As part of the study described in exercise 10, the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state. (Again, D. C. Counts as a state. ) The corre- lation between these 51 pairs of averages was 0. 97. Would the correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests-be larger than 0. 97, about 0. 97, or less than 0. 97? Explain briefly

From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.

A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.

Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.

Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.

Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.

Now, ∠KOL is calculated as follows from the triangle KLO,

[tex]\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]

Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.

Now, ∠LOM is calculated as follows from the triangle MLO,

[tex]\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]

Then,

[tex]\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}[/tex]

Using, the cosine law of the triangle KOM, we get,

[tex]\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}[/tex]

Therefore, the required answer is 1.2079.

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The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:

y = (2/3)*x - 2

A general linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.

Then a line parallel to:

y = (2/3)*x + 1

Is of the form:

y = (2/3)*x + b

And we want this line to pass through the point (3, 0), replacing these values we will get:

0 = (2/3)*3 + b

0 = 2 + b

-2 = b

Then the linear equation is:

y = (2/3)*x - 2

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A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.

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Answer:

f(n) = 72(0.5)n−1

Step-by-step explanation:

Got right.

The equation of the line in slope intercept form is y = -2.65x + 25.

The x-intercept means when the gift card has a balance of zero dollars.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore. let's find the slope of the line using (2, 19.7) and (4, 14.4).

Hence,

m = slope = 14.4 - 19.7 / 4 - 2

m = - 5.3 / 2

m = - 2.65

Therefore, let's find the y-intercept using (2, 19.7).

y = -2.65x + b

19.7 = -2.65(2) + b

b = 19.7 + 5.3

b = 25

Therefore, the equation of the line is y = -2.65x + 25.

The x-intercept is the value of x when y = 0.

Hence,

0 = -2.65x + 25

-25 = -2.65x

x = -25 / -2.65

x = 9.4

The x-intercept means the gift card has zero balance. At this point the medium cup of coffee is 9.4 .

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Answer:

55°

Step-by-step explanation:

For the line including the 110°, the angle of the supplementary angle is 70° which is the 'non-equivalent' length of the isosceles triangle. Then do:

(180°-70°)/2 = 55° to get x

Answer:

Supplementary angles, x = 55

Step-by-step explanation:

Supplementary angles: straight line means both angles add up to 180, this if the outside angle is 110 then the inside angle is 180° - 110° = 70°

Since it is an isosceles triangle, it means both angles are equal to x therefore

[tex]180 - 70 = 2x\\110 = 2x\\\frac{110}{2} = x\\x = 55[/tex]

The system of equations are:

15 + x = y

13 + 2x = y

The weight of the package is 2 pounds.

The delivery cost for both services is 17$.

Here is a system of equations you can use to represent the cost of the two courier services:

First courier: 15 + x = y

Second courier: 13 + 2x = y

Where x is the weight of the package in pounds and y is the total cost of delivery.

We know that the two courier services are equivalent in terms of cost, so we can set the two equations equal to each other:

15 + x = 13 + 2x

then we can subtract 15 from both sides

x = 13 + 2x -15

x = -2 + 2x

then we can subtract x from both sides

-x = -2

then we can divide both sides by -1

x = 2

The package weighs 2 pounds, and the delivery cost for both services is 15 + 2 = 17$.

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The expression that shows John's score will be 2x + 9.

It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, Mai has a score of x while John has 9 more than twice mai's score.

The expression for this relationship will be:

= (2 × x) + 9

= 2x + 9

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Complete question

Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.

Heat loss, according to Newton's cooling curve, is exponential. Like a half-life, it operates.

Cake temperature and ambient temperature varied by 140 F. The cake has lost half of that difference after 30 minutes, thus that is the half-life. It will shed another half or 35 F in the next 30 minutes, bringing the temperature to 105 F. It will shed 17.5 F in about 30 minutes, leaving 87.5 F.

The temperature is between the last two, at 100 F, so it will be between an hour and an hour and a half. You get an interpolated result of about an hour and ten minutes.

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Answer: 12/48 = 25%

Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.

Answer:

x=1, y=4

Step-by-step explanation:

5x+y=9

10x-7y=-18

(Multiply top equation by -2)

-10x-2y=-18

10x-7y=-18

(Add)

-9y=-36

(Divide -36 by -9)

y=4

(Substitute y(4) into the top equation)

5x+4=9

(Subtract 4)

5x=5

(Divide 5)

x=1

Answer: x=1 , y=4

Step-by-step explanation:

5x+y =9          y=9-5x

10x - 7y = -18

10x-7(9-5x)=-18                   y=9-5x

10x-63+35x=-18                  y=9-5(1)

45x-63=-18                          y=4

45x=-18+63

45x=45

x=1

The correct answer is Non-existent. If the Earth's spin axis were perpendicular to the Earth's orbital plane, the seasons and seasonal variation would be greatly reduced or eliminated.

