Which is a true statement about the number 1?
O One is a factor of every whole number since every number is divisible by itself.
O One is not a factor of any number because it is neither a prime number nor a composite number.
O One is a prime number because it has less than two factors.
O One is a composite number because it has more than two factors.

The possible coordinates of the vertex of the triangle is A = (0, 10), B = (0, - 4) and C = (4, 0).

The possible coordinates of the vertex of the triangle is calculated by applying the following formula.

A = ¹/₂bh

where;

Let the base = 4 units and let the height of the triangle = 14

A = ¹/₂ x 4 x 14

A = 28 sq units

So the coordinates of A, B and C is determined as;

A = (0, 10)

B = (0, - 4)

C = (4, 0)

from coordinates above, AB = (10 + 4) = 14

OC = 4

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According to the information, it can be inferred that Leah reaches a maximum distance of 8 blocks away from her house. Additionally, the journey takes 23 minutes.

To graph the information for Leah's commute, we must take into account the distance (in blocks) and the time it takes her (in minutes) to travel to the bank and then return home.

In this case we must take into account the speed (blocks per minute) that Leah has because this modifies the time and distance that she will take in total. According to the above, the graph ascends, then remains stable for 2 minutes, then rises more steeply and remains stable for 7 minutes, finally descends to 0 steadily.

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Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Step-by-step explanation:

5/6 is its lowest term because it cannot be divided any further

The difference between the two possible lengths of the third side is 3.2 inches.

The lengths of two sides of a right triangle are 5 inches and 8 inches. Therefore, the third side of the right triangle can be found using Pythagoras's theorem as follows:

Therefore,

c² = a² + b²

c = √5² + 8²

c = √25 + 64

c = √89

c = 9.43 inches

Then,

b² = 8² - 5²

b = √64 - 25

b = √39

b = 6.24 inches

Therefore,

the difference between the possible length = 9.43 - 6.24 = 3.2 inches

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Answer:The value of Q can refer to different things depending on the context. In statistics, Q is defined as the ratio of the gap to the range, where both "gap" and "range" are positive. The larger the value of Q, the more likely that the suspected outlier does not belong to the same population as the other data points1. In nuclear physics, the Q-value of the reaction is defined as the difference between the sum of the masses of the initial reactants and the sum of the masses of the final products in energy units (usually in MeV)2. In statistics, a Q-value is a p-value that has been adjusted for the False Discovery Rate (FDR

Step-by-step explanation:

The distance the handler moves from the starting point to the return point when creating an arc of a circle with a radius of 70 feet is approximately 109.9 feet. C.

To calculate the distance the handler moves from the starting point to the return point when creating an arc of a circle with a radius of 70 feet, we need to find the length of a quarter circle.

The formula for the circumference of a circle is C = 2πr, where r is the radius.

Since we are interested in a quarter circle, we divide the circumference by 4.

Circumference of a quarter circle = (2π × 70) / 4

To calculate this value, we can use an approximation of π as 3.14:

Circumference of a quarter circle ≈ (2 × 3.14 × 70) / 4

Simplifying this expression gives:

Circumference of a quarter circle ≈ 109.9 feet

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The handler will move approximately 109.9 feet, as this distance represents a quarter of the circumference of a circle with a radius of 70 feet.

The question is based on the circumference of a circle. The formula for the circumference of a circle is C = 2πr (where r = radius in feet). We are only interested in a quarter of the circumference for this scenario, meaning we must divide the full value by 4. So, we plug in the values given: C = (2 * π * 70) / 4.

The calculation will give us 110 feet approximately, hence the closest answer is the third one, which is 109.9 feet.

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Mr. Smith has $17 left to spend on each student.

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The total number of students Mr. Smith has 17

The money he can spent on each student is $22

The total money he can spend is $22 · 17

Total cost of calculators is $83.64

Let x is the amount left to spend on each student.

The equation that can be formed is

[tex]17 \times \text{x} = 22\times17 - 83.64[/tex]

[tex]\text{x} = 22 - \huge \text(\dfrac{83.64}{17}\huge \text)[/tex]

[tex]\text{x} = 22 - 5[/tex]

[tex]\bold{x = \$17}[/tex]

Therefore, Mr. Smith has $17 left to spend on each student.

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Mr. Smith has 17 students in his class.

He can spend $22 on each student to buy math supplies for the year.

The calculators cost a total of $83.64.

The total amount he has to spend on all 17 students is $22 x 17 = $374.

The amount he spent on calculators was $83.64.

So the amount he has left to spend is $374 - $83.64 = $290.36

He has $290.36 left to spend on 17 students.

Therefore, the amount he has left to spend on each student is $290.36 divided by 17 students, which is $17.07.

So the answer is: After buying the calculators, Mr. Smith has $17.07 left to spend on each student.

In summary:

$22 - Amount he can spend per student

$83.64 - Total cost of calculators

$374 - Total amount he has to spend on all 17 students ($22 x 17)

$290.36 - Amount he has left to spend after buying calculators ($374 - $83.64)

$17.07 - Amount he has left to spend on each student ($290.36 / 17 students)

Answer:

  see attached

Step-by-step explanation:

You want the squares of the numbers 2 to 11.

The calculator output attached shows the squares of the numbers 2 through 11.

__

Additional comment

If your knowledge of multiplication tables extends through 10×10, then there is only one more you need to memorize here. It is actually a good idea to learn the squares of numbers through 20², and be able to identify the cubes of numbers through 10³. (12³ = 1728 is also useful for cubic inches in a cubic foot.)

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The expression (f - g)(x) simplifies to 9x - 9.

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

Given f(x) = 5x - 7 and g(x) = -4x + 2, let's perform the subtraction:

(f - g)(x) = f(x) - g(x)

Substituting the given functions:

(f - g)(x) = (5x - 7) - (-4x + 2)

To simplify the expression, we can distribute the negative sign inside the parentheses:

(f - g)(x) = 5x - 7 + 4x - 2

Combining like terms, we add the coefficients of x and the constants separately:

(f - g)(x) = (5x + 4x) + (-7 - 2)

Simplifying further:

(f - g)(x) = 9x - 9

Therefore, the expression (f - g)(x) simplifies to 9x - 9.

In summary, (f - g)(x) is equal to 9x - 9, which represents the result of subtracting the function g(x) from the function f(x) according to the given expressions for f(x) and g(x).

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Answer:

Since there are 10 boys and 6 of them equal 400Kg and the average of each boy is 60kg the remaining 4 boys should equal around 250kgs

The probability that a student chosen from the class at random has either ginger hair or blonde hair is given as follows:

19/28.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For each outcome, the probability in this problem is given as follows:

The probability for either is the sum of the probabilities of each outcome, hence:

5/14 + 9/28 = 10/28 + 9/28 = 19/28.

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The maximum price you can offer for a home is approximately $82,352.94 for a 17% down payment.

To determine the maximum price you can offer for a home, you need to calculate 17% of the total price, which will be your down payment of $14,000.

Let's assume the maximum price you can offer for the home is P dollars.

According to the given information, the down payment requirement is 17% of the total price. So, we can set up the following equation:

[tex]0.17P = $14,000[/tex]

To solve for P, divide both sides of the equation by 0.17:

P = $14,000 / 0.17

Calculating this expression, we find:

P ≈ $82,352.94

Therefore, the maximum price you can offer for a home in order to have enough money for the 17% down payment is approximately $82,352.94.

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The correct statement regarding the translation in this problem is given as follows:

The graph is translated down 1 unit.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The functions for this problem are given as follows:

Due to the subtraction by 1, the function was translated down 1 unit.

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The domain of f(x) is x > -4, so the range of f⁻¹(x) is y > -4.

The range of f(x) is y ≥ 5, so the domain of the f⁻¹(x) is x ≥ -4.

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = √(x - 5) - 4

x = √(y - 5) - 4

√(y - 5) = x + 4

By taking the square of both sides of the function, we have:

y - 5 = (x + 4)²

f⁻¹(x) = (x + 4)² + 5

Therefore, the domain and range of f(x) and f⁻¹(x) are given by:

domain of f(x) = x > -4

range of f(x) = y ≥ 5

domain of f⁻¹(x) = x ≥ -4.

range of f⁻¹(x) = y > -4.

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The completed contingency table that summarizes the classification of students by weight and gender is attached below.

a. For a randomly selected student, describe the following in words

W1 is an event in which a randomly selected student is obese.

P(W1) is the probability that a randomly selected student is obese.

b. The following probabilities: (Round the answers to 4 decimal places)

i. P(W2) = (42 + 55) / 173 = 0.574

ii. P(G1) = (76 + 76) / 173 = 0.500

iii. P(W1 and G2) = (76) / 173 = 0.440

iv. P(W3 or G2) = (30 + 22 + 76 + 76) / 173 = 0.884

v. P(W3 | G2) = (22) / (22 + 76) = 0.214

c. For the following:

i. W3 and G1 are not mutually exclusive. This is because there are students who are both obese and male. For example, the value in the cell (W1, G1) is 76.

ii. W3 and G1 are not independent. This is because the probability of being obese is different for male students than it is for female students. For example, the probability of being obese is 0.440 for male students, but it is only 0.130 for female students.

iii. W3 and W2 are not mutually exclusive. This is because there are students who are both underweight and normal. For example, the value in the cell (W2, W3) is 30.

iv. W3 and W2 are not independent. This is because the probability of being underweight is different for normal students than it is for obese students. For example, the probability of being underweight is 0.300 for normal students, but it is only 0.154 for obese students.

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Answer:

Step-by-step explanation:

A is the answer

Calculate the area of 3 rectangles

4x10=40 x 3 rectangles = 120

calculate the area of 2 triangles

A=1/2bh, since you have triangles, no need to divide by 2

base x height

4 x 3.5 = 14

Surface Area is 120 + 14 = 134

12x5/3 simplifies to the whole number 20.

To simplify the expression 12x5/3, we need to perform the multiplication and division operations.

First, let's multiply 12 and 5:

12 * 5 = 60

Now, let's divide the result by 3:

60 / 3 = 20

Therefore, 12x5/3 simplifies to the whole number 20.

However, since you mentioned "In m2" in your question, it seems that there may be a variable involved. If the expression 12x5/3 represents an area in square meters, then we need more information about the variable x to provide a more specific answer.

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After 15 years, you would have approximately $3,040.19 in the account.

To calculate the future value of the account after 15 years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

A = the future value of the account

P = the initial deposit or principal amount

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the initial deposit or principal amount (P) is $2000, the annual interest rate (r) is 3% or 0.03, the interest is compounded annually (n = 1), and the time period (t) is 15 years.

Plugging in the values into the formula, we have:

[tex]A = 2000(1 + 0.03/1)^{(1\times15)[/tex]

Simplifying the calculation:

[tex]A = 2000(1.03)^{15[/tex]

Using a calculator or computer software, we can evaluate this expression:

[tex]A \approx 2000(1.03)^{15}[/tex]

≈ 2000(1.52009438088)

≈ $3,040.19.

Therefore, after 15 years, you would have approximately $3,040.19 in the account.

This calculation assumes that you make the $2000 deposit each year without any changes or interruptions and that the interest rate remains constant at 3% compounded annually.

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To solve the equation P - 12 = -27, we can isolate the variable P by performing inverse operations.

First, we want to get rid of the -12 on the left side of the equation. Since -12 is being subtracted, we can perform the opposite operation, which is addition. Adding 12 to both sides of the equation, we have:

P - 12 + 12 = -27 + 12

This simplifies to:

P = -15

Therefore, the value of P that satisfies the equation is -15.

Answer:

Step-by-step explanation:

P - 12 = -27

add 12 on both sides

P - 12 + 12 = -27 + 12

P = - 15

The volume of the cylinder is 56.52 cubic units

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

V = πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 3.14 * 3² * 2

Evaluate

V = 56.52

Hence, the volume is 56.52 cubic units

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Answer:

standered form is 0 of 0

Step-by-step explanation:

yw

Answer:A system of linear inequalities in two variables includes at least two linear inequalities in the identical variables1. The solution to all inequalities and the graph of the linear inequality is the graph displaying all solutions of the system1. For example, the system of linear inequalities that is represented by the graph are: y<−12+5 and y≥x−1

Step-by-step explanation:

Answer:

A. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

The fifth postulate of Euclidean geometry is often referred to as the Parallel Postulate.

A. Through a given point not on a given line, there is exactly one line parallel to the given line. This statement is actually the Parallel Postulate, so it is the correct answer.

B. All right angles are equal to one another. This statement is actually the Fourth Postulate, also known as the Right Angle Postulate.

C. Any straight line segment can be extended indefinitely. This statement is the Second Postulate, also known as the Line Extension Postulate.

D. A circle can be drawn with any center and radius. This statement is the Third Postulate, also known as the Circle Postulate.

Therefore, the correct answer is:

A. Through a given point not on a given line, there is exactly one line parallel to the given line.

When x = 25 and dx = 7 units per day, the rate of change of time (dt) with respect to x is 1 / (7 units/day).

In the given scenario, we have two functions: R(x) and C(x). Let's use the given information to calculate the rate of change of x with respect to time (dt) when x = 25 and dx = 7 units per day.

To find the rate of change, we can differentiate the functions with respect to x. Let's differentiate both R(x) and C(x) to obtain their derivatives:

dR/dx = 2

dC/dx = 0.02x + 0.3

Now, we need to find dt, the rate of change of time with respect to x. To do this, we can use the chain rule of differentiation, which states that dt/dx = 1 / (dx/dt)

Given that dx = 7 units per day, we can calculate dx/dt:

dx/dt = 7 units/day

Now, we can find dt by taking the reciprocal:

dt/dx = 1 / (7 units/day)

Therefore, the rate of change of time with respect to x is 1 / (7 units/day).

Note that the units cancel out in the reciprocal operation, leaving us with units/day.

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Based on your annual review score of 3.4, you would receive a merit increase of 2.5%.

To determine the merit increase based on your annual review score of 3.4, we need to calculate the increase increment based on the given scale.

First, we need to determine the number of 0.4-point increments between your score of 3.4 and the baseline score of 2.6, which is the starting point for merit increases. The difference is 3.4 - 2.6 = 0.8.

Since the merit increases go up by 1% for every 0.4 points, we divide the difference of 0.8 by 0.4 to find the number of 0.4-point increments:

0.8 / 0.4 = 2

So, there are 2 increments of 0.4 points.

Next, we calculate the merit increase percentage. The baseline increase is 0.5%, and it increases by 1% for each 0.4-point increment. Since we have 2 increments, the increase percentage would be:

0.5% + 2 * 1% = 0.5% + 2% = 2.5%

Therefore, based on your annual review score of 3.4, you would receive a merit increase of 2.5%.

It's important to note that this calculation assumes a linear progression of merit increases based on the given criteria. The actual merit increase policy may vary depending on company practices and policies.

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The surface area of the solid of revolution is 1748.45 square units

From the question, we have the following parameters that can be used in our computation:

[tex]\int\limits^{\infty}_1 {(2\pi (16 - x^2)\sqrt{1 + (2x)^2}) \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{\infty}_1 {(2\pi (16 - x^2)\sqrt{1 + (2x)^2}) \, dx = -\frac{{\pi}\cdot\left(\sqrt{4x^2+1}\left(16x^3-510x\right)-257\ln\left(\left|\sqrt{4x^2+1}+2x\right|\right)\right)}{32}[/tex]

Simplify

[tex]\int\limits^{\infty}_1 {(2\pi (16 - x^2)\sqrt{1 + (2x)^2}) \, dx = 2{\pi}\cdot\left(\frac{257arsinh(2x)}{64}-\frac{x\cdot\left(4x^2+1\right)^\frac{3}{2}}{16}+\dfrac{257x\sqrt{4x^2+1}}{32}\right)[/tex]

Simplify, further

[tex]\int\limits^{\infty}_1 {(2\pi (16 - x^2)\sqrt{1 + (2x)^2}) \, dx = \frac{{\pi}\cdot\left(257arsinh(2x)-4x\cdot\left(4x^2+1\right)^\frac{3}{2}+514x\sqrt{4x^2+1}\right)}{32}[/tex]

Recall that the x values are from -4 to 4

This means that

[tex]\int\limits^{\infty}_1 {(2\pi (16 - x^2)\sqrt{1 + (2x)^2}) \, dx = \frac{{\pi}\cdot\left(257arsinh \left(8\right)+1016\sqrt{65}\right)}{16}[/tex]

Evaluate

[tex]\int\limits^{\infty}_1 {(2\pi (16 - x^2)\sqrt{1 + (2x)^2}) \, dx = 1748.45[/tex]

Hence, the value of the integral is 1748.45

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Answer:

In the given options, the parameter is represented by the letter "p." Therefore, the correct answer is option d.

Step-by-step explanation:

Answer: Please see attached images

(2nd image is the answer, 1st image is it worked out)

Step-by-step explanation:

You are given "Use synthetic division to divide [tex]x^3 + 6x^2 +15x + 24[/tex] by [tex]x + 3[/tex]"

1) You first take the coefficients from the expression, [tex]x^3 + 6x^2 +15x + 24[/tex], and place them in a row.

    |      1      6     15     24

    |__________________

2) Next you take the expression, x + 3, and take the last coefficient and put it to the left.

3   |      1      6     15     24

    |__________________

3) Next you drop the 1 (this is the case for the first number of any synthetic division problem)

3   |      1      6     15     24

    |__ ↓_______________

           1

4) Now you multiply 3 and 1, then place that product under 6.

3   |      1      6     15     24

    |__ ↓__  3___________

           1

5) Then you subtract the column: 6 - 3, and put the answer below

3   |      1     6     15     24

    |__ ↓__  3___________

           1      3

6) Now you repeat this process (steps 4-5) but with the following numbers. So repeating step 4, You multiply 3 and 3, and put that product under 15.

3   |      1     6     15     24

    |__ ↓__  3__ 9________

           1      3

7) Repeating step 5, you subtract the column: 15 - 9, and put the answer below.

3   |      1     6     15     24

    |__ ↓__  3__ 9________

           1      3      6

8) Once again, you repeat steps 4-5. So repeating step 4, you multiply, 3 and 6, and you place the product under 24.

3   |      1     6     15     24

    |__ ↓__  3__ 9___18____

           1      3      6

9) Repeat step 5, you subtract the column: 24 - 18, and put the answer below.

3   |      1     6     15     24

    |__ ↓__  3__ 9___18____

           1      3      6      | 6  

To find the quotient, that is result of the synthetic division but with its variables,  and not including the remainder.

Quotient: [tex]x^2+3x+6[/tex]

The remainder is the remaining number that is at the bottom of the last column.

Remainder: 6