Expectation is linear, meaning
E(a X + b Y) = E(a X) + E(b Y)
= a E(X) + b E(Y)
If X = 1 and Y = 0, we see that the expectation of a constant, E(a), is equal to the constant, a.
Use this property to compute the expectations:
E(X + 10) = E(X) + E(10) = $110
E(5Y) = 5 E(Y) = $450
E(X + Y) = E(X) + E(Y) = $190
Variance has a similar property:
V(a X + b Y) = V(a X) + V(b Y) + Cov(X, Y)
= a^2 V(X) + b^2 V(Y) + Cov(X, Y)
where "Cov" denotes covariance, defined by
E[(X - E(X))(Y - E(Y))] = E(X Y) - E(X) E(Y)
Without knowing the expectation of X Y, we can't determine the covariance and thus variance of the expression a X + b Y.
However, if X and Y are independent, then E(X Y) = E(X) E(Y), which makes the covariance vanish, so that
V(a X + b Y) = a^2 V(X) + b^2 V(Y)
and this is the assumption we have to make to find the standard deviations (which is the square root of the variance).
Also, variance is defined as
V(X) = E[(X - E(X))^2] = E(X^2) - E(X)^2
and it follows from this that, if X is a constant, say a, then
V(a) = E(a^2) - E(a)^2 = a^2 - a^2 = 0
Use this property, and the assumption of independence, to compute the variances, and hence the standard deviations:
V(X + 10) = V(X) ==> SD(X + 10) = SD(X) = $90
V(5Y) = 5^2 V(Y) = 25 V(Y) ==> SD(5Y) = 5 SD(Y) = $40
V(X + Y) = V(X) + V(Y) ==> SD(X + Y) = √[SD(X)^2 + SD(Y)^2] = √8164 ≈ $90.35
Do all perpendicular lines have negative reciprocal slopes?
Not necessarily, the more correct definition is opposite reciprocal slopes.
The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.
In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.
If you vertically stretch the exponential function f(x)=2x by a factor of 3, what is the equation of the new function
Answer:
g(X)=3(2^x)
Step-by-step explanation:
Solve seven square root three plus two square root nine and explain whether the answer is rational or irrational
Answer:
Step-by-step explanation:
5
The total claim amount for a health insurance policy follows a distribution with density function 1 ( /1000) ( ) 1000 x fx e− = , x > 0. The premium for the policy is set at the expected total claim amount plus 100. If 100 policies are sold, calculate the approximate probability that the insurance company will have claims exceeding the premiums collected.
Answer:
the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Step-by-step explanation:
The probability of the density function of the total claim amount for the health insurance policy is given as :
[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]
Thus, the expected total claim amount [tex]\mu[/tex] = 1000
The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]
However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100
To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :
P(X > 1100 n )
where n = numbers of premium sold
[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]
[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]
[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
The square of a number is 12 less than 7 times the number.what is the number?
Answer:
n = 3 or n = 4
Step-by-step explanation:
Let the unknown number be n.
Then:
n² = 7n - 12
In standard quadratic form, we have:
n² - 7n + 12 = 0
In factored form, we have:
(n - 3)(n - 4) = 0, and so
n = 3 and n = 4
Which table represents a linear function?
Answer:
Top right option
Step-by-step explanation:
An AP news service story, printed in the Gainesville Sun on May 20, 1979, states the following with regard to debris from Skylab striking someone on the ground: "The odds are 1 in 150 that a piece of Skylab will hit someone. But 4 billion people ... live in the zone in which pieces could fall. So any one person’s chances of being struck are one in 150 times 4 billion—or one in 600 billion." Do you see any inaccuracies in this reasoning?
Answer:
The odds are one in approximately 27 million.Not one in 600 billionStep-by-step explanation:
From the news story, we are told that:
The odds are 1 in 150 that a piece of Skylab will hit someone.
However, 4 billion people live in the zone in which pieces could fall.
Therefore, any one person’s chances of being struck are:
[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]
Therefore, the odds are one in approximately 27 million.
The inaccuracy presented in this reasoning was that the odds are one in 600 billion.
I need help pleaseeee help meee
Answer:
x>-1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
First we need to determine what sign this inequality uses:
A closed circle represents greater than or equal to (≥) or less than or equal to (≤)An open circle represent greater than (>) or less than (<)Here we have an open circle so we know our sign will either be > or <
Our point is on the -1, and the arrow points in the direction of the sign as long as the variable x is on the left side of the answer
So the arrow is point to the right, indicating our sign will also be "pointing" to the right (>)
The inequality of this graph reads: x > -1
What is equal to 5x when x is equal 50
Answer:
250
Step-by-step explanation:
if x=50
5(x)=5*50=250
Hope it helps..Pls mark as Brainliest!!
List the important features for the graph of a quadratic function.
Answer:
VertexMinimum PointMaximum PointRootsAxis of SymmetryStep-by-step explanation:
The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.
The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.
If possible, please mark brainliest
The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The important features for the graph of a quadratic function will be
The parabola is symmetric about the line which is passing through focus.
The quadratic function can be expressed in the form of vertex form.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
More about the quadratic equation link is given below.
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The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of x^2 = 8.185 . Use α= 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?
Answer:
No the slot machine doesn't appear to function as expected.
Step-by-step explanation:
From chi-squared table , for 9 degrees of freedom and alpha 0.05,
critical value is, 3.325.
Since observed value is greater than critical value we can say that actual outcomes do not agree with the expected frequencies. The slot machine doesn't appear to function as expected.
Explain what the number 0 on the gauge represents and explain what the numbers above 0 represent
Which of the lists of letters all have rotational symmetry?
a. C, H, N, X
b. N, O, S, Z
c. H, J, N, S
d. F, H, X, Z
Answer:
So C doesn't have symmetry so that rules out a
b does though
J doesn't work so that rules out c
F doesn't work so that rules out d
B is answer
Answer:
B. is the rotational symmetry
Step-by-step explanation:
What is the solution? X/12+3< or = 7
Answer:
x <= 48
Step-by-step explanation:
Subtract 3 from both sides
x/12 <= 4
Multiply by 12
x <= 48
What is the sum of 1/6 and 1/7
1/6 + 1/7 = 13/42
aka: 7/42 + 6/42
Answer:
13/42
Step-by-step explanation:
1/6 + 1/7
We need a common denominator of 42
1/6 *7/7 + 1/7 *6/6
7/42 + 6/42
13/42
4 lines are shown. A line with points A, F, D intersects with a line with points B, F, E at point F. A line extends from point F to point G between angle E F D. Another line extends from point F to point D in between angle B F D. In the diagram, which angle is part of a linear pair and part of a vertical pair? AngleBFC AngleCFG AngleGFD AngleEFA
Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
What are linear pair and part of a vertical pair?If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.
Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.
Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.
Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
Learn more about vertical pair from
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help asap giving branlist!!!
Answer:
option 2
Step-by-step explanation:
Because (0, 900) is a point on the line it means that it costs $900 to make the commercial. A slope of 110 means that they pay $110 every time it's aired so the answer is Option 2.
Please answer this correctly
Answer:
1.5 meters
Step-by-step explanation:
The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:
3.75=h*(1.7+3.3)/2
3.75=h*2.5
h=3.75/2.5=1.5
Hope this helps!
Answer:
Step-by-step explanation:
use the formula and rearrange for h.
1/2 x h x (a + b) = A
1/2 x (1.7 + 3.3) x h = 3.75
2.5 x h = 3.75
h = 1.5
hope this helps! :)
Explain how to find the range of a data set. Choose the correct answer below. A. The range is found by subtracting the first data entry from the last data entry. B. The range is found by adding the first and last data entries. C. The range is found by subtracting the minimum data entry from the maximum data entry. D. The range is found by adding the minimum and maximum data entries.
Answer:
C
Step-by-step explanation:
The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Diameter = 11 inches.
Radius = D/2 = 5.5 inches
Volume = 4/3πr³
= 4/3(3.14)(5.5)³
= 696.6 in.³
Write the product in standard form.
(2 - 3i)(2 + i)
Answer:
Brainelist?
Step-by-step explanation:
7-4i
just use a online calculator
Answer:
7-4i
Step-by-step explanation:
(2 - 3i)(2 + i)
FOIL
first 2*2 = 4
Outer: 2i
Inner: -3i*2 = -6i
Last: -3i*i = -3i^2 = -3(-1) = 3
Add them together
4+2i-6i+3
7-4i
A random sample of 150 mortgages in the state of Florida was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is ________.
Answer:
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
Jan's All You Can Eat Restaurant charges $9.10 per customer to eat at the restaurant. Restaurant management finds that its expense per customer, based on how much the customer eats and the expense of labor, has a distribution that is skewed to the right with a mean of $8.10 and a standard deviation of $4.
A. If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.
B. Find the probability that the restaurant makes a profit that day, with the sample mean expense being
less than $8.95.
Answer:
Step-by-step explanation:
From the given question;
Given that:
Jan's All You Can Eat Restaurant charges $9.10 per customer to eat at the restaurant.
Distribution is skewed and and has a mean of $8.10 and a standard deviation of $4.
A. If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.
the mean by using the central limit theorem is 8.10
the standard error of the sampling distribution = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
the standard error of the sampling distribution = [tex]\dfrac{4}{\sqrt{100}}[/tex]
= 4/10
= 0.4
B.
P(X > $8.95) = P (Z > 8.95 - 8.10/0.4)
P(X > $8.95) = P (Z > 2.1)
P(X > $8.95) = 1 - P (Z < 2.1)
P(X > $8.95) = 1 - 0.9821
P(X > $8.95) = 0.0179
Complete the point- slope equation of the line through (8, -8 and (9, 8). Y - 8 =
The article "A Shovel with a perforated blade reduces energy expenditure required for digging wet clay" (Human Factors, 2010:492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure (measured in kilocalories per kg of subject per pounds of clay):
1 2 3 4 5 6 7 8 9 10 11 12 13 Worker Conventional 0.0011 0.0014 0.0018 0.0022 0.001 0.0016 0.0028 0.002 0.0015 0.0023 0.0017 0.002 0.0014 Perforated 0.0011 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 0.002 0.0013 0.0017 0.002 0.0013 0.0013 Carry out a test of hypotheses at significance level 0.05 to see whether the true average energy expenditure using the conventional shovel exceeds that using the perforated shovel. (hint: this is a paired-design!). Make sure to calculate a p-value!
Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
Round the following number to the nearest thousand 2385
By rounding of the following number to the nearest thousand is 2000.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
'
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
Round the following number to the nearest thousand
2385
= 2000
Thus, by rounding of the following number to the nearest thousand is 2000.
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help as quick as possible 18 points :)
Answer:
Step-by-step explanation:
1/10*5 is the answer i think...
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?
Answer:
Which earns more interest = Account B
How much more = $1,306.60
Step-by-step explanation:
Given;
Principal P = $2,000
Interest rate r = 5% = 0.05
Time t = 20 years
For account A;
Simple interest = P×r×t
Substituting the values;
Simple interest = 2,000 × 0.05 × 20 = $2000
Interest on account A = $2,000
For account B;
Compound interest
Final amount = P(1 + r)^t
Since it's compounded annually
Substituting the values;
Final amount = 2000(1+0.05)^20
Final amount = $5306.60
Interest = final amount - principal = $5306.60 -$2000
Interest = $3,306.60
Therefore, account B earns more interest.
Difference = account B interest - account A interest
Difference = $3,306.60 - $2,000
Difference = $1,306.60
Solve.
3^x+1 = 9^ 5x
a. x=3
b. x = 1/3
c. x=9
d. x= 1/9
Answer:
x = 1/9
Step-by-step explanation:
3^ (x+1) = 9 ^ (5x)
Replace 9 with 3^2
3^ (x+1) = 3^2 ^ (5x)
We know that a^b^c = a ^(b*c)
3^ (x+1) = 3^(2 * (5x))
3^ (x+1) = 3^(10x)
The bases are the same so the exponents are the same
x+1 = 10x
Subtract x from each side
x+1-x = 10x-x
1 = 9x
Divide each side by 9
1/9 = 9x/9
1/9 =x