- 2/3 is the correct answer
Step-by-step explanation:
The rate of change of function K is -2/3. Therefore, option B is the correct answer.
What is rate of change a function?The rate of change, or the slope, is calculated as Δy/Δx , or (y2−y1)/(x2−x1). The slope-intercept equation of a line is y=mx+b , where m is the slope and b is the initial value.
Given that, linear function K passes through points (-3,7) and (3,3).
Now, the rate of change
= (3-7)/(3+3)
= -4/6
= -2/3
Therefore, option B is the correct answer.
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2. Which of the following is NOT a rational number? a. 9 b. 4 c. V d. 3
From actual road tests with the tires, Hankook Tires estimated that the mean fire mileage is 36,500 miles and that the standard deviation is 5000 miles. Data is normally distributed. What percentage of the tires can be expected to last more than 40,000 miles? Assume that Hankook Tires is considering a guarantee that will provide a discount on replacement tires if the original tires do not provide the guaranteed mileage. What should the guarantee mileage be if the company wants no more than 10% of the tires to be eligible for the discount guaranfee? UNIVER
Answer:
Expert's answer
let x denote the number of tires.
x~N(36500,50002)
z=\frac{x-\mu}{\sigma}
σ
x−μ
a) P(x>40000)
z=\frac {40000-36500}{5000}
5000
40000−36500
=0.7
we check the value of p(z>0.7) from the z tables.
=0.24196
24.2% of the tires can be expected to last more than 40000 miles.
b) P(z<0.1)
the value of \phi ^{-1}(0.1)ϕ
−1
(0.1) =-1.28
z=\frac{x-\mu}{\sigma}z=
σ
x−μ
-1.28=\frac{x-36500}{5000}−1.28=
5000
x−36500
=30100 miles
BRAIN LESS ANSWER IS CORRECT
3s ≤ 19; s = -6
^^^ how do i solve this? I need major help please
Answer:
3s=19s=-6
We move all terms to the left:
3s-(19s)=0
We add all the numbers together, and all the variables
-16s=0
s=0/-16
s=0
Balloons By Sunset (BBS) is considering the purchase of two new hot air balloons so that it can expand its desert sunset tours. Various information about the proposed investment follows: (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided.)
Initial investment (for two hot air balloons) $ 399,000
Useful life 9 years
Salvage value $ 48,000
Annual net income generated 30,324
BBS’s cost of capital 8 %
Assume straight line depreciation method is used.
Required:
Help BBS evaluate this project by calculating each of the following:
1. Accounting rate of return. (Round your answer to 2 decimal places.)
2. Payback period. (Round your answer to 2 decimal places.)
3. Net present value (NPV). (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round the final answer to nearest whole dollar.)
4. Recalculate the NPV assuming BBS's cost of capital is 11 percent. (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round the final answer to nearest whole dollar.)
I'm mostly confused on NPV
The accounting rate of return is 7.6%, the payback period is 5.755 years, the Net present value is $58,072, and the net present value(11%) is $3611.
What is NPV?The Net Present Value (NPV) is a corporate finance technique for analyzing the viability of an investment or a firm. It's the disparity between the anticipated cash flows and the initial investment. Let's look more closely at NPV.
We can calculate the accounting rate of return as follows:
Accounting rate of return = (Annual net Income/ Average Investment)×100
=(30,324/399,000)×100
= 7.6%
For Payback period:
Payback = Initial investment/ Annul cash flow
Annual cash flow = Annual net income + Depreciation
Deprecition = cost - salvage value/useful life
= (399,000-48,000)/9
= $39,000
Annual cash flow = 30,324 + 39,000 = 69324
Payback= 399,000/69324
= 5.755 years
For NPV:
NPV = Total present value of investment - initial investment
= 69324×PVIFA(8%, 9 years)+48,000×PV(8%, 9 years) - 399,000
= 69324×6.2469+24,011.95 - 399,000
= $58,072
For Net value recalculate if the cost of capital is 11%
NPV = Total present value of investment - initial investment
= 69324×PVIFA(11%, 9 years)+48,000×PV(11%, 9 years) - 399,000
= 69324×5.5370+18,764.39 - 399,000
= 3610.988
= $3611
Thus, the accounting rate of return is 7.6%, the payback period is 5.755 years, the Net present value is $58,072, and the net present value(11%) is $3611.
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12) A job offers you $15 an hour. Your boss
states that a percentage of your check will
be taken out for taxes, and then $35 for
medical insurance and $4 for dental
insurance. If you worked 38 hours, and
your total paycheck (for the week) was
$462.60, what percentage is taken out for
taxes?
Answer:
12%Step-by-step explanation:
Total paycheck before taking out taxes and insurance :
38×15 = 570
Left Amount of money after applying taxes :
570 - 570×(p/100)
= 570×[1 - (p/100)]
= 570×[(100-p)/100]
= (570/100) × [100 - p]
= 5.7 × [100 - p]
After taking out the insurance amounts we can write this equation:
.,7 × [100 - p] - (35+4) = 462.6
⇔ 5.7 × [100 - p] - 39 = 462.6
⇔ 5,7 × [100 - p] = 462.6 + 39
⇔ 5,7 × [100 - p] = 501.6
⇔ 100 - p = 501.6/5.7
⇔ 100 - p = 88
⇔ p = 100 - 88
⇔ p = 12
The radius of a circle is 7 inches. What is the circle's circumference?
Use 3.14 for
Answer:
43.96
Step-by-step explanation:
2 x 7 x 3.14 = 43.96
Answer:
44 rounded to nearest whole.
[tex]C = 2\pi r = 2 * \pi * r(7) = 44~in[/tex]
all ratios equivalent to 6:4.
Answer:
Give two equivalent ratios of 6 : 4. 6 : 4 = 6/4 So, equivalent ratios are 6/4 × 2/2 = 12/8 = 12:8 6/4 × 3/3 = 18/12 = 18:12 So, 6 : 4 = 12 : 8 = 18 : 12
Step-by-step explanation:
How many grams are in 2.2 kilograms?
Step-by-step explanation:
the word kilo means thousand. By that logic we know that 2200 grams are in 2.2 kilograms
i need hellp answer it
Answer:
Step-by-step explanation:
Finding the center.
The general formula for a circle is
(x - a)^2 + (y - b)^2 = r^2
The center is a and b. The center is marked as (6,5)
So the equation becomes
(x - 6)^2 + (y - 5)^2 = r^2
Finding the radius
The radius is found by calculating the distance between the center and any point on the circumference.
The point given on the circumference is (8,8)
x1 = 8
x2 = 6
y1 = 8
y2 = 5
r^2 = (8 - 6)^2 + (8 - 5)^2
r^2 = 2^2 + 3^2
r^2 = 4 + 9
r^2 = 13
Answer
(x - 6)^2 + (y - 5)^2 = 13
(3a) to the third power's most simplified form.
Answer:
[tex]9a^3[/tex]
Step-by-step explanation:
Step 1: Determine the simplified form
[tex](3a)^{3}[/tex]
[tex](3^{3}a^{3})[/tex]
[tex]9a^3[/tex]
Answer: [tex]9a^3[/tex]
if x+y= -10 and x=2 what is the value of x
Answer:
x = 2 y = -12
Step-by-step explanation:
x+ y = -10
2 + y = -10
y = -10 -2 = -12
Mrs. Welch and her 5 children are shopping at a local grocery store. Each of the children will be allowed to select one box of cereal for their own from the 8 different boxes of cereal available (there are no two the same). In how many ways can the selections be made?
Find the Value of X. or other X finders. (worth 10 points)
Answer:
First, if we look at these angles, we can see that they are vertical.
Vertical angles are congruent(meaning they measure the same degrees).
So let's set up an equation where -2x - 6 is equal to 40°, because they are vertical angles.
-2x - 6 = 40°
Solve for x!
Get rid of constants by performing the inverse operation of subtraction which is addition(because 6 is negative).
Make sure to apply this to both sides!!
(Add 6 to both sides)
+6 +6
-2x = 46
Now, we isolate x by getting of x's co-efficient.
To do that, we also perform the inverse operations.
The inverse operation of multiplication is division (since -2 is being multiplied by x).
(Divide -2 from both sides)
÷ -2 ÷ -2
x = -23
Therefore, x measures -23°.
Answer:
x = -23
Step-by-step explanation:
Vertical Angle Theorem
A pair of opposite angles formed by intersecting lines.
Vertical angles are congruent.
⇒ -2x - 6 = 40
Add 6 to both sides:
⇒ -2x = 46
Divide both sides by -2
⇒ x = -23
??????????????????????????
base = 4 units
height = 2 units
(1/2).base.height = (1/2).4.2 = 4
area = 4 sq. units
hope it helps...!!!
Amanda invests a sum of money in a retirement account with a fixed annual interest rate of 9 % compounded ontinuously . After 19 years , the balance reaches $38,956.06. What was the amount of the initial investment ?
Answer:
$7045.82
Step-by-step explanation:
The formula for the balance of an account earning interest at rate r compounded continuously for t years is ...
A = Pe^(rt)
We want to find P, given the other parameters in this formula.
__
38956.06 = P(e^(0.09×19)) = P(5.52896148)
P = 38956.06/5.52896148 ≈ 7045.82
The amount of the initial investment was about $7045.82.
What is 40/17 rounded to the nearest hundred
no one helped me, i need this urgently :(((
trinomials method can i have some help?
Answer:
a: 3/2, -2 b: 1/5, -1/2 c: 3/2, -4
Step-by-step explanation:
a: 2x^2+x=6
Subtract 6 from both sides.
2x^2+x−6=6−6
2x^2+x−6=0
Factor left side of equation.
(2x−3)(x+2)=0
Set factors equal to 0.
2x−3=0 or x+2=0
b: 10a^2+3a=1
Subtract 1 from both sides.
10a^2+3a−1=1−1
10a^2+3a−1=0
Factor left side of equation.
(5a−1)(2a+1)=0
Set factors equal to 0.
5a−1=0 or 2a+1=0
c: 2c^2+5c=12
Subtract 12 from both sides.
2c^2+5c−12=12−12
2c^2+5c−12=0
Factor left side of equation.
(2c−3)(c+4)=0
Set factors equal to 0.
2c−3=0 or c+4=0
#1
2x²+x-62x²+4x-3x-62x(x+2)-3(x+2)(2x-3)(x+2)#2
10a²+3a-110a²+5a-2a-15a(2a+1)-1(2a+1)(5a-1)(2a+1)#3
2c²+5c-122c²+8c-3c-122c(c+4)-3(c+4)(2c-3)(c+4)What is the total value of the digit 4 in the number 34,712?
Answer:
4,000
Step-by-step explanation:
The individual places of the number are listed below:
Ten Thousands - 30,000
Thousands - 4000
Hundreds - 700
Tens - 10
Ones - 2
From this, we can see that the total value of 4 is 4000.
hope this helps! have a good day.
Please help on math.
Answer:
13.9 inches
Step-by-step explanation:
To find the height on this question i multiplied 12.8 by 4 and got 51.2 then divided 711.68 by 51.2 and got 13.9.
20 POINTS!!! PLEASE ANSWER
Answer: C
Step-by-step explanation:
[tex]5\left(4x+5\right)[/tex]
[tex]\mathrm{Apply\:the\:distributive\:property}:\quad \:a\left(b+c\right)=ab+ac[/tex]
[tex]=5\cdot \:4x+5\cdot \:5[/tex]
[tex]\bf=20x+25[/tex]
Evaluate the algebraic expression t + s - r when r = 13, s = 10, t = 7 and u = 15.
A. 2
B. 4
C. 16
D. 30
Answer:
4
Step-by-step explanation:
t + s - r
where,
r=13
s=10
t=7
u=15
substituting
7+10-13 =17-13 =4
Hey there!
t + s - r
= 7 + 10 - 13
= 17 - 13
= 4
Therefore, your answer might be:
Option B. 4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The area of a rectangular piece of paper is 1/2 square foot
Answer:
(D)
Step-by-step explanation:
The area of a rectangle is the product of length and width. We can solve this formula to find the width:
A = LW
W = A÷L . . . . . . divide both sides of the equation by L
__
For the given area and length, this looks like ...
[tex]W=\boxed{\dfrac{1}{2}\div\dfrac{2}{3}}[/tex]
Which expression is equivalent to x^2+7x+12 over x^2-x-12
Answer:
Step-by-step explanation:
Factorize the expression.
Sum = 7
Product = 12
Factors = 4 , 3
4 + 3= 7 & 4*3 = 12
x² + 7x + 12 = x² + 4x + 3x + 4*3
= x(x + 4) + 3(x + 4)
= (x + 4)(x + 3)
Sum = -1
Product = -12
Factors = (-4) , 3
(-4) + 3 = (-1) & (-4)*3 = -12
x² - x - 12 = x² - 4x + 3x - 4*3
= x(x - 4) +3(x - 4)
= (x -4)(x +3)
[tex]\sf \dfrac{x^{2}+7x+12}{x^{2}-x-12}=\dfrac{(x+4)(x + 3)}{(x -4 )(x + 3)}\\\\\bf \text{(x +3) in the numerator and denominator will get cancelled}[/tex]
[tex]=\dfrac{x+4}{x-4}[/tex]
Answer:
B
Step-by-step explanation:
Which inequality represents “six times a number is less than negative thirty-nine and three-quarters”?
6x > –39Three-fourths
6 + x > -39 Three-fourths
6x < -39Three-fourths
6 x less-than-or-equal-to negative 39 and three-fourths
Answer:
6x<-39+¾
Step-by-step explanation:
let the number be represented by x.
Answer: The third option is correct.
Step-by-step explanation: 6x means "six times a number", which the unknown number is x. The less-than sign shows the "less than" part of the equation, and -39 3/4 represents the "negative thirty-nine and three-quarters". Hope this helps, also i got it right on edge.
What is 0.353 rounded to the nearest tenth
A store's change in total revenue over a 4-month period is −$1240. What is the average change in revenue per month for that period?
Answer Choices:
−$4960
−$310
$310
$4960
Answer: -310
Step-by-step explanation:
-1240÷4
Find the equation that represents the relationship between the variables.
to get the equation of any straight line, we simply need two points off of it, hmmm let's use (0 , 10) and (8 , 30) from the table
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{30}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{30}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{0}}}\implies \cfrac{20}{8}\implies \cfrac{5}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{\cfrac{5}{2}}(x-\stackrel{x_1}{0}) \\\\\\ y-10=\cfrac{5}{2}x\implies y=\cfrac{5}{2}x+10[/tex]
What is the slope of the equation y-3 = -4(X - 5)?
04
0-3
20
023
Paige mixed 11 gallons of lemonade and poured it into
seven 6-quart jugs. How many cups of lemonade were left
over after she filled the jugs?
Answer:
152 cups
Step-by-step explanation:
1. 44 quarts are in 11 gallons.
2. 44-6=38.
3. There are 152 cups in 38 quarts.
68 is 17% of what number?
68 = 0.17 • X
x = [?]
Answer:
400
Step-by-step explanation:
Division cancels multiplication. Divide by 0.17 to isolate "x" on the right side of the equation.
68 = 0.17 * x
divide both sides by 0.17
400 = x
68 is 17 percentage of the number 400.
To find the number that 68 is 17% of, we can set up the equation:
17% of x = 68
To solve for x, we need to divide both sides of the equation by 17% (or 0.17 as a decimal):
x = 68 / 0.17
Evaluating the division:
x=400
Therefore, 68 is 17% of 400.
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