(-4a^5b^3)^2•(-3a^2b)^2

The amount of paint needed to apply a coat of paint is 1.00 m³.

Given:

a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m.

we are asked to  estimate the amount of paint needed to apply a coat of paint.

The amounts

Volume of a hemisphere, V = (2/3)πr³

r = 40/2

= 20 m

dr = 0.04 cm = 0.0004 m

dV≈2πr²dr

= 2π(20)²(0.0004) m³

=  1.0048 m³

rounding it of to two decimal places.

= 1.00 m³

Hence the amount of paint needed is 1.00 m³

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(a) The probability that two radios are being defective= 0.035

(b) The probability that all radios are not defective = (11/12)^4

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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The average profit is positive if the number of snowboards is less than 67418 .

Given:

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = (Px)/x, where P(x) is the profit function.

The profit is P ( x ) = R ( x ) - C ( x )

= -x^2 + 10x - ( 4x + 5 )

= -x^2 + 10x - 4x + 5

= -x^2 + 6x + 5

Then AP( x ) = ( P( x )) / x

= -x^2 + 6x + 5 / x > 0

As x > 0 then the sign of AP(x) depends on numerator only.

-x^2 + 6x + 5 > 0

D = 36 + 20

= 56

x = 6.7417

Therefore AP(x) > 0 if 0 < x < 6.7417

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Full question:

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x)/x, where P(x) is the profit function. Determine the production levels that make AP(x) > 0.

A solution that does not simultaneously satisfy all constraints is called an infeasible solution.

Option (C) is correct.

What is linear programming?

Linear programming, also known as linear optimization, is a method for achieving the best result in a mathematical model with requirements represented by linear relationships. Linear programming is a special case of mathematical programming.

In linear programming, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.

In some cases, there is no feasible solution area, i.e., there are no points that satisfy all constraints of the problem. An infeasible LP problem with two decision variables can be identified through its graph. For example, let us consider the following linear programming problem.

Minimize z = 200x1 + 300x2

subject to

2x1 + 3x2 ≥ 1200

x1 + x2 ≤ 400

2x1 + 1.5x2 ≥ 900

x1, x2 ≥ 0

The region located on the right of PQR includes all solutions, which satisfy the first and the third constraints. The region located on the left of ST includes all solutions, which satisfy the second constraint. Thus, the problem is infeasible because there is no set of points that satisfies all three constraints.

Hence, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.

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Answer:

19

Step-by-step explanation:

therefore the answer is 19

The analyst should provide a report addressing the following

A sale’s affect on subscription purchases is an example of customer buying behavior analysis.

Data analysis is the process of modifying, processing, and cleaning raw data in order to obtain useful, pertinent information that supports commercial decision-making. The process offers helpful insights and statistics, frequently presented in charts, graphics, tables, and graphs, which lessen the risks associated with decision-making.

Every time we make a decision in our daily lives, we can see a basic example of data analysis by assessing what has happened in the past or what will happen if we take that action. In its simplest form, this process involves looking at the past or future and making a choice based on that analysis.

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Step-by-step explanation:

1[tex] {10}^{ - 8} = \frac{1}{10^{8} } [/tex]

[tex]7 \times \frac{1}{ {10}^{8} } = \frac{7}{ {10}^{8} } [/tex]

2)

[tex]6 \times {10}^{ - 8} = 6 \times \frac{1}{ {10}^{8} } = \frac{6}{ {10}^{8} } [/tex]

Answer:

f X varies directly with Y, then the relationship between them can be expressed as Y = kX, where k is a constant. Therefore, we can calculate the value of Y when X is 3 by substituting the values into the equation: Y = (20/30) * 3 = 2

Step-by-step explanation:

The resulting regression was predicted GPA is 3.1 Predict the outcome of one variable from the outcome of a second variable.

The variable we are predicting is called the reference variable and is denoted as Y. The variable on which the prediction is based is called the predictor and is denoted as X. The magnitude of the correlation coefficient indicates the strength of the association. A prediction is a statement intended to tell you something about the future.

Predicted grades are qualifying grades that an applicant's school or college is expected to achieve under favorable circumstances. These predicted grades are used by colleges as part of the admissions process to help understand an applicant's potential. The expected result of an experiment is derived from a hypothesis or theory. This is a guess at the possible outcome of the scenario.

GPA= 3.1+3.6+1.6+3.1+4.1/ 5= 15.5/5 = 3.1

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Answer: 250 meters

Step-by-step explanation: Find the unit rate. 2000 divided by 8 will get you a unit rate of 250 meters per minute.

Answer:

[tex]z = \frac{4x}{3y}[/tex]

Step-by-step explanation:

[tex]x = \frac{3yz}{4}[/tex]

[tex]3zy = 4x[/tex]

[tex]z = \frac{4x}{3y}[/tex]

Answer:

z = (4x)/(3y)

Step-by-step explanation:

Given equation,

→ x = (3yz)/4

Now the value of z will be,

→ x = (3yz)/4

→ (3yz)/4 = x

→ 3yz = x × 4

→ z × 3y = 4x

→ [ z = 4x/3y ]

Hence, value of z is 4x/3y.

Answer: 130 cookies are left

Step-by-step explanation:

3/4 of 520 = 390

520 - 390 = 130

Answer:

130 cookies are left.

Step-by-step explanation:

1. Turn 3/4 into a decimal

3 ÷ 4 = 0.75

2. Multiply

0.75 x 520 = 390

3. Subtract

520 - 390 = 130

Solution:

130 cookies are left.

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The equation of the circle with center (−1,−2) containing the point (0,6).

(x + 1)^2 + (y + 2)^2 = 65

Remember that the equation of a circle with radius R and center (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the center of the circle is (-1, -2), then our equation is something like:

(x + 1)^2 + (y + 2)^2 = R^2

We know that our circle contains the point (0, 6), replacing these values in the equation above we get:

(0 + 1)^2 + (6 + 2)^2 = R^2

1 + 8^2 = R^2

65 = R^2

Then the circle equation is:

(x + 1)^2 + (y + 2)^2 = 65

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If each is a 4-digit number beginning with 1 that has exactly two identical digits , then there are 432 such numbers .

In the question ,

Suppose  that the two identical digits are both 1.

and since the thousands digit must be 1, only one of the other three digits can be 1. This means that the  possible forms for the required numbers are

11xy , 1x1y , 1xy1  ,

Because the number must have exactly two identical digits, x ≠ y, x ≠ 1, and y ≠ 1.

Hence, Of this form there are 3 × 9 × 8 = 216 numbers .

Now suppose that two identical digits are not 1 , we will have the following possibilities:

1xxy , 1xyx , 1yxx

Again, x ≠ y , x ≠ 1 , and y ≠ 1 .

Of this form there are 3 × 9 × 8 = 216 numbers .

So , the total numbers are 216 + 216 = 432 .

Therefore , the total  numbers are 432 .

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The probability that you picked the fair coin given that the outcome of the toss was heads is 1/3.

There is a one in two chance of drawing the fair coin. The chances of flipping heads again are 1 in 2. As a result, there is a 1 in 4 chance that the coin will land on heads.

There is a one in two chance of drawing the trick coin. The probability of flipping heads is then 2 to 1. As a result, there is a 2 in 4 chance that the coin will land on heads.

When each is multiplied by four, the resulting integers are

fair: 1 and trick: 2

and overall results: 3. (fair and tails is not counted)

The likelihood of a fair coin is one in three.

The likelihood that the chosen coin will show heads and be the fair coin is 33.333%.

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Illinois city-to-airport distances can be discovered using a distance spatial join. The utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.

A system called a geographic information system (GIS) is one that collects, organizes, processes, and maps all kinds of data.

Illinois city-to-airport distances can be discovered using a distance spatial join.

Thus, the utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.

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x = 1+i or x = 1-i are the complex roots of the graph

Below are the steps for determining the complex roots of a graph or curve:

1. Draw a vertical line passing through the vertex of the parabola or curve

2. The value of x where the line intersects the x-axis gives the real part of the root

3.  Draw a horizontal line of height twice the height of the vertex from the x-axis

4. Draw a vertical line from this point of intersection to intersect the x-axis

5. The distance of this point from the real part of the root gives you the imaginary part of the root

(Check the attached image for the labeling)

From the image attached:

Real part of the root: a = 1

Imaginary part of the root: b = 1

Remember: complex root is of the form x = a±bi

Therefore, the complex roots of the graph are x = 1+i or x = 1-i

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The shadow of the ball moving over the ground at 150 feet per second after 1 second.

How can I determine the shadow of the ball's speed?

Assuming the ball drops the distance indicated by this sentence:

S = 16t²

Additionally, the height (h) of the ball's shadow one second later is provided by

h = 30 - S

The term for the shadow of the ball would then be as follows:

OX/30 = (20 + XQ)/30 = XQ/h

30XQ = 20h + hXQ

20h = 30XQ - hXQ

20h = (30 - h)XQ

XQ = 20h/(30 - h)

Substituting the value of h, we have:

XQ = 20(30 - S)/(30 - 30 - S)

Substituting the value of S, we have:

XQ = 20(30 - 16t²)/(30 - 30 - 16t²)

XQ = 20(30 - 16t²)/16t²

XQ = (600 - 320t²)/16t²

XQ = 600/16t² - 320t²/16t²

XQ = 600/16t² - 20

Differentiating with respect to t, we have:

d(XQ)/dt = 600/16t² - 20

d(XQ)/dt = 600 (-64t/(16t²)²)

d(XQ)/dt = 600 (-64t/256t⁴)

d(XQ)/dt = 600 (-0.5/2t³)

d(XQ)/dt = -300/2t³

Then,

At t = 1, we have:

Speed = 300/2(1)

Speed = 150 ft/s.

That is,

After one second the ball's shadow was travelling over the ground at a speed of 150 feet per second.

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The error Percentage is 20%

What is Percentage?

A percentage is a component of a whole stated as a number between 0 and 100 rather than as a fraction. All of anything is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the fraction of the entire by the whole itself and multiply by 100.

Solution:

We gussed that LeBron James would score 35 points, but he only scored 28 points

So, the difference was of 7 points (35-28)

Error Percentage = 7/35 * 100

Error Percentage = 1/5 *100

Error Percentage = 20%

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Answer:

25

Step-by-step explanation:

450 divided by 18 is 25

Answer: 25 miles

Step-by-step explanation:
450/18 = 25
25 miles with 1 gallon of gas

The height of the object after 1.00 seconds launched is 24 feet.

Quadratic function is a function where the maximum power of x variable is 2. Simply you can write quadratic function as:

y = ax^2 + bx + c

y is height in feet and x is time in second.

Known 2 conditions from the question:

From second condition (0 feet in 0 second), we can substitute 0 both in y and y:

y = ax^2 + bx + c

0 = a(0)^2 + b(0) + c

0 = 0 + 0 + c

0 = c

And this, we know that the constant (c) of the function is 0.

Just substitute c with 0 in previous function.

y = ax^2 + bx + c

y = ax^2 + bx + 0

y = ax^2 + bx

From first condition (25 feet in 1.25 seconds), we can substitute x with 1.25 and y with 25:

y = ax^2 + bx

25 = a(1.25)^2 + b(1.25)

25 = 1.56625a + 1.25b

Maximum/minimum point of quadratic function can be found with dy/dx = 0, dy/dx is differential:

y = ax^2 + bx

dy/dx = 2ax + b

0 = 2ax + b

0 = 2a(1.25) + b

0 = 2.5a + b

-2.5a = b

After we know the ratio a and b, we can substitute b with -2.5a in previous equation:

25 = 1.5625a + 1.25b

25 = 1.5625a + 1.25(-2.5a)

25 = 1.5625a - 3.125a

25 = -1.5625a

15/-1.5635 = a

a = 15/-1.5625

a = 16

We got a = 16. Then we just substitute it in a b ratio equation:

b = -2.5a

b = -2.5(-16)

b = 40

After we know a, b, c, just substitute that three numbers in the function:

y = ax^2 + bx + c

y = -16x^2 + 40x

So, the function can be used in launching of the object is y = -16x^2 + 40x.

Where is the object in 1.00 seconds after launched? Just substitute x with 1.

y = -16x^2 + 40x

y = -16(1)^2 + 40(1)

y = -16 + 40

y = 24 feet

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Step-by-step explanation:

x + 1/2y = 18

2x + y = 36

x = 36 - y

18 = 36 - y + 1/2y

18 = 36 - 1/2y

36 - 18 = 1/2y

18 = 1/2y

y = 36

x = 18 - 1/2(36)

x = 18 - 18

x = 0

Therefore, you can spend 0 hours on the phone and 36 hours on the internet.

Answer: 225

Step-by-step explanation:

The requried area under the standard normal curve that lies to the right of z = 0.11 and to the left of z = 0.41 is approximately 0.1153.

To find the area under the standard normal curve that lies to the right of the z-score 0.11 and to the left of the z-score 0.41, we can use a standard normal table or a statistical calculator.

The area to the right of z = 0.11 can be found by subtracting the cumulative area to the left of z = 0.11 from 1.

The area to the left of z = 0.41 can be directly read from the standard normal table.

Using a standard normal table or a calculator, we find:

The area to the left of z = 0.11 is approximately  0.5438.

The area to the left of z = 0.41 is approximately 0.6591.

Now, let's find the area between these two z-scores:

Area = (Area to the left of z = 0.41) - (Area to the left of z = 0.11)

Area = 0.6591 - 0.5438

Area ≈ 0.1153

So, the area under the standard normal curve that lies to the right of z = 0.11 and to the left of z = 0.41 is approximately 0.1153.

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the regression equation:

y = 0.9x+ 7.5

given that:

Xi: 2; 6; 9; 13; 20

Yi: 7; 18; 9; 26; 23

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑XY = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] +  [tex]6^{2}[/tex]+[tex]9^{2}[/tex]  +  [tex]13^{2}[/tex]+ [tex]20^{2}[/tex] = 690

∑[tex]y^{2}[/tex]=  [tex]7^{2}[/tex]+ [tex]18^{2}[/tex]  + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] +[tex]23^{2}[/tex]  = 1659

the slope b is calculated:

b = ∑XY - ∑x × ∑y/n ÷ ∑ - (∑x)^2 /n

now we need to substitute the above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

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The equation of the line in slope-intercept form is: y = 5x + 3.

If the value of the slope of a line, m, is known, and the value of its y-intercept, b, is known, the equation of the line in slope-intercept form would be written as:

y = mx + b.

Given the following:

To write the equation of the line in slope-intercept form, substitute m = 5 and b = 3:

y = 5x + 3

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Question:

A line's slope is 5, and its y -intercept is 3. What is its equation in slope-intercept form?