Suppose your gross monthly income is $6,500 and your current monthly payments are $525. If the
bank will allow you to pay up to 38% of your gross monthly income (less current monthly payments)
for a monthly house payment, what is the maximum loan you can obtain if the rate for a 25-year
mortgage is 8.65%?

Note that the phrases that best describe the graph of f(x) = |x| are:

1) Note that the function given above is an Absolute Function, and as given in the attached graph, you'd notice that the graph of an absolute function is always V-shaped. Thus, option A is true.

2) One must also note that where the sign before the modulus is positive, then the graph opens up (as in the case above) otherwise it opens down. Thus, option C is correct.

3) If (x,-y) lies on the function, then f(x) is in proportion with respect to the x-axis. If (-x,y) lies on the function, then f(x) is in proportion with respect to the y-axis.

Put (x,-y) in the given function.

-y = |x| ⇒ -y ≠ y

Thus,  f(x) is not symmetric with regard to the x-axis.

Placing (-x,y) in the given function, we have

y = |x| ⇒ y = y

Because the point (-x,y) lies on the function, therefore (fx) is symmetric with regard to the y-axis. Hence, Option F is correct.

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Answer:

28 inches

Step-by-step explanation:

Answer:

D. 10

Step-by-step explanation:

8x-14=5x+34

8x-5x=34+14

3x=48

x=48/3

x=16

8x-14+5y+16 = 180

8(16)-14+5y+16 = 180

128-14+5y+16=180

5y=180-128-16+14

5y=50

Y = 10

Answer:

D is the answer

Step-by-step explanation:

AS IT IS MCQ

NO NEED OF STEP BY STEP EXPLAINATION

An inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately 4 people can go to the amusement park.

In the given question,

cost for admission parking = $15

Tickets = $25 per person

Let x be the number of people those who go to the amusement park.

On parking and admission spent not more than $115

So we get an inequality,

15 + 25x ≤ 115

We solve above inequality.

25x ≤ 115 - 15

25x ≤ 100

25x / 25 ≤ 100/25

x ≤ 4

This means that approximately 4people can go to the amusement park.

Therefore, an inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately 4 people can go to the amusement park.

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The letters of English alphabet that have parallel lines and intersecting lines and perpendicular lines are: E, F, H, I, L, and T

Parallel lines are demonstrated as the lines that are at the same distance apart from each other. These lines never intersect or meet each other in a plane.

In English alphabet, the letters E, F, H, I, M, N, W, Z are examples of parallel lines.

Intersecting lines are elucidated as the lines that cross or intersect each other at a common point in a plane. Letter X correctly exemplifies this sharing of a common point.

Perpendicular lines are described as the lines which meet or intersect each other at an angle of 90 degrees. The letters E, F, H, I, L, and T demonstrate this intersection.

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Answer:

(b) 42m

Step-by-step explanation:

Perimeter of a rectangle ⇒ P=2(l+w)

Which means P=2·(12+9)

Which equals 42

An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.

Given:

Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.

The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.

We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.

We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.

Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.

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The exponential equation is given by y = 700(2)ˣ

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population of fish after x hours.

Given that he starts with 700 fishes, hence

a = 700

The population of the fish doubles every year, hence:

b = 2

The exponential equation becomes:

y = 700(2)ˣ

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The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

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\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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The probability of events A and B occurring is given as follows:

P(A and B) = 1/3.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For each event, the probability is given as follows:

As the events are independent, the probability of both events happening is given as follows:

P(A and B) = 2/3 x 1/2

P(A and B) = 1/3.

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Answer:

1708.14 rounded

Step-by-step explanation:

Y= a•b^x

5.5% = 0.055

1+0.055=1.055

Y= 1000•1.055^10

Y= 1708.14

It has been (mathematically) proven that there is no polynomial time algorithm for any np-complete problem. the given statement is false.

In order to solve previously unsolvable issues, Leonid Khachiyan developed a polynomial-time method, in which the number of processing steps increases as a power of the number of variables rather than exponentially.

Determining whether NP-complete problems are tractable or intractable remains one of the most crucial concerns in theoretical computer science since it is unknown if any polynomial-time algorithms will ever be developed for them.

So, it is unknown if any polynomial-time algorithms will ever be developed for them.

By applying different constraints, a linear function is maximized or reduced in linear programming, a mathematical modelling approach. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

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Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."

The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:

1 / 750 = 0.001333

This means that for every 750 Hispanic females, one is expected to have the disease.

To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:

0.001333 * 26,000 = 34.658

So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

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As sink has a clearance height of only 8 inches while the height of trash can is 9 inches, Hassan trash can couldn't fit under his sink.

To determine if Hassan's trash can will fit under his sink, we need to calculate the height of the trash can based on its given base area and volume.

The trash can must be cylindrical thus volume = πr²h

Here, πr² is the base and h is height

πr² given 32² in

And volume = 288³ in

So,

height = volume / base area

height = 288 / 32

height = 9

So the height of the trash can is 9 inches.

However, As sink has a clearance height of only 8 inches while the height of trash can is 9 inches, Hassan trash can couldn't fit under his sink.

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Answer:

about 0.38 %

Step-by-step explanation:

Total = 1,400 Employees

Those who drive a bus = 530

530 / 1,400 = 0.378571428571429

round up = about 0.38 %

Answer:

48

Step-by-step explanation:

multiply the length value by 12

the length is 4ft so you multiply it by 12

so

4×12=48

so the answer is 48

The correct statement is that for each hour, the earnings go up by $7. Option A

If we have the equation of the line, we can substitute the value of 7 for the number of hours into the equation and solve for the earnings. The equation would typically be in the form of "earnings = slope * hours + y-intercept," where the slope represents the rate of earnings per hour and the y-intercept represents the earnings when no hours are worked.

We can find the slope of the graph to know as said above;

m = y2 - y1/x2 - x1

m = 14 - 0/2 - 0

m = 7

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The girls wold have 3 eggs,1 coffee packet and  6 coffee creamers per day.

The girls have 36 eggs, which can be divided into 3 dozen eggs (since 1 dozen = 12 eggs).

For each dozen eggs, they have 4 coffee packets, so they have 4 coffee packets x 3 dozen eggs = 12 coffee packets in total.

For each coffee packet, they have 6 coffee creamers, so they have 6 creamers x 12 coffee packets = 72 coffee creamers in total.

Finally, to find out how many eggs, coffee packets and creamers they can have each morning during the 12-day trip, we divide the total number by 12 days:

3 eggs / 12 days = 3 eggs per day

12 coffee packets / 12 days = 1 coffee packet per day

72 coffee creamers / 12 days = 6 coffee creamers per day.

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Answer:

72 pages

Step-by-step explanation:

If each page can hold 10 postcard 710 postcards would occupy 71 pages, requiring another page for the remainder. My answer is rounded up from the more accurate answer of 71.2 pages

Answer:

500,000 + 7,000 + 20 + 1

Step-by-step explanation:

Answer:

The expanded form of 507,021 is 500,000 + 7,000 + 20 + 1.

Step-by-step explanation:

500,000 + 7,000 + 20 + 1

Explanation:

When writing numbers in expanded form, you are essentially breaking the number apart so that the value of every individual digit is shown.

Here are some examples of a number and its expanded form:

· 874,923 = 800,000 + 70,000 + 4,000 + 900 + 20 + 3

· 3,905 = 3,000 + 9,000 + 5

· 42,069 = 40,000 + 2,000 + 60 + 9

* note:

if the number you are going to write in expanded form includes a zero (ex: the number 42,069), you do not need to include the zero when writing each digits value. However, if you or your instructor prefers to include the value of zero, you may. To solve this problem, I will not be including the value of zero.

we understand what expanded form is, let's write 507,021 in expanded form.

Start by writing a list for the values of each individual digit:

· 500,000

· 7,000

· 20

· 1

Next, write the numbers so that they show they must be added.

500,000 + 7,000 + 20 + 1

Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.

The change of amplitude of a sound wave's amplitude is linked to the change in pressure that occurs due to the wave measured at a given location.

Frequency tells the number of waves that  pass a fixed location in a specific time frame.

Sound engineers uses the basic laws of trigonometry via sine and cosine graphs.

Note that all sounds can be broken down into a lot of sine waves, as sine waves comes together to form sounds.

Therefore, Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.

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Answer:

y = 3x² + 30x + 27

Step-by-step explanation:

Formula: Ax + By = C

y = 3 (x + 9) (x + 1)

y = 3x + 27x + 3x + 7

y = 3x² + 30x + 27

Answer:

4 1/2

Step-by-step explanation:

Lee and his friends ate 9/2 pizzas.

When 9÷2 we get 4 hole 1/2

4 1/2

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !