Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 17%
C. 13%

Answer: 480 in²

Step-by-step explanation:

    To calculate the surface area, we will find the area of each side and add it together.

Area of the rectangular sides can be found with A = LW:

    A = LW

    A = (12 in)(10 in)

    A = 120 in²

    A = LW

    A = (12 in)(10 in)

    A = 120 in²

    A = LW

    A = (12 in)(12 in)

    A = 144 in²

All the rectangular sides added together:

    120 in² + 120 in² + 144 in² = 384 in²

    Now, we will find the triangle sides. The formula for a triangle is [tex]A=\frac{BH}{2}[/tex], but since we have two congruent triangles I will not be dividing by 2.

    A = BH

    A = (12 in)(8 in)

    A = 96 in²

Lastly, I will add them both together:

384 in² + 96 in² = 480 in²

Answer:

10*8y2

Step-by-step explanation:

The integer number that represents an 800 ft gain in elevation is given as follows:

+800.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For altitudes, the signs are given as follows:

Hence the integer number that represents an 800 ft gain in elevation is given as follows:

+800.

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Answer:

False

Step-by-step explanation:

The formula for the area of a circle is A = pi • r^2

Answer: False

Step-by-step explanation: A = [tex]\pi[/tex] [tex]r^{2}[/tex]

From the graph we can conclude that the x-intercept is (-2.0) and the y-intercept is (0, -4).

The graph is a logical representation of the data, to put it simply. It makes it easier for us to comprehend the facts. The numerical information gleaned via observation is referred to as data.

"Data" is derived from the Latin term datum, which means "something given."

Data are gradually gathered through observation after creating a study question. The data is then summarised, categorised, sorted, and graphically presented.

A variety of objectives are served by data and information: Data is the source of all information, whereas information can be inferred from data.

Here in the question,

From the graph we can see that the line intersects x-axis and y-axis at one point each.

So, the points where they intersect:

x-intercept is (-2.0).

y-intercept is (0, -4).

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The complete question is:

Finding intercepts of a nonlinear function give

The graph of a function is given below.

Give all y-intercepts and x-intercepts shown.

(a) y-intercept(s):

(b) x-intercept(s):

If there is more than one answer, separate them with commas.

Answer:

x=4

y=5

Step-by-step explanation:

Answer:

f(x) = x^2

Step-by-step explanation:

A function that does not have an inverse function is called a non-invertible or many-to-one function. An example of a non-invertible function is:

f(x) = x^2

To determine if a function is invertible, we need to check if it passes the horizontal line test. If a horizontal line intersects the graph of the function at more than one point, then the function is not invertible.

For the function f(x) = x^2, if we draw a horizontal line at any value of y, it will intersect the graph of the function at two points, one on the positive x-axis and the other on the negative x-axis.

Therefore, f(x) is not invertible, as it fails the horizontal line test.

In other words, there are multiple x-values that correspond to a single y-value. For example, both x = 2 and x = -2 have the same y-value of 4. As a result, there is no unique inverse function that could map a value of 4 back to a single x-value.

In conclusion, the function f(x) = x^2 is an example of a non-invertible function, as it fails the horizontal line test and does not have a unique inverse function.

The probability of winning the jackpot with one ticket is approximately 0.000000003724.

There are a total of C(41, 5) ways to choose five numbers from 41 white balls, and there are 35 possible choices for the gold ball.

Therefore, the total number of ways to win the jackpot is:

C(41, 5) * 35

And the total number of possible outcomes (i.e. all the combinations of 5 white balls and 1 gold ball) is:

C(41, 5) * 35 * C(5, 5)

Since there is only one winning combination, the probability of winning the jackpot is:

1 / (C(41, 5) * 35)

Plugging in the values, we get:

1 / (749,398,832 * 35) = 1 / 26,869,866,120

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The piecewise function graphed is defined as follows:

C)

A piecewise function is a function that is defined by multiple equations, each of which applies to a specific interval or set of inputs. The equations are pieced together to form a single function that describes the behavior of the function over its entire domain.

The intervals for this problem are given as follows:

For the first interval, we have a linear function with a slope of 1/2 and an intercept of 2, hence:

y = 1/2x + 2, x ≤ -1.

For the second interval, we have a quadratic function with a vertex of -1, hence:

y = 1/2x² - 1, x > -1.

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Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.

A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.

Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.

According to the given information:

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Therefore, the length of the altitude is 4.8 centimeters.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides and the size of its angles. The sum of the angles of a triangle is always 180 degrees. Triangles are used in various fields of mathematics and science, including trigonometry, geometry, and physics. They also have practical applications in fields such as construction, engineering, and architecture.

Here,

Let the altitude of the right triangle be 'h' and the hypotenuse be 'c'.

We know that the altitude of a right triangle divides the triangle into two similar triangles, which are also similar to the original triangle.

Therefore, we can set up the following proportion:

h/3.6 = 6.4/h

Simplifying, we get:

h² = 3.6 x 6.4

h² = 23.04

Taking the square root of both sides, we get:

h= √23.04

h = 4.8 centimeters

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The total possible points in the course is approximately 470.

Let's assume that the total possible points in the course is "x".

Since you needed 90% of the course total for an A, that means you needed to earn 90% of "x" to get an A. This is equivalent to 0.90x.

You missed an A by only 8 points, so your actual earned points must be 90% of "x" minus 8. This can be expressed as 0.90x - 8.

Given that your actual earned points for the course is 415, we can set up an equation:

0.90x - 8 = 415

Now, we can solve for "x" to determine the total possible points in the course:

0.90x = 415 + 8

0.90x = 423

x = 423 / 0.90

x ≈ 470

So, the total possible points in the course is approximately 470.

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Here are the answers to the above questions:

To calculate the locator and percentile, we need to first arrange the scores in ascending order:

6, 8, 11, 12, 14, 17, 20, 34, 36, 38, 47, 48, 49

a) To calculate the locator for the 52nd percentile, we use the following formula:

Lp = (p/100) * (N + 1)

where Lp is the locator for the pth percentile, p is the percentile we are interested in, and N is the total number of scores.

For the 52nd percentile, p = 52 and N = 13. Substituting these values into the formula, we get:

L52 = (52/100) * (13 + 1) = 6.72

Therefore, the locator for the 52nd percentile is 6.72.

b) To determine the 52nd percentile, we need to find the score corresponding to the locator L52. Looking at the ordered list of scores, we see that the score at position 6 is 17 and the score at position 7 is 20. Since the locator L52 falls between positions 6 and 7, we can use linear interpolation to estimate the 52nd percentile:

P52 = (7 - L52) / (7 - 6) * 50 + (L52 - 6) / (7 - 6) * 50

P52 = (7 - 6.72) / (7 - 6) * 50 + (6.72 - 6) / (7 - 6) * 50

P52 = 38 + 0.48 * 50

P52 = 61.4

Therefore, the 52nd percentile is approximately 61.4.

c) To find the percentage of scores that are above the 52nd percentile, we subtract the 52nd percentile from 100:

100 - 52 = 48

Therefore, approximately 48% of the scores in the dataset are above the 52nd percentile.

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The lower limit is 189.331 milligrams per one hundred milliliters, and the upper limit is 195.469 milligrams per one hundred milliliters.

To find the 90% confidence interval for the mean serum cholesterol level of all middle-aged women, we can use the formula:

CI = x' ± t(α/2, n-1) × (s/√n)

where:

x' is the sample mean serum cholesterol level

t(α/2, n-1) is the critical t-value for a two-tailed test with a 90% confidence level and n-1 degrees of freedom

s is the sample standard deviation of the serum cholesterol level

n is the sample size

Substituting the given values, we get:

CI = 192.4 ± t(0.05, 11) × (5.9/√12)

To find the critical t-value, we can use a t-distribution table or calculator. For a two-tailed test with 11 degrees of freedom and a 90% confidence level, the critical t-value is approximately 1.796.

Substituting this value and simplifying, we get:

CI = 192.4 ± 1.796 × 1.707

CI = 192.4 ± 3.069

Therefore, the 90% confidence interval for the mean serum cholesterol level of all middle-aged women is (189.331, 195.469).

This means that we can be 90% confident that the true mean serum cholesterol level for all middle-aged women falls within this interval.

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Answer:

To improve my math skills, I plan on doing the following:

1. Practice, practice, practice: I will practice math problems regularly, starting with simple problems and gradually increasing the difficulty level.

2. Use online resources: There are many online resources available that provide tutorials, practice problems, and videos to help with math skills. I will utilize these resources to supplement my learning.

3. Work with a tutor: I will consider working with a tutor if I need additional help with math concepts or if I'm struggling with specific problems.

4. Study regularly: I will set aside time each day to study math, even if it's just for a few minutes.

5. Ask questions: I will ask my teacher or tutor for help if I don't understand a concept or if I'm struggling with a problem.

6. Stay positive: I will maintain a positive attitude towards math and believe in my ability to improve my skills.

By following these steps, I'm confident that I can improve my math skills and become more confident in my abilities.

Answer:

"My plan for improving my math skills is to focus more on understanding and going over new concepts and practice problems. I also will try studying math concepts online and using a method of solving extra problems and applying math in the real world to better understand."

Step-by-step explanation:

By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).

We can use the formula for compound interest to solve this problem. The formula is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

A = the total amount in the account

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know the values for A, r, n, and t, so we can solve for P:

[tex]A = P(1 + r/n)^{(nt)[/tex]

[tex]22,099.87 = P(1 + 0.022/2)^{(2*13)[/tex]

[tex]22,099.87 = P(1.011)^{26[/tex]

22,099.87 = 1.329P

P = 22,099.87 / 1.329

P = 16,637.55

Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

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The value of the function when the quantity f divided by g of 8 is given by option D. 5.

The function are equal to,

f(x) = 3x + 1

g(x) = x - 3

The expression 'f divided by g of 8' means it is required to evaluate the function f(x) divided by g(x) at x=8.

First, find the individual values of function  f(8) and g(8) is equal to,

f(x) = 3x + 1

Substitute the value of x = 8 we get,

⇒ f(8) = 3(8) + 1

⇒ f(8) = 25

Now, for the function g(x),

g(x) = x - 3

Substitute the value of x = 8 we get,

⇒ g(8) = 8 - 3

⇒ g(8) = 5

Then, we can find the value of f(x) divided by g(x) at x=8 which is equal to,

f(x) / g(x)

= ( 3x + 1 )/ ( x - 3 )

= f(8) / g(8)

= 25 / 5

= 5

Therefore, the quantity function f divided by g of 8 is 5, which is option (D).

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The expression simplified can be written as:

6x³y  -7xy²

The correct option is the first one.

Here we have the following expression:

(4x³y - 2xy² + 3xy) + (2x³y - 5xy² - 3xy)

To simplify it, we need to group the like terms (this is terms with the same variables and correspondent exponents).

Then we can rewrite the expression as:

(4 + 2)x³y + (-2 - 5)xy² + (3 - 3)xy

6x³y  -7xy²

That is the expression simplified.

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Answer:

A:6x3y − 7xy2

Step-by-step explanation:

i took the test and got it right

Thus, Riley's maximum distance from the starting position is 55 inches.

When an input value has a defined output value in reality, functions can be applied. For instance, how long a car has been driving affects how far it has travelled (the output) (the input).

Riley is swaying on a playground swing. As stated in the table, let t denote the passing of time in seconds and let f(t) denote Riley's horizontal displacement from her starting location in inches.

t:   0 ,0.75, 1.5, 2.25, 3,  3.75, 4.5,  5.25,   6,  6.75

f(t): 0 ,38.9, 55, 38.9, 0, -28.9, -55, -38.9, 0, 38.9

Recall that f(t) is positive when Riley swings closest to the starting position and negative when Riley swings in behind starting position.

So,

started from 0 and travelled distance of 55 inches in 1.5 seconds.

She is advancing by up to 1.5 seconds.

Then she begins to move backward, returning to her starting location after 3 seconds, and continuing to do so for an additional 4.5 seconds at a distance of -55.

Then begin to advance and return to the starting position after six seconds

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The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .

The focus and directrix of the required parabola are as,

Focus (6, 0)

and, Directrix x = - 6

Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.

Therefore, the equation of the parabola is either of the form,

y² = 4ax

or, y2 = - 4ax

depending on which axis the parabola is in, that is whether negative or positive axis.

It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.

Hence, the parabola is of the form y² = 4ax.

Since, a = 6

Thus, the equation of the parabola is y² = 4(6)x

⇒ y² = 24x

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An inequality that matches this graph include the following: B} x ≥ -5.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the closed circle is at point -5 and increases to the right, an inequality that matches this graph is x ≥ -5.

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Answer:

 a.  1492 kg

  b.  20.8 m

Step-by-step explanation:

Given a tree is initially 20 m high and has a diameter of 0.5 m, you want the mass of the trunk if its density is 380 kg/m³. If it adds a growth ring of 4 mm per year and adds height of 0.2 m in the first year, you want the height of the tree after 5 years, assuming the same amount of wood is added each year.

The volume of the tree trunk is that of a cylinder. The formula is ...

  V = (π/4)d²h

  V = (π/4)(0.5 m)²(20 m) ≈ 3.9270 m³

The mass is the product of volume and density:

  M = Vρ

  M = (3.9270 m³)(380 kg/m³) ≈ 1492 kg

The mass of the tree trunk is about 1492 kg.

In the first year, the diameter of the tree increases by 8 mm, and the height increases by 0.2 m,. This means the volume of the tree increases to ...

  V = (π/4)(0.508 m)²(20.2 m) ≈ 4.0942 m³

The volume increase is the same each year for 5 years, so after 5 years, the volume is ...

  3.9270 m³ + 5(4.0942 -3.9270) m³ ≈ 4.7630 m³

At that time, the diameter is about 0.540 m. Solving the volume equation for the height, we find it to be ...

  h = 4v/(π·d²)

  h = 4(4.7630 m³)/(π·(0.54 m)²) ≈ 20.797 m

The height of the trunk after 5 years is about 20.8 m.

__

Additional comment

We note that the wood added in the first year includes the cylindrical shell represented by the tree ring, and a cylindrical "plug" that is 0.2 m high and equivalent in diameter to the rest of the tree. This seems an odd way for the tree to grow, but may be a reasonable approximation to the actual growth.

The height, diameter, and growth are all given to 1 significant figure. Hence the 4- and 3-significant figures used in the answers may be unsupported by the precision of the given numbers. Keeping 2 significant figures, we might report the initial mass as 1500 kg, and the final height as 21 m.

The graph is drawn by a function formulated to have the correct height at the x-intercept: v(d, h) - (final volume) = 0.

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The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

A number is [tex]6[/tex] more than half of the other number, which is x. This statement is represented by the mathematical equation [tex]\frac{x}{2} +6[/tex]. Mathematical expressions are used to solve complicated puzzles.

According to the problem,

The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

This is because it incorrectly adds [tex]1p to 0.035p[/tex], which would result in an overestimation of the population growth.

The correct way to calculate next year's population with a growth rate of [tex]3.5[/tex]% is to multiply the current population (p) by [tex]1[/tex] + [tex]0.035[/tex], as shown in the other three expressions: [tex]3.5p, 1.035p, (1+0.035)p[/tex].

Therefore,the expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

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The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

The straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:

Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life

The annual depreciation expense for the equipment is:

Depreciation expense = (cost - residual value) / useful life

Depreciation expense = ($212,000 - $14,000) / 15

Depreciation expense = $12,533.33 per year

The total depreciation expense for the first five years is:

Total depreciation expense = Depreciation expense x number of years

Total depreciation expense = $12,533.33 x 5

Total depreciation expense = $62,666.65

To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:

Book value = Cost - Total depreciation expense

Book value = $212,000 - $62,666.65

Book value = $149,333.35

Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

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The equation that represents the relationship between the distances each girl has run is: Marcia = -3/4 * k + 6.5

Let x be the distance run by Tamara in kilometers.

Since Tamara has completed 3/4 of the race, then x = 3/4 * k.

Since Tamara is 2.5 kilometers ahead of Marcia, then x - 2.5 = 4 - Marcia.

Substituting the first equation into the second equation, we get:

3/4 * k - 2.5 = 4 - Marcia

Multiplying both sides by -1, we get:

Marcia - 4 = -3/4 * k + 2.5

Adding 4 to both sides, we get:

Marcia = -3/4 * k + 6.5

Therefore, the equation that represents the relationship between the distances each girl has run is:

Marcia = -3/4 * k + 6.5

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Thus, equation shows the connection between the quantity of weeks, w, and the quantity of books gathered, b: b = 10w.

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (at which line crosses a vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

The table shows an increase of 10 volumes every week in the total number of books acquired.

Weeks (w) Books Collected (b)

1                   10

2                  20

3                  30

4                   40

As a result, the quantity of books gathered and the number of weeks (w) have a linear relationship (b). The following equation can be used to illustrate this relationship:

b = mw + c

where w is the number of weeks, m denotes the slope (rate of change), and c denotes the number of books aquired at week 0.

The weekly shift in the amount of books gathered, which is 10, is the slope (m). By adding one of the points from table to the equation, we can now get the y-intercept (c). Use the first and tenth points:

10 = 10 * 1 + c

c = 0

Currently, the following equation reflects the relationship among the number of weeks (w) as well as the quantity of books gathered (b):

b = 10w + 0

b = 10w

Thus, equation shows the connection between the quantity of weeks, w, and the quantity of books gathered, b: b = 10w.

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Complete question:

The data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1                   10

2                  20

3                  30

4                   40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

Answer:

To determine the number of students who voted for Candidate C, we need to first find what percent of the total votes they received. Looking at the graph, it appears that Candidate C received approximately 40% of the votes.

To find out how many students this represents, we can set up a proportion:

40% = C/150

Where C is the number of votes received by Candidate C.

To solve for C, we can cross-multiply:

0.4 x 150 = C

C = 60

Therefore, 60 students voted for Candidate C.

Charlotte's mistake was assuming that the percentage of votes for Candidate C directly corresponded to the number of students who voted for them. It's possible that more than one student voted for each candidate, and the percentage of votes represents the proportion of all votes each candidate received.

We can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml

To determine the optimal dosage amount A for each Delay Type, we need to first define the surge function for each delay type as:

Extended: f(t) = [tex]At^2e^-^0^.^3^t[/tex]

Medium: f(t) = [tex]At^3e^-^0^.^5^t[/tex]

Rapid: f(t) = [tex]At^3e^-^0^.^7^t[/tex]

To find the optimal dosage amount A, we need to maximize the treatment effect while ensuring that the dose does not exceed 100ng/ml at any time and falls to be at or below 20ng/ml by 24 hours.

The treatment effect can be calculated by integrating the surge function over time from 0 to 24 hours and then adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20ng/ml

For the Delay Type and dosage level selected, we can calculate the treatment effect over the first 24 hours by integrating the surge function from 0 to 24 hours.

Then, we can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml..

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The expected payoff for landing on a space of the board game is 2.67 points.

We need to multiply each possible outcome by its probability of occurring and then add all the products to get the expected payoff.

Let's begin by determining the likelihood of each outcome:

The number 8 appears four times, so the probability of getting an 8 is 4/12 = 1/3.

The number 1 appears four times, so the probability of getting a 1 is also 1/3.

The number -2 appears twice, so the probability of getting a -2 is 2/12 = 1/6.

The number - 4 shows up two times, so the likelihood of getting a - 4 is likewise 1/6.

After that, we add up each outcome by multiplying it by its probability:

Expected payoff = (8 * 1/3) + (8 * 1/3) + (8 * 1/3) + (8 * 1/3) + (1 * 1/3) + (1 * 1/3) + (-2 * 1/6) + (-2 * 1/6) + (-4 * 1/6) + (-4 * 1/6)

Expected payoff = 2.67

As a result, the expected reward for landing on a board game space is 2.67 points.

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Answer:

Angle 1 = 51.6°

Angle 2 = 38.4°

Step-by-step explanation:

All complimentary angles add up to 90°.

If two complimentary angles were congruent then their measures would both be 45°.

Since one angle's measure is 6.6° more than the other's measure, it's measure is 6.6° more than 45°

Vice versa for the second angle, its measure will be 6.6° less than 45°