Dane and Amber plan to buy a house for $130,000. They want to make a down payment of 20% to avoid PMI charges. How much money will they need for a down payment?

Answer:

A  =  $56,740

Step-by-step explanation:

Use the Compound Amount formula A = P(1 + r)^t.  Substitute 0.05 for r and $40,000 for P:

A = $40,000(1 + 0.05)^6

A  =  $56,740.26, or, rounded off to the nearest dollar,

A  =  $56,740

Answer:

it helps to find unknown variables

Answer:

it helps to discover unknown operations and variables

Answer:

Step-by-step explanation: 69

The vertex form of a quadratic function is:

The standard form of a quadratic function is:

We can do the following steps to solve the exercise.

Step 1: We replace the values of h,k, x, and y into the vertex form of a quadratic equation, and we solve for a.

Step 2: We replace the values of a,h, and k into the vertex form of a quadratic equation.

Step 3: We expand the expression inside the parentheses and combine like terms to convert the function into its standard form.

The equation of the graph in standard form is:

Answer: f(-2) = -7

Explanation: If f(x) = 3x - 1, then f(-2) is 3(-2) - 1 which simplifies to -7.

So the value of the function at -2 is -7.

Answer:

c

Step-by-step explanation:

Here is the completed two-way frequency table:

                         Comedy     Action     Total

Boys                    37              57              94

Girls                    68               38             106  

Total                   105              95             200

Number of boys that prefer comedy = number of students that prefer comedy - Number of girls that prefer comedy

105 - 68 = 37

Number of boys that prefer action = total numer of boys - Number of boys that prefer comedy

94 - 37 = 57

Total number of students the prefer action = Total number of students - total number of students that prefer comedy

200 - 105 = 95

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Answer:

In isosceles triangle two sides are equal,

So,

3x-1=2x+2

x=3

Perimeter=sum of all sides

=3x-1+2x+2+2x

=7x+1

Substituting value of x

Perimeter=7(3)+1

=21+1

=22

Thus x=3

:. Perimeter of a triangle=22 square units

Answer:

Answer down below!

Step-by-step explanation:

If he caught 6 fish in two hours, first, we need to find out how much he caught in one hour, and then find how many he caught in 8 hours.

If he caught 3 fish in hour one, we can times 3 x 8 to get our answer

3 x 8 = 24

So in 8 hours, he caught 24 fish!

Answer:

I got 40 aswell

Step-by-step explanation:

Step-by-step explanation:

b= base = 11 cm        h = height = 8.2 cm

Area = b * h  =  11  * 8.2 = 90.2 cm^2

The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

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

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

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Answer: Terry paid  $18.36 for the sweater.

Step-by-step explanation:

Given: Sales price of sweater = $24

Coupon states \(\dfrac14\) off the sales, i.e. Terry will get \(\dfrac14\times24=\$6\) discount.

Also, tax rate = 6%

Tax will be charged = 6% of Sales price of sweater

=  0.06 x 6

= $0.36

Now , Final amount for Terry = Sales price - discount +tax

= $(24-6+0.36)= $18.36

Hence, Terry paid  $18.36 for the sweater.

Answer:hi

Step-by-step explanation:

The value of g′(7) is 1/3 found using the increasing function.

Given that, h(x) is an increasing function, which means that the derivative of h(x) will always be positive.

If we observe the table, we can see that the values of h(x) is increasing. Thus, we can say that h'(x) is a positive value for all values of x. Let g(x) be the differentiable function such that h(g(x)) = x.

We are supposed to find the value of g′(7). We know that h(g(x)) = x, by applying the chain rule of differentiation to h(g(x)), we can write it as follows:h′(g(x)) g′(x) = 1 => g′(x) = 1 / h′(g(x))

Substituting x = 7 in the above equation,g′(7) = 1/h′(g(7))

From the given table, the value of h(7) is 16. Given that h(x) is an increasing function, we can say that h'(x) is positive for all values of x.

The derivative of h(x) at x = 7 can be calculated by finding the slope of the tangent at the point (7,16).From the given table, we can see that when x = 6, h(x) = 12, and when x = 8, h(x) = 18.

Slope of the line joining the points (6,12) and (8,18) can be calculated as follows:m = Δy / Δx= (18 - 12) / (8 - 6)= 3The slope of the tangent at the point (7,16) is 3.Thus, we can write:h′(7) = 3

Substituting h′(7) in the equation,g′(7) = 1/h′(g(7))= 1 / 3

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I'm a little rusty lol but I believe that is C, the distributive property.

Answer:

Distributive Property

Step-by-step explanation

You first ditribute the 6 to the 4x and -1.

Answer:

1 1/4 cups

Step-by-step explanation:

a) Since the new score is less than the average score, it will decrease the average.

a) Since the new score is less than the average score, it will decrease the average.

b) Sum of 27 scores = 27*79

Hence,

New average = (79*27 + 63)/28 = 78.43

c) Since the variability would increase in the overall data, the standard deviation increases.

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(a)If log₄​x = 5, the base is 4 and the logarithm is 5 , then x = 1024. (b) If log₆​x = 8 the base is 6 and the logarithm is 8  then x = 1679616.

(a) In the equation log₄​x = 5, the base is 4 and the logarithm is 5. To solve for x, we need to rewrite the equation in exponential form. In exponential form, 4 raised to the power of 5 is equal to x. Therefore, x = 4^5 = 1024.

(b) In the equation log₆​x = 8, the base is 6 and the logarithm is 8. Rewriting the equation in exponential form, 6 raised to the power of 8 is equal to x. Hence, x = 6^8 = 1679616.

In both cases, we used the property of logarithms that states: if logₐ​x = y, then a raised to the power of y equals x. By applying this property, we can convert the logarithmic equations into exponential form and find the values of x.

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Answer:

6) 9x-25+9x-25(sum of base angles)

9x-25+9x-25+104=180(sum of angles in a triangle)

collect like terms

9x+9x-25-25+104=180

18x-50+104=180

18x+54=180

18x=180-54

18x=126

divide both sides by 18

18x÷18=126÷18

x=7

The absolute deviation of the data set 7 10 14 and 20 is 4.25.

What is the mean deviation method?

When calculating the average departure from the mean value of a particular data set, statisticians employ a measure known as the mean deviation. Following the steps below will make it simple to determine the mean deviation of the data values.

In statistics, the term "deviation" refers to the discrepancy between the observed value of a data point and its expected value. As a result, mean deviation, also known as mean absolute deviation, is the typical departure of a data point from the mean, median, or mode of the data collection.

data set is 7, 10, 14, 20,

Mean = m = 51/4 = 12.75

So the MAD is 1/4 |7-12.75| |10-12.75| |14-12.75| 20-12.75|

MAD = 17/4 = 4.25

Hence the mean absolute deviation of the data set 7 10 14 and 20 is 4.25.

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The 5-day BOD (BOD5) for the river water sample is 3.30 mg/L.

To find the 5-day BOD (BOD5) for the river water, you need to calculate the difference between the initial dissolved oxygen (DO) levels and the DO levels after 5 days of incubation.

First, calculate the average initial DO level:

Average initial DO = (8.86 + 8.88 + 8.83) / 3

                  = 26.57 / 3

                  = 8.86 mg/L (rounded to two decimal places)

Next, calculate the average DO level after 5 days:

Average DO after 5 days = (5.49 + 5.65 + 5.53) / 3

                       = 16.67 / 3

                       = 5.56 mg/L (rounded to two decimal places)

Now, calculate the 5-day BOD:

BOD5 = Average initial DO - Average DO after 5 days

    = 8.86 - 5.56

    = 3.30 mg/L (rounded to two decimal places)

Therefore, the 5-day BOD (BOD5) for the river water sample is 3.30 mg/L.

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Answer: $7,358

Step-by-step explanation: $26 * 283 (each student) =7,358 dollars

Answer:

-6665

Step-by-step explanation:

The given GP is :

1, -6, 36, ...

Number of terms = 6

The sum of n terms of a GP is given by :

\(S_n=\dfrac{a(r^n-1)}{r-1}\)

Here,

a = 1, n = 6, r = 36/-6 = -6

So,

\(S_6=\dfrac{1((-6)^6-1)}{(-6)-1}\\\\=-6665\)

So, the sum of th GP is -6665.

The result of (75) base 8 + (1342) base 5 + (100111) base 2, when expressed in bases 2, 5, and 8, respectively, is: (101000010) base 2, (2242) base 5, and (520) base 8.

To evaluate and express the answer with bases 2, 5, and 8, we'll convert the given numbers into decimal form, perform the addition, and then convert the result back into the desired bases.

Let's start by converting the numbers into decimal form:

(75) base 8 = 7 * 8^1 + 5 * 8^0 = 56 + 5 = 61

(1342) base 5 = 1 * 5^3 + 3 * 5^2 + 4 * 5^1 + 2 * 5^0 = 125 + 75 + 20 + 2 = 222

(100111) base 2 = 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 32 + 0 + 0 + 4 + 2 + 1 = 39

Now, let's perform the addition:

61 + 222 + 39 = 322

To express the result in base 2, we need to convert 322 back into binary form:

322 divided by 2 gives us a quotient of 161 with a remainder of 0.

161 divided by 2 gives us a quotient of 80 with a remainder of 1.

80 divided by 2 gives us a quotient of 40 with a remainder of 0.

40 divided by 2 gives us a quotient of 20 with a remainder of 0.

20 divided by 2 gives us a quotient of 10 with a remainder of 0.

10 divided by 2 gives us a quotient of 5 with a remainder of 0.

5 divided by 2 gives us a quotient of 2 with a remainder of 1.

2 divided by 2 gives us a quotient of 1 with a remainder of 0.

1 divided by 2 gives us a quotient of 0 with a remainder of 1.

Reading the remainders from bottom to top, we have: (101000010) base 2.

To express the result in base 5, we need to convert 322 back into quinary (base 5) form:

322 divided by 5 gives us a quotient of 64 with a remainder of 2.

64 divided by 5 gives us a quotient of 12 with a remainder of 4.

12 divided by 5 gives us a quotient of 2 with a remainder of 2.

2 divided by 5 gives us a quotient of 0 with a remainder of 2.

Reading the remainders from bottom to top, we have: (2242) base 5.

To express the result in base 8, we need to convert 322 back into octal (base 8) form:

322 divided by 8 gives us a quotient of 40 with a remainder of 2.

40 divided by 8 gives us a quotient of 5 with a remainder of 0.

5 divided by 8 gives us a quotient of 0 with a remainder of 5.

Reading the remainders from bottom to top, we have: (520) base 8.

Therefore, the result of (75) base 8 + (1342) base 5 + (100111) base 2, when expressed in bases 2, 5, and 8, respectively, is: (101000010) base 2, (2242) base 5, and (520) base 8.

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The manager can evaluate the seven trainees in 78,125 different ways using the five categories of outstanding, excellent, average, below average, and poor.

The manager wants to evaluate seven trainees using five categories: outstanding, excellent, average, below average, and poor. Since each trainee can be evaluated independently, we can use the concept of permutations to determine the number of ways the manager can evaluate the trainees.

For the first trainee, there are five categories to choose from. The same goes for the second trainee, and so on, until the seventh trainee. Since the evaluations are independent, we multiply the number of choices for each trainee.

Therefore, the total number of ways the manager can evaluate the trainees is calculated as follows:

5 choices for the first trainee × 5 choices for the second trainee × 5 choices for the third trainee × 5 choices for the fourth trainee × 5 choices for the fifth trainee × 5 choices for the sixth trainee × 5 choices for the seventh trainee.

This can be expressed as 5⁷ since there are seven trainees and five categories for each trainee.

Calculating 5⁷ gives us:

5⁷ = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78125.

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The balance of the unsubsidized loan at the time of graduation is $3,691.10.

Given:

Principal amount = $2,560

Interest rate = 6.8% = 0.068

Time period = 6 months

We can use the formula for compound interest to calculate the future value:

\(Future\; Value = P (1 + \dfrac{Interest Rate}{Number of Periods}) ^{(Periods * Time )\)

Substituting the value back into the formula as

Future Value = \($2,560 (1 + \dfrac{0.068}{12} )^{(12 * 6)\)

                      = \($2,560 (1 + 0.00566667)^{(72)\)

                      = \($2,560 (1.00566667)^{(72)\)

                      = $2,560 * 1.44044291

                       = $3,691.10

Therefore, the balance is $3,691.10.

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Answer:

\(Length = Width = 6\ units\)

Step-by-step explanation:

Given

\(Area=36\)

Required

The least possible material

Sandboxes usually, are rectangles or squares.

Using the above assumption, the area is calculated as:

\(Area= Length * Width\)

\(Area= L* W\)

\(L * W = 36\)

Make L the subject

\(L = \frac{36}{W}\)

The material of the outer edge is calculated by the perimeter.

\(Perimeter = 2 * (L +W)\)

\(P = 2 * (L + W)\)

Substitute \(L = \frac{36}{W}\)

\(P = 2 * (\frac{36}{W} + W)\)

Open bracket

\(P = \frac{72}{W} + 2W\)

\(P = 72W^{-1} +2W\)

To get the minimum material needed, we differentiate P

\(P' = -72W^{-2} + 2\)

Set: \(P' = 0\)

\(-72W^{-2} + 2 = 0\)

Collect like terms

\(72W^{-2} = 2\)

Divide both sides by 72

\(W^{-2} = \frac{2}{72}\)

\(W^{-2} = \frac{1}{36}\)

Rewrite as:

\(\frac{1}{W^2} = \frac{1}{36}\)

Take positive square roots of both sides

\(\frac{1}{W} = \frac{1}{6}\)

Cross multiply

\(W = 6\)

Recall that: \(L = \frac{36}{W}\)

So, we have:

\(L =\frac{36}{6}\)

\(L = 6\)

Hence, the dimension with the littlest material as possible is:

\(Length = Width = 6\ units\)