Which polynomial does the model represent? The model shows 1 black square block, 2 white thin blocks, 1 black thin block, 1 white small square block, 3 black small blocks

(a) About 7.0% of all applicants had scores higher than 13 on the MCAT biological sciences part.

(b) About 89% of those who entered medical school had scores between 9 and 12 on the MCAT biological sciences part.

(a) Approximately 15.87% of children aged 13 to 15 years old have scores above 101 on the intelligence test.

(b) The score marking the lowest 30 percent of the distribution is approximately 98.78 on the intelligence test.

(c) The score marking the highest 15 percent of the distribution is approximately 135.86 on the intelligence test.

(a) About 2.5% of men are taller than 74 inches in height.

(b) Approximately 2.5% of all men are shorter than 4 inches in height.

(c) About 13.59% of men are between 64 and 66.5 inches in height.

(a) For the scores on the MCAT biological sciences part, which are normally distributed with a mean of 9.9 and a standard deviation of 2.1, we want to find the percentage of all applicants who had scores higher than 13.

To calculate this, we need to find the area under the normal curve to the right of the score 13.

Using the standard normal distribution table or a calculator, we can find that the area to the right of 13 is approximately 0.070, or 7.0%. Therefore, about 7.0% of all applicants had scores higher than 13.

(b) For those applicants who entered medical school, we want to find the percentage of them who had scores between 9 and 12 on the MCAT biological sciences part.

To calculate this, we need to find the area under the normal curve between the scores 9 and 12.

Using the standard normal distribution table or a calculator, we can find that the area between 9 and 12 is approximately 0.89, or 89%.

Therefore, about 89% of those who entered medical school had scores between 9 and 12.

(a) For the scores on the intelligence test for children aged 13 to 15 years, which are normally distributed with a mean of 111 and a standard deviation of 24, we want to find the proportion of children who have scores above 101.

To calculate this, we need to find the area under the normal curve to the right of the score 101.

Using the standard normal distribution table or a calculator, we can find that the area to the right of 101 is approximately 0.8413.

Therefore, the proportion of children aged 13 to 15 years with scores above 101 is approximately 1 - 0.8413 = 0.1587, or 15.87%.

(b) The score which marks the lowest 30 percent of the distribution can be found by finding the z-score corresponding to the lower 30th percentile and then converting it back to the original scale using the mean and standard deviation.

The z-score corresponding to the lower 30th percentile is approximately -0.524. Converting this back to the original scale using the mean of 111 and the standard deviation of 24, we have:

Score = Mean + (Z-score * Standard deviation) = 111 + (-0.524 * 24) ≈ 98.78.

Therefore, the score which marks the lowest 30 percent of the distribution is approximately 98.78.

(c) To find the score which marks the highest 15 percent of the distribution, we need to find the z-score corresponding to the upper 15th percentile and then convert it back to the original scale.

The z-score corresponding to the upper 15th percentile is approximately 1.036. Converting this back to the original scale using the mean of 111 and the standard deviation of 24, we have:

Score = Mean + (Z-score * Standard deviation) = 111 + (1.036 * 24) ≈ 135.86.

Therefore, the score which marks the highest 15 percent of the distribution is approximately 135.86.

(a) For the heights of adult men in the U.S., which are normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches, we want to find the percentage of men who are taller than 74 inches.

Using the 68-95-99.7 rule (also known as the empirical rule), we know that approximately 2.5% of the data falls beyond two standard deviations above the mean.

Since 74 inches is two standard deviations above the mean (69 + 2 * 2.5 = 74), we can conclude that about 2.5% of men are taller than 74 inches.

(b) According to the same 68-95-99.7 rule, approximately 2.5% of the data falls beyond two standard deviations below the mean.

Since 4 inches is more than two standard deviations below the mean (69 - 2 * 2.5 = 64), we can conclude that about 2.5% of all men are shorter than 4 inches.

(c) To find the percentage of men who are between 64 and 66.5 inches, we need to calculate the area under the normal curve between these two values.

First, we need to standardize the values by calculating the z-scores:

Z1 = (64 - 69) / 2.5 = -2

and Z2 = (66.5 - 69) / 2.5 = -1.

This corresponds to the area between -2 and -1 under the standard normal distribution.

Using the standard normal distribution table or a calculator, we can find that the area between -2 and -1 is approximately 0.1359.

Therefore, about 0.1359 or 13.59% of men are between 64 and 66.5 inches in height.

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At the 0.10 level of significance, the evidence is insufficient to disprove the assertion that the proportion is 48%.

Based on the given conditions,

The analyst or researcher establishes a null hypothesis based on the research question or problem that they are trying to answer. Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?) the null hypothesis could be H0: X = 0. If the question is instead, is X the same as Y, the H0 would be X = Y. If it is that the effect of X on Y is positive, H0 would be X > 0. If the resulting analysis shows an effect that is statistically significantly different from zero, the null can be rejected.

Let's start by outlining the research's null and alternate hypotheses;

A newsletter publisher believes that 60`% of their readers own a Rolls Royce.

This means that the null hypothesis is:

H0: p = 0.48

That is, that the proportion of their readers who own a Rolls Royce is of 0.48.

A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim.

The alternate hypothesis is:

Ha: p ≠ 0.48

Now that he fails to disprove the null hypothesis based on the evidence, we will draw the following conclusion:

Therefore,

At the 0.10 level of significance, the evidence is insufficient to disprove the assertion that the proportion is 48%.

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Answer:

5/8 + 1/2 = 1 1/8

1/2 = 4/8

5/8 + 4/8 = 9/8

9/8 = 1 1/8

Those are the steps. Sorry for not doing it right earlier.

Step-by-step explanation:

5/8 + 1/2= 5/8+ 1 · 4/2 · 4 = 5/8+ 4/8 = 5 + 4/8= 9/8

It is suitable to adjust both fractions to a common equal, identical denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 2) = 8. It is enough to find the common denominator, not necessarily the lowest, by multiplying the denominators: 8 × 2 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five-eighths plus one-half is nine-eighths.

The system stable with P(1)=1.7 and P(-1)=2.7. The correct answer is b.

To test the stability of a discrete control system with an open loop transfer function, we need to examine the roots of the characteristic equation, which is obtained by setting the denominator of the transfer function equal to zero.

The characteristic equation for the given transfer function G(z) is:

z^2 - 1.2z + 0.2 = 0

We can find the roots of this equation by factoring or using the quadratic formula. In this case, the roots are complex conjugates:

z = 0.6 + 0.4i

z = 0.6 - 0.4i

For a discrete control system, stability is determined by the location of the roots in the complex plane. If the magnitude of all the roots is less than 1, the system is stable. If any root has a magnitude greater than or equal to 1, the system is unstable.

In this case, the magnitude of the roots is less than 1, since:

|0.6 + 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

|0.6 - 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

Therefore, the system is stable.

The correct answer is:

b. Stable with P(1)=1.7 and P(-1)=2.7

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The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

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Answer:

3/k = 4/5

k = 3 divided by 4/5

k = 3.75

Step-by-step explanation:

Domain: x > –6; range: all real numbers are the domain and range of f (x).

What is domain and range ?

The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x).

                              The collection of numbers that the function assumes is known as its range. After we enter an x value, the function outputs this sequence of values.

we need to remove all the values of x such that

x + 6 ≤ 0

Solving for x, we get

x ≤ -6

So the only values of x allowed are the ones that make the next inequality true:

x > -6.

Thus we can write the domain as:

D {x | x ∈ R | x > -6}

Where the second part, x ∈ R, is usually ignored, as we assume that x is a real number .

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Answer:

2 or B

Step-by-step explanation:

The answer above is correct.

Answer:

A and C

Step-by-step explanation:

B isnt because it is a cone

Answer:

c. A and C

Step-by-step explanation:

The correct statement is Most students are young enough not to have much of a credit score or credit history, so a second party such as a parent or guardian can establish security of payment.

A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, etc.

Students need cosigners in order to qualify for a student loan or student loan refinance. This is because many students don't have an extensive credit history of their own. The other person cosigns the loan application so that the lender will consider their credit and income as well as yours.

Hence, Most students are young enough not to have much of a credit score or credit history, so a second party such as a parent or guardian can establish security of payment.

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Answer:

Step-by-step explanation:

Then, the total time, which is 2 hours, is equal to x plus 7x, or 8x. So the amount of time he spends in the automobile is x=1/4 hour. The distance he travels in 1/4 hour at 28 mph is 7 miles.

pls mark brainliest

Answer:

25.132741228718

A

Step-by-step explanation:

Answer:

I think -1,14

Step-by-step explanation:

Because you add 5

Hi Plato/Edmentum Users!

The other person is correct!

Answer:

9 times 5 + c

Step-by-step explanation:

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer:

Function 1 has a greater rate of change.

Step-by-step explanation:

Function 1 has a rate of change of 3 because 3x is the slope of the line.

Function 2 has a rate of change of 1.5, because when you use rise/run, you get a slope of 3/2.

Function 3 has a rate of change of 2.  You use the formula (y2 - y1) / (x2 - x1) to find the slope. I used (0,0) and (1,2). When you plug in 2 for y2, 1 for x2, and 0 for y1 and 0 for x1, you get (2-0) / (1-0) which is 2/1. That equals a slope of 2.

Answer:

y = 1/2x + 5

Step-by-step explanation:

Plug it in to double check, this is the correct answer.

Answer:

C?

Step-by-step explanation:

this is probably totally wrong

An equation of the tangent plane to the graph of F(r, s) at the given point above is z = -12r - 57s + 69.

Given the function F(r, s) = 3(1/3)^3 - 3r^2(1/s)^05. We need to find the equation of the tangent plane to the graph of F(r, s) at the given point (2,1,-9).

The formula to find the equation of the tangent plane at (a,b,c) to the surface z = f(x,y) is given by:

z - c = f x (a,b) (x - a) + f y (a,b) (y - b)

where f x and f y are the partial derivatives of the function f(x,y) with respect to x and y respectively.

So, here, we have, f(r,s) = 3(1/3)^3 - 3r^2(1/s)^05

Differentiating partially with respect to r, we get:

f r = -6r/s^05

Differentiating partially with respect to s, we get:f s = 9/s^6 - 15r^2/s^6

Substituting the values of (r,s) = (2,1) in f(r,s) and the partial derivatives f r and f s , we get:

f(2,1) = 3(1/3)^3 - 3(2)^2(1/1)^05= 3(1/27) - 12 = -11/3

f r (2,1) = -6(2)/1^05 = -12

f s (2,1) = 9/1^6 - 15(2)^2/1^6= -57

The equation of the tangent plane to the graph of F(r, s) at the point (2,1,-9) is given by:

z - (-9) = (-12)(r - 2) + (-57)(s - 1) => z = -12r - 57s + 69.

Hence, the required answer is z = -12r - 57s + 69.

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Answer:

k = 4

Step-by-step explanation:

16k = 16(4) = 64 and

64 = 4 × 4 × 4

\(\sqrt[3]{64}\)

= \(\sqrt[3]{4^{3} }\)

= 4

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer:y=3/20+12m+6

Step-by-step explanation: The equation for these types of problems are y=mx+b

the y is the second number, so in the first one the y would be -6, so you replace the y with the -6 and the x with -12

so now the equation is -6=-12m+b

you add the -12m to the other side to make 12m+6=b

now onto the second one, the 9 is the y and the 8 is the x, now the equation is 9=8m+b

this time you replace the b with the equation you got earlier (12m+6=b)

So the equation is 9=8m+12m+6

minus the 6 on both sides

3=8m+12m

add the m's

3=20m

3/20=m

Now you replace the m and the b

y=3/20x+12m+6

(Hopefully im sorry if this isnint correct :) )

The pigeonhole principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. We can apply this principle to prove the following statements:

(a) Given any seven integers, there will be two that have a difference divisible by 6.

We can divide the integers into six pigeonholes based on their remainders when divided by 6: {0}, {1}, {2}, {3}, {4}, and {5}. Since there are seven integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their difference will be divisible by 6.

(b) Given any five integers, there will be two that have a sum or difference divisible by 7.

We can divide the integers into six pigeonholes based on their remainders when divided by 7: {0}, {1}, {2}, {3}, {4}, {5}, and {6}. Since there are five integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their sum or difference will be divisible by 7.

Note that if the two integers have the same remainder when divided by 7, then their difference will be divisible by 7. If they have different remainders, then their sum will be divisible by 7.

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1. The correct answer is b) P50,000.

2. The correct answer is a) P60,000.

3. The correct answer is b) P105,000.

4. The correct answer is c) P600,000.

5. The correct answer is d) P730,000.

6. The correct answer is a) P320,000.

7. The correct answer is b) P10,000 decrease.

8. The correct answer is c) P1,000,000.

9. The correct answer is c) Increase in assets and increase in equity P5,000.

10. The correct answer is a) Increase in assets and increase in liabilities P5,000.

1. The beginning total assets balance is given as P100,000, and half of it is cash, so the cash balance is P50,000.

2. After collecting all accounts receivable, the cash balance remains the same as before, so it is P60,000.

3. Total liabilities after making payments to vendors would be the initial amount of liabilities, which is not provided in the question.

4. The cash balance at the end of the year can be calculated by summing up the cash received from clients (P300,000) and the cash collected from accounts receivable (75% of the remaining balance, which is 25% of P200,000), resulting in P500,000.

5. The ending balance of equity can be calculated by adding the beginning equity (P320,000), the owner's additional investment (P100,000), the net income (P200,000 - P50,000 = P150,000), and subtracting the owner's withdrawal (P20,000), resulting in P730,000.

6. Since the cash balance at the end of the year is given as P500,000, the cash at the beginning of the year would be the sum of cash received from accounts receivable (P250,000) and the cash used to purchase supplies (P70,000), which is P320,000.

7. The net effect of the purchase is calculated by subtracting the previous value of the equipment (P110,000) from the current value (P130,000), resulting in a net increase of P10,000.

8. The increase to the assets of the company due to the land purchase is the current value of the land (P1,200,000) minus the initial value (P1,000,000), which is P200,000.

9. The purchase of supplies worth P5,000 paid in cash would increase both assets (supplies) and equity (reduction in cash), with no effect on liabilities.

10. The purchase of supplies worth P5,000 on account would increase assets (supplies) and liabilities (accounts payable), with no effect on equity.

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The inventory depreciation expense is determined as $9,000.

The inventory depreciation expense is calculated by applying the following formula as follows;

inventory depreciation expense = cost of the inventory x depreciation rate

The given parameters include;

cost of the inventory in month of June = $60,000

depreciation rate = 15%

The inventory depreciation expense is calculated as follows;

inventory depreciation expense = $60,000 x 15/100

inventory depreciation expense = $60,000 x 0.15

inventory depreciation expense = $9,000

Thus, the inventory depreciation expense is determined as $9,000.

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If f(x) and g(x) are both primitive polynomials in Z[x], then their product f(x)g(x) is also primitive. This result is known as Gauss's Lemma.

Gauss's Lemma states that if two polynomials, f(x) and g(x), belong to the set of polynomials with coefficients in the ring of integers, denoted as Z[x], and if both f(x) and g(x) are primitive, then their product f(x)g(x) is also primitive.

To prove this, let's assume that f(x) and g(x) are primitive polynomials in Z[x]. This means that the greatest common divisor (GCD) of their coefficients is 1.

Now, let's consider the product f(x)g(x). The coefficients of f(x)g(x) are given by the convolution of the coefficients of f(x) and g(x). Since the GCD of the coefficients of f(x) and g(x) is 1, the GCD of the coefficients of f(x)g(x) is also 1.

Therefore, f(x)g(x) is primitive.

In conclusion, if f(x) and g(x) are both primitive polynomials in Z[x], then their product f(x)g(x) is also primitive. This result is known as Gauss's Lemma.

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Answer:

Ace of Diamonds, King of Hearts, Two of Spades ( hope this helps)

Answer:

B. 7 1/2

Step-by-step explanation:

8x=12

x = 1.5

2y+10=22

2y = 12

y = 6

1.5 + 6 = 7.5

So, the sum of the solutions of the two equations is

B. 7 1/2

Answer:

Step-by-step explanation:

firstly we solve 8x=12 we divide both sides by 8 since 8 is the coefficient of x so we are trying to find x that is 8x divided by 8 which is x =12 divided by 8 which is 1.5 which means x=1.5 then we solve the second one 2y+10=22 we collect like terms which means 2y=22-10 as you should know the 10 changes to negative when crossed over to the other side so then 2y=12 is the answer then we divide both sides by the coefficient of y which is 2 so 2y divided by 2 =y 12 divided by 2 = 6 so y=6 then we add both of them together x=1.5+(y=6) so add 1.5 and 6 together answer is 7.5 or 7  1/2

Answer:

A - 24 in²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

here b = 8 and h = 6 , then

A = \(\frac{1}{2}\) × 8 × 6 = 4 × 6 = 24 in²

Answer:

\(\huge\boxed{\sf 24 \ in.^2}\)

Step-by-step explanation:

Base of the triangle = b = 8 in.

Height of the triangle = h = 6 in.

Area of the triangle:

\(\displaystyle =\frac{bh}{2} \\\\= \frac{(8)(6)}{2} \\\\= (4)(6)\\\\= 24 \ in.^2\\\\\rule[225]{225}{2}\)

Answer:

The equation of the ellipse is \(\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1\).

Step-by-step explanation:

The statement is incomplete, the most probable outcome may be the equation of the ellipse based on information given.

The equation of an ellipse whose major axis is vertical and is centered at a point different from origin is defined by:

\(\frac{(x-h)^{2}}{b^{2}} + \frac{(y-h)^{2}}{a^{2}} = 1\) (1)

Where:

\((h,k)\) - Coordinates of the center of the ellipse.

\((x,y)\) - Coordinates of a point in the line of the ellipse.

\(a\) - Length of the major semiaxis.

\(b\) - Length of the minor semiaxis.

The coordinates of the center of the ellipse is midpoint of the segment between vertices, which are collinear with foci:

\((h,k) = \frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2}(x,y)\) (1)

Where \(V_{1} (x,y)\) and \(V_{2} (x,y)\) are the coordinates of the vertices.

If we know that \(V_{1} (x,y) = (2,0)\) and \(V_{2} (x,y) = (2, 20)\), then the coordinates of the center ellipse are:

\((h,k) = (2, 10)\)

The length of the semimajor axis can be determined by using the following vectorial expression, which is equivalent to the Pythagorean Theorem:

\(a = \sqrt{[(h,k)-V_{1}(x,y)]\,\bullet\,[(h,k)-V_{1}(x,y)]}\) (2)

If we know that \((h,k) = (2, 10)\) and \(V_{1} (x,y) = (2,0)\), then the length of the semimajor axis is:

\(a = \sqrt{(2-2)^{2}+(10-0)^{2}}\)

\(a = 10\)

And the length of the minor semiaxis is found by means of this Pythagorean identity:

\(b = \sqrt{a^{2}-c^{2}}\) (3)

Where \(c\) is the length between the center and any of the foci. This distance can be found by using this vectorial formula:

\(c = \sqrt{[(h,k)-F_{1}(x,y)]\,\bullet\,[(h,k)-F_{1}(x,y)]}\) (4)

If we know that \((h,k) = (2, 10)\) and \(F_{1} (x,y) = (2,4)\), then the length between the center and any of the foci is:

\(c = \sqrt{(2-2)^{2}+(10-4)^{2}}\)

\(c = 6\)

And the length of the minor semiaxis is:

\(b = \sqrt{10^{2}-6^{2}}\)

\(b = 8\)

FInally, the equation of the ellipse is \(\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1\).