Raise the powers of all variables and numbers indicated, and then turn the following expressions in radical form into exponential expressions in rational form. You do not need to evaluate or solve any of the expressions, just put them in simplest exponential form. [All sets of similar base variables and numbers are meant to be under the same radical sign]

The present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now is; $9215.77

An annuity is defined as a fixed amount of cash that is received or paid periodically over a certain period of time. This would mean that the amount in each cash flow of the annuity would be equal and occur for a specific period of time.

The formula for present value is;

PV = P[1 - (1 + r)⁻ⁿ)/r]

where;

PV is present value

P is periodic cash flow

r is interest rate

n is time

We are given the following;

Periodic cash flow (P) = $2525 /Year

Interest rate (r) = 10% /Year = 0.1

Time (n) = 16 Year (from 9 years to 24 years)

Thus;

PV = 2525[1 - (1 + 0.1)⁻¹⁶)/0.1]

PV = $19754.86

This is the present value in 9 years

Thus, the present value in 24 years which is now will be expressed by the formula;

PV = FV/(1 + i)^(t)

where;

PV is present value

FV is future value

i is interest rate

t is time

Thus;

PV = 19754.86/(1 + 0.1)^(8)

PV = $9215.77

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[tex]7x^2+7y^2-28x+42y-35=0 \\ \\ x^2 +y^2-4x+6y-5=0 \\ \\ x^2+y^2-4x+6y=5 \\ \\ x^2-4x+4+y^2+6y+9=18 \\ \\ \boxed{(x-2)^2+(y+3)^2=18}[/tex]

So, the center is [tex](2,-3)[/tex] and the radius is [tex]3\sqrt{2}[/tex].

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

Explanation:

Unfortunately the U from "universal set" and the union symbol look almost identical.

What I'll do to avoid confusion is to let E represent the set of everything we care about, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Feel free to use other notation if it makes better sense to you.

From this set, we'll erase items that are found inside set A = {f, g, p, q}

So we go from this

E = {f, g, h, p, q, r, x, y, z}

to this

A' = {h, r, x, y, z}

Everything found in here is guaranteed to not be inside set A.

------------------------

The next step is to union set A' with set B. This is where we combine those two sets into a larger set of items. Toss out any duplicates. Each unique letter is to be listed once.

A' u B = {h, r, x, y, z}  U  {g, h, q, x, y}

A' u B = {h, r, x, y, z,        g, h, q, x, y}

A' u B = {g, h, q, r, x, y, z}

It's recommended you sort the items in a consistent fashion.

Set this result aside for now, and come back to it later.

------------------------

Go back to the set of everything, aka universal set.

E = {f, g, h, p, q, r, x, y, z}

Cross off stuff found in set C, so we guarantee to form the opposite or complement set C'

C' = set of everything NOT found in C

C' = erase "p,q,x,y,z" from set E

C' = {f, g, h, r}

------------------------

To recap we found

Intersect those sets by looking at what they have in common. This is the overlapped region between the sets.

The three items in common are: {g, h, r}  which forms the final answer.

After 9 months each car will have the same number of miles on it.

What is a linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here,

Let miles per month be x.

then, by a linear equation, we get

4298 + x(426) = 6129 + x(223)

203x = 1831

x = 9 months

Hence, after 9 months each car will have the same number of miles on it.

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Answer: hours

Step-by-step explanation:

minutes would be way too many

seconds - just self explanatory

days- would be less than one

hours is the only possible solution

The figure given can be classified into; rhombus, quadrilateral, square.

The correct answer option is option c

Quadrilateral: This is a polygon with four sides.

Rhombus: This is a parallelogram having all sides of equal length.

Rectangle: A quadrilateral having opposing sides parallel and four right angles.

Square: A polygon with four sides of equal length and four right angle.

Parallelogram: This is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.

In conclusion, the figure can be classified into quadrilateral, rhombus and square.

Complete question:

The complete question is in the attached image.

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Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Birdseed that costs ​$0.67 a pound and sunflower seeds that cost ​$0.97 a pound. Angela​ Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for ​$0.79 per pound.

Assume that she used [x] pound and [y] pound of each type. We can write -

0.67x + 0.97y = 0.79 x 30

0.67x + 0.97y = 23.7

Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

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Answer:

3.45

Step-by-step explanation:

this is how it is supposed to be

Answer:

2 L

Step-by-step explanation:

If the first one is 12% then the 3% one would be 2L because of algebra

5.75 liters of 3 percent hydrogen peroxide solution are included by the company in the container.

A measurement used to determine a number's value out of 100 is the percentage.

Hydrogen peroxide solutions in various containers have concentrations of 35% and 3%.

Since the corporation wants an 8-liter container with a 12% hydrogen peroxide concentration.

Use mixture and allegation property,

35           3

       12

9       :       23

Total quantity = 23x + 9x = 32x

Since, the company wants 8 liters,

therefore, 32x = 8 ⇒ x = 1/4

3.5 percent hydrogen peroxide solution will be equal to = 23x = 23/4 = 5.75. 5.75 liters of 3 percent hydrogen peroxide solution are needed.

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The required pounds of peanut that can make one pound of peanut butter is given as 5 1/3

If  2/3 pounds of peanut = 1/8 pounds of peanut butter

? quantity of peanut = one pound of peanut butter

This would be better expressed in numbers as

2/3 = 1/8

? = 1

To solve for this , we would have to cross multiply

such that we would have

2/3 = 1/8?

to get the unknown, we have to divide through by 1/8

2/3 ÷ 1/8 = unknown

2/3 x 8/1

= 16/3

= 5 1/3

Hence the required pound that would be needed to make the peanut butter is given as 5 1/3

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Answer:

D? I'm not sure tho so don't be mad if it's wrong

Answer:

2x – 4 – 1 + x

Step-by-step explanation:

Answer:

Step-by-step explanation:  -15

The correct representations of the given inequality -3(2x - 5) < 5(2 - x) include the following:

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numbers and variables in an algebraic equation, especially based on any of the following inequality symbols:

For this exercise, we would evaluate and simplify the given inequality so as to enable use determine its solution as follows:

-3(2x - 5) < 5(2 - x)

Opening the bracket, we have:

-6x + 15 < 10 - 5x (correct representation)

Rearranging the algebraic equation by collecting terms, we have:

-6x + 5x < 10 - 15

-x > -5

x > 5 (correct representation)

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The required value lies Between 6 and 7, but closer to 6. Option C is correct.

Given that,
The square root of 50 minus 10 would be plotted on a number line.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

According to the question,
= √[50-10]
= √40
= 6.32
Which is closer to 6.

Thus, the required value lies Between 6 and 7, but closer to 6. Option C is correct.

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[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]

[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]

The coordinates of P is ( -1 , 0.5) .

What is section formula ?

  We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.

Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex]  in the ratio of m:n then,

=>  (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]

Here A[tex](x_1,y_1)[/tex] =( -3,2) and  B[tex](x_2,y_2)[/tex]  = (5,-4)  and m:n = 2:6

Then,

=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]

=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]

=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]

=> (x,y) = (-1,0.5)

Hence the coordinates of P is (-1 , 0.5) .

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Juan must add a volume of 7 cubic feet for the enlarged sandbox.

The volume occupied by the sandbox (V), in cubic feet, is represented by the volume formula for a parallelpiped:

V = w · l · h

Where:

Juan wants to know the additional amount of sand required for the enlarged sandbox. If we know that the initial volume is equal to a cubic foot and each length is double, then we find that the resulting volume for sandbox is:

V' = (2 · w) · (2 · l) · (2 · h)

V' = 8 · (w · l · h)

V' = 8 · V

V = 8 ft³

The addition of sand is found by the following subtraction:

ΔV = V' - V

ΔV = 8 ft³ - 1 ft³

ΔV = 7 ft³

An additional volume of 7 cubic feet is needed for the sandbox.

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Cut off for the failing score is 60.

Percentage of the student failed is 12.5%.

What is standard deviation?

The term "standard deviation" (or "SD") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

What is normail distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given that,

mean = 72

standard deviation = 6

So,

(a) Cutoff score = mean-(2 x standard deviation)  [tex]=72-(2\times 6)[/tex][tex]= 72-12[/tex]  [tex]=60[/tex].

(b) In a normal distribution, 95% of students fall on both sides of mean in 2 standard deviations range. i.e., [tex]\frac{95}{2} = 47.5[/tex] of students between mean and (mean-2 x standard deviation). So, the percentage of students below 2 standard deviations from mean = 60-47.5 = 12.5%.

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The standard deviation of the sampling distribution is 0.01767.

Standard deviation is a measure of the amount of variability or spreads in a set of data.

It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.

We have,

Given that the sample size is sufficiently large (n=400) and the population proportion is known, we can use the formula for the standard deviation of the sampling distribution of the sample proportion, which is:

[tex]\sigma_{\hat{p}} = \sqrt((p (1 - p)) / n)[/tex]

where p is the population proportion and n is the sample size.

In this case,

p = 0.53 (as given in the problem) and n = 400.

Substituting these values into the formula, we get:

[tex]\sigma_{\hat{p}} = \sqrt((0.53 (1 - 0.53)) / 400)\\\sigma_{\hat{p}} = \sqrt((0.53 0.47) / 400)\\\sigma_{\hat{p}} = \sqrt(0.0003121)\\\sigma_{\hat{p}} = 0.01767[/tex]

(rounded to five decimal places)

Therefore,

The standard deviation of the sampling distribution is 0.01767.

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Answer: (0.4k+0.6w)

Step-by-step explanation:

the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.

The total volume of the solution as an algebraic expression is

0.4k + 0.6w.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount of acid added to the solution = 40% of k  

Amount of water added to the solution= 60% of w

Now,

The total volume of the solution.

= 40% of k + 60% of w

= 40/100 x k + 60/100 x w

= 0.40k + 0.60w

Thus,

The volume is 0.4k + 0.6w.

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Answer: Let us assume speed of jet in still air =x

speed of wind =y

Jet flying against the wind

Relative speed of the jet = speed of jet in still air -speed of the wind=x-y

distance covered =3426

time =6 hours

distance = speed * time

3426=(x-y)*6

x-y =3426/6

x-y=571——(1)

Jet flying with the wind

Relative speed of the jet = speed of jet in still air +speed of the wind=x+y

distance covered =4026

time =6 hours

distance = speed * time

4026=(x+y)*6

x+y =4026/6

x+y=671———-(2)

solving 1 and 2 we get

x+y=671

x-y=571

x=621

y=50

speed of jet in the still air =x= 621 miles per hour

Step-by-step explanation:

To maximize the $40,000 allocated to reach the most people, using linear programming, 10 TV ads and 175 radio ads should be used

The number of people reached is 595,000

Linear programming is a method of maximizing a straight-line or linear function that consists of two or more variables such as the cost and the number of people reached.

Let R represent the number of radio ads and let T represent the number of television ads.

The constraints are;

200·R + 500·T ≤ 40,000

R ≥ 10

T ≥ 10

The maximum value function is 7,000·T + 3,000·R

R ≥ T

R - T ≥ 0

R ≥ T

The equations are therefore;

200·R ≤ 40,000 - 500·T

R ≤ (40,000 - 500·T)/200 = 200 - 2.5·T

R ≤ 200 - 2.5·T

When R = T, we have;

T = 200 - 2.5·T

3.5·T = 200

T = 200 ÷ 3.5 ≈ 57.14

The value of the maximizing function, 7,000·T + 3,000·R, at the vertices of the feasible region are therefore;

(T, R)

At (10, 10); 7,000 × 10 + 3,000 × 10 = 100,000

At (10, 175); 7,000 × 10 + 3,000 × 175 = 595000

At (57.14, 57.14); 7,000 × 57.14 + 3,000 × 57.14 = 571400

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The expression that represents the number of tiles on Wendy's kitchen floor is B. 8 × 8t.

An expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, Wendy lays rows of 8 tiles each to cover her kitchen floor.

Let t = the number of rows.

Therefore, the number of tiles on Wendy's kitchen floor will be:

= 8 × 8t.

Therefore, the correct option is B.

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Answer:

the answer to 2dp is 2536.02

Answer:

A 35%

Step-by-step explanation:

take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.

Answer:

a) 35%

Step-by-step explanation:

Given information,

→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.

Now we have to,

→ find the % increase of number of guests from first party to second party.

Let's solve the problem,

→ ((27 - 20)/20) × 100

→ (7/20) × 100

→ 0.35 × 100

→ 35%

Hence, the answer is 35%.

The four terms of the series will be equal to 14,20,26, and 32.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation for the series is given as, t(n) = 6n + 8. The series will be formed as,

t(n) = 6n + 8.

t(1) = 6 x 1 + 8 = 6 + 8 = 14

t(2) = 6 x 2 + 8 = 12 + 8 = 20

t(3) = 6 x 3 + 8 =  18 + 8 = 26

t(4) = 6 x 4 + 8 = 24 + 8 = 32

Therefore, the four terms of the series will be equal to 14,20,26, and 32.

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