Scott has $80 in a savings account. The interest rate is 5%, compounded annually.

To the nearest cent, how much interest will he earn in 3 years?

Answer:

x=2.345208,−2.345208

Step-by-step explanation:

x²+4=3x²−7

3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

Given, two coordinates of a line \(\left(10,8\right) and \left(4,12\right)\)

The slope of the line formula is:

\(m = \frac{y₂ - y₁}{ x₂ - x₁}\)

Let's substitute our numbers.

\(m = -\frac{8 -12}{4-10}\)  =  -4/6

The GCF of these two numbers is 2

So, our slope  =  -2/3

The general equation of a line is y = mx +c

Therefore the equation of the line is y = -2/3x + c

Since, this line passes through ( 10, 8 )

Hence, it must satisfy these coordinates

8 = -2/3 * 10 + c

44/3 = c

Thus the equation of the line is y = -2/3x +44/3

the equation of the line is 3y + 2x = 44.

Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.

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Answer:

D

Step-by-step explanation:

IM 99% SURE

(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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The polynomial with the 3rd -degree binomial with the constant term 8 is x³ - 8 and 5x³ - 8.

Given that,

A binomial of third degree with constant term of 8.

We have to find a polynomial with the conditions.

We know that,

Binomial is nothing but a polynomial which has 2 terms in it.

And one term should be a constant and that is number 8.

The degree means the degree of the polynomial which has the greatest degree that means power of the variable.

And the degree of the binomial that means power of variable should be 3.

The binomial equation are-

x³ - 8 and 5x³ - 8

Therefore, the polynomial with the 3rd -degree binomial with the constant term 8 is x³ - 8 and 5x³ - 8.

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The question is incomplete the complete question is -

Find a 3rd -degree binomial with a constant term of 8.

Answer:

9x − 3

Step-by-step explanation:

−9x + 3 = −1(−9x + 3) Multiply the expression by −1.

−1(−9x) + −1(3) Distributive Property

9x − 3 Simplify.

The additive inverse of the given expression is 9x-3​.

The given expression is -9x+3.

The additive inverse of a number is its opposite number. If a number is added to its additive inverse, the sum of both the numbers becomes zero. The simple rule is to change the positive number to a negative number and vice versa.

The additive inverse of the expression is -(expression).

Now, -(-9x+3)

= 9x-3

Therefore, the additive inverse of the given expression is 9x-3​.

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Given:

Answer:

       b1 + b2

A = ------------- * h

             2

Step-by-step explanation:

What you have here is fine as is, except that the "1/2" should be enclosed in parentheses:

A = (1/2)(b1 + b2)h.

Alternatively, write:

       b1 + b2

A = ------------- * h

             2

Need 30,529.22 pounds to buy a Lexus that costs 5,000,000 yen

To buy a Lexus that costs 5,000,000 yen, you would first need to convert the yen to pounds. You can find the updated exchange rate online.

And based on March 2, 2023, here is the current exchange rate for 1 yen = 0.0061 pounds. Therefore, you would need to multiply the cost of the Lexus in yen by the exchange rate to get the cost in pounds:

5,000,000 yen * 0.0061 pounds = 30,529.22 pounds

So you would need 30,529.22 pounds to buy a Lexus that costs 5,000,000 yen.

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Answer:

The investment firm's total profit is $4,000

Step-by-step explanation:

The Profit from Company A = 11% * $8,000

= 11 * $8,000/100

= $880

The Profit from Company B = 13% * $24,000

= 13 * $24,000/100

= $3,120

The total profit = $880 + $3120

= $4,000

Thus, the investment firm's total profit is $4,000

The perimeter of the triangle will be 37.5 units. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The sum of all the sides of the triangle will be known as the perimeter of the triangle.

From the graph, the coordinate of a triangle will be (-8, 7), (6, 3), and (2, -4).

Then the perimeter of the triangle will be given as,

\(\rm P = \sqrt{(6 + 8)^2+(3 - 7)^2} + \sqrt{(2 - 6)^2+(-4 - 3)^2} + \sqrt{(2 + 8)^2+(-4-7)^2}\\\\P = \sqrt{212} + \sqrt{65} + \sqrt{221}\)

Simplify the equation, then we have

P = 14.56 + 8.06 + 14.87

P = 37.49 ≈ 37.5 units

The perimeter of the triangle will be 37.5 units. Then the correct option is C.

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Answer:

33?

Step-by-step explanation:

Answer: Exact Form: x = 7/2

Decimal Form: x = 3.5

Mixed Number Form: x = 3 1/2

How to: Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Have a great day and stay safe !

Answer:

18 students

Step-by-step explanation:

2/5+1/5= 3/5

1/5= 30/5

     = 6

3/5= 6*3

     = 18

Answer:

Step-by-step explanation:

Answer:

Let A represent the cost of purchasing a pool membership from the Aquatics Club and let S represent the cost of purchasing a pool membership from the Swimming Hole. Then, we can write the following system of inequalities:

A ≤ y

A = 75 + 20x

S ≤ y

S = 15 + 65x

The first two inequalities represent the cost of purchasing a membership from the Aquatics Club, while the last two represent the cost of purchasing a membership from the Swimming Hole. The inequalities ensure that the cost of purchasing a membership from either company does not exceed Alfonso's budget of y dollars.

Step-by-step explanation:

I've shown the process in the picture. hope that helps

Answer:

0.41666666, to round up, the answer is 0.42

Step-by-step explanation:

\( \frac{3}{8} + \frac{1}{8} - \frac{1}{3} + \frac{1}{4} = \frac{4}{8} - \frac{1}{3} = \frac{4}{24} + \frac{1}{4} = \frac{10}{24} = \frac{5}{12} \)

We will prove the statement  \(n^n / 3^n < n!\)for n ≥ 6 by induction. The base case is n = 6, and we will assume the inequality holds for some k ≥ 6. Using the induction hypothesis, we will show that it also holds for k + 1. Thus, proving the statement for n ≥ 6.

Base case: For n = 6, we have 6⁶ / 3⁶ = 46656 / 729 ≈ 64. As 6! = 720, we can see that the statement holds for n = 6.

Inductive step: Assume that the inequality holds for some k ≥ 6, i.e.,

\(k^k / 3^k < k!.\) We need to show that it holds for k + 1 as well.

Starting with the left side of the inequality:

\((k + 1)^{k + 1} / 3^{k + 1} = (k + 1) * (k + 1)^k / 3 * 3^k\)

\(= (k + 1) * (k^k / 3^k) * (k + 1) / 3\)

Since k ≥ 6, we know that (k + 1) / 3 < 1. Therefore, we can write:

\((k + 1) * (k^k / 3^k) * (k + 1) / 3 < (k + 1) * (k^k / 3^k) * 1\)

\(= (k + 1) * (k^k / 3^k)\)

< (k + 1) * k!

= (k + 1)!

Thus, we have shown that if the inequality holds for k, then it also holds for k + 1. By the principle of mathematical induction, the statement

\(n^n / 3^n < n!\) is proven for all n ≥ 6.

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The domain for the relation y = x + 5, when the range is {2, 6, 10}, is {-3, 1, 5}.

From the question, we have the following parameters that can be used in our computation:

y = x + 5

Range {2, 6, 10}

Make x the subject

x = y - 5

Subtracting 5 from each element:

Hence, the domain for the relation y = x + 5 is {-3, 1, 5}.

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Answer:

£1.44

Step-by-step explanation:

We need to find the number of days it was due first.

26 Nov to 12 Dec: 16 days

1 day --- 9p

16 days --- 16 × 9p = 144p

                              = £1.44

Answer:chicken

Step-by-step explanation:

Put the chicken in the oven turn to 450 degrees let it sit for 4-5 hours

a) To derive the own-price elasticity, we start with the linear demand curve x = a - bp. The own-price elasticity of demand (e) is defined as the percentage change in quantity demanded divided by the percentage change in price. Mathematically, it is given by the formula e = (dx/dp) * (p/x), where dx/dp represents the derivative of x with respect to p.

Differentiating the demand equation with respect to p, we get dx/dp = -b. Substituting this into the elasticity formula, we have e = (-b) * (p/x).

Since x = a - bp, we can substitute this expression for x in terms of p into the elasticity formula: e = (-b) * (p / (a - bp)).

b) To find the price at which e = 0, we set the derived elasticity equation equal to zero and solve for p: (-b) * (p / (a - bp)) = 0. This equation holds true when the numerator, (-b) * p, is equal to zero. Therefore, the price at which e = 0 is when p = 0.

c) To find the price at which e = -os, we set the derived elasticity equation equal to -os and solve for p: (-b) * (p / (a - bp)) = -os. This equation holds true when the numerator, (-b) * p, is equal to -os times the denominator, (a - bp). Therefore, the price at which e = -os is when p = a / (b(1 + os)).

d) To find the price at which e = -1, we set the derived elasticity equation equal to -1 and solve for p: (-b) * (p / (a - bp)) = -1. This equation holds true when the numerator, (-b) * p, is equal to the negative denominator, -(a - bp). Therefore, the price at which e = -1 is when p = a / (2b).

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Answer: 7000.

Step-by-step explanation:

Answer:

700,000

Step-by-step explanation:

70000 ÷ 10% = 700000

Answer:

B.. ..... .., .........

On expanding the given expression (-2a²b⁴)³ , we get -

- 8a⁶b¹²

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given is the following expression -

(-2a²b⁴)³

On expanding the expression, we get -

(-2a²b⁴)³

- 8a⁶b¹²

The correct alternative is option [C] → - 8a⁶b¹²

Therefore, on expanding the given expression (-2a²b⁴)³ , we get -

- 8a⁶b¹²

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Mr. Brust needs 427 cans to cover the wall of dimensions 20 feet long and 9 feet tall.

Area of rectangle is the product of its sides

i.e., Area of rectangle = length  x breadth

The area of a circle is pi times the radius squared (A = π r²).

The circumference of a circle is defined as the linear distance around it.

( C= 2πr)

The can of red bull is in shape of cylinder.

If we open the cylinder it will have two circular surfaces( at bottom and top) and one rectangular sheet.

Like the given figure given.

It shows that the two circle will have the diameter 2.5 inches.

d= 2.5 inch

 = 0.208 ft

radius, r= \(\frac{d}{2}\)

r= \(\frac{0.208}{2}\)

r= 0.104 ft

Circumference of the circle be,

= 2πr

= 2 x 3.14 x 0.104

= 0.653 ft

The rectangular sheet will have,

length=  0.653 ft, breadth= 6.5 inches = 0.541 ft

      = length x breadth

      = 0.653 x 0.541

      =\(0.3532 ft^{2}\)

       = 2 x π\(r^{2}\)

       = 2 x 3.14 x 0.104 x 0.104

       = 6.28 x 0.010816

       = 0.0679 \(ft^{2}\)

        = Area of rectangular sheet + Area of 2 circle( top and bottom of can)

        = 0.3532 + 0.0679

        = 0.4211 \(ft^{2}\)

Now, we have the wall of dimensions

length= 9 ft, breadth= 20 ft

= length x breadth

=9 x 20

= 180 \(ft^{2}\)

         =\(\frac{area \;of\; wall}{area \;of\; can}\)

         =\(\frac{180}{0.4211}\)

         = 427.45 cans

         ≈ 428 cans

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Answer:

The sum of the three products.

Step-by-step explanation:

Based on the results of tossing a coin 100 times and obtaining 93 heads and 7 tails, the probability that the next flip results in a tail is 0.07 or 7%.

The probability of getting a tail on a single coin flip is usually assumed to be 0.5 in a fair coin, where both heads and tails have an equal chance of occurring. However, the probability of obtaining a tail in the next flip is not influenced by the previous outcomes. Each coin flip is an independent event, and the coin does not have a memory of its past flips.

In this case, out of the 100 coin flips, 7 resulted in tails. Since the coin is fair, we can assume that the observed proportion of tails (7 out of 100) is an estimate of the true probability of getting a tail on a single flip. Therefore, the probability of getting a tail on the next flip is approximately 7/100 = 0.07 or 7%.

It's important to note that this probability is an estimate based on the observed data and assumes that the coin is fair. If there is any reason to believe that the coin is biased or there are other factors at play, the probability may differ.

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Answer:

y=2x+7

Step-by-step explanation:

3-(-5) =8

-2-(-6) =4

8/4=2

3=2(-2)+7

3=-4+7

3=3

Answer:

the answer to ur question is y = 2x + 7

Step-by-step explanation: