47. Find the value of x

Include all three indicator variables (A1, A2, and A3) in the model

To allow different slopes in the relationship between X and Y for each level of the categorical variable, the model should include terms A1X and A2X in A1 and A2 respectively. For example, the model can be expressed as:

Bo + B1X + B2A1X + B3A2X + B4A3

where B2 and B3 represent the slope of the relationship between X and Y for people at levels 1 and 2 of the categorical variable, respectively. represent. The value of X remains constant.

Include all three indicator variables (A1, A2, and A3) in the model. This allows to compare the effect of a given level of a categorical variable on the response variable while keeping the value of X constant. For example, if you include only A1 and A2 in your model, you cannot compare the effects of level 3 of the categorical variables on the response.

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An SRS of size 26 is drawn from a population that has a Normal distribution, the standard error of the mean is 0.7844..

The standard error of the mean, or simply standard error, indicates how much the population mean can differ from the sample mean. It indicates how much the sample mean would change if the survey were repeated with new samples from a single population. It is calculated by dividing the standard deviation by the square root of the sample size.

We have given that,

SRS size , n = 26

The distribution is normal distribution,

Mean, u = 143.5

Standard deviations, sd = 4

standard error of the mean = sd/√n

= 4√26 = 0.7844

Hence, the standard error of mean is 0.7844..

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If the coordinates of (-6,4) satisfies the equations of the two lines, (-6,4) is the solution to the system of equations.

This means that if the two lines intersect at (-6,4), then (-6,4) is the solution to the system of equations.

This means that if you substitute -6 for x and 4 for y, both equations will be equal at (-6,4).

The graphic solution for a system of equations is obtained by the intersection point of all the lines that compose the system of linear equations, meaning that the ordered pair (x,y) of the intersection point will satisfy all the equations in the system.

This problem is incomplete, hence the answer was given in general terms.

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The interval of time after solving the inequality -16[tex]t^{2}[/tex] + 40t + 2 > 18 is 0.5 < t < 2

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).

-16[tex]t^{2}[/tex] + 40t -16 > 0

Dividing the equation by 8,

-2[tex]t^{2}[/tex] + 5t - 2 > 0

Rearrange gives,

2[tex]t^{2}[/tex]  - 5t + 2 < 0

Using middle term breaking,

(2t-1)(t-2) < 0

Hence, the interval is 0.5 < t < 2

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This is how the decay of radioactive nuclei is compared in the radioactive dice experiment. When a large number of six-sided dice are thrown at once, those that show a particular number are removed as decayed, while the remaining dice are counted as undecayed.

These address the undecayed cores after a given time stretch. After a second roll, the dice with the specific number representing decayed nuclei are taken out and the ones that remain are counted. The procedure is carried out a certain number of times, and as time passes, the number of dice that have not expired decreases.

Because the dice have six sides and the probability of each number being rolled is equal, only one of the numbers on the dice is considered decayed. The probability of one die decaying is 1/6, while the probability of not decaying is 5/6. Five of the six numbers are regarded as undecayed, as stated in the question: 5 won't decay, which is the most likely outcome.

The probability of decaying per unit of time is the definition of the dacay constant. Therefore, in the analogy, each time the dice are rolled can be thought of as the time interval, and a die has a probability of decaying of one sixth each time. If the initial number of dice is N0, the expected number of dice that will decay is 1/6*N0, so  = 1/6. The probability of undecayed dice multiplied by the initial number of dice after a first roll is the number of undecayed dice.

N1 = N0*(1-1/6) For a second roll, N2 = N0*(1-1/6) *(1-1/6) = N0*(1-1/6)2 If we say that n is the number of rolls, Nn = N0*(1-1/6)n Half-life is the time (rolls) required for half of the original number of dice to decay.

If probability of undecayed is 1 - 1/6, then N1 = N0*(1- As n is the number of rolls, we just need to clear it (applying logarithm properties) n = ln(0.5) / ln(1-1/6) n = 3.801 Half-life time denoted as T1/2 = 3.8 rolls The decay constant is inversely proportional to the number of faces; as more faces the dice have, the smaller the probability of decay, resulting in a smaller constant; consequently, the mean lifetime is equal to the As a result, the mean lifetime for a dice with six sides is equal to 6.

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Step-by-step explanation:

1/4 of 60

of will become multiplication sign

=1/4 ✖️ 60

= 60/4

=15

The number of lattice points in the first quadrant of the graph is equal to five (5).

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In Mathematics, a lattice point can be defined as a point on a graph whose ordered pair (x and y coordinates) are both positive and whole numbers.

By critically observing the graph of the function 3x + 4y = 59, we can reasonably infer and logically deduce that the number of lattice points in the first quadrant (where the ordered pair are both positive) are five (5).

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Answer:

To create a chocolate blend using 61% cocoa and 51% cocoa, 18 ounces of the 61% chocolate and an appropriate amount of the 51% cocoa are combined together. The exact amount of 51% cocoa required will depend on the desired concentration of the final blend.

Step-by-step explanation:

The probability of rainfall actually occurring tomorrow is 0.3465. The correct answer is therefore 0.3465.

To solve this problem, you can use Bayes' Theorem. Bayes' Theorem is a way to calculate the probability of an event occurring based on prior knowledge of conditions that might be related to the event.

In this case, we are trying to find the probability of rainfall occurring tomorrow, given that it has been predicted. Let's call this probability P(R|P), where R is the event of rainfall occurring and P is the event of rain being predicted.

According to the problem statement, the probability of rain occurring on any given day during the summer is 2/10, or P(R) = 0.2.

The probability of rain not occurring is 1 - P(R) = 0.8.

The probability of rain being predicted, given that it does rain, is 0.7, or P(P|R). The probability of rain being predicted, given that it does not rain, is 0.33, or P(P|¬R).

Using Bayes' Theorem, we can calculate the probability of rain occurring tomorrow as follows:

P(R|P) = [P(P|R) * P(R)] / [P(P|R) * P(R) + P(P|¬R) * P(¬R)]

Substituting in the values from the problem statement, we get:

P(R|P) = [0.7 * 0.2] / [0.7 * 0.2 + 0.33 * 0.8]

Simplifying this expression gives us:

P(R|P) = 0.3465

So the probability of rainfall actually occurring tomorrow is 0.3465.

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Answer:

90 * 1.33 = 119.7

The factors that  you need to consider when preparing to move gondolas are:

Height

width

length

color.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity

In choosing gondola one need to look at some  factor in decisions such as height.

Know that it is good to  consider the construction material and also the center wall configuration for its building also.

The factors that  you need to consider when preparing to move gondolas are:

Height

width

length

color.

Hence, Height, width, length and color are the other factors we need to consider while moving Gondola.

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The Fibonacci sequence is the sequence in which the numbers are written such that each succeeding number is sum of two preceding numbers.

The Fibonacci sequence is defined recursively as follows:

F0 = 0

F1 = 1

For n > 1, Fn = Fn-1 + Fn-2

(b) The sequence of partial sums is:

S0 = 0

S1 = 0 + 1 = 1

S2 = 0 + 1 + 1 = 2

S3 = 0 + 1 + 1 + 2 = 4

S4 = 0 + 1 + 1 + 2 + 3 = 7

S5 = 0 + 1 + 1 + 2 + 3 + 5 = 12

(c) A closed formula for the sequence of partial sums in terms of Fn is not possible, since the sequence of partial sums depends on the values of all previous terms in the Fibonacci sequence. However, it is possible to express the nth term of the sequence of partial sums, Sn, in terms of the nth term of the Fibonacci sequence, Fn, using the following formula:

Sn = F0 + F1 + ... + Fn = (F0 + F1) + (F1 + F2) + ... + (Fn-1 + Fn) = F1 + F2 + ... + Fn + F0 + F1 + ... + Fn-1 = 2Sn-1 - Fn + F0

This formula can be derived by considering the previous term in the sequence of partial sums and adding the current term of the Fibonacci sequence to it.

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The market research can increase the precision of the result of the study by  using a randomized block design RBD.

The best design the market research company should use for the study is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination

Reason:

The given parameters are;

The study = The effect of price and type of packaging

Number of stores in the study = 27 stores

Characteristics of the shoppers in the stores = Similar

Number of packaging type = 3 (three)

Number of price levels = 3 (three)

The number of pair combinations = ⁶₂C - (3, pairs of the same packaging +

3, pairs of the same prices) = 9

Required:

The best design to use for the study

Solution:

Given that the shoppers at each store are similar, in order to differentiate and show the effect of the price and package combination, it is possible to group the treatment into groups having a particular characteristics, while ensuring that the other available treatments are assigned to each member within a group at least once.

The above design of the study is known as a randomized block design,

Therefore the correct option is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combinations.

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Answer:

Step-by-step explanation:

You have a particle whose acceleration is a(t) = 3t²/160 -t³/800 and whose velocity at t=20 is 0. You want to show the initial speed is 0, find the maximum speed, and the distance traveled in 20 seconds.

The speed is the sum of the initial speed and that due to acceleration. The speed due to acceleration is the integral of acceleration:

  [tex]\displaystyle s(20)=s_0+\int_0^{20}{\dfrac{1}{800}(15t^2-t^3)\,dt}}=s_0+\left(\dfrac{t^3}{3200}(20-t)\right)_0^{20}=s_0=0[/tex]

The change in speed over 20 seconds is zero, so the final speed is the initial speed. The final speed is zero, so the initial speed is 0.

The maximum speed is where the acceleration is zero.

  a(t) = 0 = (t²/800)(15 -t)

The acceleration is zero at t=0 and at t=15.

From the above integral, the maximum speed is ...

  s(15) = 15³(20 -15)/3200 = 5.2734375 m/s ≈ 5.27 m/s

The distance traveled is the integral of the speed.

  [tex]\displaystyle d=\dfrac{1}{3200}\int_0^{20}{(20t^3-t^4)}\,dt=\left.\dfrac{t^4(25-t)}{16000}\right|_0^{20}}=50[/tex]

The particle traveled 50 meters from A to B.

The effective rate of the $8,000 note is (d) 0.10%

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

Principal, P = $8,000

Discount rate, r = 10%

Number of days, d = 90

The effective rate can be calculated using the following formula

Effective rate = (1 + (nominal rate ÷ number of compounding periods)) ^ (number of compounding periods) - 1

This can be expressed as

Effective rate = (1 + r/n)^n - 1

Substitute the known values in the above equation, so, we have the following representation

Effective rate = (1 + (10%/90))^(90) - 1

Evaluate

Effective rate = 0.10%

Hence, the effective rate is (d) 0.10%

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Answer:

Subtract 8 from both sides.

Divide both sides by 2.

Step-by-step explanation:

Here is an explanation.

In order to isolate the variable x, or solve for x, you need to undo the operations that are being done to x. To undo an operation, you must do the opposite operation.

The opposite of addition is subtraction.

Since 8 is being added to 2x, and you want to undo the addition of 8, you subtract 8. The rule is that you must do the same operation to both sides of the equation, so to get rid of the + 8 on the left side, you must do - 8 on both sides, like this:

2x + 8 = 10

2x + 8 - 8 = 10 - 8

2x = 2

By subtracting 8 from both sides, we got rid of the addition of 8 on the left side.

2x = 2

Now we have 2x. We want x alone. What operation is there between the 2 and the x in 2x? 2x means 2 times x. 2x is a multiplication. The opposite of multiplication is division. To undo the multiplication of x by 2, you need to divide the left side by 2. A division cancels out a multiplication. Once again, the rule is that you must do the same operation to both sides, so you must divide both sides by 2.

2x = 2

2x/2 = 2/2

x = 1

I hop that helps. If you have questions, just ask.

5, 8, 8, 5 has a population standard deviation of 3

Given,

The population is

{5, 8, 8, 5}

The population's mean is calculated as follows:

Sum of terms / Number of terms

Calculate the values and then replace them in the equation.

Sum equals 5 + 8 + 8 + 5 = 26

Number of terms = 4

The population's average is 26 / 4 = 6.5

The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²

= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²

= 2.25 + 2.25 + 2.25 + 2.25

= 9

The population's standard deviation is equal to

= 3

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Answer:

17.9 units (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the values of a and c into Pythagoras Theorem and solve for b:

[tex]\implies 11^2+b^2=21^2[/tex]

[tex]\implies 121+b^2=441[/tex]

[tex]\implies b^2=320[/tex]

[tex]\implies b=\sqrt{320}[/tex]

[tex]\implies b=17.88854...[/tex]

Therefore, the length of the third side is 17.9 units (nearest tenth).

Answer:

--------------------------------

Rocket is in the air until it hits the ground.

Therefore we need to find the value of t when h = 0.

The rocket is in the air for 6 seconds.

Answer:

6 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-16t^2+72t+144[/tex]

where:

To find how long the rocket is in the air, find the positive value of t when h(t)=0.

