Prove: 36 + 324 + 900+. . . +(12n − 6)2 = 12n(4n2 − 1)

The measure of the angle of the triangle ∠BCD = 13°

Given data ,

Let the triangle be represented as ΔBCD

Now , in triangle BCD, we are given the following angle measurements:

angle CDE = (9x - 12)°

angle BCD = (2x + 3)°

angle DBC = (3x + 5)°

From the exterior angle theorem , we get

∠CDE = ∠BCD + ∠DBC

On simplifying , we get

9x - 12 = 2x + 3 + 3x + 5

9x - 12 = 5x + 8

Subtracting 5x on both sides and adding 12 , we get

4x = 20

Divide by 4 on both sides , we get

x = 5

So , the measure of angle ∠BCD = 2(5) + 3

m∠BCD = 13°

Hence , the angle is m∠BCD = 13°

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The complete question is attached below :

In triangle BCD , BD is extended through point D to point E , ∠CDE = ( 9x - 12 )° , ∠BCD = ( 2x + 3 )°, and ∠DBC = ( 3x + 5 )°, find ∠BCD

A. The amount invested is given as follows: $252.

B. The amount being put in is given as follows: $105.

The amounts are obtained applying the proportions in the context of the problem.

For item a, the amount is of 12% of 2100, hence it is given as follows:

0.12 x 2100 = $252.

For item b, the amount is half of 10% of 2100, hence it is given as follows:

0.5 x 0.1 x 2100 = $105.

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Answer:

2(1/2)(3)(4) + 12(3) + 12(4) + 12(5)

= 12 + 36 + 48 + 60 = 156 cm^2

C is the correct answer.

Answer:

  -300

Step-by-step explanation:

You want the value of f(-10) given that f(x) = -3x².

Put the value where the variable is and do the arithmetic.

  f(-10) = -3(-10)² = -3(100) = -300

The value of f(-10) is -300.

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The missing side lengths for triangle ABC are 4, 4√3, and 8.

Based on the given information, it seems that the triangle is a right-angled triangle with angles of 30°, 60°, and 90°. Let's find the missing side lengths for triangle ABC using the given lengths and angles.
Identify the triangle type.
Since we have angles of 30°, 60°, and 90°, we are working with a 30-60-90 right-angled triangle.
Determine the ratio of side lengths.
In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.
Find the corresponding side lengths.
Using the given lengths and the 1:√3:2 ratio, we can determine the side lengths for triangle ABC:
- If the shortest side (opposite the 30° angle) is 4, then the other sides would be 4√3 (opposite the 60° angle) and 8 (hypotenuse, opposite the 90° angle).

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Answer: Themba needs a total of 7.5  cups of yogurt to make 5 bowls of fruit dip, so 0.75 cup(s) will be needed

Step-by-step explanation:

your welcome.

The surface area of the right cylindrical oil can is 120π in² and the right option is C) 120π in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

To calculate the surface area of the right cylindrical oil can, we us the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the right option is C) 120π in².

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If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.

To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.

Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:

d = √((4 - 1)² + (6 - 2)²)

d = √(3² + 4²)

d = √(9 + 16)

d = √25

d = 5

Rounded to the nearest whole number, the length of the line is also 5 units.

In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.

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Answer:

=997

Step-by-step explanation:

46-15=31

31×32=992

992+5=997

Answer:  997

Step-by-step explanation:

Using the defined iterative process, xₙ ₊ ₁ = 4xₙ(3 - xₙ) with x₀ = 5,

The value of x₁ is -40

The value of x₂ is -6880

From the question, we are to compute the values of x₁ and x₂ from the given iterative process

The definition of the iterative process is:

xₙ ₊ ₁ = 4xₙ(3 - xₙ)

From the given information,

x₀ = 5

To determine the value of x₁, we will substitute n = 0

xₙ ₊ ₁ = 4xₙ(3 - xₙ)

x₀ ₊ ₁ = 4x₀(3 - x₀)

x₁  = 4x₀(3 - x₀)

Substitute x₀ = 5

x₁  = 4(5)(3 - 5)

x₁  = 20(-2)

x₁  = -40

To determine the value of x₂, we will substitute n = 1

xₙ ₊ ₁ = 4xₙ(3 - xₙ)

x₁ ₊ ₁ = 4x₁(3 - x₁)

x₂ = 4x₁(3 - x₁)

Substitute x₁  = -40

x₂ = 4(-40)(3 - (-40))

x₂ = -160(43)

x₂ = -6880

Hence,

The value of x₁ is -40

The value of x₂ is -6880

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Based solely on the information provided in the table, spending approximately 3-4 hours per customer would give Julie the best chance of a returning customer. So, correct option is C.

To determine the amount of time Julie should spend per customer to have the greatest probability of a returning customer, we need to find the time interval with the highest probability of return. Looking at the table, we see that the probability of return is highest for the 3-4 hour time interval with a probability of 7/8.

Therefore, Julie should spend 3-4 hours designing each customer's garden to have the greatest probability of a returning customer.

So, correct option is C.

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Complete question is:

Julie designs gardens for a living. For a year she kept track of the amount of time she spent designing the garden and whether or not the customer returned. She recorded the time and probability that a customer returned.

To have the greatest probability of a returning customer, what amount of time should Julie spend per customer?

TIME DESIGNING PROBABILITY OF RETURN

1-2 Hours 5/8

2-3 Hours 5/9

3-4 Hours 7/8

4-5 Hours 3/4

5-6 Hours 1/2

6-7 Hours 3/7

7-8 Hours 2/9

A. 1-2 Hours

B. 2-3 Hours

C. 3-4 Hours

D. 4-5 Hours

Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.

Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.

Answer:

The expected value in this situation can be calculated as follows:

E(X) = P(X) * V(X), where X is the random variable representing the profit of the construction company, P(X) is the probability of X, and V(X) is the value of X.

In this case, the profit of the construction company if the bid is accepted is $96,000 - $1,100 = $94,900, and the probability of the bid being accepted is 1/10. Therefore, we have:

E(X) = (1/10) * $94,900 = $9,490

The expected value of $9,490 means that in the long run, the construction company would expect to earn this amount on average per bid. Therefore, the correct answer is option A: "In the long run, the construction company would expect to earn this amount on average per bid."

Answer: -1 1/2

Step-by-step explanation:

You simplify -3/2, which becomes -1 1/2!

Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

The expression (7√98 + 3√242) divided by 6√50 simplifies to the fraction of 4/3.

To simplify the expression (7√98 + 3√242) ÷ 6√50, we need to rationalize the denominator. This means we need to simplify the expression in such a way that there are no radical signs in the denominator. To do this, we can use the fact that the product of a radical and its conjugate is a rational number.

First, let's simplify the terms under the radicals by factoring out the perfect squares:

√98 = √(49*2) = 7√2

√242 = √(121*2) = 11√2

Now the expression becomes:

(7√2 + 311√2) ÷ (6√(252))

= (7√2 + 33√2) ÷ (6*5√2)

= 40√2 ÷ 30√2

= 4/3

In conclusion, to simplify expressions involving radicals, we need to factor out perfect squares and use the property of the conjugate to rationalize the denominator.

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The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

The dimensions for this problem are given as follows:

5 m, 12 m and 9 m.

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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Our square yard calculator allows you to easily find the total area of a surface. Additionally, if you wish to cover that surface with some material or to do some construction work, such as painting or gardening, it gives you an estimation of your material cost and labor cost.

The square yard calculator also allows you to use different units (imperial and metric) and seamlessly convert between the two. Want to enter your measurements in feet and get your area in square yards or square meters? We've got you covered. You can easily switch between units and get answers to questions like "How to convert from feet to yards?" or "How many square feet in a square yard?"

The true statements about the samples:

Both groups have the same median (4).

Group A has a lower mean than Group B (4 vs 4.25).

Both groups have multiple modes.

The range of values in Group B is greater than in Group A.

For Group A, the average number is 4 with a range of numbers from 2 to 6. The middle value, also known as the median, is 4.

Using this information, we find that values 3, 4, and 5 occur twice each within the dataset.

For Group B, the mean, or average, number is found to be 4.25 among eight total entries ranging from a low of 1 to a high of 7.

Calculating for the middle value, which is defined as the median, it can be seen that the resulting output is again equivalent to 4. Of all data inputs, the two top-occurring amounts are 4 and 5, both appearing twice in the listing.

Here are the true statements about the samples:

Both groups have the same median (4).

Group A has a lower mean than Group B (4 vs 4.25).

Both groups have multiple modes.

The range of values in Group B is greater than in Group A.

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A company sampled two groups of students and asked them "How many books did you read this month?" The table shows the data they collected:

Group A: [3, 4, 5, 2, 5, 6, 3, 4]

Group B: [1, 6, 4, 5, 2, 5, 4, 7]

The required, experimental probability that a team will consist of two girls and a boy is 0.33. Option A is correct.

To find the experimental probability that a team will consist of two girls and a boy, we need to count the number of times that Kayla got a team with two girls and one boy and divide that by the total number of trials.

So, out of 50 trials, there were 17 trials where the team had two girls and one boy. Therefore, the experimental probability is:

17/50 = 0.34

Therefore, it is 0.34, which is closest to option (A) 0.33.

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Answer:

He rented the bike for 3 hours

Step-by-step explanation:

they charge $10 for just the bike and an adittional of $8 per hour and Willie payed $34 so u subtract 10 from 34 it leaves u with 24 and u then divide by 8 and u get 3 which means that he rented the bike for 3 hours :)

If company's marginal cost function is c(x)= 14 / √x, the total cost of producing the first 25 units is $10.67.

The marginal cost function is given as c(x) = 14 / √x, where x is the number of units produced.

To find the total cost of producing the first 25 units, we need to integrate the marginal cost function from x=0 to x=25, as follows:

Total cost = ∫₀²⁵ 14 / √x dx

We can use integration by substitution to solve this integral. Let u = √x, then du/dx = 1/(2√x), and dx = 2u du. Substituting these into the integral, we get:

Total cost = ∫₀⁵ √14/u du

This can be integrated using the power rule of integration. We have:

Total cost = 2√14 [[tex]u^{(3/2)[/tex]/3]₀⁵

Substituting back u = √x, we get:

Total cost = 2√14 [[tex](\sqrt{x})^{(3/2)[/tex]/3]₀²⁵

= 2√14 [[tex](\sqrt{25})^{(3/2)[/tex]/3 - [tex](\sqrt{0})^{(3/2)[/tex]/3]

= 2√14 (5/3)

= 10.67

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Answer:6

Step-by-step explanation:

7w-6 + 8w+6 = 90

15w=90

w=90/15

w=6

The area of this​ trapezoid is 14.42 square yards.

To compose the trapezoid into a parallelogram, we need to add a triangle to the top of the trapezoid, so that the top and bottom sides are parallel. The area of the triangle is equal to half the product of the base and height.

First, we need to convert the mixed numbers to improper fractions:

Base 1: 6 1/3 yd = 19/3 yd

Base 2: 8 1/5 yd = 41/5 yd

Height: 3 3/4 yd = 15/4 yd

The length of the top side of the triangle is equal to the difference between the two bases:

Top side = 41/5 - 19/3 = (123 - 95)/15 = 28/15

Now we can calculate the area of the triangle:

Triangle area = (1/2) x (28/15) x (15/4) = 7/4

The trapezoid can now be composed into a parallelogram, with base 1 as one side and base 2 as the other side. The height of the parallelogram is the same as the height of the trapezoid, which is 15/4 yd.

The area of a parallelogram is equal to the product of its base and height, so the area of the trapezoid is:

Parallelogram area = (19/3 + 41/5) x (15/4) = 865/60 = 14.42

Therefore, the area of the trapezoid is 14.42 square yards.

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1) Brianna's average monthly income is $1,850.

2) Brianna's average monthly expenses are $3,135.

3) Brianna's total monthly cash flow is -$1,295.

The cash flow refers to the cash inflows and cash outflows.

Cash inflows are incomes while cash outflows are expenses.

Monthly Rent = $700

Gas = $120

Car Insurance = $75

Health Insurance = $140

Renter's Insurance = $25

Cell phone = $110

Utilities = $100

Groceries = $300

Entertainment/eating out = $250

Total monthly expenses = $1,820

= $21,840 ($1,820 x 12)

College = $12,000

Gifts = $1,000

Vacations = $1,500

Clothes = $800

Charity =$600

Total monthly expenses = $21,840

Total annual expenses = $37,740

Average monthly expenses = $3,135 ($37,740 ÷ 12)

Monthly Income = $1,600

Yearly Income = $ 19,200 ($1,600 x 12)

Annual Scholarship = $3,000

Total annual income = $22,200

Average monthly income = $1,850 ($22,200 ÷ 12)

Average monthly income = $1,850

Average monthly expenses = $3,135

Cash flows = -$1,295 ($1,850 - $3,135)

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Answer: Reduce the height of the ramp from 1 meter to 0.5 meters

Step-by-step explanation:

Based on this excerpt, the results that Ford helped achieve by implementing the described process was the development of an assembly line, capable of increasing productivity and production efficiency.

He was the founder of the Ford Company and the theory of Fordism, which consists of mass production, reducing costs, increasing efficiency through specialization of work.

Therefore, as we see in the excerpt, mass production generated the greatest speed and precision in each step of the work, increasing productivity and reducing losses and costs associated with production.

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The ratio of gregarious that lived in the valley is 126,00

Ratio is  the comparison of two quantities of the same kind or for comparing two or more quantities that are measured in the same units. It is also  is a relationship between two things when it is expressed in numbers or amounts.

How to determine this

The total who lived in valley = 15,300

The ratio of Reclusive = 3

The ratio of Gregarious = 14

And the ratio of reclusive gregarious = 3 : 14

The total ratio = 3 + 14 = 17

To calculate the total amount of gregarious

= 14/17 * 15,300

= 12,600

Therefore, the total amount of gregarious is 12,600

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Car Make and Model that i choose is Toyota RAV4

The Cost of this car as of today is about $27,000

To know the value of car after one year will be:

20% of $27,000

= $5,400.

So the car  value will be:

$27,000 - $5,400

= $21,600 after year 1

3.  Value of car after second year of ownership:

15% of $27,000

= $4,050.

So, the car  value will be:

$21,600 - $4,050

= $17,550 after year 2.

4 The Exponential Function if the car continues to decrease in value by 15% each year will be;

V(x) = 27,000 x (0.85)ˣ

V(5) = 27,000 x (0.85)⁵

= 27,000  x  0.44370

= $11979.9

Therefore, the value of the car after owning it for five years is  $11979.9

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See text below

Car Value: Exponential

1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.

Car Make and Model:

Cost of this car as of today:

2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?

Value of car after one year:

3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?

Value of car after second year of ownership:

4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.

Exponential Function:

Use your exponential function to calculate the predicted value of your car after you own it for five years.

Value after five years of ownership: