If x + y = x – y, then x – 2y 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.

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]

The Venn Diagram is shown at the end of the answer.

From the diagram, the percentages are given as follows:

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:

From the total bus and light rail percentages, the percentages are given as follows:

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:

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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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Answer:

1

Step-by-step explanation:

subtract the two numbers

Answer: 19

Step-by-step explanation: Imagine a number line -9 is on the left side and 10 is on the other. Now you have to clculate how many jumps or spaces it takes to reach 10. Which is 19, or 9 + 10.

I hope this helps.

The model of the function is  y = -13.75x + 27853.75 and the estimated population in 2010 is 216.25

A 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

slope (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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The final Factorisation of the expression of 5x³ + 40y⁶ is 5 ((x + 2y²) (x² - 2xy² + 4y⁴)).

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.

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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High off the ground the top of the ramp’s incline is 108.19 inch

Trigonometric ratios are what?

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

Given that :

hypotenuse = 153 inch

and angle is pi/4

Let h be the height

so sin pi/4 = h/153

h = 153 . sqrt 2/2

h = 108.19

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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 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.

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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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

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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//The end result is that samplereadings is now [85, 43, -1].

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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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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The domain is {2, -1, 4, 5} and the relation is not a function

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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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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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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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:

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.)

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.

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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The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20

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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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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The possible equation of the parabola is f(x) = (x - 1)² - 5

From 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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The 13th term of the given Arithmetic sequence is 38.

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

Here 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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Answer:

140 pennies

Step-by-step explanation:

Information:

Define the variables:

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.

Answer:

25456

Step-by-step explanation:

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.

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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(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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The eligible amount of work-related daycare expenses will be $2600

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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(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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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

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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