[tex]\implies -16t^2+72t+144=0[/tex]

[tex]\implies -8(2t^2-9t-18)=0[/tex]

[tex]\implies 2t^2-9t-18=0[/tex]

[tex]\implies 2t^2+3t-12t-18=0[/tex]

[tex]\implies t(2t+3)-6(2t+3)=0[/tex]

[tex]\implies (t-6)(2t+3)=0[/tex]

Apply the zero-product property:

[tex]t-6=0 \implies t=6[/tex]

[tex]2t+3=0 \implies t=-\dfrac{3}{2}[/tex]

Therefore, as t > 0, the rocket is in the air for 6 seconds.

No , the carpeted rooms does not have more bacteria than uncarpeted rooms .

Given ,

α=0.05

n1=8

n2 = 8

mean = ∑x / n

x1 = 11.8+10.8+7.1+14.6+8.2+10.1+13.0+14.0 / 8 = 11.2

and

x2 =12.1+12.0+3.8+10.1+8.3+11.1+7.2+13.7 /8 = 9.78

Variance ,

s1  =2.6

s2 = 3.2

HYPOTHESES

H0 : μ 1 =μ 2

H1 : μ 1  ≠μ 2

​Either the alternative hypothesis or the null hypothesis applies to the claim. The equality must be present in the null hypothesis. The alternative hypothesis declares the opposite of the null hypothesis if the claim is the null hypothesis.

On calculating we get the test statistic t as,

t = 1.771

The null hypothesis is rejected if the test statistic's value falls within the rejection zone.

0.956<1.771,

therefore , fail to reject H .

Therefore, there is no support for the null hypothesis, so we accept the alternate hypothesis as true.

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​

The interquartile range (IQR) of the salaries = 20

In descriptive statistics, the interquartile range is a measure of statistical dispersion, or the spread of the data. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the discrepancy between the data's 75th and 25th percentiles.

According to the given information

We are given that

Q1=50  and  Q3=70

Inter quartile range =IQR

                                = Q3 -Q1

                                = 70 - 50

                               = 20

The interquartile range (IQR) of the salaries = 20

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The percentage of sugar in the drink is 64%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The data given are;

The percentage of sugar in the carbohydrate can be calculated as;

Percentage = (16 / 25) * 100

Percentage = 0.64 * 100

Percentage = 64%

The percentage of sugar is 64%

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Answer:

x = 1

Step-by-step explanation:

2x + 8 = 10 ( isolate the x- term by subtracting 8 from both sides )

2x = 2 ( isolate x by dividing both sides by 2 )

x = 1

Aaron has 32 dimes and 8 quarters

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

Worth of coins = 520 cents

Type of coins = Dimes and quarters

Four times as many dimes as quarters

Represent the dimes with d and the quarters with q

So, we have the following representation

d = 4q

When the dimes and quarters are converted to dollars, we have the following representations

Dimes = $0.10

Quarters = $0.25

So, we have the following representation

0.10d + 0.25q = 5.20

Recall that

d = 4q

So, we have

0.10 * 4q + 0.25q = 5.20

Evaluate the products

0.65q = 5.20

Divide both sides by 0.65

q = 8

Recall that

d = 4q

So, we have

d = 4 * 8

Evaluate

d = 32

Hence, the number of dimes is 32

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True, Because in a transformation, the preimage is the original figure and the image is the figure in the new location.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The statement is,

''In a transformation, the preimage is the original figure and the image is the figure in the new location.''

Now,

Since, We know that;

The preimage is the original figure and the image is the figure in the new location.

Hence, In a transformation, the preimage is the original figure and the image is the figure in the new location.

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The coordinates of the circumcenter of this triangle are (3, 2) for the given triangle.

We know that -

The circumcenter is the point of intersection of the perpendicular bisectors of a triangle.

we have the coordinates A(-2, 5) , B(-2, -1), C(8, -1)

Let us find the midpoint AB using the midpoint formula as follows -

M = [tex](\frac{x_1 +x_2}{2}, \frac{y_1 +y_2}{2})[/tex]

substituting the values of A(-2, 5) and B(-2, -1), we get,

M = [tex](\frac{-2-2 }{2}, \frac{5-1}{2})[/tex]

M = (-2, -2)

Hence, the midpoint of segment AB is (-2,-2)

Similarly, we can find the midpoint of segment BC.

The midpoint of segment BC is (3,-1)

Let us now find the equation of the line perpendicular to the segment AB that passes through the point (-2,2).

This line is a horizontal line (parallel to the x-axis) hence, we get the equation y = 2.

Similarly, we can find the equation of the line perpendicular to the segment BC that passes through the point (3,-1).

This line is a vertical line (parallel to the y-axis) hence, we get the equation x = 3.

Finally, we will find the circumcentre of the triangle, which is the intersection of the line perpendicular to segment AB and the line perpendicular to segment BC i.e. (x, y) = (3, 2).

Hence, The coordinates of the circumcenter of this triangle are (3, 2).

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The target selling price per pair of boots is; $754

The computation of target selling price per pair of shoes is shown below:-

Return on investment =  $1,400,000 × 30%

= $420,000

Total variable cost = Variable manufacturing costs + Variable selling and administrative costs

= $36,000 + $18,000

= $54,000

Variable cost per unit = Total variable cost ÷ Planned production and sales

= $54,000 ÷ 1,000

= $54

Total Fixed cost = Fixed manufacturing costs + Fixed selling and administrative costs

= $120,000 + $80,000

= $200,000

Target profit = Total Contribution - Fixed cost

Total Contribution = Return on investment + Total Fixed cost

= $420,000 + $280,000

= $700,000

Contribution per unit = Total Contribution ÷Planned production and sales

= $700,000 ÷ 1000

= $700

Selling price per unit = Contribution per unit + Variable cost per unit

= $700 + $54

= $754

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The drinks are in ascending order based on the fraction of fruit they contain as follows:

Smoothie: 1:0:0 < Squash: 3:0:1 < Lemonade: 1:0:3 < Soda: 1:3:1.

The ratios of fruit to sugar to water in the four drinks are:

Lemonade: 1:0:3

Smoothie: 1:0:0

Soda: 1:3:1

Squash: 3:0:1

To put the drinks in ascending order based on the fraction of fruit they contain, we need to compare the fraction of fruit in each drink. Since the fraction of fruit is the ratio of fruit to the total amount of ingredients, we can calculate it by dividing the amount of fruit by the sum of the amounts of fruit, sugar, and water in each drink.

For lemonade, the fraction of fruit is 1/(1+0+3) = 1/4.

For the smoothie, the fraction of fruit is 1/(1+0+0) = 1.

For the soda, the fraction of fruit is 1/(1+3+1) = 1/5.

And for the squash, the fraction of fruit is 3/(3+0+1) = 3/4.

Based on these calculations, the drinks are listed in ascending order based on the percentage of fruit they contain.:

Smoothie: 1:0:0 < Squash: 3:0:1 < Lemonade: 1:0:3 < Soda: 1:3:1.

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The probability that fewer than 2 rolls result in snake eyes is approximately equal to 0.492.

To calculate the probability that fewer than 2 rolls result in snake eyes, we need to calculate the probability that exactly 0 rolls and the probability that exactly 1 roll result in snake eyes, and then sum these probabilities.

The probability that exactly 0 rolls result in snake eyes is given by the binomial probability formula:

P(exactly 0 rolls) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n = the number of rolls

k = the number of successful rolls (in this case, 0)

p = the probability of success on a single roll (in this case, 1/6, since there is a 1/6 probability of rolling snake eyes on a single roll)

Plugging in the values, we get:

P(exactly 0 rolls) = (5 choose 0) * (1/6)^0 * (5/6)^5 = 0.164

The probability that exactly 1 roll results in snake eyes can be calculated in a similar manner:

P(exactly 1 roll) = (5 choose 1) * (1/6)^1 * (5/6)^4 = 0.328

To get the probability that fewer than 2 rolls result in snake eyes, we sum these probabilities:

P(fewer than 2 rolls) = P(exactly 0 rolls) + P(exactly 1 roll) = 0.164 + 0.328 = 0.492

Therefore, it would not be surprising if fewer than 2 rolls result in snake eyes.

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Complete Question:

Question 2 (25 points) Calculating a binomial probability PROBLEM: When rolling two fair six-sided dice, getting a pair of ls is called "snake eyes." The probability of getting "snake eyes" on any roll is 1/36. Suppose that a game player rolls the two dice 80 times. Let X = the number of rolls that result in "snake cyes." Find P(X = 2). Interpret this value in context If two dice are rolled 80 times, then there is a 27.089% chance that we get a pair of snake eyes. Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.