792 different sets of 7 colors can be chosen.
In how many ways can be the 7 colors selected?Remember that if we have a set of N elements, the number of different sets of K elements that we can make out of these N elements is given by:
C(N, K) = N!/(N - K)!*K!
In this case, we have 12 distinct colors and we want to select 7, so we have:
N = 12
K = 7
Replacing that we get:
C(12, 7) = 12!/(12 - 7)!*7! = 12*11*10*9*8/(5*4*3*2*1) = 792
792 different sets of 7 colors can be chosen.
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Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2[tex]\sqrt{x-3}[/tex]. The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
please help dont understand!
Answer:
Step-by-step explanation:
C = 2 π r
A = π r²
~~~~~~~~~~~
(1). C = 8 π
Let the length of the arc ADB is "x"
x = ( 8π ÷ 360° ) × 340°
x = [tex]\frac{68}{9} \pi[/tex]
(2). A = 16 π
The area of shaded region is
( 16 π ÷ 360° ) × 340° = [tex]\frac{136}{9} \pi[/tex]
[tex]\bold{Answer} \downarrow[/tex]
[tex]Length\ of\ Arc\ ADB = \large\boxed{\frac{68\pi}{9} }[/tex]
[tex]Area\ of\ shaded\ region= \large\boxed{\frac{136\pi}{9} }[/tex]
Formulas needed:
[tex]Arc\ length=\boxed{2\pi r(\frac{\theta}{360} )}[/tex]
[tex]Area \ of\ a\ sector=\boxed{(\frac{n}{360})\times\pi \times r^2}[/tex]
[tex]Area\ of\ Circle=\boxed {\pi\times r^2}[/tex]
Step-by-step explanation:
First, let's find the arc length:
[tex]Arc\ length=2\pi r(\frac{\theta}{360})[/tex]
[tex]=2\pi (4)(\frac{340}{360})[/tex]
[tex]=2\pi (4)(\frac{17}{18})[/tex]
[tex]=2\pi(\frac{68}{18})[/tex]
[tex]=\frac{136\pi }{18}[/tex]
[tex]\longrightarrow \large\boxed{\frac{68\pi}{9} }[/tex]
Next, let's find the area of the sliver of the circle we just found the arc length of.
[tex]Area \ of\ a\ sector=(\frac{n}{360})\times\pi \times r^2[/tex]
[tex]=(\frac{20}{360} )\times \pi \times 4^2[/tex]
[tex]=(\frac{1}{18})\times \pi \times 16[/tex]
[tex]=\frac{16\pi}{18}[/tex]
[tex]\longrightarrow \frac{8 \pi}{9}[/tex]
Finally, find the area of the entire circle and subtract the sliver area by that.
[tex]Area\ of\ Circle= {\pi\times r^2[/tex]
[tex]=\pi \times 4^2[/tex]
[tex]\longrightarrow16\pi[/tex]
Subtracting the area by the sliver.
[tex]Area\ of\ entire\ circle \ -\ Area\ of\ sliver\ of\ circle[/tex]
[tex]=16\pi -\frac{8\pi}{9}[/tex]
[tex]=\frac{144\pi}{9} -\frac{8\pi }{9}[/tex]
[tex]\longrightarrow \large\boxed{\frac{136\pi}{9} }[/tex]
A book sold 42,600 copies in its first month of release. Suppose this represents 9.2% of the number of copies sold to date. How many copies have been sold to date?
The number of copies sold (x) to date is 463043
How to determine how many copies have been sold to date?The given parameters are:
Copies sold = 42,600
Proportion sold = 9.2% of the number of copies sold to date.
The number of copies sold (x) to date is calculated as:
Copies sold = Proportion * number of copies sold to date
Substitute the known values in the above equation
9.2% * x = 42,600
Divide both sides by 9.2%
x = 463043
Hence, the number of copies sold (x) to date is 463043
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The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to the find the critical values corresponding to a 0.01 significance level used to test
the null hypothesis of ρs = 0.
A) -0.881 and 0.881
B) -0.881
C) -0.738 and 0.738
D) 0.881
The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
How to determine the critical values corresponding to a 0.01 significance level?The scatter plot of the election is added as an attachment
From the scatter plot, we have the following highlights
Number of paired observations, n = 8Significance level = 0.01Start by calculating the degrees of freedom (df) using
df =n - 2
Substitute the known values in the above equation
df = 8 - 2
Evaluate the difference
df = 6
Using the critical value table;
At a degree of freedom of 6 and significance level of 0.01, the critical value is
z = 0.834
From the list of given options, 0.834 is between -0.881 and 0.881
Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
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What is the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997
Answer:
$29765.50
Step-by-step explanation:
Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.
First, arrange the salary list in an ascending order.
$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702
As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:
Median = [tex]\frac{27512 + 32019}{2}[/tex]
= [tex]\frac{59531}{2}[/tex]
= $29765.50
Answer:
$29,765.50 is the median salary
Step-by-step explanation:
To find the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997
The steps to do this is:
Arrange your numbers in numerical order.Count how many terms you have.If you have an odd number, divide by 2 and round up to get the position of the median number.If you have an even number, divide by 2, go to the number in that position and average it with the number in the next higher position to get the median.Doing the steps:
$21,971, $25,997, $27,512, $32,019, $38,860, $43,7026does not apply, not odd amount of numbers6 / 2 = 3This means take the average of $27,512 and $32,019
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Slope 0, ordered pair -8, 4
Answer:
Step-by-step explanation:
y-4=0(x+8)
y-4=0
y=4
Answer:
i
Step-by-step explanation:
y-4=0(x+8)
y-4=0
y=4
14. In a right triangle, if one acute angle has measure 10x + 6 and the other has measure 2x + 7, find the larger of these two angles.
Answer:
421/6 degrees
Step-by-step explanation:
The acute angles of a right triangle are complementary, so
[tex]10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}[/tex]
So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.
Find the equation to the line below.
y =
Answer:
[tex]y=\frac{-3}{4}x-3[/tex]
Step-by-step explanation:
This is a linear graph so the equation will be in the format of y=mx+b.
b, the y-intercept, will be -3, as that is where the line crosses the y-axis.
m, the slope, is [tex]\frac{-3}{4}[/tex], calculated from the change in y over the change in x from points (-4,0) to (0,-3).
Now substitute the values in our equation:
[tex]y=\frac{-3}{4}x-3[/tex]
Answer:
y= -3/4+[-3]
Step-by-step explanation:
Consumer math. send help
Mean = 402.5.
Variance = 77,556.3
Standard deviation = 278.5
See attachment for the complete table.
What is the Mean?The mean of a data is the sum of all data values divided by the number of data values we have in the data set.
What is the Variance?Variance is calculated by finding the sum of the squares of the deviations from the mean, find the average, then find the average.
What is the Standard Deviation?The standard deviation = the square root of variance.
The mean of the data given would be: 402.5.
402.5 is subtracted from each of the data points to get the deviations which are squared.
It is the sum of the deviations that gives us 310,225.2.
To find the variance, divide 310,225.2 by the number of data values which is 4.
Variance = 310,225.2/4
Variance = 77,556.3
Standard deviation = √77,556.3
Standard deviation = 278.5
The complete table containing the missing values is given in the image attached below.
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SOMEONE PLS HELPP ASAP
Answer:
yes
Step-by-step explanation:
f the exterior angle of a polygon is given, then the formula to find the interior angle is Interior Angle of a polygon = 180° – Exterior angle of a polygon Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides
Goldie Gold Jewelry uses direct labor hours to apply overhead and estimated total overhead costs at $52,500 and direct labor hours at 12,500 for the second quarter. The direct labor quantity standard is 1.75 direct labor hours per unit, and the company produced 5,250 units in the second month of the second quarter. This required 2,625 direct labor hours. What was the overhead rate for the second quarter?
In the case above, the value of the overhead rate for the second quarter is $17,640.
What is the overhead rate about?Note that:
In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the estimated overhead costs which is $52,500 by that of the estimated direct labor hours .
Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours
Predetermined overhead rate=$52,500/ 12,500
Predetermined overhead rate=$4.20/DLH overhead rate
Hence: $52,500/ 12,500 = $4.20/DLH overhead rate.
Since the Overhead that was applied at standard hours was said to be allowed, then:
= $4.2 x 2,400 x 1.75
= $17,640.
Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.
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find a number which decreased by 21 equals twice the opposite of the number
The required number is 7. The expression formed with the given information is x - 21 = 2(-x).
What is an expression?An expression is the combination of variables, constants, and coefficients.
If two expressions are related by an equal in between them, then that is said to be an equation.
Calculation:From the given data,
Consider the required number = x
The number is decreased by 21 i.e., x - 21
Twice the opposite of the number = 2(-x)
So, on equating,
x - 21 = 2(-x)
On simplifying,
⇒ x - 21 = -2x
⇒ x + 2x = 21
⇒ 3x = 21
∴ x = 7
Thus, the required number is 7.
Check:
7 - 21 = -14 and 2(-7) = -14.
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Helppppppoooooooo me please
Answer:
0
Step-by-step explanation:
We are looking at the change in y over the change is x. The change is y is always 0 and 0 divided by anything will be zero.
The area of a circle is 28.26 square miles. What is the circle's diameter?
Use 3.14 for л.
miles
A = 28.26 miz
a linear equation is an equation whose graph is a straight lina
The statement that a linear equation is an equation whose graph is a straight line is True.
What is a linear equation?A linear equation can be defined as an algebraic equation with each term having an exponent and the graphing of the equation results in a straight line.
From the definition, it can be deduced that the statement is True.
Thus, the statement that a linear equation is an equation whose graph is a straight line is True.
The complete question is:
True or false
A linear equation is an equation whose graph is a straight line.
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[tex]\lim _{x\to \infty }\left(\frac{tanx-sinx}{x^2}\right)[/tex]
The limit does not exist. There are infinitely many infinite discontinuities at [tex]x=n\pi[/tex], where [tex]n\in\Bbb N[/tex]. The function oscillates wildly between negative and positive infinity.
The following value 1.23456789 x 10-6
what is a answer?
Answer 1:
1.23456789 × (10-6) = 4.93827156
Answer 2:
(1.23456789 × 10) - 6 = 6.3456789
Answer 3:
1.23456789 × [tex]10^{-6}[/tex] = 0.000000123456789
Hope this helped! :)
how many significant figures are in this number 6.01x10^3
Answer:
3
Step-by-step explanation:
6.01 has 3 sig fig
I think that's how I do it
Solve the following system of equations. 4x + 3y = -5
- 3x + 7y=13
Answer: 13
Step-by-step explanation:
4x+3y=-5 solve x :
4x = -3y + -5 | -3y
1x = -0.75y + -1.25 | : 4
-3x + 7y = 13 solve x :
-3x + 7y = 13 | -7y
-3x = -7y = 13 | : (-3)
Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333
-0, 75y - 1,25 = 2,333y - 4, 333 solve y:
-0, 75y - 1,25 = 2,333y -4, 333 | -2,333y
-3, 083y - 1,25 = -4,333 | + 1, 25
-3. 083y = -3,088 | : (-3, 083)
y = 1
Plug y = 1 into the equation 4x + 3y = -5 :
4x + 3 · 1 | Multiply 3 with 1
4x + 3 = -5 | -3
4x = -8 | : 4
x = -2
So the solution is:
y = 1, x = -2
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Two debt payments of $2000 each are due now and nine months from now. If money is worth 8%, what single payment six months from now is required to settle the debt?
The single payment six months from now is required to settle the debt will be $4042.
How to calculate the amount?The interest rate monthly will be 8/1200.
The number of time period given is 6 months.
Therefore, the future value will be:
= 2000(1 - 8/1200)^6
= 2081.35
The present value will be:
= 2000(1 - 8/1200)^3
= 1960.53
Therefore, the single payment will be:
= 2081.35 + 1960.53
= 4042
In conclusion, the correct amount is $4042.
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Suppose you are still committed to owning a $190,000 BMW (see Question 9). If you believe your mutual fund can achieve a 12% annual rate of return and you want to buy the car in nine years on the day you turn 30, how much must you invest today?
The amount of money which you must invest today is equal to $68,517.85.
How to calculate the present value?Mathematically, the present value of an investment can be calculated by using this formula:
Present Value, PV = FV/(1 + r)^t
Given the following data:
Time, t = 9 years.
Future value, FA = $190,000.
Interest rate, r = 12% = 0.12.
Substituting the given parameters into the formula, we have;
PV = 190,000/(1 + 0.12)^9
PV = 190,000/(1.12)^9
PV = 190,000/2.7730
PV = $68,517.85.
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The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013. What was the cost of hiring a car for 2 days in 2013?
The cost of hiring a car for 2 days in 2013 is Rs. 316.8
How to find the cost of hiring in 2013 ?The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013.
Therefore,
cost of hiring for 2018 = Rs. 264
Therefore,
let
cost of hiring in 2013 = 20%(264) + 264
cost of hiring in 2013 = 20 / 100 × 264 + 264
cost of hiring in 2013 = 1 / 5 × 264 + 264
cost of hiring in 2013 = 264 / 5 + 264
cost of hiring in 2013 = 52.8 + 264
cost of hiring in 2013 = 316.8
Therefore, the cost of hiring a car for 2 days in 2013 is Rs. 316.8.
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find the length of the semi-major axis of the ellipse x^2/49+y^2/36=1
The length of the semi-major axis of the ellipse is 7.
What is the semi-major axis of an ellipse?
The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.
The general equation of an ellipse is :
⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis
x²/49+y²/36=1
x²/(7²)+y²/(6²)=1
x²/a²+y²/b²=1
a=7
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4. will give brainliest
The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
What is the equation of the ellipse associated with the coordinates of the foci?
By analytical geometry we know that foci are along the major axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the standard form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
a - Length of the major semiaxis.b - Length of the minor semiaxis.Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
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The equation y equals 15 times 2 to the power of t shows the number of infected people from an outbreak of the measles. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 1200?
It will take 6 weeks for the number of infected people to reach 1200
How to determine the number of weeks?The function is given as:
y equals 15 times 2 to the power of t
Rewrite the function properly as follows
y = 15 * 2^t
When the population is 1200, the equation becomes
15 * 2^t = 1200
Divide both sides by 15
2^t = 80
Take the logarithm of both sides
t * log(2) = log(80)
Divide both sides by log(2)
t = 6.3
Approximate
t = 6
Hence, it will take 6 weeks for the number of infected people to reach 1200
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Do the 1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find i. 11. 111. iv. number of students that applied for all the universities. number of students that applied for at least two of the universities. number of students that applied at most two universities. number of students that applied for Addis Ababa but not Bahir Dar University. 13Z 2. Solve the equation: = 11-3i, Z E C, where Z = x + iy, x&y E R. Z+1 3. Given that Z & W are complex numbers. 2 Prove that IZ + W1²-|Z - W² = 4Re(Z)Re(W). 4. Solve the equation: 2² + 4z +20 + iz(A + 1) = 0 where A is a constant, has complex conjugate root. If one of the roots of this quadratic is Z = B + 2i, where B is a real constant, find the possible values of A.
The number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.
Given that there are 60 students out of which 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities.
Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.
We're given the cardinalities of several sets:
total number of students n(U)=60, A applicants is n(A)=30, B applicants n(B)=25, W applicants n(W)=24, A and B applicants n(A∩B)=11, A and W applicants n(A∩W)=6, B and W applicants n(B∩W)=9 non-applicants n(U\(A∪B∪W))=4
The last cardinality tells us n(A∪B∪W),60-4=56 students applied anywhere at all.
We want to find n(A∩B∩W), the number of students that applied to each of the three universities.
By the inclusion/exclusion principle,
n(A∪B∪W)=n(A)+n(B)+n(W)-n(A∩B)-n(A∩W)-n(B∩W)+n(A∩B∩W)
56=30+25+24-11-6-9+n(A∩B∩W)
n(A∩B∩W)=3
Now, we will find the number of students that applied for at least two of the universities.
n(A∩B)=n(A∩B∩W)+n(A∩B∩W')
11=3+n(A∩B∩W')
8=n(A∩B∩W')
Similarly, we will find
n(A∩B'∩W)=3
n(A'∩B∩W)=6
n(A∩B'∩W')=16
n(A'∩B∩W')=8
n(A'∩B'∩W)=12
then the total number of students applied for at least two students is
n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B∩W)=20
Now, we will find the number of students that applied for atmost two universities, we get
n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B'∩W')+n(A'∩B∩W')+n(A'∩B'∩W)=53
now, we will find the number of students that applied for Addis Ababa but not Bahir Dar University is
n(A∩B')=n(A)-n(B)
n(A∩B')=30-25
n(A∩B')=5
hence, the total students is 60 and the number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.
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Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
48, 26, 31, 50, 38, 40, 42, 34, 44, 36
3
8
6
10
The interquartile range of 48, 26, 31, 50, 38, 40, 42, 34, 44, 36, is: D. 10.
What is the Interquartile Range of a Data Distribution?The interquartile range of a data distribution is determined as: upper quartile (Q3) - lower quartile (Q1).
How to Find the Upper Quartile and Lower Quartile of a Data Distribution?The upper quartile of a data distribution is the center of the second half of a data distribution while the lower quartile is the center of the first half of a data distribution.
Given the data, 48, 26, 31, 50, 38, 40, 42, 34, 44, 36:
Order the data set as, 26, 31, 34, 36, 38, 40, 42, 44, 48, 50
The first half of the data is: 26, 31, 34, 36, 38.
The center is 34.
Lower quartile (Q1) = 34.
The second half of the data is: 40, 42, 44, 48, 50. The center is 44.
Upper quartile (Q3) = 44.
Interquartile range = 44 - 34
Interquartile range = 10
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3-3x/4≥9 help please
Answer:
x ≤ −8
Step-by-step explanation:
Let's solve your inequality step-by-step.
3 - 3x/4 ≥ 9
Step 1: Simplify both sides of the inequality.
-3/4x + 3 ≥ 9
Step 2: Subtract 3 from both sides.
-3/4x + 3 - 3 ≥ 9 − 3
-3/4x ≥ 6
Step 3: Multiply both sides by 4/(-3).
(4/-3) * (-3/4x) ≥ (4/-3) * (6)
x ≤ −8
Answer:
x ≤ −8
Find m/1 and m/2 in the kite.
help asap
The measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°
Calculating anglesFrom the question, we are to determine the measure of angle 1 and the measure of angle 2
The given diagram is a kite and the diagonals intersect at right angles
Thus,
m ∠2 + 28° + 90° = 180°
m ∠2 = 180° - 28° - 90°
m ∠2 = 62°
Hence, the measure of angle 2 is 62°
For the measure of angle 1
Consider ΔADB
ΔADB is an isosceles triangle
Thus,
In the triangle, m ∠D = m ∠B
Then, we can write that
m ∠1 + 62° + 90° = 180°
m ∠1 = 180° - 62° - 90°
m ∠1 = 28°
∴ The measure of angle 1 is 28°
Hence, the measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°
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Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 8; = 2 P(7 ≤ x ≤ 11)
Using the normal distribution, the indicated probability is given as follows:
P(7 ≤ x ≤ 11) = 0.6247.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8, \sigma = 2[/tex]
P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:
X = 11:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11 - 8)/2
Z = 1.5
Z = 1.5 has a p-value of 0.9332.
X = 7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7- 8)/2
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
0.9332 - 0.3085 = 0.6247.
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