The default rate on government-guaranteed student loans at a certain private 4-year institution is 7 percent. The college extends 10 such loans. (a) What is the probability that none of them will default? (b) That at least three will default? (c) What is the expected number of defaults?​

The difference in cost between a one-line ad and a four-line ad is $14.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To find how much Ben paid in sales tax, we need to first calculate the amount of the sales tax.

The sales tax is 9.5% of the purchase price of the car, which can be expressed as a decimal by dividing by 100:

Sales tax rate = 9.5% = 0.095

To find the amount of sales tax, we can multiply the purchase price by the sales tax rate

Sales tax = 0.095 x $25,500 = $2,422.50

Therefore, Ben paid $2,422.50 in sales tax.

The cost of an ad in a local paper is given by the piecewise function:

c(x) = 40, for x ≤ 5 (one-line ad)

c(x) = 40 + 7(x - 4), for x > 5 (four-line ad)

To find the difference in cost between a one-line ad and a four-line ad, we can subtract the cost of a one-line ad from the cost of a four-line ad:

c(6) - c(1) = (40 + 7(6 - 4)) - 40 = 14

Therefore, the difference in cost between a one-line ad and a four-line ad is $14.

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Answer:

6%

Step-by-step explanation:

percent of change formula = difference between new and original values divided by original value, then multiply by 100 to get a percent

(159 - 150) / 150 = 9/150

9/150 = .06 = 6%

The fractions greater than 5/8 are 6/8, 7/8 and 8/8

Fractions greater than 5/8

Using the number line as a guide, we have the following:

Fractions greater = 6/8, 7/8 and 8/8

Fractions less than 3/8

Using the number line as a guide, we have the following:

Fractions less = 1/8 and 2/8

Fractions greater than 3/8

Using the number line as a guide, we have the following:

Fractions greater = 4/8, 5/8, 6/8, 7/8 and 8/8

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Answer:

Step-by-step explanation:

here is a step-by-step explanation for finding the equation of the line that passes through the points (0, -3) and (0, -8):

Identify the two points that the line passes through: (0, -3) and (0, -8)

Determine the slope of the line: The slope of a line is given by the formula "rise over run," or (y2 - y1) / (x2 - x1). However, in this case, the line is vertical and has an undefined slope.

Write the equation of the line in slope-intercept form: y = mx + b, where "m" is the slope and "b" is the y-intercept. Since the slope of the line is undefined, the equation of the line cannot be written in slope-intercept form.

Write the equation of the line in point-slope form: y - y1 = m(x - x1), where "m" is the slope and (x1, y1) is a point on the line. Since the slope of the line is undefined, the equation of the line cannot be written in point-slope form.

Write the equation of the line as an x-intercept form: The x-intercept form of a line is given by the equation x = a, where "a" is the x-coordinate of the point that the line passes through. In this case, the line passes through the point (0, -3) and (0, -8), so the equation of the line is x = 0.

So, the equation of the line that passes through the points (0, -3) and (0, -8) is x = 0.

Answer:

60% i mean it sounds right

Step-by-step explanation:

The first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

What is the first quartile of the data set?

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

Since we have given a box and whisker plot.

As we know about the box and whisker method that :

Left most part of the box represents the first quartile and the rightmost part of the box represents the third quartile.

And the middle value is for median

so, we can conclude that

First quartile = 20

Third quartile = 40

Median = 25

Hence, the first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

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Answer:

I don't know

Step-by-step explanation:

We can know that she can be any value but these 15 times the value of C. The given system is consistent to all the possible values of f and g, the reduction of the row of the augmented matrix must not result in the row of form  [0 0 ... 0 | b]where  B is nonzero.

By looking the row reduction in the system we can see the 2nd row reduces to  [0 0 ...0 | d-15c-g+f]. Since f and g can be any values we can make them both 20 which denotes d - 15 C is equals to zero, or d equals to 15C.

d-15c = 0, or d = 15c.

Therefore we can know that she can be any value but these 15 times the value of C.

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Using the equation provided, you can estimate the number of hours worked each week for a student with a GPA of 2.21. The equation can be rearranged to solve for h, the number of hours worked each week.

h = (g - 3.04) / (0.012 + 0.0007)

Plugging in the GPA of 2.21, we get:

h = (2.21 - 3.04) / (0.012 + 0.0007)

h = -4.83 hours

Therefore, a student with a GPA of 2.21 would need to work an average of -4.83 hours per week in order to achieve that GPA.

On solving the provided question, we can say that  x = central angle = 60 degrees, r = radius = 9 inches and L = 9.42

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

x = central angle = 60 degrees

r = radius = 9 inches

L = arc length

[tex]L = (x/360)*2*pi*r\\L = (60/360)*2*pi*9\\L = 3*pi\\L = 9.42477796076938\\L = 9.42[/tex]

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Answer:

[tex] \sf \: f(2) = - 2[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 4x - 5x

Now we have to,

→ Find the required value of f(2).

Then the value of f(2) will be,

→ f(x) = 4x - 5x

→ f(2) = 4(2) - 5(2)

→ f(2) = 8 - 10

→ [ f(2) = -2 ]

Hence, the value of f(2) is -2.

The driver increased altitude is 517 feet.

A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the road is inclined at an angle of 6 degrees.  After driving 4950 feet along this​ road, let's find the altitude as follows:

using trigonometric ratios,

sin 6° = opposite / hypotenuse

Therefore,

sin 6° = a / 4950

cross multiply'

a = 4950 sin 6°

a = 4950 × 0.10452846326

a = 517.415893175

Therefore,

a = 517 feet

Altitude = 517 feet

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Using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Once we have determined the value of a single unit, we may multiply that value by the number of units needed to determine the value of the other units. The concept of ratio and proportion is mostly applied using this way. Recognizing the units and values is crucial when using the unitary technique to a problem.

Given,

    Money received for each document = 25 cents

  Number of documents prepared by Bill = 2000

  The amount he received = $474

a) The correct total pay that Bill should receive = 2000*25 = 50,000cents

   Using the unitary method,

                   1 dollar = 100 cents

                  50,000 cents = 50000/100 = $500

b) The amount that his boss owes him = 500 - 474 = $26

Therefore using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let the time taken by Jeeny in both the cases be " t " ~

Now, during upstream : current flow opposes the flow of swimmer (Jenny)

Let her actual speed without current be " v ", so her speed in current (upstream) will be :

[tex]\qquad \sf  \dashrightarrow \: v - 1 \: \: kmph[/tex]

Now, according to formula :

[tex]\qquad \sf  \dashrightarrow \: distance = speed \times time[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8 = (v - 1)t \: \: \: \: \: - (1)[/tex]

Next, durijg dowstream : current flow supporta the flow of swimmer (Jenny)

So, her speed while going downstream will be :

[tex]\qquad \sf  \dashrightarrow \: v +1 \: \: kmph[/tex]

By same formula,

[tex]\qquad \sf  \dashrightarrow \: 16 = (v + 1)t \: \: \: \: \: - (2)[/tex]

Now, solve the two equations ~

[ since time taken by her in both the cases is same, we use t in both equations ]

Divide equation (1) by equation (2) :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{8}{16} = \dfrac{v - 1}{v + 1} [/tex]

[ t gets canceled out ]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{2} = \dfrac{v - 1}{v + 1} [/tex]

[ cross multiply ]

[tex]\qquad \sf  \dashrightarrow \: v + 1 = 2(v - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v + 1 = 2v - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2v - v = 1 - ( - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 1 + 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 3 \: \: kmph[/tex]

That's the required answer ~ [ Jimmy would swim at the rate of 3 kmph if she there was no current ]

Answer: A) 6

Step-by-step explanation:

This is geometry. The two angles are corresponding angles, because they are both cut by the same **transversal line**. When that occurs, corresponding angles are created.

now importantly: corresponding angles are equal to each other, or **congruent**. Knowing this, we can set them equal to each other.

17x+11=19x-1

Solve...

11=2x-1

12=2x

x=6

hope this helps

MM

On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic

volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic

total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.

Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic

Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18

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Answer: To find the total weight of 400 apples, we need to multiply the number of apples by their weight. Each apple weighs 1/4 pound, so 400 apples weigh 400 * (1/4) = 100 pounds.

Since each bag should weigh 5 pounds, we can divide the total weight of apples (100 pounds) by 5 to find the number of bags: 100 / 5 = 20 bags.

So, the answer is 20 bags.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer: a) 1.57 m .

b) 637.79 turns

Step-by-step explanation:

a) The circumference of the wheel can be used to determine how far the vehicle has travelled after making one full turn.

Circumference = 2πr = 50π

C = 157 cm

b)By dividing the entire distance traveled by the diameter of the wheel, we can determine how many times the wheel will turn over a ride of 1 km (1000 meters): 1000 m / 1.57 m = 637.79 turns.

Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

Average = (Sum of all values) / (Number of values)

Average = ($19) / (7 days)

Average = ($19) / (7)

Average = $2.71

Sunday = ($2.71) x (7)

Sunday = $19.00 + $76.00

Sunday = $95.00

Jack is working as a waiter and needs to keep track of his tips. He wants to make an average of $19 per day and needs to figure out how much he needs to make on Sunday. To calculate this, he needs to first figure out the average he wants to make per day. For this, he needs to divide the amount he wants to make daily ($19) by the number of days he is working (7). This gives him an average of $2.71 per day. To get to the amount he needs to make on Sunday, he needs to multiply this average by the number of days he is working, which is 7. This gives him an amount of $19.00 + $76.00, which equals $95.00. Thus, Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

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On solving the provided question we can say that median from the vertex in an isosceles triangle is perpendicular to the base.

ƒ(x)=sin(x)

consider Asin(Bx + C) = y +D changes the amplitude of the function (how high or low it is).

if you want to

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Let O be the circle's centre and P be the midpoint of BC. After that, OP LBC.

Let AP =x and PB = CP -y.

Applying Pythagoras theorem in As AP B and OP B, we have

AB2 = BP2 + AP2 and OB2 = OP2 +BP2

Y2 +x2 ... (i) and, 81 = (9 —x)2 + Y2

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Answer Option C

The point-slope form of the equation of the line is:

Where m is the slope and b is the intersection with the y-axis.

In the line , you can identify that:

The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).

Then the answer is the option C.

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Answer:

C

Step-by-step explanation:

Area A should be the shaded region instead of the region shaded on the graph.

The future value of the investment when interest is compounded continuously is; $3408.29

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

P= $1500, r = 3.95%, t = 5 yr

To Calculate the number of periods: in this case we have 5*12= 60 months.

- The monthly interest rate, we have to divide the annual nominal rate by 12 (the number of periods in the year).

Then, we can calculate the future value as:

A = P (1 + r/n)^nt

A = 1500(1 + 3.95/365)(365)^(5)

P = 1500/ (1 + 0.00010137)^(5)

P = $3408.29

The future value when compounded monthly is $3408.29.

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Answer:

cosΘ = [tex]\frac{\sqrt{21} }{5}[/tex]

Step-by-step explanation:

using the identity

• sin²Θ + cos²Θ = 1 ⇒ cos²Θ = 1 - sin²Θ

given Θ is in quadrant 1 , then cosΘ > 0

sinΘ = [tex]\frac{2}{5}[/tex] , then

cos²Θ = 1 - ( [tex]\frac{2}{5}[/tex] )² = 1 - [tex]\frac{4}{25}[/tex] = [tex]\frac{25}{25}[/tex] - [tex]\frac{4}{25}[/tex] = [tex]\frac{21}{25}[/tex] , then

cosΘ = [tex]\sqrt{\frac{21}{25} }[/tex] = [tex]\frac{\sqrt{21} }{\sqrt{25} }[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]

Answer:

Step-by-step explanation:

The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).

The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).

The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:

1/36 * 1/36 = 1/1296

So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.

"Communist infiltration in the entertainment industry" was the first target of the HUAC hearings among the following choices given in the question.

HUAC was created in 1938 to investigate alleged disloyalty and rebel activities on the part of private citizens, public employees and organizations suspected of having Communist ties.

Originally organized as a minor congressional committee investigating domestic subversion, HUAC (also known as the House Un-American Activities Committee) rose to such power in the late 1940's and early 1950's that the mere threat of investigation by it could ruin a person's career. By the time it was abolished in 1975, HUAC had widened its scope of investigation to include almost every aspect of American society.

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Answer: B) 56

Step-by-step explanation:

[tex]x:y=7:18[/tex]

[tex]x=49[/tex]

find the value of [tex]y[/tex]

let, [tex]x^2[/tex] [tex]7a[/tex]

and let, [tex]y^2[/tex] [tex]8a[/tex]

A/Q

[tex]x=49[/tex]

[tex]7a=49[/tex], divide both sides by 7 to let the [tex]a[/tex] alone,

[tex]a=7[/tex]

///

[tex]y=8a[/tex], so that we now that [tex]a=7[/tex]

so, [tex]y=8*7[/tex]

[tex]y=56[/tex]

hope you've understanded...

Answer:

30 mm

Step-by-step explanation:

just add the length of each side together

Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.

It is the simplest polygon and a key component in many branches of science and mathematics.

A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.

In triangle STU, right angled at T, we have:

[tex]ST = 6UT = \sqrt{(22)}[/tex]

We can use the Pythagorean theorem to find the length of TU:

[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]

Now, we can use the definition of cosine:

cos(S) = adjacent/hypotenuse

In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:

[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]

To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):

cos(S) ≈ 0.78 (rounded to the nearest hundredth)

Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.

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Answer:

120°

Step-by-step explanation:

We need to find the missing angle <SRM

The angles inside a triangle always add up to 180°. So this means:

<TSR+<STR+<TRS=180°

65°+55°+<TRS=180°

120°+<TRS=180°

<TRS=180°-120°=60°

All angles along a straight line add up to 180°. This means:

<TRS+<SRM=180°

60°+<SRM=180°

<SRM=180°-60°=120°

Answer:

120° is the answer please mark. brainly