Answer:
Step-by-step explanation:
There's a saying to this kind of equation: Rate + Time = Distance and B best fits the saying, so B must be right (Don't quote me on that, it may be wrong)
the linear equation that can be used to find the distance that Eric travels each day is A. d = rt & the total distance that Eric travels each day is C. 112.5 miles.
What is speed?Speed is measured as distance moved over time.
here, given that,
He drives at a rate of 75 mph on the interstate for a total of 1.5 hours.
so, the linear equation that can be used to find the distance that Eric travels each day is A. d = rt
i.e. d= 75*1.5
=112.5
& the total distance that Eric travels each day is C. 112.5 miles.
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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
X' + 2y' + x = 0 , x' - y' + y = 0 x(0) = 0 and y(0) = 1
This looks like a system of differential equations.
[tex]\begin{cases}x' + 2y' + x = 0 \\ x' - y' + y = 0 \\x(0)=0, y(0)=1\end{cases}[/tex]
Eliminating x' gives
[tex](x'+2y'+x)-(x'-y'+y) = 0 - 0 \implies 3y' - y + x = 0[/tex]
and eliminating y' gives
[tex](x'+2y'+x) + 2(x'-y'+y)=0+2\times0 \implies 3x' + x + 2y = 0[/tex]
so that we can rewrite the system as
[tex]\begin{cases}3x' = -x - 2y \\ 3y' = -x + y\end{cases}[/tex]
or equivalently in matrix form as
[tex]\begin{bmatrix}x\\y\end{bmatrix}' = \dfrac13 \begin{bmatrix}-1&-2\\-1&1\end{bmatrix} \begin{bmatrix}x\\y\end{bmatrix}[/tex]
Compute the eigenvalues for the coefficient matrix:
[tex]\det\begin{bmatrix}-1-\lambda&-2\\-1&1-\lambda\end{bmatrix} = (-1-\lambda)(1-\lambda) - 2 = \lambda^2 -3 = 0 \implies \lambda=\pm\sqrt3[/tex]
Compute the corresponding eigenvectors:
[tex]\lambda=\sqrt3 \implies \begin{bmatrix}-1-\sqrt3&-2\\-1&1-\sqrt3\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix} \\\\ \implies v_1=(1-\sqrt3)v_2 \implies \vec v = \begin{bmatrix}1-\sqrt3\\1\end{bmatrix}[/tex]
[tex]\lambda=-\sqrt3 \implies \begin{bmatrix}-1+\sqrt3&-2\\-1&1+\sqrt3\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix} \\\\ \implies v_1 = (1+\sqrt3)v_2 \implies \vec v = \begin{bmatrix}1+\sqrt3\\1\end{bmatrix}[/tex]
We end up multiplying the matrix by 1/3, so the eigenvalues also get scaled by 1/3 and λ = ±1/√3. The eigenvectors stay the same.
Then the characteristic solution to the system is
[tex]\begin{bmatrix}x\\y\end{bmatrix} = C_1 e^{t/\sqrt3} \begin{bmatrix}\frac{1-\sqrt3}3\\\frac13\end{bmatrix} + C_2 e^{-t/\sqrt3} \begin{bmatrix}\frac{1+\sqrt3}3\\\frac13\end{bmatrix}[/tex]
Use the initial conditions to solve for the constants.
[tex]\begin{bmatrix}0\\1\end{bmatrix} = C_1 \begin{bmatrix}\frac{1-\sqrt3}3\\\frac13\end{bmatrix} + C_2 \begin{bmatrix}\frac{1+\sqrt3}3\\\frac13\end{bmatrix}[/tex]
[tex]\implies \begin{cases}(1-\sqrt3) C_1 + (1+\sqrt3) C_2 = 0 \\ C_1 + C_2 = 3\end{cases}[/tex]
[tex]\implies C_1=\dfrac{3+\sqrt3}2, C_2=\dfrac{3-\sqrt3}2[/tex]
Then the particular solution is
[tex]\begin{bmatrix}x\\y\end{bmatrix} = \dfrac{3+\sqrt3}6 e^{t/\sqrt3} \begin{bmatrix}1-\sqrt3\\1\end{bmatrix} + \dfrac{3-\sqrt3}6 e^{-t/\sqrt3} \begin{bmatrix}1+\sqrt3\\1\end{bmatrix}[/tex]
or
[tex]\begin{cases}x(t) = -\dfrac1{\sqrt3} e^{\sqrt3 \, t} + \dfrac1{\sqrt3} e^{-\sqrt3\,t} \\\\ y(t) = \dfrac{3+\sqrt3}6 e^{\sqrt3\,t} + \dfrac{3-\sqrt3}6 e^{-\sqrt3\,t}\end{cases}[/tex]
What is 56 ÷ (-8) = ___ need fast will give brainliest
Answer:
-7
Step-by-step explanation:
^
Answer:
-7
Step-by-step explanation:
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?
What is 40/17 rounded to the nearest hundred
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]
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
??????????????????????????
base = 4 units
height = 2 units
(1/2).base.height = (1/2).4.2 = 4
area = 4 sq. units
hope it helps...!!!
Convert the decimal to a percent. 0.725
Answer:
72.5% out of 100%
Step-by-step explanation:
0.725 is 72.5% of 1. 100% technically counts as 1. so 72.5%
What is 0.353 rounded to the nearest tenth
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
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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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]
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
Please help me solve this question
Answer:D
Step-by-step explanation: Multiply the expression
Please help!!!!!!!! Determine the function which corresponds to the given graph.
The rational function shown in the graph is:
[tex]y = \frac{x - 6}{x - 5}[/tex]
How to determine the function?
First, we can see that we have an asymptote at x = 5, so the denominator becomes equal to zero when x = 5.
Then the rational function is something like:
[tex]y = \frac{g(x)}{x - 5}[/tex]
We also can see that when x = 6, the function intercepts the x-axis, then we must have that:
g(6) = 0
So we can define:
g(x) = x - 6
So the rational function is:
[tex]y = \frac{x - 6}{x - 5}[/tex]
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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
Edna, Fatimah and Toby had a sum of money. The amount of money Edna had was 4 times the amount of money Fatimah had. The ratio of the amount of money Fatimah had to the total amount of money Toby and Fatimah had was 5:8. After Fatimah gave $30 to Toby, Toby had as much money as Fatimah. How much more money did Edna have than Toby in the end?
HELP ME PLEASE ! HOMEWORK DUE IN LESS THAN 2 HOURS! NO CLUE ON HOW TO DO THIS ! OFFERING 15 POINTS
Answer:
Edna had $510 more amount of money than Toby in the end.
Step-by-step explanation:
LET :-
Edna's amount of money - x
Fatimah's amount of money - y
Toby's amount of money - z
Now,
By the question,
x = 4y
y : (y + z) = 5 : 8
y - 30 = z + 30
Now,
y : (y + z) = 5 :8
or, y/(y + z) = 5/8
or, 8y = 5y + 5z
or, 3y = 5z
so, y = 5z/3
Now,
y - 30 = z + 30
or, 5z/3 - 30 = z + 30
or, (5z - 90)/3 = z + 30
or, 5z - 90 = 3z + 90
or, 5z - 3z = 90 + 90
or, 2z = 180
so, z = 90
Toby's amount of money - $90
Now,
y = 5z/3
or, y = 5 * 90/3
or, y = 5 * 30
so, y = 150
Fatimah's amount of money - $150
Again,
x = 4y
or, x = 4*150
or, x = 600
Edna's amount of money - $600
Now,
$600 - $90
= $510
Therefore,Edna had $510 more amount of money than Toby in the end.
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.
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
What does the notation P(B|A) mean?
Answer:
the answer for this one it should be the probability or chances that the event b occurs when the event a has occured.
Step-by-step explanation: I hope this help you pal or folk and have a great day.
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.
I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
To find the missing angle's measure
⇒ important to understand the sum of the angles of a triangle
⇒ the sum of every angle of any triangle in all cases equal to 180
degrees
What is the information given:
⇒ one angle is of 94 degrees and the other of 46 degrees
Using the information in the first section and the information given in the diagram, let's set up an equation:
[tex]94+46+x = 180\\140+x = 180\\x = 40[/tex]
The measure of the missing angle is 40 degrees
Hope that helps!
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:
What is the slope of the equation y-3 = -4(X - 5)?
04
0-3
20
023
A raffle ticket is sold for $3.50 each and the prize for winning the raffle is $250. If 100
people entered the raffle, what is:
the expected value? =
are you expected to win or lose the raffle? =
a fair price for the raffle ticket? =
Nancy Regan purchased a new diamond bracelet for $12,600. The state sales tax is 6% and the federal excise tax on the jewelry is 11%. What is the total purchase price of the bracelet? Round your answer to the nearest cent.
Using proportions, it is found that the total purchase price of the bracelet is of $10,769.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, we consider the two taxes, of 6% and 11%, hence the price suffers an increase of 17%, that is, the price is multiplied by 117% = 1.17 to reach $12,600, hence:
1.17p = 12600
p = 12600/1.17
p = 10769.
The total purchase price of the bracelet is of $10,769.
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Please help meeee!!!!!
Answer:
Now plot those points in graph and find intersection hope it helps you.......
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]
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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