Use the given information to complete the proof of the following theorem

Answer:

-3

Step-by-step explanation:

-3 is 12 less than its square. Implies that 9 - 12 = -3.

Answer:

There are 4^5 ways to answer 5 multiple choice questions.

Step-by-step explanation:

The manager should charge $ 700 per camera and the maximum revenue is $ 73,000.    

Maximum revenue refers to the highest amount of money a business can earn by selling its products or services. To find the maximum revenue, we need to determine the price that would generate the maximum number of sales and then multiply it by the number of cameras sold at that price.

Here we have

Let x be the number of $20 decreases in price, and let y be the number of cameras sold per month.

From the problem statement, we can write:

y = 70 + 5x

The price of a camera after x decreases of $20 each is:

p(x) = 900 - 20x

The revenue earned per month is given by:

R(x) = p(x) × y = (900 - 20x) × (70 + 5x)

Expanding the expression and simplifying, we get:

R(x) = -100x² + 2000x + 63000

To find the value of x that maximizes revenue, we need to find the vertex of the parabola represented by R(x).

The x-coordinate of the vertex is given by:

x = -b / (2a) = -2000 / (-200) = 10

Therefore,

The manager should decrease the price by $200, or $700 per camera, to maximize monthly revenue.

The number of cameras sold per month at this price is:

y = 70 + 5x = 70 + 5(10) = 120

The maximum revenue is:

R(10) = -100(10)² + 2000(10) + 63000 = $73,000  

Therefore,

The manager should charge $ 700 per camera and the maximum revenue is $ 73,000.      

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We may infer after addressing the stated question that As a result, the equation correct answer is (a) $162,000.

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.

$6.00 x 75 = $450

$450 x 360 = $162,000

As a result, the total amount paid on a $75,000 30-year fixed loan at 6.0% is $162,000.

As a result, the correct answer is (a) $162,000.

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The length of a 30° arc of a circle with a radius of 6 feet is π feet.

What is circle ?

In geometry, a circle is a closed, two-dimensional figure that consists of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center). The distance across the circle through the center is called the diameter, which is equal to twice the radius.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, the circumference of this circle is:

C = 2π(6 feet) = 12π feet

Since a full circle is 360°, we can find the length of a 30° arc by multiplying the fraction of the circle represented by the arc by the circumference of the circle. In this case, the fraction of the circle represented by the 30° arc is:

30°÷360° = 1÷12

So the length of the 30° arc is:

(1÷12) × 12π feet = π feet

Therefore, the length of a 30° arc of a circle with a radius of 6 feet is π feet.

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Answer:

[tex]7 \: \: and \: \: 14 \frac{1}{6} [/tex]

Step-by-step explanation:

Assume, the 1st mixed number is x and the 2nd one is y

Let's write 2 equations according to the given information:

[tex]x + y = 21 \frac{1}{6} [/tex]

[tex]x - y = \frac{43}{6} [/tex]

Let's make x the subject from the 1 equation:

[tex]x = 21 \frac{1}{6} - y[/tex]

Replace x in the 2nd equation with its value from the 1st one:

[tex]( 21\frac{1}{6} - y) - y = \frac{43}{3} [/tex]

Eliminate the brackets and collect like-terms:

[tex] - 2y = \frac{43}{6} - 21 \frac{1}{6} [/tex]

Convert the number 21 1/6 to an improper fraction:

[tex] - 2y = \frac{43}{6} - \frac{21 \times 6 + 1}{6} [/tex]

[tex] - 2y = \frac{43}{6} - \frac{127}{6} = \frac{ - 84}{6} [/tex]

Multiply both sides of the equation by 6 to eliminate the fraction:

[tex] - 12y = - 84[/tex]

Divide both sides of the equation by -12 to make y the subject:

[tex]y = 7[/tex]

[tex]x = \frac{127}{6} - \frac{7}{1} = \frac{127}{6} - \frac{42}{6} = \frac{85}{6} = 14 \frac{1}{6} [/tex]

To be in the top 10% of his class, Troy needs a score of 80.28 or better. With an 83, he placed in the top 10% of his class on this exam.

The percentage is a technique to express a fraction or proportion as a percentage of 100.

We apply the following algorithm to convert Troy's score to a z-score:

z = (X - M) / SD

where X is Troy's score, M represents the class average, and SD represents the standard deviation. Using the values we have:

z = (83 - 76.80) / 3.10 = 2.00

We seek up the equivalent area in the z-table and plot this on a distribution. A z-score of 2.00 equates to a 0.9772 area.

Troy's score should be converted to We use the following formula to calculate a percentile rank:

(number of scores below X / total number of scores) x 100% = percentile rank

(0.9772) x 100% = 97.72% Percentile rank

We may accomplish this by dividing the area to the left of Troy's z-score by the area to the left of the class average's z-score:

Area = 0.9772 - 0.5000 = 0.4772

This means that around 47.72% of the scores fall between Troy's and the class average.

We can solve for X using the z-score formula:

X = (z)(SD) + M = (1.28)(3.10) + 76.80 = 80.28

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Investigate all similar responses

Answer:

4 seconds

Step-by-step explanation:

The composite function f(g(x)) has a value of -2x^2 - 6.

From the question, we have the following parameters that can be used in our computation:

Fuctions f(x) and g(x)

To find f(g(x)), we first need to evaluate g(x) and then use the result as the input for f(x).

So we have:

g(x) = x^2 + 3

Now we substitute this expression into f(x) and simplify:

f(g(x)) = f(x^2 + 3) = -2(x^2 + 3) = -2x^2 - 6

Therefore, f(g(x)) = -2x^2 - 6.

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The recent poll found that only 110 parents out of 200 indicated that they spank their children. This is less than the expected number of parents who spank based on the original poll.

A survey is a research method used to collect data from a sample of individuals or entities. Surveys can be conducted in various forms, including questionnaires, interviews, or online forms, and can be used to gather information about attitudes, opinions, behaviors, characteristics, and other aspects of a population or group.

In the given question,

If 65% of parents spank their children, then we can expect that out of 200 parents with children, the number who spank their children would be:

Expected number of parents who spank = 65% of 200 = 0.65 x 200 = 130

However, the recent poll found that only 110 parents out of 200 indicated that they spank their children. This is less than the expected number of parents who spank based on the original poll.

This could suggest that parents' attitudes towards spanking have changed since the original poll was taken. However, there could be other factors that affected the results, such as differences in the sampling methods or demographics of the participants in the two polls. To draw a more conclusive inference, further analysis and research would be required.

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It is important to use the given standard deviation to construct the control chart.

A control chart is a statistical tool used to monitor and control a process over time. It is a graphical representation of process data over time, with the addition of statistical control limits. Control charts are used to detect any unusual variation in a process and to identify when the process is out of control or deviating from its expected performance.

Yes, you need to use the given process standard deviation of 0.27 to construct the three-sigma control chart for the mean weight.

The control limits for the X-Bar Control Chart with a sample size of n = 4 and a Z-value of 3 can be calculated using the following formula:

UCL = X-Bar + Z(σ/√n)

LCL = X-Bar - Z(σ/√n)

where UCL is the upper control limit, LCL is the lower control limit, X-Bar is the sample mean, σ is the process standard deviation, n is the sample size, and Z is the number of standard deviations.

To construct the control chart, you need to calculate the UCL and LCL for each sample means in your data set using the formula above. Then, plot the sample means on the control chart along with the UCL and LCL.

It is important to use the given standard deviation to construct the control chart.

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Answer:The answer is  the last one

Step-by-step explanation:

Im goatified

Answer:

x(x+8)(x-6)

Step-by-step explanation:

The GCF is x. First, you factor out x and get x(x² + 2x - 48). Then, you x-factor it and get (x+8)(x-6). Then you add the x on it and get the final answer of x(x+8)(x-6)

Therefore, Troy's actual score is 83.10.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain. The probability of an event can be determined by dividing the number of ways that event can occur by the total number of possible outcomes. Probability is widely used in various fields, including mathematics, statistics, science, engineering, economics, and finance, to model uncertain events and make predictions.

To answer the questions, we need to calculate the z-score for Troy's exam score and then use the z-table to find the probability or percentage associated with that z-score.

First, let's calculate the z-score for Troy's exam score:

[tex]z = (X - M) / SD[/tex]

where X is Troy's score, M is the class average, and SD is the standard deviation.

[tex]z = (83 - 76.80) / 3.10[/tex]

[tex]z = 2.00[/tex]

Next, let's use the z-table to find the probability associated with a z-score of 2.00. We look up the value in the body of the table, which is 0.9772. This means that the probability of getting a z-score of 2.00 or higher (i.e., a score higher than Troy's) is 0.9772.

To find the percentage of students who scored lower than Troy, we can subtract the probability found above from 1, since the total probability for all possible outcomes is 1.0.

[tex]P(X < 83) = 1 - 0.9772[/tex]

[tex]P(X < 83) = 0.0228[/tex]

So, the percentage of students who scored lower than Troy is 2.28%.

Finally, we can use the formula provided to calculate Troy's actual score if we know his z-score, standard deviation, and class average:

[tex]X = (z)(SD) + M[/tex]

[tex]X = (2.00)(3.10) + 76.80[/tex]

[tex]X = 83.10[/tex]

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Total number of possible outcomes:

Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957

Number of ways to choose 1 number from 49: 49

Total number of possible outcomes = 22,957 * 49 = 1,128,593

Number of favorable outcomes:

Number of ways to choose 1 number from 49: 1

Number of favorable outcomes = 1

Probability of winning the minimum award:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%

The button's actual diameter, based on the diameter and the scale, would be 2.5 cm.

Since the image of the button under the magnifying glass is 2 times the button's actual size, we can find the actual diameter of the button by dividing the diameter of the image by 2.

Given:

Image diameter = 5 cm

Magnification = 2 times

Actual diameter = Image diameter / Magnification

Actual diameter = 5 cm / 2

Actual diameter = 2.5 cm

In conclusion, the button's actual diameter is 2.5 cm.

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[tex]6\dfrac{1}{6}[/tex] feet tape is left on the roll

[tex]15-8\dfrac{5}{6} =15-\huge \text(8+\dfrac{5}{6} \huge \text)=15-8-\dfrac{5}{6} =7-\dfrac{5}{6} =6\dfrac{1}{6}[/tex]

Answer:

She has 7 whole sheets with a few stickers on the 8th sheet left.

Step-by-step explanation:

First, you need to do a subtraction problem.

This is because you need to have a whole numerical amount as a whole number in order to clearly prove the exact amount of sheets Sara brought.

You take the whole which is 15 sheets and subtract it from the 8 sheets. This is needed since you need a whole numerical amount excluding fractions or decimals.

-This should be 7 whole sheets left.

So now we know that she used 8 whole sheets. But we still need to evaluate the 5/6s.

You can do 5 divided by 6 which is equal to ~0.83. This is almost equivalent to a whole sheet of stickers. This approximation would prove that 8 sheets could possibly be left.
___________________________________________________

This can also be interpreted as this:

You take 15 and subtract it with 8 5/6. This time is different since we're not approximating.
That equals 37/6 which is equivalent to 6 1/6. Thus giving 6 whole sheets left.
___________________________________________________

Hypothetically She has 7 whole sheets with a few stickers on the 8th sheet left.

Answer:

  Tuesdays

Step-by-step explanation:

Given men : women ratios of 1:6 and 2:11 on Tuesdays and Thursdays, respectively, you want to know which day has the higher proportion of women.

Ratios are most easily compared of one of the numbers is the same in both ratios. Here, we can double the first ratio to make the number units representing men be 2:

  1 : 6 = 2 : 12 . . . . . ratio on Tuesdays

  2 : 11 . . . . . . . . . . . ratio on Thursdays

There are relatively more women on Tuesdays. (12 > 11)

__

Additional comment

We can also make the number representing men be 1. Dividing the second ratio by 2 gives ...

  2 : 11 = 1 : 5.5

Now, we can see that 5.5 is less than 6, so the proportion of women is higher on Tuesdays. These ratios (6, 5.5) are effectively "unit rates", or women per man.

Answer:

(9/5) * (1156/10000)

*IG:whis.sama_ent

Answer:

a

Step-by-step explanation:

The event you are describing is called a dependent event. In a dependent event, the outcome of one event affects the probability of the outcome of another event.

what is dependent event ?

A dependent event is an event in which the outcome of one event affects the probability of the outcome of another event. In other words, the occurrence or non-occurrence of the first event affects the probability of the second event.

In the given question,

The event you are describing is called a dependent event. In a dependent event, the outcome of one event affects the probability of the outcome of another event. This is in contrast to an independent event, in which the outcome of one event does not affect the probability of the outcome of another event.

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Answer:

a = 0

b = -5

r = 3

Step-by-step explanation:

Given that the center of the circle is at (0, -5) and the diameter of the circle is 6 units, we can determine the values of a, b, and r for the standard equation of a circle: (x - a)^2 + (y - b)^2 = r^2.

a: The x-coordinate of the center of the circle, which is 0 in this case.

b: The y-coordinate of the center of the circle, which is -5 in this case.

r: The radius of the circle, which is half of the diameter. So, r = 6/2 = 3 units.

Therefore, the values for a, b, and r are:

a = 0

b = -5

r = 3

336 is the sample size needed so that the 95% confidence interval will have a margin of error of 1.1.

The margin of error (ME) of a confidence interval at a 95% confidence level is calculated as follows:

ME = 1.96 * SE

SE denotes the standard error of the mean. The standard error is determined as follows:

[tex]SE = \frac{sigma}{\sqrt{n} }[/tex]

where sigma is the population standard deviation (assumed to be 10.2726) and n represents the sample size.

When we substitute the provided values, we get:

[tex]1.1 = 1.96 * (\frac{10.276}{\sqrt{n} } )[/tex]

When we solve for n, we get:

n ≈ 336.02

In total, 337 samples are required.

As a result, the answer is 337, and the closest choice is 336.

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A) The annual rate of change between 1994 and 2003 was 0.0617.

B) The value written in percentage form is 6.17%.

C) The value of car in the year 2008 will be $2,500.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers can be described by the four fundamental operations, sometimes known as "arithmetic operations." In mathematics, the results of operations such as division, multiplication, addition, and subtraction are quotient, product, sum, and difference, respectively.

A) We are given value of car in the year 1994 as $34,000 and in the year 2003, it was $13,000.

So, using subtraction operation, we get

⇒ Amount of depreciation = $34,000 - $13,000

⇒ Amount of depreciation = $21,000

This is over the period of 10 years.

So, annual rate of change is obtained by using the division operation.

⇒ [tex]\frac{21000}{10}[/tex]

⇒ $2100

Now, rate of change is

⇒ [tex]\frac{21000}{10}[/tex]

⇒ 0.0617

B) The value in the percentage form is obtained by using the multiplication operation which is

0.0617 * 100 = 6.17%

C) Since, the value is dropping by same percentage, the value in 2008 will be:

⇒ $13,000 - (2100 * 5)

⇒ $13,000 - $10500

⇒ $2,500

Hence, the required values have been obtained.

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Question: A car was valued at $34,000 in the year 1994. The value depreciated to $13,000 by the year 2003.

A) What was the annual rate of change between 1994 and 2003?

r = Round the rate of decrease to 4 decimal places.

