You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Answer:

2 + (-10) = 2 - 10 = -8

a. Slope of WZ = -2.25; Slope of WX = 5

b. WZ = √97; WX = √41

c. WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: D. WXYZ is none of these.

Slope = change in y/change in x

Given:

W(-1, 2), X(-5, 7), Y(-1, -2), and Z (3, -7)

a. Slope of WZ and slope of WX:

Slope of WZ = (-7 - 2)/(3 -(-1)) = -2.25

Slope of WX = (7 - 2)/(-1 -(-1)) = 5

b. Use distance formula, \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), to find WZ and WX:

\(WZ = \sqrt{(3 - (-1))^2 + (-7 - 2)^2}\\\\\mathbf{WZ = \sqrt{97} }\)

\(WX = \sqrt{(-5 -(-1))^2 + (7 - 2)^2}\\\\\mathbf{WX = \sqrt{41} }\)

c. The quadrilateral WXYZ have adjacent sides that are not perpendicular to each other and have different slopes and different lengths, so therefore, WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: D. WXYZ is none of these.

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The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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Answer:

Step-by-step explanation:

hOpe this helps you

Fast food menus have increased in size and calories over the past 30-plus years due to market demand and competition.

Two all around upheld perceptions about changes in the size and calories of cheap food menu things over the beyond 30 or more years are:

The part sizes of inexpensive food menu things have expanded altogether over the long haul. During the 1980s, a run of the mill inexpensive food burger was roughly 333 calories, while today, a commonplace cheap food burger contains around 590 calories.

Likewise, the size of soda pops, french fries, and different sides has additionally expanded. This pattern is probable driven by customers' desired insight more incentive for their cash and by the inexpensive food industry's attention on expanding benefits.

The calorie content of cheap food menu things has additionally expanded after some time. The expansion in calorie content is because of the utilization of additional handled fixings and the option of fatty garnishes and sauces.

Furthermore, cheap food organizations frequently offer bigger piece sizes for just a little expansion in cost, empowering clients to eat more calories.

These progressions have added to the increasing paces of heftiness and other eating regimen related medical conditions in numerous nations.

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Step-by-step explanation:

the answer is in the image above

The equation is

To find the original amount of carbon-14 we need to substitute t=0 in our last equation

Then, the original amount of carbon-14 was 100.

To plot the solution, we need to replace the values given in the table

you need to replace this numbers in the table. Then, the graph is

Answer: x= -2/9

Step-by-step explanation:

-12x-2(x+9)=5(x+4)

= -12x-2x+18=5x+20

= -14x+18=5x+20

= -9x+18=20

= -9x=2

/-9    /-9

x= -2/9

Answer:

Step-by-step explanation:

hello

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

We want to write the expression:

in its simplest form

This is:

c. $1,293.40 is the Santos's monthly Social Security benefit, after delaying collecting for 2 years.

If Santos delays collecting his Social Security benefits for 2 years, he will be eligible for delayed retirement credits. The amount of the increase depends on his birth year and the specific rules in place at the time. As of my knowledge cutoff in September 2021, for individuals born in 1943 or later, the delayed retirement credit is 8% per year for each year of delay beyond full retirement age.

Assuming Santos's original benefit at full retirement age was $1,115.00, we can calculate the increase after a 2-year delay:

Increase = Original Benefit * (Delayed Retirement Credits per year * Number of years of delay)

Increase = $1,115.00 * (0.08 * 2)

Increase = $1,115.00 * 0.16

Increase = $178.40

To calculate Santos's monthly Social Security benefit after the 2-year delay, we add the increase to his original benefit:

New Benefit = Original Benefit + Increase

New Benefit = $1,115.00 + $178.40

New Benefit = $1,293.40

Santos's monthly Social Security benefit, after delaying collecting for 2 years, would be approximately $1,293.40. Therefore, Option c is correct.

The question was incomplete. find the full content below:

Calculate Santos's monthly Social Security benefit if he delays collecting for 2 years and his original benefit at full retirement age was $1,115.00.

a. $1,156.90

b. $1,209.35

c. $1,293.40

d. $1,315.50

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Answer:

Whole number

Step-by-step explanation:

0.75 is only 3/4 of 1

Answer:

Depends.

Step-by-step explanation:

Answer:

Since the limit resulting from the ratios test is = 1 / 729  which is < 1  the series converges absolutely

Step-by-step explanation:

Since the limit resulting from the ratios test is = 1 / 729  which is < 1  the series converges absolutely

ATTACHED BELOW IS THE DETAILED SOLUTION of the above answer

Answer:

First recipe needs = 3/8

Second recipe needs = 5/8

Step-by-step explanation:

Given:

Two recipes needs butter = 1 pound

One recipe needs 1/4 pound more

Find:

Each recipe needs butter

Computation:

Assume;

First recipe needs = x

Second recipe needs = x + (1/4)

Two recipes needs butter = First recipe needs + Second recipe needs

x + x + (1/4) = 1

2 x = 1 - (1/4)

2 x = 3/4

x = 3/8 pound

First recipe needs = 3/8

Second recipe needs = x + (1/4) = (3/8) + (1/4) = 5/8

Second recipe needs = 5/8

394 subscribers are represented in the venn diagram.

Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.

Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.

according to the venn diagram

196+41+21+52+84 = 394

There are 394 subscribers

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Answer:

5 > \(\sqrt{18\)

Step-by-step explanation:

The square root of 18 is approximately 4.24.

5 is greater than 4.24, so we can use the inequality sign >.

Answer:

list 4

Step-by-step explanation:

Answer: List 4

Step-by-step explanation:

List 1 shows all possible single marble outcomes from the bag of 4 marbles, but it does not give the sample space for pulling 2 marbles with replacement.List 2, List 3, and List 4 show all possible outcomes for pulling 2 marbles from the bag with replacement. Out of these three lists, List 4 gives the correct sample space for pulling 2 marbles with replacement.List 2 and List 3 each contain only some of the possible outcomes, and therefore do not give the complete sample space for pulling 2 marbles with replacement.

Answer:

44 inches

Step-by-step explanation:

If the width of the room is 19 feet, and the width of the scale drawing of the room is 38 inches, to determine the scale of feet to inches, divide both values by 19:

⇒ 19 ft = 38 inches

⇒ 19/19 ft = 38/19 inches

⇒ 1 ft = 2 inches

Therefore, 1 foot is represented by 2 inches on the scale drawing.

To calculate the length of the scale drawing, multiply the actual length of the room by 2:

⇒ 22 × 2 = 44 inches

Therefore, the length of the scale drawing is 44 inches.

Answer:

domain -5,4,11

range-3,0,3

Step-by-step explanation:

78

1) Since we have a Combination, we can write out the following formula:

Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.

2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.

Answer:

do  95 % times 3% or to 1% keep picking and subtract your answer thats how i would solve the problem but still this is  middle school at most level math i mean use a calculator

give me brainiest

i told you how to solve it so at least your learning a littlie

and not direct  cheating

do

.95 times .3 .229 . 228 .227  go down to i would say porbaly 1 to get your awnser

stop when u want

i would start  

.95 times  .015

Answer:

blue option

Step-by-step explanation:

4 times as many as the other

total of 1550 yards

x and y represent the individual players' yards rushed

y+x=1550

or

x+y=1500

and

y=4x

or

x=4y

the option we have is x+y=1500 and y=4x, which is option blue

Let x and y be the number of yards each team runned. In a way that y>x.

Combined they runned 1550 yards, so:

\(x+y=1550\)

And one of them is 4 times higher than the other, so:

\(x = 4\cdot y\)

So the system will be:

\(\begin{cases}x+y=1550 \\y = 4x \\\end{cases}\)

Answer:

400

+400

Step-by-step explanation:

Given

Deposit 400.00

Required

Represent as an integer

Deposit means being credited. So, we represent deposit as a positive value.

A deposit of Php 400.00 when represented with an integer is 400 or +400

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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Each friend get 296 Jelly beans.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total Jelly Beans = 1482

Now, Pat divided the jelly beans between himself and 4 friends.

So, the number of Jelly beans each friend get

= 1482 /5

= 296.4

Hence, each friend get 296 Jelly beans.

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Answer:

810.66 ft²

Step-by-step explanation:

Short answer:

Shaded region:

Answer: 810.66 ft²

I agree.