How many packages does Ellis need to buy to build the extension?

Answer: (y,x)

Step-by-step explanation:

smth like that and it is the y-axis and x-axis

Answer:

Step-by-step explanation:

1)r = 18.2

2) Square root of 56 = 7.48

3)Square of -4.7 = 22.09

4) Square of 7.6 = 57.76

5)    -tz = l/r

6)    r = -2/5

Factoring

To include something when you are doing a calculation, or when you are trying to understand something: People are earning more, but when inflation is factored in, they are no better off.

1) r=6r-91 (Factoring)

   r-6r = - 91

   -5r = -91

      r = 91/5

      r = 18.2

Square Root

Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.

2) -2r" -146 = -34 (Square Roots}

- 2r’’ = -34 + 146

- 2r’’ = 112

-r’’ = 112/2

-r’’= 56

r’’ = - 56

Square root of 56 = 7.48

3) r-14r-53 = 9 (Completing the Square)

          - 13r = 9+53

          - 13r = 62

                  - r = 62/13

            r = - 4.7

   Square of -4.7 = 22.09

4) 3r*+6r-62 =7 (Completing the Square)

9r = 7+62

r = 69/9

r = 7.6

Square of 7.6 = 57.76

5)  -rtZr=l (Quadratic Formula)

    - r(tz) = l

    - tz = l/r

6) 5r =-2 (Quadratic Formula)

      r = -2/5

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The total amount of the monthly payments and the finance charge is 144.

Instalment is one of the regular payments that anyone can  make for anything until you have fully paid that full amount.

Using the appropriate interest relation, the solution to the problems posed are :

Down payment = 0.05k

144 monthly payments

Total monthly payment made = 144g

Down payment :

5% of total cost

Total cost = k

5% × k = 0.05k

B.)

Number of monthly payments :

Number of months per year = 12

Number of years = 12

Number of monthly payments = 12 × 12 = 144

C.)

Total charge :

Monthly payment = $g

Number of monthly payments × amount paid

g × 144 = 144g

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After solving for x, the value of x in the given equation is 1/5 or 0.2

A simple equation represents a relationship between two terms on either side of an equal sign.

Simple equations also follow one or a mixture of the four mathematical operations of addition, subtraction, multiplication and division.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

So, we have the equation:

(5x+7)=8

Now, solve the equation for x as follows:
(5x+7)=8

5x+7=8

5x = 8 - 7

5x = 1

x = 1/5 or x = 0.2

Therefore, after solving for x, the value of x in the given equation is 1/5 or 0.2

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Correct question:
Solve in(5x+7)=8 rounds to the nearest thousandth

Answer:

n = 4

Step-by-step explanation:

Given equation:

[tex]\sqrt[3]{y^2} =\sqrt[6]{x}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies y^{\frac{2}{3}}=x^{\frac{1}{6}[/tex]

Take both sides of the equation to the power of ³/₂:

[tex]\implies \left(y^{\frac{2}{3}}\right)^\frac{3}{2} =\left(x^{\frac{1}{6}\right)^\frac{3}{2}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies y^{\frac{2}{3} \cdot \frac{3}{2}}=x^{\frac{1}{6} \cdot \frac{3}{2}}[/tex]

Simplify:

[tex]\implies y^{\frac{6}{6}}=x^{\frac{3}{12}[/tex]

[tex]\implies y^1=x^{\frac{1}{4}[/tex]

Apply exponent rule  a¹ = a :

[tex]\implies y=x^{\frac{1}{4}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies y=\sqrt[4]{x}[/tex]

The probability that the product of the numbers on the top faces of all four dice is a prime number is  [tex]\frac{1}{108}[/tex] .

We have given that,

six-sided dice are rolled 4 times

i.e. probability of this event is [tex]6^{4}[/tex] = 1296.

The condition is product of the numbers on the top faces of all four dice is a prime number.

The only way to get a prime number by multiplication is to have three of the numbers equal to one and the fourth number equal a prime.

The prime less than 6 are 2,3,5.

Each prime number will come on the all four dices top faces.

Therefore outcomes are,

{1,1,1,2}, {1,1,2,1, {1,2,1,1}, {2,1,1,1}, {1,1,1,3}, {1,1,3,1}, {1,3,1,1}, {3,1,1,1}, {1,1,1,5}, {1,1,5,1}, {1,5,1,1}, {5,1,1,1}.

there are 12 outcomes for the given probability.

Therefore required probability [tex]\frac{12}{1296}[/tex] i.e [tex]\frac{1}{8}[/tex].

Hence the probability that the product of the numbers on the top faces of all four dice is a prime number is [tex]\frac{1}{8}[/tex].

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The coordinates of C are (5, 4).

What is a coordinate point?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Given, A(-4,-2) and B(8,6)

Point C is 3/4 of the way from point A to B. Then,

C = A +3/4(B -A)

or, C = (3B +A)/4

or, C = (3(8, 6) +(-4, -2))/4

or, C = (24 -4, 18 -2)/4

or, C = (5, 4)

Hence, the coordinates of C are (5, 4).

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On solving we got that. he shorter pieces will therefore be 3 feet long and the longer pieces will therefore be 8 feet long.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The lengths of the shorter and longer pieces of a board should be determined.

the case

Let's say that the shorter parts are x in length.

as stated

Jared has an 11-foot wooden board with him.

In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.

The length of the longer pieces is then equal to 4x - 4.

The equation then becomes

[tex]x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft[/tex]

The shorter pieces will therefore be 3 feet long.

The longer pieces' length -

[tex]4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft[/tex]

The longer pieces will therefore be 8 feet long.

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Answer:

It will take Iliana 16 hours to get 200 total XP.

Step-by-step explanation:

To project a value on a graph, we need to first find the equation of the graph.

The graph makes the shape of a line. Therefore, the equation of a graph is a linear equation.

⭐What is a linear equation?

To make the equation for this graph, we need to find the value of the slope and the y-intercept and substitute it into the equation.

The equation for this graph will be called P(t).

⭐How do we find the slope?

Pick 2 coordinates you are given. I am going to use (2,25) and (4,50).

Substitute these coordinates into the slope formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\[/tex]

[tex]m = \frac{50-25}{4-2}[/tex]

[tex]m = \frac{25}{2}[/tex]

⭐How do we find the y-intercept?

Since we aren't given the corresponding y-value for when x=0, we have to do the second option stated.

m = 25/2 is the same thing as m = -25/-2, because:

negative/negative = positive

positive/positive = positive

Thus, we can move down from point (2,25) 25 units and left 2 units to get to point (0,0).

[tex]y-intercept = 0[/tex]

Now, substitute the values of the y-intercept and the slope into the equation for the graph.

[tex]P(t) = mt + b[/tex]

[tex]P(t) = \frac{25}{2}t[/tex]

Next, to project a value on the graph, we need to substitute the y-value into the equation to find its corresponding x-value.

The y-value we want to find is 200 XP.

[tex]200 = \frac{25}{2}t[/tex]

Multiply LHS and RHS by [tex]\frac{2}{25}[/tex] to isolate t.

[tex]\frac{2}{25}(200) = \frac{2}{25}(\frac{25}{2}t)[/tex]

[tex]\frac{400}{25} = t[/tex]

[tex]16 = t[/tex]

∴ It will take Iliana 16 hours to get 200 total XP!

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

it would take her 16 hours to get 200 XP

you could see how much XP she gets in a hour and it would help you understand it better

HOURS ( 1 2)

TOTAL XP( 12.5 ÷2)

so according to the small little graph 1 hour is 12.5 XP so you could type how much she gets for any number of hours

EQUATIONS

p=12.5t you could make (t) time by itself

t = p/12.5

HOW LONG TO GET 200 XP

you need t get the value of t cause p = to 200

t= p/12.5

since p is = to 200 p is 200 and you can replace it

t= 200/12.5

so all you have to do it the math!

t = 16

ANSWER

it takes her 16 hours to get 200 XP

The volume of both prisms is B. 105.34 cubic units

The volume of a prism is given by V = lwh where

Given the diagram If

The volume of the top prism is V = lwh where

Given that

So, V = abd

Also, the volume of the bottom prism is V' = lwh where

Given that

So, V' = a²c

So, the volume of the two prisms is V" = V + V'

= abd + a²c

= a(bd + ac)

Substituting the values of the variables into the equation, we have

V" = a(bd + ac)

= 2.3(4 × 8 + 2.3 × 6)

= 2.3(32 + 13.8)

= 2.3(45.8)

= 105.34 cubic units

So, the volume is B. 105.34 cubic units

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The amount of the pizza did Cassie eat on Saturday will be 5/9 of pizza.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

On Friday night, Cassie ate a pizza for dinner and had 5/6 of the pizza left over.

And, On Saturday, she ate 1/3 of what was left.

Now,

Since, On Saturday, she ate 1/3 of what was left.

Hence, The amount of the pizza did Cassie eat on Saturday is;

⇒ 5/6 - 1/3 of 5/6

⇒ 5/6 - 1/3 × 5/6

⇒ 5/6 - 5/18

⇒ 15/18 - 5/18

⇒ 10/18

⇒ 5/9

Thus, The amount of the pizza did Cassie eat on Saturday will be 5/9 of pizza.

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If the surface area of the rectangular box is 4 m² then the dimensions that maximize its volume is  (2/√3 , 2/√3 , 1/√3)  .

In the question ,

let length of rectangular box be = l

let width of rectangular box be = b and

let height of rectangular box be = h .

Since the box has no top ,

So , the surface area is = lb + 2bh + 2hl = 4

we get h = (4-lb)/(2l + 2b) .

The volume of the box is given as  V = l×b×h .

Substituting the value of h from above in the volume formula , we get ,

V = lb(4-lb)/(2l + 2b)

differentiating it with respect to l ,

we get ,

dV/dl = [((2l+2b)(4b-2lb²)-lb(4-lb).2)/(2l+2b)²] = 0

Simplifying further ,

we get ,

2l² + 4lb - 8 = 0       ....equation(1)

Differentiating volume with respect to "b" .

dV/db = [((2l+2b)(4l-2l²b)-lb(4-lb).2)/(2l+2b)²] = 0

simplifying further ,

we get ,

2b² + 4lb - 8 = 0        ...equation(2) .

Simplifying equation(1) and (2) , we get

l = b  ,

Substituting l = b in equation(1) ,

we get ,

2l² + 4l² = 8

l = 2/√

and b = 2/√3 .

Substituting the values in h ,

we get ,

h = (4-lb)/(2l + 2b)

h = 1/√3 .

Therefore , the dimensions of the box is (2/√3 , 2/√3 , 1/√3) .

The given question is incomplete , the complete question is

A rectangular box with no top is to have a surface area of 4 m². find the dimensions (in m) that maximize its volume.

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a)The probability that the next household on the list will be contacted but will refuse to cooperate will be 0.38

b)The probability of failing to contact a household or of contacting the household but  will refuse to cooperate is  0.62.

We are given the information that interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003.  To calculate these probabilities, we use the cooperation rate from 2003. Since the cooperation rate is 38%, this means that 38% of the people will cooperate and 62% will not cooperate. Therefore, the probability of the next household on the list not cooperating is 0.62 and the probability of the next household on the list cooperating is 0.38.

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As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. Each household, of course, is independent of the others. Using the cooperation rate from 2003, a) what is the probability that the next household on the list will be contacted but will refuse to cooperate? b) what is the probability of failing to contact a house hold or of contacting the household but will refuse to cooperate

As x approaches 0, the denominator of the expression [(1/(x)−(1/x^(2)+x))] approaches infinity and the numerator approaches 0. Therefore, the expression approaches 0 as x approaches 0.

1. Evaluate the denominator of the expression [(1/(x)−(1/x^(2)+x))] as x approaches 0.

2. The denominator of the expression [(1/(x)−(1/x^(2)+x))] approaches infinity as x approaches 0.

3. Evaluate the numerator of the expression [(1/(x)−(1/x^(2)+x))] as x approaches 0.

4. The numerator of the expression [(1/(x)−(1/x^(2)+x))] approaches 0 as x approaches 0.

5. Therefore, the expression [(1/(x)−(1/x^(2)+x))] approaches 0 as x approaches 0.

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The probability that you exit the row from the front rather than the back is 1/2.

The probability is calculated by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are the possibility of something happening divided by the likelihood that it won't happen.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

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We can factor this polynomial with 4 terms without grouping.

Factor is a thing that influence decision or the situation.

How to factor polynomials with 4 term without groupingLet P(x) be a polynomial with four terms.

To factor P(x) without grouping, substitute

x = -1, 1, -2, 2, -3, 3.......

P(-1) = 0 ----> (x + 1) is a factor of P(x)

P(1) = 0 ----> (x - 1) is a factor of P(x)

P(-2) = 0 ----> (x + 2) is a factor of P(x)

P(2) = 0 ----> (x - 2) is a factor of P(x)

If P(-1) ≠ 0, then (x + 1) is not a factor of P(x).

Then, try x = 1, x = -2, x = 2 and so on.

Once one of the linear factors of P(x) is found, the other factors can bound easily (the rest of the process has been explained in the following examples).

Factor the following polynomials without grouping :

d as (x2 + ax + b).

Then,

(x + 1)((x2 + ax + b) = x3 - 2x2 - x + 2

Comparing the coefficients of x and constants,

b + a = -1 ----(1)

b = 2

Substitute b = 2 in (1).

2 + a = -1

a = -3

x2 + ax + b = x2 - 3x + 2

Factors of (x2 - 3x + 2) are (x - 1) and (x - 2).

Therefore,

x3 - 2x2 - x + 2 = (x + 1)(x - 1)(x - 2)

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The running area does the dog have is 943 square foot.

What is area of section of a circle?

A segment is essentially the area of a circle between the chord and the arc. A circle is a path that a point equidistant from a single point on the plane can follow; this point is known as the circle's center, and the distance between it and that point is known as the circle's radius. A segment is a section of a circle's interior. A sector is the region that a segment encloses and the angle that a segment occupies. By deducting the triangle produced inside the sector from the sector that contains the segment, one can calculate the area of a circular segment.

The area of a section that made by a circle is ∏ r² × (θ/360).

Given that the radius of the circle is 20 ft.

The angle between two consecutive side of a rectangle is 90⁰.

The angle that made the running area by dog = (360⁰ - 90⁰) = 270⁰.

The area is ∏× 20² × (270⁰/360⁰) = 942.85 square foot

The nearest square foot value of 942.85 square foot is 943 square foot.

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Definition of octagon-

In geometry, an octagon is a polygon with 8 sides and 8 corners. So an octagon has 8

vertices and 8 sides. Simply put, an octagon is an eight-sided polygon, also called an octagon.

we know that,

An Apothem is a line segment from the center to the midpoint of one of the sides. You can start by dividing the octagon into 8 smaller triangles. The area of each triangle is

Side into apothem

3 x 3.5 feet = 10.5

then

10.5×8=84

84 is the total area of an octagon.

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A proportion of 0.455 and 0.505 contain the true portion of the total population of 10,000 with 95%confidence.

A sampling technique called random sampling, also known as probability sampling, enables the randomization of sample selection, meaning that each sample has the same chance of being chosen to reflect the entire population.

Every subject in your target demographic must have an equal probability of being chosen for your sample in order for it to be considered truly random. This assumption might be broken, for instance, by performing a survey to determine how much time college students spend working out each week at your campus.

If 95% of all the samples, then we expect between 45.5% and 50.5% of the total samples contain the true proportion of the population.

If we repeatedly make new samples, taking samples of size 10,000, approximately with 95% confidence of those samples would have between 45.5% and 50.5% containing true portion of population.

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Answer:

A = 5

B = 9

C = 3

D = 4

Step-by-step explanation:

A = 3+ 2 = 5

B = 5 + 4 = 9

C = 1 + 3 = 3

D = 3 + 1 = 4

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Answer:

A

Step-by-step explanation:

Plug in -15/4 in your calculator and you will see that it is equal to [tex]\frac{1}{\sqrt{8} }[/tex]

0.35355339059

Answer:

height = 5 m

Step-by-step explanation:

the volume (V) of a cuboid ( shape of room ) is calculated as

V = A h ( A is the area of the base and h the height )

here V = 235 and A = 47 , then

47h = 235 ( divide both sides by 47 )

h = 5 m

Answer:

volume= height * length * breadth = 235

area= length * breadth = 47

Step-by-step explanation:

47*height= 235

height=5sq

a) The marginal cost MC at  x=9 units is $154.70.

b) The cost of producing 1 additional unit is $154.70.

c) The cost of producing 2 additional units is $309.40.

The Marginal Cost quantifies the incremental cost incurred from the production of each additional unit of a good or service. The marginal cost of production captures the additional cost of producing one more unit of a good/service.

The analysis of the marginal cost helps determine the “optimal” production quantity, where the cost of producing an additional unit is at its lowest point. The marginal cost of production must be lower than the price per unit for a company to be profitable – thus, the marginal cost pinpoints the output volume and pricing where incremental costs are reduced.

a) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

C(x) = 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18

MC = dC/dx

MC = d( 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18) / dx

      = 1/90 (3x²) + 8 (2x) + 8

      = 1/30x² + 16x + 8

At x = 9 units, we get

MC(x=9) = 1/30 (9²) + 16 (9) + 8

              = 154.7

Rounding off to two decimal places, we get 154.70.

Thus, the marginal cost MC at  x=9 units is $154.70.

b) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

154.70 = Change in costs/ 1

Change in costs = 154.70

So, the cost of producing 1 additional unit is $154.70.

c) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

154.70 = Change in costs/ 2

Change is costs = 309.40

So, the cost of producing 2 additional units is $309.40.

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lllhl and hllll are considered different series, despite the lakers winning in 4 games in both series.The total number of possible different series is 70.

A collection of similar items or occasions occurring in close proximity to one another over time or space. a series of concerts. The corridor led to a string of compact rooms. a group of often broadcast television shows, each of which stands alone as a complete program. the shown sum of a typically endless series of...

Sequence and series types

arithmetic progressions

Sequences in geometry.

Harmonic patterns.

a fibonacci sequence.

We have to clculate nuber of series in which lakers win:

if lakers win the champion ship they must win the last game played

if there are n games played, the lakers must win the nth game and 3 games before the nth game.

since the outcome of the nth game is fixed

lakers can win 3 games out of the first n-1 in (n-1C3) ways .

if n games are played lakers can win the championship in  (n-1C3) ways  

n can vary from 4 to 7

no of series in which lakers can win =(3C3)+(4C3)+(5C3)+(6C3)=35

The total number of possible different series =2x25= 70.

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The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

[tex]((\bar p_{1} -\bar p_{2})[/tex]±[tex]Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })[/tex]

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±[tex]1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })[/tex]

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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In the above condition of positive correlation, the higher a person scores on involvement, the higher they tend to score on life satisfaction. Therefore, the option B holds true.

Positive correlation can be referred to or considered as the correlation, wherein the relationship between two or more elements, that are taken into consideration, is direct. The direct relationship means that the movement of a change in one element leads to an equal movement in the other. Positive correlation also states about the measure of life satisfaction in the above condition.

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Complete question

A researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. How should we interpret the relationship between these variables?

A) There is no relationship between involvement and life satisfaction.

B) The higher a person scores on involvement, the higher they tend to score on life satisfaction.

C) The higher a person scores on involvement, the lower they tend to score on life satisfaction.

D) Involvement and life satisfaction are probably the same variable

Answer: B, D, E (2^-1; subtract exponents)

Step-by-step explanation:

B > 1/2 = 2^-1

D > 2^-1 = 2^-1

E > Add exponents 2 + -5 = -1