A sample of 100 students was randomly selected from a middle school in a large city. These participants were asked to select their favorite type of pizza: pepperoni, cheese, veggie, or Hawaiian. Pizza preference and gender were recorded for each participant. The results of the survey are summarized in the table. Pepperoni Cheese Veggie Hawaiian Total
Male 37 18 2 7 64
Female 13 17 3 3 36
Total 50 35 5 10 100
Part A

What proportion of participants prefer cheese pizza? Enter your answer as a decimal value

Using Cramers Rule, X = 10.34, Y = 0.85. See the computations below.

Cramer's rule is an explicit formula in linear algebra for solving a system of linear expressions with as many equations as unknowns, and it is true whenever the system has a unique solution.

Given:

10x - 4y = 100; ..................1) and

8x - 100y = -2; ...................2)

First things first, let's pick off the variables we will need for Cramer's equation:

Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f. Therefore:

a = 10, b = -4, c = 100, d = 8, e = -100, f = -2

Step 1, calculate the denominator Delta (Δ):

Δ = a * e - b * d

Δ = (10 * -100) - (-4 * 8)

Δ = -1000 - -32

Δ = -968

Step 2, calculate the numerator for x

Numerator(x) = c * e - b * f

Numerator(x) = (100 * -100) - (-4 * -2)

Numerator(x) = -10000 - 8

Numerator(x) = -10008

X = Numerator (x) / Δ

x  = -10008/-968
x = 10.338842975207

x [tex]\approx[/tex] 10.34

y  =   Numerator(y)/Δ

y  =   -820/-968

y = 0.84710743801653

y [tex]\approx[/tex] 0.85

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a) The probability of a defect is  0.0668.

b. The process standard deviation can be reduced to  0.0062.

c. The advantage of reducing process variation is more efficient and reliable production process, as it reduces the need for inspection and rework.

Probability is the measure of the likelihood of an event occurring. It is used in various fields such as finance, engineering, and manufacturing to analyze and predict outcomes.

One company that utilizes probability in its production process is Motorola. In this scenario, Motorola uses the normal distribution, also known as the Gaussian distribution, to determine the probability of defects in their production process.

The normal distribution is a probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean represents the center of the distribution, while the standard deviation represents the spread of the distribution.

a. To determine the probability of a defect, we need to find the area under the normal distribution curve to the left or right of ounces. This area represents the probability of a defect occurring. We can use a standard normal distribution table or a calculator to find this area. The probability of a defect to four decimal places is approximately 0.0668.

If the production run is for 100 items, then the expected number of defects would be 0.0668 x 100 = 6.68. Since we cannot have fractional defects, we would round this number to the nearest whole number, which is 7.

b. If the process standard deviation is reduced to, then the probability of a defect will decrease. This is because a smaller standard deviation means the distribution is less spread out, and therefore, fewer items will fall outside the control limits.

To find the new probability of a defect, we would follow the same process as in part a. The probability of a defect to four decimal places is approximately 0.0062.

c. The advantage of reducing process variation is that it results in a larger distance between the mean and the control limits. This means that there is less chance of items falling outside the control limits, which in turn, reduces the probability of defects. This leads to a more efficient and reliable production process, as it reduces the need for inspection and rework. Additionally, it can lead to cost savings and improved customer satisfaction.

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Answer:The price of 10 pounds of cheese is 15.84$

Step-by-step explanation:

It's simple

The two statements  a iff b and (not a) iff (not b) has been explained

The two statements are known as biconditionals, which state that two statements are true if and only if each other.

"a iff b" means that "a" is true if "b" is true, and "a" is false if "b" is false. In other words, "a" and "b" have the same truth value.

"(not a) iff (not b)" means that "not a" is true if and only if "not b" is true, and "not a" is false if and only if "not b" is false.

Therefore, these two statements are equivalent because they express the same idea: "a" and "b" have the same truth value. If "a" is true, then "b" is true, and if "a" is false, then "b" is false. Similarly, if "b" is true, then "a" is true, and if "b" is false, then "a" is false.

These statements are true in cases where both "a" and "b" have the same truth value. If both are true or both are false, then the statements are true. If "a" is true and "b" is false, or vice versa, then the statements are false.

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Yes, both methods give the same result. The chain rule is used to differentiate a composite function, while the substitution method is used to differentiate a function after substituting a variable with its expression.

The chain rule is used to differentiate a composite function, which is a function of a function. To use the chain rule, we differentiate the inner function and multiply it by the derivative of the outer function. In this case, we would have

f(x) = ([tex]x^2 + 3x + 2[/tex]) and

g(x) = [tex]2x^3 + 5[/tex]

The derivative of f(x) would be 2x + 3 and the derivative of g(x) would be [tex]6x^2[/tex]. Taking the product of these two derivatives, we get

[tex]12x^3 + 18x^2[/tex],

which is the answer we get using the chain rule. The substitution method involves substituting a variable in a function with its expression. In this case, we substitute x with ([tex]x^2 + 3x + 2[/tex]). This gives us a new function that is a function of [tex]x^2 + 3x + 2[/tex]instead of x. We then differentiate this new function and the answer we get is the same as the one we got using the chain rule. Therefore, both methods give the same result and agree with each other.

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PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

163/30

Step-by-step explanation:

4 3/5 in mixed number form would be 23/5

5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.

23/5 + 5/6

in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.

23 times 6 = 138

5 times 6 = 30

5 times 5 = 25

5 times 6 = 30

138/30 + 25/30

at this point, we can simply just add the numerators

163/30

i hope this helps

The fraction of the students live more than 4 miles from school is 3/10.

A fraction represents a part of a number or any number of equal parts.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Given;

The percentage of students live more than 5 miles away=30%

Now,

The fraction;

=30/100

To convert it into the simplest from;

=30/100

=3/10

Therefore, the fraction in simplest form will be 3/10.

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The complete question is;

At Charles Walters Middle School, 30% of the students live more than 4 miles from school.What fraction of the students live more than 4 miles from school? Write your answer as a fraction in simplest form. ?​

Given the matrix, [tex]\begin{bmatrix}2 & 3 \\3 & 2 \end{bmatrix}[/tex], find its inverse.

First we need to find its determinant which can be done by using the following formula,

[tex]det=\begin{bmatrix}a & b \\c & d \end{bmatrix}=ad-cb[/tex]

Lets call  [tex]\begin{bmatrix}2 & 3 \\3 & 2 \end{bmatrix}[/tex] matrix "A."

So,

[tex]detA=(2)(2)-(3)(3)[/tex]

[tex]\Longrightarrow detA=4-9[/tex]

[tex]\Longrightarrow detA=-5[/tex]

We now have the determinant, we can now use the following formula to determine the inverse matrix,

[tex]A^{-1} =\frac{1}{detA} \begin{bmatrix}d & -b \\-c & a \end{bmatrix}[/tex]

[tex]A^{-1} =-\frac{1}{5} \begin{bmatrix}2 & -3 \\-3 & 2 \end{bmatrix}[/tex]

[tex]\Longrightarrow A^{-1} = \begin{bmatrix}2(-\frac{1}{5}) & -3(-\frac{1}{5}) \\-3(-\frac{1}{5}) & 2(-\frac{1}{5}) \end{bmatrix}[/tex]

[tex]\Longrightarrow A^{-1} = \begin{bmatrix}-\frac{2}{5} & \frac{3}{5} \\\frac{3}{5} & -\frac{2}{5}\end{bmatrix} \therefore \ Sol.[/tex]

*Note* I went a few more steps than the question needed. If you back up two steps on my answer is where they stopped. The last option is correct.

Answer:

58 11/12

Step-by-step explanation:

Add up each item within the suitcase + the suitcase after taking out the items to find the weight of the suitcase at the beginning.

30 + 7 1/4 + 21 2/3

Convert the fractions to have a common denominator

30 + 7 3/12 + 21 8/12

Add these up to get 58 11/12.

(i) The average values for the variables andre, pri gpa, and act is sum of all the values divided by the total number of values.

(ii) The model atenderte 5 b0 1 b1 prigpa 1 b2act 1 u in equation form  is atenderte = b₀ + b₁ x prigpa + b₂ x act + u

(iii) The slope coefficients is  b₁ and b₂

(iv) The predicted atenderte if prigpa 5 3.65 and act 5 20 is atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

(v) if student a has prigpa 5 3.1 and act 5 21 and student b has prigpa 5 2.1 and act 5 26, then the predicted difference in their attendance rates is  0.5

In this exercise, we will be exploring a regression model that predicts the attendance rate of students based on their academic performance variables. We will be using three variables to predict the attendance rate: "andre", "pri gpa", and "act". Here are the answers to the questions:

(i) To obtain the minimum, maximum, and average values for the variables "andre", "pri gpa", and "act", we need to first look at the data. The minimum value is the smallest value for each variable, the maximum value is the largest value for each variable, and the average value is the sum of all the values divided by the total number of values.

(ii) The regression model that predicts the attendance rate is written in equation form as

=> "atenderte = b₀ + b₁ x prigpa + b₂ x act + u".

This equation means that the predicted attendance rate (atenderte) is equal to the intercept (b₀) plus the product of the coefficient for "pri gpa" (b₁) and the value of "pri gpa" plus the product of the coefficient for "act" (b₂) and the value of "act".

(iii) The estimated slope coefficients (b₁ and b₂) tell us the expected change in the attendance rate for each one-unit increase in "pri gpa" or "act". If b₁ is positive, it means that as "pri gpa" increases, the attendance rate is expected to increase. Similarly, if b₂ is positive, it means that as "act" increases, the attendance rate is expected to increase.

(iv) To find the predicted attendance rate if "pri gpa" is 3.65 and "act" is 20, we can substitute these values into the regression equation:

atenderte = b₀ + b₁ x prigpa + b₂ x act + u

atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

This will give us the predicted attendance rate for a student with "pri gpa" of 3.65 and "act" of 20. If there are any students in the sample with these values of the explanatory variables, then their actual attendance rate should be close to the predicted value.

(v) To find the predicted difference in attendance rates between student A (with "pri gpa" of 3.1 and "act" of 21) and student B (with "pri gpa" of 2.1 and "act" of 26), we can first use the regression equation to predict the attendance rates for each student:

Student A:

atenderteA = b0 + b1 x 3.1 + b2 x 21 + u

Student B:

atenderteB = b0 + b1 x 2.1 + b2 x 26 + u

Then, we can take the difference between the predicted attendance rates for each student:

=> atenderteA - atenderteB

=> 52.6 - 52.1 = 0.5

This will give us the predicted difference in attendance rates between the two students.

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If the mechanic told Mr P that it will cost 50$ an hour to fix his car, then 50x will be the cost which Mr P has to pay.

An expression is combination of variables, numbers and operators.

Given that Mr P’s had some car issues and he took it into the car shop.

The mechanic told him that it will cost 50$ an hour to fix his car.

We need to find Mr P has to pay for car.

Let x represents the number of hours.

$50x represents the amount Mr P has to pay for car.

Hence, the expression 50x represents the cost Mr P has to pay for car.

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28.07 and 61.93 degree are the measure of other two angles.

The question talks about a triangle with 3 sides and angles. According to the trigonometry identities

sin x = 8/17

x = sin^1(8/17)

x = sin^-1(0.4708)
x = 28.07 degrees

Determine the measure of the longest leg

y = 45 - 28.07

y = 61.93 degrees

Hence the other two angle measures of a right triangle are 28.07 and 61.93 degree.

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The speed of the Atlas V Rocket was approximately 8,727.27 miles per hour, based on the given information that it could go one mile in 0.11 seconds.

To find the speed of the Atlas V Rocket, we need to use the formula:

speed = distance / time

In this case, the distance is 1 mile, which is equal to 1609.34 meters. The time is 110th of a second, which is equal to 0.1 seconds (since there are 10 tenths in a second).

So, plugging these values into the formula, we get:

speed = 1609.34 meters / 0.1 seconds

speed = 16093.4 meters per second

Therefore, the Atlas V Rocket traveled at a speed of 16093.4 meters per second.

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The correct order of the ratios from the least to the greatest is given below:

4/2, 11 to 2, 22:3, 30/4, 36:5

Least to greatest: 4/2 = 2, 11:2 = 5.5, 22:3 = 7.33, 30:4 = 7.5, 36:5 = 7.2

15/4, 19 to 5, 53/15, 4:1, 18 to 6

Least to greatest: 15/4 = 3.75, 19:5 = 3.8, 53:15 = 3.53, 4:1 = 4, 18:6 = 3

7:11, 8:12, 6:10, 1/2, 7:4

Least to greatest: 7:11 = 0.6364, 6:10 = 0.6, 8:12 = 0.6667, 1/2 = 0.5, 7:4 = 1.75

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Therefore,

The ratios listed in the question are ordered from least to greatest by converting each ratio into a decimal and comparing the values.

