Help me with this work sheet please!

The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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The expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t

The cost to make one donut is $0.32.

Therefore, the cost to make one dozen donuts (12 donuts) is:

12 x $0.32 = $3.84

The cost of the cardboard for one box is $0.18 per square foot. Therefore, the cost of the cardboard for a box with surface area t (in square feet) is:

$0.18t

The total cost for one dozen donuts includes the cost to make the donuts and the cost of the box.

So, the expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t

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Answer:

(−4, 7), (−2, −5), (0, −9), (2, −5), (4, 7)

Step-by-step explanation:

The ordered pairs will be (−4, 7), (−2, −5), (0, −9), (2, −5), and (4, 7).

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair.

Given that  the equation is y = x² − 9 using x = −4, −2, 0, 2 and 4. The ordered pairs will be calculated as below:-

y = x² − 9 at x = -4

y =(-4)² - 9 = 16 - 9 =7

( -4,7)

y = x² − 9 at x = -2

y =(-2)² - 9 = 4 - 9 =-5

(−2, −5 )

y = x² − 9 at x = 0

y =(0)² - 9 = 0 - 9 =-9

(0, −9)

y = x² − 9 at x = 2

y =(2)² - 9 = 4 - 9 = -5

(2, −5)

y = x² − 9 at x = 4

y =(4)² - 9 = 16 - 9 = 7

(4, 7).

Therefore, the ordered pairs will be (−4, 7), (−2, −5), (0, −9), (2, −5), and (4, 7).

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Answer:

>1

Step-by-step explanation:

1/2 = 3/6

3/6 + 4/6 = 7/6

6/6 = 1 so this has 1/6 MORE than 1

the answer is >1

The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer: 8/10

Step-by-step explanation:

if you do 5/10 plus 3/10 it equals 8/10 and that is what the question is telling you to do.

Answer:

it would be clustered because the scores are all close together :)

It would be clustered because the scores are all close together.

We have given that,

The list shows the score of each game completed at a bowling alley during a one-hour period.

90, 96, 120, 124, 130, 135, 138, 140, 145, 148, 290, 290.

Grouping similar objects into common groups, also known as clustering, is an important problem of unsupervised machine learning.

We have to determine the data graphed on a horizontal number line appear to be clustered or skewed.

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Answer:$2,884

Step-by-step explanation:

Answer:

I think the trip would cost 2,884

Step-by-step explanation:

7×412=2,884

Answer:

a) 9 miles

b) 6 miles

c) 3 miles

Step-by-step explanation:

a)  Clare's speed = 12 mph

Calculate Clare's speed in miles per minute by dividing 12 by 60 (as there are 60 minutes in an hour):

12 ÷ 60 = 0.2 miles per minutes

Therefore, position after 45 minutes:  45 x 0.2 = 9 miles

b) Han's speed = 8 mph

Calculate Han's speed in miles per minute by dividing 8 by 60 (as there are 60 minutes in an hour):

8 ÷ 60 = 2/15 miles per minutes

Therefore, position after 45 minutes:  45 x 2/15 = 6 miles

c) Distance between Clare and Han = 9 - 6 = 3 miles

The absolute maximum value of f(x,y) = x² - 2y + 1 on the set R={(x,y): x² + y²≤9} is (25/2). So, the correct option is OA.

We have the function,f(x,y) = x² - 2y + 1 and set R= {(x,y): x² + y²≤9}

Let's find the absolute maximum value of f(x,y) in R. Therefore, we have to check the values of f(x,y) on the boundary of R which is x² + y² = 9f(x,y) = x² - 2y + 1

Now, we need to convert the above function into a single variable function.f(x,y) = x² - 2y + 1 = x² - 2y + 9 - 8

Now, replace x² + y² = 9 in the above function to get a single variable function.

f(x) = x² - 8y + 9

Now, differentiate the above function to find the critical points. f'(x) = 2x = 0 => x = 0

Putting this value of x in x² + y² = 9 to get the value of y.y² = 9 => y = ±3

Hence, the critical points are (0,3) and (0,-3). Now, let's find the value of f(x,y) at the critical points and the boundary of R to find the absolute maximum and minimum values of f(x,y).f(0,3) = 10f(0,-3) = 10

Now, let's find the value of f(x,y) on the boundary of R. f(x,y) = x² - 2y + 1At (x,y) = (±3,0)f(±3,0) = 10 f(x,y) has a critical point (0,3), which is the absolute maximum value in the set R={(x,y): x² + y²≤9}.

The absolute maximum value is (25/2). Therefore, the correct option is OA.

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The output when three workers are hired is 5 units..

To find the output when three workers are hired, we need to first determine the total cost and then use the marginal cost to calculate the output.

Find the total cost when three workers are hired.
Average total cost (ATC) = Total cost (TC) / Output (Q)
$50 = TC / Q
Since fixed cost (FC) is $130 and the marginal cost (MC) is $40 per worker, the total cost can be found by adding the fixed cost and the cost of the three workers.
TC = FC + 3(MC)
TC = $130 + 3($40)

Calculate the total cost.
TC = $130 + $120
TC = $250

Use the total cost and average total cost to find the output.
$50 = $250 / Q
Q = $250 / $50
Q = 5

Therefore, the output when three workers are hired is 5 units.

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To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.

Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.

Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.

When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.

Hence the unit of analysis is objective of the section.

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Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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Answer:

9

Step-by-step explanation:

1.08 divided by 0.12 equals 9

The probability of Jeremy selecting a jelly bean that is not lemon or orange is: 26/48 = 0.54 or 54%.

To find the probability that Jeremy randomly selects a jelly bean that is not lemon or orange, we need to first find the total number of jelly beans that are not lemon or orange.

The number of grape jelly beans is 10, the number of cherry jelly beans is 16, so the total number of jelly beans that are not lemon or orange is:

10 + 16 = 26

The total number of jelly beans in the dish is:

10 + 8 + 14 + 16 = 48

Therefore, the probability of Jeremy selecting a jelly bean that is not lemon or orange is:

26/48 = 0.54 or 54%.

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The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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The solution is x^-5y^3 = y^3/x^5.

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

x^-5×y^3      

[ as, the power of x is negative 5, so, we make it positive 5 by dividing}

=1/x^5 * y^3

=y^3/x^5

Hence, The solution is x^-5y^3 = y^3/x^5.

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Using the tangent ratio, the length of side p in the right-angled triangle is: p = 15√2.

The formula to use to find the length of side p in the given right-angled triangle above is the Tangent Ratio, which is given as:

Tan θ = opposite/adjacent.

Given the following:

Reference angle (θ) = 60°

Opposite = p

Adjacent = 5√6 cm.

Substitute

tan 60 = p / 5/√6

√3 = p / 5√6 (tan 60° = √3)

√3 * 5√6 = p

p = √3 * 5√6

p = 5√18

p = 5 * 3√2

p = 15√2

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Length of the median of the triangle is b. 18

How to find the length of the median of a triangle?
Given that the centroid of a triangle is located 12 units from one of the vertices of a triangle. We need to find the length of the median of the triangle drawn from that same vertex.

Let ABC be a triangle.

Let AD be median of the triangle.

Let E be centroid of ΔABC

Length of the median of triangle = AD

AD = Length of AE + Length of ED

But,

AE = 12

ED = x

So,

AD = 12 + x

Since, centroid divides median in 2:1 ratio.

Then,

\(12 : x = 2 : 1\\12/x = 2/1\\\\12= 2x\\\)

Divide by 2 each side

\(x = 6\)

So,  AD = 12 + x = 12 + 6 = 18

Thus, Length of the median of triangle is 18.

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Function

It is a function

Answer:

i dont have an answere but i would suggest the app desmos for the graphing part

Answer:

x^2 + y^ = 36

Step-by-step explanation:

See attached worksheet.

Answer: 0=1620=162

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Answer:

C

Step-by-step explanation:

When you multiply -1(x+8)(x+7)

                                 (-x-8)(x+7)

                                  -x(x+7)-8(x+7)

                                   \(-x^{2}-15x-56\)

Answer:

  -1/11, +1/11

Step-by-step explanation:

You want the two square roots of 1/121.

A square root can be either positive or negative.

  \(\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}\)

__

Additional comment

The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).