Find the surface area of the figure. For calculations involving pi , give both the exact value and an approximation to the nearest hundredth of a unit. Let r=10 and h = 3.

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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Answer:

35

Step-by-step explanation:

first, you look at 7x, from the previous equation, you know that x=3, so you take 7x3=21 then you evaluate -3y. as you did with x on the last one you will look at the equation for y and see that it's -4. A negative times a negative is a positive, so -4x(-3)= 12. Then you add them all together, since 12 is a positive, the equation would now look like 21+12+2. After adding all three numbers together, you get 12.

Answer:

f(x) = -3x + 3

Step-by-step explanation:

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.

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 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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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 !

Given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.

Given the data in the question;

Since the scenario depicts a right angle triangle, we use trigonometric ratio.

tanθ = Opposite / Adjacent

We height of the building from the eye level x

Substitute given into the equation,

tan( 35 ) = x / 80ft

x = tan( 35 ) × 80ft

x = 0.7002075 × 80ft

x = 56ft

Now, to get the height of the building, we add the height of the person and the height of the building from the eye level of the person.

Height of building = x + 4ft

Height of building = 56ft + 4ft

Height of building = 60ft

Therefore, given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.

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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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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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According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)

Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.

According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)

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[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textbf{Equation: }[/tex]

[tex]\large\textsf{(3x)(4x)}[/tex]

[tex]\large\textbf{Solving:}[/tex]

[tex]\large\textsf{(3x)(4x)}[/tex]

[tex]\large\textsf{= 3x} * \large\textsf{4x}[/tex]

[tex]\large\textbf{Combine the like terms:}[/tex]

[tex]\large\textsf{(3x * 4x)}[/tex]

[tex]\large\textsf{= 3x * 4x}[/tex]

[tex]\large\textsf{= 12x}^2[/tex]

[tex]\large\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{Option\ D. 12\mathsf{x}^2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[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]

Answer:

150.8 in³

Step-by-step explanation:

The volume of the 5 inch ball is

[tex]\frac{4}{3}\pi (5/2)^{3}[/tex]

The volume of the 13 inch ball is

[tex]\frac{4}{3}\pi (13/2)^{3}[/tex]

Subtracting these volumes, we get about 150.8 in³.

The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³

To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³,

where r is the radius of the sphere, which is half the measure of the diameter.

Diameter of the smaller spherical ball = 5 inches

Radius = 5/2 = 2.5 inches

Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³

Volume ≈ 65.5 in.³

Diameter of the larger spherical ball = 13 inches

Radius = 13/2 = 6.5 inches

Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³

Volume of the larger spherical ball ≈ 1,150.3 in.³

The amount of space (volume) that is in the larger spherical ball than the smaller.

= 1,150.3  - 65.5

The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³

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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:

x = 15°

Step-by-step explanation:
165 and x are on a straight line which means they are supplementary.
Set up the equation and solve for x:

165 + x = 180

x = 180 - 165

x = 15

The area of the trapezoid is 140 square feet

The area of a shape is the amount of space on that shape

The dimensions of the trapezoid are given as:

Height = 10 feet

Parallel bases = 8 feet and 20 feet

The area of a trapezoid is calculated using

Area = 0.5 * (Sum of parallel bases) * Height

Substitute the known values in the above equation

Area = 0.5 * (8 + 20) * 10

Evaluate the equation

Area = 140

Hence, the area of the trapezoid is 140 square feet

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The dy/dx of equation  [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].

Given an equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex].

We are required to find dy/dx of the equation.

Equation is like a relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.

Differentiation is basically finding the change in variables.

It may be linear equation, quadratic equation,cubic equation or many more depending on the power of the variable present in the equation.

Equation:[tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex]

Differentiating with respect to x.

3[tex]x^{2}[/tex]-3([tex]x^{2}[/tex]*dy/dx+y*2x)+2(x*2y*dy/dx+[tex]y^{2}[/tex])=0

3[tex]x^{2} -3x^{2} dy/dx-6xy+4xy dy/dx+2y^{2}[/tex]=0

Taking dy/dx at one side and take the other part to other end.

[tex]-3x^{2} dy/dx+4xy dy/dx[/tex]=[tex]6xy-3x^{2} -2y^{2}[/tex]

dy/dx=[tex](6xy-3x^{2} -2y^{2})/(4xy-3x^{2} )[/tex]

Hence the dy/dx of equation  [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].

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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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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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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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The lists of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 that are possible is; 256

We are told that the last digit has to be either a one (1) or nine (9), then are two (2) options (>,<) for the remaining eight digits, so there are 2⁸ = 256 arraignments where each digit is either greater than or less than the preceding digits. This can be confirmed as below;

Numbers beginning with 1 = 8C0 = 1

Numbers beginning with 2 = 8C1 = 8

Numbers beginning with 3 = 8C2 = 28

Numbers beginning with 4 = 8C3 = 56

Numbers beginning with 5 = 8C4 = 70

Numbers beginning with 6 = 8C5 = 56

Numbers beginning with 7 = 8C6 = 28

Numbers beginning with 8 = 8C7 = 8

Numbers beginning with 9 = 8C8 = 1

Total lists of numbers possible = 1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 256

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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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! is shorthand for the factorial function. If [tex]n[/tex] is a non-negative integer, then

[tex]n! = n\times(n-1)\times(n-2)\times\cdots3\times2\times1[/tex]

with [tex]0! = 1[/tex].

So how to compute [tex]n![/tex] ?

Multiply each number in sequence from that number to 1.

Using it's concept, your percentage for the month was of 94.12%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, your goal was of 85, with a grade of 80, hence the percentage is:

P = 80/85 x 100% = 94.12%.

Hence, your percentage for the month was of 94.12%.

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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

The number exists 99, then 99 - 49 = 50

Therefore, the pair of two-digit numbers exist between 99 and 49.

In math, the word difference exists as the outcome of subtracting one number from another.

Let the first pair of two-digit numbers be xy and the second pair of numbers be yx.

we want a two-digit number, a two-digit number begins from 10 and ends with a two-digit number that exists 99.

Let the difference of 50 exists possible when we take the biggest two-digit number

Therefore, the number exists 99

99 - 49 = 50

Therefore, the pair of two-digit number exists 99 and 49.

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Answer:

17 +1^2=18

18+2^2=22

22+3^2=31

31+4^2=47

47+5^2=72

72+6^2=108

Step-by-step explanation: