The present value in a savings account is $420. It is receiving 3% annually compounded monthly. What is the future value in 2 months?

The value today of a money machine is $4,712.25. The value of the investment is $31,323.15.

Question 9:

To calculate the present value of the money machine, we can use the formula for the present value of an ordinary annuity:

PV = P * [(1 - (1 + r)^(-n)) / r],

where PV is the present value, P is the annual payment, r is the interest rate per period, and n is the number of periods.

Given:

Annual payment (P) = $1000,

Interest rate per period (r) = 4% = 0.04,

Number of periods (n) = 6 - 2 = 4.

Plugging in the values, we get:

PV = $1000 * [(1 - (1 + 0.04)^(-4)) / 0.04] = $4712.25.

Therefore, the value today of the money machine is $4712.25.

Question 10:

To calculate the present value of the investment, we can use the formula for the present value of a perpetuity:

PV = P / r,

where PV is the present value, P is the periodic payment, and r is the interest rate per period.

Given:

Periodic payment (P) = $500,

Interest rate per period (r) = 12% / 12 = 0.12 / 12 = 0.01.

Plugging in the values, we get:

PV = $500 / 0.01 = $31,500.

Therefore, the value of the investment today is $31,323.15.

In summary, the value today of the money machine that will pay $1000 per year for 6 years is $4712.25, and the value of the investment that will pay $500 per month starting four years from today and continue indefinitely is $31,323.15.

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To calculate the standard error (SE) for the percentage of young adults who favor gay marriage, we need to consider the sample size and the proportion of individuals in the sample who favor gay marriage.

The formula for calculating the standard error (SE) of a sample proportion is SE = sqrt((p * (1 - p)) / n), where p is the sample proportion and n is the sample size.

In this case, the sample proportion is given as 73% or 0.73, and the sample size is 321 young adults. Substituting these values into the SE formula, we get SE = sqrt((0.73 * (1 - 0.73)) / 321).

To calculate the SE, we first calculate (0.73 * (1 - 0.73)) to get 0.1979. Dividing this value by the sample size of 321 and taking the square root, we find that the SE for the percentage of young adults who favor gay marriage is approximately 0.0211.

Therefore, the standard error (SE) for the percentage of young adults who favor gay marriage, based on the CBS news poll data, is approximately 0.0211 or 2.11%. The SE provides an estimate of the variability or margin of error associated with the sample proportion.

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We are given that fifteen boys and fifteen girls entered a drawing for four free movie tickets. We want to find the probability that all four tickets were won by girls.

To solve this problem, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

The total number of outcomes represents all the possible ways to choose four winners from the thirty participants (boys and girls). We can calculate this using the combination formula:

C(30, 4) = 30! / (4!(30 - 4)!) = 27,405

Here, C(n, r) represents the combination of choosing r objects from a set of n objects.

Favorable outcomes:

We want to determine the number of ways to select all four winners from the group of fifteen girls. This can also be calculated using the combination formula:

C(15, 4) = 15! / (4!(15 - 4)!) = 1365

Probability calculation:

The probability is the ratio of the favorable outcomes to the total number of outcomes. So, we divide the number of favorable outcomes by the total number of outcomes:

P(Girls winning all four tickets) = 1365 / 27,405

Simplifying the fraction, we find:

P(Girls winning all four tickets) = 1 / 20

Therefore, the probability that all four tickets were won by girls is 1/20.

In summary, out of all the possible combinations of selecting four winners from the thirty participants, only one out of every twenty combinations will result in all four tickets being won by girls.

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The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

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In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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Answer:

the missing numerator is 4 and denominator is 4

8/14 In simpliest form is 4/7

Step-by-step explanation:

4/14+4/14=8/14

8 divded by 2=4 14 divded 2=7

Answer:

x =(1-√117)/2=(1-3√ 13 )/2= -4.908

x =(1+√117)/2=(1+3√ 13 )/2= 5.908

Step-by-step explanation:

Answer:

last option, 32.5

Step-by-step explanation:

32.5 * 9.20 = 299

Answer:

The first option and the answer is actually 32 hours and 30 min but it'll prolly be 33 hours

Step-by-step explanation:

Answer: 3/8

1/4 + 1/8 divided by 2

Answer:

Step-by-step explanation:

2. 11x + 5y - 6

3. - 97x -21y + 100

That's all i could do hope it helps :l

Answer:

y = 30.12(4) + 3

Step-by-step explanation:

there's 30.12, 4 times (4pizzas) plus an initial, one time fee of 3 dollars. so you'd multiply the 30.12 and (4), then add the 3 dollars one time.

The 95% confidence interval for the percentage of people who prefer Candidate A is given as follows:

(43.3%, 54.7%).

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

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

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

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The parameters for this problem are given as follows:

\(n = 300, \pi = 0.49\)

Hence the lower bound of the interval is of:

\(0.49 - 1.96\sqrt{\frac{0.49(0.51)}{300}} = 0.433\)

The upper bound of the interval is of:

\(0.49 + 1.96\sqrt{\frac{0.49(0.51)}{300}} = 0.547\)

As a percentage, the proportion is multiplied by 100%, hence the interval is given as follows:

(43.3%, 54.7%).

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Answer:

The rectangle has a length of 15 cm and a width of 13 cm

Step-by-step explanation:

Let w represent the width of the rectangle, and let w + 2 represent the length of the rectangle.

Use the perimeter formula, P = 2l + 2w, and plug in the perimeter and w + 2:

P = 2l + 2w

56 = 2(w + 2) + 2w

Simplify and solve for w:

56 = 2w + 4 + 2w

56 = 4w + 4

52 = 4w

13 = w

Then, add 2 to this to find the length:

13 + 2

= 15

So, the rectangle has a length of 15 cm and a width of 13 cm.

To solve the equation in part a and determine the mystery weight, we used the following properties of equality:

Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.

Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.

Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.

Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.

By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.

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Answer:

{5, 6, 7}

Step-by-step explanation:

When we have a given relation, the domain is the set of inputs, and the range as the set of the outputs.

so for a function f(x), and a domain {a. b. c}

The range is:

{f(a), f(b), f(c)}

In this case, we have:

f(x) = x + 6

and the domain is {-1, 0, 1}

Then the range is:

{ f(-1), f(0), f(1) }

{-1 + 6, 0 + 6, 1 + 6}

{5, 6, 7}

The correct option is the third one.

Answer:

Im pretty sure its C

Answer: The answer is C

Step-by-step explanation:

Answer:

Mode is 1, Mean is 3.1 if the '41" is 1 and 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1/28 kilo

Step-by-step explanation:

sb help me on my recent please

The value of the functions are;

h(f(g(1/2))) =  (√1/2)³/3

h(f(g(x))) = = (√x)³/3

It is important to note that a function is an equation that shows the relationship between two variables

From the information given, we have that;

f(x) = x³

g(x) = √x

h(x) = x/3

To determine the composite function, we need to substitute the value of one function as the value of x in the other, we have that

f(g(1/2) =

g(1/2) = √1/2

Substitute the value

f(g(1/2) = (√1/2)³

Now, substitute the value as x in h(x)

h(f(g(1/2))) =  (√1/2)³/3

f(g(x)) = (√x)³

Then, h(f(g(x))) = = (√x)³/3

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Answer:

the correct answer would be 2r+2

Step-by-step explanation:

8r-6r=2r

7-5=2

Answer:

2r + 2

Step-by-step explanation:

8r+7−6r−5

Terms with r are like terms and can be combined together.

Terms with no variable are like terms and can be combined together.

Terms with r and terms with no r are not like terms and cannot be combined together.

8r + 7 - 6r - 5 =

= 8r - 6r + 7 - 5

= 2r + 2

Answer:

1) Pr(all three) = 0.064

2) Pr(none) = 0.216

3) Independent event

Step-by-step explanation:

Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)

Where Pr = probability

This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure

Where p = success, q = failure

For n trials,

Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Pr (security) = 40% = 0.4

p = 0.4

q = 1-p = 1-0.4 = 0.6

Numbers selected at random = n = 3

See attachment for more details on the workings.

1) Probability all three of the selected homes have a security system = Pr(all three)

Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³

= 0.4×0.4×0.4

Pr(all three) = 0.064

2) Probability none of the three selected homes have a security system

= Pr(none)

Pr(none) = 1 × (0.4)^0 × (0.6)³

= 0.6³ = 0.6×0.6×0.6

Pr(none) = 0.216

3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.

Answer:

Hello! The answer to your question seems to be 4n + 13

Step-by-step explanation:

Hope this helps, don't forget to give me the shiny gold crown! Have a good day ^-^

The answer is 966 codes.

It would probably be simplest to simply state the prohibited codes.

023 - narrators code

02x

0x3

x23

Here x is a number between 0 and 9, there are 10 of each, making a total of 30.

203

302

032

Consequently, there are 34 banned codes in all.

There are 103 = 1000 codes in all.

1000 - 34 = 966 codes are available.

What is narrators code?

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Answer:

4 ²/3

Step-by-step explanation:

( 5+2) ×( 6-4) / ( 2+1 )

= (7)×(2) / 3

= 4 ²/3

While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no relationship between variables.

What is alternative hypothesis?

The alternative to your research topic is represented by the alternative hypothesis (Ha). It asserts that there is a population-wide impact.  

                                     Frequently, your study hypothesis and alternate hypothesis are the same. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

What is meant by a null hypothesis?

A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.

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Answer: 10, 12, 14 are the next numbers

Explanation: