Answer:
Hence the correct option is Option b that is the same for each interval.
Step-by-step explanation:
The PDF for Uniform distribution in [a,b] is given by
[tex]f(x)=\frac{1}{b-a}~~~~~~a\leq x\leq b[/tex]
So the probability that the random variable assumes a value in [a,b] is given by
[tex]\int_{a}^{b}f(x)dx=\int_{a}^{b}\frac{1}{b-a}dx=1[/tex]
Therefore the correct option is b. the same for each interval.
pls help fast, appreciated
Answer:
x = 6.9
Step-by-step explanation:
[tex]\frac{sin(90)}{12} = \frac{sin(35)}{x} \\\\x = 6.9[/tex]solve for x
Find value a when the angle between vectors U=(2,a) and V = (-6;8) is pie/4
Answer:
Step-by-step explanation:
The formula to find the angle between 2 vectors is
[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is
u·v = (2×(-6)) + (a×8) so
u·v = -12 + 8a. Then we need the magnitudes of both u and v:
[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and
[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]
Putting all of together looks like this:
[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get
[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is
[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:
100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get
800 + 200a² = 256a² -768a + 576. Combine like terms to come up with
0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.
Therefore, the value for a is 14. I checked it...it works
Answer:
a = 14, U = (2, 14)
Step-by-step explanation:
the other answer is correct.
just to add the solution path for the quadratic equation
0 = 56a² - 768a - 224
in general, a quadratic equation usually expressed in x
0 = ax² + bx + c
has its solution as
x = (-b ± sqrt(b² - 4ac))/(2a)
for us here this looks like this then
a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =
= (768 ± sqrt(589824 + 4×56×224))/112 =
= (768 ± sqrt(589824 + 50176))/112 =
= (768 ± sqrt(640000))/112 = (768 ± 800)/112
a1 = (768 + 800)/112 = 1568/112 = 14
a2 = (768 - 800)/112 = -32/112 = -0.29
and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.
so, 14 is the solution for U.
find the equation of the line that passes through a point A(1,-5) B(-2,-7)
Answer:what’s the answer?
Step-by-step explanation:
Find the value of x. Round to the nearest 10th
Answer:
44.94
Step-by-step explanation:
In a certain year, 86% of all Caucasians in the U.S., 77% of all African-Americans, 77% of all Hispanics, and 84% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 11% African-American, and 10% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic
Answer:
Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%
Step-by-step explanation:
We are given that
Population was Caucasian=64%
Population was African-American=11%
Population was Hispanic=10%
Let the population of U.S=10000
Now,
Population was Caucasian=[tex]\frac{64}{100}\times10000=6400[/tex]
Population was African-American=[tex]\frac{11}{100}\times 10000=1100[/tex]
Population was Hispanic=[tex]\frac{10}{100}\times 10000=1000[/tex]
Population of others=10000-(6400+1100+1000)=1500
Population of Caucasians used the Internet for e-mail=86% of 6400
Population of Caucasians used the Internet for e-mail=[tex]\frac{86}{100}\times 6400[/tex]
Population of Caucasians used the Internet for e-mail=5504
Population of African-American used the Internet for e-mail=77% of 1100
Population of African-American used the Internet for e-mail=[tex]\frac{77}{100}\times 1100=847[/tex]
Population of Hispanics used the Internet for e-mail=77% of 1000
Population of Hispanics used the Internet for e-mail=[tex]\frac{77}{100}\times 1000=770[/tex]
Population of others used the Internet for e-mail=84% of 1500
Population of others used the Internet for e-mail=[tex]\frac{84}{100}\times 1500=1260[/tex]
Total population used the Internet for e-mail=5504+847+770+1260
Total population used the Internet for e-mail=8381
Percentage of U.S resident who used the Internet for e-mail were Hispanic
=[tex]\frac{Population \;of \;Hispanics \;used \;the \;Internet \;for \;e-mail}{total\;population\; used \;the \;Internet \;for\; e-mail}\times 100[/tex]
Percentage of U.S resident who used the Internet for e-mail were Hispanic=[tex]\frac{770}{8381}\times 100[/tex]
Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%
for the following right triangle find the side length x round your answer to the nearest hundredth
Answer:
4.58
Step-by-step explanation:
How do I uses these
Answer:
To understand a graph you need to interpret a graph or a chart, read the title, look at the key, read the numbers and lables. then study the graph to understand what it shows. read the title graph or chart. the title tells what information is being displayed.
Step-by-step explanation:
affgfgghffbvcxddgjjjbvccf
Answer:
2x(7×3)+(7×6)+(3×6)= 162ft
A small county has two property appraisers, Tim and Julie. Does Tim appraise property differently on average than the Julie? Each appraiser looks at 20 properties and each independently determines the value of the property. (Tim - Julie)
How should we write the alternative hypothesis?
(mud is the population mean difference)
A. Ha: mud = 0.
B. Ha: mud > 0.
C. Ha: mud < 0.
D. Ha: mud does not equal zero.
Answer:
The answer is "Option D"
Step-by-step explanation:
In this question the "choice D" is wrong because [tex]H_a: \mu_d \neq 0[/tex].
If the number of orders at a production center this month is a Geom(0.7) random variable, find the probability that we'll have at most 3 orders.
Answer: 0.973
Step-by-step explanation:
The probability mass function of geometric distribution is
[tex]f(x)=(1-p)^{x-1}p,\ \ \ x=1,2,3,...[/tex], p= probability of success on a trial.
As per given, we have
p=0.7
The probability that we'll have at most 3 orders [tex]P(X\leq3)=P(x=1)+P(x=2)+P(x=3)[/tex]
[tex]=(1-0.7)^{1-1}(0.7)+(1-0.7)^{2-1}(0.7)+(1-0.7)^{3-1}(0.7)\\\\=0.7+0.21+0.063\\\\=0.973[/tex]
hence, the required probability = 0.973
The probability that we'll have at most 3 orders will be "0.973".
According to the question,
→ [tex]x \sim Geometric (p)[/tex]
here,
p = 0.7
then,
→ [tex]P(X=x) = (1-p)^{x-1}\times p[/tex]
By putting the given values, we get
[tex]= (1-0.7)^{x-1}\times 0.7[/tex]
hence,
The probability that we'll have at most 3 orders will be:
→ [tex]P(X \leq 3)=P(X=1)+P(X=2)+P(X=3)[/tex]
[tex]=0.7+0.21+0.063[/tex]
[tex]=0.973[/tex]
Thus the above response is correct.
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The total cost of a truck rental, y, for x days, can be modeled by y=24x+39. What is the rate of change for this function?
Answer:
24 per day
Step-by-step explanation:
'x' = days, so since 24 is with x, the rate of change is 24
ANSWER ASAP!! The graph of f(t)=4•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer:
the value of a rare coin in the beginning of the first year,
t = 0, so f(0) = 4• 2^0 = 4•1 = 4 (y-intercept)
Answer:
the y-intercept is at t=0, so in the model no time has past yet. it's the initial value of the coin
The school has a population of 500 students.
Supposed 200 students play soccer, 170 students play basketball, and 100 play both soccer and basketball.
1) How many students didn’t participate in either sport?
2) How many students played only soccer or only basketball?
3) How many students play either sport?
4) How many students played both soccer and basketball?
PLEASE HELP TY!
Answer:
1. 30
2. 370
3. 470
4. 100
Step-by-step explanation:
for one, add the amount of students that play sports and subtract it from 500. for two, add the number of people that only play soccer and only play basketball. for three, take away the 30 people from the 500 kids that don't play. for four, it says 100 people play both.
El opuesto y el semejante de 8xy
Answer:
No entiendo
Step-by-step explanation:
The volume of the triangular prism is 1008 cubic centimeters.
Find the base height. *
1
21 cm
12 cm
8
You
7
Answer:
?
Step-by-step explanation:
i dont understanding that
A 12 sided die is rolled. Find the probability of rolling and even number
Answer:
0.5
Step-by-step explanation:
Wanted outcome / possible outcomes = 0.5 in this case.
Which graph represents y-1 = 2(x - 2)?
Answer:
The second graph
Step-by-step explanation:
This is because as you can see the equatin they're using is point slope form (y-y1=m(x-x1)) and the m stands for slope. the slope in the equation you gave us is 2 or a rise of 2 and a run of 1 (2/1) and the frist graph has a slope of 3/1
The midpoint of a line segment from P1 to P2 is (-5,2). If P1 = (-1,7), what is P2?
Hope it helps you!
-miraculousfanx-
Answer:
p2 = (-9 , -3)
Step-by-step explanation:
let p2 be (a , b)
given :
p1(-1 , 7) = (x1 , y1)
p2(a , b) = (x2 , y2)
using midpoint formula:
midpoint = (x1 + x2/2 , y1 + y2/2)
(-5 , 2) = (-1 + a/2 , 7 + b/2)
Now , compare corresponding elements
-5 = -1 + a/2
-5*2 = -1 + a
-10 = -1 + a
-10 + 1 = a
-9 = a
2 = 7 + b/2
2*2 = 7 + b
4 = 7 + b
4 - 7 = b
-3 = b
therefore p2 = (-9 , -3)
Find the solution(s) for x in the equation below.
x^2 - 25 = 0
A. x = -5
В. no solutions
C. x = 5
D. x = 5; x = -5
Answer:
D. x = 5; x = -5
Step-by-step explanation:
x^2 - 25 = 0
Add 25 to each side
x^2 - 25+25 = 0+25
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = ±5
The manager of a local car dealership wants to conduct a customer satisfaction survey. Which group of people should make up a sample of the population?
A. sales people in the dealership
B. mechanics who work at the dealership
C. people who bought cars from the dealership
D. prospective buyers who visit the dealership
Answer:
Step-by-step explanation:
A customer satisfaction survey refers to a questionnaire that's designed by a company in order for businesses to know what customers think about their products.
Since the manager of a local car dealership wants to conduct a customer satisfaction survey, then the group of people should make up a sample of the population will be the people who bought cars from the dealership
Answer:
c
Step-by-step explanation:
PLEASE HELP
A store is giving out cards labeled 1 through 10 when customers enter the store. If the
card is an even number, you get a 15% discount on your purchase that day. If the card is an odd
number greater than 6, you get a 30% discount. Otherwise, you get a 20% discount. The table
shows the results of 500 customers. What is the relative frequency for each discount? Use pencil
and paper. If the manager of the store wants approximately half of the customers to receive the
20% discount does this seem like an appropriate method? Explain.
Step-by-step explanation:
The relative frequency for a 15% discount is 52.1%.
What is a relative frequency?The relative frequency is the quotient of a particular frequency divided by the total number of frequencies.
Given:
A store is giving out cards labeled 1 through 10 when customers enter the store.
If the card is an even number, you get a 15% discount on your purchase that day.
The subgroup for even numbers = 2, 4, 6, 8, 10
The subgroup frequency = 56 + 50 + 54 + 49 + 54 = 263
The total frequency = 500
The relative frequency = 263/500 = 0.521 = 52.1%
Therefore, 52.1% is the relative frequency.
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who is the mathematics creator ?
its my final, please help!!!!!!!!!!
Answer:
both apply
Step-by-step explanation:
i guessed just do it
How do I do this this question I really need help on this
Answer:
-2
Step-by-step explanation:
If you draw a line from a to a^1 and cut that line in half, that’s the line of reflection (or think of it as a line of symmetry if that helps). You use a and a^1 because a^1 is the reflection of point a
1. Name a decimal between 0.2222 and 0.2223.
2. if you laid 4 million bills end to end, how long (in miles) would that be? (use 6.14 inches for the length of a single bill. round your answer to one decimal place.)
2a. how long (in miles) would 4 billion dollars be? ( Round answer to one decimal place.)
3. what base is c in this statement?
695 base ten = 852 base x
4. order the numbers to smallest to largest.
3/11, 0.027, 0.27, -13
Step-by-step explanation:
You should be breaking this up
One
Decimal between 0.2222 and 0.2223 would be something like 0.22225
Two
1 mile = 5280 feet
1 mile = 5280 feet * 12 = 63360 inches
4 miles = 253440 inches
answered on my cell phone. I can't really do this.
wv^2 / Fg = r
Substitute the given values to find the value of the indicated letter.
r = ?
Given F = 11,000; W = 22,000; v = 164; g = 32
What is the approximate radius of a sphere with a volume of 268 cm^3?
Answer:
Step-by-step explanation:
[tex]V=\frac{4}{3}\pi r^3~=>r=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3*260cm^3}{4\pi}}=3.96 \approx4[/tex]
Can someone help me please
Answer:
Ishaan is correct because snakes with 17 1/4 inches occured most often in the dot plot. Raj is incorrect because 17 3/4 didnt occur the most often but it was the highest length of the snake. Ishaan is correct.
Step-by-step explanation:
a. We will attempt to answer the question "What is the average height of RCCC male students?" using data we collected the first week of this semester. Be sure to give explanations in context and include units when appropriate.
Describe the population of interest?
A sample of____(state the number) RCCC male students was taken. We found the sample mean____(symbol) to be Interpretation: In the sample of male RCCC students, the____"mean") height was approximately____inches.
The median is____Interpretation (use the one for mean as a guide):
The mode is____Interpretation (use the one for mean as a guide):
b. We know the measures of central tendency don't tell us the whole story, so we then investigated the measures of variation as well. We found that the heights had a range of_____with a standard deviation____(symbol) of_____(2 decimal places) and a variance_____(symbol) of (2 decimal places).
Height (inches) Note: There are 31 male heights.
1 70
2 70
3 70
4 70
5 71
6 64
7 64
8 65
9 65
10 66
11 66
12 67
13 67
14 68
15 68
16 68
17 69
18 72
19 72
20 72
21 72
22 73
23 73
24 73
25 73
26 73
27 73
28 74
29 75
30 75
31 75
32 75
70 70 70 70 71 64 64 65 65 66 66 67 67 68 68 68 69 72 72 72 72 73 73 73 73 73 73 74 75 75 75 22
The population of interest: Male RCCC students.
Sample size: 31.
The sample mean: 69.68 inches.
Median: 69 inches.
Mode: 70 inches.
Range: 11 inches.
Standard deviation: 3.32 (rounded to 2 decimal places).
Variance: 11.02 (rounded to 2 decimal places).
We have,
Mean:
To find the mean, we sum up all the heights and divide by the total number of data points (31 in this case):
Mean = (70 + 70 + 70 + ... + 75) / 31
Mean ≈ 69.68 inches
Median:
The median represents the middle value in the dataset when arranged in ascending order. Since the dataset has an odd number of values (31), the median will be the value in the middle position when ordered:
Median = 69 inches
Mode:
The mode represents the value(s) that occur most frequently in the dataset. In this case, the mode is the height that appears most often:
Mode = 70 inches
Range:
The range is calculated by subtracting the minimum value from the maximum value in the dataset:
Range = Maximum height - Minimum height
Range = 75 - 64 = 11 inches
Standard Deviation (σ):
To find the standard deviation, we can use the formula that involves finding the difference between each value and the mean, squaring those differences, averaging them, and taking the square root:
Standard Deviation (σ) ≈ 3.32 (rounded to 2 decimal places)
Variance (σ²):
The variance is the square of the standard deviation.
We can square the value of the standard deviation to find the variance:
Variance (σ²) ≈ 11.02 (rounded to 2 decimal places)
The height dataset (in inches) for the 31 male RCCC students is as follows:
1 70
2 70
3 70
4 70
5 71
6 64
7 64
8 65
9 65
10 66
11 66
12 67
13 67
14 68
15 68
16 68
17 69
18 72
19 72
20 72
21 72
22 73
23 73
24 73
25 73
26 73
27 73
28 74
29 75
30 75
31 75
32 75
Thus,
The population of interest: Male RCCC students.
Sample size: 31.
The sample mean: 69.68 inches.
Median: 69 inches.
Mode: 70 inches.
Range: 11 inches.
Standard deviation: 3.32 (rounded to 2 decimal places).
Variance: 11.02 (rounded to 2 decimal places).
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Three men and seven women have been shortlisted for the post of HR Manager. What is the probability of a man getting the job?
Answer:
3/10.
Step-by-step explanation:
The 3 men will be on the numerator, to signify they're the group we're focusing on.
Then you add all of the people together (7 + 3 = 10) and put that on the denominator.
therefore, you get 3/10.
The probability of a man getting the job for the post of HR Manager is 3/10.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
We know, The ratio of favorable events to unfavorable events for a given event is known as the odds in favor.
Given, Three men and seven women have been shortlisted for the post of HR Manager.
Therefore, The probability of a man getting the job is,
= (3/(3 + 7)).
= 3/10.
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