how many of your 500 clients would you expect to have major depressive disorder (mdd)? if you used the phq-2 to screen for mdd, what number of those who are depressed would screen positive? among those who screened positive, what number would you expect to be confirmed for mdd at the follow-up visit?

Micah's best long jump is 3 meters long.

In this question we have been given Avi and Micah are teammates on a track and field team.

We need to find the how long is Micah's best long jump.

Let Micah's best long jump is x meters and Avi's  best long jump is y meters.

Avi's best long jump is 3 1/2 meters.

⇒ y = 3 1/2 meters

We write this improper fraction as proper fraction.

3 1/2 = 7/2

Also, Avi's best long jump is 1 1/6 times as long as Micah's.

So, we get an equation

y = (1 1/6) * x

We write improper fraction 1 1/6 as 7/6

So equation becomes,

y = 7/6 * x

Subatitute the value of y

7/2 = 7/6  * x

x = (7/2)/(7/6)

x = 6/2

x = 3 meters

Therefore, Micah's jump is 3 meters long.

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At least 75% of his total credits were certain to have a grade point average between 2.00 and 4.0.

By looking at the standard deviation of 0.25, we can calculate the range of the grade point averages which are within two standard deviations away from the mean. In this case, the mean is 3.00, so two standard deviations away would be 2.00 (3.00 - 0.25 x 2) and 4.00 (3.00 + 0.25 x 2). Since the grade point averages within this range are certain to have a grade point average between 2.00 and 4.0, at least 75% of the total credits are certain to have a grade point average between these two numbers.

Lower limit (2 standard deviations away from the mean):

3.00 - (0.25 x 2) = 2.00

Upper limit (2 standard deviations away from the mean):

3.00 + (0.25 x 2) = 4.00

Therefore, at least 75% of the total credits have a grade point average between 2.00 and 4.00.

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Answer:

–27

Step-by-step explanation:

f(x) = 2x² + 9x

f(–3) = 2(–3)² + 9(–3)

= 2(9) + –27

= 18 – 27

= –9

since p= f(–3) = –9

3p = 3 × – 9 = –27

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Answer:

Indentify a pair of segments that are marked perpendicular to each other on the diagram below

Step-by-step explanation:

OQ

The probability for all sample of 5 that the sample mean will be greater than 22 pounds is approximately 0.05.

The distribution of backpack with mean deviation = 19.7 pounds

And the standard deviation = 3.1 pounds

According to this question,

He normal probability distribution and the central limit theorem were used.

Normal probability distribution, ; Problems of normally distributed samples are solved using the z-score formula.

Mean standard deviation, the z-score of a measure X is given by:

Z = x-μ/σ

The Z-score measures how many standard deviations. the measure is from the mean.

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score.

This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Subtracting 1 by the p value,

We get the value probability that of the measure is greater than X.

Central Limit Theorem;  The Central Limit Theorem establishes  that, for a normally distributed random variable X, with mean  and standard deviation the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For samples of size 5, which of the following is the best interpretation of P(ä > 22) = 0.05

No matter the size of the sample mean will be the same.

However, the standard deviation will be changed.

P(ä > 22) is the probability of the sample means being above 22.

For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

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Answer:

Marsha earn $1350.

Step-by-step explanation:

So,

9000 × 5 × 3 ÷ 100

135000/100

$1350

Thus, Marsha earn $1350.

However, the information is not complete but we can see parallel lines in general to solve it.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Perpendicular lines are those that cross at a straight angle of 90 degrees.

Lines that are perpendicular to one another are those that are 90 degrees apart. In light of this definition, we could conclude that for lines lll and mmm to be perpendicular, they must intersect and form a right angle (90°) to one another.

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}[/tex]

Answer: The tax is $3.28.

Step-by-step explanation:

8% is equal to 0.08.

If you multiply 41 x 0.08 you get 3.28.

Answer:

w < 65 is the correct inequality.

Answer:

Below

Step-by-step explanation:

1 2 and 3 do not pass the vertical line test because you can draw a vertical line that will cross the graph two times

The distance between the library and the school using the coordinates plane is 7.28 miles.

A coordinate plane is a two-dimensional plane which is formed by the intersection of two number lines - a horizontal number line called the x-axis and is a vertical number line called the y-axis. It is a graphing and description system for points and lines. On the provided coordinate plane, the coordinate of the library is (-3,3) and the coordinate of the school is (4, 1).

The distance formula between two coordinates is given by:

d =√((x2 – x1)^2 + (y2 - y1)^2)

Using the distance formula, the distance between the library and the school are:

d =√((-3 – 4)^2 + (3 - 1)^2)

d =√((-7)^2 + (2)^2)

d =√((-7)^2 + (2)^2)

d =√(49 + 4)

d =√53

d = 7.28 miles

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Some of the coordinates on the graph are (0, -15), (1, -13), (2, -11).

The graph of the equation is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of the equation y + 7 = 2 (x - 4).

y + 7 = 2 (x - 4)

y = 2(x - 4) - 7

y = 2x - 8 - 7

y = 2x - 15

For x = 0,

y = - 15

(0, -15)

For x = 1,

y = 2 - 15 = -13

(1, -13)

For x = 2,

y = 4 - 15 = -11

(2, -11)

And so on...

Thus,

The graph of the equation is given below.

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Answer:

The number of downloads of the standard version is 230.

Step-by-step explanation:

Let x be the number of downloads of the standard version.

The number of downloads of the high-quality version is 4x.

The total size downloaded for the standard version is 2.8x MB.

The total size downloaded for the high-quality version is 4.3(4x) = 17.2x MB.

The total size downloaded for both versions is 2.8x + 17.2x = 4600 MB.

Combining like terms, we have 20x = 4600 MB.

Dividing both sides by 20, we have x = 230 downloads of the standard version

Answer:

The answer is below; I have put the equation and graphed it!

Step-by-step explanation:

2x - 3 > 1

x represents an integer and 3 is less than twice an integer which is 2x. So it's 2x - 3.

2x - 3 is greater than 1.

So therefore, the answer is 2x - 3 > 1

Answer:

2x-3>1

Step-by-step explanation:

lets say x is the interger

so twice an interger would be 2*x or 2x

and three less than that would be 2x-3

and 2x-3 is greater than one

so, 2x-3>1

Some of the coordinates on the graph are (0, -15), (1, -13), (2, -11).

The graph of the equation is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of the equation y + 7 = 2 (x - 4).

y + 7 = 2 (x - 4)

y = 2(x - 4) - 7

y = 2x - 8 - 7

y = 2x - 15

For x = 0,

y = - 15

(0, -15)

For x = 1,

y = 2 - 15 = -13

(1, -13)

For x = 2,

y = 4 - 15 = -11

(2, -11)

And so on...

Thus,

The graph of the equation is given below.

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Answer:

p = 19

x = 64

y = 100

Step-by-step explanation:

114 = 6p

Divide by 6 into both sides

p = 19

x/4 = 16

Times 4 into both sides

x = 64

75 = y - 25

Add 25 to both sides

y = 100

Answer:

-6

Step-by-step explanation:

Do whats in the parentheses first (3-5=-2)

so you have 3(-2), and that equals -6

Answer:

Step-by-step explanation:

3(x - 5) when x = 3

Substitute x with 3:-

[tex]\tt 3\left((3)-5\right)[/tex]

[tex]\tt 3\left(-2\right)[/tex]

[tex]\tt -6[/tex]

Therefore, your answer is -6!

______________________

Hope this helps you!

Have a nice day!

let x as the total sales

26 250 = 14 250 + 0.06x

26 250 - 14 250 = 14 250 - 14 250 + 0.06x  (subtract 14 250 both sides)

12 000 = 0.06x

x = 200 000

26 250 = 14 250 + 0.06(200 000)

26 250 = 14 250 + 12 000

26 250 = 26 250

Therefore, Peter have total sales of RS 200 000.

Step-by-step explanation:

The coordinates of the recycle bin will be = ( -1, 2.5 )

According to the information given in the question,

The coordinates of the vertices of the park are,

( 1, 1 ), ( 1, 4 ), and ( -3, 4 )

We have to find the coordinates of the recycle bin.

Let us consider the equation of the circle,

[tex]x^{2} +y^{2}+Dx + Ey+ F =0[/tex]

So putting the values of the coordinates into the equation,

First Equation,

[tex]1^{2}+1^{2} + D + E + F = 0[/tex]

Second Equation,

[tex]1^{2} +4^{2} +D + 4E + F=0[/tex]

Third Equation,

[tex](-3)^{2} + 4^{2} - 3D+4E+F=0[/tex]

Subtracting the first equation from the second,

[tex]1^{2} +4^{2} +D + 4E -E=0[/tex]

15 + 3E = 0

3E = -15

E = -5

Subtracting the third equation from the second,

1 + 16 - 9 - 16 + D + 3D = 0

4D = 8

D = 2

Putting the values of E and D in the first equation,

1 + 1 + D + E + F = 0

F = -2 - D - E

F = 1

So now the equation of the circle becomes,

[tex]x^{2} +y^{2}+2x - 5y+ 1 =0[/tex]

By expanding the above equation we can find the standard equation,

[tex]x+2x+1^{2} +y^{2} -5y+ 2.5^{2}- 1^{2} -2.5^{2} +1 =0[/tex]

[tex](x+1)^{2} + (y - 2.5)^{2} = 1^{2} + 2.5^{2} -1[/tex]

[tex](x+1)^{2} + (y - 2.5)^{2} = 2.5^{2}[/tex]

So the required circumcenter will be = ( -1, 2.5 )

Therefore, the coordinates of the recycle bin will be = ( -1, 2.5 )

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A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1,4), and (-3,4). The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?

Step-by-step explanation:

Let the larger angle be x.

Smaller angle = x - 8

As both angles are supplementary,

x + (x - 8) = 180°

2x - 8 = 180°

2x = 188°

x = 94°

Therefore, larger angle = 94°

Smaller angle = 94° - 8° = 86°

The probability the card is red, given that it is a face card is 1/2 and  the probability the card is a king, given that it is a face card is 1/3.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

A card is drawn from a standard 52-card deck (no jokers).

We have to match each event with its probability.

Since, a deck of cards contains the face cards J, Q, and K.

Let's say there are four different kinds of cards: spades, clubs, hearts, and diamonds.

King, Queen, and Jack are contained in each of these types.

Thus, the total number of face cards is 12 (3 x 4).

(1)  Let the face cards are 12 and there are 6 red cards in that 12 face cards.

So, the probability the card is red, given that it is a face card is

= 6/12 = 1/2.

(2)  There are 4 king in a 12 face cards.

So, the probability the card is a king, given that it is a face card

= 4/12 = 1/3.

Hence the probability the card is red, given that it is a face card is 1/2 and  the probability the card is a king, given that it is a face card is 1/3.

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In a regression analysis, the error term ε is a random variable with a mean or expected value of zero.

The model used in regression analysis is known as the regression model it is used to estimate the relationships between a dependent variable and one or more independent variables.

It helps us to find the strength between two given relations thus determining whether a plan is correct or not. It helps us to make plans based on certain reports .

Another way of analyzing things is by using multiple regression analysis, it can be used to assess the connection between a dependent variable and two or more independent variables. For example, you may assess the relationship between a person's income and their experience, education, and geographic area.

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As per the Pythagoras theorem, the number of feet along the ground from the tent pole to the rope is 8 feet.

Here we have given that A 15-foot tall tent pole incurred to the ground using a piece of rope 17 feet long that goes from the top of the tent pole to the ground. If the tent pole make a 90-degree angle with the ground,

And we need to determine the number of feet along the ground from the tent pole to the rope.

AS per the given data, here we have consider that the pole makes 90° with the ground and is supported by a rope.

And for the clear observation, here we can realize that the pole, rope and ground form a right-angled triangle, where

The value of Hypotenuse (h) = length of rope = 17 feet

And the Side 1 (p) = length of tent pole = 15 feet

Then the Side 2 (b) = distance between pole and rope along the ground

Now, we have to applying the Pythagorean theorem, the following equation is obtained:

=> h² = p² + b²

Then we have to apply the values on it, then we get

=> 17² = 15² + b²

=> b² = 289 - 225

Therefore, the value of is calculated as,

=> b = √64

=> b = 8 feet

Therefore the distance between the tent pole and the rope along the ground is 8 feet.

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Answer:

Here are 5 ordered pairs whose first and second coordinates are equal:

(2,2)

(3,3)

(4,4)

(5,5)

(6,6)

If we plot these points and connect them, we get a straight line that runs from the bottom left to the top right of the coordinate plane. This line is called the "diagonal" of the coordinate plane and it divides the plane into 4 quadrants.

The figure that we get lies in all 4 quadrants of the coordinate plane. The top right and bottom left quadrants are the "positive" quadrants, where both the x- and y-coordinates are positive. The top left and bottom right quadrants are the "negative" quadrants, where both the x- and y-coordinates are negative.

There will be a total of 720 4- permutations of a set of six objects. And there will be a total of 72 2- permutations of a set of nine objects.

The calculation for 4-permutations of a set containing six objects

P(6,4)! = 6! / (6-4)1

P(6,4)! = 6×5×4×3x2

P(6,4)! = 720

Therefore, there will be a total of 720 permutations.

The calculation for 2- permutation of a set containing 9 objects

P(9,2)! = (9,7)! = (9-2) = 9! / 7!

P(9,2)! = 9×8x7! / 7!

P(9,2)! = 72

Therefore, there will be a total of 72 permutations.

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Answer:

Samantha has a total of 12 chickens. if she has 3 times as many chickens as dogs. The correct answer is 3x = 12; x = 4.

Samantha has a total of 12 chickens. if she has 3 times as many chickens as dogs.  First you have to divide by 3 on both sides.

Therefore, Samantha has a total of 12 chickens. if she has 3 times as many chickens as dogs. The correct answer is 3x = 12; x = 4.

The correct answer is a. margin of error.

The margin of error is a measure of the precision of a survey or poll. It represents the range of values within which the true value of the population parameter being measured is likely to fall, based on the sample data collected. A smaller margin of error indicates a higher level of precision and a more reliable estimate of the population parameter. In general, a margin of error of less than +/- 5 is considered to be a good benchmark for a reliable public opinion poll.

The modal response is the most common response to a survey question. The sample size is the number of people included in the survey. Standard deviation is a measure of the dispersion of a set of data. Self-selection bias refers to the possibility that the people who choose to participate in a survey are not representative of the entire population being studied.

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Answer:

the length is 15

Step-by-step explanation:

So the height of the pole(Opposite) = 9m

The steel wire fixed to the ground(Adjacent) = 12m

the length( Hypotenuse) = ?

using the formula

Hyp² = opp² + Adj²

Hyp² = 9² + 12²

Hyp² = 81 + 144

Hyp² = 225

Hyp = √225

Hyp = 15

i hope this helps