4. What happens to the cost per DVD? Why do you think this happens? BONUS: Write a function D(x), that can be used to find the cost per DVD for any value of x. Refer to the diagram of f(x) shown below for questions 5-6 2 o o § 5. What is the domain and range of f(x)? Write your answer in interval notation 6. Sketch the graph of each of the following. Describe the transformation in each graph a. g(x) = f(x) - 1 b. h(x) = -f(x) 10
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The cost per DVD goes down when the amount of DVD produced is bigger than 1000, this is because the cost of producing produnct in a bigger scale are always more profitable.
The bonus question ask us to find a function for the price of DVD at any value of x. The provided function
[tex]C(x)=\begin{cases}2500+1.5x\text{ if}x\le1000 \\ 2500+1.25x\text{ if}x>1000\end{cases}[/tex]Already fulfill that purpose, then we can write
[tex]D(x)=\begin{cases}2500+1.5x\text{ if}x\le1000 \\ 2500+1.25x\text{ if}x>1000\end{cases}[/tex]Related Questions
Choose the equation that satisfies the data in the table.-10 1-4CY0A.y = -11 +4B.y = 21 + 4○ C.y = 4x - 4D.y = -4x -4-8
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Given a table represents a linear relation between x and y
We will use two points from the table to write the equation of the line in the slope-intercept form: y = mx + b
As shown in the table:
When x = -1, y = 0
When x = 0, y = -4
we will find the slope (m) as follows:
[tex]slope=m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-0}{0-(-1)}=\frac{-4}{1}=-4[/tex]The value of b = the value of y when x = 0
So, b = -4
So, the answer will be option D. y = -4x - 4
can someone help answer all 3 of these please i need helppp!!
Answers
Answer
f(h(-3) = 23
Explanation:
Given that
f(x) = 5x - 10
g(x) = 1/3x - 1
h(x) = x^2 + 4x
Find f(h(-3))?
Firstly, substitute the function of h(x) into f(x)
f(h(x) = 5(x^2 + 4x) - 10
f(h(x) = 5x^2 + 4x - 10
f(h(-3)) implies that substitute x with 3
f(h(-3)) = 5(-3)^2 + 4(-3) - 10
f(h(-3)) = 5(9) + 4(-3) - 10
f(h(-3) = 45 - 12 - 10
f(h(-3) = 23
Elijah invested $610 in an account paying an interest rate of 4.1% compoundedannually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $900?
Answers
Use the formula for the compounding of interest
[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex]since the compounding is annually, n=1 which reduces the formula to
[tex]A=p(1+r)^t[/tex]use values for
A=900
p=610
r=0.041
solve the equation for t
[tex]900=610\cdot(1+0.041)^t[/tex][tex]\frac{900}{610}=(1.041)^t[/tex][tex]\ln (\frac{900}{610})=\ln (1.041)^t[/tex]apply the log properties
[tex]\ln (\frac{900}{610})=t\cdot\ln (1.041)[/tex]solve for t
[tex]\begin{gathered} t=\frac{\ln (\frac{900}{610})}{\ln (1.041)} \\ t\approx9.68 \end{gathered}[/tex]It would take about 10 years to reach 900 in the account
8x10⁵ is how many times as great as 8x10 negative 1
Answers
Explanation:
To find how many times is one number greater than another number we have to find the quotient between the two of them:
[tex]\frac{8\times10^5}{8\times10^{-1}}=\frac{8}{8}\times\frac{10^5}{10^{-1}}=10^{5-(-1)}=10^{5+1}=10^6[/tex]Answer:
8x10⁵ is 10⁶ times greater than 8x10⁻¹
||Initial Knowledge CheckA container holds 6 gallons of juice. How much is this inpints?
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Solution:
From conversion;
[tex]1gallon=9.6076pints[/tex]Thus;
[tex]\begin{gathered} 6gallons=6\times9.6076pints \\ \\ 6gallons=57.6456pints \end{gathered}[/tex]ANSWER: 57.65 pints
a random survey of 250 students was conducted at a middle school to determine which flavor of ice cream students prefer.
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ANSWER
[tex]96\%[/tex]EXPLANATION
Probability is defined as the likeliness of an event occurring.
Hence,
Probability;
[tex]P=\frac{favourableoutcome}{Total\text{ outcome}}[/tex]The number of students that do not prefer butter Pecan are;
[tex]75+25+9+8+11+112=240[/tex]Total number of student is 250;
The probability of students that do not prefer Butter Pecan is;
[tex]\begin{gathered} \frac{240}{250}\times100 \\ =96 \end{gathered}[/tex]Kawan buy some protein bars at $0.90 and each water bottle cost $0.70 for each group hike he buys twice as many bottles of water as protein bars if he spends $46 in total how many bottles of water and protein bars does he buy?
Answers
Answer:
Bottles of water: 40
Protein Bars: 20
Explanation:
If we call
B = number of protein Bars
W = number of Water bottles
Since each B costs $0.9, each W costs $0.7 and the total spend is $46
We can write the equation:
[tex]0.9B+0.7W=46[/tex]Because, the total of $46 is equal to the number of W times the price, plus the number of B times the price.
We also know that there are twice as many W as B, we can write:
[tex]2B=W[/tex]We have these two equations:
[tex]\begin{cases}0.9B+0.7W={46} \\ 2B={W}\end{cases}[/tex]We can substitute the second equation in the first one:
[tex]0.9B+0.7W=46\Rightarrow0.9B+0.7(2B)=46[/tex]Now we can solve:
[tex]\begin{gathered} \begin{equation*} 0.9B+0.7(2B)=46 \end{equation*} \\ 0.9B+1.4B=46 \\ 2.3B=46 \\ . \\ B=\frac{46}{2.3}=20 \end{gathered}[/tex]B = 20, means that the amount of protein bars bought is 20.
Now, since there are twice as many bottles of water as protein bars:
[tex]2\cdot20=40[/tex]There are 40 water bottles and 20 protein bars
Five students stepped onto five scales. Wyn, Chen, Ramon and two Gails. Rather than list all their weights, they summed up their data to state: Range: 30 Mode: 74 Median: 80 Mean: 85 And now we would like you to say how much each of the five might weigh.
Answers
3 clear values are the mean and at least two values of 74 since it is the mode
[tex]\begin{gathered} 74 \\ 74 \\ 80 \\ a \\ b \end{gathered}[/tex]if the range is 30 the difference between 74 and greater number is 30
then
[tex]\begin{gathered} b-74=30 \\ b=104 \end{gathered}[/tex][tex]\begin{gathered} 74 \\ 74 \\ 80 \\ a \\ 104 \end{gathered}[/tex]now we apply the mean to find a
we add all numbers and divide between 5 to obtain the mean(85)
[tex]\begin{gathered} \frac{74+74+80+104+a}{5}=85 \\ \\ \frac{332+a}{5}=85 \end{gathered}[/tex]and solve for a
[tex]\begin{gathered} 332+a=85\times5 \\ 332+a=425 \\ a=425-332 \\ a=93 \end{gathered}[/tex]Finall data is
[tex]\begin{gathered} 74 \\ 74 \\ 80 \\ 93 \\ 104 \end{gathered}[/tex]Instructions: Find the missing side. Round your answer to the nearesttenth.59028XX=
Answers
Solution:
Given the ΔABC below:
To find the missing side,
Step 1: Identify the sides of the triangle.
Thus,
[tex]\begin{gathered} hypotenuse\Rightarrow AB(longest\text{ side of the triangle\rparen} \\ opposite\Rightarrow AC(side\text{ facing the angle\rparen} \\ adjacent\Rightarrow BC \end{gathered}[/tex]Step 2: Evaluate the value of x, using trigonometric ratios.
From trigonometric ratios,
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]where
[tex]\theta=\angle B[/tex]Thus,
[tex]\begin{gathered} \cos B=\frac{adjacent}{hypotenuse} \\ =\frac{BC}{AB} \\ \Rightarrow\cos B=\frac{x}{28} \\ cross-multiply, \\ x=28\times\cos B \\ but\text{ B=59} \\ \Rightarrow x=28\times\cos59 \\ =28\times0.5150380749 \\ =14.4210661 \\ \Rightarrow x\approx14.4 \end{gathered}[/tex]Hence, the value of x, to the nearest tenth, is
[tex]14.4[/tex]Write the equation of the line when the slope is - and the y-intercept is 12.
Answers
Solution
The y - intercept = 12
Hi tutor,Using first principles, find the derivative of y=3x^2+5x-2 please? Here is an image of the formula if you need it:
Answers
GIVEN
The function is given to be:
[tex]y=3x^2+5x-2[/tex]SOLUTION
The first principle formula is given to be:
[tex]f^{\prime}(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]Rewrite the function:
[tex]f(x)=3x^2+5x-2[/tex]Evaluate f(x + h):
[tex]\begin{gathered} f(x+h)=3(x+h)^2+5(x+h)-2 \\ Expand \\ f(x+h)=3x^2+6xh+3h^2+5x+5h-2 \end{gathered}[/tex]Substitute into the equation:
[tex]f^{\prime}(x)=\lim_{h\to0}\frac{3x^2+6xh+3h^2+5x+5h-2-(3x^2+5x-2)}{h}[/tex]Simplify:
[tex]\begin{gathered} f^{\prime}(x)=\lim_{h\to0}\frac{6xh+3h^2+5h}{h} \\ \therefore \\ f^{\prime}(x)=\lim_{h\to0}\frac{h(6x+3h+5)}{h} \\ f^{\prime}(x)=\lim_{h\to0}(6x+3h+5) \end{gathered}[/tex]Evaluate the limit:
[tex]f^{\prime}(x)=6x+5[/tex]Therefore, the derivative is:
[tex]f^{\prime}(x)=6x+5[/tex]Properties of EqualityUse properties to solve each equation for x.5. x + 9.8 = 14.2 6. 14x = 91 7. ⅓x = 24Like Terms Combine like terms in each expression8. ¼k + ¼m - ⅔k + 5/8m 9. -4b + 2w + (-4b) + 8w 10. 6 - 5z + 8 - 4z + 1
Answers
Question 5
x + 9.8 = 14.2
subtract 9.8 from both sides
x + 9.8 - 9.8 = 14.2 - 9.8
x = 4.4
Question 6
14x = 91
Divide both sides by coefficient of x
[tex]\begin{gathered} \frac{14x}{14}\text{ =}\frac{91}{14} \\ \\ x\text{ = 6.5} \\ \end{gathered}[/tex]Question 7
[tex]\begin{gathered} \frac{1}{3}x\text{ =24} \\ \\ Mul\text{tiply both sides by 3} \\ 3\text{ x }\frac{1}{3}x\text{ = 24 x 3} \\ \\ x\text{ = 72} \end{gathered}[/tex]Question 8
[tex]\begin{gathered} \frac{1}{4}k\text{ + }\frac{1}{4}m\text{ -}\frac{2}{3}k\text{ + }\frac{5}{8}m \\ \\ \text{collect like terms} \\ \\ \frac{1}{4}k\text{ -}\frac{2}{3}k\text{ +}\frac{1}{4}m\text{ +}\frac{5}{8}m \\ solve\text{ }\frac{1}{4}k\text{ -}\frac{2}{3}k\text{ } \\ \Rightarrow\text{ }\frac{3k\text{ - 8k}}{12} \\ \Rightarrow\frac{-5k}{12} \\ \text{Also for the m coefficient} \\ \frac{1}{4}m+\text{ }\frac{5}{8}m \\ \Rightarrow\text{ }\frac{2m\text{ + 5m}}{8} \\ \frac{7m}{8} \end{gathered}[/tex][tex]\begin{gathered} \text{Combining the m and k coeficient} \\ \frac{-5k}{12}+\frac{7m}{8} \end{gathered}[/tex]Question 9
-4b +2w + (-4b) + 8w
=> -4b + 2w - 4b + 8w
collect like terms
=> -4b -4b + 2w + 8w
=> -8b + 10w
Question 10
6 - 5z + 8 - 4z + 1
collect the like terms
=> 6 + 8 + 1 - 5z - 4z
=> 15 - 9z
comparing fractions 5th grade math 2/4 and 3/6 which one is greater or smaller
Answers
Explanation
The question wants us to select the option that is bigger or smaller
The fractions are
[tex]\frac{2}{4}\text{ and }\frac{3}{6}[/tex]To do so, we will have to simplify each fraction to its lowest term and then compare
This will be obtained as shown below
[tex]\frac{2}{4}=\frac{1}{2}[/tex]Also
[tex]\frac{3}{6}=\frac{1}{2}[/tex]Thus, we can see that
[tex]\begin{gathered} \frac{2}{4}=\frac{1}{2} \\ \text{and} \\ \frac{3}{6}=\frac{1}{2} \\ \\ \text{Thus} \\ \frac{2}{4}=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Hence, the two fractions are equal
Solve the equation 2x^2-x- 21 = 0 by factoring. Be sure to show each step and include your solutions in your answer.Enter your solutions and your work or explanations in the box provided.
Answers
Solution
- The question gives us the following quadratic equation:
[tex]2x^2-x-21=0[/tex]- In order to factorize the equation, we need to rewrite the quadratic equation's x-terms. In order to do this, we follow these steps:
[tex]undefined[/tex]Liz earns a salary of 2200 per month plus a commission of 4% of her sales she wants to earn at least $2,400 a month.enter an inequality to find out amount of cells that will meet her go identify what your variable represents into the commission rate as a decimal
Answers
Liz earns a salary of 2200 per month plus a commission of 4% of her sales she wants to earn at least $2,400 a month.enter an inequality to find out amount of cells that will meet her go identify what your variable represents into the commission rate as a decimal
Let
x -----> the amount of her sales
we have that
4%=4/100=0.04
so
The inequality that represent this situation is
[tex]2,200+0.04x\ge2,400[/tex]Make Sense and Preserve If you knew the length of DF in parallelogram DEFG, how would you find the length of DK? Explain.
Answers
If I am given the length of DF in the parallelogram DEFG, I can find the length of DK by dividing DF by 2. The reason being that the two diagonals bisect each other at angle 90 degrees. Note: to bisect means to divide into 2 equal lengths.
So,
DK = 1/2 of DF.
Hence, the correct answer is divide DF by 2 to get length DK.
Consider the following equation: 6x + 2y = 13A) Write the above equation in the form y = mx + b. Enter the values of m and b in theappropriate boxes below as integers or reduced fractions (in the form A/B.)Answer: y =2 +Preview m: ; Preview b:B) Use your answer in part (A) to find the ordered pair that lies on this line when x = 2.Answer: (2,Enter your answer as an integer or a reduced fraction in the form A/B.
Answers
Conider the equation given below;
[tex]6x+2y=13[/tex]To express this equation in the form
[tex]y=mx+b[/tex]We shall begin by making y the subject of the equation, a follows;
[tex]\begin{gathered} 6x+2y=13 \\ \text{Subtract 6x from both sides;} \\ 6x-6x+2y=13-6x \\ 2y=13-6x \\ \text{Divide both sides by 2, and you'll have;} \\ \frac{2y}{2}=\frac{13-6x}{2} \\ y=\frac{13-6x}{2} \\ \text{Simplify the right side;} \\ y=\frac{13}{2}-\frac{6x}{2} \\ y=\frac{13}{2}-3x \\ \text{Written in the slope-intercept form, it now becomes;} \\ y=-3x+\frac{13}{2} \end{gathered}[/tex]The values of m and b are;
[tex]\begin{gathered} y=mx+b \\ y=-3x+\frac{13}{2} \\ \text{Hence;} \\ m=-3,b=\frac{13}{2} \end{gathered}[/tex]Part B:
Therefore, for a point on this line where x = 2, we would have;
[tex]\begin{gathered} y=-3x+\frac{13}{2} \\ \text{Substitute for the value of x}=2 \\ y=-3(2)+\frac{13}{2} \\ y=-6+\frac{13}{2} \\ y=\frac{13}{2}-6 \\ \text{Take the LCM of both numbers and we'll now have;} \\ y=\frac{13-12}{2} \\ y=\frac{1}{2} \\ \text{Therefore the ordered pair would be;} \\ (2,\frac{1}{2}) \end{gathered}[/tex]ANSWER:
Part A;
[tex]y=-3x+\frac{13}{2}[/tex]Part B:
[tex](2,\frac{1}{2})[/tex]after the Sun the closest star to Earth is Proxima Centauri the next closest star is called Original can terrorist AKA Alpha Centauri Rachel Contreras is about 4.3 light years from Earth how many parsecs away is Virgil Contreras round your answer to the nearest tenth of a parsec
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
distance = 4.3 light years
distance => parsecs = ?
Step 02:
1 parsec = 3.26 light year
distance = 4.3 light year * (1 parsec / 3.26 light year)
= 1.319 parsecs
The answer is:
The distance is 1.3 parsecs.
(05.02 MC)Solve log x = 3.
Answers
We need to solve the equation:
[tex]logx=3[/tex]In order to do so, we can write:
[tex]e^{logx}=e^3[/tex]Now notice that the exponential is the inverse function of the logarithm. Thus:
[tex]e^{logx}=x[/tex]Therefore, we have:
[tex]x=e^3[/tex]Nick tried to evaluate 42 x 36 using partial products. His work is:42 X 36Step 1: 1.200 = 30 x 4 tensStep 2: 600 = 30 x 2 tensStep 3: 240 = 6 x 4 tensStep 4: 12 = 6 x 2 onesStep 5 2,052Find Nick's mistake.
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In order to calculate a partial product, we need to separate each digit from each number, then we multiply them similar to the distributive property:
[tex]\begin{gathered} 42=40+2 \\ 36=30+6 \\ 42\cdot36=(40+2)\cdot(30+6)=40\cdot30+40\cdot6+2\cdot30+2\cdot6 \end{gathered}[/tex]The mistake in Nick's steps was made in Step 2, where he multiplied 30 by 2 tens, that is, 30 by 20, resulting in 600. The correct product in this step should be 30 by 2 ones, that is, 30 by 2, resulting in 60.
6x+16+=2x+28solve for x
Answers
The given equation is
[tex]6x+16=2x+28[/tex]We want to solve the above equation for x.
The first step is to combine the like terms.
Bring the 2x to the left side of the equation and bring 16 to the right side of the equation.
[tex]6x-2x=28-16[/tex]Simplify the equation.
[tex]\begin{gathered} 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Therefore, the value of x is 3
The sales tax in fort worth, Texas is 8.25% . find the tax charged on a purchase of 26.52
Answers
Given data:
The sales tax is 8.25 %
Purchase = $26.52
To get the tax charged, we can apply the formula below:
[tex]\text{Tax chaged=Sales tax }\times\text{ Purchase}[/tex]Thus, applying the formula, we will obtain
[tex]\begin{gathered} \text{Tax charged =8.25\% }\times26.52 \\ =\frac{8.25}{100}\times26.52 \\ =\frac{218.79}{100} \\ =2.1879 \end{gathered}[/tex]This gives $2.19.
Hence, a tax of $2.19 will be charged on the purchase
I was given the answer but don’t really understand how it got to that answer—please explain!
Answers
Given:
The line is reflected across the y-axis.
The triangle is formed that is enclosed by two lines and the x-axis.
The triangle is,
In the above triangle, the base is 6+6=12 units. and heights is 3 unit.
[tex]\begin{gathered} A(\text{triangle)=}\frac{1}{2}\times height\times base \\ =\frac{1}{2}\times3\times12 \\ =18 \end{gathered}[/tex]Answer: 18 square unit.
mr jhonson buys 5 bottles of lemonade for the school picnic he buys 4 28 ounces bottles and 0ne 64 ounces bottle. using rounding to the nearest ten about how much lemonade does mr jhonson buy in all?
Answers
Mr. Johnson buys 5 bottles
The price of four lemonde is 28 ounces each
Total price of four lemonde =28*4
=112 ounces.
Price of ine lemondae is 64 ounces.
So, the total price is 64+112 ounces
Write the system of inequality for thisparagraph:Mary needs to purchase supplies ofanswer sheets and pencils for astandardized test to be given to the juniorsat her high school. The number of theanswer sheets needed is at least 5 morethan the number of pencils. The pencilscost $2 and the answer sheets cost $1.Mary's budget for these supplies allowsfor a maximum cost of $400.
Answers
Step 1
Let x represent the answer sheet and y represent the number of pencils
From the question;
[tex]\begin{gathered} x\ge5+y \\ x+2y\leq400 \end{gathered}[/tex]Therefore, the system of inequalities is from the paragraph is;
[tex]\begin{gathered} x\ge5+y \\ x+2y\leq400 \end{gathered}[/tex]what is the range of the function
Answers
The range of the function is defined as the set of values that the function can take.
Then, the set of values that the image or f(x) takes is the range.
In the case, the ste of values that are the image are: 2, 4, 9 and 16, so the range is {2,4,9,16}.
Answer: Option A = {2,4,9,16}
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.A. similar; SAS similarity; ΔTLMB. similar; SSS similarity; ΔTLMC. not similarD. similar; SAS similarity; ΔTML
Answers
Solution:
Given ΔTUV and ΔTLM;
Where the side are measure are as follow below
[tex]\begin{gathered} TU=24\text{ units} \\ TV=36\text{ units} \\ TL=6\text{ units} \\ TM=9\text{ units} \end{gathered}[/tex]The ratio of the sides, applying the proportionality formula will be
[tex]\begin{gathered} \frac{TL}{TU}=\frac{6}{24}=\frac{1}{4} \\ \frac{TM}{TV}=\frac{9}{36}=\frac{1}{4} \\ \frac{TL}{TU}=\frac{TM}{TV}=\frac{1}{4} \end{gathered}[/tex]From the deductions above,
The sides are similar.
And
[tex]m\angle UTV=m\angle LTM\text{ \lparen verticala angles\rparen}[/tex]Since, an angle is included, then
Then, they are similar and ΔTUV is similar to ΔTLM.
Hence, the triangles are similar; SAS similarity; ΔTLM
The answer is option A
2. (08.01 MC)A cone has a volume of 5 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? (1 point)15 in^320 in^325 in^3 30 in^3
Answers
According to the information given in the exercise, the volume of a cone is:
[tex]V_{co}=5in^3[/tex]You need to remember that:
- The formula for calculating the volume of a cone is:
[tex]V_{co}=\frac{\pi r^2h}{3}[/tex]Where "r" is the radius and "h" is the height.
- The formula for calculating the volume of a cylinder is:
[tex]V_{cy}=\pi r^2h[/tex]Where "r" is the radius and "h" is the height of the cylinder.
In this case, you know that the cone fits exactly inside of the cylinder. That indicates that the height and the radius of both solids are equal.
Then to find the volume of the cylinder, you need to:
1. Substitute the volume of the cone into the formula for calculating the volume of a cone:
[tex]5in^3=\frac{\pi r^2h}{3}[/tex]2. Solve for:
[tex]\pi r^2h[/tex]Then, you get:
[tex]\begin{gathered} (3)(5in^3)=\pi r^2h \\ \\ 15^{}in^3=\pi r^2h \end{gathered}[/tex]3. Substitute that value into the formula for calculating the volume of a cylinder:
[tex]V_{cy}=15in^3[/tex]Hence, the answer is: First option.
Find the time it takes for $940,000 to double when invested at an annual interest rate of 18%, compounded continuously.
Answers
1)
Principal : 940,000
Future Value : 1,880,000
i= 18% = 0.18
Compounded Continuously
2) Let's use the formula for Compounded Interest, to express this exponential growth.
[tex]undefined[/tex]A consumer organization estimates that over a 1 year period 15% of cars will need to be repaired once, 8% will need repairs twice, and 3% will require three or more repairs. What is the probability that a car chosen at random will needNo repairs ______No more than 1 repair ______Some repairs ______
Answers
First of all we are being asked about the probability of a car not needing repairs. We will have to work with the percentages like fractions, for example a 15% chance would be 0.15.
The probability of picking a car that doesn't need repairs ( P(nr) ) can be calculated using the probability of car needing at least one repair ( P(r) ). There are two possible outcomes when you pick a car: or the car needs no repairs or it needs at least one. This means that sum of the probabilities of both outcomes is 1:
[tex]\begin{gathered} P(nr)+P(r)=1 \\ P(nr)=1-P(r) \end{gathered}[/tex]Now, the probability of needing at least 1 repairs P(r) is given by the sum of the probabilities of needing 1, 2, 3 or more repairs. These probabilities are given to us so:
[tex]P(r)=0.15+0.08+0.03=0.26[/tex]So the probability of needing no repairs is:
[tex]P(nr)=1-0.26=0.74[/tex]Writting as a percentage the probability of needing no repairs is 74%.
While solving this one we also find the solution for the third item since P(r) is the probability of needing some repairs. Since P(r)=0.26 then that probability is 26%.
For the second item we need to find the probability of needing no more than 1 repair. This probability is given by the probability of needing no repairs and the probability of needing one (and only one) repair. Then:
[tex]0.74+0.15=0.89[/tex]Therefore this probability is 89%.
In summary, the correct answers are 74%, 89% and 26% respectively.