Angie’s rotation maps triangle XYZ to triangle X’Y’Z’.

X(3, –6) maps to X’(–3, 6)
Y(1, –2) maps to Y’(–1, 2)
Z(–1, –5) maps to Z’(1, 5)

Which describes the rotation?

Sampling distribution type distribution is simulated with the sample proportion with n = 15 and p = 0.65.

It is defined as a probability distribution of a statistic that is from a larger number of samples from a specific population.

We are given that

The probability of tails of a weighted coin, p=0.65 and n=15

We have to find the type of distribution that is simulated if this procedure is repeated 100 times.

The random variable is a proportion of a number of tails therefore, the type of distribution is the sampling distribution of the sample proportion.

Probability is something that is to happen.

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Using the TI-83 Plus/TI-84 Plus calculator, the probability that the sample mean (x) will be between 25 and 27 is calculated to be approximately 0.7468. The 55th percentile of the population is estimated to be 26.38.

(a) To find the probability that x will be between 25 and 27, we use the Central Limit Theorem and assume that x follows a normal distribution.

With a sample size of 126, the mean of the distribution is still 26 (the same as the population mean), but the standard deviation is now σ/√n = 3/√126 ≈ 0.2673.

Using the calculator's normal distribution function, we find the probability to be approximately 0.7468.

(b) To find the 55th percentile of the population, we want to determine the value below which 55% of the data falls. Using the inverse normal distribution function on the calculator, we input the percentile (55%) and the mean (26) with the standard deviation (3), and obtain an estimated value of 26.38.

This means that approximately 55% of the population has a value below 26.38.

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Answer:

20

Step-by-step explanation:

28 - {8/2 x (6-2)} + (4 - 2) ^ 3

28 - {4 x 4} + 2^3

28 - 16 + 8

12 + 8                

20

If A is a symmetric matrix, then A³ is also a symmetric matrix.

To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.

Now, let's look at A³:

A³ = A * A * A

We can replace each A with A^T, since they are equal:

A³ = A^T * A^T * A^T

Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:

A³ = (A^T * A^T * A^T)^T

A³ = (A^T)^T * (A^T)^T * (A^T)^T

Since the transpose of a transpose is the original matrix, we can simplify:

A³ = A * A * A

Therefore, A³ is also a symmetric matrix.

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Answer:

539.7

Step-by-step explanation:

Multiply 25.7 to 21 to get the answer.

Answer:

539.7 pounds

Step-by-step explanation:

you have 21 cartons and each one weights 25.7 pounds so you do 21•25.7=539.7

The diameter of each round pizza should be approximately d ≈ 2r ≈ 39.6

Rounding to the nearest tenth, we get a diameter of 39.6 cm.

The rectangular pizza has an area of:

35 cm x 70 cm = 2450 \(cm^2\)

Dividing the area by 24 gives us the area of each square piece:

\(2450 cm^2 / 24 = 102.08 cm^2\)

For the round pizzas, each slice is a sector of the circle, and the area of each sector is given by:

\(A = (θ/360)\pi r^2\)

where θ is the angle of the sector in degrees, and r is the radius (half the diameter) of the circle.

Since each round pizza is cut into 12 slices, each slice covers an angle of:

θ = 360/12 = 30 degrees

We want the area of each slice to be equal to the area of each square piece from the rectangular pizza, which is 102.08 \(cm^2\). Therefore, we can set up the equation:

\((30/360)\pi r^2 = 102.08\)

Simplifying, we get:

\(\pi r^2/12 = 102.08\)

\(\pi r^2 = 1224.96\)

\(r^2\) ≈ 391.2

r ≈ 19.8

Therefore, the diameter of each round pizza should be approximately:

d ≈ 2r ≈ 39.6

Rounding to the nearest tenth, we get a diameter of 39.6 cm.

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The most appropriate characterization for a student with a percentile rank of 75 is that they scored higher than 75% of the test takers. The correct option is C.

A student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers (Option C).

Percentile rank represents the percentage of scores that fall below a particular score. In this case, a percentile rank of 75 means that the student's score is higher than 75% of the test takers. Put differently, if 100 students took the test, the student would have performed better than 75 of those students.

Option A, ranking 75th from the top in a group of 100 test takers, is incorrect because the percentile rank represents the relative position of the student's score within the entire distribution, not just within a specific group of test takers.

Option B, answering 75% of the test questions correctly, is incorrect because the percentile rank does not directly measure the percentage of correct answers. It reflects the student's position relative to other test takers, regardless of the number of questions answered correctly.

Option D, scoring 75% higher than the average test taker, and Option E, scoring 75% of the highest score, do not accurately describe the meaning of percentile rank.

Therefore, the most appropriate characterization for a student with a percentile rank of 75 is that they scored higher than 75% of the test takers.

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Answer:

29

Step-by-step explanation:

showing what equal it is to it

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b  So now we know the y-intercept and slope. We just put them together now

y=3x-7

Answer:

1990

Step-by-step explanation:

Since the mother was 50 years old in 2000, she was 50 - (2000-1974) = 50 - 26 = 24 years old in 1974.

Hence, the daughter was 24/6 = 4 years old in 1974.

In "x" years after 1974, the daughter will be 4+x years old, while the mother will be 24+x years old.

We need to find "x" from the equation

2(4 + x) = 24+x.

8 + 2x = 24 + x,

x = 24 - 8 = 16.

1974 + 16 = 1990.

Answer In 1990 the mother doubles her daughter's age

Check In 1990 mother's age is/was 24 + 16 = 40 years.

In 1990 the daughter's age is/was 4 + 16 = 20 years.

Given the following equations C = 100 + 0.6YDI = 200G = 150T = 0.1YM = 100 + 0.2YX = 200V- = V - TWe can obtain the equilibrium GDP value by using the formula Y = C + I + G + X - M

We are given that T = 0.1Y and V- = V - T

Therefore, V - 0.1Y = 0.8YD0.9Y = V

We can substitute the value of T and V in the consumption function,

C = 100 + 0.6YD and get

C = 100 + 0.6(0.8Y)C = 100 + 0.48YC + I + G + X - M

= Y

Substituting the given values, we get

100 + 0.48Y + 200 + 150 + 200 - (100 + 0.2Y) = YY

= 900/1.06

≈849.05

Therefore, equilibrium GDP is approximately 849.05.

The equilibrium GDP value for the given equations is approximately 849.05.

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer:

8x +36

Step-by-step explanation:

(-2x - 9)(-4).

Distribute

-4* -2x  -4 * -9

8x +36

Answer:

8x + 36

Step-by-step explanation:

Because everytime you multiply 2 negative numbers the sign changes to plus.

The times spent in training is an illustration of proportions

The times spent in training is 80 hours

The given parameters are:

Time spent = 6 hours

Time spent as a percentage = 7.5%

Let the total time spent in training be x.

The scenario is represented by the following equation

Time spent = Time spent as a percentage  * Total Time

So, we have:

6 = 7.5% * x

Express percentage as decimal

6 = 0.075 * x

Divide both sides by 0.075

80 = x

Rewrite as:

x = 80

Hence, the times spent in training is 80 hours

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Solving a system of equations we will see that the two numbers are:

4 - √384*i and 4 + √384*i.

We want to find two numbers x and y such that the product is 400 and the sum is 8, then we can write a system of equations:

x*y = 400

x + y = 8

Let's isolate x on the second equation to geT:

x = 8 - y

And replace that in the first equation to get:

(8 - y)*y = 400

8y - y² = 400

Now we have the quadratic equation:

-y²  + 8y - 400 = 0

Using the quadratic formula we will get:

\(y = \frac{-8 \pm \sqrt{8^2 - 4*(-1)*-400} }{2*-1} \\\\y = \frac{-8 \pm \sqrt{-1,536} }{-2} \\\\y = 4 \pm \sqrt{384}i\)

So there are two possible values of y.

if we take the first one, then:

y = 4 + √384*i

In this case the value of x will be:

x = 8 - y = 8 - (4 + √384*i) =  4 - √384*i

We got the other value for x.

So the two numbers are  4 - √384*i and 4 + √384*i.

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the total amount of money that jayden made when both paychecks were the same is $99.45

To determine the number of hours Jayden worked the week his paycheck was the same for both jobs, we can solve an equation. The equation we'll use is 14.86h + 17.10 = 99.45. We can subtract 17.10 from both sides, leaving 14.86h = 82.35. Then we cane b divide both sides of the equation by 14.86, which will give us the result of h = 5.55 hours. The total amount of money that Jayden made when both paychecks were the same is 99.45. This can be confirmed by combining his earnings for both jobs, which would be 9.64h + 82.35 + 14.86h + 17.10 = 99.45.

Jayden worked 5.55 hours in the week his paycheck was the same for both jobs, and he earned a total of $99.45.

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Answer:

Step-by-step explanation:

Angles x and z are supplementary, meaning that they add up to 180.  From the markings on the diagram, angle z and the angle measuring 20 are complementary, meaning they add up to 90. So the game plan is to find out the measure of angle z first, then use that to find the measure of angle x.

angle z = 90 - 20 so

angle z = 70 degrees. And

angle z + angle x = 180.  Subbing in our value for z:

70 + angle x = 180 and

angle x = 180 - 70 so

angle x = 110 degrees

A scatter plot which represents relationship between the street distance (in centimeters) and weight (in Newtons) has been plotted in the image attached below.

In this scenario, the street distance (in centimeters) would be plotted on the x-axis (x-coordinate) of the scatter plot while the weight (in Newtons) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the street distance (in centimeters) and weight (in Newtons), a linear equation for the line of best fit is given by:

y = 1.30x - 2.30

In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates a linear relationship between the street distance (in centimeters) and weight (in Newtons).

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Answer:9

Step-by-step explanation

the equation (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions. Therefore the correct option is a.

To determine which equation(s) have both 2 and -5 as solutions, substitute these values into each equation and see if they satisfy the equation. Let's check each option:

a. \(x^2 + 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 + 3(2) - 10 = 4 + 6 - 10 = 0\)

Substituting x = -5:

\((-5)^2 + 3(-5) - 10 = 25 - 15 - 10 = 0\)

Both 2 and -5 satisfy the equation, so option a has both 2 and -5 as solutions.

b. \(x^2 - 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 - 3(2) - 10 = 4 - 6 - 10 = -12\)

Substituting x = -5:

\((-5)^2 - 3(-5) - 10 = 25 + 15 - 10 = 30\)

Neither 2 nor -5 satisfy the equation, so option b does not have both 2 and -5 as solutions.

c. \(x^2 + 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 + 7(2) + 10 = 4 + 14 + 10 = 28\)

Substituting x = -5:

\((-5)^2 + 7(-5) + 10 = 25 - 35 + 10 = 0\)

Only -5 satisfies the equation, so option c does not have both 2 and -5 as solutions.

d. \(x^2 - 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 - 7(2) + 10 = 4 - 14 + 10 = 0\)

Substituting x = -5:

\((-5)^2 - 7(-5) + 10 = 25 + 35 + 10 = 70\)

Only 2 satisfies the equation, so option d does not have both 2 and -5 as solutions.

In conclusion, the equation in option a (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions.

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The number of cars that must be made to minimize the unit cost is 300 cars which is determined by differentiation.

Differentiation is a mathematical process that determines the instantaneous rate of change of a function based on one of its variables. The most common example is velocity, which is the rate of change of displacement with respect to time. Anti-differentiation is the inverse of finding a derivative.
Differentiation is used to calculate the rate of change of quantities in real time.

Since, we have been given the cost function to be function \((cx)= 1.1^{2} - 660x+107,357\) then we have to find the first differentiation in order to get the value and this will be:-

\((cx)= 1.1^{2} -660x+107,357\\2.2x=660\\x=\frac{660}{2.2} \\x=300\)

Therefore, the number of cars that must be made to minimize the unit cost is 300 cars.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The number of the 1(3/4) inch blocks will be 34 out of the 5 feet of stock.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 1 3/4-inch long machine bolt blanks can be cut from a 5-foot length of the stock. The number of the blocks will be calculated as below:-

Number = 5 foot / ( 1(3/4)

Number = 60 / ( 7/4)

Number = 34.2

Therefore, the number of the 1(3/4) inch blocks will be 34.

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Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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9514 1404 393

Answer:

  $14

Step-by-step explanation:

Computing 40% can be done a couple of ways.

  40% = 40/100 = 4/10 = 2/5

  40% of 35 = (2/5)(35) = 2(35/5) = 2(7) = 14

__

  40% = 4/10 = 2(2(1/10))

  40% of 36 = 2(2(1/10)(35)) = 2(2(3.5)) = 2(7) = 14

The amount discounted is $14.

Answer:

89010

Step-by-step explanation:

1978 times 45 will equal 89010 its very simple step wise.

Answer:

89010

Step-by-step explanation:

Answer:

c.5p

Step-by-step explanation:

we know that p + 4p can be simplified as 5 p.

Therefore when compared if theses 2 are equal or not , p+4p=5p

we can simply add p+4p(as p is 1p) which gives 5 p

Answer:

5p

Step-by-step explanation: