Answer:

**$389,200**

**$21,200**

Since,

[tex]\text{PMT}=\frac{PV}{\text{PVA}}[/tex]We are to find PV when the PMT is $35000. Since the PVA is 11.12,

[tex]PV=\text{PVA}\cdot\text{PMT}[/tex][tex]PV=(11.12)(35000)=389200[/tex]Hence, Austin would need to deposit **$389,200**.

For the last part, we first need to solve the PV at 4% in 20 years.

The PVIF would be:

[tex]\text{PVIF}=\frac{1}{(1+0.04)^{20}}=0.46[/tex]Then, solving for the PV:

[tex]PV=800000(0.46)=368000[/tex]Now, to know how much more should Austin deposit, we need to subtract the original PV from the PV that we got from part B.

That would be,

[tex]389200-368000=21200[/tex]Austin would need to deposit **$21,200** more to achieve his withdrawal goal.

Choose the equation that represents a line that passes through points (−3, 2) and (2, 1)

5x + y = −13

5x − y = 17

x − 5y = −13

x + 5y = 7

The **equation** that represents a line that passes through points (−3, 2) and (2, 1) is x + 5y = 7.

The **equation of the line** passes through the points (−3, 2) and (2, 1). The **equation of the line** can be represented as follows;

y = mx + b

where

m = slopeb = y-interceptTherefore, let's find the slope using (−3, 2) and (2, 1)

m = slope = 1 - 2 / 2 + 3

m = - 1 / 5

Therefore,

slope = - 1 / 5

Let's find the y-intercept of the line using (2, 1)

y = - 1 / 5 x + b

1 = - 1 / 5 (2) + b

b = 1 + 2 / 5

b = 5 + 2/ 5

b = 7 / 5

Therefore, the **equation of the line** can be represented as follows:

y = - 1 / 5 x + 7 / 5

5y = -x + 7

5y + x = 7

x + 5y = 7

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Find the equation of a line perpendicular to y +1 = -x that passesthrough the point (-8, 7).

Two lines are perpendicular if the product of their slopes is equal to -1.

Find the slope of the given line. Then, use that result to find the slope of a line perpendicular to it. Use the slope of the line perpendicular to the given line to find the equation of the one that passes through the point (-8,7).

To find the slope of the given line, write it in **slope-intercept** form by isolating **y**:

The coefficient of **x** is **-1**. Then, the slope of the given line is **-1.**

Let **m** be the line perpendicular to y+1=-x.

Since the product of the slopes of perpendicular lines is equal to -1, then:

[tex]\begin{gathered} -1\times m=-1 \\ \Rightarrow m=\frac{-1}{-1} \\ \therefore m=1 \end{gathered}[/tex]The equation of a line with slope **m** that passes through the point **(a,b)** in **slope-point** form is:

Replace m=1, a=-8 and b=7 to find the equation of the line perpendicular to y+1=-x that passes through the point (-8,7):

[tex]\begin{gathered} y=1(x-(-8))+7 \\ \Rightarrow y=(x+8)+7 \\ \therefore y=x+15 \end{gathered}[/tex]**Therefore, the equation of the line perpendicular to y+1=-x that passes through (-8,7) is:**

Given l ∥ m ∥ n, find the value of x.

**Answer:**

[tex]x = \frac{ - 23}{3} [/tex]

**Step-by-step explanation:**

everything u need is in the picture

get me some help with it she of them

We are given the following expression:

[tex](6+4i)(9-11i)[/tex]Using the distributive property:

[tex](6)(9)+(6)(-11i)+(4i)(9)+(4i)(-11i)[/tex]Solving the products:

[tex]54-66i+36i-44i^2[/tex]Now we use the following property:

[tex]i^2=-1[/tex]Substituting:

[tex]54-66i+36i+44[/tex]Adding like terms:

[tex]98-22i[/tex]Since we can't simplify any further this is the answer.

Find f(g(3)).f(x)=2x-5g(x) = 1 + x²f(g(3)) = [?]

[tex]\begin{gathered} f(x)=2x-5 \\ g(x)=1+x^2 \end{gathered}[/tex]

To find the value of the given composition of functions you follow the next steps:

1. Find g(3):

[tex]\begin{gathered} g(3)=1+3^2 \\ g(3)=1+9 \\ g(3)=10 \end{gathered}[/tex]2. Find f(g(3)) or f(10):

[tex]\begin{gathered} f(g(3))=f(10) \\ f(g(3))=2(10)-5 \\ f(g(3))=20-5 \\ f(g(3))=15 \end{gathered}[/tex]Then, f(g(3)) is equal to 15c(n) = -6 (-1/3) *n-1What is the 2nd term in the sequence ?

We are given the following sequence

[tex]c(n)=-6(-\frac{1}{3})^{n-1}[/tex]We are asked to find the 2nd term of the above sequence

Let us substitute **n = 2** into the given sequence

Therefore, the 2nd term of the given sequence is **2**

2. A membership to the theme park is $48 per year. Marcos cancelled his membership early and is only required to pay for 0.25 of a year. How much will he need to pay?

**Marcos** needs to pay $12 for 0.25 of a year due to **cancelling** the **membership**

Membership cost to the **theme** park per year = $48

**Payment** required to be made by Marcos = 0.25 of a year

When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a **decimal** number has the same decimal place value system as the complete number. However, as we proceed to the right following the decimal point, we obtain the fractional portion of the decimal number.

Converting the decimal into a fraction we get:

=0.25

= 25/100

= 1/4 of a year

So, Marcos needs to pay the membership fees for only 1/4 of a year

According to which we get: 48*1/4 = $12

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Jolie is redesigning a water bottle to fit better in her cup holder. The diameter will have to be no larger 2.5 in. The water bottle is straight up and down. What would the height of the bottle be if she wants it to have a 99.34 in3 volume. (Round to nearest whole number)

Answer:

20in

Explanations:The water bottle in question is known to be **cylindrical in shape.** The formula for calculating the** volume of a cylinder** is expressed as:

where;

r is the **radius**

h is the **height**

**Given the following** parameters

diameter = 2.5in

radius = 2.5/2 = 1.25in

volume = 99.34 in^3

**Required**

Height of the water bottle

**Substitute the given parameters** intothe formula

The **height** of the water bottle will be** 20in**

You are dressing a mannequin for a clothingstore display. You have 4 types of shoes, 5necklaces, 10 tops, and 7 bottoms to choosefrom. How many distinct outfits can youcréate? >

Given:

• Types of shoes = 4

,• Number if necklaces = 5

,• Number of tops = 10

,• Number of bottoms = 7

Let's find how many distinct outfits you can create.

To find the number of distinct outfits you can create, we have:

[tex]\begin{gathered} n=4*5*10*7 \\ \\ n=1400 \end{gathered}[/tex]**Therefore, the number of distinct outfits you can create is **** 1400.**

**ANSWER:**

**1400**

Could you please help me with this exercise? Thanks for your help!

**ANSWER**

• Distance:, 7.81

,• Midpoint: ,(-4.5, -6)

**EXPLANATION**

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,

[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2_{}}[/tex]In this problem, the points are (-7, -9) and (-2, -3),

[tex]\begin{gathered} d=\sqrt[]{(-7-(-2))^2+(-9-(-3))^2} \\ d=\sqrt[]{(-7+2)^2+(-9+3)^2}\text{ } \\ d=\sqrt[]{(-5)^2+(-6)^2}=\sqrt[]{25+36} \\ d=\sqrt[]{61}\approx7.81 \end{gathered}[/tex]Hence, the **distance between P1 and P2 is ****7.81**** units**.

To find the midpoint, we have to find the average between the coordinates of the points,

[tex](x_m,y_m)=\mleft(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mright)[/tex]The midpoint in this problem is,

[tex](x,y)=\mleft(\frac{-7-2}{2},\frac{-9-3}{2}\mright)=\mleft(\frac{-9}{2},\frac{-12}{2}\mright)=(-4.5,-6)[/tex]Hence, the **midpoint between P1 and P2 is ****(-4.5, -6)**.

on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers

Solution:

Given the points below

[tex]p\left(4,2\right)and\text{ }q\left(8,12\right)[/tex]To find the distance between two points, the formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where point p represents coordinates 1 and point q represents coordinates 2

Substitute the coordinates into the formula above

[tex]\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}[/tex]Since, 1 unit represents 1 kilometer on the map,

**Hence, the answer is**

Write the inequality shown by the shaded region in the graph with the boundary line y = -3x +5

Inequality is an inequality comparison of numbers or expressions.

Given inequality:

y < -3x+5, y < x+2, y < -1

Graph the above inequality using Geogebra's online graphing calculator.

**Answer:**

...................... Hoffe er u

Scientific notation of 100+6*10^2

**Answer: The answer is 700 **

**Step-by-step explanation:**

is that the answer you're looking for?

**Answer:**

7e2

**Step-by-step explanation:**

10^2=100

100*6=600

600+100=700

there are 2 zeros in 700 so

7e2

(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)

From the given information, we know that the decreasing function values is

[tex]V(t)=3600(3^{-0.15t})[/tex]and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have

[tex]1200=3600(3^{-0.15t})[/tex]By dividing both sides by 3600, we get

[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]So we have the equations

[tex]3^{-0.15t}=\frac{1}{3}[/tex]From the exponents properties, we know that

[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]so we have

[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]or equivalently,

[tex]3^{0.15t}=3[/tex]This means that

[tex]0.15t=1[/tex]Then, by dividing both sides by 0.15, we obtain

[tex]t=\frac{1}{0.15}=6.6666[/tex]So, by rounding to the nearest hundreadth, **the answer is 6.67 years**

All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having a vowel written on it?

Let:

A = Get a paper having a vowel written on it

N = Total number of letters = 11

a = Number of vowels = 4

so:

[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{4}{11} \\ P(A)\approx0.36 \end{gathered}[/tex]**Answer:**

**36%**

In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.

We are given a distribution graph.

The mean of the distribution is the center that is **125.**

The **standard deviation** is given by

**Therefore, the mean of the distribution is 125 and the standard deviation is 28.**

Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4

**Given the trigonometry equation below,**

**Solving each part separately**

**Therefore, **

**Hence, ****Option D**** is the correct answer.**

If 5 books of equal weight, weigh 1.755 kilograms, how many books will weigh 1.404 kilograms?

If 5** books **of equal **weight**, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books

The 5 books are equal weights

The weight of 5 books = 1.755 kilograms

Then the** weight of one book** = The weight of 5 books / 5

Substitute the values in the equation

The weight of one book = 1.755/5

= 0.351 kilograms

To find the number of books we have to use **division** again

**The number of books **will weight 1.404 kilograms = 1.404 / The weight of one book

=1.404/0.351

= 4 books

Hence, If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books

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Find the indicated angle 0. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 120 and c = 136. Round your answer to two decimal places.)

Base on the given data, the triangle is shown below.

Apply law of sine to this triangle implies,

[tex]\sin \theta=\frac{a}{c}[/tex]Given that, *a=*120 and *c=*136. Thefore, the given equation becomes,

Take the inverse to find the the measure of indicated angle.

[tex]\begin{gathered} \theta=\sin ^{-1}0.88 \\ \theta=61.64 \end{gathered}[/tex]Therefore, the angle is 61.64 degree.

the side opposite the right angle measures 8 in. what is the measurement of the side opposite of the 60 degree angle (draw and label the triangle before solving)

[tex]4\sqrt[]{3}[/tex]

**1) ** The best way to tackle this question is by sketching out the triangle:

**2) **Considering that 60º angle we can write out the following trig ratio:

Note that if we had drawn the 60º angle to the lowe right in that triangle we would find the same measure, by using the cosine of (30º) instead.

**And that's the answer**

A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant.

Answer in the form of a polynomial equals a constant:

2w^3-4w^

need help for mathhh

Using **implicit differentiation,** the rates are given as follows:

**2.** dV/dt = 144π cm³/sec.

**3. **dh/dt = 2/5π cm/s.

**4. **dr/dt = -0.2/π cm/day.

The volume of an sphere of **radius r **is given by the following equation:

[tex]V = \frac{4}{3}\pi r^3[/tex]

Applying implicit differentiation, differentiating both variables relative to t, the **rate of change** is given as follows:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

For **item 2,** the parameters are given as follows:

[tex]\frac{dr}{dt} = 2, r = 4[/tex]

Hence the **rate **is given as follows:

dV/dt = 4π x 4² x 2 = 144π cm³/sec.

For** item 4,** the **parameters **are:

[tex]\frac{dV}{dt} = -0.2, r = 5[/tex]

Negative because the orange is shrinking.

Hence the **rate **of the radius can be found as follows:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]-0.2 = 4\pi (5)^2\frac{dr}{dt}[/tex]

dr/dt = -0.2/100π

dr/dt = -0.2/π cm/day.

What is the rate of change of the volume of an cylinder?The volume of a cylinder of **radius r and height h** is given as follows:

[tex]V = \pi r^2h[/tex]

The **rate of change** of the volume as a function of time is given by:

[tex]\frac{dV}{dt} = 2\pi rh\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]

For **item 3**, the parameters are given as follows:

[tex]r = 5, \frac{dV}{dt} = 10, \frac{dr}{dt} = 0[/tex]

The radius is of 5 as r² = 25, due to the area of the base.

Hence the **rate **of change of the **height **is found as follows:

[tex]\frac{dV}{dt} = \pi r^2\frac{dh}{dt}[/tex]

10 = 25π dh/dt

dh/dt = 10/25π

dh/dt = 2/5π cm/s.

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An attic floor is shaped like a triangle with a height of n yd and a base of 6 yd.Which expression represents the area of the floor? 6n3nn + 63n2

In order to calculate the area, we can use the formula for the triangle area:

[tex]A=\frac{b\cdot h}{2}[/tex]Where b is the base length and h is the height relative to this base.

So, for b = 6 and h = n, we have:

[tex]\begin{gathered} A=\frac{6\cdot n}{2} \\ A=3n \end{gathered}[/tex]Therefore **the correct option is the second one.**

Use inverse matrices to find the solution to the system of equations represented by this matrix equation

[tex]\frac{1}{detA}\begin{bmatrix}{d} & {-b} \\ {-c} & {a}\end{bmatrix}[/tex]

if you replace it in that order, it should give you the answer

[tex]\begin{bmatrix}{2} & {-3} \\ {-3} & {5}\end{bmatrix}[/tex]Identify a solution to the system of equation

-4x+ 3y=23

x - y =7

**x = - 44 and y = - 51**

**How are the linear equations solved?**

-4x+ 3y=23 ---(1)

x - y =7 ----(2)

4*(2) => 4x- 4y =28 ---- (3)

(3) + (1)

4x- 4y =28 (+)-4x+ 3y=23

- y = 51

** y = -51**

Substituting y in (2)

x - y =7

x + 51 = 7

**x = -44**

**What are linear equations ?**

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**Answer: x = -2**

** y = 5**

**Step-by-step explanation:**

-4x+3y=23

x-y= -7

First take x-y= -7 and make it x=-7+y place it into the first equation

-4 (-7+y)+3y = 23

28-4y+3y = 23

28-y = 23

+y +y

28=23+y

-23 -23

5=y

Not that you have y you can replace it into the original

-4x+3(5)=23

-4x+15=23

-15=-15

-4x = 8

x= -2

The answer would be (-2,5)

Shiori is working on a stem project and her model is represented by the quadratic function below. She eventually wants to build a 3D model si she needs to understand each part of the function . She is trying to find the coordinate of the vertex of the following function and determine whether the graph opens up or down. F(x)=3x^2-2x-71. What are the coordinates of the vertex of the parabola of the function. There are several wars to determine this answer but state clearly all the steps you look to find the solution.2.Just by looking at the equation (without graphing it) does the graph open up or down(How do you know).3.what does the -7 tell you about the parabola specifically.

1) To get the vertex of the function, the formulae is given as:

[tex]x=-\frac{b}{2a}[/tex]This gives the x coordinate of the vertex. Where a and b are the coefficients of the 1st and 2nd terms respectiely.

[tex]x=\frac{-(-2)}{2(3)}=\frac{1}{3}=0.333333[/tex]To get the y coordinate, we substitute this x value into the original equation.

[tex]f(x)\text{ = 3(}\frac{1}{3})^2-2(\frac{1}{3})-7=\frac{-22}{3}=-7.333333[/tex]**The coordinates of the the vertex (0.33, -7.33)**

**2) The graph opens upwards. Because the coefficient of the 2nd power of x is a negative number.**

**3) The -7 tells us that the graph cuts the vertical axis at -7.**

Identify the pre-image and the image. Then determine if the transformation is a rigid motion or not

The pre-image is the figured formed by the points VWUST and the image is V'W'U'S'T'.

To produce the image from the pre-image a rotation is performed around the point (2, -2). A rotation doesn't change the dimensions of the figure, therefore** it is not a rigid motion**.

If g(x) = 5x, h(x) = √x , find the composition. (g . h)(0)

The **composition **(g . h)(0) has a value of 0

The definitions of the **functions **are given as

g(x) = 5x and h(x) = √x

To find the **composition **(g . h)(o), we make use of

(g . f)(x) = g(x) * h(x)

This can also be expressed as

(g . f)(x) = h(x) * g(x)

Substitute g(x) = 5x and h(x) = √x

So, we have

(g . f)(x) = 5x * √x

Substitute 0 for x

So, we have the following equation

(g . f)(0) = 5 x 0 * √0

Evaluate the product

So, we have the following equation

(g . f)(0) = 0

Hence, the value of the **composition **is 0

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I dont know how to answer this pls help

The hedgehog's **total change in weight** is -2.5 ounces.

A relationship is **proportiona**l if the ratio of the variables is constant. The variables can either increase or decrease at a constant rate. A **proportional relationship** can be modelled with a linear equation.

Ratio = change in weight / days of hibernation

-0.18 / 9 = -0.02

-0.56 / 28 = -0.02

-1.44 / 76 = -0.02

-1.96 / 98 = -0.02

Weight when the day of **hibernation **is 125 = number of days x ratio

125 x -0.02 = -2.5

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The product of the digits of a five-digit number is 6! (factorial). How many such numbers are there

There are 720 of such numbers that consists of five-digits which their product is 6! by **permutation**.

The mathematical term **permutation** can simply be defined as a process of **arrangement** or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.

We can apply the formula for **permutation**;

[tex]p(n,r) = \frac{n!}{(n - r)!} [/tex]

where n = total number of object and r = number of objects selected.

We can calculate the **arrangement** by applying the **permutation** formula as follows

[tex]p(6,5) = \frac{6!}{(6- 5)!}[/tex]

[tex]p(6,5) = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1!}[/tex]

[tex]p(6,5) = \frac{720}{1}[/tex]

[tex]p(6,5) = 720[/tex]

Hence, with good application of the formula for **permutation**, we can say that there are 720 **arrangement** of such numbers which their product is 6!.

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what was simla deputation
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