A group project last semester looked to see how many services students knew about on campus. They collected data from 50 students and found that 23 had used tutoring and found it beneficial. Calculate a 95% confidence interval for the true proportion of Mesa students that have used tutoring and found it beneficial.

Answer:

Step-by-step explanation: a mouse

The area of the shaded region will be 24 square units.

Given that:

AB = 4

BC = 12

Point E is located halfway between sides AB and CD of the rectangle ABCD and halfway between sides AD and BC.

The area of the shaded region will be given as,

A = 2 x (1/2 x 12 x 2

A = 2 x 6 x 2

A = 24 square units

The area of the shaded region will be 24 square units.

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The missing image is given below.

Answer:

78.5in^3

Step-by-step explanation:

The correct formula for the volume of a cone is actually V=1/3(3.14)r^2h.

Plugging in the variables to this formula, we have  V=1/3(3.14)(5^2)(3) giving us the answer of 78.5in^3

The slope of one user per second is not correct based on the February and April numbers of users.

The slope refers to the unit rate or the constant of proportionality.

The slope also refers to the gradient.

The slope is determined as the quotient between the Rise and the Run.

The number of days between February 1 and April 30 = 88 days

The number of seconds between February 1 and April 30 (the Run) = 7,603,200 seconds (88 x 24 x 60 x 60)

The difference between 90,000,000 and 80,000,000 users (the Rise) = 10,000,000 users (90,000,000 - 80,000,000)

The slope = 1.315 (10,000,000 ÷ 7,603,200)

Thus, we can conclude that the slope of one user per second is not correct but 1.315 users per second.

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The solutions for the equation (3x + 12)(x + 4) = (4x² + 8x + 18x²)/2 are given by, x = -3/2, 4.

Given that the equation is,

(3x + 12)(x + 4) = (4x² + 8x + 18x²)/2

we have to find the solution that is the value(s) of the x for which this relation is true.

Solving the the equation we get,

3x*x + 12x + 3x*4 + 12*4 = (22x² + 8x)/2

3x² + 12x + 12x + 48 = 2 (11x² + 4x)/2

3x² + 24x + 48 = 11x² + 4x

11x² - 3x² + 4x - 24x - 48 = 0

8x² - 20x - 48 = 0

4(2x² - 5x - 12) = 0

2x² - 5x - 12 = 0

2x² - 8x + 3x - 12 = 0

2x(x - 4) + 3(x - 4) = 0

(2x + 3)(x - 4) = 0

Either 2x + 3 =0

x = -3/2

Or, x - 4 = 0

x = 4

Hence the solutions are, x = -3/2, 4.

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3. If x = 4, x2 = 16

This statement can be written as x = 4 → x2 = 16. It is true because if x is 4, then x2 is 16 by the definition of squaring.

The converse of this statement is x2 = 16 → x = 4. It is false because there are two possible values of x that satisfy x2 = 16, namely 4 and -4. A counterexample is x = -4.

4. If one angle of a quadrilateral is a right angle, then the quadrilateral is a rectangle.

This statement can be written as one angle of a quadrilateral is a right angle → the quadrilateral is a rectangle. It is false because there are quadrilaterals with one right angle that are not rectangles, such as trapezoids or kites. A counterexample is a trapezoid with one right angle.

The converse of this statement is the quadrilateral is a rectangle → one angle of a quadrilateral is a right angle. It is true because all rectangles have four right angles by definition.

5. If a triangle is equilateral, then it has three equal angles.

This statement can be written as a triangle is equilateral → it has three equal angles. It is true because all equilateral triangles have three equal angles of 60 degrees by definition.

The converse of this statement is it has three equal angles → a triangle is equilateral. It is true because if a triangle has three equal angles, then they must be 60 degrees each, and therefore the triangle must be equilateral by definition.

The probability of choosing a green marble first and a blue marble second is 2/15 or approximately 0.133.

The multiplication rule of probability, which states that the probability of two distinct events occurring simultaneously is the product of their individual probabilities, must be utilized in order to resolve this issue.

We need to determine the probability of the sequence GB, which means selecting a green marble first and a blue marble second, after denoting the event of choosing a green marble as G and the event of selecting a blue marble as B.

Expecting that the primary marble isn't supplanted before the subsequent draw, the likelihood of picking a green marble on the main draw is P(G) = 4/10, since there are four green marbles out of ten taken care of.

Nine marbles, including three blue ones, will remain in the bag after the first marble is selected.

Given that the first marble was green, the probability of selecting a blue marble on the second draw is therefore P(B|G) = 3/9, as there will be three blue marbles out of the remaining nine.

Using the multiplication rule, the probability of the sequence GB is:

P(GB) = P(G) * P(B|G) = (4/10) * (3/9) = 2/15

Therefore, picking a green marble first and a blue marble second has a chance of 2/15, or roughly 0.133.

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The another inequality that is equivalent to 3x>2 and 9x > 6 is x > 2/3.

We are given that;

3x>2 and 9x > 6

Now,

One way to do this is to multiply both sides of 3x > 2 by a positive number, say 4. This will give us:

3x > 2 12x > 8 (by multiplying both sides by 4)

This inequality is equivalent to 3x > 2 and 9x > 6, because they all have the same solution of x > 2/3.

Another way to do this is to divide both sides of 9x > 6 by a positive number, say 3. This will give us:

9x > 6 3x > 2 (by dividing both sides by 3)

This inequality is also equivalent to 3x > 2 and 9x > 6, because they all have the same solution of x > 2/3.

Therefore, by inequality the answer will be x > 2/3.

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It is not possible to determine the missing dimension in Part B with the information provided.

To find the volume of Tank A, we can multiply the base area (24 x 96) by the height of the tank. So, the volume of Tank A is 24 x 96 x h, where h is the height of Tank A.

Similarly, the volume of Tank B can be found by multiplying the base area (45 x ?) by the height of the tank. So, the volume of Tank B is 45 x ? x h, where h is the height of Tank B and ? is the missing dimension of the base.

We are given that the total volume of the two tanks is 4,608 cubic feet. So, we can set up an equation:

24 x 96 x h + 45 x ? x h = 4,608

Simplifying the equation, we get:

2,304h + 45h? = 4,608

Dividing both sides by 9h, we get:

256 + 5? = 512/3

Solving for ?, we get:

? = (512/3 - 256)/5

? = 32/3

Therefore, the missing dimension of the base of Tank B is 32/3 feet, and the volume of Tank B is:

45 x 32/3 x h = 1,440h

Since the total volume of the two tanks is 4,608 cubic feet, we can set up another equation:

24 x 96 x h + 1,440h = 4,608

Solving for h, we get:

h = 2

Therefore, the height of each tank is 2 feet, and the missing dimension of the base of Tank B is 32/3 feet. The volume of each tank is:

Tank A: 24 x 96 x 2 = 4,608 cubic feet

Tank B: 45 x 32/3 x 2 = 1,440 cubic feet

So, the answer to Part B is indeed 2,304 for Tank A, but the answer for Tank B is 1,440

The graph of function y = |x| - 2 by translating the parent function is shown in image.

We have to given that;

Function is,

⇒ y = |x| - 2

Now, We can formulate;

Since, Function is,

⇒ y = |x| - 2

It is translation of parent function y = |x| by 2 units down.

Thus, The graph of function y = |x| - 2 by translating the parent function is shown in image.

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The values of A and B are,

⇒ A = 16

⇒ B = 4

We have to given that;

The expression is,

⇒ x² + 8x

Now, Complete the square of the expression as;

⇒ x² + 8x + 16

⇒ (x + 4)²

Hence, By comparing we get;

The values of A and B are,

⇒ A = 16

⇒ B = 4

Thus, The values of A and B are,

⇒ A = 16

⇒ B = 4

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The equation that represents line perpendicular to y = 2x - 4 is: D. y = -(1/2)x + 5

The equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Now, let us write each of the given equations in slope intercept form to get:

A. y = 2x - 3

B. y = -(1/2)x + 3/2

C. y = 2x + 5/2

D. y = -(1/2)x + 5

E. y = (1/2)x - 7

Now, the given equation is:

y = 2x - 4

Thus, the slope that is perpendicular to it will be the negative reciprocal which is: -1/2.

Thus, option D is correct

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Answer:

A) 208 = (10 + x)( 13 + x)

Step-by-step explanation:

The first option is correct. When the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified the result is -x² + 3x - 8.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

We shall simply the polynomial -3x² + 2x - 4 - (-2x² - x + 4) as follows:

open bracket;

-3x² + 2x - 4 + 2x² + x - 4

group like terms;

-3x² + 2x² + 2x + x - 4 - 4

- x² + 3x - 8.

Therefore, the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified to give the result is -x² + 3x - 8.

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Answer:

a

Step-by-step explanation:

Hydrofluoric acid used to make anti-depressant medications can be considered as  industrial good

The industrial goods are products that are used in the production process of other goods or services.

From the given options, only "hydrofluoric acid used to make anti-depressant medications" can be considered an industrial good because it is used as a raw material in the production of anti-depressant medications.

The other options, such as Windex window cleaner, recreational vehicles, and gummy bear candy, are not considered industrial goods as they are not used in the production process of other goods or services, but rather for household cleaning, personal use or enjoyment.

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As a result, the proportionality constant in the supplied recipe that connects the number of cups of cereal to the number of cups of pretzel sticks is 2.5.

In a proportional connection, the constant of proportionality is the value by which one variable is multiplied to get the other variable. For example, if we have two proportional variables, x and y, we may write the connection as y=kx, where k is the proportionality constant.

k = y/x

where k is the proportionality constant.

Because the recipe calls for 10 cups of cereal and 4 cups of pretzel sticks in this example, we may enter these numbers into the formula:

k = 10/4

When we simplify, we get:

k = 2.5

As a result, the proportionality constant in the supplied recipe that connects the number of cups of cereal to the number of cups of pretzel sticks is 2.5.

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Answer:

Step-by-step explanation:

Answer:

$5.04

Step-by-step explanation:

We Know

A stock selling for $56 per share pays a 9% dividend.

Find the dividend per share.

We Take

9% = 0.09

56 · 0.09 = $5.04

So, the dividend per share is $5.04

B. 3

triangles only have 3 lines of symmetry and circles have infinite

The value of the vertex of this parabola is, (0, 0)

We have to given that;

Equation of parabola is,

⇒ y = f (x) = x²

Since, The standard form of a parabolic equation is,

⇒ y = a(x - h)² + k,

where a, h, and k are constants that determine the shape, position, and orientation of the parabola.

In this case, a = 1 , h = 0 and k = 0.

Therefore, the vertex of this parabola is located at the point (h, k) = (0, 0)

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The value of X+z whose ratio is given above would be = 44

The ratio between three figures are given such as;

X:y:z = 3:6:8

Therefore,

if y = 6

X = 3

the y = 24

X = ?

make X the subject of formula;

X = 24×3/6

= 12

if y = 6

z = 8

then y = 24

z = ?

Make z the subject of formula;

z = 24×8/6

= 32

therefore X +Z= 12+32 = 44.

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Let's use "j" to represent the cost per pound of jelly beans, and "t" to represent the cost per pound of trail mix.

From the first sentence of the problem, we can write an equation for the total cost of 8 pounds of jelly beans and 4 pounds of trail mix:

8j + 4t = 37

From the second sentence of the problem, we can write an equation for the total cost of 3 pounds of jelly beans and 2 pounds of trail mix:

3j + 2t = 15

Now we have two equations with two variables, which we can solve using algebra.

Multiplying the second equation by 4, we get:

12j + 8t = 60

We can now use the first equation to solve for one of the variables in terms of the other. Solving for j, we get:

j = (37 - 4t)/8

Substituting this expression for j into the second equation, we get:

3(37 - 4t)/8 + 2t = 15

Multiplying both sides by 8 to eliminate the fraction, we get:

111 - 12t + 16t = 120

4t = 9

t = 2.25

Substituting this value for t into the expression we found for j, we get:

j = (37 - 4(2.25))/8 = 2.125

Therefore, the cost per pound of jelly beans is $2.125 and the cost per pound of trail mix is $2.25.

Let x be the cost per pound of jelly beans and y be the cost per pound of trail mix. Then we can set up two equations:

8x + 4y = 37 (equation 1)

3x + 2y = 15 (equation 2)

We can solve for x and y by using the substitution method. Solve equation 2 for y:

y = (15 - 3x) / 2

Substitute this into equation 1:

8x + 4((15 - 3x) / 2) = 37

Simplify and solve for x:

8x + 30 - 6x = 37

2x = 7

x = 3.5

Now we can substitute x = 3.5 back into equation 2 to find y:

3(3.5) + 2y = 15

10.5 + 2y = 15

2y = 4.5

y = 2.25

Therefore, the cost per pound of jelly beans is $3.50 and the cost per pound of trail mix is $2.25.

Answer:

There are 6 cards, 5 of which do not have the number 4.

So P(not 4) = 5/6 = 83.3%

The area of the figure is

Information given in the problem includes

The figure would be a trapezoid and the area of a trapezoid is

= 1/2 (sum of parallel lines) x height

The parallel lines are

top side = 2.2 yards + 19.2 yards = 21.4 yards

bottom side = 21.4 yards

= 1/2 (21.4 + 21.4) x 9

= 21.4 x 9

= 192.6 square yds

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The probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order without replacement is 0.000303.

The probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order is determined as follows:

Probability of selecting the first red ball = 10/24

Probability of selecting the second red ball = 9/23.

Probability of selecting the first blue ball = 8/22.

Probability of selecting the second blue ball = 7/21.

Probability of selecting the third blue ball = 6/20.

Probability of selecting the yellow ball = 6/19.

Hence;

The probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order will be:

Probability = (10/24) * (9/23) * (8/22) * (7/21) * (6/20) * (6/19)

Probability = 0.000303

Therefore, the probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order without replacement is 0.000303.

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Answer:

Step-by-step explanation:

Using algebra to solve this problem

Let x be the number of adult tickets sold and y be the number of student tickets sold. We can set up a system of two equations to represent the information given in the problem:

x + y = 1098 (equation 1) (the total number of tickets sold is 1,098)
5x + 1y = 2366 (equation 2) (the total amount collected is $2,366)

To solve for x and y, we can use substitution or elimination method. Let's use the substitution method.

From equation 1, we can solve for y as follows:

y = 1098 - x

Substituting this expression for y into equation 2, we get:

5x + 1(1098 - x) = 2366

Simplifying and solving for x, we get:

5x + 1098 - x = 2366
4x = 1268
x = 317

So, 317 adult tickets were sold. To find the number of student tickets sold, we can substitute this value for x into equation 1 and solve for y:

317 + y = 1098
y = 1098 - 317
y = 781

Therefore, 781 student tickets were sold.

Answer:

x+y= 1098

5x+1y= 2366

y= 1098 - x

5x+ 1(1098-x) = 2366

5x + 1098 - x = 2366

4x= 1268

x= 317

x+y= 1098

317 + y= 1098

y= 781

So the answer is: 317 adult tickets and 781 student tickets were sold.

The avg response time to customer service calls was between 2.50 and 4.50

The captured percentage of the total sales or revenue within any specific market that a corporation or brand earns is called market share.

This measure showcases a company's competitive position in the marketplace and portrays its performance relative to its business rivals. Market share can be determined in multiple ways, namely by volume or value, and can range from being worldwide, nationwide or regional.

Given that it imparts insights into current market trends, tracking this statistic becomes particularly imperative for businesses looking to fashion sound marketing strategies. Without a doubt, market share acts as an indispensable metric for companies seeking to secure a spot in today's world of interminable industrial competition.

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The x and y-intercepts of the equation, rounded to the nearest hundredth are:

Blank 1 = 1.60.

Blank 1 = -0.70.

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

f(x) = log(5x + 2) - 1

0 = log(5x + 2) - 1

1 = log(5x + 2)

By applying log rule for base 10, we have the following:

10 = 5x + 2

5x = 8

x = 8/5

x = 1.60.

When the x-value = 0, the y-intercept can be calculated as follows;

f(x) = log(5x + 2) - 1

f(0) = log(5(0) + 2) - 1

f(0) = log(2) - 1

f(0) = 0.3010 - 1

f(0) = -0.70

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the equation function in the form y = ab^x that passes through the points (2,12) and (3,24) is: [tex]y = 3(2)^x[/tex]

What is Cartesian coordinate?

A coordinate system, also known as a Cartesian coordinate system, is a system used to describe the position of points in space. It is named after the French mathematician and philosopher René Descartes, who introduced the concept in the 17th century. In a coordinate system, each point is assigned a unique pair of numbers, called coordinates, that describe its position relative to two perpendicular lines, called axes. The horizontal axis is usually labeled x and the vertical axis is usually labeled y.

Using the point (2,12), we get:

[tex]12 = ab^2[/tex]

Using the point (3,24), we get:

[tex]24 = ab^3[/tex]

Dividing the second equation by the first equation, we get:

[tex]24/12 = ab^3/ab^22 = b[/tex]

Substituting b = 2 into either of the two equations, we can solve for a:

[tex]12 = a(2)^2a = 3[/tex]

Therefore, the equation function in the form y = ab^x that passes through the points (2,12) and (3,24) is: [tex]y = 3(2)^x[/tex]

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