The Quality loss function QLF incurred as a result of a deviation from a target setting is $17.5
How to determine the QLF for the lossesQLF is acronym for quality loss function, this solved using the formula
= kv^2
where
k = constant
v = mean square deviation = 1/5
the constant k is solved by the formula
= c/T^2
where
c = cost of item = 350
T = variation acceptable = 2
= 350 / 2^2
= 87.5
QLF = kv^2\
= 87.5 * 1/5
= 17.5
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What is the distance between -3 and 2 on the number line? O -5O -1O 1O 5
The distance between two numbers on the number line can be found by counting the units between those two numbers:
Also it's de difference between the greater number and the lower one:
[tex]2-(-3)=2+3=5[/tex]Many water bottles contain 16 fluid ounces, or 1 pint, of water. Drink labels often show the number of fluid ounces and the number of milliliters in a container. How many milliliters are in a 16-fluid-ounce drink?29.6 milliliters = 1 fluid ouncesPart A-D
Answer:
473.6 milliliters
Explanation:
A. One rate is the conversion factor
First, we know that 29.6 milliliters are equivalent to 1 fluid ounce, so the first rate of the conversion factor is:
[tex]\frac{29.6mL}{1\text{ fl oz}}[/tex]B. The other rate relates the known amount to the unknown converted amount
Then, we want to know how many milliliters are in 16 fluid ounces, so the other rate is:
[tex]\frac{x\text{ mL}}{16\text{ fl oz}}[/tex]C. Set the rates equal to one another.
[tex]\frac{29.6\text{ mL}}{1\text{ fl oz}}=\frac{x\text{ mL}}{16\text{ fl oz}}[/tex]D. multiply both parts of the left rate by a number that will make the number of fluid ounces in the two rates the same.
The number that will make the fluid ounces in the two rates the same is 16, so we need to multiply by 16
[tex]\frac{29.6\text{ mL x 16}}{1\text{ fl oz x 16}}=\frac{473.6\text{ mL}}{16\text{ fl oz}}[/tex]Therefore, there are about 473.6 milliliters in 16 fluid ounces.
Given the equation y = 3x + 8, what would the value of y be when x= 3?14O 151O 17
y = 3x + 8
When x = 3, we substitute the value of x into the equation
y = 3(3) + 8
y = 9 + 8
y = 17
You phone a plumber for a quote on fixing your leaky pipes. You are quoted $190 for the service call and $90 per hour for the work. You are on a budget and can afford no more then $460 . Write an inequality to find the number of hours of work h you can afford. ( assume h greater than or equal 0) then solve the inequality
We want to find h which represents the number of hours of work that you can afford.
From the information given,
The charge per hour of work is $90. This means that the charge for h hours of work is
90 x h = 90h
The service fee is $190. This is a constant fee that must be paid irrespective of the number of hours. Thus, the total cost of h hours of work is
90h + 190
Again, you are on a budget and can afford no more then $460. This means that the amount that you can spend is less than or equal to $460. the symbol for representing 'less than or equal to' is '≤'
Therefore, the inequality that will be used to find the number of hours of work h you can afford is
90h + 190 ≤ 460
To solve the inequality, we would subtract 190 from both sides of the inequality. We have
90h + 190 - 190 ≤ 460 - 190
90h ≤ 270
We would divide both sides of the inequality by 90. We have
90h/90 ≤ 270/90
h ≤ 3
What is the area, in square feet, of the trapezoid below?8.8 ft4 ft5-3 ft
We are asked to find the area of the trapezoid.
Recall that the area of the trapezoid is given by
[tex]A=\frac{1}{2}(b_1+b_2)\times h[/tex]Where b₁ is the length of base 1 that is 8.8 ft
b₂ is the length of base 2 that is 5.3 ft
h is the height that is 4 ft
Let us substitute the given values into the above formula
[tex]\begin{gathered} A=\frac{1}{2}(8.8+5.3)\times4 \\ A=\frac{1}{2}(14.1)\times4 \\ A=\frac{1}{2}(56.4)_{} \\ A=28.2ft^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 28.2 ft²
After paying $7 for a movie ticket Grace still had $3.75 how much money did Grace have before buying the ticket A. $3.25B. $10.25C. $4.52D. $10.75
D. $10.75
To solve this we have to write an equation:
Movie ticket price: $7
Money left : $3.75
Original amount: x
The original amount (x) minus the price of the ticket(7) must be equal to the money left after the purchase (3.75)
x-7 =3.75
Solving for x:
x = 3.75+7
x = 10.75
find each percent of change 50.5 and 75
Answer: 48.5%
Explanation:
The quantity 50.5 incresed to 75. The change in value is:
[tex]75-50.5=24.5[/tex]The change was 24.5, so we need to find what percentage of 50.5 is 24.5.
