8 cubed times 8 Superscript negative 5 Baseline times 8 Superscript negative 2 Baseline = StartFraction 1 Over 8 squared EndFraction

If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.

In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.

To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.

In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.

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Answer:

(x+2)^2 + (y+2)^2 = 0.75^2

Step-by-step explanation:

equation of a circle in standard form: (x-h)^2 + (y-k)^2 = r^2

center: (-2, -2)

radius: 0.75

equation of the circle in provided graph: (x+2)^2 + (y+2)^2 = 0.75^2

A sequence is characterised as one that adheres to a predetermined pattern. The following term is created by increasing or decreasing the previous word by a certain amount.

On occasion, an expression is followed by every term in the series. The general formula for an AP is T n = a + (n - 1) d.

Understanding the underlying pattern or rule that creates the sequence is necessary for formulating the general term an of the sequence. Finding a formula for the overall term of a series can be done in a number of ways, including:

1) Finding a pattern: In some cases, a pattern can be found by examining the terms of the sequence and looking for a common ratio or difference. For instance, the formula for the general term can be written as a = a1 + (n - 1)d, where a1 is the first term and d is the common difference, assuming the terms of a sequence are rising by a constant amount.

2) Recurrence relations are used to characterise some sequences. These relations define the nth term in terms of the phrases that came before it. If the recurrence relation, for instance, is a = an-1 + an-2, then the general term's formula can be discovered by resolving the recurrence relation.

3) Making use of generating functions: Sequences can be represented mathematically using generating functions. A formula for the general term of a sequence can be discovered by fiddling with the generating function.

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The standard method for a graph is :

0. f(x) + n - shift the graph n units up

1. f(x) - n - shift the graph n units down

2. f(x - n) - shift the graph n units to the right

3. f(x + n) - shift the graph n units to the left

Since from the given equation we have graph y = x^2-8

to make it y= x^2 -3

add 5 on the both side of equation y = x^2-8

y = x^2-8

y + 5 = x^2 - 8 + 5

y + 5 = x^2 - 3

From the above condition (1),

The graph y + 5 = x^2 - 3 will moves 5 units up

Answer : The graph y = x^2 - 3 will moves 5 units up

Answer:

\(y=\dfrac{\boxed{1}}{\boxed{2}}\:x+\boxed{4}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Therefore, the slope of the given line  y = -2x + 5  is -2.

If two lines are perpendicular to each other, their slopes are negative reciprocals.  

Therefore, the slope of a perpendicular line ¹/₂.

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Substitute the found slope and point (-4, 2) into the point-slope formula:

\(\implies y-2=\dfrac{1}{2}(x-(-4))\)

Rearrange to slope-intercept form:

\(\implies y-2=\dfrac{1}{2}(x+4)\)

\(\implies y-2=\dfrac{1}{2}x+2\)

\(\implies y=\dfrac{1}{2}x+4\)

A perfect square trinomial is a trinomial that factors as two identical binomials.

For example, x² + 8x + 16 factors as (x + 4)(x + 4) or (x + 4)².

Another example would be x² - 12x - 36 which factors as (x - 6)².

Answer:A b and ddI just know

Step-by-step explanation:

Suppose you have 10 black, 10 white, 10 blue, and 10 brown socks. The minimum number of socks to pick that all 3 brothers wear the same color socks is 4 of the same color.

You are required to determine how many socks to pick blindly since there is no light in the room so all three brothers wear the same color socks. In this question, we have 4 types of socks. Therefore, we can apply Pigeonhole Principle here. Pigeonhole Principle states that If n+1 items are put into n boxes, then at least one box must contain two or more items.

Assuming that a brother needs to wear 3 socks of the same color. Therefore, for all 3 brothers to wear the same color socks, we must pick 4 socks of the same color. Therefore, the minimum number of socks that needs to be picked = 4.  

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Answer:

D

Step-by-step explanation:

your maximum "point" of the polynomial is the highest point that the curve makes which in this case is around x=-3.6 and y=17

The point of maxima for the given function is (-3.6, 17).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

As per the graph of the function following conclusion are as below,

It has a maxima in second quadrant.

After the point of maxima, its value starts to decrease.

Then, it reaches it lowest value in fourth quadrant after which it increases again.

By examining the given options, the correct point of maxima can be found as (-3.6, 17).

Hence, the point of relative maxima for the graph can be evaluated as (-3.6, 17).

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Answer:

8 sides

Step-by-step explanation:

(n-2)×180=1080

180n-360=1080

180n=1080+360

180n=1440

n=1440/180

n=8 sides

it's an octagon

Answer:

It has 8 sides

Step-by-step explanation:

This is because the formula is 180(n-2) where n is the amount of sides. An octagon has 8 sides so the sum of the angles is 180(8-2)=180(6)=180×6=1080 degrees

Hope that helps :)

Sam's maximum willingness to pay to buy a cakeIf the reference point is the status quo, Sam's utility function is given by;u(c,m) = c + m + μ(c - rc) + μ(m - rm)The marginal utility of a good is its derivative, thus.

∂u/∂c = 1 + μ′(c - rc)∂u/∂m

= 1 + μ′(m - rm)The maximum amount Sam is willing to pay to buy a cake will occur where the marginal utility of the cake is equal to the price. That is;∂u/∂c = 0⇒ 1 + μ′(c - rc)

= 0⇒ μ′(c - rc)

= -1⇒ c - rc

= -1/μ′Since μ(z) is decreasing and convex, we haveμ′(z) ≤ 0, μ′′(z) ≥ 0Hence, if the reference point is the status quo, Sam will not buy a cake whose price is more than rc.2. Sam's minimum willingness to accept to sell a cakeIf Sam wants to sell his cake, he would do so for a price that would give him at least as much utility as eating the cake himself.

That is;∂u/∂c = 0⇒ 1 + μ′(c - rc)

= 0⇒ μ′(c - rc)

= -1⇒ c - rc

= -1/μ′Therefore, the minimum amount that Sam will be willing to accept to sell his cake is rc - 1/μ′.3. Sam's minimum compensation in moneyIf Sam is offered a cake, then the minimum amount of money he will accept in exchange for the cake would be such that the utility from the money is at least as much as the utility from the cake. That is;u(c,m) = u(c, m')⇒ c + m + μ(c - rc) + μ(m - rm)

= c + m' + μ(c - rc) + μ(m' - rm)⇒ m - m'

= μ-1[μ(m' - rm) - μ(m - rm)]Thus, the minimum amount of money that Sam would demand in compensation for not accepting the cake would be given by m - μ-1[μ(m' - rm) - μ(m - rm)].4. The endowment effectSam exhibits the endowment effect when his willingness to sell his cake is less than his willingness to buy the same cake.

The endowment effect occurs when people demand more to give up a good than they are willing to pay to acquire the same good.Let λ be the marginal utility of money. Sam's willingness to pay for a cake can be expressed as;∂u/∂c = 1 + μ′(c - rc)

= 0⇒ μ′(c - rc)

= -1⇒ c - rc

= -1/μ′The willingness to sell the cake will be given by the minimum amount that Sam will accept for the cake, which is;∂u/∂c = 1 + μ′(c - rc)

= 0⇒ μ′(c - rc)

= -1⇒ c - rc

= -1/μ′Hence, Sam exhibits the endowment effect when;rc - 1/μ′ < rc + 1/λ, μ′ < λ.

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Answer:

(c)

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0

Then the product of the roots = \(\frac{c}{a}\)

(k - 2)x² - 6x + 12 = 0 ← is in standard form

with a = k - 2 and c = 12 , thus

\(\frac{12}{k-2}\) = 3 ( multiply both sides by (k - 1) )

12 = 3(k - 2) = 3k - 6 ( add 6 to both sides )

18 = 3k ( divide both sides by 3 )

6 = k → (c)

The solution to the given initial-value problem is \(\(y(t) = 5 - 5e^{-t}\)\).

To solve the initial-value problem using the Laplace transform, we will apply the Laplace transform to both sides of the given differential equation and then solve for the transformed variable. Let's denote the Laplace transform of the function \(y(t)\) as \(Y(s)\) and the Laplace transform of the function \(f(t)\) as \(F(s)\).

Applying the Laplace transform to the differential equation \(y' + y = f(t)\), we have:

\[sY(s) - y(0) + Y(s) = F(s)\]

Substituting the initial condition \(y(0) = 0\), we simplify the equation to:

\[sY(s) + Y(s) = F(s)\]

Factoring out \(Y(s)\), we obtain:

\[(s + 1)Y(s) = F(s)\]

Now, let's express the function \(f(t)\) in terms of its Laplace transform \(F(s)\) using the given piecewise definition:

\[f(t) = \begin{cases} 0, & \text{if } 0 \leq t < 1 \\ 5, & \text{if } t \geq 1 \end{cases}\]

Taking the Laplace transform of \(f(t)\), we have:

\[F(s) = \int_0^\infty f(t)e^{-st}dt = \int_0^1 0 \cdot e^{-st} dt + \int_1^\infty 5 \cdot e^{-st} dt\]

Simplifying the integral, we get:

\[F(s) = \int_1^\infty 5 \cdot e^{-st} dt = \left[ -\frac{5}{s} \cdot e^{-st} \right]_1^\infty = -\frac{5}{s} \cdot e^{-s} + \frac{5}{s}\]

Substituting \(F(s)\) back into the previous equation, we have:

\[(s + 1)Y(s) = -\frac{5}{s} \cdot e^{-s} + \frac{5}{s}\]

Solving for \(Y(s)\), we get:

\[Y(s) = \frac{-\frac{5}{s} \cdot e^{-s} + \frac{5}{s}}{s + 1} = \frac{5}{s(s + 1)} - \frac{5e^{-s}}{s(s + 1)}\]

Now, we can find the inverse Laplace transform of \(Y(s)\) to obtain the solution \(y(t)\). Using partial fraction decomposition, we can rewrite \(Y(s)\) as:

\[Y(s) = \frac{A}{s} + \frac{B}{s + 1}\]

Solving for \(A\) and \(B\), we find that \(A = 5\) and \(B = -5\).

Taking the inverse Laplace transform, we have:

\[y(t) = \mathcal{L}^{-1}\left\{Y(s)\right\} = 5 - 5e^{-t}\]

Therefore, the solution to the given initial-value problem is \(y(t) = 5 - 5e^{-t}\).

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Answer:

28+12x

Step-by-step explanation:

Multiply 7 with 4

Multiply 3x with 4

Answer:

28+12x

im pretty sure that is right

Answer: The coefficients of binomial expansions are calculated using Pascal's triangle.

Answer:

D = 1.9

You can find for d by using the associative property of division (divide instead of multiply):

5.7 divided -3 = 1.9

Step-by-step explanation:

Hope it helps! =D

Answer: 23.333

Step-by-step explanation:

Look at the photo for explanation and answer

The solution of expression is,

⇒ \(\frac{4}{\sqrt{5} - \sqrt{3} } - \frac{4}{\sqrt{5} + \sqrt{3}}\) = 2 (2√3)

We have to give that,

An expression to solve,

⇒ \(\frac{4}{\sqrt{5} - \sqrt{3} } - \frac{4}{\sqrt{5} + \sqrt{3}}\)

Now, Simplify the expression by adding or subtraction as,

⇒ \(\frac{4}{\sqrt{5} - \sqrt{3} } - \frac{4}{\sqrt{5} + \sqrt{3}}\)

Take 4 as common,

⇒ 4 (\(\frac{1}{\sqrt{5} - \sqrt{3} } - \frac{1}{\sqrt{5} + \sqrt{3}}\))

⇒ 4 (√5 + √3)- (√5 - √3) / (5 - 3)

⇒ 4 (√5 + √3 - √5 + √3) / 2

⇒ 2 (2√3)

Therefore, The solution is,

⇒ \(\frac{4}{\sqrt{5} - \sqrt{3} } - \frac{4}{\sqrt{5} + \sqrt{3}}\) = 2 (2√3)

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Answer:

P= 3w + D; d=p−3

I will solve the second part rn

Answer:

0.43 cup of water

Step-by-step explanation:

We know

For every 1 1/8 cups of water, she uses 2 5/8 of flour.

1 1/8 = 9/8 = 1.125

2 5/8 = 21/8 = 2.625

How much water does Cindy need for each cup of flour?

1.125 divided by 2.625 = 0.43 cup of water

So, Cindy needs 0.43 cup of eater for each cup of flour

Answer:

C= 5.4

Step-by-step explanation:

Rise: 5

Run: 2

a²+b²=c²

c=√a²+b²

c=√rise²+run²

c=√5²+2²

c=√25+4

c=√29

c=5.385164807

c=5.4

*c=hypothesis

The perimeter of the triangle is 96, rounded to the nearest hundredth.

To calculate the perimeter of the triangle, we need to first calculate the length of the hypotenuse.

The hypotenuse of a right triangle is calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two sides.

Therefore, for this triangle, we have:

(Hypotenuse)² = (24)² + (32)²

Therefore, the Hypotenuse = √(24² + 32²)

Hypotenuse = √(576 + 1024)

Hypotenuse = √1600

Hypotenuse = 40

To calculate the perimeter, we need to add up all three sides of the triangle.

the perimeter = 24 + 32 + 40

the perimeter = 96

Therefore, the perimeter of the triangle is 96, rounded to the nearest hundredth.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4570\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4570\left(1+\frac{0.045}{1}\right)^{1\cdot 5}\implies A=4570(1.045)^5\implies A\approx 5695.05\)

Answer:

The correct answer is D.

Step-by-step explanation:

$5695.05

Hence, Kate collected 11/4 bins of bottles.

gather, collect, assemble, congregate mean to come or bring together into a group, mass, or unit. gather is the most general term for bringing or coming together from a spread-out or scattered state. collect often implies careful selection or orderly arrangement.

Albert collected 1/2 of a bin of glass bottles to recycle. Kate collected 5 1/2 times as many bins as Albert. How many bins of bottles did Kate collect?

Albert collected 1/2 bin of glass bottles to recycle.The number of bins Kate collected is represented by b. Kate collected 5 1/2 times as many bins as Albert, so:b = 5 1/2(1/2)Multiplying both sides by 2 gives:b × 2 = 11/2 b

Simplifying the left side gives:2b = 11/2

Multiplying both sides by 1/2 gives:

b = 11/4

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The value of the function f(x) = 3x - 5 when x = 2 is f(2) = 1

A function is a mathematical equation that shows the relationship between two variables.

Given the function f(x) = 3x - 5, we desire to find f(2).

To find f(2), we substitute x = 2 into the equation. So, we have that

f(x) = 3x - 5. So substituting x = 2 into the equation, w ehave

f(2) = 3(2) - 5

f(2) = 6 - 5

f(2) = 1

So, the value of the function f(x) = 3x - 5 when x = 2 is f(2) = 1

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1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Answer:

E = 27.125

Step-by-step explanation:

Hope this helps you.

Answer:

e=56

Step-by-step explanation:

since the denominator is 8, what can you divide by 8 to get something that you can add to 23 and get 30.

30-23=7

56//8=7