A couple found a house selling for ​$113,500. The taxes on the house are ​$1300 per​ year, and insurance is ​$340 per year. They are requesting a conventional loan from the local bank. The bank is currently requiring a​ 15% down payment and 3​ points, and the interest rate is​ 10%. The ​ couple's gross monthly income is ​$4950. They have more than 10 monthly payments remaining on a​ car, a​ boat, and furniture. The total monthly payments for these items is ​$420. Their bank will approve a loan that has a total monthly mortgage payment of​ principal, interest, property​ taxes, and​ homeowners' insurance that is less than or equal to​ 28% of their adjusted monthly income.
Complete parts ​a) through ​g) below.

​a) Determine the required down payment.

Answer: 435

Step-by-step explanation:

The simplified form of the expression (mp)⁶ is equal to m⁶×p⁶.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

The given expression is (mp)⁶.

We know, 2²×2² = 2⁴ but 2²×3² = (2×3)² = 6².

Therefore, (mp)⁶ = m⁶×p⁶.

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Answer:

see explanation

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

consider the slope of the middle dotted line

with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line

m = [tex]\frac{-2-(-4)}{3-(-3)}[/tex] = [tex]\frac{-2+4}{3+3}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

consider the slope of the line of reflection ( the solid line )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, 3) ← 2 points on the line

m = [tex]\frac{3-0}{-2-(-1)}[/tex] = [tex]\frac{3}{-2+1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3

note the product of the slopes = [tex]\frac{1}{3}[/tex] × - 3 = - 1

indicating the lines are perpendicular to each other

Answer: The equation that can be solved for t to find the time (in seconds) when the diver hits the water is:

h(t) = 25 - 16e^(-ft) = 0

Where h(t) is the height of the diver in feet at time t, and f is a positive constant related to the speed of the fall.

To find the time when the diver hits the water, we set h(t) equal to zero and solve for t. This gives us the time when the height of the diver is equal to the water surface.

25 - 16e^(-ft) = 0

25 = 16e^(-ft)

e^(-ft) = 25/16

-ft = ln(25/16)

t = -ln(25/16)/f

Note that the negative sign in the equation for t indicates that the time is counted from the moment the diver starts falling. The constant f can be determined from the physical characteristics of the diver and the conditions of the fall, but it is not necessary to know the exact value of f to find the time when the diver hits the water.

Step-by-step explanation:

The cheapest alternative that Valentino can select is to make the computation and discover which is less expensive when compared to others.

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

Given that the info is incomplete, Valentino needs to analyze the three options and make additions for extra charges or deductions for discount and make a purchase of the cheapest alternative.

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Answer:

see below

Step-by-step explanation:

3540/3820 = 93%

so 7% decline

if linearly = every year decline 7%

so back in 1990, 3 years ago, the population was

p° = 3820/(1-7%)^3 =3820/.8=4749

so from 1990

p = 4749 * (1-7%)^t

2009 is 16 years from 1993

so p = 3820 * (1-7%)^16 =1196

Answer:

  A)  P(t) = 3820 -70t

  B)  2700

Step-by-step explanation:

You want a linear equation for the moose population that changed from 3820 in 1993 to 3540 in 1997, and you want the predicted population in 2009.

The slope of the linear function can be found from ...

  m = (p2 -p1)/(t2 -t1)

If we let t represent years after 1993, then this is ...

  m = (3540 -3820)/(4 -0) = -280/4 = -70

P(t) = 3820 -70t . . . . . . . . population is 3820 when t=0, 70 less each year

2009 is 16 years after 1993, so we want P(16):

  P(16) = 3820 -70·16 = 3820 -1120

  P(16) = 2700

The population is predicted to be 2700 in 2009.

Yes the statement of my cousin that rotations, translations, and reflections will result in the congruence of corresponding lines, line segments, and angles is true

Yes, this is true. Congruence refers to the idea that two geometric figures are identical in size and shape. Translations, rotations, and reflections are rigid motions that preserve distances and angles, meaning that corresponding lines, line segments, and angles in the figures will remain congruent after the transformation.