For this we can use the rule of three.
Quantity Percentage
50.5 ---> 100%
24.5 ---> x
this means that if 50.5 is the 100%, 24.5 is a percentage x. This percentage x is found using the rule of three by multiplying que cross quantities in the last table (24.5 by 100), and then dividing by the remaining amount (50.5).
Thus:
[tex]x=\frac{24.5\cdot100}{50.5}=\frac{2450}{50.5}=48.5[/tex]The percentage change between 50.5 and 75 is 48.5%
write an inequality to represent each situation. Do not solve the inequality. define the variable 3. Leslie is driving 850 miles home from vacation. She drives a constant speed of 65 miles per hour. She wants to stopfor the night when she is no more than 300 miles from home. How many hours will she need to drive?4. Steve earns $16 per hour plus $150 in bonuses. Carly earns $14 per hour and $200 in bonuses. After how many hourswill Steve's pay be more than Carly's?5. The science club is going on a field trip to the science museum. The club has at most $800 to spend on the trip. Thebus for the trip costs $100, and meals at the museum cost $4.50 per student. If admission to the museum is $12 perstudent and $16 per adult, and there are six chaperones attending, how many students can go on the trip?
According to the problem, Leslie will need to drive 850. As she is driving at a constant speed of 65 miles per hour, if you take h as the number of hours she drives, the distance she covers in h hours is 65h. She wants to stop when she is not more than 300 miles from home, which means that she wants to stop when the difference between 850 and 65h is less than or equal to 300.
This expressed as an inequality is:
[tex]850-65h\leq300[/tex]The area of the parallelogram is 273in squared what’s the height ?
The formula for determining the area of a parallelogram is expressed as
Area = base x height
Given that
base = 39
area = 273
Then,
273 = 39 x height
height = 273/39
height = 7 ft
If you will conduct a research about the poor study habits of Grade 7 students, how will you present your research problem using mathematical function?
I would define what a poor study habit is, using a parameter like study time in hours or days.
Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.
Let f(x) be the study habit of a particular grade, so we write:
Good study time as:
[tex]f(x)\ge2[/tex]Bad study time as:
[tex]f(x)<2[/tex]The last one can represent the study habits of Grade 7 students.
Evaluate each of the following. Illustrate with a point on the graph g(-2)=g(3)=g(0)=g(7)=
Solution
From the graph given we have this:
g(-2)= -3
g(3)= 4
g(0)= -3
g(7)= 0
Out of 50 students, 17 want pepperoni pizza, 19 want sausage pizza and the rest want a supreme pizza. What percent of the students want a supreme pizza?
First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:
[tex]x+17+19=50[/tex]solving for 'x', we get:
[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]we have that x = 14 students want a supreme pizza.
Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:
[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]therefore, 28% of the students want a supreme pizza
19. Which of the following regions represent the points in the solution of the inequality x ≤ 1? a. Left of the line x = 1 b. On and left of the line x = 1 c. On and right of the line x = 1 d. Right of the line x = 1
ANSWER
b. On and left of the line x = 1.
EXPLANATION
The inequality is x less than or equal to 1. This means that the line x = 1 is included in the solution, which leaves us with options b or c.
To represent the values less than x = 1, we would take the values to the left of the line.
Hence, the region that represents the solutions of x ≤ 1 is on and left of line x = 1.
Write the equation of the line on the graph.
Answer:
The correct equation is
[tex]y = - \frac{7}{5} x + 4[/tex]
Jim borrows $300 at 7% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
Answer:
[tex]I=\text{ \$187.62}[/tex]Step-by-step explanation:
Compounded interest is represented as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ P=\text{ principal } \\ r=\text{ interest rate} \\ n=\text{ times compounded per unit time} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, for a principal of $300 at 7% per annum compounded quarterly;
[tex]\begin{gathered} A=300\cdot(1+\frac{0.07}{4})^{4\cdot7} \\ A=487.62 \\ \text{Then, the interest due would be the subtraction of A-P} \\ I=487.62-300 \\ I=\text{ \$187.62} \end{gathered}[/tex]At basketball tryouts, Jeremiah will shoot a 1-point shot, 2-point shot, and a 3-point shot one after theother. The table below shows Jeremiah's probability of making each shot:ShotProbability of making1-point80%2-point50%3-point30%Assume the outcome of one shot doesn't change the probability of other shots.The coach will record the total points Jeremiah scores from these 3 shots.Which graph represents the theoretical probability distribution of Jeremiah's total points?Choose 1 answer:
The graph that represents the theoretical probability distribution of Jeremiah's total points is given by:
Graph A.
What is a probability distribution?The probability of an event in an experiment is calculated as the absolute frequency of the desired outcomes in the experiment divided by the total number of outcomes in the experiment.
The probability distribution gives the probability of all possible events in the context of the problem.
For Jeremiah to make zero points, he needs to:
Miss the 1 - point shot: 0.2 probability.Miss the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 1) = 0.2 x 0.5 x 0.7 = 0.07 = 7%.
For Jeremiah to make one point, he needs to:
Make the 1 - point shot: 0.8 probability.Miss the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 1) = 0.8 x 0.5 x 0.7 = 0.28 = 28%.
For Jeremiah to make two points, he needs to:
Miss the 1 - point shot: 0.2 probability.Make the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 2) = 0.2 x 0.5 x 0.7 = 0.07.
For Jeremiah to make three points, he needs to either:
Miss the 1 - point shot: 0.2 probability.Miss the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Or:
Make the 1 - point shot: 0.8 probability.Make the 2 - point shot: 0.5 probability.Miss the 3 - point show: 0.7 probability.Hence:
P(X = 3) = 0.2 x 0.5 x 0.3 + 0.8 x 0.5 x 0.7 = 0.31.
For Jeremiah to make four points, he needs to:
Make the 1 - point shot: 0.8 probability.Miss the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 4) = 0.8 x 0.5 x 0.3 = 0.12.
For Jeremiah to make five points, he needs to:
Miss the 1 - point shot: 0.2 probability.Make the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 5) = 0.2 x 0.5 x 0.3 = 0.03.
For Jeremiah to make six points, he needs to:
Make the 1 - point shot: 0.8 probability.Make the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 6) = 0.8 x 0.5 x 0.3 = 0.12.
Hence Graph A is correct, as it contains these probabilities.
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Which point has the coordinates (-2.5, 5.5)? A.point EB.point FC.point GD.point H
If △STU is similar to △XYZ, the sides of △STU must be congruent to thecorresponding sides of △XYZ.A. TrueB. False
Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
[tex]\frac{ST}{XY}=\frac{TU}{YZ}=\frac{SU}{XZ}[/tex]The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
what digit is in the
Explanation:
A.
1. We did not start with 1 because 1 is less than 3. Because of that, we start with 16. 16 divide by 3 = 5.
2. 5 times 3 = 15
3. 16 minus 15 = 1.
B.
1. Since 1 is again less than 3, we brought down another 6. The new dividend is 16. 16 divide by 3 = 5.
2. 5 times 3 = 15
3. 16 minus 15 = 1.
C.
1. Again, 1 is less than 3. We bring down the next number which is 2. The new dividend is now 12. 12 divided by 3 = 4.
2. 4 times 3 = 12.
3. 12 minus 12 = 0
D.
1. Again, zero is less than 3. We bring down the last number 4. The new dividend is 4. 4 divided by 3 = 1.
2. 1 times 3 = 3.
3. 4 minus 3 = 1. Since there is no more number to bring down, 1 is the remainder.
The answer for this division is 5 541 with a remainder of 1.
1. You invest $28,000 into an account earning 9.3% interest compounded monthly. This interest is used for both parts.A. How much money is in the account after 5 years? Be sure to show the formula you used with the numbers plugged in to find the solution.B. How much money is in the account after 29 years? Be sure to show the equation you used with the numbers plugged in to find the solution.
A.
In order to calculate the amount after 5 years for compound interest, we can use the formula:
[tex]P=P_0\cdot(1+\frac{i}{n})^{nt}[/tex]Where P is the final amount after t years, P0 is the initial value, i is the interest rate and n depends on the compound period (since it's monthly, let's use n = 12).
So we have:
[tex]\begin{gathered} P=28000(1+\frac{0.093}{12})^{5\cdot12} \\ P=28000\cdot(1+0.00775)^{60} \\ P=44496.56 \end{gathered}[/tex]B.
For t = 29, we have:
[tex]\begin{gathered} P=28000\cdot(1.00775)^{12\cdot29} \\ P=411088.01 \end{gathered}[/tex]TRIGfind the following in triangle CAT.lineAT is 16.5angleT is 43degrees how do I solve?
h= 22.6, CT =47º, CA=15.4
1) We're going to use trig ratios for that. So to find CT, the hypotenuse, and considering the angle 43º as our reference, we can write:
[tex]\begin{gathered} \cos (43)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (43)\text{ =}\frac{16.5}{h} \\ \cos (43)h=16.5 \\ h=\frac{16.5}{\cos (43)} \\ h=22.5609\approx22.6 \end{gathered}[/tex]So the CT is equal approximately to 22.6.
2) Now let's find out the measure of angle C. The simplest way is to consider the fact that every triangle has the sum of its interior angles as 180º
90º +43º + C = 180º
133º + C = 180º
C =180º -133º
C = 47º
3) Let's focus on CA leg.
Concerning that, we can make use of another trig ratio. Since we know the measure of angle C
[tex]\begin{gathered} \tan (47)=\frac{opposite}{\text{adjacent}} \\ \tan (47)\text{ =}\frac{16.5}{CA} \\ CA=\frac{16.5}{\tan (47)} \\ CA\text{ =15.38649}\approx15.4 \end{gathered}[/tex]CA is approximately 15.4
A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the number of points, p, the bowler scores also increased. The equation for the line of best fit for the data is p = 25s + 40. Estimate the number of strikes made by a bowler with 140 points. A) 4B) 6C) 25D) 40
The model variables the relationship between the strikes (s) and the number of points scored (p)
[tex]p=25s+40[/tex]To determine the number of strikes made, so that 140 points where scored, you have to replace the model with p=140 and solve for s
[tex]140=25s+40[/tex]The first step is to pass "40" to the others side of the equal sing, by performing the inverse operation "-40" to both sides of the expression
[tex]\begin{gathered} 140-40=25s+40-40 \\ 100=25s \end{gathered}[/tex]Then you have to divide both sides of the expression by 25 to determine the value of s
[tex]\begin{gathered} \frac{100}{25}=\frac{25s}{25} \\ 4=s \end{gathered}[/tex]The bowler made s=4 strikes, the correct choice is A.
3|x + 1| - 9 = 0? Solution set?
x = (2, -4)
Explanation:Given:
[tex]\begin{gathered} 3|x+1|-9=0 \\ \\ 3|x+1|=9 \\ \\ |x+1|=3 \\ \\ x+1=3 \\ \Rightarrow x=2 \\ \\ OR \\ -(x+1)=3 \\ \\ -x-1=3 \\ \\ -x=3+1 \\ \\ -x=4 \\ \\ x=-4 \end{gathered}[/tex]x = (2, -4)
What is the slope of the line that passes through the points (9, 5) and (21,-5)?
The equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
How does the slope intercept form made?The slope-intercept form of an a line is a method of writing the equation of a line so that the slope as well as y-intercept are easily identifiable.The the line's slope represents its steepness, and also the y-intercept is the point at which the line intersects a y-axis.For the given question;
The line passes through points are-
(x1, y1) =(9, 5) and
(x2, y2) = (21,-5)
Slope = m = (y2 - y1)/(x2 - x1)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Equation of the line is found using slope intercept form.
y - y1 = m (x - x1)
y - 5 = (-5/6)(x - 9)
y = (-5/6)x - 25/2
Thus, the equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
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writing exponential functions (4, 112/81), (-1, 21/2)
The given points are (4, 112/81) and (-1, 21/2).
To find an exponential function from the given points, we have to use the forms.
[tex]\begin{gathered} y_1=ab^{x_1} \\ y_2=ab^{x_2} \end{gathered}[/tex]Now, we replace each point in each equation.
[tex]\begin{gathered} \frac{112}{81}=ab^4 \\ \frac{21}{8}=ab^{-1} \end{gathered}[/tex]We solve this system of equations.
Let's isolate a in the second equation.
[tex]\begin{gathered} \frac{21}{8}=\frac{a}{b} \\ \frac{21b}{8}=a \end{gathered}[/tex]Then, we replace it in the first equation
[tex]\frac{112}{81}=(\frac{21b}{8})\cdot b^4[/tex]We solve for b.
[tex]\begin{gathered} \frac{112\cdot8}{81\cdot21}=b\cdot b^4 \\ \frac{896}{1701}=b^5 \\ b=\sqrt[5]{\frac{896}{1701}}=\frac{2\sqrt[5]{4}}{3} \\ b\approx0.88 \end{gathered}[/tex]Once we have the base of the exponential function, we look for the coefficient a.
[tex]a=\frac{21b}{8}=\frac{21}{8}(\frac{2\sqrt[5]{4}}{3})=\frac{7\sqrt[5]{4}}{4}[/tex]Therefore, the exponential function is[tex]y=\frac{7\sqrt[5]{4}}{4}\cdot(\frac{2\sqrt[5]{4}}{3})^x[/tex]The image below shows the graph of this function.
Properties of Equality Addition Property of Equality Subtraction Property of Equality For real numbers a, b, and c, if a = b, For real numbers o, b, and c, if a = b, then a +C= then a-c= Multiplication Property of Equality Division Property of Equality For real numbers a, b, andc, if a = b and For real numbers o, b, and c, ifo =b and cz0, C0, then a c then = C
y = -9
Explanation:
we simplify the expression to get y: 2/3 y + 15 = 9
[tex]\begin{gathered} \frac{2}{3}y\text{ + 15 = 9} \\ \text{Subtract both sides }by\text{ 15} \\ \frac{2}{3}y\text{ + 15 -15 = 9 - 15} \\ \text{This is a subtraction property of equality} \\ \frac{2}{3}y\text{ = -}6 \end{gathered}[/tex][tex]\begin{gathered} \text{Multiply both sides by the inverse of }the\text{ coefficient of y} \\ \text{coefficent of y = 2/3 } \\ inverse\text{ of the }coefficent\text{ of y = 2/3} \\ \frac{2}{3}y\times\frac{3}{2}\text{ = -6}\times\text{ }\frac{3}{2} \\ it\text{ is a Multiplication property of equality: }a\times c\text{ = b}\times\text{ c} \\ y\text{ = -18/2} \\ \end{gathered}[/tex][tex]y\text{ = -9 }[/tex]The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238 . Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size =500 of young adults ages 20–39 in the United States.Use a normal approximation to find the probability that the number of individuals, , in Lance's sample who regularly skip breakfast is greater than 124 .(>124)= (Round to 3 decimal places)
Answer
The answer is 0.300
Problem Statement
We are asked to find the probability that the number of individuals in a survey of 500 people would skip breakfast given that the proportion of people who skip breakfast, in general, is 0.238.
Method
- The proportion of people greater than 124 out of 500 is easily gotten to be:
[tex]\begin{gathered} p>\frac{124}{500} \\ p>0.248 \end{gathered}[/tex]- We now need to know the probability that the proportion of people that skip breakfast would be greater than 0.248.
- To calculate this probability, we need to find the Z-score associated with this value. This is a good way to approximate the probability because the number of people in the survey is well above 30 and we have been told to apply a normal approximation.
- Once we have the Z-score associated with this proportion of 0.248 in relation to the general population proportion statistic of 0.238, we can then convert the Z-score into a probability using a Z-score calculator or a Z-table.
- If the Z-score is "z", then, the probability we are looking for on the Z-score table or calculator is P(x > z).
- Thus, we can solve the question using the following steps:
1. Calculate the Z-score using the formula below:
[tex]\begin{gathered} z=\frac{p-p_0}{\sqrt[]{\frac{p_0(1-p_0)}{n}}} \\ \\ \text{where,} \\ p=\text{sample proportion} \\ p_0=\text{population proportion} \\ n=\text{ Total number of people in the survey} \end{gathered}[/tex]2. Convert the Z-score into probability
Implementation
Step 1: Calculate the Z-score:
[tex]\begin{gathered} p=0.248,p_0=0.238 \\ \\ z=\frac{0.248-0.238}{\sqrt[]{\frac{0.238(1-0.238)}{500}}} \\ \\ z=\frac{0.01}{0.019045} \\ \\ z=0.5251 \end{gathered}[/tex]2. Convert the Z-score into probability:
Using the Z-score calculator, we have:
Because we are asked to find the probability that the number of people who skipped breakfast is greater than 124, the correct probability here is P(x > Z).
Thus, the probability that the number of individuals that skipped breakfast is greater than 124 is 0.29977 ≅ 0.300 (To 3 decimal places)
Final Answer
The answer is 0.300.
A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Problem
A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Solution
For this case we can find the total number of apples like this:
4+7+5= 16 apples
And the number of apples not red are:
4 + 5= 9 apples
Then the probability of being not red would be:
p = 9/16
why aren't 38 and 40 relatively prime
No they aren't relatively because they don't come from the same prime number
during 24 ow much hours Allan spend lisining music
spendlisteningSolution
Note: we need to find the time he will be using for listenng to music and playing Tennis and then subtract them
[tex]\begin{gathered} 1)\text{Time use for listening to music : } \\ \frac{12}{100}\times\text{ 24 = }\frac{288}{100}\text{ = 2.88hours} \\ \\ 2)\text{Time spendth in playing Tennis} \\ \frac{10}{100}\times24\text{ = }\frac{240}{100}=\text{ 2.4hours} \\ \\ \text{Difference in time = }2.88\text{ - 2.4} \\ \text{ = 0.48} \\ \text{Answer = 0.48 hour.} \end{gathered}[/tex]