Answer:
Step-by-step explanation:
Reference angle for 68° in QII = 180°-68° = 112°
Reference angle for 75° in QIV = 360°-75° = 285°
An engine operating on Dual cycle has a compression ratio of 12. The pressure and temperature at the start of adiabatic compression is 100 KPa. and 37 degree Centigrade. The peak pressure of the cycle is not no exceed 8000 KPa. and the heat supplied to the cycle is 2000 KJ per Kg. of air. Determine the cycle thermal efficiency
A manufacturer orders lots of steel rods from a supplier (each lot consists of thousands of rods). Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter. The quality manager accepts a lot if the mean length of the randomly selected sample of 64 rods from that lot is at least 4.005 meters, otherwise the lot is returned to the supplier. a) What percentage of the lots received by the manufacturer will be returned to the supplier
Answer:
84.13% of the lots received by the manufacturer will be returned to the supplier
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter.
This means that [tex]\mu = 4, \sigma = 0.04[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{0.04}{\sqrt{64}} = 0.005[/tex]
a) What percentage of the lots received by the manufacturer will be returned to the supplier
The proportion is the pvalue of Z when X = 4.005. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.005 - 4}{0.005}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413*100% = 84.13%
84.13% of the lots received by the manufacturer will be returned to the supplier
What is the volume of the prism?
2 cm
3cm
11 cm PLS HURRY
Answer:
66
Step-by-step explanation:
multiply everything together
If I have 10 apples, 3 oranges and 7 pears how may oranges do i have?
Answer:
20 oranges.
Step-by-step explanation:
If you add 10 and 3 that gives you 13,
now add the 7 and that should give you 20.
If C is the incenter of ∆AMD, m∠A M C = 3 x + 6 and m∠ DMC= 8 x − 49.
find ∠ M A D (just numbers, no degrees signs).
Hope this will help you lot.
Answer:
<MAD=66
Step-by-step explanation:
to find x:
8x-49=3x+6
x=11
to find DMC:
8(11)-49
<DMC=39
<ADM=36
to find ADC:
36/2
<ADC=18
the number y divided by 100 y. ?
Answer:
1/100
Step-by-step explanation:
On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (negative 10, negative 10), (negative 10, negative 4), and (4, negative 10). Triangle D E F has points (0, 8), (12, 4), and (5, 0). Which statement is true of the right triangles ABC and DEF? Area of ABC is greater than area of DEF. Area of ABC is less than area of DEF. Area of ABC is equal to the area of DEF. There is not enough information to compare the areas of triangles ABC and DEF.
Answer:
Area of ABC is greater than area of DEF
Step-by-step explanation:
Answer:
A. Area of ABC is greater than area of DEF.
A. one solution
B. infinitely many solutions
C. no solution
. Use 3.14
plss help
Answer:
A≈494.13
R = 12.54
D = 25.08
Step-by-step explanation:
Here is all the answers.
PLZZZZ give me brainliest!!!
Consider the expression 40+24 . Find the greatest common factor of the two numbers and use the distributive property to rewrite the expression
Hi there!
[tex]\large\boxed{8(5+3)}}[/tex]
The greatest common factor of 40 and 24 is 8.
8 goes into 40 5 times:
8 goes into 24 3 times.
We can rewrite this expression for distribution using the amount of times 8 goes into both numbers:
8(5 + 3)
Using this, we get:
8(5) + 8(3) = 40 + 24.
A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen? Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 28 balloons that can be chosen is . (b) If the store has only 12 red balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question. If the store has only 12 red balloons, then the number of different selections of 28 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let T be the set of all possible selections, assuming that there are at least 28 balloons of each type, let R≤12 be the set of selections in T that contain 12 or fewer red balloons, and let R≥13 be the set of selections from T that contain 13 or more red balloons. Use the relationships among R≤12, R≥13, and T to find that the number of different combinations of 28 balloons that can be chosen is . (c) If the store has only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? (d) If the store has only 12 red balloons and only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
Answer:
(a) [tex]Selection = 6724520[/tex]
(b) [tex]At\ most\ 12 = 6553976[/tex]
(c) [tex]At\ most\ 8 = 6066720[/tex]
(d) [tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638[/tex]
Step-by-step explanation:
Given
[tex]Colors = 8[/tex]
[tex]Balloons = 28[/tex] --- at least
Solving (a): 28 combinations
From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
[tex]n => 28 + 8-1[/tex][tex]= 35[/tex]
[tex]r = 28[/tex]
[tex]Selection = ^{35}^C_{28[/tex]
[tex]Selection = \frac{35!}{(35 - 28)!28!}[/tex]
[tex]Selection = \frac{35!}{7!28!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29}{7!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}[/tex]
[tex]Selection = \frac{33891580800}{5040}[/tex]
[tex]Selection = 6724520[/tex]
Solving (b): At most 12 red balloons
First, we calculate the ways of selecting at least 13 balloons
Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)
So:
[tex]n => 15 + 8 -1 = 22[/tex]
[tex]r = 15[/tex]
Selection of at least 13 =
[tex]At\ least\ 13 = ^{22}C_{15}[/tex]
[tex]At\ least\ 13 = \frac{22!}{(22-15)!15!}[/tex]
[tex]At\ least\ 13 = \frac{22!}{7!15!}[/tex]
[tex]At\ least\ 13 = 170544[/tex]
Ways of selecting at most 12 =
[tex]At\ most\ 12 = Total - At\ least\ 13[/tex] --- Complement rule
[tex]At\ most\ 12 = 6724520- 170544[/tex]
[tex]At\ most\ 12 = 6553976[/tex]
Solving (c): At most 8 blue balloons
First, we calculate the ways of selecting at least 9 balloons
Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)
So:
[tex]n => 19+ 8 -1 = 26[/tex]
[tex]r = 19[/tex]
Selection of at least 9 =
[tex]At\ least\ 9 = ^{26}C_{19}[/tex]
[tex]At\ least\ 9 = \frac{26!}{(26-19)!19!}[/tex]
[tex]At\ least\ 9 = \frac{26!}{7!19!}[/tex]
[tex]At\ least\ 9 = 657800[/tex]
Ways of selecting at most 8 =
[tex]At\ most\ 8 = Total - At\ least\ 9[/tex] --- Complement rule
[tex]At\ most\ 8 = 6724520- 657800[/tex]
[tex]At\ most\ 8 = 6066720[/tex]
Solving (d): 12 red and 8 blue balloons
First, we calculate the ways for selecting 13 red balloons and 9 blue balloons
Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)
So:
[tex]n =6+6-1 = 11[/tex]
[tex]r = 6[/tex]
Selection =
[tex]^{11}C_6 = \frac{11!}{(11-6)!6!}[/tex]
[tex]^{11}C_6 = \frac{11!}{5!6!}[/tex]
[tex]^{11}C_6 = 462[/tex]
Using inclusion/exclusion rule of two sets:
[tex]Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)[/tex]
[tex]Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462[/tex]
[tex]Only\ 12\ red\ and\ only\ 8\ blue\ = 827882[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638[/tex]
For the most recent year available, the mean annual cost to attend a private university in the United States was $50,900. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500. Ninety-five percent of all students at private universities pay less than what amount
Answer:
95% of all students at private universities pay less than $58,302.5.
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 $50,900, standard deviation of $4,500
This means that [tex]\mu = 50900, \sigma = 4500[/tex]
Ninety-five percent of all students at private universities pay less than what amount?
Pay less than the 95th percentile, and the amount is given by X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 50900}{4500}[/tex]
[tex]X - 50900 = 1.645*4500[/tex]
[tex]X = 58302.5[/tex]
95% of all students at private universities pay less than $58,302.5.
Then determine whether the relation is discrete or continuous?
Answer:
Can you please include the complete question?
Step-by-step explanation:
Tamar surveyed six friends, asking each how many times he or she had ridden in a helicopter. The numbers of times she recorded were 0, 0, 0, 1, 3, and 8.
What is the mean absolute deviation of the number of times?
Round to the nearest tenth, if needed.
a. 0
b. 2
c. 2.3
d. 2.5
well, to do this we first need to find the mean of all values.
we need to find the distance of each value from that mean (subtract the mean from each value, ignore minus signs)
Then find the mean of those distances.
so, after we do all of that with the given numbers, our final result would be 2.333333333..... (It goes on) we round it up to 2.3, and viola! the answer is C.
Answer: the answer is c
Step-by-step explanation: i took the test
Selma went shopping and bought identical sweaters for each of 3 friends. If she spent $42, what was the cost of each sweater? Include your equation with your answer.
Answer:
14 dollars
Step-by-step explanation:
42 / 3 = x amount of dollars
14 = x
so every one sweater costs 14 dollars
PLEASE ANSWER ASAP FOR BRAINESLT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Find the measure of CD in parallelogram ABCD .
Answer:
Picture would be appreciated.
Blake is going to invest $79,000 and leave it in an account for 9 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Blake to end up with $96,000?
Answer:
r =2.2%
Step-by-step explanation:
Which values are solutions to × > 7? A. × = 11 and × = 1 B. × = 0 and × = 8 C. × = 8 and × = 11 D. × = -8 and × = 0
Answer:
C
Step-by-step explanation:
what is the volume of this composite solid
Answer:
C
Step-by-step explanation:
198 cubic meters
Each of 200 subjects were shown a proposed commercial and asked to identify the marketed product 5 minutes after the viewing. A 95% confidence interval was calculated, but the client indicated that the resultant margin of error is too large and must be one-fourth its current size. How large does the new sample need to be?
Answer:
Step-by-step explanation:
first off we need to know the original sample size and if it is in there then im just cant see it
All whole numbers greater than 0 are also called the ____________ integers.
Answer: positive integers
Step-by-step explanation:
All whole numbers greater than 0 are also called the positive integers.
Answer:
[tex]\Large \boxed{\sf positive}[/tex]
Step-by-step explanation:
Whole numbers greater than zero on the number line are always positive integersAll whole numbers are integersZero is neither positive or negativeEmma is choosing a weekly meeting time. She hopes to have two different
managers attend on a regular basis. The table shows the probabilities that
the managers can attend on the days she is proposing.
Assuming that manager A's availability is independent of manager B's
availability, which day should Emma choose to maximize the probability that
both managers will be available?
A. Monday. The probability that both managers will be available is
0.94.
B. Monday. The probability that both managers will be available is
0.67.
C. Wednesday. The probability that both managers will be available is
0.91.
D. Wednesday. The probability that both managers will be available is
0.71.
Answer:
Probability that both managers can attend:
Monday- 0.73x0.94 = 0.69
Tuesday- 0.78 x 0.91 = 0.71
So, d is correct.
Let me know if this helps!
The day Wednesday choose to maximize the probability that both managers will be available. The probability that both managers will be available is 0.71.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Probability that both managers can attend, consider that manager A's availability is independent of manager B's availability,
Monday;
0.73x0.94 = 0.69
Tuesday;
0.78 x 0.91 = 0.71
So, the option d is correct.
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ7
Please help:( I’m stuck on this problem
Answer:
x=33
Step-by-step explanation:
If you didn't know all of the angles in a triangle add up to equal 180
We are given to angles, 90 (the square indicates that its a right angle which is equal to 90) and 57
So to find the missing anlge we subtract the given angles from 180
180-90=90
90-57=33
therefore x=33
Solve for t. t + -24 = -29 -8
what is t value?
Hope this helps
Step-by-step explanation:
t-24= -37
t= -34+24
t= -13
Answer:
t = -13
Step-by-step explanation:
Add or subtract the numbers
t- 24 = - 37t−24=−37
Separate the constants and variables
t = - 37 + 24t=−37+24
Add or subtract the numbers
t = - 13t
Evaluate the following expression.
3 to power of 1
Answer:
3
Step-by-step explanation:
it is 3 3x1 is 3
Scan QR code and it takes to homework so u can answer question i will give brainliest to correct answer please answer correct
im just gonna take the points for falling for that.
You score an 83 on the first of two exams. Write and solve an
equation to find the score x that you need on the second exam to
have a mean score of 85.
Answer: The mean is the same as the average. In order to find the mean, or average score of the two tests, you need to take the sum of the two tests, and then divide by the number of tests, which is two.
We don't know the score of the second exam. Let it = x
Then we have the following equation:
(88 + x)/2 = 93
88 + x = 2 * 93
88 + x = 186
x = 186 - 88 = 98
You need to score a 98 on the second test
Ms. Gittens went out to dinner and the total bill was $60. She wants to give the waiter a %20 tip. How much money should Ms. Gittens give the waiter for a tip?
Answer:
$12
Step-by-step explanation:
20% of 60 = 12
Answer:
12 .....20% of 60 is = 12
Step-by-step explanation:
please help guys asap
Answer:
28 i think
Step-by-step explanation: