Which option is an example of an experiment?
A. Counting how many times two sixes are rolled if two dice are
rolled 100 times
B. Testing the effectiveness of a new dog training class by allowing
one group to use it and comparing results against a control group
that doesn't use it
C. Asking moms how many times a week teenagers must be
reminded to do their chores
D. Asking students in a school how much time they spend exercising

\(\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = ±8}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

➺ \( {x}^{2} = 64\)

➺ \( \: x = \sqrt{64} \)

➺ \( \: x = \sqrt{8 \times 8} \)

➺ \( \: x = \sqrt{ ({8})^{2} } \)

➺ \( \: x = ±8\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So,  if a commutes with d, then it must be block diagonal.

Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,

d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),

where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.

Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.

Then, for any \(i \in {1, 2, \dots, k}\), we have

\(ad_{ii} = da_{ii}\)

Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and

hence

\(ad_{ij} = da_{ij} = 0\)

for all \(i \neq j\).

Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have

\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)

Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.

Therefore, if a commutes with d, then it must be block diagonal.

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A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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The amount of money in dollars I can save by using the lower-price vendor is 6750 dollars.

A percentage is a value per hundredth.

Brand A offers a list price of $400 per dozen for microwavable serving bowls and I want to order 500 dozen.

∴ The listed price I have to pay is (500×400) = 200000 dollars.

Given brand A offers a 35% of trade discount, So the actual price I have to pay is 65% of the listed price which is,

= (65/100)×200000 dollars.

= 130000 dollars for 500 dozens.

Similarly, brand B has a list price of $425 for a dozen and offers a 42% trade discount, So the price of 500 dozen microwavable serving bowels for the trade will be,

= (58/100)(425×500) dollars.

= 123250 dollars.

∴ The amount of money I will save is the lower the 6750 dollars.price vendor is

= (130000 - 123250) dollars.

= 6750 dollars.

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Answer:

A: On average, the number of students going to an office hour varies from the mean by about 2.2 students.

Step-by-step explanation:

We are given that:

- Random variable Q is used to represent the number of students who go to a certain teachers office hour each day.

-The standard deviation of Q is 2.2.

Now, standard deviation in relation to mean is defined as the statistic that measures the dispersion of a set of data relative to its mean.

Applying that definition to the question means that the number of students on the average varies from the mean by 2.2.

Thus, option A is correct.

Answer:

A: On average, the number of students going to an office hour varies from the mean by about 2.2 students.

Step-by-step explanation:

I second the person below me i got it right on asigmnemnt  

Answer:

Sin X = 15/17

Cos X = 8/17

Tan X = 15/8

Step-by-step explanation:

Recall, SOHCAHTOA.

Thus:

Sin X = opp/hyp

opp = 15

hyp = 17

✅Sin X = 15/17

Cos X = adj/hyp

Adj = 8

Hyp = 17

✅Cos X = 8/17

Tan X = opp/adj

Opp = 15

Adj = 8

✅Tan X = 15/8

Answer:

10c - 2

Step-by-step explanation:

Answer:

B. 10c + - 2

Step-by-step explanation:

(7c + 2) - (-3c + 4)

(7c + 2) - (-3c - 4)

7c + 2 + 3c - 4

10c + 2 - 4

10c - 2

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

The cardinal number of the set is 5.

The cardinal number of the given set A = {13, 19, 25, 31, 39} is 5.

Cardinal number is the number of elements present in a set, so counting the number of elements of the set will give us the cardinal number of the set.

In this case, we have the set A with 5 elements: 13, 19, 25, 31, and 39.

Thus, the cardinal number of the set is 5.

Hence, the answer is 5.

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Answer:

(-1, -2)

Step-by-step explanation:

If it is reflected in the Y-Axis the X-Axis will be opposite to its original value.

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Answer:

(-2, -1)

Step-by-step explanation:

Answer:

cyclist will travel 64 kilometres in 4 hours

Step-by-step explanation:

speed of cyclist = 10 miles per hour

given 1 mile is equal to 1.6 kilometres.

1*10 miles will be equal to 1.6*10 kilometres

thus , 10 mile is equal to 16 kilometres

using 16 km in place of 10 miles in 10 miles per hour

we have

speed of cyclist = 16 kilometres per hour

we know that distance = speed * time

speed is 16 kilometres per hour

time 4 hours

thus , distance = 16*4 kilometres= 64 kilometres.

cyclist will travel 64 kilometres in 4 hours.

(Hope this helps can I pls have brainlist (crown)☺️)

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

16, think of 4 plus 4 plus 4 plus 4.

2x + 3x + 3x + 12 = 180° [Sum of all angles of a triangle is 180°]

=> 7 x = 180° - 12°

=> 7 x = 168°

=> x = \(\frac{168}{7}\)°

=> x = 24°

\(\\\)

? = 2x + 3x

=> 2×24° + 3×24°

=> 48° + 72°

\(\\\\\\\)

HOPE IT HELPS

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The probability of getting a head and a prime number when a coin is flipped and a die rolled is 1/4

Probability is numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

.A die has 6 faces and a coin has 2 faces

Therefore Total outcome of a die is 6 and Total outcome of a coin is 2

probability for an event to occur is sample space/ total possible outcome

P(H)= 1/2

P(2,3,5)= 3/6= 1/2

therefore P(H)×P(2,3,5)= 1/2×1/2

= 1/4

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Answer:

9

Step-by-step explanation:

After considering all the given data we conclude that the measure of m∠E is 54.46° under the condition that ADEF is a right angled triangle.

We already know that ADEF is a right angled triangle having sides EF = 6 and FD = 4, we can apply the Pythagorean theorem to evaluate the length of the hypotenuse AD.
AD = √(6² + 4²)
= √52)
≈ 7.21
Now we can apply the sine function to find the measure of angle E.
sin(E) = opposite/hypotenuse = EF/AD
E = arcsin(EF/AD)
≈ 54.46°
Therefore,  m∠E  ≈ 54.46°.
The Pythagorean Theorem is considered a fundamental relation in the context of Euclidean geometry comparing the three sides of a right triangle.
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Answer:

790,000

Step-by-step explanation:

Take the place behind the place you're trying to round from, (thousands place in this case) and if that number is 5 or above, which it is, you round up. (790,000). If it's 4 or below, keep it as is.

The mixed numbers that have 12 as the LCD are 2 11/12 and 6 4/5. All other fractions do not have 12 as the denominator and are not equivalent.

Mixed numbers consist of a whole number and a fractional part. To add or subtract mixed numbers, the fractions must have the same denominator (the bottom number of the fraction).

The LCD (lowest common denominator) is the smallest number that all of the denominators can be divided into evenly. In this case, the LCD is 12.

2 11/12 and 6 4/5 both have 12 as the denominator. The denominator of 11/12 can be divided by 11 and 12, so it is the same as 12/12. The denominator of 4/5 can be divided by 4 and 12, so it is the same as 48/12 (4 x 12 = 48). Therefore, both fractions have the same denominator.

The other fractions do not have 12 as their denominator. 3 1/7 can be divided by 3, 7, and 12, so it is the same as 21/12 (3 x 7 = 21). 5 3/4 can be divided by 4, 5, and 12, so it is the same as 60/12 (4 x 5 = 60). 8 38/47 can be divided by 8, 47, and 12, so it is the same as 376/12 (8 x 47 = 376). Since none of these fractions are equal to 12/12, they are not equivalent to the other two fractions.

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Question :

Which mixed numbers have 12 as the LCD (lowest common denominator)?

2 11/12

3 1/7

5 3/4

6 4/5

8 38/47

Answer:

19.8

Step-by-step explanation:

Answer:

Do 99 divided by 5

Step-by-step explanation:

Use cross multiplication

Answer:

10240

Step-by-step explanation:

Answer:

If x = 3, then y = -2 since the corresponding value of y for x=3 is -2 in the given table.

Step-by-step explanation:

Answer:

Mean = 60

Median = 56

Mode = 48

Range = 32

Step-by-step explanation: You can find the Mean by adding all the number together then dividing by how many number in the problem. So, 48 + 64 + 80 + 48 = 240 then, divide by 4, which is how many numbers are in this equation.  You can find the Median by putting the numbers in the equation in order, 48, 48, 64, 80. Then, you will find what number is in the middle, or look at it as for the number in the middle to have the same amount of numbers on each side. So, in this case 48 and 64 are in the middle. There are two numbers in the middle instead of one, so you have to add them together to get 112 then divide by 2, because it is how many numbers you added together. You can find the Mode by seeing what number occurs the most, which in this case is 48, it appears two times. Sometimes, there will be no mode. You can find the Range by putting the numbers in order and subtracting the highest amount from the lowest amount, which in this case is 80 - 48 = 32. Hope this helps ^-^

The correct answers are:

Functions are expressions separated by an equal sign. They have both dependent and independent variables.

* Lets explain how to solve the problem

- The table of the function has two column

# First column labeled x with entries:

 -6 , 7 , 4 , 3 , -5

# Second column labeled f(x) with entries:

  8 , 3 , -5 , -2 , 12

∴ The ordered pairs of the function f(x) are:

 (-6 , 8) , (7 , 3) , (4 , -5) , (3 , -2) , (-5 , 12)

* Lets complete the missing

∵ The value of x in the first row is -6

∵ The value of f(x) in the first row is 8

∴ The function notation in the 1st row is f(-6) = 8

- The ordered pair given in the first row of the table can be

 written using function notation as f(-6) = 8

∵ The ordered pair whose x = 3 is (3 , -2)

∴ The value of f(x) when x = 3 is -2

∴ f(3) = -2

∵ The ordered pair whose f(x) = -5 is (4 , -5)

∴ The value of x when f(x) = -5 is 4

∴ f(x) = -5 when x is 4

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The sixth term of the geometric sequence is 2048.

The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.

The formula for the nth term (an) of a geometric sequence is given by:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:

an = 2 * 4^(n-1)

To find a6, we substitute n = 6 into the formula:

a6 = 2 * 4^(6-1)

  = 2 * 4^5

  = 2 * 1024

  = 2048

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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,

Then find a6. Round to the nearest tenth if necessary.

a = 5×4 X

a1 = n-1 X

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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See the attachment  for the graphed inequalities.

The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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