B) What is the correct answer to part A written in percentage form?

r = %.

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2008 ?

value = $ Round to the nearest 50 dollars

Answer:

9.18%

Step-by-step explanation:

The probability of getting a tail on a fair coin flip is 0.5, and the probability of getting a head is also 0.5. Since each coin flip is independent, we can use the binomial probability formula to calculate the probability of getting exactly 5 tails in 15 flips:

P(X = 5) = (15 choose 5) * (0.5)^5 * (0.5)^(15-5)

where (15 choose 5) is the number of ways to choose 5 tails out of 15 flips, which can be calculated as:

(15 choose 5) = 15! / (5! * 10!) = 3003

Substituting the values, we get:

P(X = 5) = 3003 * (0.5)^15 ≈ 0.0918

Therefore, the probability of getting exactly 5 tails in 15 coin flips is approximately 0.0918 or 9.18%.

Answer:

40 sandwiches

Step-by-step explanation:

First, we need to figure out how many sandwiches each teenager eats per day. According to the information given, each teenager eats one sandwich for every half sandwich that a small child eats. Since each small child eats 1 sandwich per day, each teenager would eat 2 sandwiches per day.

So, for 5 days, the 2 small children would need a total of 2 x 1 x 5 = 10 sandwiches.

And for 5 days, the 3 teenagers would need a total of 3 x 2 x 5 = 30 sandwiches.

Therefore, to pack lunches for all 5 kids for 5 days, Andy would need to pack a total of 10 + 30 = 40 sandwiches.

Answer:

132 yd²

Step-by-step explanation:

This shape is a rectangle.

Area of rectangle = L · W

L = 12 yd

W = 11 yd

We Take

12 · 11 = 132 yd²

So, the area of this shape is 132 yd².

Hence, the approximated circle of area 4500[tex]m^{2}[/tex].

A circle is a particular type of ellipse in geometry where the eccentricity is zero and the two focus coincide. The locus of points drawn equally a part from the center is known as a circle. The radius of a circle is measured from the center to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice of radius.A circle is a 2 Dimensional figure . The interior and exterior parts of the are separated by the circles. It re assembles a line segment in several ways. Consider the line segment being twisted till it reaches its ends.

Each graph's y-axis should the following labels:

Circumference  given in Graph A

Area given in Graph B

Radius given in Graph C

Now find the diameter of circle A:

Circle of area A =[tex]r^{2}[/tex] =500

⇒r =[tex]\sqrt{500}[/tex]

⇒r=22.36 m

Circle A has a diameter that is twice its radius, so:

circle A of  diameter is 2 r= 2×22.36 m.=44.72 m.

Circle A of diameter is three times that of circle B,

that is 3×44.72 =134.16

If circle B of radius is equal to half its diameter,

[tex]\frac{134.16}{2}[/tex]=67.08 m is the radius of circle B.

now We find the area of circle B:

area of circle B =[tex]67.08^{2}[/tex]= 4499.73 [tex]m^{2}[/tex].

Hence, the approximated circle of area 4500[tex]m^{2}[/tex].

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The probability is 0.9999045772. Round up to 6 decimal places if necessary.

The probability distribution of a random experiment or event shows the chance of each conceivable outcome. It gives the likelihoods of several potential events. Additionally, see Probability of Events. A measure of the uncertainty of different phenomena is the likelihood. Like when you throw a die, the probability determines the various results. To determine this distribution, any random experiment with ambiguous or unanticipated outcomes could be employed.

First, we determine the likelihood of receiving a particular sort of hand.

The likelihood of receiving this kind of hand is:

P(deal) = 248/2598560

P(dealt) = 1 - P(not dealt)

Then we find probability of not being dealt with one type of hand.

P(not dealt) = 1 - P( dealt)

P(not dealt) = 1 - 248/2598560

P(not dealt) = 25898960-248/2598960

= 2598712/2598960

= 0.9999045772

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The complete question is,