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To determine the percentage of Sara's students who answered at least half of the quiz questions incorrectly, we need more information than the relative cumulative frequency of students who earned a score of 21 or higher.

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The mean is 18.6.

Given the following information; z = 2.25, x = 22.2, and σ = 1.6, to find the mean, we have to apply the formula for z-score. z = (x - μ)/σWhere; z-score is represented by z, the value of X is represented by x, the mean is represented by μ and the standard deviation is represented by σSubstituting the values into the equation above;2.25 = (22.2 - μ)/1.6Multiplying both sides of the equation by 1.6, we have;1.6(2.25) = (22.2 - μ)3.6 = 22.2 - μ Subtracting 22.2 from both sides of the equation;3.6 - 22.2 = - μ-18.6 = - μ Multiplying both sides of the equation by -1, we have;μ = 18.6

Simply said, a z-score, also known as a standard score, informs you of how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve. Z-scores range from -3 standard deviations, which would fall to the extreme left of the normal distribution curve, to +3 standard deviations, which would fall to the far right. You must be aware of the mean and population standard deviation in order to use a z-score.

The z-score can show you how that person's weight compares to the mean weight of the general population.

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Answer:  2^2 x 3^2 x 5

You can use a star symbol * in place of the x symbols.

==================================================

Explanation:

We simply circle the primes where they have the largest exponent.

The unique primes listed here are: 2, 3, 5

Answer:

She can write 2 pages and 4/5 extra.

Step-by-step explanation:

What you're going to do is multiply 14 by 1/5.

14/1 x 1/5 = 14/5

14/5 = 2 4/5

Answer:

3

Step-by-step explanation:

First, we need to find the area of the base

since the height is 3/4, we multiply that with 2 in, then divide by 2

(3/4 * 2)/2 = 3/4

then we multiply that by the length, which is 4, so

3/4 * 4 = 3

so 3 is the answer

Answer:

(9, -4)

Step-by-step explanation:

The question says to solve using elimination. Subtract the 2nd equation from the 1st equation, thus eliminating the y term completely. You will be left with an equation in terms of x, which you will then solve for and substitute into one of the original equations to calculate y.

      -x - 2y = -1

-   (-2x - 2y = -10)
_____________

Distribute the negative sign throughout the entire equation to reduce chance of making mistakes.

       -x - 2y = -1

+    (2x + 2y = 10)
______________

      x + 0y = 9

               x = 9

Now substitute this value into the first equation to solve for y.

-(9) - 2y = -1

  -9 - 2y = -1

        -2y = 8

            y = -4

So the solution of the equation is (9, -4).

(-9, -4)

Firstly we will arrange the equations one after the other:

-2x - 2y = -10  -----(i)

 -x -  2y  =  -1  ------(ii)

+     +          +  (We are eliminating by subtracting equations signs change)

x           =    -9  (value of x)

putting value of x in equation (i)  

-x -2y = -1 i.e.  -(-9) -2y = -1   i.e. -9 -2y= -1

which gives y = -4.

The correct explanation for preferring the mean over the median as a measure of center is option 3: The mean is the same as the median for symmetric data.

The mean over the median as a measure of center is that the mean takes into account all values in a data set, making it more representative of the data as a whole. On the other hand, the median only considers the middle value(s), and is less sensitive to outliers. This means that extreme values in a data set have less impact on the median than they do on the mean. However, if the data set is skewed or has outliers that significantly affect the mean, the median may be a better measure of central tendency. In summary, the choice between the mean and the median depends on the characteristics of the data set being analyzed and the research question being asked.
In symmetric data, the mean and median provide the same central value, giving an accurate representation of the data's center. However, it's important to note that the mean is more sensitive to outliers than the median, which might affect its accuracy in skewed data sets.

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it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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The statements which best describes the value of the expression 18x – 35, when x = 2 is that the result is a whole number that is neither prime nor composite and is denoted as option D.

This is referred to as the number which is divided by one and itself and there must be exactly two numbers involved.

18x – 35 =  18(2) – 35

                = 36 - 35 = 1

In the case of 1, the numbers involved is just one which 1 which is why it isn't regarded as a prime number. A composite number can be formed with two small integers and the formation of 1 is 1 × 1 which is why 1 isn't.

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Answer:

The Answer Is: D.! The Results is A Whole Number That is Neither Prime nor Composite

Step-by-step explanation:

Hope This Helped! You Have a Great Day!

x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.

According to the question,

The two numbers are positive and the sum of the two numbers is 16 and the sum of the squares of the two numbers is the minimum.

Now to solve the question we will consider,

x and y are the two numbers, such that x > 0 and y > 0

Sum of the numbers : x + y = 16

Sum of squares of the numbers: S = x²+ y²

x + y = 16 y = (16 - x)

Assume, S = x² + y²

S = x² + (16 - x)²

Now we will differentiate with respect to x

dS/dx = 2x+ 2(16-x)(-1)

2x-2(16-x)=0

2x-32+2x=0

4x-32=0

4x=32

x=32/4

x=8

As x > 0, x = 8

d²S/dx² = d/dx [2x+ 2(16-x)(-1)]

d²S/dx² = d/dx (2x) - 2 d/dx (16-x)

d²S/dx² = 2 - 2[0-1]

d²S/dx² = 4

Now when x=8

d²S/dx²  = 4 ≥0

Therefore, the function S = sum of the squares of the two numbers is minimum at x = 8.

y = 16-8 = 8

Therefore, x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.

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A Type II error occurs when we fail to reject a null hypothesis that is actually false. In this case, the null hypothesis is that the proportion of students who were quarantined at some point during the Fall Semester of 2020 is equal to or less than 0.65.

The alternative hypothesis is that the proportion is greater than 0.65. If we make a Type II error, we fail to reject the null hypothesis when it is actually false, meaning we do not conclude that the proportion is higher than 0.65 even though it actually is higher.

Therefore, the correct explanation for a Type II error, in this case, we would be: "Did not conclude the percent was higher than 65%, but it was higher."

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Answer:

the correct answer is A, y=3.5x + 7

\(tan(\theta )=\sqrt{3}\implies tan(\theta )=\cfrac{\sqrt{3}}{1}\implies tan(\theta )=\cfrac{\sqrt{3}}{1}\cdot \cfrac{2}{2} \implies tan(\theta )=\cfrac{\sqrt{3}}{2}\cdot \cfrac{2}{1} \\\\\\ tan(\theta )=\cfrac{~~\stackrel{sin(\theta )}{\frac{\sqrt{3}}{2}} ~~}{\underset{cos(\theta )}{\frac{1}{2}}}\implies \theta =tan^{-1}\left( \cfrac{~~\frac{\sqrt{3}}{2} ~~}{\frac{1}{2}} \right)\implies \theta = \begin{cases} \stackrel{I~Quadrant}{60^o}\\\\ \stackrel{III~Quadrant}{240^o} \end{cases}\)

Check the picture below.

Answer:

Step-by-step explanation:

Given:

Use point slope form:

So the equation is:

Answer:

3 feet

Step-by-step explanation:

To begin, find the width of the first painting by dividing 32 by 4. You get 8 feet as the width. Since the second painting has a width of 8, divide 24 by 8 to get the length (area of a rectangle is length times width). You get that the length of the second painting is 3 feet.

Hopefully this helps- let me know if you have any questions!

Answer:

7!

Step-by-step explanation:

The awnser would be 7 as 7 goes into 14 and so does 7!

Answer:

x=$3

Step-by-step explanation:

2x+5=3x+2

-2 from both sides

2x+3=3x

-2x from both sides

3=x

The statement is true in this scenario.

In a binary search of an array with 1,000 elements, if the search fails to find the item on the first attempt, there are indeed 999 elements left to search. Binary search is a divide-and-conquer algorithm that efficiently searches sorted arrays by repeatedly dividing the search space in half. If the target item is not found in the initial comparison, the search narrows down to either the lower or upper half of the remaining elements. In this case, it reduces the remaining elements from 1,000 to 999. This process continues with subsequent comparisons until the target item is found or until no more elements are left to search. Therefore, the statement is true in this context.

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The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints is the meaning of perpendicular bisector theorem

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment ,then it is equidistant from the segment's endpoints.

The perpendicular bisector of a triangle is the line segment that is drawn from a vertex to the opposite side bisecting the side at a right angle. The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into two equal parts. The point at which all the three perpendicular bisectors of a triangle meets is called the circumcenter of a triangle.

It is the meaning of perpendicular bisector theorem.

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Question:

What is the measure of an interior angle of a 21-gon?

Concept:

Define a 21-gon

A 21-gon is a 21 sided polygon also know as An icosikaihenagon

In the case of this polygon, the value of n is

We will then calculate the sum of interior angles of a 21-gon and then divide the sum by the number of sides n...

Therefore,

The formula we will use to calculate the measure of an interior angle of a 21-gon is given below as

The formula for the sum of interior angles is given below as

Hence,

We will have

Step 2:

Substitute the value of n=21 in the formula above, we will have

Hence,

The final answer = 162.86°

It determines statistic.

Since the researcher is studying a sample of 50 women who have lost weight of  pounds so since it is a sample and of a definite size so it means it is a sample so they determines statistic.

A statistic (singular) or sample statistic is any quantity calculated from values ​​in a sample that is considered for statistical purposes. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The mean (or average) of the sample values ​​is a statistic. The term statistic is used both for a function and for the value of the function on a given sample. When a statistic is used for a specific purpose, it may be labeled with a name indicating its purpose.

When a statistic is used to estimate a population parameter, the statistic is called an estimator. A population parameter is any characteristic of the population under study, but when it is not possible to directly measure the value of the population parameter, statistical methods are used to derive the probable value of the parameter based on statistics calculated from the sample. drawn from the population. For example, the sample mean is an unbiased estimate of the population mean. This means that the expected value of the sample mean is equal to the true population mean

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Answer:

  A.  y ≥ -3x +4

Step-by-step explanation:

The boundary line crosses the y-axis at +4, so the y-intercept of it is +4. This eliminates choices C and D.

The shading is above the line, where y-values are greater than those on the line. This eliminates choice B.

The correct inequality is ...

  A. y ≥ -3x +4

Answer:

Below.

Step-by-step explanation:

Ok so, Since its 510 - x = 410. Speeds equals the wind.

SO?

100=2x

x=50

410+50 = 460!

Answer:

Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function is the set of values that we are allowed to plug into our function. While a functions range, is the set of values that the function can take.

To be more precise, he domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

A relation's domain can also be discussed, where one element in the domain may be mapped to more than one element in the range.

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Answer:

2.85

Step-by-step explanation:

Reason 19.50 - 22.35 = 2.85

Answer:

2

Step-by-step explanation:

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➡k x 9≤ 18

➡x≥18/9=2

Answer:

x+5

Step-by-step explanation:

so first you would divide by x (which means you would multiply x+2 by -x)

x^2 + 7x + 10

-x^2 - 2x

5x + 10

then you would divide by 5 (which means you would multiply x+2 by -5)

5x + 10

5x +10

0

So then to check it you would multiply x+5 by x+2

(x+5)(x+2)

x^2 + 2x + 5x + 10

then simplify to get

x^2 + 7x + 10

So the point farthest from the xy-plane is A = (12,10,-17). The distance of point A from xy-plane is 17 units.

The equation of the yz-plane is x=0.

So the yz-plane is the plane which passes through the points (0,1,0), (0,0,1) and (0,0,0).

For a point P(x,y,z), the distance between P and

the plane Ax + By + Cz + D = 0 is

|Ax+By+Cz+D| / sqrt(A²+B²+C²).

Thus, the distance from a point to the yz-plane is |x|.

Using this formula for the given points:

A = (12,10,-17) : |x| = |12| = 12B

= (-18,0,-6) : |x| = |-18| = 18C

= (-9,-3,15) : |x| = |-9| = 9

So the point closest to the yz-plane is C = (-9,-3,15).

The distance of point C from yz-plane is 9 units.

So the answer is: 9.

The equation of the xy-plane is z=0.

So the xy-plane is the plane which passes through the points (0,0,1) and (0,0,0).

The distance from a point to the xy-plane is |z|.

Using this formula for the given points:

A = (12,10,-17) : |z| = |-17| = 17B

= (-18,0,-6) : |z| = |-6| = 6C

= (-9,-3,15) : |z| = |15|

= 15

So the point farthest from the xy-plane is A = (12,10,-17).

The distance of point A from xy-plane is 17 units.

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