In each case, the fraction is divided, the ratio of two numbers is expressed as a decimal, and then the decimals are ordered from least to greatest.

For example, in the first list, the ratio "11 to 2" is expressed as the decimal 11/2, which is equal to 5.5. The other ratios are similarly expressed as decimals and then ordered to get the final answer.

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The geometric mean of 20 and 30 is 24.49.

What is geometric mean?

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

We are given two numbers as 20 and 30.

Formula for geometric mean is

G.M = √x₁ × ... × xₐ  

So, using this we get

⇒G.M = √20 × 30

⇒G.M = √600

⇒G.M = 24.49

Hence, the geometric mean of 20 and 30 is 24.49.

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Answer:

Step-by-step explanation:

Use PEMDAS to determine order of operations.

P = Parentheses

E = Exponents

M/D = Multiplication/Division

A/S = Addition/Subtraction

The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.

The next operation to perform is multiplication, which is 415 times (6.1 + 12).

The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.

6.1 + 12 = 18.1

8.3 - 415(18.1)

8.3 - 7511.5 = -7503.2

Based on the distance covered by Zebra and Giraffe in mentioned time, the Zebra can be said to run faster.

Firstly, the question requires a candidate to be familiar with the concept of speed. We know that speed is associated with distance and time as -

Speed = distance/time

So, taking the case for Giraffe

Speed = 280/20

Performing division

Speed = 14 m/s

Taking the case of Zebra

Speed = 204/12

Performing division

Speed = 17 m/s

We see that in unit time or one second, the distance covered by the two animals is different. The one covering larger distance comparatively will be said to run faster. So, zebra runs faster.

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The table of question is attached in the picture.

Answer:

The ratio computed shows that the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

How to illustrate the ratio?

From the information given, there are 36 marbles in the bag. The number of red marbles will be:

= 5/9 × 36

= 20 marbles

The number of blue marbles will be:

= 4/9 × 36

= 16 marbles

When a student removes 1 blue marble from the bag, the number of blue marbles will be:

= 16 - 1

= 15 marbles.

Therefore, the ratio of red to blue marbles will be:

= 20:15 = 4:3

Therefore, the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

4214.7 is the balance in the account after 2 months .

What does compound and simple interest mean?

A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.

                               Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.

P = $4200

R = 2.1% = 2.1/100 = 0.021  =

    T = 2 month = 2/12 = 1/6

   I = PRT

    = 4200 * 0.021 * 1/6 = 14.7

Amount = P + I = 4200 + 14.7  = 4214.7

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Two expressions p/12 and 12/p gives different values, and thus they are not equivalent so Darla is correct and Matt is incorrect.

A fraction represents a part of a whole.

To Check if Matt or Darla is correct, we need to check if the expressions 12 ÷ p and p ÷ 12 are equivalent.

To see whether the two fractions equivalent or not,  we can choose a specific value of p

Compare the two expressions.

let p = 6, then:

12 ÷ p

12 ÷ 6 = 2

p ÷ 12

6 ÷ 12 = 1/2

The two expressions give different values, and thus they are not equivalent.

Hence, Two expressions p/12 and 12/p gives different values, and thus they are not equivalent so Darla is correct and Matt is incorrect.

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Percentage of the tickets were discount tickets is 36 %, if 144 out of 400 tickets sold were discount tickets.

Percentage is a number or ratio that can be expressed as a fraction of 100. According to the question, at an amusement park, 144 out of 400 tickets sold were discount tickets.

This means total number of tickets = 400

number of discount tickets = 144

we, have to find percentage of the tickets were discount tickets

Let the percentage be x

therefore x% of 400 = 144

              [tex]\frac{x}{100}[/tex] * 400 = 144

               x = 144 ÷ 4

               x = 36

so, percentage of the tickets were discount tickets is 36%

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If Paul uses the function y = 8x + 38 to model the situation, then the model predicts a score of:

86 for 6 hours of homework.

In the given problem, we are given a linear equation of the form y = 8x + 38, where y represents the score obtained by Paul and x represents the number of hours of homework done by Paul.

To predict the score for 6 hours of homework, we need to substitute 6 for x in the equation and solve for y. By substituting x = 6 in the equation, we get:

Therefore, the model predicts a score of 86 for 6 hours of homework.

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One chocolate chip cookie costs $0.50. This is found by setting up two equations using the given information and solving for the cost of one cookie.

To solve this problem, we can assume that the cost of one jumbo popcorn is P and the cost of one chocolate chip cookie is C. We can then set up two equations based on the given information.

The first equation comes from Julia's purchase, which includes one jumbo popcorn and two chocolate chip cookies. We know the total cost is $5.0, so we can write:

1P + 2C = 5.0

The second equation comes from Marvin's purchase, which includes one jumbo popcorn and four chocolate chip cookies. We know the total cost is $6.0, so we can write:

1P + 4C = 6.0

To solve for the cost of one chocolate chip cookie, we can eliminate P by adding the two equations. This gives us:

2P + 6C = 11.0

Dividing both sides by 2, we get:

P + 3C = 5.5

We can then substitute the value of P in terms of C from either of the two original equations into this equation, and solve for C. In this case, it's easier to use the first equation:

1P + 2C = 5.0

P = 5.0 - 2C

Substituting into the equation we just obtained:

(5.0 - 2C) + 3C

= 5.5

Simplifying and solving for C, we get:

C = 0.5

Therefore, one chocolate chip cookie costs $0.50.

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The probability that a person responded Yes or was under the Age of 55 was C. 57 %

The probability that a person who responded either said yes or was under the Age of 55 is:

= Probability that a person answers yes + probability that a person is under 55 - Probability that a person was under 55 and answered yes

The probability a person who responded either said yes or was under the Age of 55 is therefore:

= ( 25 / 103 ) + ( 59 / 103 ) - 17 / 103

= 57 %

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Answer:  None of the above

Step-by-step explanation: It's none because we need to divide the 70 apples by the 4 in the sample ratio. That's 17.5. Now, we need to multiply 3 by that. So, 17.5 * 3 = 52.5. That's equal to about 53 oranges. But, as we see that is not an answer choice. So, I believe it's none of the above.

4:3 = 53:70 (about 53)

We can estimate that there is about 1000 joules of kinetic energy in an average size helium balloon.

The amount of kinetic energy in an average size helium balloon can be estimated using the ideal gas law and the equipartition theorem.

Assuming the balloon is filled with helium at room temperature (around 298 K) and atmospheric pressure (around 1 atm), the volume of the balloon can be estimated to be around 0.5 m^3. The number of helium atoms in the balloon can be estimated using Avogadro's number, which is around 6.02 x 10^23.

Using the equipartition theorem, we can estimate the average kinetic energy of each helium atom in the balloon. At room temperature, each atom has an average kinetic energy of (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K).

Therefore, the total kinetic energy of the helium atoms in the balloon can be estimated as:

KE = (3/2)kT * N

where N is the number of helium atoms in the balloon.

Plugging in the estimated values, we get:

KE = (3/2) * (1.38 x 10^-23 J/K) * 298 K * 6.02 x 10^23

KE ≈ 9.95 x 10^2 J

Therefore, An average-sized helium balloon contains roughly 1000 joules of kinetic energy, according to our estimation. It's important to note that this is just an estimate, and the actual amount of kinetic energy in a helium balloon can vary depending on a number of factors such as the temperature, pressure, and size of the balloon.

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Answer:

2/21

simplify 8/84

Answer:

The experimental probability of the next vehicle sold being a minivan is 8/84 = 1/10.

Step-by-step explanation:

The experimental probability of an event can be calculated by dividing the number of successful outcomes by the total number of trials. In this case, we want to find the probability of selling a minivan, so we want to find the number of minivans sold divided by the total number of vehicles sold.

Therefore, the experimental probability can be calculated as follows:

Number of minivans sold / Total number of vehicles sold = 8 / 84

So, the experimental probability that the next vehicle sold will be a minivan is 8/84.

The probability at least one of the two television does not work will be 7/9.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Suppose you just received a shipment of ten television. Five of the televisions are defective. If two televisions are randomly selected. Then the probability is given as,

P = (5/10) x (5 / 9) + (5/10) x (5/9) + (5/10) x (4/9)

P = 25/90 + 25/90 + 20/90

P = 70 / 90

P = 7/9

The probability at least one of the two television does not work will be 7/9.

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