Explanation
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication,hence
Let's check every option
Step 1
a)
[tex]\begin{gathered} (10+5)\cdot(30+6)=15\cdot36 \\ \end{gathered}[/tex]this does not show the commutative property
b)
[tex]\begin{gathered} 36\cdot15=15\cdot36 \\ \end{gathered}[/tex]as we can see the factor were moved, and by the commutative property the result is not afected, so
[tex]\begin{gathered} \\ 36\cdot15=15\cdot36 \end{gathered}[/tex]is the answer.
I hope this helps you
cube A has a volume of 125 cubic inches The Edge length of cube B measures 4.8 inches. which group is larger and why?select the corrects responses1. Cube A, because it's volume is greater than the volume of cube B 2. Cube A, because its surface area is greater than the volume of cube B 3. Cube B, because it's volume is greater than the volume of cube A4. Cube B, because its side length is greater than the side length of cube A
Answer:
1. Cube A, because it's volume is greater than the volume of cube B
Explanation:
Cube A
Volume = 125 cubic inches
[tex]\begin{gathered} \text{Volume}=s^3(s=\text{side length)} \\ 125=s^3 \\ s^3=125 \\ s^3=5^3 \\ s=5\text{ inches} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \text{Surface Area=}6s^2 \\ =6(5)^2 \\ =6\times25 \\ =150\text{ square inches} \end{gathered}[/tex]Cube B
The edge length, s = 4.8 inches.
[tex]\begin{gathered} \text{Volume}=4.8^3=110.592\text{ cubic inches} \\ \text{Surface Area=}6(4.8)^2=138.24\text{ cubic inches} \end{gathered}[/tex]We see that Cube A is the larger group because it's volume is greater than the volume of cube B.
what is the slope of the line that passes through the points of (5,3) (5.-9)
Answer:
undefined
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-9 - 3)/(5 - 5)
slope = -12/0
Since the slope calculation involves division by zero, this line has undefined slope. The two points have the same x-coordinate, so the line is vertical. The slope of a vertical line is undefined.
Carlos is adding insulation to a room he just finished framing in his home. The room is 16ft. by 12ft., and the ceilings are 9ft. tall. There are two windows in the room measuring 5ft. by 6ft. each. How many square feet of insulation does Carlos need?
Solution
Now
[tex]A=2(16\times12)+2(16\times9)+2(9\times12)-2(5\times6)[/tex][tex]828ft^2[/tex]square feet of insulation Carlos need is
[tex]828ft^2[/tex]Calculate the five-number summary of the given data. Use the approximation method.19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Answer:
Explanation:
Given the data:
19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Step 1: Write in an order (we are writing in an ascending order here)
2, 2, 2, 4, 8, 8, 10, 11, 16, 18, 19, 20, 23, 25,
1. Write the equation of the line with a slope of -3 that passes through the point (1,9).y=3x + 12y=3x + 6y=-32 +6y=-3x+12
Answer:
y = -3x + 12
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing m by -3, and (x1, y1) by (1, 9), we get:
[tex]y-9=-3(x-1)[/tex]Finally, solving for y, we get:
[tex]\begin{gathered} y-9=-3x-3(-1) \\ y-9=-3x+3 \\ y-9+9=-3x+3+9 \\ y=-3x+12 \end{gathered}[/tex]Therefore, the answer is:
y = -3x + 12
A can of diced tomatoes has a height of 11.5 cm and a diameter of 10 cm. What is the volume of the can? Use 3.14 for pie.DO NOT round your answer.
Answer:
902.75 cubic cm.
Explanation:
Given a can with:
• Height, h = 11.5 cm
,• Diameter = 10 cm
A can is in the shape of a cylinder; and the volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]First, find the radius by dividing the diameter by 2.
[tex]r=\frac{10}{2}=5\;cm[/tex]Next, substitute r=5, h=11.5 and π=3.14 into the formula given above:
[tex]\begin{gathered} V=3.14\times5^2\times11.5 \\ =902.75\text{ cubic cm} \end{gathered}[/tex]The volume of the can is 902.75 cubic cm.
A population forms a normal distribution with a meanof μ = 85 and a standard deviation of o = 24. Foreach of the following samples, compute the z-score forthe sample mean.a. M=91 for n = 4 scoresb. M=91 for n = 9 scoresc. M=91 for n = 16 scoresd. M-91 for n = 36 scores
In this problem, we have a population with a normal distribution with:
• mean μ = 85,
,• standard deviation σ = 24.
We must compute the z-score for different samples.
The standard deviation of a sample with mean M and size n is:
[tex]σ_M=\frac{σ}{\sqrt{n}}.[/tex]The z-score of the sample is given by:
[tex]z(M,n)=\frac{M-\mu}{\sigma_M}=\sqrt{n}\cdot(\frac{M-\mu}{\sigma})[/tex]Using these formulas, we compute the z-score of each sample:
(a) M = 91, n = 4
[tex]z(91,4)=\sqrt{4}\cdot(\frac{91-85}{24})=0.5.[/tex](b) M = 91, n = 9
[tex]z(91,9)=\sqrt{9}\cdot(\frac{91-85}{24})=0.75.[/tex](c) M = 91, n = 16
[tex]z(91,16)=\sqrt{16}\cdot(\frac{91-85}{24})=1.[/tex](d) M = 91, n = 36
[tex]z(91,9)=\sqrt{36}\cdot(\frac{91-85}{24})=1.5.[/tex]Answera. z = 0.5
b. z = 0.75
c. z = 1
d. z = 1.5
What are the coordinates of A B C after a Dilation with a scale factor of 1/2 followed by a reflection over the x-axis
In general, a dilation is the outcome of applying the following transformation on a point,
[tex]D(x,y)\to(kx,ky)[/tex]Where k is the scale factor, this kind of dilation is about the origin, and we will use it since the problem does not specify otherwise.
In our case, the transformation is
[tex]D(x,y)\to(\frac{x}{2},\frac{y}{2})[/tex]Then,
[tex]\begin{gathered} D(A)=D(-6,5)\to(-3,\frac{5}{2}) \\ D(B)=D(3,2)\to(\frac{3}{2},1)_{} \\ D(C)=D(0,-1)\to(0,-\frac{1}{2}) \end{gathered}[/tex]On the other hand, a reflection over the x-axis is given by the following transformation.
[tex](x,y)\to R_x(x,y)=(x,-y)[/tex]Then, in our case,
[tex]\begin{gathered} A^{\prime}=R_x(-3,\frac{5}{2})=(-3,-\frac{5}{2}) \\ B´=R_x(\frac{3}{2},1)=(\frac{3}{2},-1) \\ C^{\prime}=R_x(0,-\frac{1}{2})=(0,\frac{1}{2}) \end{gathered}[/tex]Thus, the answers are
A'=(-3,-5/2)
B'=(3/2,-1)
C'=(0,1/2)
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Problem
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Solution
For this case we can find the real price with this operation:
95+265= 360
And the rate of discount can be founded as:
(95/265)*100= 35.85%
Rounded to the nearest percent would be 36%
Find a standard form of the equation for the circle with the following property
Solution:
Given:
[tex]Endpoints\text{ }(-7,5)\text{ and }(-5,-1)[/tex]To get the equation of the circle, the center of the circle and the radius are needed.
The center of the circle is the midpoint of the endpoints.
Using the midpoint formula;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} M=(\frac{-7+(-5)}{2},\frac{5+(-1)}{2}) \\ M=(\frac{-12}{2},\frac{4}{2}) \\ M=(-6,2) \end{gathered}[/tex]Hence, the coordinates of the center of the circle is (-6,2)
The length of the diameter can be gotten using the distance between two points formula;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \\ Hence, \\ d=\sqrt{(-5-(-7))^2+(-1-5)^2} \\ d=\sqrt{2^2+(-6)^2} \\ d=\sqrt{4+36} \\ d=\sqrt{40} \end{gathered}[/tex]The diameter is twice the radius. Hence, the radius is;
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{\sqrt{40}}{2}=\frac{2\sqrt{10}}{2} \\ r=\sqrt{10} \end{gathered}[/tex]Hence, the equation of the circle with center (-6,2)
[tex]with\text{ radius }\sqrt{10}[/tex]Using the standard form of the equation of a circle;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where: \\ (h,k)\text{ }is\text{ }the\text{ center} \\ r\text{ is the radius} \\ h=-6 \\ k=2 \\ r=\sqrt{10} \end{gathered}[/tex]Hence, the equation is;
[tex]\begin{gathered} (x-(-6))^2+(y-2)^2=(\sqrt{10})^2 \\ (x+6)^2+(y-2)^2=10 \end{gathered}[/tex]Therefore, the equation of the circle is;
[tex](x+6)^{2}+(y-2)^{2}=10[/tex]
Hi, could I have some help answering this question in the picture attached?simplify the question
Expand and collect like terms:
[tex]\begin{gathered} =\text{ }7s^{\frac{7}{4}}\times t^{\frac{-5}{3}}\times-6s^{\frac{-11}{4}}\times t^{\frac{7}{3}} \\ =\text{ }7\times s^{\frac{7}{4}}\times-6\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \\ =\text{ 7 }\times-6\text{ }\times\text{ }s^{\frac{7}{4}}\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \\ =\text{ -42}\times\text{ }s^{\frac{7}{4}}\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \end{gathered}[/tex]Bring the exponents having same base together:
[tex]\begin{gathered} \text{The multiplication betwe}en\text{ same base becomes addition } \\ \text{when the exponents are brought together} \\ =-42\text{ }\times\text{ }s^{\frac{7}{4}-\frac{11}{4}}\times t^{\frac{-5}{3}+\frac{7}{3}} \\ =\text{ -42 }\times s^{\frac{7-11}{4}}\times t^{\frac{-5+7}{3}} \\ =\text{ -42 }\times s^{\frac{-4}{4}}\times t^{\frac{2}{3}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ -42 }\times s^{\frac{-4}{4}}\times t^{\frac{2}{3}} \\ =\text{ -42 }\times s^{-1}\times t^{\frac{2}{3}} \\ =\text{ -42}s^{-1}t^{\frac{2}{3}} \end{gathered}[/tex]Find any value of x that makes the equation x + 100 = x - 100 true.
Since the sides are the same, this problem is unsolvable
The circumference of a circle is 278.71m. What is the approximate area of the circle? Use 3.14 for pi. Explain how the area of a circle changes when the circumference of a circle changes ( round the final answer to the nearest whole number as needed , round all the intermediate values to the nearest thousandth as needed )
The circumference of a circle can be found through the formula:
[tex]C=2\cdot\pi\cdot r[/tex]clear the equation for the radius
[tex]r=\frac{C}{2\pi}[/tex]find the radius of the circumference
[tex]\begin{gathered} r=\frac{278.71}{2\pi} \\ r\approx44.358 \end{gathered}[/tex]find the area of the circle using the formula
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot(44.358)^2 \\ A\approx6181 \end{gathered}[/tex]Andrew says the scale factor used was 3\2. Annie says the scale factor used was 2\3.Which student is correct and why?
Answer:
Annie is right, beause the coordinates of the points A'B'C' are 2/3 of the coodinates of the points ABC
and the size of the triangle A'B'C' is 2/3 of the size of the triangle ABC
for example:
Side AC lenght is 6 units and A'C' is 4
To go from 6 to 4, the factor must be 2/3
translating words into algebraic symbols its not -70 or -7
translating words into algebraic symbols
a number x = x
decreased by seventy = -7
y= x-70
___________________
Answer
x-70
You need a shelf for a small space in your house, so you make a measurement with your meter stick and head to the store. Once there, you find that the dimension of the shelves you want is given in cm.If your space measured 0.9 m, and the shelves at the store measure 30 cm, answer the following questions:1) How many meters wide is the shelf you want to buy?
We will have the following:
[tex]0.9m=90cm[/tex]So, the number of shelves you need is 3.
