It is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].
How to obtain the variance of the distribution of the sum?When two variables are added, we have that:
The mean of the sum variable is given by the sum of of the means of each variable.The standard deviation of the sum variable is given by the square root of the sum of the variances of each variable.The variances for each variable are given as follows:
Income of husband: [tex]\sigma_x^2[/tex].Income of wife: [tex]\sigma_y^2[/tex].Then the standard deviation of the total income, which is the combination of the income of the husband and of the wife, is calculated as follows:
[tex]\sigma = \sqrt{\sigma_x^2 + \sigma_y^2}[/tex]
The variance is the square root of the variance, hence it is obtained as follows:
[tex](\sigma)^2 = (\sqrt{\sigma_x^2 + \sigma_y^2})^2 = \sigma_x^2 + \sigma_y^2[/tex]
Which means that it is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].
Missing InformationThe problem asks if it is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].
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please help me with this
The correct matching regarding the linear functions are given as follows:
i. A set of points where the coordinates of each point has a sum of 2: Line n.
ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.
b - i) Two numbers with a sum of 2: A and C.
b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.
b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.
How to match the options?The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function
x + y = 2.
In slope-intercept form, it is of:
y = 2 - x.
Which is the decreasing line n, with an intercept of 2.
A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function
y = x - 10.
Which is the increasing line m, which an intercept of m.
The coordinates of each point are given as follows:
A(-2,4).B(6,-4).C(12,-10).D(2,-8).E(13,3).These points are then used to match the sentences in item b.
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You are given the statement: Vertical angles are equal in measure.
A. Rewrite the statement as an if-then statement.
B. Write the converse of the implication.
The if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
What is the Converse Statement?
That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.
We have given the statement:
Vertical angles are equal in measure.
A). Rewrite the statement as an if-then statement.
If angles are vertical angles then their measure is equal.
B). Write the converse of the implication
If the measure of angles is equal then they are vertical angles.
Hence, the if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
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Knowledge Check
Find x
x=
Answer:
x is 44 Hope that helps.
Which two triangles are congruent by the AAS theorem? Complete the congruence statement.
Answer:
Step-by-step explanation:
w
Can someone please solve this its on computer and im only good on paper
By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)
How to Solve a System of Equations by Graphing?The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.
To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.
Given the system of equations,
y = 5x + 2
y = x - 2
The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.
The point of intersection is at (-1, -3). Therefore, the solution is:
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Age of Senators The average age of senators in the 108" Congress was 57.5 years. If the standard deviation was 11.5 years, find the -scores corresponding to the oldest and youngest senators of age 87 and 44. Round scores to two decimal places. find the z-score corresponding to the oldest senator of age 85 is
The z-scores correspond to the oldest and youngest senators of ages 87 and 44 are 2.57 and -1.17. The z-score corresponding to the oldest senator of age 85 is 2.39.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. The formula to calculate this score [tex]z=\frac{x-\mu}{\sigma}[/tex]. Where z is the z-score, x is the observed value, μ is the sample mean, and σ is the sample standard deviation.
Given μ = 57.5 and σ = 11.5.
When x = 87, the z-score value is,
[tex]\begin{aligned}z&=\frac{87-57.5}{11.5}\\&=2.57\end{aligned}[/tex]
When x = 44, the z-score value is,
[tex]\begin{aligned}z&=\frac{44-57.5}{11.5}\\&=-1.17\end{aligned}[/tex]
When x = 85, the z-score value is,
[tex]\begin{aligned}z&=\frac{85-57.5}{11.5}\\&=2.39\end{aligned}[/tex]
The required answers are 2.57, -1.17, and 2.39.
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Actuarial math
A 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, is bought to yield 8% convertible semiannually. Find the price. Verify that all four formulas produce the same answer.
The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.
What is the price of a bond?The price of a bond is its present value.
The present value can be computed by setting the following parameters:
Number of periods = 20Effective interest rate = 8%Periodic interest payment = $5 ($100 x 10% x 6/12)Future value = $105.This can be done using an online finance calculator with the results as follows:
N (# of periods) = 20 semiannual periods (10 years x 2)
I/Y (Interest per year) = 8%
PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)
FV (Future Value) = $105
Results:
Present Value (PV) = $115.87
Sum of all periodic payments = $100 ($5 x 20)
Total Interest = $89.13
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Question Completion:Answer: 115.87 (If you don't get this answer then the solution is incorrect.)
-3x ≤ -36 What is the solution?
Answer:
x≤12
Step-by-step explanation:
-3x≥36
÷-3 ÷-3
What is the angle of Q?
66°
Step-by-step explanation:
X=22°
3x= 3*22=66°
to find value of x:
(2x+3)+3x+67=180°
5x+70=180°
x=22°
1/3x= -2/5 solve for x
Answer:
Below
Step-by-step explanation:
1/3 x = - 2/5 <=====multiply both sides of the equation by 3 to get
x = -6/5 = - 1 1/5
PLEASE HELP ME THIS IS MY LAST QUESTION.
Answer:
A
Step-by-step explanation:
as the graphic suggests : reflect (mirror) ABD across the line BD, and CBD is a mirrored but otherwise equal copy of ABD, which also makes angle C equal to angle A.
all the other answer options are creating new triangle that do not map to CBD.
Daniel ran 5 kilometers less then Abhasra last week. Daniel ran 16 kilometers. how many kilometers did Abhasra run?
A company has computed a seasonal index for its quarterly sales. Which of the following statements is not correct?
Multiple Choice
The sum of the four quarterly seasonal index numbers is 4.
The index for any quarter must be between 0 and 2.
The average index is 1.
An index of 0.75 for quarter-one sales indicates that sales were 25 percent lower than average sales.
An index of 1.10 indicates sales 10% above the norm.
The option b "The index for any quarter must be between 0 and 2" is correct.
In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.
For its quarterly sales, the corporation has created a seasonal indicator.
Consequently, it is correct that the four quarterly seasonal index figures add up to 4.
True, the average index is 1.
In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.
Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.
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Anna wants to go del taco with her best friend.they can spend no more than $20. Each fish taco is $2.00 and two drinks are $3.75. How many tacos they can order
The maximum no. of fish tacos they can order is 8.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
let, The no. of fish taco be 'F'.
Therefore, 2F + 3.75 ≤ 20.
So, The no. of fish tacos they order is,
2F ≤ 20 - 3.75.
2F ≤ 16.25.
F ≤ 16.25/2.
F ≤ 8.125 Or 8 as the no. of fish tacos must be in integers.
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Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by f(t) = 160e0.03tin thousands of dollars per year. Find the total income from the machines over the first 5 years. (Round your answer to the nearest thousand dollars.)$______
The total income from the machines over the first 5 years is $185.89
How to determine the total income from the machines over the first 5 yearsFrom the question, we have the following parameters that can be used in our computation:
f(t) = 160e0.03t
Where
t = Number of yearsf(t) = thousands of dollars per yearRewrite the function properly
so, we have the following representation
f(t) = 160e⁰.⁰³ⁿ
The above function is an exponential function
So: In the first 5 years, we have the value of t to be 5
This is represented as follows
t = 5
Substitute the known values in the above equation, so, we have the following representation
f(5) = 160e⁰.⁰³ ˣ ⁵
Evaluate the product of the exponents
f(5) = 160e⁰.¹⁵
The products above give
f(5) = 185.89
Hence, the total income is $185.89
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Go step by step to reduce the radical.
Answer:
[tex] \sqrt{176} [/tex]
[tex] \sqrt{16 + 11} [/tex]
[tex]4 \sqrt{11} [/tex]
Step-by-step explanation:
The answer is
[tex]4 \sqrt{11} [/tex]
We
need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.
i hope this helped
Which property justifies the statement below? X(y+5)=xy+5x
interpret r(t) as the position of a moving object at a time t. use the following information to find the curvature of the path
If the position of a moving object at a time t the curvature of the earth would be 1/4t.
A curved path having various radii of curvature is known as a variable-curvature path. from: 2020 Control Systems Design of Bio-Robotics and Bio-mechatronics with Advanced Applications.
A straight line has zero curvature. In contrast to the tangent, which is a vector quantity, the curvature at a point is often a scalar quantity or one that can be described by a single real integer.
|| r (t) || = 3[tex]t^{2}[/tex], || r' (t) || = 2t, || T (t) || = 1
|| T' || = 1/2
Curvature K = || T' (t) || / || r' (t) || = (1/2) / 2t
K = 1/4t
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The window measures 32 inches wide 48 inches tall to put lights around the window how many inches will I need
Answer: 160 inches
Step-by-step explanation:
To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.
2(x - 6) + 2 = 4x - 4
Answer:
x = - 3
Step-by-step explanation:
2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify
2x - 12 + 2 = 4x - 4
2x - 10 = 4x - 4 ( subtract 4x from both sides )
- 2x - 10 = 4x - 4 ( add 10 to both sides )
- 2x = 6 ( divide both sides by - 2 )
x = - 3
Answer:
SOLUTION
2(X-6)+2=4X-4
open the blanket by multiplication
2x-12+2=4x-4
2x-10=4x-4
collect like term
2x+4x=-4+10
6x=6
divide both side by 6
x=1
Keisha and David each found the same value for cos0, as shown below, given sin0=-8/17. Keisha's Solution
tan²8+1 = sec²e
sin² e
cos² e
=+1=
17
cos² e
(-) + Co
+1=
1
cos² e
cos² e
+ cos²9=1
64
cos 9-1-
-- 289
15
cose=17
David's Solution
sin²+ cos² = 1
cos²8-1-(-17)
Со
cos = ±
225
289
15
cose=¹17 whose procedure is correct?
The procedure is correct is 1 + tan²(theta) = sec²(theta)
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
And
cos²(theta) = 1 - sin²(theta)
Are both valid identities
Keisha and the David.
As per the question Kisha and the David found the same value of the cosine theta as given by the Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).
Thus the answer is both procedures are correct.
As they both wanted to find the solutions to the numerical problems they made two different methods.
Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).
Hence both options are the same and true.
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Waves that make up light have peaks and valleys just like the ocean. What are the scientific terms for peaks and valleys?
highs and lows
crests and troughs
ebbs and flows
protos and parallax
The scientific terms for peaks and valleys is B. Crests and troughs.
What are crests?The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.
The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.
The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.
Therefore, based on the information given, the correct option is B.
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How do you graph 5x= -50
Answer:
you cannot
Step-by-step explanation:
you cannot graph something like that, it is not a equation of a line nor a point or if you want to solve it it is x = -10
Answer:
Step-by-step explanation:
given in the question that 5x=-50
on solving the equation
we get, x=-10
on the graph on the negative x-axis locate the point x=-10
Find the product. Write fractions in simplest form.
-2/7 x 7/4=
The product of -2/7 x 7/4 to the simplest form in fraction is -1/2.
FractionIn arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
[tex]\frac{-2}{7} x \frac{7}{4}[/tex]
Solving this we multiply the fraction by multiply the numerator by numerator and also Denominator by Denominator
= [tex]\frac{-14}{28}[/tex]
Simplify further by dividing the numerator by denominator we have:
= [tex]\frac{-1}{2}[/tex]
Therefore, the the product of the fraction to the simplest form is -1/2 and this can also be written in decimal; -0.5
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A wooden box is in the shape of a regular pentagonal prism. The sides, top, and bottom of the box are 1 centimeter thick. Approximate the volume of wood used to construct the box. Round your answer to the nearest tenth.
The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.
What is a pentagonal prism?A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.
The expression for the volume of a regular pentagon is given as V = 5/2 × abh
Where h is the height and a and b are the length of the sides.
Now, the value of a, b and h as per the question is given as,
a = b = h = 1.
Then, the volume can be calculated as,
V = 5/2 × 1 ×1 × 1
= 2.5
Hence, the volume of the regular pentagonal prism is given as 2.5 cm³.
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what a literal ratio
Answer: The relationship in quantity, amount, or size between two or more things: proportion.
To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.25 inch and standard deviation 0.006 inch and that the diameter of a randomly selected hole is a random variable with mean 0.253 and standard deviation 0.002. Let x1= peg diameter, and let x2= denote hole diameter.Why would the random variable , defined as y=x2-x1 , be of interest to the furniture manufacturer?What is the mean value of the random variable y?Assuming that x1 and x2 are independent, what is the standard deviation of y?Is it reasonable to think that x1 and x2 are independent? Explain.Based on your answers to Parts (b) and (c), do you think that finding a peg that is too big to fit in the predrilled hole would be a relatively common or a relatively rare occurrence? Explain.
(a) Using y the manufacture can find the required diameter of the hole.
(b) The mean of the random variable y is 0.003.
(c) The standard deviation of the y is 0.0063.
(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.
(e) We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.
Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.
a) y=x2-x1 denote the difference between hole and peg diameter
if y<0 , the peg won’t go inside the hole and
if y>0 ,the peg be loose to the hole
So using y the manufacture can find the required diameter of the hole.
b)Now, we have to find the mean of the random variable y
μ(y) = μ(x2) - μ(x1)
μ(y) = 0.253-0.25
μ(y) = 0.003
c) Now we have to find the standard deviation of the y
σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)
σ(y) = √0.000036+0.000004
σ(y) = √0.00004
σ(y) = 0.0063
d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.
e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.
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Question
Taylor is competing in a 30 kilometers race. She has already run 12.35 kilometers through a park and swam 3.75 kilometers. She will bike the rest of the way.
How far does Taylor need to bike to finish the race?
Responses
8.6 km
13.9 km
16.1 km
17.65 km
Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.
Step-by-step explanation:
==> 30 = 3.75 + 12.35 + x
Take 16.1 from both sides:
==> 30 = 16.1 + x
==> 30 = 13.9km
Answer:
Step-by-step explanation:
The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30
Sandra has 5.2 pounds of trail mix that she is splitting
2)
equally into bowls of 0.65 pounds. How many bowls does Sandra need?
Sandra needs 8 bowls to divide the trail mix equally.
To determine the number of bowls Sandra needs, we need to divide the total weight of the trail mix by the weight of each bowl.
First, we need to convert the weight of the trail mix from pounds to ounces. There are 16 ounces in a pound, so 5.2 pounds is equal to 5.2 x 16 = 83.2 ounces.
Next, we need to convert the weight of each bowl from pounds to ounces. There are 16 ounces in a pound, so 0.65 pounds is equal to 0.65 x 16 = 10.4 ounces.
Now that we have both weights in the same units, we can divide the total weight of the trail mix by the weight of each bowl to find the number of bowls needed.
⇒ 83.2 ounces / 10.4 ounces per bowl
Apply the division operation,
⇒ 8 bowls.
Therefore, she needs 8 bowls to divide the trail mix equally.
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Find the degree to the nearest point
The degree to turn before walking 673 paces is 59 degrees
How to determine the degree to walk?From the question, we have the following parameters that can be used in our computation:
Lengths = 989 paces, 673 paces and 861 paces
These paces can be represented as
x = 989
y = 673
z = 861
The measure of the required angle (angle Z) i.e. the degree to walk can be calculated using the following cosine rule
z² = x² + y² - 2xy * cos(Z)
Substitute the known values in the above equation, so, we have the following representation
861² = 989² + 673² - 2 * 989 * 673 * cos(Z)
Evaluate the exponents, the products and the summation
So, we have the following representation
741321 = 1431050 - 1331194 * cos(Z)
Evaluate the like terms
- 1331194 * cos(Z) = -689729
Divide both sides by - 1331194
cos(Z) = 0.51812808651
Take the arc-cos of both sides
Z = 58.7
Approximate
Z= 59 degrees
Hence, the measure of the angle is 59 degrees
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