The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet

Using the z-distribution, since the p-value of the test is less than 0.01, there is enough evidence to conclude that the claim is correct.

At the null hypothesis, it is tested if there is not enough evidence that the proportion is above 0.5, hence:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is above 0.5, hence:

[tex]H_1: p > 0.5[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]n = 825, \overline{p} = \frac{500}{825} = 0.606, p = 0.5[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.606 - 0.5}{\sqrt{0.5(0.5)}{825}}}[/tex]

z = 6.1.

We have a right-tailed test, as we are testing if the proportion is greater than a value. Using a z-distribution calculator, with z = 6.1, the p-value is of 0.

Since the p-value is less than 0.01, there is enough evidence to conclude that the claim is correct.

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The probability that a person in this income bracket will be audited this year is of 3%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 30 out of 1000 people are audited, hence the probability that a person in this income bracket will be audited this year is given by:

p = 30/1000 = 0.03 = 3%.

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Answer:

The answer is G.

f-5 drop the class while s class is 3(f-5)

therefore, s=3(f-5)

The graphed system of inequalities is:

So the correct option is the third one.

On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).

We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:

Only with that, we conclude that the correct option is the third option:

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The graphs of the equations are:

In fig. 1:

a) y = x (red line)

b) y = -x (blue line)

c) y = x + 5 (green line)

In Fig. 2:

a. y = 3x + 2 (red line)

b. y = 3x - 2 (blue line)

A linear equation can be expressed in slope-intercept form as, y = mx + b, where m is the slope of the line and b is the y-intercept where the line cuts across the vertical axis (y-axis).

Given the equations:

a) y = x, the slope is 1, while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the red line on the graph plotted).

b) y= -x, the slope is -1 (declining slope), while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the blue line on the graph plotted).

c) y = x + 5, the slope is 1 (rising slope), while the y-intercept is 5. This means the line of the graph passes the y-axis at 5. (It is the green line on the graph plotted).

In Figure 2, we have the second graph with the following equations:

a. y = 3x + 2, the slope is 3 (rising slope), while the y-intercept is 2. This means the line of the graph passes the y-axis at 2. (It is the red line on the graph plotted).

b. y = 3x - 2, the slope is 3 (rising slope), while the y-intercept is -2. This means the line of the graph passes the y-axis at -2. (It is the blue line on the graph plotted).

In summary, the graphs of the equations are:

In fig. 1:

a) y = x (red line)

b) y = -x (blue line)

c) y = x + 5 (green line)

In Fig. 2:

a. y = 3x + 2 (red line)

b. y = 3x - 2 (blue line)

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In order to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.

It should be noted that shapes play an important part in geometry.

Here, to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.

Also, it should be noted that a 4D tesseract can be used to project the image.

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It should be noted that a trial balance is a report which lists the balances of the ledger accounts of a company.

It should be noted that the information is incomplete. Therefore, an overview will be given. It should be noted that the accounts that are reflected on a trial balance are related to the accounting items.

The adjusted trial balance simply lists the general ledger account balances after the adjustments have been made. In such a case, these adjustments typically include prepaid and accrued expenses, and non-cash expenses such as depreciation.

Furthermore, a trial balance is a list of the closing balances of ledger account while adjusted balance is a list of general account. An adjusted trial balance is typically prepared by creating a series of journal entries which are designed to account for any transactions that haven't been completed.

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The proportion of the variation in y that can be explained by the variation in the values of x is 0.2025

The complete question requires that we calculate the proportion of the variation in y that can be explained by the variation in the values of x

The given parameters in the question are:

The regression equation is reported as

y = − 10.51x + 15.05

r = − 0.45

Take the square of both sides in the equation r = − 0.45

r^2 = − 0.45^2

Evaluate the squares

r^2 = 0.2025

This represents the proportion of the variation in y that can be explained by the variation in the values of x

Hence, the proportion of the variation in y that can be explained by the variation in the values of x is 0.2025

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Answer:

Step-by-step explanation

Answer:

$13.47 per hour

Step-by-step explanation:

Total earnings = 9.25 (h) + 8 (t/20)

Where h is the number of hours and t is the number of transformers.

Since he worked for 36 hours and assembled 380 transformers:

Total earnings = 9.25 (36) + 8 (380/20)

Total earnings = 333+152 = $485

Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):

485/36 = $13.47 per hour.

Answer:

Step-by-step explanation:

C = 2 π r

A = π r²

~~~~~~~~~~~

(1). C = 8 π

Let the length of the arc ADB is "x"

x = ( 8π ÷ 360° ) × 340°

x = [tex]\frac{68}{9} \pi[/tex]

(2). A = 16 π

The area of shaded region is

( 16 π ÷ 360° ) × 340° = [tex]\frac{136}{9} \pi[/tex]

[tex]\bold{Answer} \downarrow[/tex]

[tex]Length\ of\ Arc\ ADB = \large\boxed{\frac{68\pi}{9} }[/tex]

[tex]Area\ of\ shaded\ region= \large\boxed{\frac{136\pi}{9} }[/tex]

Formulas needed:

[tex]Arc\ length=\boxed{2\pi r(\frac{\theta}{360} )}[/tex]

[tex]Area \ of\ a\ sector=\boxed{(\frac{n}{360})\times\pi \times r^2}[/tex]

[tex]Area\ of\ Circle=\boxed {\pi\times r^2}[/tex]

Step-by-step explanation:

First, let's find the arc length:

[tex]Arc\ length=2\pi r(\frac{\theta}{360})[/tex]

[tex]=2\pi (4)(\frac{340}{360})[/tex]

[tex]=2\pi (4)(\frac{17}{18})[/tex]

[tex]=2\pi(\frac{68}{18})[/tex]

[tex]=\frac{136\pi }{18}[/tex]

[tex]\longrightarrow \large\boxed{\frac{68\pi}{9} }[/tex]

Next, let's find the area of the sliver of the circle we just found the arc length of.

[tex]Area \ of\ a\ sector=(\frac{n}{360})\times\pi \times r^2[/tex]

[tex]=(\frac{20}{360} )\times \pi \times 4^2[/tex]

[tex]=(\frac{1}{18})\times \pi \times 16[/tex]

[tex]=\frac{16\pi}{18}[/tex]

[tex]\longrightarrow \frac{8 \pi}{9}[/tex]

Finally, find the area of the entire circle and subtract the sliver area by that.

[tex]Area\ of\ Circle= {\pi\times r^2[/tex]

[tex]=\pi \times 4^2[/tex]

[tex]\longrightarrow16\pi[/tex]

Subtracting the area by the sliver.

[tex]Area\ of\ entire\ circle \ -\ Area\ of\ sliver\ of\ circle[/tex]

[tex]=16\pi -\frac{8\pi}{9}[/tex]

[tex]=\frac{144\pi}{9} -\frac{8\pi }{9}[/tex]

[tex]\longrightarrow \large\boxed{\frac{136\pi}{9} }[/tex]

Answer:

2.52 m

Step-by-step explanation:

let the height be h m.

let the shorter ladder be x m away from the base of wall.

(x+1.96)²+h²=5.6²

x²+h²=4.2²

subtract

(x+1.96)²-x²=5.6²-4.2²

(x+1.96+x)(x+1.96-x)=31.36-17.64

(2x+1.96)(1.96)=13.72

2x+1.96=13.72/1.96=7

2x=7-1.96=5.04

x=5.04/2=2.52

Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6

Probability is the likelihood or chance that an event will occur. Mathematically, the formula for calculating probability is expressed as:

Probability = expected outcome/Total outcome

Sample space is the total number of element in a given set of probability. The subsets if this sets are called event

Let the six children the couple plan to have ne 1, 2, 3, 4, 5,6 such that the sample space will be:

S = {1, 2, 3, 4, 5, 6}

Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6

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From the constraint, we have

[tex]x+y+z=9 \implies z = 9-x-y[/tex]

so that [tex]s[/tex] depends only on [tex]x,y[/tex].

[tex]s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy[/tex]

Find the critical points of [tex]g[/tex].

[tex]\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9[/tex]

[tex]\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0[/tex]

Using the given constraint again, we have the condition

[tex]x+y+z = 2x+y \implies x=z[/tex]

so that

[tex]x = 9 - x - y \implies y = 9 - 2x[/tex]

and [tex]s[/tex] depends only on [tex]x[/tex].

[tex]s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2[/tex]

Find the critical points of [tex]h[/tex].

[tex]\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3[/tex]

It follows that [tex]y = 9-2\cdot3 = 3[/tex] and [tex]z=3[/tex], so the only critical point of [tex]s[/tex] is at (3, 3, 3).

Differentiate [tex]h[/tex] again and check the sign of the second derivative at the critical point.

[tex]\dfrac{d^2h}{dx^2} = -6 < 0[/tex]

for all [tex]x[/tex], which indicates a maximum.

We find that

[tex]\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)[/tex]

The second derivative at the critical point exists

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex] for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

[tex]$&\frac{\partial g}{\partial x}[/tex] = 9 - 2x - y = 0

[tex]$&\frac{\partial g}{\partial y}[/tex] = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

[tex]$\frac{d h}{d x}=18-6 x=0[/tex]

⇒ x = 3

It pursues that y = 9 - 2 [tex]*[/tex] 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex]

for all x, which suggests a maximum.

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The equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

In step 4 of the proof, we have the following equation

m<w + m<x = m<y + m<z

In step 5, we have

m<x = m<y

When m<x = m<y is substituted to the equation in step 4, we have:

m<w + m<x = m<x + m<z

Hence, the equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

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Answer:

a)

Step-by-step explanation:

Answer:

$29765.50

Step-by-step explanation:

Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.

First, arrange the salary list in an ascending order.

$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702

As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:

Median = [tex]\frac{27512 + 32019}{2}[/tex]

= [tex]\frac{59531}{2}[/tex]

= $29765.50

Answer:

$29,765.50 is the median salary

Step-by-step explanation:

To find the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997

The steps to do this is:

Doing the steps:

This means take the average of $27,512 and $32,019

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Answer: C: 43

Step-by-step explanation:

As we are calling the function with 2 for x, we can substitute 2 for every x we see in the function and solve.

[tex]f(2)=2(2)^3-19(2)^2+28(2)+47\\=2(8)-19(4)+28(2)+47\\=16-76+56+47\\=43[/tex]

Hence, f(2) is 43.

The quartic equation behind the graph is y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8.

Quartic functions are fourth grade polynomials and according to the fundamental theorem of algebra, such kind of expressions have at least two real roots and at most four real roots. The graph of the picture shows a polynomial with two roots of multiplicity 2: x₁ = - 1, x₂ = 2.

y = a · (x + 1)² · (x - 2)²      (1)

Where a is the leading coefficient.

If we know that (x, y) = (0, 4), then the leading coefficient of the polynomial is:

4 = a · (0 + 1) · (0 - 2)

4 = - 2 · a

a = - 2

Then, the quartic equation is equal to:

y = - 2 · (x + 1)² · (x - 2)²

y = - 2 · (x² + 2 · x + 1) · (x² - 4 · x + 4)

y = - 2 · [(x² + 2 · x + 1) · x² + (x² + 2 · x + 1) · (- 4 · x) + (x² + 2 · x + 1) · 4]

y = - 2 · (x⁴ + 2 · x³ + x² - 4 · x³ - 8 · x² - 4 · x + 4 · x² + 8 · x + 4)

y = - 2 · (x⁴ - 2 · x³ - 3 · x² + 4 · x + 4)

y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8

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[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\small\leadsto\bold{Substitute:}[/tex]

[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]

[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]

[tex]\longrightarrow\sf{e^0=1}[/tex]

[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]

[tex]\therefore\sf{5=Ce^{k*5}}[/tex]

[tex]\\[/tex]

[tex] \bold{Solve \: to \: find \: k:}[/tex]

[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]

[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]

[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]

[tex]\longrightarrow\sf{1.76=5k}[/tex]

[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

The equation is given by:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

In which:

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

[tex]20 = 10\log{\frac{p}{p_0}}[/tex]

[tex]\log{\frac{p}{p_0}} = 2[/tex]

The logarithm is inverse of the function [tex]10^x[/tex], hence we apply the function to both sides to find the ratio.

[tex]\frac{p}{p_0} = 10^2[/tex]

[tex]\frac{p}{p_0} = 100[/tex]

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

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The required answers are calculated by using the simple interest formula:

a. She needs to deposit $793.65 in the account each month

b. The total money she put into an account for a year is $285,714.29

c. The total interest she earns is $514,285.71

The formula for the simple interest is

A = P(1 + RT)

Where,

A - amount after T years

P - principal amount

R - the rate of interest

T - time (years)

It is given that,

A = 8,00,000

T = 30 years

R = 6% = 0.06

So,

a. Finding the amount needs to deposit in the account each month:

We have A = P(1 + RT)

⇒ P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

Thus, the amount needs to deposit in the account for each month

= P/T×12

= 285,714.29/30×12

= $793.65

b. Finding the total money that she put into account:

That is nothing but,

P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

c. FInding the total interest:

We have I = A - P

⇒ I = 8,00,000 - 285,714.29

∴ I = $514,285.71

Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71

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Answer:

  A.  (-1, -4)

Step-by-step explanation:

The vertex can be found by converting the equation from standard form to vertex form.

Considering the x-terms, we have ...

  y = (x^2 +2x) -3

where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...

  y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2

  y = (x +1)^2 -4

Compare this to the vertex form equation ...

  y = a(x -h)^2 +k

which has vertex (h, k).

We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).

On the attached graph, the vertex is the turning point, the minimum.

The graph of the function, f(x) = (1/4)ˣ, can be seen in the attached graph, following the given steps.

In the question, we are given the function, f(x) = (1/4)ˣ.

Step 1, has asked us to find the initial value of the graph, f(0).

This can be calculated by substituting x = 0, in the given function, which gives us:

f(0) = (1/4)⁰ = 1.

Step 2, has asked us to plot the initial value of the function at (0, 1). This is plotted using the graphing tools.

Step 3, has asked us to evaluate f(1) and f(-1). By substituting x = 1, and x = -1, we get:

f(-1) = (1/4)⁻¹ = 4,

f(1) = (1/4)¹ = 1/4.

Step 4, has asked us to plot the points (1, 1/4), and (-1, 4). This is plotted using the graphing tools.

Step 5, has made us identify the asymptote y = 0.

Step 6, gives us the final curve for the function, f(x) = (1/4)ˣ.

The provided question is incomplete. The complete question is:

"Graph: f(x) = (1/4)ˣ

Step 1: Calculate the initial value of the function. f(0) =

Step 2: Plot the initial value of the function at (0, 1).

Step 3: Evaluate the function at two more points. f(1) = 1/4, f(-1) = 4

Step 4: Plot the points (1, 1/4) and (-1, 4)

Step 5: Identify the horizontal asymptote of the function. The asymptote is the line y = 0

Step 6: The smooth curve that includes these points and approaches to the asymptote shows the graph of the function"

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Answer: 4.6 (rounded to the nearest tenth)

Step-by-step explanation:

I assume that 1.6 is the coefficient of x, which is what we're trying to find out in this case.

Therefore, dividing 1.6 on both sides we get

from

1.6x = 7.37

to

x = 7.37/1.6 = 4.6 (approximately, rounded to the nearest tenth).

Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.

The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².

We are given the following regarding a right triangle:

a = 10 (one of the smallest side)

c = 15 (the longest side/hypotenuse)

Plug in the values into a² + b² = c²:

10² + b² = 15²

100 + b² = 225

Subtract 100 from both sides

100 + b² - 100 = 225 - 100

b² = 125

Square both sides

√b² = √125

b ≈ 11.2

The length of b, to the nearest tenth, is: 11.2.

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Answer:

Step-by-step explanation:

85!/82! = 85*84*83 = 592620

n choose 0 is always equals 1

n P n also always equals 1

Answer:

See below

Step-by-step explanation:

Question is unclear

could be (11-2)^3  = 9^3 = 729

could be  11 - 2^3 = 11 - 8 = 3       Pick the one you want !

Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

The number of moles of hydrogen is 185 moles.

We know that the mole refers to the number of elementary entities that make up a substance. According to Avogadro, one mole of a substance contains 6.02 * 10^23 elementary entities which includes atoms, molecules and ions.

Now, we know the number of moles is obtained as the ratio of the mass to the molar mass of the substance.

Thus;

Mass of hydrogen = 370.g

Molar mass of hydrogen = 2 g/mol

Number of moles of hydrogen = 370.g/2 g/mol = 185 moles

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Answer:

f(x) = -3x + 3

Step-by-step explanation: