Using the normal distribution, it is found that:
a) The 65th percentile is of 37.31.
b) The 90th percentile is of 42.68.
c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 35, hence [tex]\mu = 35[/tex]The standard deviation is of 6, hence [tex]\sigma = 6[/tex]Question a:
The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.385 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 0.385(6)[/tex]
[tex]X = 37.31[/tex]
The 65th percentile is of 37.31.
Question b:
The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 1.28(6)[/tex]
[tex]X = 42.68[/tex]
The 90th percentile is of 42.68.
Question c:
The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:
X = 38:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35}{6}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 35}{6}[/tex]
[tex]Z = -1.17[/tex]
[tex]Z = -1.17[/tex] has a p-value of 0.121.
0.6915 - 0.121 = 0.5705.
There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
Question d:
The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:
X = 44:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44 - 35}{6}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 35}{6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.9332 - 0.8413 = 0.0919
There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
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Which equation represents a line that passes through (-9, -3) and has a slope of -6? - = y-9 = -6(x-3) y + 9 = -6(x + 3) y-3 = -6(x-9) O y + 3 = -6(x + 9) = x
Answer:
(y+3)=−6(x+9) ( y + 3 ) = − 6 ( x + 9 )
Step-by-step explanation:
Write an equation for the line in slope intercept form
Answer:
y=4x+2
Step-by-step explanation:
Like and give 5 star rating
What a person puts into their relationship is proportional to what they feel they receive; this balance is called
Answer:
Equity
Step-by-step explanation:
A person puts into their relationship is proportional to what they feel they receive; this balance is called equity.
What is the relationship?The happiest, most enduring relationships are between best friends, They relish each other's company, trust on one another for love and attention, devote their free time apart, and have a lot of similarities.
A situation when people's benefits from relationships are inversely correlated with their contributions. These consequences don't necessarily have to be equal.
A person who is firmly attached has a strong feeling of merit and anticipates that most others will be receptive and sympathetic.
Because it fosters familiarity—which increases attraction—proximity counts in the attraction process. The probability that we will become interested to someone simply increases when we are in their presence or are exposed to them frequently.
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How do you factor an expression to the 4 exponent.
Answer:
We can factor a difference of fourth powers (and higher powers) by treating each term as the square of another base, using the power to a power rule. For example, to factor x4 - y4, we treat x4 as (x2)2 and y4 as (y2)2. Thus, x4 - y4 = (x2)2 - (y2)2 = (x2 + y2)(x2 - y2) = (x2 + y2)(x + y)(x - y).
Answer: How do you factor variables with exponents? To do this, take the greatest common factor of the numbers and the smallest exponent of each variable. 2. Divide the original expression by the greatest common factor. To do this, divide the coefficients, and subtract the exponents of the variables.
Explanation: Expressions with fractional or negative exponents can be factored by pulling out a GCF. Look for the variable or exponent that is common to each term of the expression and pull out that variable or exponent raised to the lowest power. These expressions follow the same factoring rules as those with integer exponents.
Find the zeros of the function.
h(x) = x2 + 19x + 84
Answer:
X=7
Step-by-step explanation:
x-12)=0
x-12+12=0+12
x=12
Solve:
(x-7) = 0
x-7+7 = 0+7
x=7
simplify -9 with an exponent of -3
Sara poured 3/4 of the juice from a 2 liter bottle while serving guest party.
How much juice, in liters, is still left in the bottle
Answer:The juice left in bottle is 0.5 litre
Step-by-step explanation:Sara poured 3/4 of the juice from a 2 liter bottle while serving guests at a party how many Juice in liters is still left in the bottle. 2.
Write a function g whose graph is a vertical stretch by a factor of 3 of the graph of f(x)=|x|-5. g(x)=
Answer:
See belowStep-by-step explanation:
A vertical stretch by a factor of 3 of the graph of f(x) will result in:
g(x) = 3 f(x)This gives us:
g(x) = 3( |x| - 5) = 3|x| - 15The function g(x) after a vertical stretch by a factor of 3 can be defined as follows:
g(x) = 3(|x| - 5)
To create a function g(x) that is a vertical stretch by a factor of 3 of the graph of f(x) = |x| - 5, you can simply multiply the entire function f(x) by 3.
This will stretch the graph vertically while maintaining the same shape.
Therefore, the function g(x) can be defined as follows:
g(x) = 3(|x| - 5)
This function takes the absolute value of x, subtracts 5, and then multiplies the result by 3, resulting in a vertical stretch of the graph of f(x).
The vertical stretch by a factor of 3 means that the y-coordinates of all points on the graph are multiplied by 3, making the graph taller compared to the original f(x) graph.
Hence the function g(x) after the vertical stretch is g(x) = 3(|x|-5).
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If the supplies on shelf A are normally $7 each and the supplies on shelf B are normally $6 each, how much will you save on each package plan from part a? Buying the first package will save $ and buying the second package will save $
evaluate 4g -2 (-h) + 4
Answer:
Hi There I Used A Calculator
Step-by-step explanation:
the awnser is 4+2ℎ+4
Andrew owns a plumbing company .the table shows the total amount charged based on the number of hours it takes to complete a job . Which equation best represents this situation?
Andrew's charges is an illustration of a linear function
The equation that represents the situation is [tex]\mathbf{y = 12x +45}[/tex]
From the table (see attachment), we have the following points
(x,y) = (1,57) and (2,69)
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{69 - 57}{2 -1}}\\[/tex]
Simplify fraction
[tex]\mathbf{m = \frac{12}{1}}[/tex]
Divide
[tex]\mathbf{m = 12}[/tex]
The equation is then calculated using:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{y = 12(x - 1) + 57}[/tex]
Open brackets
[tex]\mathbf{y = 12x - 12 + 57}[/tex]
Evaluate like terms
[tex]\mathbf{y = 12x +45}[/tex]
Hence, the equation that represents the situation is [tex]\mathbf{y = 12x +45}[/tex]
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She ran 415 miles on Monday.
She ran a different distance on Tuesday.
She ran a total of 712 miles on both days
Answer:
she ran 297 miles on tuesday
Step-by-step explanation:
Answer:
Distance ran on Tuesday: 297 miles
Step-by-step explanation:
total distance ran = distance ran on Monday + distance ran on Tuesday
⇒ 712 = 415 + x
⇒ 712 - 415 = x
⇒ 297 = x
emma makes 21 laps during a 5 minute song how many laps per minute did emma make how do I show my work?
Answer:
4.2 laps per minute
Step-by-step explanation:
21laps/5min = 4.2laps/1min
How do you Form an equation for x and then solve to find the value of x
9514 1404 393
Answer:
x = 38.2
Step-by-step explanation:
Each of the functions of x represents the measure of an angle in the triangle. You write an equation for x by using what you know about the relationships of angles in a triangle: their sum is 180°.
(2x) +(x -18) +(2x +7) = 180
5x -11 = 180 . . . . . . . collect terms
5x = 191 . . . . . . . . . . add 11
x = 38.2 . . . . . . . . . divide by 5
Approximate 23 by following the steps below.
V23 must lie between the whole numbers
and
You must answer all questions above in order to submit.
Answer:
4 and 5
Step-by-step explanation:
Well, 23 is less than 25, which is 5^2. Moreover, its more than 16, or 4^2
You have 5 shirts, 6 pairs of pants, and 8 hats. How many outfits can you make consisting of one shirt, one pair of pants, and one hat
Answer:
240
Step-by-step explanation:
You would do 5x6x8 to get all the combinations, and that would equal 240
A function is represented by the values in the table.
THIS FUNCTION REPRESENTED IN THE TABLE (CHOOSE IS or IS NOT) LINEAR PIC BELOW
Answer:
IS LINEAR
Step-by-step explanation:
please help meeeeeeeeeeeeeeee
plz plz plz plz plz plz plz plz plz
Answer:
Step-by-step explanation:
I've done this just cant see the whole thing
Manuel cuya estatura es de 1.75 m observa la parte alta de un poste de 18.25 m de altura, con un ángulo de elevación de 30°. La distancia horizontal que hay entre el hombre y el poste es¬
Answer:
i don't understand
Step-by-step explanation:
Add and write in standard form: (-3x^4 + 6x^3 - 43) + (8x^5 - x^2 + 12x + 10)
A.) 8x^5 - 3x^4 + 6x^3 - x^2 + 12x - 33
B.) x^5 - 5x^3 + 12 - 33
C.) -33 + 12x - x^2 + 6x^3 - 3x^4 + 8x^5
D.) -13x^14
Answer:
A.) 8x^5 - 3x^4 + 6x^3 - x^2 + 12x - 33
Answer: A
Step-by-step explanation:
Because the only thing that can be combined is - 43 and 10, you just need to combine that and write everything else out.
- 43 + 10 = - 33
Now just write everything out...
8x^5 - 3x^4 + 6x^3 - x^2 + 12x - 33
Which is A
(X+9)(x-2)-9x-6 is equivalent to?
Answer:
[tex]x^{2}[/tex] - 2x - 24
Step-by-step explanation:
(x + 9)(x - 2) - 9x - 6
[tex]x^{2}[/tex] - 2x + 9x - 18 - 9x - 6 Multiply.
[tex]x^{2}[/tex] - 2x - 24 Combine the like terms.
Which would be the most appropriate way to estimate -6.1(0.22)? Check all that apply.
Use rounding to get -6(0.2), and then multiply.
Use compatible numbers, such as -6(0.5), and then multiply.
Use the benchmark numbers -6 and 1, and then multiply.
Use front-end estimation to get -6(0.2), and then multiply.
Round the factors to the nearest whole number, and then multiply.
Answers to choose Please help me.
Use rounding to get -6(0.2), and then multiply.
Use compatible numbers, such as -6(0.5), and then multiply.
Use front-end estimation to get -6(0.2), and then multiply.
Estimate -6.1(0.22)
Answer:
Use rounding to get -6(0.2), and then multiply.
Use front-end estimation to get -6(0.2), and then multiply.
Round the factors to the nearest whole number, and then multiply.
Step-by-step explanation:
Actual answer:
-6.1(0.22) = -1.342
Estimate answer:
-6 (.2) = 1.2
Answer:
A B D
Step-by-step explanation:
Mia is 7.04304 x 10 minutes old. Convert her age to more appropriate units using years, months, and
days. Assume a year has 365 days and a month has 30 days.
a
Mia is 13
years
months and
days old
Answer:13 years,1 month, and 29 days
Step-by-step explanation:
Please help. I need to get this right.
Answer:
∡SYZ = 34.2°
∡XYZ = 68.4°
Step-by-step explanation:
∡SYZ = 34.2° this must be true because this angle is congruent to ∡XYS
∡XYZ = 68.4° this must be true because ∡XYZ = ∡WYS + ∡SYZ
Can someone help me with this question
Answer:
A. x=-2
Step-by-step explanation: your welcome
Find the value of z
Answer:
z = 9 I think
Step-by-step explanation:
Because I did the quiz
14. At a local fruit stand, Luisa spends $5.25 for 2 pounds of strawberries. At this rate, how much can she expect to pay for 3.5 pounds of strawberries? (round to the nearest hundredt
h) Proportion Answer
What's the circumference of a
circle with a radius of 5 inches?
Use 3.14 for i.
C = [?] inches
Answer:
31.4 inches
Step-by-step explanation:
c = 2 * 3.14 * r
c = 2 * 3.14 * 5
C = 31.4 inches
10. El siguiente circulo está dividido en 8 rebanadas iguales. ¿Qué fracción del circulo está sombreada?
Answer:
2/8
Step-by-step explanation:
2/8 porque ahy 8 y 2 estan coloridas.Si gustarias simplifar seria .25