Which of the following statements could be a correct step in solving this equation:

12x−7=13(x−12)


A. 12x−7=13x−12


B. 3x−42=2(x−12)


C. 3x−7=2(x−12)


D. 3x−7=2x−12

Answer:

Step-by-step explanation:

18x² + 2 = 2 * 9x² + 2 *1

             = 2*(9x² + 1)

The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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Answer:

225

Step-by-step explanation:

10% less than 250 is 225. To solve you must first find 10% of 250, an easy way to do this is to move the decimal point one left. 250.0 becomes 25.0. Then subtract that from the original number 250-25=225.

Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

The binomial expansion of the \((x-4)^5\) is  \(x^5+20x^4+160x^3+640x^2+1280x+1024\)

According to the statement

we have given that a equation and we have to expand it by use of the binomial theorem.

So, For this purpose we know that the

A binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.

And the general formula is

\((x+y)^n= ^nC_0x^ny^0+^nC_1x^(n-1)y^1+^nC_2x^(n-2)y^2+...+^nC_nx^0y^n\)

And we have to solve it with the given equation (x-4)^5.

Then

\((x-4)^5=x^5+20x^4+(20)/(2)x^3(4^2)+(60)/(6)x^2(4)^3+(120)/(24)x^1(4)^4+(120)/(120)x^0(4)^5\)

Now after solving the equation become

\((x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024\)

So, The after expanding the given statement with the binomial theorem the result output is

\((x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024\)

So, The binomial expansion of the \((x-4)^5\) is  \(x^5+20x^4+160x^3+640x^2+1280x+1024\)

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Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

Answer:

$36570

Step-by-step explanation:

The original price is 34500, so the %given must be the increase in price :

34500x(1+6%)

=34500x1.06

=36570//

The various answers to the question are:

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

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Answer:

its B

Step-by-step explanation:

I calaulated all the numbers

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer: A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

Step-by-step explanation:

To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.

Given dimensions:

Room length: 26 feet

Room width: 18 feet

Room height: 9 feet

Door dimensions:

Height: 6 feet 6 inches

Width: 4 feet

Window dimensions (each):

Width: 2 feet

Height: 2 feet 6 inches

A: Carpeting the floor:

To find the area of the floor, we multiply the length and width of the room:

Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.

To convert to square yards (since the carpet is sold per square yard), we divide by 9:

Floor area in square yards = 468 square feet / 9 = 52 square yards.

Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.

B: Wallpapering the walls:

To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:

Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.

Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.

C: Painting the ceiling:

To find the area of the ceiling, we multiply the length and width of the room:

Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.

Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:

Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.

Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.

Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.

D: Cost of the entire project:

Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling

= $936.00 + $297.00 + $33.25 = $1266.25.

Therefore:

A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

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Answer:

4900cm³is a required answer.

The volume of cone B when the Surface area ratio of cone A to cone B = 4:49 is 9.35 cm³.

Given:

Surface area ratio of cone A to cone B = 4:49

The surface area of a cone is proportional to the square of its radius.

Let the radius of cone A be "r" and the radius of cone B be "R."

\(\[(\text{Surface area of cone A}) : (\text{Surface area of cone B}) = \frac{\pi r^2}{\pi R^2} = \frac{4}{49}\]\)

\(\[\frac{r^2}{R^2} = \frac{4}{49}\]\)

Now, the volume of a cone is proportional to the cube of its radius.

\(\[(\text{Volume of cone A}) : (\text{Volume of cone B}) = \frac{\frac{1}{3} \pi r^3}{\frac{1}{3} \pi R^3} = \frac{r^3}{R^3}\]\)

Now, the volume of cone A is 400 cm³. So:

\(\[\frac{r^3}{R^3} = \frac{400}{V_B}\]\)

Now,  the value of \(R^2\) to determine the volume of cone B.

\(\[\frac{r^2}{R^2} = \frac{4}{49}\]\)

\(\[49r^2 = 4R^2\]\)

Now, divide by 4:

\(\[R^2 = \frac{49r^2}{4}\]\)

\(\[R^2 = \frac{49}{4} \times r^2\]\)

Next, substitute the value of \(R^2\) into the volume ratio equation:

\(\[\frac{r^3}{\left(\frac{49}{4} \times r^2\right)^{3/2}} = \frac{400}{V_B}\]\)

\(\[\frac{r^3}{\left(\frac{49}{4}\right)^{3/2} \times r^3} = \frac{400}{V_B}\]\)

Since \(r^3/r^3\) cancels out, we get:

\(\[\frac{1}{\left(\dfrac{49}{4}\right)^{3/2}} = \frac{400}{V_B}\]\)

\(\[V_B = \frac{400}{\left(\frac{49}{4}\right)^{3/2}}\]\)

\(\[V_B = 400 \times \left(\frac{4}{49}\right)^{3/2}\]\)

Now, let's calculate the value of \(\(\left(\frac{4}{49}\right)^{3/2}\)\):

\(\[\left(\frac{4}{49}\right)^{3/2} = \sqrt{\left(\frac{4}{49}\right)^3}\)

               \(= \sqrt{\frac{4^3}{49^3}}\)

              \(= \sqrt{\frac{64}{117649}}\]\)

\(\[\left(\dfrac{4}{49}\right)^{3/2} = \dfrac{8}{343}\]\)

Finally, the volume of cone B:

\(\[V_B = 400 \times \left(\dfrac{8}{343}\right)\]\)

\(\[V_B =9.35 \text{ cm}^3\]\)

Thys, the volume is 9.35 cm³.

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Answer:

104

Step-by-step explanation:

If is wrong i'm sorry

The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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Answer:

4,300 square feet

Step-by-step explanation:

First, calculate the area of Jayden's front yard.

50 feet × 80 feet = 4,000 square feet

Next, find the area of half of Jayden's back yard.

1/2(20 feet × 30 feet) = 300 square feet

Last, add the two areas together.

4,000 feet + 300 feet = 4,300 square feet

So, Jayden needs to purchase 4,300 square feet of sod

Answer:

Step-by-step explanation:

multiply and divide your equation then subtarct it and you get your answer

9514 1404 393

Answer:

Step-by-step explanation:

Neither linear nor exponential functions have a "wiggle" in their graph, so the piece in the region x < 0 is polynomial.

The piece in the interval [0, 3] is concave upward and has increasing slope. It could be polynomial, but is most likely the exponential piece of the function.

For x > 3, the function is linear.

There are no gaps in function value where the transition is made from one piece to another, so the function is continuous.

The function tends upward at the right side of the graph. It tends downward at the left side of the graph. This tells you the sign of the infinity they tend toward matches the sign of the infinity x tends toward.

__

On the interval [0, 3], h(x) is represented by an exponential function.

H(x) is a continuous function.

As x approaches +∞, h(x) approaches +∞.

As x approaches -∞, h(x) approaches -∞.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

0.035

Step-by-step explanation:

hope this helps :)

Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

No solution

Step-by-step explanation:

You will get zero

The value that is the input of the function is 4.

A function relates input and output. In other words,  a function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable is the x values or the input value while the dependent variable is the y values of the output values.

Hence, the values of the input(x) of the function are 4, 6, 8, 10. 12 etc.

Therefore, base on the option, the input of the function is 4.

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The statement that accurately describes the difference between short-term and long-term capital gains in terms of taxes is A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains.

A capital gains tax is a tax levied on profits made from the sale of a non-inventory asset. Capital gains from the sale of stocks, bonds, precious metals, real estate, and property are the most common.

Short-term capital gains are profits made from selling assets held for a year or less. Long-term capital gains, on the other hand, are gains from assets held for more than a year.

In conclusion, based on the information illustrated, the correct option is A.

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Answer:

$1,420.11

Step-by-step explanation:

I just took the test and got it right

Cassidy's approximate monthly payment is $1420.11 if Cassidy is planning to obtain a loan from her bank for $210,000 for a new home option (D) is correct.

It is defined as the systematic way of representing of loan payments according to the time in which the principal amount and interest are mentioned in a list manner

It is given that:

Cassidy is planning to obtain a loan from her bank for $210,000 for a new home.

A fixed annual interest rate of 2.7% compounded monthly for 15 years.

The formula is:

\(P=\rm \dfrac{Fp(i)}{1-(1+i)^{-1}}\)

Plug all the values in the above formula:

\(P=\rm \dfrac{210000(2.7\%/12)}{1-(1+(2.7\%/12))^{-15\times12}}\)

After calculating:

P = $1420.11

Thus, Cassidy's approximate monthly payment is $1420.11 if Cassidy is planning to obtain a loan from her bank for $210,000 for a new home.

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2731 tickets should be sold at $27 and 2269 tickets should be sold at $40.

Given that,
A 5000-seat theater has tickets for sale at ​$27 and $40.
How many tickets should be sold at each price for a sellout performance to generate total revenue of $154,500 is to be determined.

Here,
Let the number of seats sold for $27 be x and for $40 be y
For a 5000-seat theater
x + y = 5000
x = 5000 - y - - - - - - (1)

Total revenue generated is  $154,500 by selling x tickets at ​$27 and y tickets at $40.

27x +40y = 154,500  - - - - - - (2)

Solving equations 1 and 2
27(5000 - y )+ 40y = 154,500
125,000- 27y + 40y = 154,500
13 y = 29500
y =2269
Putting y in equation 1
x = 5000 - 2269
x = 2731

Thus, 2731 tickets should be sold at $27 and 2269 tickets should be sold at $40.

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(( - 12 \div 3) \times 2 + 23 = \)

\(( - 4) \times 2 + 23\)

\( - 8 + 23 = \)

\(23 - 3 - 5 = \)

\(20 - 5 = 15\)

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