Thus, the shelves you can buy are 0.3 m long each.
the 9th term of arithmetic sequence. Use the formula for 'an' to find 'a20', the 20th term of the sequence 7,3,-1,-5
We will find the value of the 20th term of the sequence 7, 3, -1, and -5.
We have the following sequence:
[tex]7,3,-1,-5[/tex]Finding the common differenceIf we have an arithmetic sequence here, we need to find the common difference for this sequence, and we can do that by finding the difference between the second term and the first term, the difference between the third term and the second term, and so on. If we obtain the same value for the common difference, we have an arithmetic sequence here.
Then we have:
[tex]\begin{gathered} d=3-7=-4 \\ \\ d=-1-3=-4 \\ \\ d=-5-(-1)=-5+1=-4 \end{gathered}[/tex]Then the common difference in this arithmetic sequence is d = -4.
Finding the formula for the arithmetic sequenceWe know that the explicit formula for an arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]For this case, we have that d = -4, and that the first term, a1 = 7. Then we have the formula for the arithmetic sequence:
[tex]a_n=7+(n-1)(-4)[/tex]Notice that we can expand this expression as follows:
[tex]\begin{gathered} a_n=7+(-4)(n)+(-4)(-1) \\ \\ a_n=7-4n+4 \\ \\ a_n=11-4n \\ \end{gathered}[/tex]Finding the 20th termThen to find the 20th term of the sequence, we have:
[tex]\begin{gathered} a_{20}=7+(20-1)(-4) \\ \\ a_{20}=7+(19)(-4) \\ \\ a_{20}=7-76=-69 \\ \\ a_{20}=-69 \end{gathered}[/tex]Therefore, in summary, we have that the value for the 20th term of the sequence 7, 3, -1, and -5 is -69.
,
If L = 4 inches and KL = 7 inches, what is the length of the diameter JK? Round your answer to at least the nearest hundredth of an inch (2 decimal places).
We have a right triangle and two sides we will use the Pythagorean theorem in order to find the missing side
[tex]c^2=a^2+b^2[/tex]a=7 in
b= 4 in
c=JK
we substitute the values
[tex]JK=\sqrt[]{7^2+4^2}[/tex][tex]JK=8.06[/tex]5. Jeannette has $5 and $10 bills in her wallet. The number of fives iseight more than five times the number of tens. Let t represent theNumber of tens. Write an expression for the number of fives.
The number of fives is eight more than five times the number of tens.
Therefore,
[tex]F=5\cdot T+8[/tex]where F represents the number of fives and T the number of tens
The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Find the probability of wearing a seat belt, given that the driver did not survive a car accident. Part 1: The probability as a decimal is _ (Round to 3 decimal places as needed.) Part 2: The probability as a fraction is _
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.
Let's call:
A = The event of the driver wearing a seat belt in a car accident.
B = The event of the driver dying in a car accident
The conditional probability is calculated as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.
The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.
From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:
[tex]P(A\cap B)=\frac{511}{583,470}[/tex]The probability of B is:
[tex]P(B)=\frac{2217}{583,470}[/tex]The required probability is:
[tex]P(A|B)=\frac{\frac{511}{583,470}}{\frac{2217}{583,470}}[/tex]Simplifying the common denominators:
[tex]P(A|B)=\frac{511}{2217}=0.230[/tex]Which statements are true?Select all that apply.A.The slope of AC is equal to the slope of BC.B.The slope of AC is equal to the slope of BD.C.The slope of AC is equal to the slope of line t.D.ECThe slope of line t is equal toAEE.FBThe slope of line t is equal toFDF.The slope of line t is equal to AB
Line t, segments AC, BC and BD are colinear, that is, all of them are in the same line. Then, the true statements are
A, B, and C
Please step-by-step help me how much of a circle is shaded
The given data is ratio from the the total are of circle is 1 .
let the shaded area is x then:
All area is equal to one.
[tex]\begin{gathered} \frac{1}{2}+\frac{2}{9}+x=1 \\ \frac{9+4}{18}+x=1 \\ \frac{13}{18}+x=1 \\ x=1-\frac{13}{18} \\ x=\frac{18-13}{18} \\ x=\frac{5}{18} \end{gathered}[/tex]So area of shaded region is
[tex]\frac{5}{18}[/tex]You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 4 minutes and you record the data point of (12,y), what is the value of y? Use slope to justify your answer
Answer:
51
Step-by-step explanation:
so we can use the variable x for minutes & y for water level. (4,17) is what we start with. its asking after 12 minutes what is the water level, 4 x 3 is 12 so we would multiply 17 x 3 as well which is 51.
shron spent 1 1/4 hours reading her book report and 2 2/5 hours doing her other homework. how much longer did sharon spent doing her homework than reading her book report
sharon spent 23/20 hour doing her homework than reading.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Sharon spent reading the book = [tex]1 \frac{1}{4}[/tex] = 5/4 hours
= 25/20 hours
Sharon spend doing homework = [tex]2 \frac{2}{5}[/tex] = 12/5 hours
= 48/20 hours
So, the difference between both activities
= 48/20- 25/20
= 23/20
Hence, sharon spent 23/20 hour doing her homework than reading.
Learn more about fraction here:
https://brainly.com/question/10354322
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Which is the best interpretation of the averagerate of change of this function?
We can calculate the rate of change as the slope between two points, like (1,2) and (2,4).
The slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{2-1}=\frac{2}{1}=2[/tex]If this is a linear function, this slope m has to be constant.
We will calculate the slope between other points, like (3,8) and (4,16):
[tex]m=\frac{y_4-y_3}{x_4-x_3}=\frac{16-8}{4-3}=\frac{8}{1}=8[/tex]The slope is not constant, so this function is not a linear function.
If we look at how f(x) increases, we can prove that f(x) is:
[tex]f(x)=2^x[/tex]and this function is an exponential function.
Answer: Option B (exponential function).
Determine the function that represents the following tables. Time (seconds) 1, 4, 7, 10, 13, the Distance (miles) 5 20 35 50 65.
the function is d= f(t)
when t1= 1 , d1= 5
when t2= 4, d2= 20
[tex]\text{rate od change = }\frac{d_2-d_1}{t_2-t_1}[/tex][tex]\text{rate of change = }\frac{20-5}{4-1}=\text{ }\frac{15}{3}=\text{ 5}[/tex][tex]\begin{gathered} ifd_{2\text{ }}=20,d_{3\text{ }}=35,t_{2\text{ }}=4,t_{3\text{ }}=7 \\ \text{rate of change = }\frac{d_3-d_2}{t_3-t_2}\text{ = }\frac{35-20}{7-4}=\text{ }\frac{15}{3}=\text{ 5} \end{gathered}[/tex]Thus if d is a function of t
and the rate of change is constant
then d = 5t is the function
Find a polynomial function with real coefficients that has the given zeros
1 -√3i, 2
Answer:
[tex]x^3-4x^2+8x-8[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(x-(1-\sqrt{3} i)(x-(1+\sqrt{3} i)(x-2)=\\\\(x^2-(1-\sqrt{3} i)x-(1+\sqrt{3} i)x+(1-\sqrt{3} i)(1+\sqrt{3} i))(x-2)=\\\\(x^2-x+\sqrt{3} i-x-\sqrt{3} i+1-(\sqrt{3} i)^2)(x-2)=\\\\(x^2-2x-3\cdot(-1))(x-2)=\\\\(x^2-2x+4)(x-2)=\\\\x^3-2x^2+4x-2x^2+4x-8=\\\\x^3-4x^2+8x-8[/tex]
114. If plane X averages 800 mph and plane Y averages 400 mph, how manyhours will plane X travel before it overtakes plane Y if plane Y has a 2 hourand 30 minute head start?a.1b. 2c. 5d. 72
To determine the time taken for the plane X to travel:
If plane X averages 800 mph and plane Y averages 400 mph
Distance column is found by multiplying the rate
by time.
The time taken for plane Y to travel = 2hr 30 minutes = 2.5hrs head start
Be sure to distribute the 400(t +2.5)for Plane Y,
and Plane X to distribute 800t
As they cover the same distance
[tex]\begin{gathered} Dis\tan ce\text{ is equal ,} \\ 800t=400(t+2.5) \\ 800t=400t+1000 \\ 800t-400t=1000 \\ 400t=1000 \\ t=\frac{1000}{400} \\ t=2\frac{1}{2}hr \end{gathered}[/tex]Therefore the plane X will travel for 2 1/2 hours
Hence the correct answer is Option B
A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walkercharge for a 45 minute walk? Write an equation in function notation for the situation, and then use it tosolve the problem. Determine if the given statement is True or False.
hello
from the question given, the dog walker charges a flat rate of $6 and an extra $30 per hour.
we can write out an equation in function notation
let the number of hours be represented by x
[tex]f(x)=6+30x[/tex]now we can proceed to solve the cost of the walk for 45 minutes
[tex]\begin{gathered} 1hr=60\min s \\ \text{xhr}=45\min s \\ x=\frac{45}{60} \\ x=\frac{3}{4} \\ \text{therefore 45mins = 3/4 hours} \end{gathered}[/tex]now we can input the value into the equation and know the cost for 45 minutes walk
[tex]\begin{gathered} f(x)=6+30x \\ x=\frac{3}{4} \\ f(x)=6+30(\frac{3}{4}) \\ f(x)=6+22.5 \\ f(x)=28.5 \end{gathered}[/tex]from the calculation above, the cost of 45 minutes walk will cost $28.5
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.9 ppm and standard deviation 1.8 ppm. 39 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
ANSWER:
a. 9.9, 1.8
b. 9.9, 0.2882
c. 0.5239
d. 0.6368
e. No
f.
Q1 = 9.7069
Q3 = 10.0931
IQR = 0.3862
STEP-BY-STEP EXPLANATION:
a.
X ~ N (9.9, 1.8)
b.
x ~ N (9.9, 1.8/√39)
x ~ N (9.9, 0.2882)
c.
P(X > 9.8)
We calculate the probability as follows:
[tex]\begin{gathered} P\left(X>9.8\right)=1-p\left(\frac{X-9.9}{1.8}<\frac{9.8-9.9}{1.8}\right) \\ \\ P\left(X>9.8\right)=1-p(z<-0.06) \\ \\ P\left(X>9.8\right)=1-0.4761 \\ \\ P\left(X>9.8\right)=0.5239 \end{gathered}[/tex]d.
p (x > 9.8)
We calculate the probability as follows:
[tex]\begin{gathered} P\left(x>9.8\right)=1-p\left(\frac{X-9.9}{\frac{1.8}{\sqrt{39}}}<\frac{9.8-9.9}{\frac{1.8}{\sqrt{39}}}\right) \\ \\ P\left(x>9.8\right)=1-p(z<-0.35) \\ \\ P\left(x>9.8\right)=1-0.3632 \\ \\ P\left(x>9.8\right)=0.6368 \end{gathered}[/tex]e.
No, you don't need to make the assumption
f.
Q1 = 0.25
In this case the value of z = 0.25, so we look for the closest value in the normal table, like this:
Thanks to this, we make the following equation:
[tex]\begin{gathered} -0.67=\frac{x-9.9}{\frac{1.8}{\sqrt{35}}} \\ \\ x-9.9=-0.19311 \\ \\ x=-0.1931+9.9 \\ \\ x=9.7069 \\ \\ Q_1=9.7069 \end{gathered}[/tex]Q3 = 0.75
In this case the value of z = 0.75, so we look for the closest value in the normal table, like this:
Therefore:
[tex]\begin{gathered} -0.67=\frac{x-9.9}{\frac{1.8}{\sqrt{39}}} \\ \\ x-9.9=0.1931 \\ \\ x=0.1931+9.9 \\ \\ x=10.0931 \\ \\ Q_3=10.0931-9.7069 \end{gathered}[/tex]Therefore, the interquartile range would be:
[tex]\begin{gathered} IQR=Q_3-Q_1 \\ \\ IQR=10.0931-9.7069 \\ \\ IQR=0.3862 \end{gathered}[/tex]