log in with the same account you used on the phone
Answer:
try to restart and delete then re download the app:)
Step-by-step explanation:
A firm produces two types of earphones per year: x thousand of type A and y thousand of type B. The cost function (in thousands of dollars) is given by
C(x,y)=110+80x+130y
If the selling price of type A is p and the selling price of type B is q, the price-demand equations are
p=120-3x+y
q=210+x-7y
Determine how many of each type of earphone should be produced per year to maximize profit? What should be the selling prices p and q? What is the maximum profit?
Answer:
9000 A and 7000 B should be producedp = 100, q = 170$350,000 is the maximum profitStep-by-step explanation:
We assume that "p" and "q" are given in dollars, so that the profit function (in thousands of dollars) can be written:
P = xp +yq -C(x, y)
Profit will be maximized when the partial derivatives of P with respect to x and y are both zero:
∂P/∂x = p +x(∂p/∂x) +y(∂q/∂x) -∂C/∂x = 0
(120 -3x +y) +x(-3) +y(1) -80 = 0
-6x +2y +40 = 0
3x -y = 20 . . . . put in standard form
and ...
∂P/∂y = x(∂p/∂y) +q +y(∂q/∂y) -∂C/∂y = 0
x(1) +(210 +x -7y) +y(-7) -(130) = 0
2x -14y +80 = 0
x -7y = -40 . . . . put in standard form
__
The solution to these simultaneous equations can be found a variety of ways. Using Cramer's Rule, we have ...
x = ((-1)(-40) -(-7)(20))/(-1·1-(-7)(3)) = 180/20 = 9
y = (20(1) -(-40)(3))/20 = 140/20 = 7
9000 type A and 7000 type B earphones should be produced.
__
The corresponding selling prices are ...
p = 120 -3(9) +7 = 100
q = 210 +9 -7(7) = 170
The selling prices should be ...
p = $100, q = $170
__
The maximum profit is ...
P = xp +yq -C(x, y) = (9)(100) +(7)(170) -(110 +80(9) +130(7))
P = 9(100 -180) +7(170 -130) -110 = 180 +280 -110
P = 350
The maximum profit is $350,000.
100 POINTS.
PLEASE PROVIDES STEPS.
FIND THE INTEGRALS.
Answer:
10. ⅔ − ∛e
11. 79 + 3√3
Step-by-step explanation:
10. ∫ (1 + 1/x) dx
∫ dx + ∫ (1/x) dx
These are both standard integrals.
x + ln|x| + C
Evaluate between x = ∛e and x = 1.
(1 + ln|1| + C) − (∛e + ln|∛e| + C)
1 + 0 + C − ∛e − ⅓ − C
⅔ − ∛e
11. ∫₁³ (4x³ + ³/₂√x) dx
∫₁³ 4x³ dx + ∫₁³ (³/₂ x^½) dx
(x⁴ + x^(³/₂) + C) |₁³
(x⁴ + x√x + C) |₁³
(3⁴ + 3√3 + C) − (1⁴ + 1√1 + C)
81 + 3√3 + C − 1 − 1 − C
79 + 3√3
The solutions and answers are in the picture below.
Best of Luck!
