The sum of normally distributed random variables is also a normally distributed random variable.
Given [tex]n[/tex] random variables with [tex]X_i\sim\mathrm{Normal}(\mu_i,\sigma_i^2)[/tex], their sum is
[tex]\displaystyle\sum_{i=1}^n X_i \sim \mathrm{Normal}\left(\sum_{i=1}^n \mu_i, \sum_{i=1}^n \sigma_i^2\right)[/tex]
i.e. normally distributed with mean and variance equal to the sums of the means and variances of the [tex]X_i[/tex].
In this case, each of [tex]X_1,X_2,X_3[/tex] are normally distributed with [tex]\mu=4[/tex] and [tex]\sigma^2[/tex] = ... I'm not sure what you meant for the variance, so I'll keep it symbolic. Then
[tex]V = X_1+X_2+X_3 \sim \mathrm{Normal}(12, 3\sigma^2)[/tex]
Which of the following is equivalent to √√8?
02
O√√2
2√√√2
2 + √2
Answer:
The correct answer is √2 (√√2)
Step-by-step explanation:
√8 = √(4.2) = 2 √2
√√8 = √(2√2) = √2 (√√2)
Answer:
2 √2 (C)
and to the second question the answer is..
1 (B)
9 (C)
Step-by-step explanation:
I answered it on ed 2022
Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
P(-0.78≤Z≤c)=0.7657
For a standard normal distribution, the value of the z-score represented as c in P(-0.78≤Z≤c)=0.7657 is 0.0166
How to find the p-value from 2 z-scores?We want to find the p-value between 2 z-scores expressed as;
P(-0.78 < z < c) = 0.7657
To solve this, we will solve it as;
0/7657= 1 - [P(z < -0.78) + P(z > c)]
From normal distribution table, we have that;
P(z < -0.78) = 0.217695
Thus;
0.7657 = 1 - (0.217695 + c)
c = 1 - 0.7657 - 0.217695
c = 0.0166
Thus, For a standard normal distribution, the value of the z-score represented as c in P(-0.78≤Z≤c)=0.7657 is 0.0166
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What is the component form of the vector that translates the top house figure to the
bottom house figure?
The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).
What is the vector component form?The component form of a vector is known to be depicted as < x, y >.
Note that:
x - tells the distance or how far to the right or left, a vector is known or seen to be going.
y - tells the distance or how far to the upper part or downward a vector is known or seen to be going.
From the question and looking at the image attached, we were able to obtain (-4,4) and (2, 0)
So:
⇒ (-4,4) --------(-4+6)(4-4)-------(2,0)
⇒ (6,-4)
Hence, The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).
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3
Select the correct answer.
What is the inverse of the function f(x)=19/x2
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
What is the meaning of inverse function?An inverse function in mathematics exists function which "reverses" the another function.
Let f(x) = y, then the inverse function, [tex]$x=f^{-1}(y)$[/tex]
[tex]$&f(x)=\frac{19}{x^{2}} \\[/tex]
[tex]$&y=\frac{19}{x^{2}} \\[/tex]
[tex]$&x^{2}=\frac{19}{y} \\[/tex]
simplifying the equation, we get
[tex]$&x=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\[/tex]
[tex]$&f^{-1}(y)=\sqrt{\frac{19}{y}},[/tex] then [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
If [tex]$&f(x)=\frac{19}{x^{2}} \\[/tex] then the inverse function exists [tex]$&f^{-1}(x)=\sqrt{\frac{19}{x}}[/tex].
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Use a graphing tool to solve the equation for x. -4x − 1 = 5x + 4
Answer:
-5/9
Step-by-step explanation:
-4x - 1 = 5x +4 Add 4x to both sides
-1 = 9x + 4 Subtract 4 from both sides
-5 = 9x Divide both sides by 9
-5/9 = x
Simplify: 9x + 2(x - 3) - 2x + 10
Answer: 9x+4
Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.
Answer:
9x + 4
Step-by-step explanation:
9x + 2x - 6 - 2x + 10
Rearranging,
=> 9x + 2x - 2x + 10 - 6
=> 9x + 4
The angle bisectors of a triangle intersect at a point called the
Answer:
incenter
Step-by-step explanation:
An electrician plans to install solar panels on a rectangular section of roof with an area 180m2. This width of this section of roof is 7 1/5 m across. What is the length of this section of roof?
Answer: I believe the answer is 25.
Step-by-step explanation:
You convert 1/5 to a decimal.
1/5 = 0.2
then you divide
180 divided by 7.2 = 25
answer is 25.
evaluate 2n-1, where N -7
The value of the expression 2n - 1 when n = 7 is 13.
Equation2n - 1
when n = 7
Substitute n = 7 into the equation2n - 1
= 2(7) - 1
= 14 - 1
= 13
What is mathematical expression?Mathematical expression is an expression which involves the combination of numbers and variables in a valid way, in a function of addition, subtraction, multiplication, division and exponentiation
Therefore, the value of the expression 2n - 1 when n = 7 is 13.
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Find the distance between each pair of points. Round your answer to the nearest tenth if necessary
(IMAGE)
suppose you are using a=.01 to test the claim than mu is greater than or equal to 32 using a p-value. you are given the sample statistics n=40 , x bar =33.8 and o =4.3. Find the p-value.
0.0040, 0.0211, 0.1030, 0.9960
Using the z-distribution, the p-value for the test is of 0.0040.
What is the test statistic for the z-distribution?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are given as follows:
[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]
Hence the value of the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
z = (33.8 - 32)/(4.3/sqrt(40))
z = 2.65.
What is the p-value?Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.
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What are the intercept of 2X+3y= 6z=30
Answers:
A (15,0,0) ,(0,27,0) ,(0,0,-5)
B (15,0,0),(0,10,0) ,(0,0,5)
C (10,0,0),(0,15,0,)(0,0,5)
D (15,0,0),(0,10,0),(0,0,-5)
The intercepts of the given equations is as given in the task content is; Choice B; (15,0,0),(0,10,0) ,(0,0,5).
What are the intercepts of the equation as give in the task content?The x-intercept of the given equation can be determined by setting values of y and z to zero.
The y-intercept can be determined by setting x and z to zero.
While the z-intercept can be determined by setting x and y to zero.
Consequently, the X-intercept of the given equations is; 2x +3(0) = 30; x = 15.
Therefore, we have; (15,0,0)
The y-intercept is therefore; 2(0) +3y = 30; 3y = 30; y = 30/3 = 10 and. we have; (0,15,0)
And hence, the z-intercept is; z = 30/6 = 5.
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A total load of 28,800 watts is distributed equally over 15 circuits. What is the load per circuit in watts? i need help with solving this, need a step by step for later on
Answer:
1,920 watts per circuit
Step-by-step explanation:
To find the load for 1 circuit (per circuit) we can divide 28,800 watts by 15 circuits
28800/15 = 1,920 watts per circuit
The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?
The area of the rectangle with a perimeter of 36 cm is determined as: 80.1 cm².
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the following:Angle of measure 78 degree enclosed by the diagonals of the rectangle
Perimeter = 36 cm
To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.
A side of the rectangle = x cm
The other side = (36 - 2x)/2 = (18 - x) cm
Angle of the diagonal base = (180 - 78)/2 = 51°
Apply the tangent ratio to find x:
Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,
∅ = 51°
Opposite side = x cm
Adjacent side = (18 - x) cm
Tan 51° = x/(18 - x)
1.235 = x/(18 - x)
1.235(18 - x) = x
22.23 - 1.235x = x
22.23 = x + 1.235x
22.23 = 2.235x
22.23/2.235 = 2.235x/2.235
x = 9.946 cm (one side length)
The other side length = 18 - x = 18 - 9.946 = 8.054 cm
Area of the rectangle = (9.946)(8.054)
Area of the rectangle = 80.1 cm²
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Which of the following proves these triangles are congruent
Answer:
SAA
Step-by-step explanation:
Identify the corresponding congruent parts as either sides or angles. Look at their order of appearance around the triangle.
Corresponding partsThe sides marked with a single hash mark are identified as corresponding and congruent.
The angles marked with a single arc are identified as corresponding and congruent.
The vertical angles where the lines cross are congruent.
SequenceWorking counterclockwise around the left triangle, we encounter ...
side marked congruentvertical angles (congruent)angle marked congruentThese same features appear in the same order working counterclockwise around the triangle on the right.
The "side," "angle," and "angle" are referenced in the congruence postulate as S, A, and A.
Congruence is proved by the SAA congruence postulate.
There are 3 denominations of bills in a wallet: $1, 5$, and $10. There are five fewer $5-bills than $1-bills. There are half as many $10-billsas $5-bills. If there are $115 altogether, find the number of each type of bill in the wallet.
Answer:
15 $1 bills
10 $5 bills
10 $10 bills
Step-by-step explanation:
Let x = number of $1 bills
"There are five fewer $5-bills than $1-bills."
The number of $5 bills is x - 5
"There are half as many $10-bills as $5-bills."
The number of $10 bills is (x - 5)/2.
A $1 bill is worth $1.
x $1 bills are worth x × 1 = x dollars
A $5 bill is worth $5.
x - 5 $5 are worth 5(x - 5) dollars.
A $10 bill is worth $10.
(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.
Now we add the value of each type of bills and set it equal to $115.
x + 5(x - 5) + 5(x - 5) = 115
x + 10(x - 5) = 115
x + 10x - 50 = 115
11x = 165
x = 15
There are 15 $1 bills.
$5 bills: x - 5 = 10 - 5 = 10
There are 10 $5 bills
$10 bills: (x - 5)/2 = (15 - 5)/2 = 5
There are 5 $10 bills
Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills
Check:
First, we check the total value of the bills.
15 $1 bills are worth $15
10 $5 bills are worth $50
10 $10 bills are worth $50
$15 + $50 + $50 = $115
The total does add up to $115.
Now we check the numbers of bills of each denomination.
The number of $1 is 15.
The number of $5 is 5 fewer that 15, so it is 10.
The number of $10 bills is half the number of $5 bills, so it is 5.
All the given information checks out in the answer. The answer is correct.
4) One-fourth cup of yogurt contains 27.5 calories. How many calories are there in 3 1/2 cups of yogurt?
Answer:
385
Step-by-step explanation:
Find (g*f)(3)
f(x)= 7x + 8
g(x)= -1/x
Answer:
-21-24/x
Step-by-step explanation:
f(x) is a function on his own which is f(x)=7x+8
we multiple it with another function which is g(x)=-1/x
that gives us (g*f)=-7-8/x
then multiple it by 3 we have -21-24x
Evaluate the following functions for the given value.
19. f(x) = -x3 + x2; -2
Answer:
12
Step-by-step explanation:
f(x) = -x^3 + x^2
Let x = -2
Evaluate the expression
f(-2) = -(-2)^3 + (-2)^2
= - (-2)*(-2) * (-2) + ( -2) * (-2)
= -(-8) + ( 4)
= 8 + 4
= 12
Please answer asap! If 2 or more people answer I will give brainliest
Answer:
the answer will be 6 centimeter
MARCELLA LANDON WINS THIRD PRIZE IN THE CLEARINGHOUSE SWEEPSTAKES AND
RECEIVES A CHECK FOR $250,000. AFTER SPENDING $10,000 ON VACATION, SHE
DECIDES TO INVEST THE REST IN A MONEY MARKET ACCOUNT THAT PAYS 1.5%
INTEREST COMPOUNDED MONTHLY. HOW MUCH MONEY WILL BE IN THE ACCOUNT
AFTER 10 YEAR
The amount of money in the account after 10 years is $278,814.10.
What will be the value of the account after 10 years?The first step is to determine the amount she has left to invest.
Amount invested = amount won - amount spent on vacation
$250,000 - $10,000 = $240,000
The second step is to determine the future value of the account. The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate = 1/5/12 = 0.125%m = number of compounding =12N = number of years240,000 x 1.00125^(12 x10) = $278,814.10
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y=3x-2
y=-2x+8 solve this equation
Answer:
x = 2
Step-by-step explanation:
3x - 2 = - 2x + 8
→ Add 2x on both sides
5x - 2 = 8
→ Add 2 on both sides
5x = 10
→ Divide both sides by
x = 2
Answer:
x = 2, y = 4 (2,4)
Step-by-step explanation:
Put both the equation in ax + by = c
-3x + y = -2
2x + y = 8
Find x:
Multiply 8 times 1, -2 by 1, 2 times 1, and -3 by 1
8 - (-) 2/2 - (-) 3 = x
10/5
x = 2
Plug x back into equation:
-3(2)+y = -2
y = 4
The line 2x + 3y - k = 0 bisects the line segment joining the points A(4, -3) and B(-2, 5). Find the value of k.
Answer:
5
Step-by-step explanation:
The midpoint of segment AB is (1, 1).
Substituting these coordinates into the equation of the line,
[tex]2(1)+3(1)-k=0 \\ \\ 5-k=0 \\ \\ k=5[/tex]
What is the measure of the third angle?
Answer:
108
Step-by-step explanation:
11+61=72
We use 180 and subtract it by 72 because we know that all angles in a triangle add up to 180.
180-72=108
4 Given that
120 = 2 × 2 ×2×3×5
70 = 2 x 5 x 7
30 = 2 × 3 × 5
a find the highest common factor
b find the lowest common multiple.
Answer:
hcf is 2*5=10
lcm is 2*2*2*5*3*7*3
ASAPP help me with this question
Answer:
AD-DB
Step-by-step explanation:
Because ti joins altogether
Answer:
4th option
Step-by-step explanation:
given Δ ABD and Δ CBD are congruent then corresponding sides are congruent, that is
AB ≡ BC
john likes to walk the steps of the department he works for during lunch break. There are s steps in his department. Today John would like to walk the steps of the taller building next door. The number of steps in the taller building next door is 27 less than 6 times the number of steps in John's department. Which expression represents the number of steps in the taller building next door in terms of s?
A 25-pound bag of fertilizer is on sale for $40. What is the price per ounce of the fertilizer?
Answer:
1.60
Step-by-step explanation:
3. Working with Percent: Determine each amount. a) 1.6% of $150 b) 11.3% of $950 c) 0.29% of $2000 (3)
Answer:
a) (1,6 x 150)/100 = 2,4 dollars
b) (11,3 x 950)/100 = 107,35 dollars
c) (0,29 x 2000)/100 = 5,8 dollars
pls help, i will give brainliest to correct answer
Answer:
5,-1
Step-by-step explanation:
edited.... I gave 1/3 AC earlier (misread the Q)
This means AC is divided into fourths
x from 6 to 2 is -4 1/4th of this added to 6 is
6 - 1/4 * 4 = 5
y from 1 to -7 is -8 1/4th of this added to 1 is
1 - 1/4 * 8 = -1