This is because these transformations only involve shifting, rotating, or flipping the figure, but not changing its shape or size.

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The ratio of malts to shakes is 3:7 if 14 shakes are sold for every 6 malts.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.

Let the number of shakes be S and the number of malts be M.

Given: Number of shakes sold = 14 shakes

Number of malts sold = 6 malts

To find the ratio of malts to shakes:

The ratio of malts to shakes exists given by the expression:

M/S = Number of malts sold/Number of shakes sold

Substituting the given parameters into the formula, we have;

M/S = 6/14

M/S = 3/7

Therefore, the ratio of malts to shakes is 3 : 7.

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a) The function is increasing on the following interval: (3, ∞).

b) The function is not decreasing on any interval of it's domain.

c) The function is not constant on any interval of it's domain.

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Anita can type between 60 and 75 words per minute and it took her 43 minutes to type a 12 page report.

The formula to calculate the total number of words in a report is: (words per minute * minutes) = total words. In this case, anita can type between 60 and 75 words per minute, so to solve for the total words in the 12 page report, we need to average her words per minute. This would be (60 + 75) / 2 = 67.5 words per minute. So, now the equation looks like this: (67.5 words per minute * 43 minutes) = 2,888.5 total words in the report.

To break the equation down further, we can say that for every minute Anita types, she is typing 67.5 words. This means that for every minute she types, she is typing 1.125 pages. In other words, for every 8 minutes she types, she is typing 9 pages. Therefore, to type 12 pages in 43 minutes, Anita is typing approximately 9.2 pages per 8 minutes.

To summarize, Anita can type between 60 and 75 words per minute and it took her 43 minutes to type a 12 page report. Using the formula (words per minute * minutes) = total words, we can calculate that the total number of words in the report is 2,888.

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Part C: The ordered pair (0, 150) represents the initial value in the table. The initial value represents the altitude of the airplane when it started descending, i.e., the altitude of the airplane before it began its descent.

Part D: The rate of change in this equation is -5, which is the coefficient of x. The rate of change represents the decrease in altitude, in feet, per minute as the airplane descends for a landing. In other words, the altitude decreases by 5 feet for every minute that the airplane descends.

The number of starting points a ray has is one.

Option B is the correct answer.

A ray is a line that has a starting point and no end.

We have,

A ray is a line that has one fixed point and the other point is endless.

So,

A ray has one starting point.

Thus,

A ray has one starting point.

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Answer:

Step-by-step explanation:

Part A:

x = # of days

R:  1 hr + 3/4 hr/day(x)

J:  4 hr + 1/2 hr/day(x)

1 + 3/4x = 4 + 1/2x

3/4x - 2/4x = 3

1/4x = 3

x = 12 days

After 12 days of practicing (not including the first Saturday), they each will have practiced 10 hours

Part B:

Saturday plus 12 more days →

Saturday 1-Sun 2- Mon 3-Tues 4-Wed 5-Thurs 6-Fri 7-Sat 8-Sun 9-Mon 10-Tues 11-Wed 12-Thursday

They both will have practiced 10 hours on the second Thursday after they started on Saturday

Answer:

x = 8

Step-by-step explanation:

To solve the equation x(x - 2) = 48 for x, we can first expand the left side:

x^2 - 2x = 48

Next, we'll add 2x to both sides to isolate x^2:

x^2 = 48 + 2x

Then, we'll subtract 2x from both sides:

x^2 - 2x = 48

Now we have a quadratic equation that we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -2, and c = 48. Plugging these values into the formula:

x = (-(-2) ± √((-2)^2 - 4(1)(48))) / 2(1)

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

So the two solutions are x = (2 + 14) / 2 = 8 and x = (2 - 14) / 2 = -6.

Keep in mind that x cannot be negative in this context as it represents a measurement. Therefore, x = 8 is the only solution that has a meaningful value in this context.

Step-by-step explanation:

x(x-2)=48

Remove the parentheses

x²-2x=48

Move the constant to the left

x²- 2x - 48=0

Rewrite the expression

x² + 6x - 8x - 48 = 0

Factor the expressions

x(x+6) - 8(x+6) = 0

Separate into possible cases

(x+6) (x-8)=0

x + 6 = 0

x - 8 = 0

x = - 6 or x = 8

Answer:

323/7 or about 46.143

Step-by-step explanation:

We can infer that the measure of B + C is 90 degrees, so 6x + 1 + 8x - 11 must be equal to 90.

6x + 1 + 8x - 11 = 90
14x - 10 = 90

14x = 100

x = 100/14

x = 50/7

Solve for the measure of C by substituting x with 50/7.

50/7 * 8 = 400/7

400/7 - 11 = 323/7

the measure of C is 323/7

Angles given in degrees, arcminutes, and arcseconds converted to decimal fraction of degrees.

A. 2 degrees 18′ 36′′ can be rewritten in decimal fraction of degrees as :

    2 + (18/60) + (36/3600) = 2.3111 degrees.

B. 36′ 18′′ can be rewritten in decimal fraction of degrees as :

   (36/60) + (18/3600) = 0.6050 degrees.

C. 7 degrees 59′ 59′′ can be rewritten in decimal fraction of degrees as:

     7 + (59/60) + (59/3600) = 7.9999 degrees.

D. 1′ can be rewritten in decimal fraction of degrees as:

    (1/60) = 0.0167 degrees.

E. 1′′ can be rewritten in decimal fraction of degrees as:

    (1/3600) = 0.0003 degrees.

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The complete question is :

The following angles are given in degrees, arcminutes, and arcseconds. Rewrite them in degrees and decimal fractions of degrees.

A. 2 degrees 18 ′ 36 ′′

B. 36 ′ 18 ′′

C. 7 degrees 59′ 59′′

D. 1′

E. 1′′

When Daniel creates the linear equation, he will notice that the relationship between time spent and distance travelled is proportional.

The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.

Now,

When we create a linear equation for the distance of the hike, we will get a graph with a straight line.

A straight line's general equation is

y = mx + c

where m = is the slope of the line and

          c  = is the y-intercept

          y = the distance covered

          x = the time taken

Because distance is directly proportional to time,

more distance is covered in less time

Distance ∝ time

Hence,

          Daniel will notice that the relationship between the time spent and distance covered are proportional.

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4a - 8 + 4a - 8 + 4a - 8 = 180°

The sum of interior angle of triangle is 180°

12a - 24 = 180°

12a = 204

[tex]a = \frac{204}{12} \\ [/tex]

a = 17°

1) to obtain the value of x, we must equate AC and BD based on the diagonal properties of a rectangle. Note that a rectangle's diagonal divides it into two congruent right triangles.

A rectangle's diagonals are all the same length. A square is a quadrilateral whose diagonals bisect each other, intersect at right angles, and are congruent.

Thus,

Since BD = AC

2x + 19 = 5x - 2

To solve the equation 2x + 19 = 5x - 2, we need to isolate x on one side of the equation.

First, we can simplify both sides by combining like terms. Subtracting 2x from both sides gives:

19 = 3x - 2

Next, we can isolate x by adding 2 to both sides:

21 = 3x

Finally, we can solve for x by dividing both sides by 3:

x = 7

Therefore, the solution to the equation 2x + 19 = 5x - 2 is x = 7

b) The Properties of Parallel Lines Intersected by a Transverse Postulate states that when a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are supplementary. This means that

∠LMN + ∠MNK = 180°

Thus,

115 +  ∠MNK = 180

∠MNK = 180 - 115

∠MNK = 65°

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Answer:

1

Step-by-step explanation:

There are 15 men in total;

If each committee is to have 8 men (and assuming one man cannot be in multiple committees), we can simply do the following:

15/8 = 1.875

This means only 1 committee can be made containing exactly 8 men.

You can also think of it like this:
If 8 men make up 1 committee, then this leaves 7 (15 - 8) men left;

Since you need 8 men, there is not enough for a second committee (once again, assuming that one man cannot be in more than one committee).

For this data, the median is the best indicator of central tendency.

The correct option is B.

A summary measure called a measure of central tendency, also known as a measure of central or a measure of central placement, aims to summaries the entirety of a set of data using a single number that corresponds to the middle or central of its distribution.

The mean, median, mode, and the midpoint are the four indicators of central tendency. The arithmetic mean of the maximum and minimum values in a data set is used here to define the midpoint or mid-extreme of a set of statistical data values.

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I understand that the question you are looking for is:

A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students. However, one of the participants fails to solve the problems so the researcher has an undetermined score. What is the best measure of central tendency for these data?

a) the mean

b) the median*

c) the mode

d) central tendency cannot be determined for these data

m and n are the two numbers that form the fraction which is the probability of a randomly chosen positive divisor of [tex]10^99[/tex] being an integral multiple of [tex]10^88[/tex].

Let the probability of a randomly chosen positive divisor of [tex]10^99[/tex]being an integral multiple of 10^88 be represented as m/n.

Since [tex]10^99[/tex]is a multiple of [tex]10^88[/tex], its positive divisors will also be multiples of [tex]10^88[/tex].

Therefore, the probability that a randomly chosen divisor of [tex]10^99[/tex]is an integral multiple of [tex]10^88[/tex] will be 1, i.e., m/n = 1.

Therefore, m+n = 1+1 = 2

Hence, the value of (m+n) is 2.

m and n are two numbers that form a fraction in lowest terms, which is the probability that a randomly chosen positive divisor of [tex]10^99[/tex] is an integral multiple of [tex]10^88[/tex]. To find the value of (m+n), we need to first determine the value of m and n. To do this, we must first calculate the total number of positive divisors of [tex]10^99[/tex]that are integral multiples of [tex]10^88[/tex]. We can then divide this number by the total number of positive divisors of [tex]10^99[/tex] to get the fraction. The numerator of this fraction is m and the denominator is n. The sum of m and n is the answer to the question. This is because the fraction gives us the probability that a randomly chosen positive divisor of [tex]10^99[/tex] is an integral multiple of [tex]10^88[/tex], and the sum of m and n is the total number of positive divisors of[tex]10^99[/tex], which is the denominator of the fraction. Therefore, the value of (m+n) is the sum of the numerator and denominator of the fraction.

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Answer: 1200 dollars

Step-by-step explanation:For this question we use the formula:

principal amount x interest rate/100 x time

4000 x 6/100 x 5

4000 x 0.06 x 5

1200

Answer:

$5,387.42

Step-by-step explanation:

Use the formula:

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\\[/tex]

where A = amount accrued (principal + interest)
P = initial deposit

r = annual interest rate as a decimal

n = number of times compounded annually

t = number of years

Given
P = 4000
r = 6/100 = 0.06
n = 4 times a year
t = 5 years

[tex]A = 4000\left( 1 + \dfrac{0.06}{4}\right)^{4\cdot 5}\\\\A = 4000 ( 1+ 0.015)^{20}\\\\A = 4000 (1.015)^{20}\\\\A = \$5,387.42[/tex]

Answer: 1,638

Step-by-step explanation:

Answer:

1638

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Answer:

Step-by-step explanation:

The entry "EQUIPMENT $12,000" is listed as a debit in the T-account, which means it is an increase in assets. Therefore, the correct answer is (b) increase in assets.

Answer:

Substitute y = 12x + 7

12x+7=-6+25

Simplify

12x+7=19

Solve

19-7=12

12x=12

x=1

Answer:

The correct answer is C. $575. The business bought equipment with $150 cash and put $425 on credit, so the total value of the asset is $575 ($150 + $425).