MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $928 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin 13,800 . Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.
Answers
MotoWin can expected to make money from offering these warranties.
In the long-run, they should expect to make 514 dollars from each warranty sold
What is expected value of replacement?
The expected value to MotoWin Auto Superstore of a replacing a car is the sum of the costs to be incurred when there is replacement multiplied by its probability of occurrence plus the cost of no replacement multiplied by its likelihood of occurrence expressed in percentage terms
expected value of replacement=(cost of replacement*its probability)*(cost of no replacement*its probability)
cost of replacement=$13,800
probability of replacement=7%
cost of no replacement=$0(when there is no to replace no cost is incurred)
probability of no replacement=93%
expected value of replacement=($13,800*3%)+($0*97%)
expected value of replacement=$414
profit on replacement=replacement price-expected value of replacement
profit on replacement=$928-$414
profit on replacement=$514
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Related Questions
Sarah used the Quadratic Formula to solve the equation x² - 4x - 16 = 0. What should her solutions be?
Answers
Answer
x = (2 + 2√5)
OR
x = (2 - 2√5)
Explanation
In order to use the quadratic formula for the general quadratic equation,
ax² + bx + c = 0 is given as
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For x² - 4x - 16 = 0,
a = 1
b = -4
c = -16
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1\times-16)}}{2(1)} \\ x=\frac{4\pm\sqrt[]{16+64}}{2} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ \sqrt[]{80}=\sqrt[]{16\times5}=\sqrt[]{16}\times\sqrt[]{5}=4\sqrt[]{5} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ x=\frac{4\pm4\sqrt[]{5}}{2} \\ x=2\pm2\sqrt[]{5} \\ x=2+2\sqrt[]{5} \\ OR \\ x=2-2\sqrt[]{5} \end{gathered}[/tex]Hope this Helps!!!
Which expression is equivalent to the following complex fraction?SIMI3+3y+5x2(y-2x)2(y-2x)3y-5xo122(y-2x)(3y-5x)x²,2x²y²2(y-2x) (3y-5x
Answers
Solution
For this case we can do the following:
[tex]\frac{\frac{2}{x}-\frac{4}{y}}{-\frac{5}{y}+\frac{3}{x}}[/tex]We can start with the numerator and we have:
[tex]\frac{2}{x}-\frac{4}{y}=\frac{2y-4x}{xy}=\frac{2(y-2x)}{xy}[/tex]For the denominator we have:
[tex]-\frac{5}{y}+\frac{3}{x}=\frac{3y-5x}{xy}[/tex]And replacing we got:
[tex]\frac{\frac{2(y-2x)}{xy}}{\frac{3y-5x}{xy}}=\frac{2(y-2x)}{3y-5x}[/tex]Then the correct answer would be:
[tex]\frac{2(y-2x)}{3y-5x}[/tex]What is the sign of -2 to the power of 49
Answers
Answer:
negative
Step-by-step explanation:
-2 to the power of odd numbers is negative
to the power of even numbers is positive
Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. Then find the exact values of the other five trigonometric functions of
Answers
Solution:
Given:
[tex]cot(\theta)=2[/tex]Using the trig ratio of cot;
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ tan\theta=\frac{opposite}{adjacent} \\ Hence, \\ cot\theta=\frac{adjacent}{opposite} \\ cot\theta=\frac{2}{1} \\ adjacent=2 \\ opposite=1 \end{gathered}[/tex]The hypotenuse is gotten using the Pythagoras theorem;
[tex]\begin{gathered} h^2=2^2+1^2 \\ h^2=4+1 \\ h^2=5 \\ h=\sqrt{5} \end{gathered}[/tex]Thus, the sketch of the right triangle is;
[tex]\begin{gathered} Thus, \\ opposite=1 \\ adjacent=2 \\ hypotenuse=\sqrt{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ sin\theta=\frac{1}{\sqrt{5}} \\ sin\theta=\frac{1}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{5} \\ sin\theta=\frac{\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ cos\theta=\frac{2}{\sqrt{5}} \\ cos\theta=\frac{2\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ csc\theta=\frac{1}{\frac{\sqrt{5}}{5}} \\ csc\theta=\sqrt{5} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ sec\theta=\frac{1}{\frac{2\sqrt{5}}{5}} \\ sec\theta=\frac{\sqrt{5}}{2} \end{gathered}[/tex]I need help solving this question
Answers
The three numbers are 61, 427 and 161.
What is the sum of numbers?
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
As given, one number is 7 times the first number, third number is 100 more than the first number and the sum of three numbers is 649.
Suppose the first number is x, then the second number is 7x and the third number is x + 100.
Sum of these three numbers is, 649.
x + 7x + x + 100 = 649
9x = 549
x = 61
Therefore, the first number is 61, the second number is 7x = 427, and the third number is x + 100 = 161.
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(1)/(3)(12+x)=-8(6-x)
Answers
the answer is -6.24
evaluate 7x^2+2(3x-8)-5x for x=3. show your work
Answers
The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 will be 50.
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The expression is,
7x² + 2(3x - 8) - 5x
Now, The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 calculated as;
The expression is,
7x² + 2(3x - 8) - 5x
Now, For the value of expression 7x² + 2(3x - 8) - 5x for x = 3 , we can substitute x = 3;
7x² + 2(3x - 8) - 5x
7 (3)² + 2 (3 × 3 - 8) - 5 × 3
7 × 9 + 2 (9 - 8) - 15
7 × 9 + 2 × 1 - 15
63 + 2 - 15
65 - 15
50
So, For x = 3,
⇒ 7x² + 2(3x - 8) - 5x = 50
Thus, The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 will be 50.
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Consider the quadratic equation below. 412 - 5= 3 + 4 Determine the correct set-up for solving the equation using the quadratic formula.
Answers
Given:
[tex]4x^2-5=3x+4[/tex]To find:
The correct setup for solving the equation using the quadratic formula.
Explanation:
It can be simplified as,
[tex]\begin{gathered} 4x^2-5-3x-4=0 \\ 4x^2-3x-9=0 \end{gathered}[/tex]Here,
[tex]\begin{gathered} a=4 \\ b=-3 \\ c=-9 \end{gathered}[/tex]Using the quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging in the values, we get
[tex]x=\frac{-(-3)\pm\sqrt{(-3)^2-4(4)(-9)}}{2(4)}[/tex]Final answer:
The correct choice is D.
help please thank you
Answers
Problem
Express the number 0.00005348 in terms of a power of 10
Solution
For this case we just need to count the number of zeros before the first number different from 0 and if we do this we have 5 numbers before 5 so we can write the number like this:
5.348 x10^-5
[tex]5.348x10^{-5}[/tex]4) At a farm the ratio of cows to horses was 7: 1. If there were 49 cows at the farm, how
many horses were there?
Answers
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.09.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
Answers
0.4834
There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.
The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14
The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.
The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.
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which is greater a unit rate of -4 or 2
Answers
Answer: Hi that would be 2, hope that helps!
Step-by-step explanation:
4. Jason can travél 24 miles in hour. What is his average speed in miles per hour?
Answers
Answer:
24 miles in 1 hour
speed = distance/time
so 24/1
24 mph (miles per hour) is the speed
hope it helps, mark as brainliest :D
use the equation 1/4+s=18/20 pls help
Answers
The value of (s) that satisfy the given equation → 1/4+s=18/20 is 0.65.
What is equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. There are different types of equation such as - Linear Equations, Radical Equations, Exponential Equations, Rational Equations etc.
Given is the following equation written in variable (s)
1/4 + s = 18/20
We have -
1/4 + s = 18/20
We will solve the given expression using the transpose method -
1/4 + s = 18/20
Shifting (s) to the left hand side and constant numbers to right hand side, and then solving for (s), we get -
s = 18/20 - 1/4
s = 9/10 - 1/4
s = 0.9 - 0.25
s = 0.65
The value of s will be 0.65
Therefore, the value of (s) that satisfy the given equation → 1/4+s=18/20 is 0.65.
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Use the net to find the surface area of the prism. 5 ITL 13 m 5 IT 13 m 12 m 29 m 12 m 13 YTL 5 ICE 29 YTL 5 YC Not drawn to scale 930 m2 o 11,310 m2 0 45,240 m2 118 m2
Answers
To find the surface area of the prism, we will consider the areas of each part of the net
For part A
Area of A = L x B = 29 x 5 = 145
Area of B = L X B = 29 x 13 = 377
Area of C = L x B = 29 x 12 =348
Area of D = 1/2 x H X B = 1/2 x 12 x 5 = 30
Area of E = 1/2 x H x B = 1/2 x 12 x 5 = 30
Total Area = 145 + 377 + 348 + 30 + 30
You invest $940 into an account that
earns 8% simple interest. What is the final
In the account after 6 years
Answers
The final amount in the account after 6 years is $6,354.4
This is a problem with simple interest. We can solve this problem by following a few steps.
I have invested $940 into an account that earns 8% simple interest.
We have to use a formula to solve this problem.
I = P× r× t
Where I = amount of interest.P is denoted as the principal amount of money which is $940 as per the question.r is denoted as simple interest which is 8%, according to the question.t represents the period which is 6 years or 72 months as 1 year is equal to 12 months.So, the interest after 6 years is, (940 × 8 × 72) / 100 = $5,414.4
The total amount after 6 years is ( 940+ 5414.4 ) = $6,354.4 [ Total amount = principal amount + interest ]
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Estimate the point(s) at which the graph of f has a local maximum or a local minimum.
Answers
The graph of f has a local maximum of coordinates at (-2.5, 30) and a local minimum of coordinates at (2.5, -30)
What are Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
As per the given graph,
From the given graph it is noticed that the highest point of the function is (-2.5, 30), therefore the local maxima is (-2.5, 30).
From the given graph it is noticed that the lowest point of the function is (2.5, -30), therefore the local maxima is (2.5, -30).
The graph of f has a local maximum of coordinates at (-2.5, 30)
The graph of f has a local minimum of coordinates at (2.5, -30)
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5.8. The lifetime in hours of an electronic tube is a random variable having a probability density function given by
f(x)= xe^-x. x>-0
Answers
The lifetime in hours of an electronic tube will be of 2 hours.
A probability density function, also known as the density of a continuous random variable, is a function used in probability theory whose value at any given sample (or point) in the sample space can be interpreted as giving a relative likelihood that the random variable's value would be close to that sample. While the absolute likelihood of a continuous random variable taking on any given value is 0, probability density (PDF) at two different samples can be used to infer, in any given draw of the random variable, how much more likely it would be that the random variable would be close to one sample compared to the other sample.
We have,
f(x) = xe^(-x) x>0
= 0 o.w.
Consider,
[tex]E(X) = \int\limits^a_0 {xf} (x)\, dx \\\\E(X) = \int\limits^a_0 {xxe}^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{2}e^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{b-1}e^{-mx} \, dx = \frac{n}{m^{n} } \\\\= 2! = 2[/tex]
Therefore, a tube of this type should last for 2 hours.
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Translate and solve, what percentage of 375 is 225
Answers
The mathematical expression for the word statement is,
[tex]x\text{ \% of 375=225}[/tex]Solve for x
[tex]\frac{x}{100}\times375=225[/tex][tex]\frac{375x}{100}=225[/tex]Multiply both sides by 100
[tex]\begin{gathered} 100\times\frac{375x}{100}=100\times225 \\ 375x=22500 \end{gathered}[/tex]Divide both sides by 375
[tex]\begin{gathered} \frac{375x}{375}=\frac{22500}{375} \\ x=60\text{ \%} \end{gathered}[/tex]Hence, the answer is
[tex]60\text{ \%}[/tex]Ty ordered a storage pod in the shape of a rectangular prism to store some extra things at his house. The storage pod has a length of 16 feet and a height of 8 feet. If the volume of the storage pod is 896 cubic feet, what is the width of the storage pod?
Answers
Answer:
7 cubic feet
Step-by-step explanation:
so first you do length times height in this case it would be 16 times 8
you get 128 now you divide 896 by 128 and you get an answer of 7.
One way to check is you do length times width times height.
So 16 × 7 × 8 =896
Answer: 7 feet cubed
What is 7/9 ÷ 2/3 please help
Answers
Solution:
Given;
[tex]\frac{7}{9}\div\frac{2}{3}[/tex]Change the division sign to multiplication and reciprocate the other side;
[tex]\frac{7}{9}\times\frac{3}{2}=\frac{7}{6}[/tex]ANSWER:
[tex]\frac{7}{6}=1\frac{1}{6}[/tex]find the value or measure. Assume all lines that appear to be tangent are tangent.m(angle) TUV=
Answers
Answer:
Angle TUV = 46 degrees.
Explanation:
In the diagram, angle TUV is the external angle.
The external angle is always half the difference of the internal angles.
Therefore:
[tex]\angle\text{TUV}=\frac{1}{2}(145^0-53^0)[/tex]We simplify to obtain our result.
[tex]\begin{gathered} \angle\text{TUV}=\frac{1}{2}\times92^0 \\ =46^0 \end{gathered}[/tex]The measure of angle TUV is 46 degrees.
x y w z is a quadrilateral with verticals W 1 - -4 - x - -4
Answers
Midpoint formula
We are given the points
X=(-4,2)
Y=(1,-1)
Z=(-2,-3)
W=(1,-4)
They define the quadrilateral XYWZ
To find the intersection of the diagonals, we can use the Midpoint Formula
This formula gives us the midpoint of a segment defined by points (x1,y1) (x2,y2) as follows:
[tex]xm=\frac{x1+x2}{2},\text{ ym=}\frac{y1+y2}{2}[/tex]We must identify the opposite points of the quadrilateral and calculate the midpoint between them
Segment XY:
Midpoint of XY:
[tex]x_m=\frac{-4+1}{2}=-\frac{3}{2}[/tex][tex]y_m=\frac{2-1}{2}=\frac{1}{2}[/tex]Midpoint of ZW:
[tex]x_m=\frac{1-2}{2}=-\frac{1}{2}[/tex][tex]y_m=\frac{-3-4}{2}=-\frac{7}{2}[/tex]Finally, find the midpoint of the opposite sides' midpoints:
[tex]x_c=\frac{-\frac{3}{2}-\frac{1}{2}}{2}=-1[/tex][tex]y_c=\frac{\frac{1}{2}-\frac{7}{2}}{2}=-\frac{3}{2}[/tex]The intersection of the diagonals is the point (-1,-3/2)
The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.Is f one-to-one?
Answers
A function is called being one-to-one if, for every value of x, there is only one value of y and vice-versa.
If the graph of the function is given, a practical rule to determine if the function is one-to-one is to use the horizontal-line test.
This test is as follows: Imagine you have a horizontal line (maybe a ruler) and you can move it up and down the grid.
If your line touches the graph only once at every vertical position, then your function is one-to-one.
Now if we test our function drawn in blue, we can touch it only once as we move our line up and down, thus:
Is f one-to-one?
Yes
Find the equation of a line parallel to the line y = −5/4x + 7. Write the equation in Standard Form (Ax + By = C).
Answers
The equation to be found is parallel to
[tex]y=2x+5[/tex]2 lines that are parallel have the same slope. Therefore,
[tex]\begin{gathered} m_1=m_2 \\ m_2=2 \end{gathered}[/tex]The equation to be found is containing the point (3, 3)
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \\ 3=2(3)+b \\ 3-6=b \\ b=-3 \end{gathered}[/tex][tex]y=2x-3[/tex]Geri encarga arreglos florales para un almuerzo de agradecimiento para un maestro.Planea comprar hasta ocho arreglos de mesa que cuestan $5 cada una,con una tarifa de $10 por todo el pedido.Representa gráficamente la función para el precio.
Answers
From the graph drawn above, we can see the relationship between the flower arrangements and the cost of ordering each of them.
On the x axis you have the number of orders,and on the y axis you have the cost of each order. Each flower arrangement costs $5, and the cost of fare is $10. That means the cost for each order would shown as follows;
1 order = 5 + 10 (15)
2 orders = 10 + 10 (20)
3 orders = 15 + 10 (25)
4 orders = 20 + 10 (30)
5 orders = 25 + 10 (35)
6 orders = 30 + 10 (40)
7 orders = 35 + 10 (45)
8 orders = 40 + 10 (50)
Therefore, the ordered pair for this graph is as follows;
(1, 15), (2, 20), (3, 25), (4, 30), (5, 35), (6, 40), (7, 45), (8, 50)
That is, when x = 1, y = 15, when x = 2, y = 20..., and so on.
Antoine purchased 1.8 kilograms of apples and 315 dekagrams of oranges. This was 1,350 grams more than the weight of bananas he purchased. What was the weight of the bananas Antoine purchased in grams?
Answers
First, let's get all the values to grams.
1.8 kilograms is equal to 1800 grams.
315 deka grams is equal to 3150 grams.
1350 is already in grams.
So Antoine purchased 1800 grams of apples and 3150 grams of oranges. Adding them up, we have a total of:
[tex]1800+3150=4950[/tex]Since this: 4950 grams, is 1350 grams more than the wieght of bananas, than, the weight of banas, "b", is:
[tex]\begin{gathered} b+1350=4950 \\ b=4950-1350 \\ b=3600 \end{gathered}[/tex]This is already in grams, so the wieght of the banaas in grams is 3600.
Match the coordinate rule with the reflection that produces it.Column AColumn B1.Reflect across the x-axisa. (b, a)2.Reflect across the y-axisb. (a, b)3.Reflect across the originC. (-b, -a)4.Reflect across the line y = xd. (-a, -b)5.Reflect across any horizontal line. Ex: y = -2e. (a, -b)f. (2x-a, b)6.Reflect across any vertical line. Ex: x = 5g. (a, 2y-b)
Answers
4. Reflect across the line y = x ------- (b,a)
for reflection across the line y=x, the value of x and y coordinates are interchanged;
[tex](x,y)\rightarrow(y,x)[/tex]5. Reflect across any horizontal line. Ex: y = -2 ......... (a,2y-b)
for reflection across any horizontal line, the x coordinate remain the same but the y coordinate is subtracted from twice the value of the y coordinate of the line of reflection.
[tex](x,y)\rightarrow(x,2y_1-y)[/tex]6. Reflect across any vertical line. Ex: x = 5 ---------- (2x-a, b)
for reflection across any vertical line, the y coordinate remain the same but the x coordinate is subtracted from twice the value of the x coordinate of the line of reflection.
[tex](x,y)\rightarrow(2x_1-x,y)[/tex]Consider the market for jet ski rentals in the small town of Isleton. Suppose that in Isleton, there are many sellers of jet ski rentals, each one selling an identical jet ski. Therefore, each seller is a perfectly competitive firm and possesses no market power. The following graph shows the demand (D) and supply curves (S = MC) in the jet ski rental industry in Isleton.
Answers
A line that passes through (3, 1) and (0, -3) A line that passes through (-1,-5) and (2, 4)
Answers
The equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a point on the line.
The slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Fisrt line:
In this case the slope is
[tex]\begin{gathered} m=\frac{-3-1}{0-3} \\ =\frac{-4}{-3} \\ =\frac{4}{3} \end{gathered}[/tex]The the equation is
[tex]y-1=\frac{4}{3}(x-3)[/tex]Second line:
In this case the slope is
[tex]\begin{gathered} m=\frac{4-(-5)}{2-(-1)} \\ =\frac{4+5}{2+1} \\ =\frac{9}{3} \\ =3 \end{gathered}[/tex]Then the equation is
[tex]\begin{gathered} y-(-5)=9(x-(-1)) \\ y+5=9(x+1) \end{gathered}[/tex]