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Answer:
domain: x < -2range: y > 1Step-by-step explanation:
Domain and range of the inverse function are swapped: the domain of the function is the range of its inverse, and vice versa.
__
The graph shows an example of a function and its inverse with the given domain and range. The function is red; its inverse is blue.
Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities. a. The student makes more than $15,000. b. The student makes between $13,000 and $14,000.
Answer:
a) 0.0749 = 7.49% probability that the student makes more than $15,000.
b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.
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.
Full-time Ph.D. students receive an average of $12,837 per year.
This means that [tex]\mu = 12837[/tex]
Standard deviation of $1500
This means that [tex]\sigma = 1500[/tex]
a. The student makes more than $15,000.
This is 1 subtracted by the p-value of Z when X = 15000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15000 - 12837}{1500}[/tex]
[tex]Z = 1.44[/tex]
[tex]Z = 1.44[/tex] has a p-value of 0.9251.
1 - 0.9251 = 0.0749
0.0749 = 7.49% probability that the student makes more than $15,000.
b. The student makes between $13,000 and $14,000.
This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.
X = 14000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14000 - 12837}{1500}[/tex]
[tex]Z = 0.775[/tex]
[tex]Z = 0.775[/tex] has a p-value of 0.7708.
X = 13000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13000 - 12837}{1500}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
0.7708 - 0.5438 = 0.227
0.227 = 22.7% probability that the student makes between $13,000 and $14,000.
7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given that:
Mean = $12837, standard deviation = $1500
a) For >15000:
z = (15000 - 12837)/1500 = 1.44
P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749
b) For >13000:
z = (13000 - 12837)/1500 = 0.11
For <14000:
z = (14000 - 12837)/1500 = 0.78
P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385
7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000
Find out more on z score at: https://brainly.com/question/25638875
Hello my ''brainiest intelligent minds'' once again I'm counting on you, lol, I'm trying to figure this out.
f(x)=2x+3
g(x)=3x+2
What does (f+g)(x) equal?
Answer:
(f + g)(x) = 5x + 5
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 2x + 3
g(x) = 3x + 2
Step 2: Find
Substitute in function values: (f + g)(x) = 2x + 3 + 3x + 2Combine like terms: (f + g)(x) = 5x + 57. 20x + 10 = 110
a. X= 1
b. X= 5
c. x= 12
Answer:
b x=5
Step-by-step explanation:
20x+10=110
20x+10-10=110-10
20x/20=100/20
x=5
Answer:
x=5
Step-by-step explanation:
20x + 10 = 110
Subtract 10 from each side
20x +10-10 = 110-10
20x = 100
divide by 20
20x/20 =100/20
x= 5
The ratio of boys to girls in a high school is found to be three to five. If a class has 12boys, how many girls would you expect to be in the class?
Answer:
20 girls
Step-by-step explanation:
boys: girls
3 5
There are 12 boys
12/3 = 4
Multiply each side by 4
boys: girls
3*4 5*4
12 20
Answer:
20 girls
Step-by-step explanation:
Divide 12 by 3 : 12/3 = 4
Multiply 4 by 5 : 4*5 = 20
Solve the following equation for the given variable.
4x + 19 + 3x = -5
Round your answers to the nearest tenths place.
Step-by-step explanation:
4x + 19 + 3x = - 5
4x + 3x + 19 = - 5 collect the like terms
7x + 19 = - 5
7x = - 5 - 19 bring 19 to the right
7x/ 7x = - 24/ 7
x = - 3.4
I hope this answers your question
(4x - 3) × (x + 2)=0
Hi,
AxB = 0 means A=0. or B=0
so 2 solutions :
4x-3= 0
4x=3
x = 3/4
and x+2 = 0.
x= -2
solutions are : -2 +and 3/4
2 answers
1) -2
2) -3/4
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 242
(ii) 1280
(iii) 245
(iv)968
(v) 1728
(vi) 4851
Answer:
BELOW
Step-by-step explanation:
242: multiply it by 2 to get 484 and its square root is 22
1280: multiply it by 5 to get 6400 and its square root is 80.
245: multiply it by 5 to get 1225 and its square root is 35.
968: multiply it by 2 to get 1936 and its square root is 44.
1728: multiply it by 3 to get 5184 and its square root is 72
4851: multiply it by 11 to get 53361 and its square root is 231.
HOPE THIS HELPED
The lengths of two sides of the right triangle ABC shown in the illustration given
a= 7cm and b= 24cm
Answer:
25 cm.
Step-by-step explaination:
Given,
Two sides of a triangle:
a = 7cm
b = 24 cm
To find,
Third side:
c = ?
By Pythagorean Theorem;
a² + b² = c²
[where c is the longest side,hypotenuse]
Putting the value of a and b;
we get,
7² + 24² = c²
49 + 576 = c²
625 = c²
25² = c² (square root)
25 = c
c = 25
Therefore, the length of the third side will be equal to 25 cm.
The lengths of two sides of the right triangle ABC shown in the illustration given
a= 7cm and b= 24cm
Given,> a= 7cm
> b= 24cm
To find?Side c (third side)
Solution:-Using Pythagoras theorem,
▶️ a² + b² = c
▶️ 7cm ² + 24cm² = c²
▶️ 49cm + 576cm = c²
▶️ 625cm = c²
▶️ 25² = c² (25×25 = 625)
▶️ c = 25
The value of c is 25 cm.
How many permutations of letter of the word APPLE are there?
Answer:
There are 60 permutations.
Step-by-step explanation:
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
With repetition:
For each element that repeats, with [tex]n_1, n_2, ..., n_n[/tex] times, the formula is:
[tex]A_n^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n}[/tex]
In this question:
Apple has 5 letters.
P appears two times. So
[tex]A _5^{2} = \frac{5!}{2!} = 60[/tex]
There are 60 permutations.
A random sample of 25 graduates of four-year business colleges by the American Bankers Association revealed a mean amount owed in student loans was $14,381 with a standard deviation of $1,892. Assuming the pop is normally distributed:
a) Compute a 90% confidence interval, as well as the margin of error.
b) Interpret the confidence interval you have computed.
Answer:
a) The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.
b) We are 90% sure that the mean amount owed in student loans of graduates of all four-year business colleges is between $13,600 and $15,162.
Step-by-step explanation:
Question a:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 25 - 1 = 24
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0639
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{1892}{\sqrt{25}} = 781[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 14381 - 781 = $13,600
The upper end of the interval is the sample mean added to M. So it is 14381 + 781 = $15,162
The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.
b) Interpret the confidence interval you have computed.
We are 90% sure that the mean amount owed in student loans of graduates of all four-year business colleges is between $13,600 and $15,162.
If car eyelashes sold for $13.99. If you bud double that, how much would you have paid for them? (Hint if needed: if they had been exactly $14, how different would your answer be?)
Answer:
13.99 x 2 = 27.98 dollars
now if they were 14 dollars exactly and you doubled that it would be 28 dollars so the difference would be 0.02 cents
Step-by-step explanation:
15. On Sports Day, Mike runs 100 metres in 13.89 seconds and Neal runs the same distance in 13.01 seconds. Who is the FASTER runner?
Answer:
Neal
Step-by-step explanation:
13.01 < 13.89
Cho biết tỉ lệ máy tính bảng sử dụng hệ điều hành A là 70%, tỉ lệ máy tính bảng sử
dụng hệ điều hành W là 30%. Xác suất để một máy tính bảng có hệ điều hành sử dụng ổn định
(không phải cài đặt lại) trong 2 năm đầu tiên là 0, 75. Tỉ lệ sử dụng ổn định của các máy tính
bảng có hệ điều hành A cao hơn tỉ lệ sử dụng ổn định của các máy tính bảng có hệ điều hành
W là 20%. Hãy tính xác suất để một máy tính bảng có hệ điều hành W sử dụng ổn định trong
2 năm đầu tiên.
Answer:
máy ...
xác suất để một máy tính bảng có hệ điều hành B sử dụng ổn định trong 2 năm đầu tiên. Add answer
Question 7
In circle P below, angle OPM equals 124 degrees and line segments ON and MN are tangents to the circle
What is the measure of Angle ONM?
A 56
B 62
С 74
D 90
Answer:
B) 62 is the answer. I'm sure
If 10 wholes are divided into pieces that are one half of a whole each how many pieces are there?
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Answer:
20
Step-by-step explanation:
A whole can be divided into two pieces that are each 1/2 of the whole.
(10 wholes) × (2 pieces per whole) = 20 pieces
(02.02 MC) Use the graph to fill in the blank with the correct number.
Numerical Answers Expected!
Answer for Blank 1:
Answer:
The answer is "2"
Step-by-step explanation:
When we check the points where the x is -2
by calculating the "y-value":
It is 2, right?
it implies that [tex]f(-2)=2[/tex]
that's why the final answer is "2"
Using traditional methods it takes 92 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 70 students and observed that they had a mean of 93 hours. Assume the population variance is known to be 36. Is there evidence at the 0.05 level that the technique lengthens the training time?
Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is z = 1.39.
The p-value of the test is 0.0823 > 0.05, which means that there is not evidence at the 0.05 level that the technique lengthens the training time.
Step-by-step explanation:
Using traditional methods it takes 92 hours to receive an advanced flying license.
This means that at the null hypothesis, it is tested if the mean is of 92, that is:
[tex]H_0: \mu = 92[/tex]
Test if there is evidence that the technique lengthens the training time
At the alternative hypothesis, it is tested if the mean is more than 92, that is:
[tex]H_1: \mu > 92[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
92 is tested at the null hypothesis:
This means that [tex]\mu = 92[/tex]
A researcher used the technique on 70 students and observed that they had a mean of 93 hours. Assume the population variance is known to be 36.
This means that [tex]n = 70, X = 93, \sigma = \sqrt{36} = 6[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{93 - 92}{\frac{6}{\sqrt{70}}}[/tex]
[tex]z = 1.39[/tex]
The value of the test statistic is z = 1.39.
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 93, which is 1 subtracted by the p-value of z = 1.39.
Looking at the z-table, z = 1.39 has a p-value of 0.9177.
1 - 0.9177 = 0.0823.
The p-value of the test is 0.0823 > 0.05, which means that there is not evidence at the 0.05 level that the technique lengthens the training time.
What type of line is PQ?
A. side bisector
B. angle bisector
C. median
D. altitude
Answer:
B: I think
Step-by-step explanation:
correct me if im wrong
The line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have a triangle shown in the picture.
As we know,
in terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
From the figure the segment PQ divides the angle into two equal half.
From the definition of the angle bisector, the angle bisector can be defined as a line segment that divides the angle into two half.
Angle P = 40 + 40 = 80 degrees
Thus, the line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.
Learn more about the angle here:
brainly.com/question/7116550
#SPJ5
Michelle rode her bicycle from her house to school at an average speed of 8 miles per hour. Later that day, she rode from school back home along the same route at an average speed of 12 miles per hour. If the round trip took one hour, how many miles long is the round trip?
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Answer:
9.6 miles
Step-by-step explanation:
Let x represent the round trip distance. Then Michelle's time was ...
t = distance/speed
1 = (x/2)/8 +(x/2)/12 = x(1/16 +1/24) = x(3/48 +2/48) = x(5/48)
48/5 = x = 9.6
The round trip is 9.6 miles.
72
60
48
36
Number of Computers
The graph shows a proportional relationship between
the number of computers produced at a factory per
day in three days, 36 computers are produced, 48
computers are produced in 4 days, and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the
graph.
Unit rate
computers per day
I
24
12
3 4 5 6 7 8 9 10 11 12
Number of Days
Intro
Done
Graph is attached below ;
Answer:
Unit rate = 12 computers per day
Step-by-step explanation:
To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
That is ; the gradient ;
Slope = change in y / change in x
Slope = (y2 - y1) / (x2 - x1)
y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3
Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12
Slope = 12
Unit rate = 12 computers per day
the quotient of (x^4 - 3x^2 + 4x - 3) and a polynomial is (x^2 + x - 3) what is the polynormial
Answer:
Hello,
polynomial is x²-x+1
Step-by-step explanation:
if a=b*c+r then a=c*b+r
Using a long division, see the picture.
Arrange the following rational numbers in descending order. 5/8 ,-11/15 , 17/(-24) ,7/12
Need help plotting this on number line
Refer to the attaachment
Factorise: 25x^2 - 1/49
Answer:
[tex] (5x + \frac{1}{7} )(5x - \frac{1}{7} )[/tex]Step-by-step explanation:
Given,
[tex] {25x}^{2} - \frac{1}{49} [/tex]
[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]
Since,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Then,
[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]
What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?
A. 9 miles
B. 16 miles
C. 38 miles
D. 48 miles
Answer:
the answer is B 16 miles
Step-by-step explanation:
so because every 3 cm is 1 mile if to make it to City Hall you would do 7 x 3 which would be 21 cm so you have 7 miles already so to make it to the post office from city hall it would be another 7 miles then 3 more cm and that would be 1 mile so 7 + 7 + 1 = 15 so then the closest number to 15 is 16 I know its right because I did the test and got it right.
Answer:
B
Step-by-step explanation:
Meena's family took a road trip to Niagara Falls. Meena slept through
the last 49% of the trip. If the total length of the trip was 500 miles, how many miles had they travelled when Meena fell asleep?
245 miles
49/100*500 i guess it's the answer
Answer: 255 miles
Explanation:
Total length of the trip = 500 miles
Then 49% = 49/100×500
= 245 miles
Therefore she slept for 245 miles
How many miles had they travelled when meena fell asleep
= 51%
= 51/100×500
= 255 miles
Or
500 - 245
= 255 miles
Answered by Gauthmath must click thanks and mark brainliest
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 indicating that their financial security was more than fair. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.
Answer:
hey, how you're day going
Step-by-step explanation:
.................
The critical value of F for an upper tail test at a 0.05 significance level when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____. a. 2.94 b. 2.45 c. 2.10 d. 2.37
Answer:
2.45
Step-by-step explanation:
Given that :
α = 0.05
Larger sample variance= numerator, sample size = 9
Smaller sample variance = denominator, sample size = 21
Hence,
DFnumerator = n - 1 = 9 - 1 = 8
DFdenominator = n - 1 = 21 - 1 = 20
Critical value for upper tail test using the F distribution table at α = 0.05 ; DFnumerator on horizontal ; Df denominator as vertical ;
F critical = 2.447
F critical = 2.45
(WILL GIVE YOU 30 POINTS!!!)
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 3 multiplied by 1.2 to the power of x. The straight line f of x joins ordered pairs minus 3, minus 3 and 4, 4 and is extended on both sides. The straight line p of x joins the ordered pairs minus 6, 1 and minus 3, minus 3 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)
Part B: Write any two solutions for f(x). (3 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Answer:
(a) No solution
(b)
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
(c) [tex](-6,1)[/tex]
Step-by-step explanation:
Given
See attachment for graph
Solving (a): Solution to p(x) and f(x)
Curve p(x) and line f(x) do not intersect.
So, there is no solution to the pair of p(x) and f(x)
Solving (b): Two solutions to f(x)
This means that we select any two point on straight line f(x)
From the line of f(x), we have:
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
Solving (c): Solution to p(x) = g(x)
Here, we write out the point of intersection of p(x) and g(x)
From the graph, the point of intersection is: [tex](-6,1)[/tex]
what vulnerable does the 4 represents in the number 487.009
Answer:
400 :D
Step-by-step explanation:
