Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected.

a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree?

b. What is the probability that exactly seven of the college graduates plan to pursue a graduate degree?

c. What is the probability that at least six but no more than nine of the college graduates plan to pursue a graduate degree?

Answer:

B: y ≥ 2r-4.

Step-by-step explanation:

To solve for y, we need to isolate y on one side of the inequality. First, we can simplify the left side of the inequality by dividing both sides by 2:

2x - y ≤ 4

Then, we can subtract 2x from both sides to get:

-y ≤ -2x + 4

Finally, we need to isolate y by multiplying both sides by -1 and flipping the direction of the inequality:

y ≥ 2x - 4

Now we can see that the equivalent inequality is option B: y ≥ 2r-4.

Answer:

Solve the inequality for

x

by finding

a

,

b

, and

c

of the quadratic then applying the quadratic formula.

All real numbers

Interval Notation:

(

−

∞

,

∞

)

Step-by-step explanation:

The vertex is (4,1), and the parabola opens b since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.

A parabola is a symmetrical U-shaped curve that can be formed by intersecting a cone with a plane parallel to one of its sides. It is a type of quadratic function, which can be expressed in the form of y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.

f(x) = x²+8x-3

To complete the square, we need to add and subtract the square of half the coefficient of x:

f(x) = (x²+8x+16) - 19 --> (x+4)² - 19

So, the equation in vertex form is: f(x) = (x+4)² - 19.

The vertex is (-4,-19), and the parabola opens upwards since the coefficient of the squared term is positive. The axis of symmetry is x=-4, and the domain is all real numbers. The range is [-19, ∞), since the minimum value is -19.

f(x)=-2x² + 16x-31

To complete the square, we need to factor out the leading coefficient of -2, and then add and subtract the square of half the coefficient of x:

f(x) = -2(x² - 8x + 16) - 31 + 32 --> -2(x-4)² + 1

So, the equation in vertex form is: f(x) = -2(x-4)² + 1.

The vertex is (4,1), and the parabola opens downwards since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.

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Answer:

29°

Step-by-step explanation:

In the first triangle,

46 + 30 + x = 180 (Angle sum property)

76 + x = 180

x = 180 - 76

x = 104

In the second triangle,

47 + 104 + y = 180

151 + y = 180

y = 29

Thus, the required angle is 29°.

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Answer:

the answer is 29 degrees

Step-by-step explanation:

look at the picture below

Answer: The probability of reaching into the jar and retrieving a black button is 0.64. Therefore, the probability of reaching into the jar and retrieving a button that is not black is the complement of this probability, which is 1 - 0.64 = 0.36.

In other words, the probability of not getting a black button is the same as the probability of getting a non-black button, which includes all the other colored buttons in the jar. Since there are no other details given in the problem regarding the number of non-black buttons or the probability of retrieving each non-black button, we assume that they are all equally likely to be retrieved and simply calculate the probability of not getting a black button as the complement of the probability of getting a black button.

Therefore, the probability of reaching in the jar and retrieving a button that is not black is 0.36 or 36%.

Step-by-step explanation:

Both formulations convey the same meaning and represent the same equation mathematical operation: x raised to the power of 5 divided by x raised to the power of 10.

In this format, the expression is shown using exponent notation. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The phrase can therefore be written as x⁵/x¹⁰.

In this method, the division symbol serves to represent the expression. The denominator (bottom) of the fraction is x raised to the power of 10, while the numerator (top) of the fraction is x raised to the power of 5. The expression is therefore (x⁵)/. (x¹⁰).

Therefore, the same mathematical operation is represented by both formulations, which both express the same meaning: x to the power of 5 divided by x to the power of 10.

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Answer:

Step-by-step explanation:

number of books are 5 so you will have to do 5 by hundred  which will lead to twenty percent

The likelihood that the manager will choose the longest just-received nonfiction book and the shortest recently arrived fiction book is 1/20, or 5%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

The probability of selecting the shortest fiction book is 1/5 and the probability of selecting the longest nonfiction book is 1/4. Since these events are independent, we can multiply their probabilities to find the probability of both events happening:

P(shortest fiction book and longest nonfiction book) = P(shortest fiction book) x P(longest nonfiction book) = 1/5 x 1/4 = 1/20

So the probability that the manager will select the shortest of the newly arrived fiction books and the longest of the newly arrived nonfiction books is 1/20, which is equivalent to 5%.

Therefore, the answer is option A.

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Total surface area of right triangular prism is 750cm²

A right triangular prism is a three-dimensional geometric shape with three rectangular faces connecting the edges of its two parallel, congruent triangular bases.

Area of the two opposite side triangles (A₁) = 2 × ( [tex]\frac{1}{2}[/tex] × 12 × 5)

Area of the two opposite side triangles (A₁) = 60 cm²

Area of upper, lower and side rectangles (A₂) = (5×23) + (12×23) + (13×23)

Area of upper, lower and side rectangles (A₂) = 115 + 276 + 299

Area of upper, lower and side rectangles (A₂) =  690 cm²

Total surface area of right triangular prism = A₁ + A₂

Total surface area of right triangular prism = 60 + 690

Total surface area of right triangular prism = 750 cm²

Therefore, the total area of the right triangular prism is 750cm²

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In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.

In exchange for using borrowed funds or assets, a borrower must pay the lender interest. It is charged for a certain duration of time, typically until the loan is fully returned, and is typically stated as a percentage of the amount borrowed. This fee is known as the interest rate. For instance, if a bank lends you $1,000 at a 5% annual interest rate, after a year of borrowing the money you would still owe the bank $50 more in interest. The creditworthiness of the borrower, the risk of the loan, and current market conditions are frequently used to establish the interest rate.

given

We know that Fwam expects the account to be worth $91,000 in 12 years and that the interest rate is 5.9% compounded daily in this situation.

We must convert the interest rate and the time period to the proper units before we can use the formula.

We begin by converting the 5.9% yearly interest rate to a daily rate:

daily rate is equal to (1 + 0.059/365)(365/365)-(1-1) = 0.00015999.

4,380 days in 12 years, or 365 days per year.

We can now enter the values into the formula to find P:

$91,000 = P × 2.3226

P = $39,165.95

In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.

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If TV cable company has 2400 subscribers who are each paying ​$16 per month, charging $52 per month will yield a maximum revenue of $98,304.

To find the rate that will yield the maximum revenue, we can use the formula:

r = -b / 2a

where r is the rate, a is the coefficient of the quadratic term, and b is the coefficient of the linear term in the revenue equation.

The revenue equation is:

R = (2400 + 120x)(16 - 0.5x)

Expanding and simplifying, we get:

R = -0.5x^2 + 52x + 38400

So, a = -0.5 and b = 52. Plugging these values into the formula, we get:

r = -52 / 2(-0.5) = 52

This means that the company should charge $52 per month to maximize revenue. To find the maximum revenue, we can plug this value into the revenue equation:

R = (2400 + 120(52))(16 - 0.5(52)) = $98,304

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The radius οf the rain barrels is apprοximately 40.03 cm.

A value knοwn as the square rοοt οf a number is οne that, when multiplied by itself, yields the οriginal number. An alternative tο square rοοting a number is tο use it. Therefοre, the cοncepts οf squares and square rοοts are cοnnected. The οriginal number is equal tο the square rοοt οf any integer, which is equivalent tο a number.

The tοtal surface area is given as 40,212 square centimeters. Therefοre, we can write the equatiοn:

[tex]2\pi r^2 +\pir^2 + 4\pi r^2 + \pi r^2 = 40212[/tex]

Simplifying this equatiοn, we get:

[tex]8\pi r^2 = 40212[/tex]

Dividing bοth sides by 8π, we get:

[tex]r^2 = 1602.62[/tex]

Taking the square rοοt οf bοth sides, we get:

r ≈ 40.03 cm

Therefοre, the radius οf the rain barrels is apprοximately 40.03 cm.

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Step-by-step explanation:

4n - 3 = 0

4n = 0 + 3

4n = 3

[tex]n \: = \frac{3}{4} [/tex]

Answer:

28

Step-by-step explanation:

2×12-(-4) - and - = +

24+4 + and + = +

28 + and - = -

- and + = -

Answer:21.33 is the right answer for x

The two forms of the expression

[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]

when simplified are

[tex] = {x}^{ - 5} [/tex]

x exponents negative 5 and

[tex]\frac{1}{ {x}^{5} } [/tex]

numerator 1 over denominator x exponents 5.

Given:

[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]

When we have the same base but different powers in indices division, one of the bases is chosen and the powers are subtracted.

[tex] = {x}^{5 - 10} [/tex]

[tex] = {x}^{ - 5} [/tex]

[tex] = \frac{1}{ {x}^{5} } [/tex]

Therefore, the simplified expressions are x exponents negative 5 and numerator 1 over denominator x exponents 5.

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The three true statements are

Step-by-step explanation:

Standard form for a circle is  ( x -h)^2 + ( y-k)^2 = r^2

     h, k   is the center      r is the radius

x^2 -2x + y^2 = 8     arrange into standard form ( complete the square for 'x')

(x-1)^2 + y^2 = 8+1

(x-1)^2 + y^2 = 9        shows center is at   1, 0

                                   radius = 3

 So

The radius of the circle is 3 units.

The center of the circle lies on the x-axis    (1,0 is on the x axis)

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The length of the ramp we need to build should be at least 38.61 feet to pass code.

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.

We can use trigonometry to solve the problem. Let x be the length of the ramp we need to build. Then, the angle the ramp makes with the ground is given by:

sin(theta) = opposite/hypotenuse

where theta is the angle the ramp makes with the ground, opposite is the vertical increase of 10 feet, and hypotenuse is the length of the ramp x.

Solving for x, we get:

x = opposite/sin(theta) = 10/sin(15)

Using a calculator, we can evaluate sin(15) to be approximately 0.2588. Then, we can divide 10 by 0.2588 to get:

x ≈ 38.61

Therefore, the length of the ramp we need to build should be at least 38.61 feet to pass code.

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Evan sold half his story books and then bought 17 more. Evan had thirty bucks.

A mathematical statement is known as an equation, and the equal sign ('=') connects two expressions. At least one unknown variable must be determinable. For instance, an equation is 3x - 8 = 16. We achieve x = 8.

We will sοlve the prοblem by fοrming a οne variable equatiοn.

Let's say Evan started out with a lot of problems. Evan gave up half of his regular wares. He split two separate cakes.

He now has (x-x/2)=x/2 straight numbers.

He then gained 17 pounds.

Sο subsequent to purchasing 17 bοοks he has nοw (x/2+17) story bοοks

Given number οf stοry bοοks he has right nοw is 32.

By equating the two, we can construct a equation for one variable.

(x/2+17) = 32 Solving for x will be the equation:

(x/2+17) = 32; x/2 = 32- 17; x/2 = 15; x = 152; x = 30.

According to the initial equation, Evan had 30 books.

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Step-by-step explanation:

the angle at Y = 1/2 × (arc angle WZ - arc angle ZX).

so,

42 = (arc angle WZ - 51)/2

84 = arc angle WZ - 51

135° = arc angle WZ

the arc angle WX is the remainder of the whole circle to the sum of the arc angles WZ and ZX :

arc angle WX = 360 - 135 - 51 = 174°

Hello!

1= 122

2= 58

3= 58

4= 122

5= 122

6= 58

7= 58

8= 122

To find angle 2, you subtract 122 from 180 because angles 1 and 2 are supplementary angles. You can find angle 3 by using the vertical angles theorem. This means that angle 2 and 3 are congruent to each other. You can use the same for angle 4, meaning 1 and 4 are also congruent. You can use the alternate interior angles theorem to prove that 3 and 6 are congruent and then use the vertical angles theorem to prove that 6 and 7 are congruent. You can find angles 5 and 8 by proving that 5 is congruent to 4 using the alternate interior angles theorem and then once again using the vertical angles theorem to prove that angle 5 is congruent to angle 8. Let me know if this is too hard to understand, I will happily simplify it.

Answer:23 degrees

Step-by-step explanation:

Ok! I'm a high school student so this is what I can see.

Angles A and the 130 are supper- angles meaning they add up to 180.

So that means A is 50.

Next I noticed by experience that A and B are vertical angles. So that means B is 50 as well.

And since this all have to equal to 360 angles. The equation is

360= 50+130+50+107+x or X= 360- (50+130+50+107)

And that is  x=23

Happy Soving

The volume of cylinder is 191 cubic centimeters.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here cylinder with height 6 cm ,

Volume = 128 cubic centimeters.

Now using volume of cylinder formula then,

=> Volume V =

=> 128 = 3.14**6

=>  =  = 6.79406

=> r = 2.6 cm.

Now volume of cylinder with height 9 cm is ,

=> Volume V = 3.14**9 = 191 cubic centimeters.

Hence the volume of cylinder is 191 cubic centimeters.

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Answer: prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.

Step-by-step explanation:

prohibits debt collection companies from using abusive, unfair or deceptive practices to collect debts from you.

The right to verify the amount owed is the right the Fair Debt Collection Practices Act (FDCPA) give borrowers The correct option is C.

The Fair Debt Collection Practices Act (FDCPA) is a federal law that governs the conduct of third-party debt collectors who attempt to collect debts on creditors' behalf.

Borrowers who are being pursued by debt collectors have several rights under the FDCPA.

One of the rights granted to borrowers by the FDCPA is the right to verify the amount owed.

This means that borrowers have the right to ask the debt collector for written confirmation of the debt, including the amount owed and the creditor's name.

The debt collector is required to provide this information within a reasonable time after receiving the request.

Thus, the correct option is C.

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Answer: $5.40

Step-by-step explanation:

First, let's calculate the tax for each purchase and then find the total amount paid by Dave and James.

For Dave:

Basketball cost = $15

Tax = 8% of $15 = 0.08 * 15 = $1.20

Total amount paid by Dave = Cost + Tax = $15 + $1.20 = $16.20

For James:

Football cost = $20

Tax = 8% of $20 = 0.08 * 20 = $1.60

Total amount paid by James = Cost + Tax = $20 + $1.60 = $21.60

Now, let's find the difference between the amounts paid by Dave and James.

Difference = Amount paid by James - Amount paid by Dave = $21.60 - $16.20 = $5.40

So, the difference in the amounts paid by Dave and James, including tax, is $5.40.

Answer:

D. -22.25

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses

|-3.5| = 3.5

Next, we can simplify the expression inside the parentheses:

-7 ÷ |-3.5| = -2

Now we can simplify the entire expression:

3/10^2 - 17 + (-2) x 2.67 = 0.09 - 17 - 5.34 = -22.25

The expansion of the multiplication is [tex]-16+12\sqrt{3}[/tex] and [tex]5-13\sqrt{5}[/tex]

Irrational numbers are real numbers that cannot be represented as simple fractions. If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to zero. [tex]\sqrt{2}, \sqrt{3}[/tex] are two examples.

distributive law

This property states that multiplying the total of two or more addends by a number produces the same result as multiplying each addend separately by the number and then putting the products together.

That is A(B+C)=AB+AC

According to the given information:

[tex](-2\sqrt{3} +2)(\sqrt{3}-5) = -2\sqrt{3}*\sqrt{3} + 10\sqrt{3} +2\sqrt{3} -10[/tex]

                                 =[tex]-6+12\sqrt{3}-10[/tex]

                               = [tex]-16+12\sqrt{3}[/tex]

[tex](-2-3\sqrt{5})(5-\sqrt{5}) = -10+2\sqrt{5}-15\sqrt{5}+3*5[/tex]

                               = [tex]-10-13\sqrt{5}+15[/tex]

                              =[tex]5-13\sqrt{5}[/tex]

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Step-by-step explanation:

To solve for x, we'll first need to simplify the equation by combining like terms:

0.6x - 5 = 0.1x + 7

0.6x - 0.1x = 7 + 5

0.5x = 12

x = 12 / 0.5

x = 24

Therefore, the value of x that makes the equation true is 24.

Answer:

The correct answers for this question are:

A. Diagonals bisect each other.

C. Opposite angles are congruent.

D. Opposite sides are parallel.

E. Consecutive angles are supplementary. Those are the statements that describe properties of parallelograms. They are also belong to the family of quadrilateral.

Step-by-step explanation:

Answer:

7.38%

Step-by-step explanation: