The given quadrilateral (call it Q) is a trapezoid with "base" lengths of 6 and 12, and "height" 2, so its area is (6 + 12)/2*2 = 18. This means the joint density is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac1{18}&\text{for }(x,y)\in Q\\0&\text{otherwise}\end{cases}[/tex]
where Q is the set of points
[tex]Q=\{(x,y)\mid0\le x\le 2\land0\le y\le12-3x\}[/tex]
(y = 12 - 3x is the equation of the line through the points (0, 12) and (2, 6))
Recall the definition of expectation:
[tex]E[g(X,Y)]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty g(x,y)f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy[/tex]
(a) Using the definition above, we have
[tex]E[X]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty xf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac x{18}\,\mathrm dy\,\mathrm dx=\frac89[/tex]
(b) Likewise,
[tex]E[Y]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\ifnty yf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac y{18}\,\mathrm dy\,\mathrm dx=\frac{14}3[/tex]
In four years,George saved $540. His twin sister, Georgette, saved 10 times as much. How much did Georgette saved?
5400 dollars
540x10= 5400
Bob decided to give up a full-time salary of $45000 a year to go to school for 4 years. The total cost of going to school will not include the loss of income because he has saved money and has grants/scholarships to support living cost during this time. But the cost of going to school will be $2,858 per semester, plus $391 per semester for books. If he wants to recover his investment in 6 years or less what is the minimum salary he would need to earn upon earning his degree.
Answer:
Step-by-step explanation:
Semester Costs = 8*2858 = 22864
Books / semester= 8 * 391 = 3128
Total 25992
If he wants to repay all this in six years the answer would be
45000 + 25992/6 = 45000 + 4332 = 49332
Answer:
49332
Step-by-step explanation:
An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).
Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.
a. True
b. False
Answer:
False
Step-by-step explanation:
Here, we want to check the validity of the given statement. The statement is false.
Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.
Please check attachment for diagrammatic representation of the empirical rule.
Please help! Anyways how was your day? lol
Answer:
>
Step-by-step explanation:
the less negative the greater the number
What is the measure of x?
Answer:
22
Step-by-step explanation:
This is a right angle so the sum of those would be equal to 90 degrees
x + 7 + 3x - 5 = 90 add like terms
4x + 2 = 90 subtract 2 from both sides
4x = 88 divide both sides by 4
x = 22
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel
Answer:
the probability of no defects in 10 feet of steel = 0.1353
Step-by-step explanation:
GIven that:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.
Let consider β to be the average value for defecting
So;
β = 2
Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.
Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2
i.e
[tex]Y \sim P( \beta = 2)[/tex]
the probability mass function can be represented as follows:
[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]
where;
y = 0,1,2,3 ...
Hence, the probability of no defects in 10 feet of steel
y = 0
[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]
[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]
P(y =0) = 0.1353
what should be added to 4x get 9X please help me in this pic also all
Answer:
[tex]thank \: you[/tex]
The one-sample z test is: a. a hypothesis test b. used to test hypotheses c. concerning a single population with a known variance d. concerning at least one population e. concerning the variance in a population d. all of the above
Answer:
d. all of the above
Step-by-step explanation:
A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used
on a 25 square grid how many squares need to be shaded to make 60% shaded
Answer:
15 squares
Step-by-step explanation:
60/100 * 25 = 15
is [tex]\sqrt[4]{5x^{5} }[/tex] equal [tex](\sqrt[4]{5x} )^{5}[/tex] ?
i need help quick!!!
Answer: A,C, and D
Step-by-step explanation:
Answer:
the answer to this question may be option B, C and D
3. A medical devices company wants to know the number of MRI machines needed per day. A previous study found a standard deviation of four hours. How many MRI machines must the company study in order to have a margin of error of 0.5 hours when calculating a 90% confidence interval
Answer:
173 MRI machines
Step-by-step explanation:
Margin of error E = 0.5
Confidence interval 90% = 1-0.9 = 0.1
Standard deviation = 4 hours
Number of MRI machines needed per day n, = [(z alpha/2 * SD)/E]²
Z alpha/2 = 1.645 at alpha = 0.1
Inputting these values into n we have that
[(1.645*4)/0.5]²
= 13.16²
= 173.18 is approximately equal to 173
The company has to study 173 machines.
A mutual fund owns 20,000 shares in Company Y. Company Y has 2 million shares issued. In one particular year, Company Y announces annual profits of $6 million, and decides to pay dividends to its shareholders at a rate of 15% of its annual profits. How much will the mutual fund receive in the form of dividends from Company Y? Round your answer to the nearest dollar.
Answer: $9,000
Step-by-step explanation:
Step 1
Calculate the amount of dividends the company will pay to all its shareholders.
= 15% of profits
= 15% * 6,000,000
= $900,000
Step 2
Calculate how much dividends each share will get;
$900,000 to 2 million shares of Company Y.
= 900,000/2,000,000
= $0.45
Step 3
Calculate how much the Mutual fund will get for its 20,000 shares
= 20,000 * 0.45
= $9,000
If a triangular pyramid has a base area of 10ft and a height of 6ft, what is the volume?
. 20ft^3
. 40ft^3
.60ft^3
.80ft^3
.120ft^3
Answer: 20 ft³
Step-by-step explanation:
volume of triangular pyramid = [tex]\frac{1}{3} bh[/tex]
b = base area = 10 fth = height = 6 ftTherefore, the volume is:
[tex]\frac{1}{3} *10*6=\frac{1}{3}*60=\frac{60}{3}=20[/tex]
If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire tub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.
Answer:
46.2÷m=x
Step-by-step explanation:
u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).
16.5/min
time = m
gallons / minutes = rate
46.2 = 16.5 (m)
46.2 / 16.5 = 16.5 (m) / 16.5
2.8 = minutes
Problem is attached in a photo
Answer:
y<(x-2)^2
Step-by-step explanation:
To graph this inequality, we first identify the function.
This is a quadratic function y=x^2
The function is translated horizontally to the right two. (x-2)^2
It is also a dotted line, <.
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80Use the dot product to determine whether v and w are orthogonal.
v=-i-j, w=-i+j
Select the correct choice below and fill in the answer box to complete your choice.
O A. The vectors v and w are not orthogonal because their dot product is ___
O B. The vectors v and w are orthogonal because their dot product is ___
Answer:
B. The vectors v and w are orthogonal because their dot product is 0
Step-by-step explanation:
Given that :
v= - i - j
w= - i + j
Therefore;
vw = ( - i - j ) ( - i + j )
Taking each set of integer of the vector into consideration:
vw = ( -1 × - 1) ( -1 × 1)
vw = 1 - 1
vw = 0
Hence, we can conclude that :
The vectors v and w are orthogonal because their dot product is 0
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Answer:
y=-1/7x + 12/7
Step-by-step explanation:
Start by finding the slope
m=(1-0)/(-5-2)
m=-1/7
next plug the slope and the point (-5,1) into point slope formula
y-y1=m(x-x1)
y1=1
x1= -5
m=-1/7
y- 1 = -1/7(x - -5)
y-1=-1/7(x+5)
Distribute -1/7 first
y- 1=-1/7x + 5/7
Add 1 on both sides, but since its a fraction add 7/7
y=-1/7x + (5/7+7/7)
y=-1/7x+12/7
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a
continuous rate of 25% every day (that's why they're magic). How many grams of
crystals will you have after one week (7 days)?!
ANSWER IS BRAINLEIST
Answer:
After 7 days the crystals will be 57.57 grams.
Step-by-step explanation:
In this the continuous exponential growth formula will be used.
y = A e ^rt
Where A = original amount = 10 grams
y is the growth after 7 days
e is Euler's number= 2.719
t is the time in hours , weeks, years etc.= 7 days
r is the rate in decimals = 25% = 0.25
Putting the values in the formula:
y = A e ^rt
y = 10 e ^0.25 (7)
Calculating with the calculator
y = 10* 2.719^1.75
y= 57.57 grams.
After 7 days the crystals will be 57.57 grams.
Answer:
57.55g
Step-by-step explanation:
Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.
Use a calculator to find
the mean of the data.
{217, 253, 214, 247,
217, 253, 232, 246,
223, 227, 229, 247,
206, 241, 239, 223,
222, 216, 252, 209,
236, 256}
A. 230.811
B. 231.045
C. 232.045
D. 232.811
Answer:
232.045
Step-by-step explanation:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
5105 / 22 = 232.045454545
Question: 2. Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West And Finally 50 Steps On A Bearing Of 3150 Sketch Musah's Movement Mark 41 Ii. How Far West Is Musah's Final Point From The Centre? [Mark 41 Iv. How Far North Is Musah's Final Point From The Centre? Mark 41 Describe How You Would Guide A JHS Student
Answer:
60.36 steps West from centre
85.36 steps North from centre
Step-by-step explanation:
Refer to attached
Musah start point and movement is captured in the picture.
1. He moves 50 steps to North, 2. Then 25 steps to West, 3. Then 50 steps on a bearing of 315°. We now North is measured 0°or 360°, so bearing of 315° is same as North-West 45°.
Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.
How far West Is Musah's final point from the centre?
25 + 50/√2 ≈ 60.36 stepsHow far North Is Musah's final point from the centre?
50 + 50/√2 ≈ 85.36 stepsUse a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥8 300, α = 0.10
Sample statistics: x = 8000, s = 440, n = 24
A. What are the null and alternative hypotheses?
B. What is the value of the standardized test statistic?
C. What is the p-value?
D. Decide whether to reject or fail to reject the null hypothesis.
Answer:
A
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
B
[tex]t = -3.34[/tex]
C
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
D
reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 8300[/tex]
The sample mean is [tex]\ = x = 8000[/tex]
The standard deviation is [tex]s = 440[/tex]
The sample size is [tex]n = 24[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
The test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]
=> [tex]t = -3.34[/tex]
The p-value is obtained from the z -table ( reference calculator dot net ) , the value is
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
Looking at the values of [tex]p-value and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis
bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab
Answer:
[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]
Step-by-step explanation:
Bananas represented by b
1 banana costs $4 so b bananas will cost $ 4 b
Apples represented by a
1 apples costs 0.60 $ so a apples will cost $ 0.60 a
Totally, they will cost:
=> $ (4 b + 0.60 a)
Answer:
hiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim
Answer:
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at least 64%, that is:
[tex]H_0: p \geq 0.64[/tex]
At the alternative hypothesis, we test if the proportion is of less than 64%, that is:
[tex]H_1: p < 0.64[/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.
64% is tested at the null hypothesis:
This means that [tex]\mu = 0.64, \sigma = \sqrt{0.64*0.36}[/tex]
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.
This means that [tex]n = 900, X = 0.61[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}[/tex]
[tex]z = -1.88[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.
Looking at the z-table, z = -1.88 has a p-value of 0.0301.
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
Help due today
No links
Answer:
-6
Step-by-step explanation:
Answer:
[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]
18. Solve the equation for X.
Answer:
Option a is the correct answer
* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.
Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = event that the diagnostic test is accurate
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
Now, the probability that the diagnosis is correct is given by;
Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')
= (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.