Find the measure of each angle.
Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors
Sample Size 102 258 319 31
x :2.00 3.10 3.06 2.81
s :1.59 1.66 1.69 1.87
For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using α = 0.01.
Calculate the test statistic. (Round your answer to two decimal places.) F = ?
What can be said about the P-value for this test?
P-value > 0.100
0.050 < P-value < 0.100
0.010 < P-value < 0.050
0.001 < P-value < 0.010
P-value < 0.001
What can you conclude?
Reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
Reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
You may need to use the appropriate table in Appendix A to answer this question.
Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors
Sample Size 102 258 319 31
x :2.00 3.10 3.06 2.81
s :1.59 1.66 1.69 1.87
for this test
P-value > 0.100
0.050 < P-value < 0.100
0.010 < P-value < 0.050
0.001 < P-value < 0.010
P-value < 0.001
Hence , Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
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Can you figure out what the answer is here
The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20
What is logical reasoning?Logical or deductive reasoning involves using a given set of facts or data to deduce other facts by reasoning logically. It involves drawing specific conclusions based on premises.
Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.
Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.
Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4
Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.
Hence, The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20
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Hello, I need help with this problem. Please explain with work.
Thank you.
The Venn Diagram is shown at the end of the answer.
From the diagram, the percentages are given as follows:
Light rail or bus, but not carpool: 10%.Carpool and bus: 0%.Did not answer light rail, carpool or bus: 72%.Exactly one: 21%.Light rail, carpool, or bus: 28%.How to fill the Venn Diagram?The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.
2% of people answered all three, hence space V on the diagram has a value of 2%, which is the intersection of the three sets.
3% of people answered light rail and bus, hence space IV has a value of 1%, as light rail and bus also involve light rail, bus and carpool.
6% of people answered light rail and carpool, hence space II has a percentage of 4%, following the same logic above.
2% of people answered carpool and bus, hence space V has a percentage of 0%.
11% of people answered carpool, hence space III has a percentage of 5%, as this percentage is a combination of:
Carpool and bus.Carpool and rail.Carpool, bus and rail.Only carpool.From the total bus and light rail percentages, the percentages are given as follows:
VI = 7%.I = 9%.The percentage of people that use at least one of these mediums is given as follows:
9 + 7 + 5 + 1 + 2 + 4 = 28%.
The percentage of people who use none of these mediums is given as follows:
100 - 28 = 72%.
Then the missing percentages at the end of the problem, along with their spaces, are given as follows:
Light rail or bus, but not carpool: I + IV = 9 + 1 = 10%.Carpool and bus: VI = 0%.Exactly one: I + III + VII = 9 + 5 + 7 = 21%.More can be learned about Venn Diagrams at brainly.com/question/24713052
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Cliff (W-2 wages: $16,228) and Deb (W-2 wages: $2,600) send their daughter Julia (born 10-1-2010) to daycare while they both worked. They paid $250 per month for daycare. They are filing MFJ. They can claim the credit for child and dependent care expenses. What is their eligible amount of work-related daycare expenses?
The eligible amount of work-related daycare expenses will be $2600
What is MFJ?Married filing jointly is a filing status for married couples, allowing them to file joint tax returns. When filing taxes under married filing jointly status, a married couple can record their respective incomes, deductions, credits, and exemptions on the same tax return.
Given here wages of the cliff are $16,228 and if the deb is $2,600
now the mfj is 35% hence cliffs credit is 35% × $16,228 = $5679.8
and daycare yearly expenses are = $250×12
= $3000
but deb's income is $2600 and thus credit cannot exceed deb's wages therefore the revised credit would be $2600
Hence, the eligible amount of work-related daycare expenses will be $2600
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6. If A and B are supplementary angles
and mA = 8m ZB, find m2 A and m2 B.
[A] 78.75, 11.25
[C] 160, 20
[B] 80, 10
(D) 157.5, 22.5
Answer:
C) 160, 20-----------------------
Given:Angles A and B are supplementary,Angle A is 8 times the angle B.Find the angle measures:We know supplementary angles sum to 180 deg:
m∠A + m∠B = 180,And we are given:
m∠A = 8 m∠BSubstitute the second equation into the first one and solve for m∠B:
8m∠B + m∠B = 1809m∠B = 180m∠B = 180/9m∠B = 20Find m∠A:
m∠A = 8*20m∠A = 160Correct choice is C.
factor this expression completely, then place the factors in the proper location on the grid. 5x 3 40y 6
The final Factorisation of the expression of 5x³ + 40y⁶ is 5 ((x + 2y²) (x² - 2xy² + 4y⁴)).
Describe factorization.When an algebraic equation is expressed as the sum of its factors, it has been factorized. There might be these variables, elements, or algebraic expressions.
A number is broken down for the factor into components that may be multiplied to produce the original number.
Briefing:According to the question,
We have to factorize the expression
5x³ + 40y⁶
Taking a Common factor 5 out ,
5 (x³ + 8y⁶)
When the expression between the parenthesis is factored, we get:
5 ((x + 2y²) (x² - 2xy² + 4y⁴))
Right now, we cannot add another element.
Hence , The factored expression is given by: 5 ((x + 2y²) (x² - 2xy² + 4y⁴))
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MODELING REAL LIFE There are a total of 64 students in a filmmaking club and a yearbook club. The filmmaking club has 14 more students than the yearbook club.
a. Write a system of linear equations that represents this situation. Let x represent the number of students in the filmmaking club and y represent the number of students in the yearbook club.
System of equations: x=?
?x+?y=64
b. How many students are in the filmmaking club? the yearbook club?
There are . students in the filmmaking club and students in the yearbook club.
(a) The System of equations that representing this situation is
x= y+14; x+y = 64
(b) There are 39 students in the film-making club and 25 students in the yearbook club.
In the given question, there are a total of 64 students in a film-making club and a yearbook club.
The film-making club has 14 more students than the yearbook club.
a. We have to write a system of linear equations that represents this situation.
Let x represent the number of students in the film-making club
Let y represent the number of students in the yearbook club.
As given that the film-making club has 14 more students than the yearbook club.
So x = y+14
Total students are 64.
So x+y = 64
System of equations:
x= y+14
x+y = 64
b. Now we have to find how many students are in the film-making club and the yearbook club.
The system of equations are;
x= y+14...................(1)
x+y = 64...................(2)
Now putting the value of x in equation 2.
y+14+y = 64
2y+14 = 64
Subtract 14 on both side, we get;
2y = 50
Divide by 2 on both side, we get;
y = 25
Now putting the value of y in equation 1.
x = 25+14
x = 39
There are 39 students in the film-making club and 25 students in the yearbook club.
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The scale on a map reads 1 / 2 inch =30 miles. If two cities on the map are 5 3 / 4 inches apart, find the actual distance between the cities.
A. 300 miles
B. 315 miles
C. 327 miles
D. 345 miles
No answer provided
a. A
b. B
c. C
d. D
The ratio of empty seats to full seats in an auditorium is 3: 7. If there are 203 full seats, find the total number of seats.
A. 87 seats
B. 275 seats
C. 290 seats
D. 298 seats
A No answer provided
a. A
b. B
c. C
d. D
The ratio of empty seats to full seats in an auditorium is 3: 7. If there are 203 full seats, find the total number of seats.
A. 87 seats
B. 275 seats
C. 290 seats
D. 298 seats
A No answer provided
a. A
b. B
c. C
d. D
If two cities on map are [tex]5\frac{3}{4}[/tex] inches apart, then the actual distance between the cities is 345 miles .
In the question ,
it is given that ,
the scale on the map is 1/2 inches is = 30 miles .
So , 1 inches on the map is = 60 miles.
So , the scale factor is 1 inch = 60 miles .
also given that the distance between the two cities on the map is = [tex]5\frac{3}{4}[/tex] inches ,
means , 23/4 inches .
So , the actual distance is = 23/4 × 60
Simplifying further ,
we get ,
= 345 miles .
Therefore , the actual distance is 345 miles , the correct option is (d) .
The given question is incomplete , the complete question is
The scale on a map reads 1/2 inch = 30 miles. If two cities on the map are [tex]5\frac{3}{4}[/tex] inches apart, find the actual distance between the cities.
A. 300 miles
B. 315 miles
C. 327 miles
D. 345 miles
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A piggy bank contains 350 pennies
and nickels worth $11.90. How many
pennies are in the piggy bank?
Answer:
140 pennies
Step-by-step explanation:
Information:
1 penny (cent) = $0.011 nickel = $0.05Define the variables:
Let x be the number of pennies.Let y be the number of nickels.If the piggy bank contains 350 pennies and nickels:
[tex]\implies x+y=350[/tex]
If the piggy bank contains pennies and nickels worth $11.90:
[tex]\implies 0.01x+0.05y=11.90[/tex]
Rearrange the first equation to make y the subject:
[tex]\implies y=350-x[/tex]
Substitute the expression for y into the second equation and solve for x:
[tex]\implies 0.01x+0.05(350-x)=11.90[/tex]
[tex]\implies 0.01x+17.5-0.05x=11.90[/tex]
[tex]\implies -0.04x=-5.6[/tex]
[tex]\implies x=140[/tex]
Therefore, there are 140 pennies in the piggy bank.
592 × 43 in standard algorithm answer needs to be showed
Answer:
25456
Step-by-step explanation:
group consisting of anne, bert, carl, and diana is about to select one out of five possible alternatives, a, b, c, d, e. the true utilities of the four individuals for the five alternatives are as follows:
a) U(6) UC) Ud) U(e) Anne 0.9 0.8 0.6 0.5 0.4 Bert 0.6 1.0 0.5 0.3 0.4 Carl 0.4 0.3 0.7 0.9 0.2 Diana 0.7 0.6 0.5 0.2 0.1 Which alternative will be selected if the following decision making methods are used: (i) the decision is based on the traditional voting procedure (each voter gets one vote). (ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected. (iii) the group uses the Borda count with 5 points for the most preferred alternative, and 1 point for the least preferred alternative. (iv) the group follows a dot-voting scheme, where each person gets 10 "dots", and they assign the number of dots to each alternative that are roughly proportional to their Utility. (v) the group uses the "maximin rule" which prescribes that the group should prefer the alternative in which the worse-off person is as well-off as possible.
(vi) the sum of individual utilities is maximized for the group. Discuss the pros and cons of the group decision making methods listed above.
(ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected
the best is always to look for points on the line that are exactly corner points of grid squares.
the true utilities of the four individuals for the five alternatives
(0.3, 0.4) and (0.6, 0.8)
so, the linear equation is
y = ax + b
0.4 = a×0.3 + b
0.8 = a×0.6 + b
let's subtract the second from the first equation :
-0.4 = a×-0.3 + 0
a = -0.4/-0.3 = 0.4/0.3 = 4/3
so, the equation is
y = (4/3)x
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Clarks Inc., a shoe retailer, sells boots in different styles. In early November the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100.
Required:
1. How many performance obligations are in a contract to buy a pair of SunBoots?
2. Assume Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon. Prepare a journal entry to record revenue for the sale of 1,000 pairs of SunBoots.
1. There are two performance obligations in a contract to buy a pair of SunBoots from Clarks Inc: Delivery of Sunboots and Discount Coupon.
2. The journal entry to record the revenue for the sale of 1,000 pairs of SunBoots when Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon is as follows:
Journal Entry:Debit Cash $70,000
Credit Sales Revenue $65,800
Credit Deferred Revenue from Discount Coupon $4,200
(To record the sale of 1,000 pairs of SunBoots, including the discount coupon.)
What are performance obligations?Performance obligations refer to distinct goods and services agreed to be provided in a contract between the two parties.
Performance obligations arise because each separate goods or services benefit the customer distinctly from others.
In accounting for the revenue or costs, efforts should be geared toward recognizing the activity as soon as they bestow or transfer economic benefits to the buyer.
Transaction Analysis:Selling price per pair = $70
Discount coupon = 30%
Estimated percentage of customers who will utilize the coupon = 20%
The number of SunBoots sold = 1,000
Cash $70,000 Sales Revenue $65,800 Deferred Revenue from Discount Coupon $4,200 ($70,000 x 30% x 20%)
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A tank is full of water. The tank is a right circular cylinder lying on its side (length is parallel to horizon), with radius 2 m, and length 5 m. Find the work required to pump the water out of a spout that rises 2 m above the tank. Set up the integral, but do NOT evaluate. The base of a solid is a circular disk with radius
W =∫ lower power (-r) to higher power (r + h) (h + r - x) 2pgl [tex]\sqrt{r^2+x^2}[/tex] dx is the integral for the effort needed to pump water out of a spout that is 2 m above the tank.
What is meant by Integral?Integral: In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
r = 2m
l= 5m
sinθ=x/r
[tex]dv=2l\sqrt{r^2+x^2} dx[/tex]
Let g be the acceleration brought on by gravity, and let p be the density of water.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2lpg (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
Therefore, the integral for the work required to pump the water out of a
spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
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A new telivision is marked down 75% if this is a 15%decrease what is the sales price
Answer:
Step-by-step explanation:The Sales Price is $425Explanation:First, we need to find the original price or: 15% of what is $75"Percent" or "%" means "out of 100" or "per 100", Therefore 15% can be written as 15100.When dealing with percents the word "of" means "times" or "to multiply".Finally, lets call the number we are looking for, or "what", n.Putting this altogether we can write this equation and solve for n while keeping the equation balanced:15100×n=$7510015⋅15100×n=10015⋅$7510015⋅15100×n=$750015n=$500Now that we know the original price we can subtract the discount or mark down from it.So, the Sales Price =$500−$75=$425
State the domain and range of the following relation: {(2,4), (-1,8), (4,-2), (5,6), (2,-2)}. State whether the relation is a function.
The domain is {2, -1, 4, 5} and the relation is not a function
How to determine the domain?From the question, we have the following parameters that can be used in our computation:
{(2,4), (-1,8), (4,-2), (5,6), (2,-2)}
The domain is the set of the x values
So, we have the following representation
x = {2, -1, 4, 5, 2}
Remove repeated entries
x = {2, -1, 4, 5}
So, the domain is {2, -1, 4, 5}
Also, the relation is not a function
This is because the x value 2 has several y values
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v\a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure. if the perimeter of the window is 16 feet, what dimensions will admit the most light?
The dimension of rectangle window to admit the most light is x = 16 / ( 8 - √3) and y = 24 - 8√3 / 8 - √3
According to the question,
The perimeter of the window is 16 feet
Also, Window is surmounted by an equilateral triangle
Let x and y be the dimensions of rectangular part of window and x be side of equilateral part. If A be the total area of window, then
A = x.y + (√3/4)x² -------------(1)
Also, x + 2y + 2x = 16
=> 3x + 2y= 16
=> y = 16-3x / 2
Replacing the value of y in equation (1)
=> A = x.(16-3x / 2) + (√3/4)x²
=> A = 8x - 3x²/2 + (√3/4)x²
Differentiating A w.r.t x
=> A' = 8 - 3x + (√3/2)x
For critical value , we put A'=0
=> 8 - 3x + (√3/2)x = 0
=> x = 16 / ( 8 - √3)
Again, Differentiating A' w.r.t x ,
=> A'' = -3 + √3/2
which is Less than 0 ,
Therefore , A is maximum if x = 16 / ( 8 - √3) and y = 24 - 8√3 / 8 - √3
Hence, For admitting the most light the area should be largest , dimensions of rectangle are x = 16 / ( 8 - √3) and y = 24 - 8√3 / 8 - √3
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write a statement to shift the contents of array samplereadings 1 position to the left. assign the rightmost element with -1. ex: if samplereadings is [12, 85, 43], then samplereadings becomes [85, 43, -1]
//The end result is that samplereadings is now [85, 43, -1].
What is samplereadings?Samplereadings is a website that offers free reading material for students. The website provides a variety of texts, including classic literature, non-fiction, and current topics. Users can read the texts online, or download a PDF version. Samplereadings also offers a range of additional resources, such as discussion questions, vocab lists, and comprehension quizzes to help students better understand and engage with the material.
samplereadings.unshift(samplereadings.pop()); //pop() removes the last element of the array and returns it, then unshift() adds the element to the beginning of the array.
samplereadings[samplereadings.length - 1] = -1; //sets the last element of the array to -1.
//The end result is that samplereadings is now [85, 43, -1].
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Find all fixed points of the linear transformation. Recall that the vector v is a fixed point of T when T(v) v. (Give your answer in terms of the parameter t.) A reflection in the x-axis.
{ _____ : t is rea}
The set of all T's fixed points is {(x,0): x € R} of the linear transformation of vector(v).
linear transformation:
It is a function from one vector space to another that respects the structure of each vector space, which is also known as a linear operator or map
Two important examples of linear transformations are zero and identity transformation. The zero transformation defined by T(→x)=→(0) for all →x is an example of a linear transformation.
Similarly, the identity transformation defined by T(→x)=→(x) is also linear.
Note that the representation matrix for the reflection in the y-axis:
[tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right][/tex]
Here the condition
T(x,y)=
[tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}x\\-y\\\end{array}\right] =\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]
can only happen when y=0 and x is arbitrary.
Thus the fixed points for all T are points with y=0 or all points on the x-axis
Thus, The set of all T's fixed points is {(x,0): x€R}
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How many calories in the candy bars
Answer:
A = 267 calories; B = 257 calories
Step-by-step explanation:
We can set up a system of equations to find how many calories each candy bar provides.
The information gives us:
A + 2B = 781 and 2A + B = 791.
Substitution will be easier, and we can isolate A from the first equation and then plug it in for A in the second equation:
[tex]A+2B=781\\2A+B=791\\\\A=781-2B\\\\2(781-2B)+B=791\\1562-4B+B=791\\1562-3B=791\\-3B=-771\\B=257[/tex]
Now we can plug in B into the first equation to find A:
[tex]A+2(257)=781\\A+514=781\\A=267[/tex]
18. A living room set lists for $2,400 and carries a trade discount of 30%. Freight charges are $200. Calculate the final price of the living room set.
A. $1,880
B. $1,800
C. $1,008 D. $8,100
Answer: The final price of the living room set is $1,880 (Option A)
Step-by-step explanation: Market price of living room set = $2400
Trade Discount offered= 30%
Therefore we deduct Trade Discount from the Market Price to arrive at the final price.
= 2400 - (2400*30%)
=2400-720
=1680
Freight charges incurred to bring an asset to use are added to the final price of the asset.
Therefore the Final Price = 1680+200
=$1,880
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c. in cell d63, use the count function in the in-cell dropdown to calculate the number of members using the values in the animal field.
the number of members using the values in the animal field. then the value is 63
1. Application layer: this is the interface that connects a user to a network, the files or data are generated and seek from this layer. Protocols in this layer are FTP, TFTP, DNS, SMTP, SNMP etc.
2. Presentation layer: it is the sixth layer in the OSI model. It is used to present data in a well organized syntax and format to and application and also for document format encryption. Protocols in this layer are XDR, TLS, SSL and MIME.
3. Session layer: this layer is used to create and terminate sessions between the destination and source node, in a network. Protocols in this layer are PPTP, SAP, L2TP and NETBIOS.
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James received total scholarships of $30,000 to pursue his accounting degree at State University. He spent $15,000 of the money on tuition, $1,000 on books, and $14,000 on rent for his off-campus apartment. James must include _______ in gross income on his tax return.
14000
James received total scholarships of $30,000 to pursue his accounting degree at State University. He spent $15,000 of the money on tuition, $1,000 on books, and $14,000 on rent for his off-campus apartment. James must include 14000 in gross income on his tax return.
Your wages, dividends, capital gains, business income, and retirement distributions are all included in your gross income. Acclimations to Pay incorporate such things as Instructor costs, Understudy loan revenue, Provision installments or commitments to a retirement account.
Where can I find my tax return's gross revenue?The total amount of your earnings and income for the tax year minus certain income adjustments is your adjusted gross income (AGI). Your AGI is listed on Line 11 of Forms 1040, 1040-SR, and 1040NR for the tax year 2022.
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A husband and wife plan to save money for their daughter's college education in 5 years. They decide to purchase an annuity with a semiannual payment earning 10.5% compounded semiannually. Find the future value of the annuity in 5years if the semiannual payment is $3150. Round your answer to the nearest cent.
The future value of the annuity is ?
Answer:
$40,601.92
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 1.5/100
r = 0.015 per year,
Then, solve the equation for P
P = I / ((1 + r/n)nt - 1)
P = 3150 / ((1 + 0.015/2)(2)(5) - 1)
P = 3150 / ((1 + 0.0075)(10) - 1)
P = $40,601.92
Summary:
The principal investment required to get a total interest of $3150 from compound interest at a rate of 1.5% per year compounded 2 times per year over 5 years is $40,601.92.
Question 27 of 40
The vertex of the parabola below is at the point (1,-5). Which of the following
could be this parabola's equation?
-10
-20-
20
(1.-5)
10
A. y= (x + 1)² +5
B. y= 2x² +5
O
OC. y=x5
OD. y=(x-1)2-5
The possible equation of the parabola is f(x) = (x - 1)² - 5
How to determine the possible equation of the parabolaFrom the question, we have the following parameters that can be used in our computation:
Vertex = (1, -5)
Rewrite the vertex as follows
So, we have the following representation
(h, k) = (1, -5)
A quadratic function can be represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
Substitute the known values in the above equation, so, we have the following representation
f(x) = a(x - 1)² - 5
Set a = 1
f(x) = (x - 1)² - 5
Hence, the function is (d) f(x) = (x - 1)² - 5
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Solve for x thank you!
