A farmer fills a rectangular water trough to a depth of 1 foot.
The trough is 4 feet long and 2 feet wide. How much water
is in the trough?

Answer:

41°

Step-by-step explanation:

Sum of angle measures in a triangle: 180°

So,

108 + x + 5 + x - 5 = 180

Simplify.

2x + 108 = 180

Subtract 108 from both sides.

2x = 72

x = 36

Substitute x = 36 into (x + 5)

m∠A = 36 + 5 = 41

Thus, the answer is 41°

If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.

Monthly payment can be defined as the amount a person received on a monthly basis.

Now let find the monthly payment

Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷  ( 1+ 0.0429/12)^12×10 -1

Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷  ( 1+ 0.003575)^120 -1

Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷  ( 1.003575)^120 -1

Monthly payment = $87.31

Therefore the monthly payment is $87.31.

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The complete question is:

Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.  Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?

You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).

What is function ?

A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Have given ,

Two functions , f(x) and g(x)

The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .

So , You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).

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0.71 percentage points greater is wyatt’s effective interest rate than his nominal interest rate.

Interest is a fee paid by a borrower to a lender for the use of borrowed money. It is calculated as a percentage of the amount borrowed, and is usually paid periodically at intervals. Interest is generally considered to be a form of compensation for the time and risk taken by the lender in providing a loan or other form of credit.

The effective interest rate is calculated by taking the (1 + nominal interest rate/number of compounding periods per year) to the number of compounding periods per year power minus 1. In this case, the effective interest rate would be 0.1362 x (1 + 0.1362/4)^4 - 1, which is 0.1439 or 14.39%. The difference between the nominal interest rate of 13.62% and the effective interest rate of 14.39% is 0.71 percentage points.

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Answer:

The probability would be 2/5

Step-by-step explanation:

There is five numbers on the spinning and the chance of getting one certain number would be 1/5, and if you add the two probabilities together would be 2/5, I am pretty sure.

A numerical equation using addition as the only operator, for instance, is 2 + 17.

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Answer:

C.,77°{interior alternate angle}

hope it helps.

Answer:

y=2x-7

Step-by-step explanation:

y=mx+b  ==> m is the slope and b is the y-intercept

y=(2)x + (-7)  ==> plugin 2 for m=slope and -7 for b = y-intercept

y=2x-7 ==> simplify

The statement given here is true as 5x and 5 are like terms.

This is because like terms have the variables of same degree . Therefore, 5x and x are like terms as both of them have x to the power 1 , which means both are of degree 1.

Like terms differs from the unlike terms only in case of numerical component.  By summing the coefficients of  like terms , similar phrases can be regrouped. Like terms in a polynomial equation are those terms  that have the same variables and these variables have the same powers, but with different coefficients.

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Answer: A

Step-by-step explanation:

Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.

A: correct

Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.

B: incorrect

Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.

C: incorrect

Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.

Therefore, A is the correct answer.

Given:

A length of a side of an equilateral triangle = 32 cm

Formula Used:

If in an equilateral triangle with side length 'a' then,

Area of an equilateral triangle = [(√3)/4] × a2 

Calculations:

Area of an equilateral triangle = [(√3)/4] × 322

⇒ (1024 × √3)/4

⇒ 256√3 cm2

y = 4 is a horizontal line.

The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

Now, According to the question:

Let's know:

What is Horizontal lines?

If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.

The equation is y = 4.

The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

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The complete question is this :

Is y = 4  a vertical line?

The dots in the expression - 321⋅35⋅7⋅15 represents multiplication.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

From higher classes, we write a dot sign in between two terms to represent that the terms are being multiplied.

Given, - 321⋅35⋅7⋅15 this represents multiplication between the numbers

- 321, 35, 7, and 15.

The result of this product is,

- 321×35×7×15

= - 1,179,675.

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The additional charge per mile for Service B is less than 30 cents per mile of the trip. This is because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips.

For a trip of 10 miles, Service B would cost

(10 x 0.20) + 10

= $12.

For a trip of 20 miles, Service B would cost

(20 x 0.20) + 10

= $22.

Therefore, the additional charge per mile for Service B is

(12/10)

= 1.2 for the 10 mile trip and

(22/20)

= 1.1 for the 20 mile trip.

Both of these are less than 30 cents per mile.

The additional charge per mile for Service B is less than 30 cents per mile of the trip because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips. To demonstrate this, for a 10 mile trip, the total cost would be $12, and for a 20 mile trip, the total cost would be $22. This works out to an additional charge per mile of 1.2 and 1.1 cents respectively, which are both less than 30 cents per mile.

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Answer:

18

Step-by-step explanation:

2

2

+

3

9

=

−

1

8

2x^{2}+39=-18

2x2+39=−18

2

2

+

3

9

−

(

−

1

8

)

=

0

Answer:

26.3

Step-by-step explanation:

The altitude splits the 7-inch base into two 3.5-inch pieces find the missing sides:

3.5^2+9^2=c^2

9.656603=c

7+9.657+9.657=the perimeter

26.314 or 26.3

The weight of the baby after five months is 15 Kg.

Step 1:

Given:

New-born baby weight = 5kg

Monthly average weight gained = 2kg

To find:

The weight of the baby after 5 months.

Average Weight of Baby:

Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).

Step 2:

Represent the unknown.

Let x-the number of months .

Let y-weight of the baby after 5 months.

Step 3:

Formulate the equation.

The mathematical equation is:

5+2x = y

Step 4:

Solve the equation.

5+2x = y

5+2(5) = y

5+10 = y

y = 15

Thus, the baby weight is 15kg after 5 months.

Step 5:

Using the equation 5+2x=y.

5+2x = y

5+2(5) = 15

5+10 = 15

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Answer:

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

4.8 + 2.2 = 7

8.8 - 7 = 1.8

Answer:

2/3

Step-by-step explanation:

you reduce the fraction to get the scale factor. so 8/12 reduces down to 2/3 which is the scale factor

Answer:

3/15 probability she will select a pink from the bag and 6/30 she will select from the jar.

Step-by-step explanation:

If you simplify she has just as equal a probability of selecting a pink from the jar and the bag

Answer:

8¹

Step-by-step explanation:

The given expression is :

8 to the power 1.

We need to write it in exponential form.

If we write 10³, here 10 is base and 3 is exponent.

8 to the power 1 = 8¹

The base is 8 and exponent is 1.

Hence, the exponential form is 8¹.

The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:

6,766.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error of the interval is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

We have no prior estimate, hence the proportion is given as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of M = 0.01, the needed sample size n is obtained as follows:

[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]

n = 6,766.

(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).

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Therefore , the solution of the given problem of area comes out to be AB/DC =5 Imagine that your square is made out of more compact unit squares.

Area is the quantity that describes how much space .A surface or an object's shape occupy. Use a pencil to mark a square on the paper. Specifically, a 2-D figure. A shape's area on paper is referred to as its "Area" in this sentence. Imagine that your square is made out of more compact unit squares.

Since the heights of both trapezoids are equal, and the area of ABEF is twice the area of FECD, AB+ EF/2 = 2(DC+EF /2) AB + EF / 2= DC + EF,

AB + EF = 2DC + 2EF. EF is exactly halfway between AB and DC, so EF = AB + (AB+ DC)/2 = 2DC+ AB + DC, so 3/2 AB +  1/2DC = 3DC+AB, 1/2AB =5/2DC => AB/DC =5 Therefore , the solution of the given problem of area comes out to be AB/DC =5.

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If Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1) then the scale factor used is 1/3

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1).

A(−3, −3)---->A(−3/3, −3/3)---->A′(−1, −1)

B(3, 3)---->B(3/3, 3/3)---->B′(1, 1)

C(0, 1)---->C(0/3, 1/3)---->B′(0, 1/3)

Hence, the scale factor used is 1/3.

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The blank words are 5 cm, 5 cm, 5 cm, 5 cm, adjacent, equal, 3/4, -4/3, 3/4, -4/3, adjacent, perpendicular, equal.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

I will prove that quadrilateral KLMN is a square by demonstrating that

all sides are of equal measure,

and adjacent sides are perpendicular.

To prove all sides are equal:

KL = 5 cm

LM = 5 cm

MN = 5 cm

NK = 5 cm

The four sides are of 5 measure.

To prove adjacent sides are perpendicular:

slope of KL = 3/4

slope of LM = -4/3

slope of MN = 3/4

slope of NK = -4/3

The slopes of any pair of adjacent sides are perpendicular.

That being the case, those sides are equal.

Therefore,  5 cm, 5 cm, 5 cm, 5 cm, adjacent, equal, 3/4, -4/3, 3/4, -4/3, adjacent, perpendicular, equal are the blank words.

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