The circle has a diameter of 0.2 m.
The height of the square is a fifth of the diameter
of the circle.
Calculate the shaded area in cm.
Give your answer to 2 decimal places.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. The expected value of his or her total winnings for the four spins is $800.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again.

We have to determine the expected value of his or her total winnings for the four spins.

Total winning depends on the fourth term.

Outcome              Skunk        100        200        500

Probability              1/4            1/4          1/4          1/4

Total Winning          0             900       1000       1300

Expected Total Winning = 1/4 (0 + 900 + 1000 + 1300)

Expected Total Winning = 1/4 × 3200

Expected Total Winning = 800

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The complete question is:

Contestants on a game show spin a wheel like the one shown in the figure above. Each of the four outcomes on this wheel is equally likely and outcomes are independent from one spin to the next.

The contestant spins the wheel.

If the result is a skunk, no money is won and the contestant's turn is finished.

If the result is a number, the corresponding amount in dollars is won.

The contestant can then stop with those winnings or can choose to spin again, and his or her turn continues.

If the contestant spins again and the result is a skunk, all of the money earned on that turn is lost and the turn ends.

The contestant may continue adding to his or her winnings until he or she chooses to stop or until a spin results in a skunk.

Suppose a contestant has earned $800 on his or her first three spins and chooses to spin the wheel again. What is the expected value of his or her total winnings for the four spins?

Answer:

Below

Step-by-step explanation:

y ( 5.98x - 5.81) - 2.19 y =

5.98xy - 5.81y      - 2.19 y

5.98xy + ( - 5.81y - 2.19 y)

5.98xy + ( - 8y )

5.98xy - 8y       or   y ( 5.98x-8)

Answer:

a. x= –10

b. x= 7

Step-by-step explanation:

a. 2(x+3)=x–4

2x+6=x–4

C.L.T

2x–x= –6–4

x= –10

b.4(5x–2)=2(9x+3)

20x–8=18x+6

C.L.T

20x–18x=6+8

2x=14

divide both sides by 2

x= 7

Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]

Product of an Equation:

In mathematics, a product is a number or quantity obtained by multiplying two or more numbers. Example: 4 × 7 = 28, where the number 28 is said to be the product of 4 and 7. Another example: 6 times 4 is 24, so 6 multiplied by 4 is 24. The product of two positive numbers is a positive number, as if the product of two negative numbers is also positive (e.g., -6 × -4 = 24).

Now,

(A) We need to find the product of two given expressions.

[tex]\frac{1}{2x} -\frac{1}{4}[/tex] ×  [tex]5x^{2} -2x +6[/tex]

To multiply two given expressions, first multiply the first term in the first parenthesis by the entire expression in the second term, then do the same for the second term in the first parentheses.

[tex]\frac{1}{2x} -\frac{1}{4}[/tex] × [tex]5x^{2} -2x +6[/tex]

⇒ [tex]\frac{1}{2x} * [5x^{2} -2x +6] - \frac{1}{4} * [5x^2 - 2x +6][/tex]

⇒ [[tex]\frac{1}{2x} * 5x^2[/tex] - [tex]\frac{1}{2x} *2x[/tex] + [tex]\frac{1}{2x}* 6[/tex] ] - [ [tex]\frac{1}{4} * 5x^2 + \frac{1}{4} * 2x - \frac{1}{4}*6[/tex]]

Now, simplify the equation:

[tex]\frac{5x}{2} -1 + \frac{3}{x} - \frac{5x^2}{4} +\frac{x}{2} +\frac{3}{2}[/tex]

Rearranging the equation:

[tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]

Thus, the product of the two expressions is [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex].

(B) To compare the two expressions we will find the value of the two given expressions,

[tex]\frac{1}{2x} -\frac{1}{4} * 5x^{2} -2x +6[/tex] = [tex]-\frac{5x^2}{4} + \frac{6x}{2} -2.5 +\frac{3}{x}[/tex]

For the value of:

[tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]

simplifying the equation:

    [tex]\frac{1}{4x} - \frac{1}{2} * 5x^{2} -2x +6[/tex]

⇒ [tex][\frac{1}{4x} * (5x^{2} -2x +6)] - [\frac{1}{2} * (5x^{2} -2x +6)][/tex]

⇒ [tex]-\frac{5x^2}{2} + \frac{9x}{4} + 3.5 +\frac{3}{2x}[/tex]

As you can see, the result of the product of the two expressions is different.

Expressions consist of basic mathematical operators. The product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] & [tex]5x^{2} -2x +6[/tex] is not equal to the product of [tex]\frac{1}{2x} -\frac{1}{4}[/tex] and [tex]5x^{2} -2x +6[/tex]

Complete Question:

What is the product of 1/2x-1/4 & 5x^2-2x+6? Write your answer in standard form.

(A) show your work.

(B) is the product of 1/2x-1/4 & 5x^2-2x+6 equal to the product of 1/4x-1/2 & 5x^2-2x+6? Explain your answer

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Answer:

x | y

0 | 2

2 | 3

3 | 4

4 | 5

5 | 6

6 | 7

7 | 8

So, completing the table:

x | y

3 | 4

5 | 6

7 | 8

Step-by-step explanation:

Please study well it is a very easy question

If the equation be x + 2(51 - x) = 83 then the value of x be 19.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

In mathematics, a numerical expression is a mixture of numbers and integers combined using addition, subtraction, multiplication, or division.

Let x be the number of 1 point shots.

51 - x be the number of 2 point shots

Let the equation be x + 2(51 - x) = 83

Expanding the above equation as

x + 2(51 - x) = -x + 102

simplifying the above equation, we get

-x + 102 = 83

-x = -19

Divide both sides by -1

[tex]$\frac{-x}{-1}=\frac{-19}{-1}[/tex]

x = 19

Therefore, the value of x be 19.

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Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x)

Volumes and their variations, mathematics and supporting structures, types and their placements, and locations where they can be collected are all included in the study of mathematics. This same relationship between a group of inputs, each of which produces going support, is referred to as a "function.". Every function has a territory and a codomain, usually known as a scope. F is typically used to denote operations (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one operations, several more functions, within functions, and also on functions.

given

According to the table, the function's value at x = 10 is:

h(10) is not defined.

the values of the function change as x exceeds x = 10 to:

h(x+) = 18.5......

When roughly speaking, we have:

h(x+) = 18.5

Consequently, when x gets closer to 10 plus, the limit of h (x) is 18.5 by the table shows that the limit of h (x) .

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The complete question :-

What is Limit of h (x) as x approaches 10 plus?

Answer: IS easy you only need to put your answer that you got when you multiply the numbers:)

Step-by-step explanation:

Answer:

[tex]x < \dfrac{18}{5}[/tex]

Step-by-step explanation:

      7x - 5 < 13

Add 5 to both sides

            7x < 13 + 5

            7x < 18

Divide both sides by 7,

             [tex]\sf x < \dfrac{18}{7}[/tex]

Answer:

[tex]x < \dfrac{18}{7}[/tex]

Step-by-step explanation:

We are being asked to solve for x as an improper fraction in simplest form given the equation: [tex]7x - 5 < 13[/tex].

First, we must isolate the variables (x's) from the constants (numbers). We can achieve this by adding 5 to both sides.

[tex]7x - 5 + 5 < 13 + 5[/tex]

           [tex]7x < 18[/tex]

Then, we can solve for one multiple of x by dividing both sides by x's coefficient, which is 7.

[tex]7x < 18\\\overline{\ 7\ } \ \ \ \: \overline{\ 7\ }[/tex]

[tex]x < \dfrac{18}{7}[/tex]

The answer to the quadratic equation is x=1±√33/4.

In mathematics, a quadratic equation is one of degree 2, which means that its maximum exponent is 2. A quadratic has the formula y = ax2 + bx + c, where a, b, and c are all integers and a cannot be zero.

Use the quadratic formula to find the solutions.

−b±√b²−4(ac)/2a

Substitute the values a=2, b=−1, and c=−4 into the quadratic formula and solve for x.

1±√(−1)²−4⋅(2⋅−4)/2⋅2

Simplify.

Simplify the numerator

Raise −1 to the power of 2.

x=1±√1−4⋅2⋅−4/2⋅2

Multiply −4⋅2⋅−4.

Multiply −4 by 2.

x=1±√1−8⋅−4/2⋅2

Multiply −8 by −4.

x=1±√1+32/2⋅2

Add 1 and 32.

x=1±√33/2⋅2

Multiply 2 by 2.

x=1±√33/4

The result can be shown in multiple forms.

x=1±√33/4

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Answer: 11

Step-by-step explanation:

410 * 65 = 26,650 sq ft

26,650/2500 = 10.66 bags

Answer:

11 bags.

Step-by-step explanation:

We know that the area is 410 x 65 = 26650

Now, we need to divide to find how many bags is needed.

26240/2500 = 10.66, which we round up cause we can't have a half bag.

The profit of the swimming club is 3x + 7 bucks, can be addressed by the articulation: 5x + 10 - (2x + 3),

Utilizing the upward technique:

5x + 10

2x + 3

=3x + 7

In this way, the benefit of the swimming club is 3x + 7 bucks.

The adage "5x + 10" addresses how much cash in dollars that the swimming club procures by selling x school soul shirts. To ascertain their benefit, the group's costs must be deducted from the pay. The saying "2x + 3" addresses the costs brought about by the group. To work on the articulation for benefit, the upward strategy can be utilized where the two articulations are thought of one over the other, with the comparing terms adjusted, and the subsequent articulation is deducted from the first. The last saying, "3x + 7", addresses the benefit of the swimming club in dollars, where every unit expansion in the quantity of shirts offered prompts an expansion in benefit by 3 bucks.

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Answer:

i cant be botherd to help but

Step-by-step explanation:

use the knolage 180 degrees = full triangle

180 degress = 1 stright line

Answer:

40⁰

Step-by-step explanation:

Angles subtended by the same chord on the circumference

y= 40⁰

The number of peanut butter sandwiches in the first bag is 6 and in the second bag is 4. So, the probability of picking a peanut butter sandwich from each bag is 1/6.

The probability of an event happening is the number of successful outcomes divided by the number of total possible outcomes. In this case, there are two bags of sandwiches and John is picking one sandwich from each bag.

The first bag has 12 sandwiches in total, 6 of which are peanut butter. So, the probability of picking a peanut butter sandwich from the first bag is 6/12 or 1/2.

The second bag has 12 sandwiches in total, 4 of which are peanut butter. So, the probability of picking a peanut butter sandwich from the second bag is 4/12 or 1/3.

To find the probability of both sandwiches being peanut butter, you multiply the individual probabilities:

1/2 * 1/3 = 1/6.

So, the probability of both sandwiches being peanut butter is 1/6.

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If the variance of a sample of 169 observations equals 576, then the standard deviation of the sample equals to 24.

It is given that number of observations are 169 and their variance is 576,

now we have to find the standard deviation of the sample :

The Standard Deviation is a measure of how spread out numbers are. It's symbol is σ. It is the square root of the Variance. Variance is the average squared deviations from the mean.

Standard deviation (σ) = [tex]\sqrt{variance}[/tex]

Standard deviation (σ) = [tex]\sqrt{576}[/tex]

Standard deviation (σ) = 24

so the  standard deviation of the sample is 24.

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The value of 'x' satisfying the statement is x = 32 or x = 27.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement 23 equals x - 9, x - 14 which can be numerically expressed as, 23 = x - 9 or 23 = x - 14.

Therefore,

x - 9 = 23 or x - 14 = 23.

x = 23 + 9 or x = 23 + 14.

x = 32 or x = 37.

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The survey does not result in a simple random sample of Cubs fans who sit in the bleachers. So, option E) is correct.

Simple random sampling is a method of selecting a sample from a population such that each element in the population has an equal chance of being selected. This is achieved by using a random number generator or by randomly assigning a number to each element in the population and then selecting a sample based on those numbers.

In this case, the survey plan to select every one-hundredth fan entering the bleachers is not a simple random sample because not every sample of the intended size has an equal chance of being selected. For example, the first fan entering the bleachers has a 1 in 100 chance of being selected, while the second fan has a 2 in 100 chance of being selected. This creates a non-uniform selection process, which is not representative of simple random sampling.

Therefore, the survey plan to select every one-hundredth fan entering the bleachers results in a form of systematic sampling, which is not a simple random sample.

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Complete Question: One afternoon, a surveyor intends to pick every fan entering the bleachers to get the views of those who sit in them at Wrigley Field. Will this lead to a straightforward random sample of Cubs supporters seated in the stands?

A. Yes, as each bleacher spectator has an equal chance of getting chosen.

B. The answer is yes, but only if the bleachers have a single entrance.

C. The control group will consist of the 99 out of 100 bleacher spectators who were not chosen.

D. The answer is "yes," as this is an illustration of systematic sampling, a subset of basic random sampling.

E. No, since there are unequal odds of selecting each sample of the intended size.

Answer:

Step-by-step explanation:

Since the balls are drawn with replacement, the probability of drawing a black ball on any single draw is 7/15. The probability of drawing 6 black balls in succession is the product of the probabilities of each individual draw being a black ball. Therefore, the probability is:

(7/15)^6 ≈ 0.019

Rounding to three decimal places, the probability is 0.019.

Answer:

0.003

Step-by-step explanation:

The probability of drawing a black ball on any given draw is 7/15, since there are 7 black balls and 15 total balls in the urn. Because the balls are replaced after each draw, the probability of drawing a black ball on each of the 6 successive draws is (7/15) x (7/15) x (7/15) x (7/15) x (7/15) x (7/15) = (7/15)^6.

Therefore, the probability of drawing 6 black balls in succession is:(7/15)^6 = 0.0028 (rounded to three decimal places)

So the probability that all 6 balls drawn from the urn are black is approximately 0.003.

There is an evidence that suggest that the survey is biased because the proportion of African Americans in the population, in our test, is less than 11%.

To determine if the survey is biased, we can use hypothesis testing.  Let's define our null hypothesis as: "the proportion of African Americans in the population is 11%". Let's define our alternative hypothesis as "the proportion of African Americans in the population is less than 11%".

We can then use a one-tailed z-test to test our hypothesis, with a significance level of 0.05. The formula for the test statistic is:

z = (p - P) / sqrt(P(1-P)/n)

Plugging in the values, we get:

z = (0.08 - 0.11) / sqrt(0.11(1-0.11)/600)

x = -2.23

Looking up the critical value for a one-tailed test with a significance level of 0.05, we find it to be -1.645. Since our calculated z-value (-2.23) is less than the critical value (-1.645), we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of African Americans in the population is less than 11%.

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The wavelength of red light is exactly the same as the wavelength of violet light, so it is not longer or shorter.

1. First, we need to identify the wavelengths of red light and violet light.

2. Red light has a wavelength of 8x10 to the -7 power meters and violet light has a wavelength of 8x10 to the -7 power meters.

3. Since both wavelengths are the same, the wavelength of red light is not longer or shorter than the wavelength of violet light.

The wavelength of light is measured in meters, and the wavelength of red light is 8x10 to the -7 power meters, while the wavelength of violet light is 8x10 to the -7 power meters. This means that both the wavelengths are exactly the same and the wavelength of red light is not longer or shorter than the wavelength of violet light. This is because the wavelength of light is a fundamental property that determines the color of light and the wavelength of red light and violet light are both the same.-

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The exponential decay model for the investment of $38,976 with decreased rate 3.5% for 't' years is equal to option b. 38,976 (0.965 )^t.

Invested amount by Kindred =  $38,976

Each year investment decreased by 3.5%

Number of years represented by 't' = 3 years

Amount decreased by 100 - 3.5% = 96.5%

                                                        = 0.965

Total amount decreased in three years = $38,976  × ( 0.965 )³

                                                                  = $35,025.085

Exponential decay model for 't' years at the same rate is given by the equation :

= 38,976  × ( 0.965 )^t

Therefore, the exponential decay model for the given situation of investment with decreasing rate is given by option b. 38,976 (0.965 )^t.

The above question is incomplete , the complete question is:

Kindred invested $38,976 into his first company. His investment decreased by 3.5% each year over the first 3 years. Which exponential decay model could Kindred use to determine the amount his investment will be worth if it continues to decrease at the same rate?

a. 38,976 (1.035 )^t

b. 38,976 (0.965 )^t

c. 38,976 (1 -r )^3.5

d. 38,976 (1 -r )^0.035

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Class A and Class C sell 187.5 altogether

Represent the classes with their initials

So, we have

B = 2A

C = 3/4 * B = 3/4 * 2A

C = 3/2A

The total number of bars they had initially was

A + B + C = Total

A + 2A + 3/2A = Total

Total = 4.5A

The average number of bars the 3 classes had initially was 225,

So

4.5A = 225

A = 75

For Class A and Class C together, we have

Class A and C = A + 3/2A

Class A and C = 75 + 3/2 * 75

Class A and C = 187.5

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The ball is 7 feet high when it leaves the child’s hand

Given that

h(x) = -x^2 + 6x + 7

When it leaves his hand, we have

x = 0

This gives

h(0) = -(0)^2 + 6(0) + 7

Evaluate

h(0) = 7

Here, we have

h(x) = -x^2 + 6x + 7

Differentiate and set to 0

-2x + 6 = 0

So, we have

x = 3

The maximum height is

hmax = -3^2 + 6(3) + 7

hmax = 16

This means that h(x) = 0

So, we have

-x^2 + 6x + 7 = 0

This gives

x^2 - 6x - 7 = 0

Expand

x^2 + x - 7x - 7 = 0

Factor

x(x + 1) -7(x + 1) = 0

So, we have

(x - 7)(x + 1) = 0

Solve for x

x = 7 or x = -1

Hence, the distance is 7 feet

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Answer: The tip is 20% of the cost including tax. Thus .20 * X=3.50.Divide both sides of the equation by .20..20 divided into .20 = 1, so “X” = 1.And 3.50 divided by .20 = 17.50 So X = 17.50, cost of the meal plus the tax.The tax is .07, so we know that 100% of the meal cost PLUS 7% of the meal cost is 107% of the meal cost. That is 1.07 * Meal without tax = 17.50. Divide 17.50 by 1.07 and you get 16.355. Round up to 16.36.Is that right? Let’s see:7% tax on meal at 16.36 is 16.36 * .07 = 1.1452. Round up to 1.15.$1.15 + 16.36 = 17.51.And 20% (the tip) of 17.51 is .20 * 17.51 = 3.50Cost of the whole meal; food, tax and tip is 16.36+1.15+3.50 = 21.01. 

Step-by-step explanation: my big brain

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{11}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{x}-\underset{x_1}{3}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 2 }\implies \cfrac{10}{x-3}=2\implies 10=2x-6 \\\\\\ 16=2x\implies \cfrac{16}{2}=x\implies \boxed{8=x}[/tex]

It is better to buy 2-64 oz bottles of liquid dish soap for $8.39.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Given that, the store sells 2-64 oz bottles of liquid dish soap for $8.39 or 3 - 40 oz bottles at $7.20.

2 pounds = 32 oz

So, 32+64=96 oz

Now, 8.39/96

= $0.087 per oz

Here, 3 - 40 oz = 88 oz

Unit rate = 7.20/88

= $0.081 per oz

Therefore, it is better to buy 2-64 oz bottles of liquid dish soap for $8.39.

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The probability of getting a heart on the fourth card but not before that is 0.2278

The probability of getting a heart on the fourth card can be calculated by multiplying the probability of not getting a heart in the first three cards by the probability of getting a heart on the fourth card.

The probability of not getting a heart in the first three cards can be calculated as follows:

(39/52) * (38/51) * (37/50) = 0.862

where 39/52 is the probability of not getting a heart on the first card, 38/51 is the probability of not getting a heart on the second card (given that no heart was drawn in the first card), and 37/50 is the probability of not getting a heart on the third card (given that no heart was drawn in the first two cards).

The probability of getting a heart on the fourth card can be calculated as follows:

13/49 = 0.265

where 13/49 is the probability of getting a heart on the fourth card (given that no heart was drawn in the first three cards).

So, the probability of getting a heart on the fourth card, but not before, can be calculated as:

0.862 * 0.265 = 0.2278

So, the chance of getting a heart on the fourth card, but not before, is approximately 22.78%.

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Answer:

-3x -4

Step-by-step explanation:

(-7x +1) + (4x-5)
= -7x +1 + 4x-5 (brackets are unnecessary due to the commutative law of addition)
= -3x -4

The expression evaluates to 14x + 22.

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

3/4(24x + 28) - (4x - 1)

We can start by simplifying the expression inside the parentheses:

3/4(24x + 28) - (4x - 1)

Remove the brackets

18x + 21 - 4x + 1

Evaluate the like terms

14x + 22

So, the value of the expression evaluates to 14x + 22.

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