if rick has monthly expenses that total $2600 and he makes $6900 a month what is his debt to income ratio? Will the bank give him mortgage based on this information?

To find the number of minutes at which the costs of the two plans will be equal, we set up an equation and solve for x. The costs will be equal after 250 minutes of calls.

To find the number of minutes of calls at which the costs of the two plans will be equal, we can set up an equation. Let's denote the number of minutes as x. For the first plan, the total cost is given by:

Total Cost = $13 + $0.17x.

For the second plan, the total cost is given by:

Total Cost = $23 + $0.13x.

Setting these two equations equal to each other, we have:

$13 + $0.17x = $23 + $0.13x.

Simplifying this equation, we get:

$0.17x - $0.13x = $23 - $13.

$0.04x = $10.

Dividing both sides by $0.04, we get:

x = $10/$0.04 = 250 minutes.

Therefore, the costs of the two plans will be equal after 250 minutes of calls.

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Answer: Second Option

[tex]g(x)=-\frac{5}{7}(\frac{3}{5})^{-x}[/tex]

Step-by-step explanation:

The function  [tex]g(x)=(\frac{3}{5})^x[/tex] is an exponential function.

Functions of this type have a range that goes from (0, ∞)

When multiplying the function by a negative coefficient  [tex]-\frac{5}{7}[/tex], now all the values of g(x) will be negative and the range of  [tex]g(x)=-\frac{5}{7}(\frac{3}{5})^x[/tex] will be: (-∞, 0)

Then we must search among the options a function with range (-∞, 0)

Since the exponential functions of the form [tex](a) ^ x[/tex], where [tex]a>0[/tex] always have range (0, ∞)  Then the correct option will be the one with a negative coefficient.

The correct option is the second option

The function [tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex]same range of [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex].

In this question we must determine a second function whose range is equal to the range of the first one. In geometry, a rigid transformation is a transformation experimented by a function such that euclidean distance is conserved. The range is the set of values of [tex]h(x)[/tex] associated to the function.

If we apply a reflection around the y-axis, then the range is conserved but relationship between the range and the domain is changed in rigid manner. The reflection around the y-axis follows the following formula:

[tex]h(x) = f(-x)[/tex]    (1)

If we know that [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex], then the resulting function is:

[tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex]

The function [tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex] has the same range of [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex]. [tex]\blacksquare[/tex]

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Answer:

1. $60

2. $240

Step-by-step explanation:

Use the formula for simple interest. Put your numbers in the formula and do the arithmetic.

i = Prt . . . . where i is the interest amount, P is the principal, r is the rate, t is the time period

1. P = $600, r = 0.05, t = 2, so you have ...

i = $600·0.05·2 = $60

__

2. P = $1500, r = 0.04, t = 4, so you have ...

i = $1500·0.04·4 = $240

Answer:

Option B is correct.

Step-by-step explanation:

Given:

A Solid Figure made up pf cuboid and a triangular based prism.

To find: Total Surface area of the figure.

Total Surface Area = Area of front + Area of top + Area of Back + 2 × Area of side + Area of bottom

Area of Front = Area of Square + Area of rectangle

                      = 10 × 10

                      = 100 in.²

Area of top = Area of Rectangle

                   = 13 × 10

                   = 130 in.²

Area of back =  Area of square in down + Area of rectangle in up

                      = 10 × 10 + 5 × 10

                      = 100 + 50

                      = 150 in.²

Area of the bottom = Area of the rectangle

                                = 12 × 10

                                = 120 in.²

Area of the side = Area of rectangle + Area of the triangle

                           = 12 × 10 + 1/2 × 5 × 12

                           = 120 + 5 × 6

                           = 120 + 30

                           = 150 in.²

Total Surface Area = 100 + 130 +150 + 120 + 2 × 150

                               = 500 + 300

                               = 800 in.²

Therefore, Option B is correct.

Julius bought a total of 2 gallons of beverages, including 2 quarts of orange juice and 16 cups of chocolate milk.

To find out how many gallons of beverages Julius bought, we need to convert each quantity to gallons and then sum them up:

1. **2 pints of milk**:

  - 1 pint = 0.125 gallons

  - 2 pints = [tex]\(2 \times 0.125 = 0.25\)[/tex] gallons

2. **2 quarts of orange juice**:

  - 1 quart = 0.25 gallons

  - 2 quarts = [tex]\(2 \times 0.25 = 0.5\)[/tex] gallons

3. **16 cups of chocolate milk**:

  - 1 cup = 0.0625 gallons

  - 16 cups =[tex]\(16 \times 0.0625 = 1\)[/tex] gallon

4. **32 ounces of lemonade**:

  - 1 ounce = 0.0078125 gallons

  - 32 ounces = [tex]\(32 \times 0.0078125 = 0.25\)[/tex] gallons

Now, let's sum up the quantities:

[tex]\[ 0.25 + 0.5 + 1 + 0.25 = 2 \][/tex]

So, Julius bought a total of 2 gallons of beverages.

Answer:

18 combinations

Step-by-step explanation:

Assuming you can only have one slice of cheese per cracker, then you would have to multiply the number of types of crackers by how many types of cheeses there are to find the total amount of combinations.

3 crackers * 6 cheeses = 18 combinations

Answer:

62 square units

Step-by-step explanation:

The area of a rectangular prism is the sum of the areas of its six faces. Opposite faces have the same area, so it is the sum of 3 pairs of faces. The area of one face of each pair is the product of the dimensions of that face. Those three areas are ...

• L·W

• W·H

• H·L

so the total surface area is ...

A = 2(LW +WH +HL)

For hand calculation, this can be simplified a bit to ...

A = 2(LW +H(L+W)) . . . . . requires one less multiplication

For your prism, the area is ...

A = 2(5·2 + 3(5+2)) = 2(10 +21) = 62 . . . square units

A rectangular prism is a three-dimensional shape with six faces. The opposite faces are equal in length. It has twelve sides and six vertices

The formula for the surface area of a rectangular prism = SA=2lw+2lh+2hw

Where:

l = length

w = width

h  = height

Surface area = (2 x 5 x 2) + (2 x 5 x 3) + (2 x 3 x 2)

= 20 + 30 + 12

= 62 square units

Please find attached an image of a rectangular prism. A similar question was solved here: https://brainly.com/question/21226782?referrer=searchResults

Answers:

1. x[tex]\geq[/tex] [tex]\frac{y+4}{3}[/tex]

2. x [tex]\neq[/tex][tex] \frac {y} {2} [/tex]

3. x<y-5

4. x>2(y+3)

5. x [tex]\leq[/tex] [tex]\frac{y-2}{4}[/tex]

6. x < [tex]\frac{5-y}{5}[/tex]

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Answer:

Step-by-step explanation:

1. x\geq\frac{y+4}{3}

2. x \neq \frac {y} {2}

3. x<y-5

4. x>2(y+3)

5. x \leq\frac{y-2}{4}

6. x < \frac{5-y}{5}

Answer: 36 in²

Step-by-step explanation:

You can calculate the area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are:  Three different rectangles and two equal triangles.

The formula for calculate the  area of a rectangle is:

[tex]A=lw[/tex]

 Where "l" is the lenght and "w" is the width.

The formula for calculate the  area of a triangle is:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

 You can observe that the hypotenuse of the each triangle is the length of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

[tex]a=\sqrt{b^2+c^2}[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

[tex]a=\sqrt{(4in)^2+(3in)^2}=5in[/tex]

Therefore, you can add the areas of the faces to find the area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

[tex]A=(2in)(5in)+(3in)(2in)+(4in)(2in)+2(\frac{3in*4in}{2})=36in^2[/tex]

Answer:

B. -14

Step-by-step explanation:

If you solve the system using the method of elimination, the y terms will automatically cancel each other out without any manipulation at all.  So go with it and solve for x first.  If the y terms cancel out, you're left with x = -3.

If x = -3, sub that value in for x in eitheer one of the original equations and solve for y:

[tex]3x-y=5[/tex] becomes

[tex]3(-3)-y=5[/tex] and

[tex]-9-y=5[/tex] so

[tex]y=-14[/tex]

Answer:

They are 3, 11 and 55.

Step-by-step explanation:

x +y + z = 69

y = x - 8

z = 5x

Substitute z = 5x in the first equation:

x + y + 5x = 69

6x + y = 69.........(1)

From the second equation

-x + y = -8.........(2)

Subtract equations (1) - (2):

7x = 77

x = 11

So z = 5x = 5*11 = 55 and

y =  x - 8 = 11 - 8 = 3..

Answer:

x = 11, y = 3 and z = 55

Step-by-step explanation:

Let the three numbers be x, y and z.  Then x + y + z = 69

Then y = x - 8, and z = 5x.  Substituting these expressions in x into

x + y + z = 69, we get:  x + x - 8 + 5x = 69, or

7x = 77, so that x = 11.

If x = 11, then:

y = x - 8 = 11 - 8 = 3, and:

z = 5x = 5(11) = 55

Then x = 11, y = 3 and z = 55.

Check:  Do these three numbers add up to 69?  11 + 3 + 55 = 69?  YES

Answer:

See attachment

Step-by-step explanation:

The given equation is:

[tex]3x^2+3y^2=75[/tex]

We divide through by 3 to obtain;

[tex]x^2+y^2=25[/tex]

This is rewritten as:

[tex]x^2+y^2=5^2[/tex]

This is the equation of a circle centered at the origin with radius 5 units.

Answer:

49

Step-by-step explanation:

Given

f(x) = - (x - 3)(x + 11)

Find the zeros by setting f(x) = 0, that is

- (x - 3)(x + 11) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 11 = 0 ⇒ x = - 11

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros

[tex]x_{vertex}[/tex] = [tex]\frac{3-11}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4

Substitute x = - 4 into f(x) for y- coordinate of vertex

f(- 4) = -(- 7)(7) = 49 ← y- value of vertex

Answer:

Part 1) The central angle is equal to ∠EOD+∠DOG or the central angle is equal to 360°-∠EOG

Part 2) The central angle is equal to ∠KOL

Part 3) The arc made by the ∠4 is the arc LI

Part 4) The arc made by the ∠2 is the arc FG

Step-by-step explanation:

Part 1) Name the central angle of the given arc

Arc EDG

The central angle is equal to ∠EOD+∠DOG

or

The central angle is equal to 360°-∠EOG

Part 2) Name the central angle of the given arc

Arc KL

The central angle is equal to ∠KOL

Part 3) Name the arc made by the given angle

∠4

The arc made by the ∠4 is the arc LI

Part 4) Name the arc made by the given angle

∠2

The arc made by the ∠2 is the arc FG

Answer:

π

Step-by-step explanation:

The standard form of the sine function is

y = a sin(bx + c)

where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and

phase shift = - [tex]\frac{c}{b}[/tex]

here b = [tex]\frac{1}{2}[/tex], c = - [tex]\frac{\pi }{2}[/tex]

phase shift = - [tex]\frac{-\frac{\pi }{2} }{\frac{1}{2} }[/tex]

= [tex]\frac{\pi }{2}[/tex] × 2 = π

Answer:

A is the best answer.

Step-by-step explanation:

A is. It can be written as y [ or v] = -2(x + 3)^2 + 7 which is the pure form of a vertex equation.

C doesn't work since that is a linear function. Nothing is squared.

D doesn't work. That is just the way an ordinary quadratic is written. (Standard form).

B doesn't work. The quadratic is written in factored form.

ANSWER

[tex]y - 7= - 2 {(x + 3)}^{2} [/tex]

EXPLANATION

The vertex form of a quadratic function is given by:

[tex]y = a {(x - h)}^{2} + k[/tex]

From the given options, the first choice is

[tex]y - 7= - 2 {(x + 3)}^{2} [/tex]

[tex]y=- 2 {(x + 3)}^{2} + 7[/tex]

where a=-2, h=-3, and k=7.

Therefore the vertex is (-3,7)

Hence the first choice is the correct option.

Answer:

[tex]JK=2.25\ units[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

so

[tex]\frac{JK}{ST}=\frac{KL}{TU}[/tex]

substitute the given value and solve for JK

[tex]\frac{JK}{1.5}=\frac{6}{4}[/tex]

[tex]JK=(1.5)\frac{6}{4}[/tex]

[tex]JK=2.25\ units[/tex]

Answer:

6 in^2.

Step-by-step explanation:

The area of 2 similar figures are in the ratio of the squares of corresponding sides. So we have the equation:

3^2 / 6^2 = x / 24

9/36 = x /24

1 / 4 = x / 24

x =  24/4 = 6 in^2 (answer).

Answer:

A) 15 hours

B) 108 hours

C) 2073.45 miles

Step-by-step explanation:

The earth rotates fully 1 time in 24 hours. Fully rotate means that it goes through 360 degrees in 24 hours.

A)

For this, we can set up unit ratio to solve.

"If earth rotates 360 degrees in 24 hours, 225 degrees take how much time (let it be x)?"

[tex]\frac{360}{24}=\frac{225}{x}\\360x=24*225\\360x=5400\\x=\frac{5400}{360}\\x=15[/tex]

So , it takes 15 hours.

B)

Here, the rotation is given in radian, NOT degrees. We know that  2π radians is 360 degrees, thus we can say:

"If earth rotates 2π radians in 24 hours, 9π radians take how much time (let it be y)?"

[tex]\frac{2\pi}{24}=\frac{9\pi}{y}\\2\pi y=9\pi * 24\\2\pi y = 216\pi\\y=\frac{216\pi}{2\pi}\\y=108[/tex]

So, it take 108 hours.

C)

The point on the equator is on the "outside" of the earth. So we need to figure out the circumference of the earth, given diameter is approximately 7920.

Circumference formula is  C = 2πr, where C is the circumference, r is the radius (half of diameter, which is 7920/2 = 3960)

Hence

C = 2πr = 2π(3960) = 7920π

Hence, is 24 hours, a point travels  7920π  miles. 2 hours is 1/12th of 24 hours, so in 2 hours the point will travel 1/12th the distance is travels in 24 hours. So:

[tex]\frac{7920\pi}{12}=2073.45[/tex]

Thus, it will travel 2073.45 miles in 2 hours.

Answer:

A). 15 hours

B). 108 hours

C). 2074.28 miles

Step-by-step explanation:

A). The Earth completely rotates on its axis once every 24 hours.

It means the Earth takes 24 hours to complete 360° or 2π radians

Per hour rotation of the Earth will be = [tex]\frac{\text{Angle rotated in one rotation}}{\text{Time taken for one rotation}}[/tex]

= [tex]\frac{360}{24}=15[/tex] degree per hour

or [tex]\frac{2\pi }{24}=\frac{\pi }{12}[/tex] radians per hour

Now we have to calculate the time taken in 225° rotation.

∵ In 15° rotation was time taken = 1 hour

∴ In 1° rotation time taken by the Earth = [tex]\frac{1}{15}[/tex]

∴ In 225° time spent by the Earth = [tex]\frac{(1)(225)}{15}=15[/tex] hours

B). ∵ [tex]\frac{\pi }{12}[/tex] radians rotation was completed in the time = 1 hour

∴ 1 radian rotation was completed in time = [tex]\frac{1}{\frac{\pi }{12}}=\frac{12}{\pi }[/tex]

∴ 9π radians rotation will be completed in time = [tex]\frac{12(9\pi )}{\pi }= 108[/tex] hours

Therefore, time taken in 9π rotation will be 108 hours.

C). If the diameter of the earth is 7920 miles then we have to calculate angle of rotation of a point on equator in 2 hours.

Since Length of arc = radius × angle of rotation

Since angle of rotation in 1 hour = [tex]\frac{\pi }{12}[/tex] radians

So angle of rotation in 2 hours = [tex]\frac{2\pi }{12}=\frac{\pi }{6}[/tex]

Now we put these values in the formula

Length of arc = [tex]\frac{7920}{2}(\frac{\pi }{6})=660\pi[/tex] miles

                      = 660(3.1428)

                      = 2074.28 miles

Answer:

  6w³ cubic units

Step-by-step explanation:

The volume of a right rectangular prism is the product of its dimensions:

  V = LWH

  = (2w)(w)(3w) = 6w³ . . . . cubic units

Answer:

6*W^3 cubic units

Step-by-step explanation:

Right rectangular prism volume (V) is calculated as

V = L*W*H

where L is length, W is width and H is height

The height is three times the width of the base means

H = 3*W

The length of the base is twice the width means

L = 2*W

Replacing in volume formula

V = 2*W*W*3W

V = 6*W^3

Answer:

8 bags

Step-by-step explanation:

The area of the path is equal to the area of the overall square minus the area of the garden.

Area of a square is the side length squared:

A = s²

The overall square has a side length of 11 feet.  The side length of the garden is 11 - 2 - 2 = 7 feet.  So the area of the path is:

A = 11² - 7²

A = 121 - 49

A = 72

The area of the path is 72 ft².  If one bag of gravel covers 9 ft², then the number of bags needed is:

72 ft² × (1 bag / 9 ft²) = 8 bags

Answer:

The answer is 12. There are 12 pens in each pack.

Step-by-step explanation:

The constant of proportionality between the number of packs and the number of pens that Frank buys is 12 pens per pack, calculated by dividing the total pens by the number of packs in both given scenarios.

The student asks about the constant of proportionality between the number of packs of pens and the number of pens. To find this, we divide the number of pens by the number of packs for each given scenario to ensure the ratio is consistent.

Given Frank buys three packs and ends up with 36 pens, we divide 36 pens by 3 packs to get 12 pens per pack.

When he buys five packs and has 60 pens, we again divide 60 pens by 5 packs and get the same result, 12 pens per pack. Therefore, the constant of proportionality is 12 pens per pack.

1 yard = 3 feet

The foundation is 2/3 yard wide, by 1 yard deep by 10 yards long.

Volume is Length x width x height.

Volume = 2/3 x 1 x 10 = 6.66 cubic yards.

The answer is B.

Answer:

The lengths of the other sides is equal to 10 units

Step-by-step explanation:

we know that

An equilateral triangle is a triangle that have three equal sides and three equal interior angles (each internal angle measure 60 degrees)

so

If the triangle has two interior angle measures of 60° and 60°, then the measure of the third interior angle must be equal to 60 degrees (remember that the sum of the interior angles in a triangle must be equal to 180 degrees)

Therefore

The triangle is an equilateral triangle and the length of the three sides is equal to 10 units

Answer:

10 and 10

Step-by-step explanation:

I took it on edge

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$350\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=350\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=350(1.03)^2\implies A=371.315[/tex]

Reciprocal means to flip it, so in this case swap the numerator and denominator and the answer will be:

[tex] - \frac{5}{3} \: \: or \: \: - 1 \frac{2}{3} [/tex]

I would choose A

Answer:

The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.

Step-by-step explanation:

Answer:

Option C. linear: slope = -5, y-intercept = 50

Step-by-step explanation:

Let

b ----> is the automatic decrease on the gift card balance

m ---->  is the number of months beyond two years

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem the linear equation that represent this situation is

[tex]b=-5m+50[/tex] ---> equation of the line into slope intercept form

so

The slope is -5

The y-intercept is 50

Answer:

This function is linear. True

The slope of this function is 50. False

The y-intercept of this function is 50. True

Answer:   25 km

Step-by-step explanation:

500 km / 5 = 100 km up stream

500 km / 4 =  125 km down stream

125 - 100 = 25 km in still water