Answer:
x = 25
Step-by-step explanation:
the angle in a semicircle is 90°
given the legs of the triangle are congruent then the triangle is isosceles with the 2 base angles congruent.
the sum of the 3 angles in the triangle = 180°
base angle = (180 - 90)° ÷ 2 = 90° ÷ 2 = 45° , then
2x - 5 = 45 ( add 5 to both sides )
2x = 50 ( divide both sides by 2 )
x = 25
let x be a bern(p) random variable. find the moment generating function of x. let y be a bin(n, p) random variable. use moment generating function of x to find the moment generating function of random variable y .
The moment generating function of a Bern(p) random variable x is given by: M(t) = pe^(pt) + (1 - p).The moment generating function of a Bin(n, p) random variable y is given by:M(t) = (pe^(pt))^n + (1 - p)^n
To find the moment generating function of a Bern(p) random variable x, we first need to calculate the probability mass function of x.
p(x) = p^x (1-p)^(1-x).
The moment generating function of x is then given by the formula:
M(t) = pe^(pt) + (1-p).
To use the moment generating function of x to find the moment generating function of a Bin(n, p) random variable y, we first need to calculate the probability mass function of y.
p(y) = (n choose y)p^y(1-p)^(n-y).
The moment generating function of y is then given by the formula:
M(t) = (pe^(pt))^n + (1-p)^n.
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Question 4
The roof of a patio is in the shape of a triangle.
What is the value of x, the distance from the base of the roof to the top of the roof?
(A) 2 feet
B 8 feet
C) 13 feet
(D) 22 feet
The value of x, the distance from the base of the roof to the top of the roof is 8 feet
The length of the base of the triangle = 30 feet
The side of the triangle = 17 feet
The triangle is the combination of two right triangles
Consider one right triangle
The base length = 30 / 2 = 15 feet
The side of the triangle = 17 feet
The length of the third side = x
Here we have to apply Pythagorean theorem
Then
17^2 = 15^2 + x^2
x^2 = 17^2 - 15^2
x^2 = 289 - 225
x^2 = 64
x = 8 feet
Therefore, the height of the roof is 8 feet
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Find the 13th term in the following
arithmetic sequence :
2, 5, 8, 11, .
The 13th term of the given Arithmetic sequence is 38.
Arithmetic sequence:A list of integers with a distinct pattern is known as an arithmetic sequence. It is an arithmetic sequence if you can subtract any number in the sequence from the one before it and get a value that is either constant or always the same. Here the constant value is called a common difference.
The formula for the nth term of the Arithmetic sequence is given by
a[tex]_{n}[/tex] = a+(n-1)dHere we have
Arithmetic sequence: 2, 5, 8, 11,....
Where first term a = 2
And common difference d = term2 - term 1 = 5 - 2 = 3
As we know nth term of AP = a + (n-1)d
=> 13th term of AP = a + (13-1)d = a + 12d
From the give data, a = 2 and d = 3
=> 13th term = a + 12d
= 2 + 12(3)
= 2 + 36
= 38
Therefore,
The 13th term of the given Arithmetic sequence is 38
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The fox population in 2001 was measured to be 340. By 2005, the population was measured again to be 285. The population changes linearly. Let the input be years since 2001.
a) Find a formula for the fox population, P. Let the input be years since 2001.
I think it's P=-13.75(x-2001)+340, but I'm not sure.
b) What does your model predict the fox population to be in 2010?
If the above is correct, then it's P=216.25
The model of the function is y = -13.75x + 27853.75 and the estimated population in 2010 is 216.25
Linear FunctionA linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
In this problem, we can take the two points to find the slope and y-intercept of the function.
using a linear function model;
y = mx + c
m = slopec = y - interceptslope (m) = y₂ - y₁ / x₂ - x₁
m = 285 - 340 / 2005 - 2001
m = -13.75
Using the slope, we can find the y-intercept
y = mx + c
Taking one point;
285 = -13.75(2005) + c
c = 27853.75
The model of the function is y = -13.75x + 27853.75
b) The population in 2010 will be
y = -13.75(2010) + 27853.75
y = 216.25
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