The brady bunch has three boys who ages are consecutive even integers. The sum of the boy's ages is equal to four times the youngest boy's age. What are the ages Brady boys?

Final answer:

The value of an investment of $4500 at a 7.25% annual interest rate, compounded continuously, is calculated using the compound interest formula [tex]P = P_0e^{rt}[/tex], where P0 is the initial amount, r is the rate as a decimal, and t is the time in years.

Explanation:

The subject of this question is Mathematics, and it falls under the High School grade level. To find the value of an investment compounded continuously, we use the formula:

[tex]P = P_0e^{rt}[/tex]

Where:

Given a $4500 investment at a 7.25% annual interest rate, compounded continuously, we can calculate the future value of the investment after t years. Convert the percentage to a decimal by dividing by 100:

r = 7.25 / 100 = 0.0725

So the formula becomes:

[tex]P = $4500e^{0.0725t}[/tex]

Plug in the number of years into 't' to calculate the future value for that specific duration.

After 2, 4, and 6 years of continuous compounding, the investment values are approximately $5198.85, $6014.70, and $6953.85 respectively.

To find the value of the investment after a certain number of years with continuous compounding, we use the formula:

[tex]\[ A = P e^{rt} \][/tex]

Given:

-  P = $4500

-  r = 7.25% = 0.0725  (as a decimal)

We need to calculate the value of the investment after 2, 4, and 6 years.

(a) For 2 years:

[tex]\( A = 4500 \times e^{0.0725 \times 2} \)\\\( A = 4500 \times e^{0.145} \)\\\( A \approx 4500 \times 1.1553 \)\\\( A \approx \$5198.85 \)[/tex]

(b) For 4 years:

[tex]\( A = 4500 \times e^{0.0725 \times 4} \)\\\( A = 4500 \times e^{0.29} \)\\\( A \approx 4500 \times 1.3366 \)\\\( A \approx \$6014.70 \)[/tex]

(c) For 6 years:

[tex]\( A = 4500 \times e^{0.0725 \times 6} \)\\\(A = 4500 \times e^{0.435} \)\\\(A \approx 4500 \times 1.5453 \)\\\( A \approx \$6953.85 \)[/tex]

So, the values of the investment after 2, 4, and 6 years respectively are approximately:

(a) $5198.85

(b) $6014.70

(c) $6953.85

Complete Question:
If $ 4500 is invested at an interest rate of 7.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

(a) 2 years

(b) 4 years

(c) 6 years

The z-score corresponding to this value will be negative 0.6667.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

Test scores are typically conveyed with a mean of 100 and a standard deviation of 15. A singular's level of intelligence score is viewed as 90.

The z-value is given as,

z = (90 - 100) / 15

z = - 10 / 15

z = - 0.6667

The z-score relating to this worth will be negative 0.6667.

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Answer:

true....

Step-by-step explanation:

The value of the given expression is -0.9

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression -4.2+3.3 = ? we need to find the answer in the decimal form,

To find the same, we have to simply subtract 3.3 from 4.2 and since the greater number is in negative the result will also be in negative,

3.3-4.2 = -0.9

Hence, the value of the given expression is -0.9

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Answer:

The correct answer is: False

The probability that at most 11 of them have brown eyes is 0.9994

What is Binomial Distribution Function?

If a random variable X denotes the number of successes in n trials each with probability of success p, then we say that X ∼ Bin (n, p) , and the probability of exactly x successes in n trials P [X = x] is given by the binomial distribution function,  f(x) , where f(x) is

                            [tex]f(x) = P[X=x] = (\frac{n}{x} ) p^{x} (1-p)^{n-x}[/tex]

where x = successes , n = trials

Therefore ,          [tex]f(x) = \frac{n!}{x!(n-x)!} p^{x} (1-p)^{n-x}[/tex]

Given data , we have

p = 40 % = 0.4

n = 14

Let X be the number out of a sample of 14 whose eyes are brown.

So the probability that at most 11 of them have brown eyes is calculated as P( X [tex]\leq[/tex] 11 ) and

P( X [tex]\leq[/tex] 11 ) = 1 - P( X > 11 )

where P( X > 11 ) = 0.0006

Therefore , P( X [tex]\leq[/tex] 11 ) = 1 - 0.0006

                                     = 0.9994

Hence , the probability that at most 11 of them have brown eyes is 0.9994.

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We can assume that Bill's store is in danger of experiencing a diseconomy of scale.

Given Bill's grocery store chain's 2,000 total employees, 900 of whom are managers, it may be more logical to believe that Bill's store is in danger of suffering a diseconomy of scale.

Diseconomies of scale relate to a situation in which a company expands so much that its costs per unit rise.

When a corporation suffers diseconomies of scale, needless expenditures frequently develop as a result of greater management issues and inefficiencies in the flow of work and commodities.

Almost half of Bill's employees are managers of some kind. This will reduce his company's productivity and cause costs to increase as output expands.

Complete question:

Bill owns a grocery store chain with 2,000 total employees. nine hundred of his employees are managers. what can we assume about the total productivity of bill’s chain?

a. bill’s store is in danger of experiencing a diseconomy of scale

b. the grocery store is experiencing a constant return to scale

c. the grocery store is experiencing an economy of scale

d. bill’s store is run very efficiently.

Answer:

Both the equation and its inverse are functions.

Step-by-step explanation:

A function is relation in which one input gives one and only one output.

Here, the given function,

[tex]f(x)=5x+1[/tex]

Which is a polynomial,

A polynomial is a function because for each input value it gives only one output value.

⇒ f(x) is a function.

Now, For finding the inverse of f(x),

Replace f(x) by y,

y = 5x + 1

Switch x and y,

x = 5y + 1

Isolate y on the left side,

-5y = 1 - x

[tex]y = \frac{1-x}{-5}=\frac{x-1}{5}[/tex]

Replace y by [tex]f^{-1}(x)[/tex],

[tex]f^{-1}(x)=\frac{x-1}{5}[/tex]

Which is also a polynomial,

Hence, the inverse of f(x) is also a function,

Last option is correct.

Answer:

69.74 feet per second is the velocity of an object that has fallen 76 feet

Step-by-step explanation:

As per the statement:

The formula v = square root of 64h gives the velocity v in feet per second of an object that has fallen h feet.

⇒[tex]v = \sqrt{64h}[/tex]

where, v is the velocity in feet per second and an object that has fallen h feet.

We have to find the velocity of an object that has fallen 76 feet.

⇒ h = 76 feet.

Substitute in the given formula we have;

[tex]v = \sqrt{64 \cdot 76} = \sqrt{4864} = 69.7423831[/tex] feet per second

Therefore, the velocity of an object that has fallen 76 feet to the nearest hundredth is, 69.74 feet per second

Answer:

the other answer is wrong number 2 is correct

Step-by-step explanation:

The interval on which f(x) is integrable is:

                             [-2, ∞)

We are given a function f(x) as:

               [tex]f(x)=\sqrt{x+2}[/tex]

We know that a function is integrable over a given interval if it is continuous over a given interval.

Now, we know that the square root function is well defined if the function under the square root sign is positive.

This means here the function is well defined if:

[tex]x+2\geq 0[/tex]

i.e.

[tex]x\geq -2[/tex]

Also, the square root function is continuous over it's domain.

and hence it is integrable over it's domain.

This means that the function is integrable over:

                       [-2,∞)

to get an A, she needs >=160 points and she already has 125 points

let 'x' be the number of points on the last part of her project then

125 + x >= 160

x >= 160 - 125

x >= 35

Sarah needs at least 35 points on the last part of her project.

Answer:

P ≥ 35

Step-by-step explanation:

Naming P to the Points needed for the last part of Sarah's project,

we can define an inequation modelling in which cases Sarah will have enough points for an A or better:

It is stated that:

Then the inequation can be written:

[Points-so-far] + [Points-needed] greater or equal than 160

In math symbols:

[tex]125+P\geq 160\\P\geq 160-125\\P\geq 35[/tex]

For the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the given expression is 2(v-h)/k=r

We have to solve the expression in the term v as,

2(v-h)/k=r

Open the brackets and multiply 2 in the bracket as

(2v-2h)/k=r

Apply the cross-multiplication operation as

2v-2h=r·k

Rearrange the equation as

2v=r·k+2h

The equation for v in terms of all other variables involved is obtained as,

v=(r·k)/2+h

Thus, for the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.

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Final answer:

The expression to represent Jonas's total purchase is 3x - $20, where x is the price of one book.

Explanation:

To create an expression that represents the total purchase of Jonas's books, let's denote the price of each book as x. Jonas bought 3 books at the same price, so the cost of the books is 3x. However, with the coupon, Jonas gets $20 off the total cost. Therefore, the expression that represents the total purchase is:

3x - $20

This expression first calculates the total cost of the books (3 times the price of one book) and then subtracts the $20 discount from the coupon.