Solution :
Using the TI-84 PLUS calculator
a). Area : 0.41
μ = 75
σ = 9
InvNorm(0.41,75,9)
= 72.95209525
Therefore, the 41st percentile of the scores is 72.95209525
b). Area : 0.74
μ = 75
σ = 9
InvNorm(0.74,75,9)
= 80.79010862
Therefore, the 74st percentile of the scores is 80.79010862
c). 8%
So, Area : 0.92
μ = 75
σ = 9
InvNorm(0.92,75,9)
= 87.64564405
Therefore, X = 80.79010862
Mrs. Taylor is planning a pizza party for her students. She plans to purchase cheese pizza and pepperoni pizza for her students to enjoy. Cheese pizzas cost $8 each and pepperoni pizzas cost $11 each. She needs to purchase at least 12 pizzas, while spending no more than $180.
What are two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit?
Let x represent the number of cheese pizzas purchased and y represent the number of pepperoni pizzas purchased.
Answer:
Step-by-step explanation:
She needs 12 pizzas
x + y = 12
She also can't spend more than 180 dollars.
8x + 11y < 180 She can get all 12 pizzas and have the bill come to 132 dollars
11 * 12 = 132
She could really be kind to her pocket book and get all cheese pizzas
8*12 = 96 which saves her 36 dollars.
So any number of either kind will do.
(0,12) = 132
(1,11) = 8*1 + 11*11 = 129
and so on down the line
At a local university the students have been overdosing on caffeine to help them study for exams. However, many students have been getting quite sick from taking too much coffee and cola.
A. How many cups of coffee would be too much and at the dangerous level (3.00 g)? You know that coffee contains 21.5 mg caffeince per ounce and a cup is 8 oz.
B. How many cans of cola would be too much and at the dangerous level? You know that cola contains 4.20 mg per ounce and a soft drink can contain 12.0 oz.
Answer:
A) Hence, the number of coffee cups that are risky = 17.4 Cups.
B) Here, the number of coffee cups that are risky = 59.5 Colas.
Step-by-step explanation:
A)
In 1 cup coffee =[tex]8\times21.5mg= 172.0 mg[/tex]
Hence one cup of coffee contains 172 mg of caffeine. The risky level is 3000mg.
Therefore, the number of coffee cups that are risky
[tex]= 3000/172\\ \\=17.4 cups[/tex]
Here, the number of coffee cups that are risky = 17.4 cups.
B)
[tex]1 cola=12\times4.2mg\\\\ = 50.4mg / day[/tex]
Hence, one can cola contains 50.4 mg of caffeine.
The dangerous level is 3000 mg.
Therefore, the number of cola cans that are risky [tex]=3000/50.4= 59.5[/tex] cola is risky.
To teach computer programming to employees, many firms use on the job training. A human resources administrator wishes to review the performance of trainees on the final test of the training. The mean of the test scores is 72 with a standard deviation of 5. The distribution of test scores is approximately normal. Find the z-score for a trainee, given a score of 82.
Answer:
The z-score for the trainee is of 2.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean of the test scores is 72 with a standard deviation of 5.
This means that [tex]\mu = 72, \sigma = 5[/tex]
Find the z-score for a trainee, given a score of 82.
This is Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 72}{5}[/tex]
[tex]Z = 2[/tex]
The z-score for the trainee is of 2.
Private nonprofit four-year colleges charge, on average, $26,208 per year in tuition and fees. The standard deviation is $7,040. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
26208
Correct,
7040
Correct)
b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 22,924 per year.
c. Find the 60th percentile for this distribution. $
(Round to the nearest dollar.)
Answer:
#########
Step-by-step explanation:
What does y equal in the solution of the system of equations below? 5y-3x-4z=22 2z-2x=-6 2z+3x=-6
9514 1404 393
Answer:
y = 2
Step-by-step explanation:
Subtracting the second equation from the third gives ...
(2z +3x) -(2z -2x) = (-6) -(-6)
5x = 0
x = 0
Using this in the third equation, we have ...
2z +0 = -6
z = -3
And substituting these values into the first equation, we have ...
5y -3(0) -4(-3) = 22
5y = 10 . . . . . subtract 12
y = 2
__
The solution to the system is (x, y, z) = (0, 2, -3).
Joe bikes at the speed of 30 km/h from his home toward his work. If Joe's wife leaves home 5 mins later by car, how fast should she drive in order to overtake him in 10 minutes.
Answer:
Joe's wife must drive at a rate of 45km/hour.
Step-by-step explanation:
We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.
Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.
Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:
[tex]2.5+0.5t[/tex]
Where t represents the time in minutes after his wife left the house.
And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:
[tex]2.5+0.5(10)=7.5\text{ km}[/tex]
Let s represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:
[tex]10s=7.5[/tex]
Solve for s:
[tex]\displaystye s=0.75\text{ km/min}[/tex]
Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.
The diagram shows triangle ABC.
С
Work out the sizes of angles x, y and z.
40°
110°
х
Z
A
В
Answer:
x=70
y=30
z=20
Step-by-step explanation:
x=180-110 (angles on a straight line)
y=180-110-40 (angle sum of triangle)
z= 180-90-70 (angle sum of triangle)
Answer:
x=70°
y=30°
z=20°
Step-by-step explanation:
x=180°-110°(anlges on a straight line)
x=70°
y+110°+40°=180°(sum of angles of triangle)
y+150°=180°
y=180°-150°
y=30°
z+x+90°=180°(sum of angles of triangle)
z+70°+90°=180°
z+160°=180°
z=180°-160°
z=20°
Find the first derivative for y = f(x). fox ) 3x² -5x-1 at a Pocat where a = 4
Answer:
Step-by-step explanation:
f(x) = 3x² -5x - 1
f'(x) =2*3x - 5*1 +0
= 6x - 5
f'(4) = 6*4 - 5
= 24 - 5
= 19
Find m angle RQH if m angle HQP=95^ and m angle RQP=152^
Answer:
[tex] \large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]
[tex] \large{ \tt{✽ \: m \: \angle \: RQP = m \: \angle \: RQH + m \: \angle \: HQP}}[/tex]
[tex] \large{ \tt{⇾ \: 152 \degree = \: m \: \angle \: \: RQH + 95 \degree}}[/tex]
[tex] \large{ \tt{⇾ \: 152 \degree - 95 \degree = m \: \angle \: RQH}}[/tex]
[tex] \boxed{ \large{ \tt{⇾ \: 57 \degree = m \: \angle \: RQH}}}[/tex]
Our final answer : 57° . Hope I helped! Let me know if you have any questions regarding my answer! :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
[tex]5.5=2\pi \sqrt{\frac{L}{9.8}[/tex]
9514 1404 393
Answer:
7.51 m
Step-by-step explanation:
The equation matches that required for finding the length of a pendulum that has a period of 5.5 seconds. We can solve for L to find the length.
[tex]5.5=2\pi\sqrt{\dfrac{L}{9.8}}\\\\\dfrac{5.5}{2\pi}=\sqrt{\dfrac{L}{9.8}}\\\\\left(\dfrac{5.5}{2\pi}\right)^2=\dfrac{L}{9.8}\\\\L=74.1125/\pi^2\approx7.509[/tex]
The length of a pendulum with period 5.5 seconds is about 7.51 meters.
Answer:
The length, L = 7.52 m.
Step-by-step explanation:
The given expression is
[tex]5.5= 2 \pi \sqrt\frac{L}{9.8}\\\\Sqauring on both the sides\\\\5.5 \times 5.5 = 4\pi^2 \times \frac{L}{9.8}\\\\L = 7.52 m[/tex]
The value of length is 7.52 m.
What is the y-intercept of the graph of y = 2.5x? a. 2.5 c. 0 b. 1 d. -1
Answer:
answer is C
Step-by-step explanation:
General equation of a line is expressed as shown:
y = mx+c where;
m is the slope or gradient of the line
c is the intercept of the line
Given the equation of the line graph as y =2.5x
Comparing the given equation with the general equation, it is seen that m = 2.5 and c = 0 (since there is no value for the intercept)
Based on the explanation, the y-intercept of the graph is therefore 0
Answer:
B
Step-by-step explanation:
To find the x-intercept, substitute in
0 for y and solve for x
To find the y-intercept, substitute in 0 for x and solve for y
x-intercept(s): None
y-intercept(s): (0,1)
Helppp me with this ,I will mark brainlest
5. Lisa has a cubed-shaped box with a
volume of 512 cm. If Lisa fills the box
with 1-cubic centimeter blocks, how
many blocks make up each layer?
Answer:
64
Step-by-step explanation:
[tex]\sqrt[3]{512} = 8\\8x8 = 64[/tex]
which of the following function shows the absolute value parent function FX=lxl shifted up
Answer:
The answer is C.
as for C . the value of f(x) increases by 7 and so the graph goes up by units 7.
OR
g(x) = |x| + 7
we know that |x| is f(x), so :-
g(x) = f(x) + 7
and since f(x) is plot on y- axis the graph climbs the y axis by 7 units
*The graph shifts right or left for the other functions*
For P = {5, 12, 13, 14), Q = {2, 7, 11), and R = {4, 7, 8, 11}, find PU (Q n R).
Answer:
(5 7 11 12 13 14)
Step-by-step explanation:
Q inter R = 7 and 11
So the union between p and 7 and 11 is the answer above
Meghan sells advertisements for a radio station. Each 30 second ad costs $20 per play, and each 60 second ad
costs $35 per play. Meghan sold 12 ads for $315. She wrote the system below letting x represent the number of 30
second ads and y represent the number of 60 second ads.
X+ y = 12
20x+35y = 315
What is the solution to the system of equations?
Need answers ASAP!!!!
Answer:
usai964s46s694s4o6s64694s946649s469 opps
Answer:
[tex](x,y)=(7,5)[/tex]
Step-by-step explanation:
Megan's equation will be:
[tex]20x+35y=315[/tex]
[tex]x+y=12[/tex]
Substitute [tex]x=12-y[/tex] in the first equation:
[tex]20(12-y)+35y=315[/tex]
[tex]15y=75[/tex]
[tex]y=75/15[/tex]
[tex]y=5[/tex]
Find x:
[tex]x=12-5[/tex]
[tex]x=7[/tex]
Where x and y represent 30-second and 60-second ads sold, we find that Meghan's sales were:
[tex](x,y)=(7,5)[/tex]
hope this helps....
Find the range of the data.
Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88
Answer:
24
Step-by-step explanation:
To find the range, you must subtract the lowest value from the highest value in the data set. If you organize the set from least to greatest, 72 is the lowest, and 96 is the highest.
So, 96 - 72 = 24, which is the range.
The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected? The slant height of the larger cone is equal to the slant height of the smaller cone. The slant height of the larger cone is double the slant height of the smaller cone. The slant height of the larger cone is 4 times the slant height of the smaller cone. The slant height of the larger cone is 8 times the slant height of the smaller cone.
Answer:
The slant height of the cone affected is two times the slant height of original cone
Step-by-step explanation:
we know that
If the height and base radius of a cone are increased by a factor of to create a similar cone
then
the scale factor is equal to
therefore
the slant height of the cone affected is equal to the slant height of the original cone multiplied by the scale factor
Find the slant height of the original cone
Let
l-----> slant height of original cone
la-----> slant height of the cone affected
Applying the Pythagoras theorem
so
The slant height of the cone affected is two times the slant height of original cone
(I GOT THIS FROM SOMEONE ELSES ANSWER IN 2017 SO I HOPE THIS HELPS)
The slant height of the larger cone is double the slant height of the smaller cone.
Option B is the correct answer.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3 πr²h
We have,
The slant height of the cone is affected by a factor of 2.
When the height and base radius of a cone are multiplied by 2, the dimensions of the new cone are doubled.
Therefore,
The slant height of the larger cone is double the slant height of the smaller cone.
Learn more about cones here:
https://brainly.com/question/13798146
#SPJ5
At one point in history, the NBA finals required that one of the two teams win at least three of five games in order to win the Championship. If one team wins the first two games, what is the probability that the same team wins the Championship, assuming that the two teams are well matched and each team is equally likely to win each game
Answer:
50% i believe
Step-by-step explanation:
because in every scenario theres 2 teams and if they are well matched it be half and half on every game assuming they're the same level of comp
Show all the steps to solve the following
942.6 - 19.734
Answer:
922.868
Step-by-step explanation:
1. Thousandth place of 942.6002. Subtracting[tex]942.600-19.732=922.868[/tex]
translate to a system of equations but do not solve.
A non-toxic floor wax can be made from lemon juice and food grade linseed oil. The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 30 oz of floor wax?
let x represent the number of ounces of lemon juice and y represent the number of ounces of linseed oil.
complete the system of equations.
y =
x+y =
Answer:
x + y = 30
y = 2x
Step-by-step explanation:
x = number of ounces of lemon juice
y = number of ounces of linseed oil
How much of each ingredient is needed to make 30 oz of floor wax?
x + y = 30
The amount of oil should be twice the amount of lemon juice.
y = 2x
Answer:
x + y = 30
y = 2x
The graph of f(x)=x^2 is shown. Compare the graph of f(x) with the graph of d(x)=x^2-26
A es aaaaaaaaaaaaaaaaaaaaaaa
The lengths of nails produced in a factory are normally distributed with a mean of 6.13 centimeters and a standard deviation of 0.06 centimeters. Find the two lengths that separate the top 7% and the bottom 7%. These lengths could serve as limits used to identify which nails should be rejected.
Answer:
A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 6.13 centimeters and a standard deviation of 0.06 centimeters.
This means that [tex]\mu = 6.13, \sigma = 0.06[/tex]
Value that separated the top 7%:
The 100 - 7 = 93rd percentile, which is X when Z has a p-value of 0.93, so X when Z = 1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.475 = \frac{X - 6.13}{0.06}[/tex]
[tex]X - 6.13 = 1.475*0.06[/tex]
[tex]X = 6.2185[/tex]
Value that separates the bottom 7%:
The 7th percentile, which is X when Z has a p-value of 0.07, so X when Z = -1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.475 = \frac{X - 6.13}{0.06}[/tex]
[tex]X - 6.13 = -1.475*0.06[/tex]
[tex]X = 6.0415[/tex]
A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
Answer:
AAS
Step-by-step explanation:
It will be angle angle side because you are given a side and two angles, and when you put them in the correct order, you will get AAS, or SAA (not the correct way to say it)
Please help Quick this is hard so you’ll get brainliest thank you so much
Answer:
number 1: no
number 2: no
number 3: no
Yellowstone National Park is a popular held trip destination. This year the senior class at
High School A and the senior class at High School B both planned trips there. The senior
class at High School A rented and filed 2 vans and 3 buses with 153 students. High
School Brented and nited il vans and 10 buses with 534 students. Every van had the
same number of students in it as did the buses. Find the number of students in each van
and in each bus.
Van: 39
Bus: 18
Van: 21
Bus: 21
o
Van: 27
Bus: 19
.
Van: 18
Bus: 39
Answer:
Who was the first president of United States?
Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company Inc. invoices.
13 13 13 20 26 29 32 33 34 34 35 35 36 37 38
41 41 41 45 46 47 47 48 52 54 55 56 62 67 82
(Round your answers to 2 decimal places.)
a. Determine the first and third quartiles.
Q1 =
Q3 =
b. Determine the second decile and the eighth decile.
D2 =
D8 =
c. Determine the 67th per
Answer:
Q1 = 32.5
Q3 = 50
D2 = 29
D8 = 52
67th percentile = 46.5
Step-by-step explanation:
Given the ordered data:
13, 13, 13, 20, 26, 29, 32, 33, 34, 34, 35, 35, 36, 37, 38, 41, 41, 41, 45, 46, 47, 47, 48, 52, 54, 55, 56, 62, 67, 82
The first quartile :
Q1 = 1/4(n+1)th term
n = sample size = 30
Q1 = 1/4(31) = 7.75 = (7th + 8th) / 2 = (32+33) / 2 = 32.5
Q3 = 3/4(n+1)th term
n = sample size = 30
Q3 = 3/4(31) = 23.25 = (23rd + 24th) / 2 = (48+52) / 2 = 50
D2 = 2nd decile
2 * 10% = 20%
20% * n
0.2 * 30 = 6th = 29
D8 = 8th decile
8 * 10% = 80%
80% * 30 = 24th = 52
67th percentile :
0.67 * 30 = 20.1 th
(20th + 21th) / 2
(46 + 47) / 2
= 46.5
from an observer o, the angles of elevation of the bottom and the top of a flagpole are 40° and 45° respectively.find the height of the flagpole?
Answer:
Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.
We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.
Remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
So, if we define H as the height of the cliff
X as the distance between the observer and the cliff
and h as the height of the flagopole
we can write:
tan(40°) = H/X
tan(45°) = (H + h)/X
Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.
But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.
We want to find the value of h.
If we take the quotient between both equations, we get:
Tan(45°)/Tan(40°) = (H + h)/H
1.192 = (H + h)/H
1.192*H = H + h
1.192*H - H = h
0.192*H = h
So the height of the flagpole is 0.192 times the height of the cliff.
Using law of sines please show process and answer
Hello,
[tex]\widehat{A}=180^o-24.4^o-103.6^o=52^o\\\\\dfrac{sin(24.4^o)}{37.3} =\dfrac{sin(103.6^o)}{c} \\\\\\c=87.760246\approx{87.8}\\\\\\\dfrac{sin(52^o)}{a} =\dfrac{sin(24.4^o)}{37.3} \\\\\\a=71.1510189...\approx{71.2}\\[/tex]
Suppose that you are thinking about buying a car and have narrowed down your choices to two options.
The new-car option: The new car costs $25,000 and can be financed with a four-year loan at 6.12%.
The used-car option: A three-year old model of the same car costs $17,000 and can be financed with a three-year loan at 7.72%.
=||)
[1-(2-4) 11
What is the difference in monthly payments between financing the new car and financing the used car? Use PMT
The difference in monthly payments between financing the new car and financing the used car is $
(Round to the nearest cent as needed.)
Answer:
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