This is because the tilt of the Earth's axis (currently at 23.5 degrees) causes the change in the amount of sunlight received at different latitudes during the year, leading to the seasons we experience.

After all, it causes our seasons in the first place. If the Earth's axis were vertical to its orbital airplane, there would be no seasons. Still, there would be minor variations in temperatures and rush throughout each time as Earth moves slightly closer and further down from the sun If the earth and ringed in an upright position around the sun.

If the Earth's spin axis were perpendicular to the ecliptic plane, the Northern and Southern hemispheres would receive roughly the same amount of sunlight throughout the year, and there would be little temperature variation, thus leading to little or no seasonal changes.

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The right response is Nonexistent. Seasons and seasonal fluctuation would be significantly diminished or completely gone if the Earth's spin axis were parallel to its orbital plane.

This is so that the seasons we experience may be attributed to the tilt of the Earth's axis, which is now 23.5 degrees, which affects the quantity of sunlight received at various latitudes throughout the year.

After all, it is the primary cause of our seasons. Seasons wouldn't exist if the Earth's axis were vertical to its orbital plane. If the earth were circled in an upright position around the sun, there would still be modest fluctuations in temperature and rush throughout each period as Earth travels a little closer to and further away from the sun.

The Northern and Southern hemispheres would get nearly the same amount of sunshine throughout the year, and there would be no temperature difference, which would result in little to no seasonal variations if the Earth's spin axis were perpendicular to the ecliptic plane.

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The transformation represented by the figure is (c) translation

From the question, we have the following parameters that can be used in our computation:

The figure

On the figure, we have the following

A figure and its translated image

When a shape is translated to form another, then the transformation is a translation

Hence, the transformation is translation

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A list that shows the possible outcomes of one day one method of travel:

Monday, bus,

Monday, subway,

Monday, taxi,

Tuesday, bus,

Tuesday, subway,

Tuesday, taxi

The correct answer is an option (B)

Let A represents the set of days.

A = {Monday, Tuesday}

And set B represents the method of transportaion/travel.

B = {bus, subway,  taxi }

To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.

We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.

It is a set of all ordered pairs (a, b)

For above sets A and B,

A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}

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Find the complete question below.

The relative frequencies for the car riders are given as follows:

A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

The total number of car riders is given as follows:

78.

The number in each grade is given as follows:

Hence the relative frequencies are given as follows:

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Answer: x=10

Step-by-step explanation:

x is an unknown number trying to figure out what number equals 20? You subtract 10 from 20 to figure out x.

The standard deviation of the household income will be increased by $5,000.

The standard deviation is a measure of variation from the mean that takes spread, dispersion, and spread into account. The standard deviation reveals a "typical" divergence from the mean. It is a popular measure of variability since it retains the original units of measurement from the data set.

standard deviation is increased by 5x/100 = 0.05x

Change in standard deviation = $5000

There is little variety when data points are near to the mean, and there is a lot of variation when they are far from the mean. How much the data differ from the mean is determined by the standard deviation. Standard deviation, which is based on all data, is the most often used metric for measuring dispersion. As a result, the standard deviation's value can be affected by even a slight change in one number.

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According to the equation of the trend line the population will reach 52900 in 27831 years.

A mathematical statement known as an equation is a combination of two expressions joined together by the equal sign.

The equation of the trend line is:

y = 1.9x + 21

where, y is the population and x indicate the year.

To find the number of years in which the population reach 52900, substitute y = 52900.

y = 1.9x + 21

52900 = 1.9x + 21

52900 - 21 = 1.9x

52879/ 1.9 = x

x = 27831

Hence, according to the equation of the trend line the population will reach 52900 in 27831 years.

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The probability that a death will result from an accident is 0.105, or 10.5%.

Given:

In foggy conditions, 25% of accidents result in fatalities.

Rain-related accidents result in fatalities in 12.5% of cases.

In sunny weather, 5% of accidents result in fatalities.

To find : The probability that a death will result from an accidents

The likelihood that a death will ensue from an accident

5% of 60%(sunny) (sunny)

25% of 20%(foggy) (foggy)

12.5% of 20%(rainy) (rainy)

Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22

Chance is 0.105

Chance is 10.5%.

There is a 10.5% chance that a fatal accident may occur.

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We would need to add 8 more sets of 3 candies to 23 candies in order to have the same amount as Casey.

To find this, we can divide the total amount of candy Johnny has (23) by the amount of candy Casey has (3) and round up to the nearest whole number:

(23) / (3) = 7.666...

Since we can't have a fraction of a set of candies, we must round up to the nearest whole number, which is 8.

So, to have the same amount of candy as Casey, we would need to add 8 more sets of 3 candies to Johnny's 23 candies.

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The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

A line is known as a perpendicular bisector when it divides a specified line segment in half, by creating a 90° angle at the intersection.

The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler.

On both sides of the line segment being divided, it forms a 90° angle.

Here we have

On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). It's midpoint M. The coordinates of M (3, 2).  

Slope from A(-1,-1) and B(7,5)  

=> [ 5 + 1]/[7 + 1 ] = 6/8 = 3/4

When we draw a perpendicular bisector of AB on the grid. It will pass through the point (0, 6)  

The slope of the perpendicular bisector i.e from (0, 6) to (3, 2)  

=> [2 - 6]/[3 - 0] = - 4/3

Let the equation of the bisector is y = mx + c

=> y = (-4/3)x + c

=> 3y = - 4x + 3c           [ ∵ Slope = -4/3 ]

As we know the bisector will pass through (3, 2)

=> 3(2) = -4(3) + 3c

=> 3c = 12 + 6

=> 3c = 18

Hence, the required equation of the line is 3y = - 4x + 18  

Therefore,

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

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Answer:

The gravitational force acting on the 6-kg bowling ball at the top of the 120-meter tall building is approximately 58.64 Newtons.

Step-by-step explanation:

The frequency table has been created in the attachment

Given that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.

Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:

x = 2 * 56

Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:

y = 56 - 10

Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:

z = 2*w

Now we have the following system of equations:

x = 2 * 56

y = 56 - 10

z = 2*w

x+z = 150

y+w = 150

By solving the above system of equations we get:

x = 112

y = 46

z = 112

w = 56

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Correct option is D, the fraction of area of square region ABCD is 1/4.

A + B + C = D + E + F since diagonal QS divides the square into two equal portions.

We can see that the areas of regions A and F must be equal because they have the exact same measurements and form. Similar reasoning leads us to the conclusion that the areas of regions D and C are equal.

As a result, it follows that the size of regions E and B must likewise be equal. Due to the fact that URPT is a parallelogram, its area equals (base)(height)=(1)(2)=2.

Area of region E = Area of region B = 1 as a result.

The percentage of the square PQRS's area is represented by the darkened region 1/4 is a fraction.

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Complete question -

Answer:

Step-by-step explanation:

X =90

keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]

Answer: To solve the equation -3(x+2)^2-4 = 5 by factoring, we can follow these steps:

Move all the terms to one side of the equation by adding 3(x+2)^2 and 4 to both sides: -3(x+2)^2-4+3(x+2)^2+4 = 5+3(x+2)^2

Combine like terms: 3(x+2)^2 = 5

Take the square root of both sides of the equation: (x+2)^2 = 5/3

Isolate x+2 on one side of the equation by taking the square root of both sides: x+2 = ±sqrt(5/3)

Solve for x by subtracting 2 from both sides of the equation: x = ±sqrt(5/3) - 2

So the solutions to the equation -3(x+2)^2-4 = 5 by factoring is x = ±sqrt(5/3) - 2.

It's important to note that the square root of a fraction is a positive and negative solution, so the solutions are x = sqrt(5/3) - 2 and x = -sqrt(5/3) - 2

Step-by-step explanation:

She needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

To determine how many times you need to go to the swimming pool to make the membership fee worth paying, you can use the following formula:

Number of visits = membership fee / (cost without the membership - cost with membership)

Plugging in the values, we get:

Number of visits = $50 / ($5 - $3.50)

The savings from the membership's lower entrance price will have surpassed the cost of the membership after 14 visits.

Hence, she needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

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You can "find algebraically" if a function is even, odd, or neither by taking it, substituting -x for x, simplifying it, and then comparing the results to what you had initially.

The function is even if it is exactly the same as what you started with (that is, if f(-x) = f (x), with all the signs remaining the same. The function is odd if it is exactly the opposite of what you started with (that is, if f(-x) = -f(x), with all the signs switched.

The function is neither even nor odd if the outcome is neither exactly the same nor exactly the opposite (that is, neither having all the same words but with all the signs reversed).

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The equation for the linear function is  y=3x -5.

A linear function can be represented by a linear equation. The standard form for the linear equation is: y= mx+b , for example, y=10x+6.

The standard for the linear equation( y= mx+b), also it is known as the Slope-Intercept Form.

Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=10 and b=6.

The question gives some points of the linear function, see below.

x    y

1    -2

2   1

3   4

4  7

From the given data you can find the slope by solving the system linear equation.

For example, you can write a system linear equation from the points: (1,-2) and (4,7).

-2=m+b  (1)

7=4m+b    (2)

Multiplying equation 1 by -1, you have

2= -m -b     (1)

7= 4m+b    (2)

Summing the previous equation, you can find the slope (m):

9=3m

m= 9/3

m= 3

If m=3, from equation 2, you can find the coefficient b.

7 = 4m + b

7 = 4*3 +b

7=12 + b

b= 7-12

b= -5

Thus, the standard form for the linear equation represented by the given table is y=3x -5.

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Work Shown:

|x - 5| < 3

-3 < x-5 < 3

-3+5 < x-5+5 < 3+5

2 < x < 8

The graph will have open circles at 2 and 8, then shade between the open circles. The open circles indicate "do not include this endpoint". This is why choice A is the final answer.