approximately 10.5% of american high school students drop out of school before graduation. assume the variable is binomial. choose 15 students entering high school at random. find these probabilities. round intermediate calculations and final answers to three decimal places. part: 0 / 30 of 3 parts complete part 1 of 3 (a) at least 13 graduate

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

area

Step-by-step explanation:

area of parallelogram = base × height

= 10× 3

= 30 cm²

plz mark my answer as brainlist plzzzz vote .

hope this will be helpful to you .

The area of the parallelogram is \(30cm^2\).

Given that,

Now the area of the parallelogram is

\(= base \times height\\\\= 3 \times 10\\\\= 3cm^2\)

Therefore we can conclude that the area of the parallelogram is \(30cm^2\)

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The estimate of 645,547 to the nearest hundred thousand is 600,000

The number is given as:

Number = 645,547

To estimate the number means that we approximate the number.

In this case, we round the number to the nearest 100,000.

This means that:

645,547 approximates to 600000

Hence, the estimate of 645,547 to the nearest hundred thousand is 600,000

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Answer:

An equivalent expression = 8b + (-4)

Step-by-step explanation:

In Mathematics, numbers exhibit or are guided by certain properties that they can show.

Some of those of properties are :

a) Commutative property where:

a + b = b + a

b) Associative property

a+( b + c) = (a + b) + c

c) Additive inverse property

a - b = a + ( - b)

For the question above, we are told that the total cost of what Karen bough is represented by the expression 8b - 4. We are asked find the equivalent expression.

An equivalent expression is defined as an expression that has the exact value for all the values obtained from the variable.

Hence, using the Additive inverse property

a - b = a + ( - b)

The equivalent expression for 8b - 4 = 8b + ( -4)

Explanation:

The probability of picking red is 0.13

The probability of picking orange is 0.20

The probability of picking either of these is 0.13+0.20 = 0.33

So the probability of picking neither of them is 1 - 0.33 = 0.67

There's a 67% of this happening.

Answer:

0.34

Step-by-step explanation:

because the probability of red is 20 and the probability of orange is 14 20 + 14 is 34.

No; multiplication of polynomials is not necessarily commutative.

So, the correct answer is D.

The expressions given are not equal when simplified. To see why, we can use the distributive property of multiplication over addition to expand each expression.

For the first expression, we have:

(x³ − 5x²)(2x + 3) + (² − 4x) = 2x⁴ - 10x³ + 3x³ - 15x²+ x²- 4x = 2x⁴ - 7x³ - 14x² - 4x

For the second expression, we have:

(x² − 4x) + (2x + 3)(x³ − 5x²) = x² - 4x + 2x⁴ - 10x³ + 3x² - 15x = 2x⁴ - 10x³ + 4x² - 19x

As we can see, the two expressions are not the same.

To answer the question about whether the expressions would be equal if simplified, the correct answer is D.

This is because multiplication of polynomials is not necessarily commutative, meaning that the order in which we multiply the terms can affect the result.

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The solutions to the equations are

1. x = 4

2. x = -12

3. x = 0 and x = 4

The solutions to the inequalities are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

From the question, we have the following equations

1. 4x + 6 = 8x - 10

2. -3/4x - 2 = -1/2x + 1

3. |4 - 2x| + 5 = 9

Next, we split the equations to 2

So, we have

1. y = 4x + 6 and y = 8x - 10

2. y = -3/4x - 2 and y = -1/2x + 1

3. y = |4 - 2x| + 5 and y = 9

Next, we plot the system of equations (see attachment) and write out the solutions

The solutions are

1. x = 4

2. x = -12

3. x = 0 and x = 4

From the question, we have the following inequalities

4. x² + 4x - 5 < 0

5. x² - x - 12 ≥ 0

Next, we plot the system of inequalities (see attachment) and write out the solutions

The solutions are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

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Your friend's claim that every quadratic function with a restricted domain to non-negative values has an inverse function is not correct.

To have an inverse function, a function must be one-to-one, which means that each input corresponds to a unique output and each output corresponds to a unique input. However, quadratic functions whose domains are restricted to non-negative values are not necessarily one-to-one.

For example, the quadratic function f(x) = x^2 with a domain of [0, infinity) is not one-to-one since both -2 and 2 produce an output of 4 when plugged into the function. Therefore, this function does not have an inverse function.

However, there are ways to restrict the domain of a quadratic function in a way that makes it one-to-one and thus invertible. For instance, by restricting the domain of f(x) = x^2 to [0, infinity), we can define its inverse function as g(x) = sqrt(x), where sqrt represents the square root function. This inverse function maps each non-negative real number x to its unique non-negative square root, which makes it a valid inverse for f(x) over its restricted domain.

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Answer:

B) 7.4

C) 3.7

Step-by-step explanation:

B) The opposite of squaring is to square root. Therefore we do the square root of 55.11 to find the radius. (√55.11)

This is 7.4 (to one decimal place)

C) The diameter is half of the radius.

We divide the value in our calculator by 2

We get 3.7 (to one decimal place)

Sorry hon, just saw the comment on the last answer!

B. Approximately 7.4m

   To get to the answer... the equation was 55.11= r^2, so you would just find the square root of 55.11 to eliminate r.

C. Approximately 14.8m

  To get to the answer... diameter is just from one end of the circle to the opposite.  This being said, it is just double the radius.

Answer:

Step-by-step explanation:

(2/3-1/4)=8/12-3/12=5/12

(5/6 divided by 3)=5/6 times 1/3=5/18

5/12 times 5/18=25/216

The statement which is true for the inequality will be equal to 9 > -5, so 9 is located to the right of -5 on a horizontal number line.

A straight line of numbers is shown visually as a number line. This line is employed to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

As per the given inequalities given in the question,

1.

-10 > -15, so -10 is located to the left of -15 on a horizontal number line.

The statement is wrong because -10 is located on the right side of -15

2.

8 > -13, so 8 is located to the left of -13 on a horizontal number line.

The statement is wrong because 8 is located on the right side of -13.

3.

9 > -5, so 9 is located to the right of -5 on a horizontal number line.

This statement is true, that 9 is located to the right of -5.

4.

-6 < 1, so -6 is located below 1 on a vertical number line.

This statement is true, that -6 is located to the below of -5.

5.

-14 > 7, so -14 is located below 7 on a vertical number line.

This statement is false.

6.

11 < -13, so 11 is located to the right of -13 on a horizontal number line.

This statement is also false.

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Answer:

10

Step-by-step explanation:

it is 10 because 60-20 is 40 and 40 divided by 4 is 10.

In Japanese criminal trials, approximately 95% of the defendants are found guilty, while in the United States, about 60% of defendants are found guilty, according to "The Book of Risks" by Larry Laudan.

The statistics provided indicate a stark contrast in conviction rates between Japanese and American criminal trials. In Japan, the overwhelming majority of defendants, around 95%, are found guilty. This suggests a high degree of confidence in the prosecution's ability to prove guilt. On the other hand, in the United States, about 60% of defendants are found guilty, implying a comparatively lower conviction rate. This discrepancy could be due to several factors, such as differences in legal systems, standards of proof, evidence presentation, and judicial practices. It is essential to note that these statistics provide a general overview and may vary depending on specific circumstances and cases within each country's legal system.

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If Q and R have coordinates of (xQ, yQ) and (xR, yR), respectively, then Q' and R' have coordinates of : Q' = (xQ + a, yQ + b) and R' = (xR + a, yR + b)

Assuming that "triangle PQR is translated to trinagle PQR" is a typo, and the second triangle should be denoted as triangle P'Q'R', we can find the coordinates of Q' and R' after the translation.

Let's say that the translation vector is (a, b), where a and b are the horizontal and vertical shifts, respectively. Then, the coordinates of Q' and R' can be found by adding (a, b) to the coordinates of Q and R, respectively.

If we assume that the coordinates of Q and R are (xQ, yQ) and (xR, yR), respectively, then the coordinates of Q' and R' are:

Q' = (xQ + a, yQ + b)

R' = (xR + a, yR + b)

Note that the coordinates of point P do not change, as it is not part of the triangle being translated.

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Answer: 3rd one I think

Step-by-step explanation: I had smth like this

Answer:

You got it right! The answer is [A].

Step-by-step explanation:

Visualize a rectangle 4 units long and 2 units wide. Doesn't each part of the triangle seem to be a half of different parts of the rectangle?

Step-by-step explanation:

5x + 2 = 50 - x (vertically opp angle)

5x + x = 50 - 2

6x = 48

x = 8

if you wanna check it,

5x + 2 = 50 - x

5(8) + 2 = 50 - 8

40 + 2 = 42

42 = 42

Answer:

The diameter of a circle passes through the center of the circle and has its endpoints on the circle itself. The diameter of any circle is two times the length of that circle's radius.

Step-by-step explanation:

To find the diameter of a circle, you need to know the radius of the circle, double it to get the diameter. The radius is the distance from the center of the circle to its edge. If the radius of the circle is 4 cm, then the diameter of the circle is 4 cm x 2, or 8 cm. If you know the circumference of the circle, divide it by π to get the diameter.

The required commission earned by the salesperson is given as $156.

Given that,
The salesperson's commission on a $1300 sale, if the commission rate is 12%, is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Amount = $1300
Commission = 12% of ammount
Commission = 0.12 × 1300
Commission = $156

Thus, the required commission earned by the salesperson is given as $156.

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Answer:

Step-by-step explanation:

A = {2,8,10,14}

B= {6,8,20}

C={8,18,20,24}

A ∩ B --> intersection means elements that  are in both sets A & B

A ∩ B = {8}

A∩ C =  {8}

B ∩ C = {8 , 20}

A∩B ∩ C = {8}

First blue box = { 2,10, 14}

Second blue box = {18, 24}

First green box = { 8}

Second green box = { 20}

b) A ∩ B = {8}

n [ A ∩ B] = 1

Probability of the number to be a member of A∩B =  1 / 25

Answer:

4 : 2 = 10 : 5.

Step-by-step explanation:

Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)

Answer: 80

Step-by-step explanation:

4500-2500 is 2000 dollars reduction, or money paid off.

For every 250 dollars, there is a 10 points increase. 2000 divided by 250 is 8. There are 8 sets of 250 dollars. So, for every 250 dollars (you have 8 of them), 10 points increase. Therefore, you multiply 10 by 8.

10x8 = 80. Your credit score has increased by 80 points.

Answer: 1hr

Step-by-step explanation: Distance = speed × time

Time = Distance / Speed = 60/60

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles.

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red and blue marbles. This is because the expected value of an event is the sum of the probability of each outcome multiplied by the associated outcome. Since Zuri is randomly removing marbles from the bag, one at a time and without replacement, the probability of each outcome (red or blue) is equal. Therefore, the expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles. This is because each marble has an equal chance of being removed and, therefore, each marble has the same expected value.

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Using the empirical rule, we can determine that approximately 15.87% of IQ scores are at least 77.

According to the empirical rule, for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

To find the percentage of IQ scores that are at least 77, we need to calculate the z-score for 77 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (77 - 101) / 12 = -24 / 12 = -2

Since 77 is 2 standard deviations below the mean, we know that approximately 95% - 2% = 15.87% of the IQ scores will be at least 77. Therefore, approximately 15.87% of IQ scores are at least 77, based on the empirical rule.

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Answer:

\(y = log_{\sqrt{(-1)} } (x - 5.5) + 2 - 0.25817i\)

Step-by-step explanation:

The general form of a logarithmic function is given as follows;

\(y = log_b (x - h) + k\)

From the given data, we have;

When x = 1, y = -30

Therefore;

\(b^{-30 - k} = 1 - h\)

When x = 4, y = 0

Therefore;

\(b^{0 - k} = 4 - h\)

\(b^{ - k} = 4 - h\)

When x = 5, y = 6

Therefore;

\(b^{6 - k} = 5 - h\)

\(b^{6 - k} = b^{6} \times b^{- k} = 5 - h\)

\(\therefore b^{6} =\dfrac{5 - h}{b^{- k}} = \dfrac{5 - h}{4 - h}\)

When x = 6, y = 4

Therefore;

\(b^{4 - k} = 6 - h\)

\(b^{4 - k} = b^{4} \times b^{- k} = 6 - h\)

\(\therefore b^{4} = \dfrac{6 - h}{b^{- k}} = \dfrac{6 - h}{4 - h}\)

Which gives;

\(\therefore \dfrac{b^{6}}{b^{4}} =b^{2} = \dfrac{\dfrac{5 - h}{4 - h}}{\dfrac{6 - h}{4 - h}} = \dfrac{5 - h}{6 - h}\)

When x = 7, y = 2

Therefore;

\(b^{2 - k} = 7 - h\)

\(b^{2} \times b^{- k} = 7 - h\)

\(\therefore b^{2} =\dfrac{7 - h}{4 - h}\)

From which we have;

\(\dfrac{5 - h}{6 - h} = \dfrac{7 - h}{4 - h}\)

20 - 5·h - 4·h + h² = 42 - 7·h - 6·h + h²

20 - 9·h = 42 - 13·h

4·h = 22

h = 22/4 = 5.5

\(\therefore b^{2} =\dfrac{7 - h}{4 - h} =\dfrac{7 - 5.5}{4 - 5.5} = \dfrac{1.5}{-1.5} = -1\)

b = √(-1)

\(b^{ - k} = 4 - h\)

-k = log(-1.5)/log(√-1)

k = 2 - 0.258127·i

The logarithmic function is therefore;

\(y = log_{\sqrt{(-1)} } (x - 5.5) + 2 - 0.25817i\)

Answer:

6. 4/1  7. 4/2

Step-by-step explanation:

that's all I got I hope it helps.

The sum of the numbers written on the faces of the cube is 333.

A vertex, also known as a point, is a fundamental part of a shape or an object. It is the point at which two or more lines, edges, or faces meet. Vertex can also refer to the corner of a polygon, where multiple lines meet. In 3D geometry, a vertex is a point where three or more edges meet. In a 3D object, each vertex is considered to be a corner of the object. Vertices are a crucial part of the structure and design of shapes, and can be used to define a shape's size, shape and dimension.

The sum of the numbers written on the faces of the cube is equal to the sum of the products of the numbers assigned to the vertices of the cube divided by three. Since the sum of the numbers assigned to all the vertices is equal to 1001, the sum of the numbers written on the faces of the cube is equal to 1001/3, which is equal to 333. Therefore, the sum of the numbers written on the faces of the cube is 333.

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If we will start by solving for y, it means that x is substituted in one of the equations.

If we clear the value of x from the first equation and replace it in the second equation, we would get:

Option A does not correspond to an equation of the system as it would be:

It is ignoring the coefficient -5 that multiplies x in the second equation.

Option B is exactly the result we have obtained from the substitution, so this is the equation.

Option C has the sign wrong as x=-3y+14.

Option D does not substitute x, so it won't be the step to solve for y.

Answer: Option B.

The expected amount of each cube in the complete bag is given as follows:

20 blue cubes.

20 red cubes.

12 green cubes.

8 white cubes.

The expected amounts are obtained by applying the proportions in the context of the problem.

We are told that a bag has 60 cubes a random sample of 15 cubes is collected from the bag the results from the random sample.

15 cubes were selected from a bag of 60, hence the fraction collected is given as follows:

15/60 = 1/4.

Meaning that the expected amounts on the bag are given by the amounts on the sample multiplied by 4.

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