Grace purchased a chocolate cheesecake costing $17.04. She gave the cashier $19.68. How much change did the cashier give back to Grace?Grace purchased a chocolate cheesecake costing $17.04. She gave the cashier $19.68. How much change did the cashier give back to Grace?

The two solutions that satisfy the equation 4lx+8l=4 are -9 and -7.

Given the equation,

4lx+8l=4

|x+8| = 4/4

|x+8| = 1

x + 8 = ± 1

When x = + 1

Then,

x = 1 - 8

x = -7

When x = - 1

x = -1 - 8

x = -9

Therefore the two solution of equation is -9 and -7.

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Using division operation, the number of weeks a bag of cat food lasts is 4 weeks.

Division operation is one of the four basic mathematical operations.

The division operation produces a result known as the quotient.

The quotient results when the dividend is divided by the divisor.

The quantity in a bag of cat food = 3lbs

The quantity that the cat eats per week = 3/4 = 0.75

The number of weeks that the bag of 3lbs will last = 4 (3/0.75)

Thus, we can conclude that the shopper's one bag of cat food will last her cat for 4 weeks.

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Consider the problem: A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4lb each week. How many weeks does one bag last?

Two numbers have the sum of 19. If one of the numbers is c, express the other number in terms of c. The other number is 19 - c.

Given: two numbers have the sum of 19

Let: c be one of those numbers

We want to express the other number in terms of c

The other number = 19 - c

Given two numbers, we want to express one of them in terms of the other. We can let one of the numbers be represented by the variable c. Since the sum of the two numbers is 19, the other number can be expressed as 19 minus c. Therefore, the other number can be written as 19 - c.

We are given two numbers and we want to express one of them in terms of the other. We can represent one of the numbers with the variable c. Since the sum of the two numbers is 19, the other number can be expressed as 19 minus c. In other words, the other number can be written as 19 - c. This means that if the value of c is known, the value of the other number can be calculated by subtracting c from 19. For example, if c is 10, then the other number is 19 - 10 = 9. Similarly, if c is 5, then the other number is 19 - 5 = 14. Therefore, the other number can be expressed as 19 - c.

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Therefore , the solution of the given problem of expression comes out to be √15 -4 < √15 -7  and so on.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

to find which is greatest expression among them

=> √15 -4 < √15 -7

=> 2√18  < 2√21

=>-³√30  > -3

=>√8 + 1 < √17 -2

Therefore , the solution of the given problem of expression comes out to be √15 -4 < √15 -7  and so on.

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Answer:

f(3) = 14

Step-by-step explanation:

f(x) = 3x +5

Let x = 3

f(3) = 3*3 +5

      = 9 + 5

      = 14

Answer:

Step-by-step explanation:

fș

The inverse demand function is P = 2400 + 5Q

Given that

Q = 480 - 0.2P

We simply make P the subject of the formula

So, we have

0.2P = 480 - Q

Divide by 0.2

P = 2400 + 5Q

To find the marginal revenue function, we can use the inverse demand function P = 2400 + 5Q, and take the derivative of this function with respect to Q.

The derivative of P with respect to Q is dP/dQ = 5. This represents the change in price for a one unit change in the quantity of operations performed.

So the Marginal Revenue function is MR = dP/dQ * Q = 5Q

To maximize profit, the doctor should equate marginal revenue to marginal cost, which is

MC = dAVC/dQ

So, we have

MC = d(2Q² - 15Q + 400)/dQ

Evaluate

MC = 4Q - 15.

So, we have

5Q = 4Q - 15

Q = -15

Take the absolute value

Q = 15

So, the number of operations is 15

We have

P = 2400 + 5Q

This gives

P = 2400 + 5 * 15

Evaluate

P = 2475

To find the profit, we need to subtract the total cost from the total revenue.

The total revenue is found by multiplying the price by the quantity of operations performed: TR = P * Q = 2475 * 15 = 37125

The total variable cost is found by multiplying the average variable cost by the quantity of operations performed: TVC = AVC * Q = (2Q^2 - 15Q + 400) * Q = 2Q^3 - 15Q^2 + 400Q

The total fixed cost is the fixed cost that doesn't change regardless of the level of output : TFC = $8000

The total cost is the sum of the total variable cost and total fixed cost: TC = TVC + TFC = 2Q^3 - 15Q^2 + 400Q + $8000

The profit is the difference between total revenue and total cost:

π = TR - TC = 37125 - (2Q^3 - 15Q^2 + 400Q + $8000)

When Q = 15,

profit is π = 37125 - (2(15)^3 - 15(15)^2 + 400(15) + $8000)

= 19750

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The determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1

The determinant of an n-by-n tridiagonal matrix containing only 1s as nonzero elements is given by the formula:

det(A) = 1^n-2 + 1^n-3 + ... + 1^2 + 1

For example, consider the 3x3 matrix:

A = [1 1 0; 1 1 1; 0 1 1]

Using the formula above, the determinant of A can be calculated as:

det(A) = 1^2 + 1 = 2

More generally, the determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1. This sum can then be taken to the power of 1 to obtain the determinant of the matrix.

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According to the information, the concentration of sugar in this solution is 62.5%.

To calculate the concentration of sugar we have to divide the mass of the solute by the mass of the solution and then multiply it for 100.

Equation:

The sugar concentration = 50g/80g x 100 = 62.5%

Therefore, the sugar concentration is 62.5%.

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Answer:Taking into account that X + Y = X + X + B = A, one can obtain the following formulas for finding X and Y:

X = (A – B) / 2.

Y = X + B = (A + B) / 2.

Step-by-step explanation:

Based on the definition of complementary angles, he measure of each of the angles are: 10.4 degrees and 79.6 degrees.

Complementary angles are defined as any two angles whose sum will be equal to 90 degrees when added together.

Therefore, let x be the measure of the angle.

According to the problem statement, the angle measures 69.2° less than the measure of its complementary angle.

So we have x + (x + 69.2) = 90

By simplifying the equation:

2x + 69.2 = 90

2x = 90 - 69.2

2x = 20.8

x = 20.8/2 = 10.4

So the angle measures 10.4 and the complement of angle is (10.4 + 69.2) = 79.6.

Thus, the measure of each of the angles are: 10.4 degrees and 79.6 degrees.

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Answer:

The answer is 0.165 inches.

Step-by-step explanation:

The volume of a rectangular pool can be calculated as the product of its length, width, and depth. To find out how much the water level increased, we'll calculate the volume of one quart of water and compare it to the volume of the pool.

One quart is equivalent to 0.946 liters, and 1 liter of water has a volume of 1000 cubic centimeters. Therefore, one quart of water has a volume of 0.946 liters x 1000 cubic centimeters/liter = 946 cubic centimeters.

Since 1 cubic foot is equivalent to approximately 28,317 cubic centimeters, the volume of one quart of water in cubic feet is:

946 cubic centimeters / 28,317 cubic centimeters/cubic foot = 0.033 cubic feet.

The volume of the pool can be calculated as:

12 ft x 20 ft x depth (in feet) = 240 cubic feet

So, if the pool is 12 ft x 20 ft, the water level increased by:

0.033 cubic feet / 240 cubic feet = 0.0001375 feet = 0.165 inches.

Therefore, the water level in the pool increased by approximately 0.165 inches.

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The point where x = -1 is the location of a relative maximum.

What is the critical point?

The concept of "critical point" is used in a lot of different ways, particularly, the most common way in which it is used is to describe the points where the slope of the tangent line is zero in continuous functions.

A critical point is a point where the first derivative of a function is equal to zero or is undefined.

A relative maximum occurs when the first derivative is zero and the second derivative is negative, while a relative minimum occurs when the first derivative is zero and the second derivative is positive.

The given information tells us that f'(x) is positive in the interval x < -1, negative in the interval -1 < x < 0, and positive in the interval x > 0.

This means that f'(x) is increasing in the interval x < -1, decreasing in the interval -1 < x < 0, and increasing in the interval x > 0. Therefore, at the critical point x = -1, f'(x) is zero and f''(x) is negative.

This means that the function changes from an increasing function to a decreasing function, indicating that the point where x = -1 is the location of a relative maximum.

Hence, the point where x = -1 is the location of a relative maximum.

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Answer:11160              

i calculated

For n = 8, the sum of squares from 1 to 8 would be:

Σ i² = 8(8 + 1)(2(8) + 1) / 6 = 204.

The act of adding anything up is called summarizing. To produce an action potential in the nervous system, numerous stimuli that are each individually subthreshold must be combined to reach a suprathreshold level (a response). Usually, a sum of numerous terms is indicated by the symbol "sigma." To include all terms that must be taken into account when computing the sum, this symbol is typically followed by an index that varies.

The summation notation "Σ" is used to represent the sum of a sequence of numbers. The expression "Σ i²" means the sum of the squares of the numbers from i=1 to i=8.

The formula to find the sum of the squares from 1 to n is given by:

Σ i² = n(n + 1)(2n + 1) / 6

So, for n = 8, the sum of squares from 1 to 8 would be:

Σ i² = 8(8 + 1)(2(8) + 1) / 6 = 204.

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The triangle is obtuse because 11^2 + 21^2 does not equal 29^2.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

We can use this theorem to determine the type of triangle by calculating the square of the longest side (29^2), and then comparing it to the sum of the squares of the other two sides (11^2 + 21^2). Since 11^2 + 21^2 does not equal 29^2, the triangle is obtuse.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

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This matches the given volume of 108 cubic inches.

Volume is a measure of the amount of space an object or substance occupies. It is measured in units such as liters, gallons, cubic meters, and milliliters. It is often used to measure the size of a container, the amount of a material, or the size of a space. Volume is an important property for understanding physical objects, as it helps to determine mass and density.

The volume of a triangular prism can be calculated by taking the area of the base, which is the area of an equilateral triangle (all sides equal) multiplied by the height of the prism. In this case, the area of the triangle is ((√3/4)*(12^2)) = 108 square inches and the height is 9 inches, so the volume is 108*9 = 108 cubic inches. This matches the given volume of 108 cubic inches.

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[tex]t+7.87 > 9.87[/tex]

Subtract 7.87 from both sides:

[tex]t+7.87-7.87 > 9.87-7.87[/tex]

Answer:

[tex]t > 2[/tex]

Answer:

[tex] \sf \: t > 2[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of t.

The inequation is,

→ t + 7.87 > 9.87

Then the value of t will be,

→ t + 7.87 > 9.87

→ t > 9.87 - 7.87

→ [ t > 2 ]

Hence, the value of t is 2.

Reason:

c = Craig's score

c+12 = twelve more than Craig's score

c+12 = 70 because the key term "is" translates to "equals". As an example, saying "x is 5" means "x = 5".

The volume of the solid is 32/3.

The volume of the solid whose base is bounded by the circle x2 + y2 = 4 and the cross sections perpendicular to the x-axis are squares can be calculated using the formula for the volume of a solid of revolution. This formula states that the volume is equal to the integral of the area of the cross sections from the lower limit to the upper limit.

Since the cross sections are squares, the area of each cross section is given by the equation A = x2. The lower limit is given by the equation x2 + y2 = 4, which is x=-2, and the upper limit is x=2. Thus, the volume is given by the integral ∫(-2)2x2dx = 8∫x2dx = 8(x3/3)|(-2)2 = 8(2^3/3 - (-2)^3/3) = 8(8/3 - -8/3) = 32/3. Therefore, the volume of the solid is 32/3.

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If Ellie purchased a laptop for $1,400, but she still owes $600 which she borrowed to purchase the laptop. Her equity in the case of the laptop is; A. $1400+ $600 = $2000.

Using this formula to determine her equity

Equity = Cost of laptop + Amount owes

Where:

Cost of laptop = $1,400

Amount owes = $600

Let plug in the formula

Equity = $1,400 + $600

Equity = $2,000

Therefore we can conclude that the correct option is A.

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There is not enough evidence to conclude that the percent at her school is less than 40%.

The conclusion of the hypothesis test is reached depending on the confidence interval as follows:

The upper bound of the interval is given as follows:

0.4240 = 42.40%.

Hence not enough evidence to conclude that the percent at her school is less than 40%.

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Answer:

The answer is 85/1. To calculate 5 × 17, first multiply 5 × 10 = 50, then add 5 to the result to get 50 + 5 = 55. Finally, divide the result by 1 to get 55/1 = 85/1.

Answer:

The fraction is 5/7

Step-by-step explanation:

5 * 1/7

Multiplying a whole number times a fraction

Multiply the whole number times the numerator.

5 * 1 = 5

Divide by the denominator

5/7

The fraction is 5/7

If the both coordinates are equal and has same sign then interchanging them will not have any effect and they will meet at the right location

Interchanging the x coordinate for the y coordinate when both are equal and have same sign will create no effect and hence this will not affect their meeting place

In  a situation where the coordinates are different, interchanging the two coordinates will lead to meeting at a different point.

The point of meeting when the coordinates are different either in sign or in value is at reflection over the line y = x

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The value of the company after 5 years is given as follows:

$75,631.5.

The value will decline below $140,000 when:

3.27 years.

The exponential function for this problem is defined as follows:

V(x) = 450000(0.7)^x.

The value after 5 years is found replacing the lone instance of x by 5, hence:

V(5) = 450000(0.7)^5

V(5) = $75,631.5.

The value will decline below $140,000 when at x for which V(x) = 140000, hence:

140000 = 450000(0.7)^x.

(0.7)^x = 140000/450000

(0.7)^x = 0.311111

xlog(0.7) = log(0.311111)

x = log(0.311111)/log(0.7)

x = 3.27 years.

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Answer:

An algebraic expression for the total amount of money in both accounts is m+2000

Step-by-step explanation:

If there are 2000 dollars in one account and m dollars in the other, the sum of both accounts can be expressed as 2000+m (or m+2000).

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable  sum range of .05 fluid ounces or less.

The simulation did not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces, indicating that the variability of the juice dispensed was within the acceptable sum of range

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable range of .05 fluid ounces or less.

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The sample size for part(A)=318  and part(B) is 423 and the difference of samples is 105.

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC.

Part(A)

it is given in the question that.

margin of error E=0.04

guessed value p=75%=0.75

confidence interval =90%=0.90

now to find the sample size,

[tex]n=\frac{{[z_{a/2}}]^2p(1-p) }{E^{2}}[/tex]

[tex]n=\frac{1.645^2(0.75)(.25)}{0.04^2} \\\\n=318[/tex]

therefore, the sample size is 318.

Part(B)

find the new sample size by the above formula.

p=0.5

so, n'=423.

thus, the new sample size is 423.

for the difference between the two sample sizes.

N=105.

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The result of the quotient expression as required to be determined in the task content is; 2^(8x + 3).

It follows from the laws of indices that 8 = 2³.

On this note, the given expression; 8^(3x + 1) ÷ 2^x can be solved as follows;

2^( 3 (3x + 1) ) ÷ 2^x

= 2^( 9x + 3 ) ÷ 2^x

= 2^(9x + 3 - x)

= 2^(8x + 3)

Ultimately, the result of the quotient is; 2^(8x + 3).

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Answer:

9(5 + 8)

Step-by-step explanation:

We got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

Therefore, x³+2x² +x-7=0 is correct answer.

An a non real solution uses non real numbers to solve the equation, which cannot be solved with real numbers. Back to the school answer: A non-real solution to a math equation is a solution that has “imaginary numbers” (also called “complex numbers”) in it because it cannot be solved with real numbers.

Step1

We need to find equation that has exactly two real and two non real solutions

2 real  and 2 non real solution means 4 solutions

x³ equation has maximum of 3 solutions

So we ignore equation that has largest exponent x³

We ignore options B  and D

Let check option A

x⁴ 36x² =0

factor the left hand side

Factor out x^2

x² (x² -36)=0

WE set each factor =0  and solve for x

x² =0  so x=0

x²  - 36 =0 so x= +-6

So solutions are x=0, x=6 , x= -6. Only 3 real solutions we got

LETS check with option C

x⁴  - 5x² -36=0

Factor left hand side

(x² -9)(x² +4)=0

set each factor =0  and solve for x

x² -9 =0  so x= -3, + 3

x² + 4 =0 , x² = -4, so x= +2i, -2i

So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

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