The table represents some points on the graph of a linear function. x f(x) −6 −5 −2 −2 2 1 6 4 10 7 Which equation represents the same relationship? A.3x−4y=5 B.4x−3y=−2 C.4x−3y=5 D.3x−4y=2

Answer:

9. Associative property

10. Distributive property

Name the property shown.

9. 2 x= x 2

td

11. 7(z+ y) = 7z+ 7y

10. 231= 23

12. a + (2b + 3c) = (a + 2b) + 3c

Answer:

The probability of Shenanigans selling a Peanut Butter Cup cone next is approximately 31.22%.

To calculate the probability of Shenanigans selling a Peanut Butter Cup cone next, we need to determine the number of cones sold that were not Peanut Butter Cup cones and divide that by the total number of cones sold.

Given that Shenanigans sold a total of 711 ice cream cones last week and 489 of those were either Coffee Cream or Oreo, we can subtract 489 from 711 to find the number of cones that were not Coffee Cream or Oreo;

Number of cones that were not Coffee Cream or Oreo = 711 - 489 = 222

So, out of the total 711 cones sold, 222 were not Coffee Cream or Oreo cones. Therefore, the remaining cones must be Peanut Butter Cup cones.

Now, we can calculate the probability of selling a Peanut Butter Cup cone next by dividing the number of Peanut Butter Cup cones by the total number of cones sold, and then multiplying by 100 to find the result as a percentage;

Probability of selling a Peanut Butter Cup cone next = (Number of Peanut Butter Cup cones / Total number of cones sold) × 100

Probability of selling a Peanut Butter Cup cone next = (222 / 711) × 100

≈ 31.22%

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Answer:Garret had 1/10 of the pizza left.

Step-by-step explanation:thats good

That kx^2 > 0 for x > 0, so we have 1+(k+1)x+kx^2 > 1+(k+1)x. Therefore, (1+x)^(k+1) > 1+(k+1)x, and the result follows by mathematical induction.

(a) To study the variations of f(x) = r - ln(1+x), we need to find the derivative of f(x) and analyze its sign.

The derivative is f'(x) = -1/(1+x), which is negative for all x > 0.

Therefore, f(x) is a decreasing function on (0, ∞).

Also, lim x→0 f(x) = r > -∞, and lim x→∞ f(x) = -∞.

Therefore, f(x) has a maximum at x = 0, which is r.

(b) To study the variations of g(x) = (1 + x) ln(1 + x) - 2, we need to find the derivative of g(x) and analyze its sign.

The derivative is g'(x) = ln(1 + x), which is positive for all x > -1.

Therefore, g(x) is an increasing function on (-1, ∞). Also, lim x→-1+ g(x) = -∞, and lim x→∞ g(x) = ∞.

Therefore, g(x) has a minimum at some point in (-1, ∞).

(c) To conclude that for all positive integer n, we have (1+x)^n > 1+nx, we can use mathematical induction.

For n = 1, we have (1+x)^1 = 1+x > 1+1x. Assume that (1+x)^k > 1+kx for some positive integer k. Then, for n = k+1, we have (1+x)^(k+1) = (1+x)^k * (1+x) > (1+kx) * (1+x) = 1+(k+1)x+kx^2.

Note that kx^2 > 0 for x > 0, so we have 1+(k+1)x+kx^2 > 1+(k+1)x. Therefore, (1+x)^(k+1) > 1+(k+1)x, and the result follows by mathematical induction.

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The solution of the system of equations 3x − 3y = 6 and 2x + 6y = 12 is x = 3 and y = 1, hence option is b is correct.

We must eliminate one of the variables by adding or subtracting the two equations in order to solve for (x, y) using elimination. Let us multiply the equation by 2 and 3 respectively so that the equations becomes,

6x - 6y = 12

6x + 18y = 36

Now, using the equations,

24y = 24

So, y = 1. Substituting this back into either of the original equations gives:

3x - 3(1) = 6

3x = 9

So, x = 3. Therefore, the answer of equation is (b) (3, 1).

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Answer:

A = 120; C = 95

Step-by-step explanation:

We will need a system of equations to solve for C, the number of child tickets and A, the number of adult tickets.

We know that the sum of the revenue earned from both the child tickets and the adult tickets = the total revenue

Thus, our first equation is 3C + 14A = 1965

We also know that the sum of the total number of child and adult tickets = the the total number of tickets

Thus, our other equation is C + A = 215

We can solve using substitution by first isolating c in the second equation:

[tex]C+A=215\\C=-A+215[/tex]

Now, we can plug in the equation we just made for C in the first equation in our system to solve for A:

[tex]3(-A+215)+14A=1965\\-3A+645+14A=1965\\11A+645=1965\\11A=1320\\A=120[/tex]

Finally, we can solve for C using the second equation in our system by plugging in 120 for A:

[tex]C+120=215\\C=95[/tex]

The series converges for all values of p < -1, and diverges for all values of p ≥ -1.

To apply the Integral Test, we need to verify that the terms of the series are positive and decreasing for all n greater than some fixed integer. For this series, note that the terms are positive since both the base and the natural logarithm are positive. To show that the terms are decreasing, we take the ratio of successive terms:

[tex]a(n+1)/a(n) = [(n+1)ln(n+1)]^p / [nln(n)]^p[/tex]

[tex]= [(n+1)/n]^p * [(1+1/n)ln(1+1/n)]^p[/tex]

Since (n+1)/n > 1 and ln(1+1/n) > 0 for all n, it follows that the ratio is greater than 1 and therefore the terms are decreasing.

To use the Integral Test, we need to find a function f(x) such that f(n) = a(n) for all n and f(x) is positive and decreasing for x ≥ 3. A natural choice is [tex]f(x) = x(ln(x))^p[/tex]. Note that f(n) = a(n) for all n and f(x) is positive and decreasing for x ≥ 3. Then we have:

integral from 3 to infinity of f(x) dx = integral from 3 to infinity of x(ln(x))^p dx

To evaluate this integral, we use integration by substitution with u = ln(x):

[tex]du/dx = 1/x, dx = x du[/tex]

So the integral becomes:

integral from ln(3) to infinity of [tex]u^p e^u du[/tex]

This integral converges for p < -1, by the Integral Test for Improper Integrals.

Therefore, the series converges for all values of p < -1, and diverges for all values of p ≥ -1.

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When using the -x^2 - V command in WolframAlpha, it is important to correctly use parentheses to ensure the proper order of operations. The command should be written as "-(x^2) - V" to subtract x squared from V, rather than "-x^2 - V" which would subtract V from x squared.

To use the WolframAlpha method introduced in the Section 7.1 Learning Guidance and Section 7.1 Homework solutions to match the function Z = x^2y^3e^(-x-y) given by Problem 32 on Page 392 with a graph and a contour map on Page 393, you can follow these steps:

1. Go to the WolframAlpha website (www.wolframalpha.com).
2. In the search bar, type in "plot x^2*y^3*e^(-x-y)" and press enter.
3. WolframAlpha will generate a graph of the function Z = x^2y^3e^(-x-y), which can be used to match with the graph and contour maps on Page 393.
4. To generate a contour map, type in "contour plot x^2*y^3*e^(-x-y)" and press enter. WolframAlpha will generate a contour map of the function, which can be compared to the contour maps on Page 393.

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Answer:

Step-by-step explanation:

Answer: A=38.48

Step-by-step explanation:

A=πr^2

7/2=3.5

3.5x3.5=12.25

12.25π

38.48

Hope this helps! :)

Answer:

cos A = 45

Step-by-step explanation:

90 - sin A = 45 = cos A

90 Minus whatever the cos value for the angle is = the sin and vice versa.

Answer:

n = 18

Step-by-step explanation:

We can use the following equation to solve for n:

[tex]1/2n+15=24\\1/2n=9\\n=18[/tex]

If we check, we see that half of 18 is 9 and 9 + 15 is indeed 24

The given equation is a constant function with a horizontal line passing through (0, 1). Here option E is the correct answer.

The given equation, f(x) = 1, represents a constant function, where the output or value of the function is always equal to 1 for any input value of x. This is a special case of a linear function, where the slope is zero and the y-intercept is a non-zero constant value.

Among the four given options, none of them is a constant function. A reciprocal function, y = 1/x, has a variable slope and a vertical asymptote at x = 0. A square root function, y = √x, has a non-linear shape and a domain of x ≥ 0. An absolute value function, y = |x|, has a V-shaped graph and is symmetric around the y-axis. A cube root function, y = ∛x, is also non-linear and has a domain of all real numbers.

Therefore, the correct answer is not listed among the options, and the function f(x) = 1 does not belong to any of the parent functions mentioned. It is a simple constant function with a horizontal line as its graph, passing through the point (0, 1) on the y-axis.

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Complete question:

Which type of parent function does the equation f(x) = 1 represent?

A. Reciprocal

B. Square root

C. Absolute value

D. Cube root

E. None of these

The rectangle has 222.2 cm² more area than the square.

We have,

The area of the rectangle is:

= 6 cm x 41.2 cm

= 247.2 cm²

The area of the square is:

= 5 cm x 5 cm

= 25 cm²

The rectangle has a greater area than the square, by:

= 247.2 cm² - 25 cm²

= 222.2 cm²

Therefore,

The rectangle has 222.2 cm² more area than the square.

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The area of a regular polygon with perimeter of 58 and apothem 10 is 290 square units

It is important to note that the formula for calculating the area of a regular polygon is expressed as;

A = 1/2(ap)

This is so, such that the parameters of the formula are given as;

Now, substitute the values into the equation;

Area = 1/2 × 58 × 10

Multiply the values

Area = 580/2

Divide the values, we get;

Area = 290 square units

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For the first differential equation, dx/dy = 5x/y, we can separate the variables and integrate:

dy/dx = y/5x
(1/y)dy = (1/5x)dx
Integrating both sides, we get:
ln|y| = (1/5)ln|x| + C
where C is the constant of integration.

To solve for y, we can exponentiate both sides:
|y| = e^(ln|x|/5 + C)
|y| = Ce^(ln|x|/5)
where C is a constant of integration.

Since we don't know whether x and y are positive or negative, we can write the general solution as:
y = ± Cx^(1/5)

For the second differential equation, dx/dy = x^4, we can again separate the variables and integrate:

dy/dx = 1/x^4
x^4dy = dx
Integrating both sides, we get:
(1/3)x^3y = x + C
where C is the constant of integration.

To solve for y, we can multiply both sides by (3/x^3):
y = (3/x^3)(x + C)
y = 3/x^2 + 3Cx^(-3)

So the general solution to the differential equation dx/dy = x^4 is:
y = 3/x^2 + 3Cx^(-3), where C is a constant of integration.

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The negation of the statement without using any negation terms is: (∀x ∈ Z)(∃y ∈ Z)(xy ≤ y).

To find the negation of the statement (∃x ∈ Z)(∀y ∈ Z)(xy > y) without using any negation terms, we need to negate each part of the statement individually. Here's the step-by-step explanation:

Original statement: (∃x ∈ Z)(∀y ∈ Z)(xy > y)

1. Negate the existential quantifier (∃x ∈ Z): This changes to a universal quantifier (∀x ∈ Z).
2. Negate the universal quantifier (∀y ∈ Z): This changes to an existential quantifier (∃y ∈ Z).
3. Negate the inequality (xy > y): This changes to (xy ≤ y).

So the negation of the statement without using any negation terms is: (∀x ∈ Z)(∃y ∈ Z)(xy ≤ y).

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The inequality that shows how many questions, q, will be on Mr. Pham's quiz is: 0 ≤ q ≤ 15

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

This inequality states that the number of questions, q, must be greater than or equal to zero (since there cannot be a negative number of questions), but less than or equal to 15 (since Mr. Pham's quiz will have at most 15 questions).

Therefore, the inequality that shows how many questions, q, will be on Mr. Pham's quiz is: 0 ≤ q ≤ 15

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Answer:

--------------------------

Area of a trapezoid formula:

We have the following values as per picture:

Substitute the given values into formula to get the area:

Hence the area of the trapezoid is 15h cm².

Answer:

15h cm²

Step-by-step explanation:

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The person must leave the money in the bank for approximately 10.8 years (rounded to the nearest tenth of a year) for it to reach $2900 with 5.75% interest compounded monthly.

We can use the formula for compound interest to solve this problem:

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

where:

A is the amount of money after t years

P is the principal (the initial amount of money invested)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

We want to find t, the time required for the investment to grow from $1000 to $2900. We know that P = 1000 and A = 2900. We also know that r = 0.0575 (5.75% as a decimal) and that the interest is compounded monthly, so n = 12.

Substituting these values into the formula, we get:

2900 = [tex]1000(1 + 0.0575/12)^(12t)[/tex]

Dividing both sides by 1000, we get:

2.9 = [tex](1 + 0.0575/12)^(12t)[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2.9) = 12t ln(1 + 0.0575/12)[/tex]

Solving for t, we get:

[tex]t = ln(2.9) / (12 ln(1 + 0.0575/12))[/tex]

Using a calculator, we get:

t ≈ 10.8

Therefore, the person must leave the money in the bank for approximately 10.8 years (rounded to the nearest tenth of a year) for it to reach $2900 with 5.75% interest compounded monthly.

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The midpoint of the two points of P (-3,-7) and Q (3,-5) is (0, -6).

When you have the vertices of two points, you can find the midpoint by the formula :

= ( ( x 1 + x 2 ) / 2 , ( y 1 + y 2 ) / 2 )

Solving for the midpoint therefore gives:

= ( ( - 3 + 3 ) / 2 , ( - 7 + ( - 5 ) ) / 2 )

=  ( 0 / 2 , ( - 12 ) / 2 )

= (0, -6)

In conclusion, the midpoint is (0, -6).

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If two samples from the same population have the same mean and are both n = 100, they will probably still have different sample variances.

We have,

If two samples from the same population have the same mean and are both n=100, they will probably still have different sample variances.

This is because sample variance refers to the dispersion or spread of data points within each individual sample, and this can vary even if the samples have the same mean and sample size (n=100).

It's important to note that the other options (t-statistics, standard errors, and alpha values) are related to the sampling distribution or hypothesis testing, which may not be different simply due to having the same mean and sample size.

Thus,

If two samples from the same population have the same mean and are both n = 100, they will probably still have different sample variances.

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The volume of the right rectangular prism is 156 cubic centimeters.

We have,

The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

Using the given values, we can substitute them into the formula to find the volume of the rectangular prism:

V = 13 cm x 4 cm x 3 cm

V = 156 cm^3

Therefore,

The volume of the right rectangular prism is 156 cubic centimeters.

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Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.

In this case, the diameter of the cooler is 30 inches, which means the radius is 15 inches (since the radius is half the diameter). The height is 24 inches.

Using the formula for the volume of a cylinder, we have:

V = π[tex]r^2h[/tex]

= π([tex]15^2)(24[/tex])

= 5400π cubic inches

To convert cubic inches to gallons, we need to divide by the conversion factor 231 cubic inches per gallon. Therefore, the volume of the cooler in gallons is:

[tex]V_gal[/tex]= (5400π cubic inches) / (231 cubic inches/gallon) ≈ 74.0 gallons

Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.

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Every composite number has at least one natural number factor other than 1 and itself. The correct answer is option D.

A composite number is a natural number larger than one that is not a prime number, implying that it has at least one element other than 1 and itself.

As a result, every composite number has at least one natural number factor that is neither 1 nor itself.

The smallest natural number that can divide all of the numbers in the integer list is 1.

When we divide a number by itself, we obtain 1 as the component.

Hence, the correct answer is option D.

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The complete question is as follows:

What is 1 of a natural number factor?

A. every

B. odd

C. even

D. composite

After 3 days, Emilio will have collected 28 + 8(3) = 52 signatures, and Belle will have collected 25 + 9(3) = 52 signatures as well.

To determine the number of signatures both Emilio and Belle will have, we can set up an equation:

28 + 8x = 25 + 9x

where x is the number of days it takes for both of them to collect the same number of signatures.

Simplifying the equation, we get:

3x = 3

x = 1

So it will take them one more day for Belle to collect the same number of signatures as Emilio.

To find out how many signatures they will both have, we can substitute x=1 into either of the equations and solve for the number of signatures. Let's use Emilio's equation:

28 + 8(1) = 36

Therefore, both Emilio and Belle will have 36 signatures.

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The graph is attached.

Given is a triangle ABC, we need to find its coordinates if it is reflected over y = -x,

The rule of reflection over y = -x is,

(x, y) = (-x, -y)

So,

A = (-5, -4)

B = (1, -4)

C = (-1, -5)

After reflection,

A' = (5, 4)

B' = (-1, 4)

C' = (1, 5)

Hence the points after reflection are A' = (5, 4), B' = (-1, 4) and C' = (1, 5)

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To model the population of a city, we can use the formula:

f(x) = 1,596,000 * (1 + 0.035)^x

Where x is the number of years since 2020 and 0.035 represents the annual increase rate of 3.5%.

To model the population of a city, we need to take into account the initial population in 2020 and the annual increase rate of 3.5%. The annual increase rate of 3.5% means that the population is expected to grow by 3.5% every year from the previous year's population. To incorporate this growth rate into our model, we can use the formula for compound interest:

A = P * (1 + r)^t

Where A is the final amount, P is the initial amount, r is the annual interest rate, and t is the number of years. In our case, the final amount is the population after x years since 2020, the initial amount is the population in 2020 (1,596,000), the annual interest rate is 3.5%, and the number of years is x.

By substituting the values into the formula, we get:

f(x) = 1,596,000 * (1 + 0.035)^x

This formula can be used to calculate the expected population of the city for any year in the future. For example, if we want to know the population in 2025, we can substitute x = 5 into the formula:

f(5) = 1,596,000 * (1 + 0.035)^5

= 1,825,854

Therefore, we can expect the population of the city to be around 1,825,854 in 2025, assuming the same annual increase rate of 3.5%.

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The length of diagonal of square is 6√2 inch.

We have,

side length  = 6 inches

Now, the formula for diagonal length of square as

d = √2a

where a is the side of square.

So, the length of diagonal of square is

= 6√2 inch.

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The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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