The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with σ=10. Find the probability that a randomly selected chocolate bar will have :

The probability illustrated here is experimental. So the correct option is Option A

When we roll a dice which have a number 1 to 6, once. Then the probability of obtaining each number becomes

                                       P=1/6                                          

                                       =0.17

Now, when we roll a dice 12 times, the probability of obtaining each number becomes

                                    P = [1/6]¹²

As we can see here it is given that,

                                      P(5) = 2/3

                                              = 0.67

Which shows it is experimental probability rather than theoretical probability

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To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:sqrt 83, b

Step-by-step explanation:

After running the pump for 4 hours, the NTU measurement would be approximately 0.52.

To determine the NTU measurement after running the pump for 4 hours, we need to consider that the pump reduces the NTU by 10% each hour.

Here's the chart with the NTU values for each hour, rounded to the nearest hundredth:

Hours | NTU

0 | 0.80

1 | 0.72 (0.80 * (1 - 0.10) = 0.80 * 0.9)

2 | 0.65 (0.72 * (1 - 0.10) = 0.72 * 0.9)

3 | 0.58 (0.65 * (1 - 0.10) = 0.65 * 0.9)

4 | 0.52 (0.58 * (1 - 0.10) = 0.58 * 0.9)

After running the pump for 4 hours, the NTU measurement would be approximately 0.52.

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Approximately 84% (34% + 50%) of the jumpers were in the group jumping below 79.5 inches. This can be answered by the concept of Standard deviation.

In a high school high jump contest, the mean height was 76 inches, and the standard deviation was 3.5 inches. To find the percentage of jumpers below 79.5 inches, we first need to determine how many standard deviations away 79.5 inches is from the mean.

To do this, subtract the mean from 79.5 inches and divide by the standard deviation:
(79.5 - 76) / 3.5 = 3.5 / 3.5 = 1

So, 79.5 inches is 1 standard deviation above the mean. According to the empirical rule, approximately 68% of the data falls within 1 standard deviation of the mean in a normal distribution. Since we are looking for jumpers below 79.5 inches, we need to consider the lower half of this 68%, which is 34%. Additionally, 50% of the data is below the mean.

Therefore, approximately 84% (34% + 50%) of the jumpers were in the group jumping below 79.5 inches.

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The time taken by the service technician to change the oil in a car is soved by probability distribution, such as a normal distribution.

We would need to know the mean and standard deviation of the distribution to calculate the probability that a randomly selected technician will take at most 20 minutes.

If we assume that the mean time to change the oil is μ and the standard deviation is σ, we could use the cumulative distribution function (CDF) of the normal distribution to calculate the probability that a randomly selected technician will take at most 20 minutes:

P(X ≤ 20) = Φ((20 - μ) / σ)

where Φ(z) is the CDF of the standard normal distribution, which gives the probability that a standard normal random variable is less than or equal to z.

Without knowing the values of μ and σ, we can't calculate this probability. However, we could make some assumptions or estimates based on data or prior knowledge to come up with reasonable values for these parameters.

Alternatively, if we have discrete data on the time, we could use a different probability distribution, such as the binomial distribution.

In this case, we would need to know the sample size and the probability of a technician taking at most 20 minutes, and we could use the binomial probability mass function to calculate the probability of getting a certain number of technicians who meet this criterion.

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The factor of tree of 54 is prime numbers 2, 3, and 3.

To find the factor tree of 54, we can start by dividing 54 by its smallest prime factor, which is 2:

                  54

                 /   \

                2    27

Now, we can see that 27 is still divisible by 3, another prime factor:

                  54

                 /   \

                2    27

                    /   \

                   3     9

Next, we can see that 9 is divisible by 3 as well:

                  54

                 /   \

                2    27

                    /   \

                   3     9

                        /  \

                       3    3

We can see that all the numbers in the tree are prime factors, and the branches end with the number 2 and the two factors of 3. Therefore, the factor tree of 54 is:

  54

 /   \

2    27

    /   \

   3     9

        /  \

       3    3

This shows that 54 can be expressed as the product of its prime factors, which are 2, 3, and 3.

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Answer:

708

Step-by-step explanation:

We are adding 7 each time

15+7 = 22

22+7 = 29

29+7 = 36

So the common difference is 7

The first term is 15

The formula is

an = a1+d(n-1)  where n is the term number

an = 15+7(n-1)

We want to find the 100th term

a100 = 15+7(100-1)

a100 = 15+7(99)

       = 15+693

     = 708

Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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Answer:

C.....................m

SOLUTION

(c) The values of x for which f(x) = -1

Looking from the graph, this does not exist.

Hence the answer is "None"

(d) The values of x for which f(x) = -3

Looking form the graph, this is between 0 and 1

So we have this as

So in interval notation, the answer is

(e) The x-intercept is where the graph cuts the x-axis

The graph cuts the x-axis at -1

Hence the answer is (-1, 0)

Answer:

8384742

Step-by-step explanation:

Answer:

there is no cow there because they have been barn

Answer:

both are reciprocals

Step-by-step explanation:

15.

\(\frac{5}{8}\cdot \frac{16}{20}\\\\=\frac{5}{8}\cdot\frac{8}{5}=1\)

so they are reciprocals

17.

\(\frac{2}{3}\cdot\frac{12}{18}\\\\=\frac{2}{3}\cdot \frac{3}{2}=1\)

so they are reciprocals

A scaled score is a standard score that has been transformed into a specific scale. In this case, the scaled score is 583 on the HMH scale.

The quantile interval is the range of scores within which a particular score falls. In this case, the quantile interval is 835q to 985q, which means that the score of 583 falls within this range. This information may be used to compare a student's performance to a certain benchmark or to other students who have taken the same test.

A quantile interval is a range of values within a distribution of scores. In this case, the quantile interval for a score of 583 is 835q to 985q, which means that the score falls within the range of the 835th to 985th quantiles of the distribution. The quantile interval provides information about the relative standing of a score within the distribution, with lower quantile intervals indicating scores that are closer to the minimum of the distribution and higher quantile intervals indicating scores that are closer to the maximum of the distribution.

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Answer:

x = 32.5

Step-by-step explanation:

Answer:

A. -1

Step-by-step explanation:

To find the slope, subtract the x-coordinates, subtract the y-coordinates, lastly, divide the differences.

(3,1) (4,0)

3 - 4 = -1

1 - 0 = 1

-1 ÷ 1 = -1

-1 is the slope.

Answer:

55

Step-by-step explanation:

Answer:

2.1 hr

Step-by-step explanation:

[0.8 m × (100 cm)/(1 m)]/(38.2 cm/hr) = 2.1 hr

Solution:

Given;

The x-intercepts are;

CORRECT OPTION: D

Step-by-step explanation:

Equation of circle with center h,k and radius r

  (x-h)^2  + (y-k)^2  = r^2

for this one this becomes    (center  9,-2  and radius 4 )

  (x-9)^2 + ( y+2)^2 =  16

Answer:

29 feet

Step-by-step explanation:

14 × 3 = 42

100 - 42 = 58

58 ÷ 2 = 29

One of the longer chains is 29 feet long.

Hope this helps.

Answer: SHE MADE ANOTHER QUESTION!

Step-by-step explanation:

The point (3,-8) is a solution of the inverse of function. Then the coordinate of inverse of function.Because the coordinate of inverse function get interchanged with each others.

An inverse function that returns the original value for which a function has given the output. If f is bijective then inverse of f exists and if it does then f(x,y) will become f(y,x).in inverse function two coordinate x and y interchanged to each other.It get reverse process.

We can write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

By Interchange x and y. In other words, replace every x by a y and vice versa and Then solve for y.

At the end we replace y by f-1(x).

Now we get

f(x,y) =f(y,x)

f(-8,3)=f(3,-8)

Hence by interchanging we can find inverse of function.

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Answer:

1- \(\frac{1}{2}\)

2- 1

3- -2

Step-by-step explanation:

1-

Add the numbers : \(\frac{5}{10}\)

Reduce the fraction with 5 : \(\frac{1}{2}\)

Solution : \(\frac{1}{2}\)

2-

Calculate the difference: \(\frac{-3}{-3}\)

Divide: 1

Solution: 1

3-

Subtract the numbers: \(\frac{6}{-3}\)

Reduce the fraction : -2

Solution: -2

Answer:

1. 1/2 or (2,1)

2. 1 or (-3,-3)

3. -2/1 or (-3,6)

Step-by-step explanation:

1. 2-(-3) = 2 + 3 =5

   6-(-4)= 6 +  4= 10

so 1/2 or (2,1)

2. 1-4 = 1 + (-4) = -3

  -2-1 = -2 + (-1)= -3

so 1 or (-3,-3)

3.  12-6 = 12 + (-6) = 6

    2-5 = 2 + (-5) = -3

so  -2/1 or (-3,6)

Answer:

$33.35

Step-by-step explanation:

If the four friends shared it equally, we need to divide 133.4 by 4, which is 33.35.

Answer: $33.35

Step-by-step explanation:

133.40 / 4 = 33.35

each friend paid $33.35

Answer:

235

Step-by-step explanation:

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

An isomorphism is a bijective linear transformation, that is both one-to-one and onto. The determinant of a linear transformation can help determine if it is an isomorphism. If the determinant is non-zero, the linear transformation is invertible, and therefore an isomorphism. A linear transformation is an isomorphism if and only if its determinant is nonzero.
Additionally, another way to check if a linear transformation is an isomorphism is to check if the kernel, which is the set of all vectors that get mapped to zero, is equal to only the zero vector. If the kernel is only the zero vector, then the linear transformation is one-to-one and therefore an isomorphism.

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

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The value of gross margin is,

⇒ 30%

We have to given that;

A teddy bear sells for $5.00.

And, It only cost $3.50 to make.

Hence, The value of gross margin is,

⇒ Profit / Original cost x 100

⇒ (5 - 3.5) / 5 x 100

⇒ 1.5/5 x 100

⇒ 150/5

⇒ 30%

Thus, The gross margin is,

⇒ 30%

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The probability of getting two red balls when two balls are drawn without replacement from a jar containing 10 blue balls and 11 red balls is 11/42. We can use the formula for probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)

First, we need to determine the total number of outcomes. When two balls are drawn without replacement from a jar containing 10 blue balls and 11 red balls, there are 21 balls in total. Therefore, the total number of outcomes is:
Total number of outcomes = 21C2 = (21 x 20) / (2 x 1) = 210
Now, we need to determine the number of favorable outcomes, which is the number of ways to draw two red balls. There are 11 red balls in the jar, so the first ball drawn has a probability of 11/21 of being red. Once that ball is drawn, there are 10 red balls left in the jar, out of a total of 20 balls. Therefore, the second ball drawn has a probability of 10/20 = 1/2 of being red. We can multiply these probabilities to get the probability of drawing two red balls:
Probability of drawing two red balls = (11/21) x (10/20) = 55/210 = 11/42

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Answer:

y=4x+3

Step-by-step explanation:

For the slope you can do the reciprocal of 1/4 which is 4 and the y axis is 3 because from -3 to 0 it's 3.