ABC Bookstore sells packages of books that include both new and used
books. New books cost $18 and used books cost $9. The bookstore wants to
sell packages that have 36 books total, and the store charges $432 for each
package. How many new and used books will be in each package?
OA. 18 new, 9 used
O B. 9 new, 18 used
O C. 12 new, 24 used
о D. 24 new, 12 used

There are 72 different sums that can be obtained by rolling the die, spinning the spinner, and picking a card.

To determine the number of different sums possible, we need to consider the outcomes of rolling the die, spinning the spinner, and picking a card.

Let's analyze each component separately:

1. Rolling the die: The die has 6 sides, numbered 1 to 6. Therefore, there are 6 possible outcomes when rolling the die.

2. Spinning the spinner: The spinner has 6 sections labeled 1 to 6. Again, there are 6 possible outcomes when spinning the spinner.

3. Picking a card: The card has two options, either 6 or 7. Thus, there are 2 possible outcomes when picking a card.

To find the total number of different sums, we need to multiply the number of outcomes for each component. Therefore, the total number of different sums is obtained by multiplying 6 (die outcomes) by 6 (spinner outcomes) by 2 (card outcomes), resulting in 6 * 6 * 2 = 72 different possible sums.

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The percentage increase in the winner's check for the U.S. Open Golf Championship from 1895 to 2019 was approximately 4.33% per year. If the winner's prize continues to increase at the same rate, it would be around $11,655,984.98 in 2044.

To calculate the percentage increase per year in the winner's check, we need to find the annual growth rate. We can use the formula for compound interest to do this. The initial prize in 1895 was $150, and the final prize in 2019 was $2.25 million (or $2,250,000).

First, we find the total number of years between 1895 and 2019: 2019 - 1895 = 124 years.

Next, we calculate the percentage increase using the compound interest formula:

Percentage Increase = ((Final Amount / Initial Amount)^(1 / Number of Years) - 1) * 100

Percentage Increase = ((2,250,000 / 150)^(1 / 124) - 1) * 100 ≈ 4.33%

Now, to find the prize money in 2044, we need to use the compound interest formula again. The number of years from 2019 to 2044 is 25 years.

Final Amount = Initial Amount * (1 + Percentage Increase)^Number of Years

Final Amount = 2,250,000 * (1 + 0.0433)^25 ≈ 11,655,984.98

Thus, if the winner's prize continues to increase at the same rate, it will be approximately $11,655,984.98 in 2044.

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Answer:

Step-by-step explanation:

Slope - intercept formula: y = mx + b, where m- slope, b- y-intercept

1. Points are:

Slope is:

y-intercept is - 6 as per graph

Then the formula is

2. Points are:

Slope is:

y-intercept is 5 as per point

Then the formula is

3. Points are:

Slope is

y-intercept is -5 as per graph

Then the formula is

Answer:

30 degrees/ An Acute Angle (If I'm wrong please comment on my answer)

Step-by-step explanation:

Answer:

If a is negative or zero  there are no real solutions

Step-by-step explanation:

y=ax^2-8

Set equal to zero to find the solution

0 =ax^2-8

Add 8 to each side

8 = ax^2

Divide by a  a cannot be zero or we cannot divide by it

8/a = x^2

Take the square root of each side

sqrt(8/a) = sqrt(x^2)

We need 8/a to be positive for it to have real solutions

That means a has to be positive

If a is negative or zero  there are no real solutions

Answer:

1) not a function

2)function

3)not a function

4)function

The value of the triple integral ∭E 7x dV, where E is bounded by the paraboloid x = 7y^2 + 7z^2 and the plane x = 7, is 0.

To evaluate this triple integral, we need to determine the limits of integration for each variable. Let's express the paraboloid equation in terms of y and z:

x = 7y^2 + 7z^2

Since the paraboloid is bounded by the plane x = 7, we can set up the following limits:

0 ≤ x ≤ 7
0 ≤ y
0 ≤ z

Now we can rewrite the integral as:

∭E 7x dV = ∫[0 to 7] ∫[0 to ∞] ∫[0 to ∞] 7x dy dz dx

To evaluate this integral, we integrate with respect to y first:

∫[0 to 7] ∫[0 to ∞] 7x dy dz = 7 ∫[0 to 7] xy |[0 to ∞] dz

Simplifying further, we have:

7 ∫[0 to 7] ∞ dz = ∞

Therefore, the value of the triple integral ∭E 7x dV is 0.

In conclusion, the triple integral evaluates to 0, indicating that the integral over the given region is zero.

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Answer:

125 degrees

Step-by-step explanation:

Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals   inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.

Hope this is helpful! :)

Answer: For every apple you sell, you earn 4 bucks. y is the number of apples, 4 is the constant price.

Answer:

A hexagon

Step-by-step explanation:

A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.

The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.

The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.

The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.

The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.

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The expression is equivalent to 45m^-6p^2v^12/15m^-2p^8v^-4 is Option b 3v^16/m^4p^6 .

Given :

expression is equivalent to for all values of m , p , and v where the expression is defined

= ( 45m^-6 ) * p^2 * v^12 / 15m^-2 * p^8 * v^-4

= ( 45 / 15 ) ( m^-6 / m^-2 ) ( p^2 / p^8 ) ( v^12 / v^-4 )

= 3 ( m^-6 - ( -2 ) ( p^2 - 8 ) ( v^12 - ( - 4 )

= 3 ( m^-6 + 2 ) ( p^-6 ) ( v^12 + 4 )

= 3 ( m^-4 ) ( p^-6 ) ( v^16)

= 3 * v^16 / m^4 * p^6

= 3v^16 / m^4p^6

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Answer:

Price after discount: $33.75

You saved: $11.25

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Answer:

80 total students

Step-by-step explanation:

hope this helps!

Answer:

80

Step-by-step explanation:

If 16 is %20 then it represents 1/5 of the class. Multiply 16 x 5 = 80

Step-by-step explanation:

1. 6 factors of 2 means, 2 multiplied by itself 6 times.  It can be written in the form of exponents as 2⁶.

2. \(2^m{\cdot} 2^n\)

The law of exponent is : \(x^a{\cdot} x^b=x^{a+b}\)

So,

\(2^m{\cdot} 2^n=2^{m+n}\)

The correct option is (A).

3. If the power of any number is 0, then the value of that number is equal to 1.

So,

\(23^0=1\)

Hence, this is the required solution.

A) mpg = 28.67 - 3.59 * drat + -5.34 * wt

B) The predicted miles per gallon will decrease by 5.34, controlling for the drag ratio.

C)  We can perform a hypothesis test on the coefficient of wt using a t-test with a significance level of 0.05.

D) The p-value associated with the wt coefficient is 1.29e-10 which is much smaller than the significance level of 0.05.

a. The estimated model is:

mpg = 28.67 - 3.59 * drat + -5.34 * wt

b. The estimated coefficient on wt, β_2, is -5.34. This means that for each increase in weight by 1000 pounds, the predicted miles per gallon will decrease by 5.34, controlling for the drag ratio.

c. To test if weight is a significant predictor of mpg given drag ratio is controlled for, we can perform a hypothesis test on the coefficient of wt using a t-test with a significance level of 0.05.

Null hypothesis: β_2 = 0 (weight is not a significant predictor of mpg)

Alternative hypothesis: β_2 ≠ 0 (weight is a significant predictor of mpg)

We can look at the p-value of the wt coefficient from the summary of the model:

Coefficients:

Estimate Std. Error t-value Pr(>|t|)

(Intercept) 28.66667    1.22972  23.335  < 2e-16 ***

drat        -3.58720    1.37387  -2.611  0.01497 *

wt          -5.34447    0.55910  -9.559 1.29e-10 ***

The p-value associated with the wt coefficient is 1.29e-10 which is much smaller than the significance level of 0.05. Thus, we reject the null hypothesis and conclude that weight is a significant predictor of mpg, controlling for the drag ratio.

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There are 26 different sums of 3 primes that can be created in an L-shaped pattern of 3 cells from the given 3x3 grid of the first 9 prime numbers.

To determine the number of different sums, we need to consider all possible combinations of 3 primes in an L-shaped pattern. The L-shaped pattern can be formed by selecting any 3 adjacent cells (horizontally or vertically) from the 3x3 grid.

Let's list all the possible L-shaped patterns of 3 cells:

(1, 2, 4)

(1, 2, 6)

(1, 4, 5)

(1, 4, 9)

(2, 3, 6)

(2, 4, 5)

(2, 4, 7)

(3, 2, 8)

(3, 4, 7)

(3, 5, 8)

(4, 5, 6)

(4, 5, 9)

(4, 7, 8)

(5, 4, 6)

(5, 4, 9)

(5, 6, 8)

(6, 2, 3)

(6, 5, 8)

(6, 8, 9)

(7, 4, 8)

(7, 6, 9)

(7, 8, 9)

(8, 3, 7)

(8, 6, 9)

(9, 1, 4)

(9, 5, 4)

By considering all possible combinations of 3 primes in these L-shaped patterns, we can calculate the corresponding sums. Each unique sum will be counted as a different sum.

Hence, there are 26 different sums of 3 primes that can be created in an L-shaped pattern of 3 cells from the given 3x3 grid of the first 9 prime numbers.

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Answer:

14.81%

Step-by-step explanation:

A fair six-sided dice has a total of six sides meaning that there are 6 possible outcomes for each dice roll. If two of the faces on the dice are red, then the possibility of rolling a red on a single dice roll would be 2/6, while the probability of rolling anything else would be 4/6 because there are 4 other sides left. Now if we roll three seperate dice, in order to calculate the probability of getting only one red face we need to multiply the probability of getting a red face on the first dice by the probability of the other two dice getting anything else.

2/6 * 4/6 * 4/6 = 32/216 or 0.1481

We can multiply this decimal by 100 to get the percentage value...

0.1481 * 100 = 14.81%

Answer:

1.41 inches per hour

Step-by-step explanation:

volume of water for 3 hrs=4.23 inches

v of water for 1 hours=4.23/3=1.21inches

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

The simple interest earned can be calculated by using this formula

A = P(1 + rt)

A is the future value.

P is the principal value.

r is the interest rate.

t is the time.

Now Substituting the values into the formula, we have,

A = 16,000[1 + (0.08 × 3)]

A = 16,000[1 + 0.24]

A = 16,000× 1.24

Future value, A = $19,840.

Following that, we will compute the monthly payment over a 36-month period as follows:

Monthly payment = Future value/Time

Monthly payment = 19,840/36

Monthly payment = $551.11

Similarly, we will compute the credit card's compound interest:

A = 16000[1 + (0.15/12)]⁽¹² ˣ ⁷⁾

A = 16000[1 + 0.025]⁸⁴

A = 16000× 1.025⁸⁴

A = 9000 × 3.49258954

Future value, A = $45425.80

Following that, we will compute the monthly payment over an 84-month period as follows;

Monthly payment = Future value/Time

Monthly payment = 45425.80/84

Monthly payment = $540.78.

Thus, the monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

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Answer:

ur answer should be C. But I'm not really sure..

The table in which y is a linear function of x is; Choice C

According to the question;

The slope of a linear function is always constant.

Hence, By observing the table in Choice C;

Slope = (8-6)/(0-(-1)) = (10-8)/(1-0) = 2.

Hence, since slope of the function is constant, the required table is: Choice C.

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Two triangles are congruent if they have exactly the same three side and exactly same three angles. There are five ways to find if two triangles are congruent such as SSS, SAS, ASA, AAS and HL.

SSS stands for Side-Side-Side and states that we have two ttriangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then the triangles are congruent.

SAS stands for Side-Angle-Side and it states that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then the triangles are congruent.

So if the three sides are similar then we can say that triangle is SSS and if two sides and one angle is similar to another triangle then we can say that triangle is SAS.

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Answer:

Let BB be the point where the crew measures the angle of elevation to the lighthouse's beacon-light. Also, let CC be the point where the perpendicular from the lighthouse to the ground intersects the line segment AB, where AB represents the path of the boat.

We know that the angle of elevation from point AA to the lighthouse's beacon-light is 14^{\circ} ∘ . Therefore, angle ACC is also 14^{\circ} ∘ , as it is alternate interior angle with respect to line AB. Similarly, we can show that angle BCC is 6^{\circ} ∘ .

Now, we can use trigonometry to find the distance from point AA to point BB. Let's call this distance x. Then, we have:

\tan(14^{\circ}) = \frac{BC}{734}

\tan(6^{\circ}) = \frac{BC + x}{734}

Solving for BC in the first equation, we get:

BC = 734\tan(14^{\circ}) \approx 193.9

Substituting this value into the second equation and solving for x, we get:

x = 734\tan(6^{\circ}) - BC \approx 30.5

Therefore, the distance from point AA to point BB is approximately 30.5 feet.

Answer:

a. 12 students had received college credit for math

b. 26 students had received college credit for science

If  a petrol station wants to make 100% profit. the cost of fuel per litre at this petrol station is 1.4 pence.

Given, the formula to calculate the cost of fuel per litre:

(1 + 100) X + X 160 C = cost of oil per barrel.

Where :

X = cost of oil per litre

C= rate of fuel duty tax in %.

We know that fuel duty is 50% and oil costs £128 per barrel, so we can substitute these values into the equation:

(1 + 100) X + X 160 * 0.5 = 128

Expanding the equation:

100 X + 80 X = 128

180 X = 128

Dividing both sides by 180:

X = 128/180 = 7/10 = 0.7

So, the cost of oil per litre is 0.7 pence.

The petrol station wants to make 100% profit, so we add the profit to the cost of oil per litre:

0.7 + 0.7 * (100/100) = 1.4 pence

Therefore, the cost of fuel per litre at this petrol station is 1.4 pence.

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The total cost of the carpet, foam padding, and labor charges for Randi's house would be $2,353.78 for the downstairs area, $665.39 for the halls, and $3,446.78 for the bedrooms upstairs.

Randi went to Lowe's to purchase wall-to-wall carpeting for her house. She needs different amounts of carpet for different areas of her home. For the downstairs area, Randi needs 110.18 square yards of carpet. The halls require 31.18 square yards, and the bedrooms upstairs need 161.28 square yards.

Randi chose a shag carpet that costs $14.37 per square yard. In addition to the carpet, she also ordered foam padding, which costs $3.17 per square yard. The carpet installers quoted a labor charge of $3.82 per square yard.

To calculate the cost of the carpet, we need to multiply the square yardage needed by the price per square yard. For the downstairs area, the cost would be

110.18 * $14.37 = $1,583.83.

Similarly, for the halls, the cost would be

31.18 * $14.37 = $447.65

and for the bedrooms upstairs, the cost would be

161.28 * $14.37 = $2,318.64.

For the foam padding, we need to calculate the square yardage needed and multiply it by the price per square yard. The cost of the foam padding for the downstairs area would be

110.18 * $3.17 = $349.37.

For the halls, it would be

31.18 * $3.17 = $98.62,

and for the bedrooms upstairs, it would be

161.28 * $3.17 = $511.80.

To calculate the labor charge, we multiply the square yardage needed by the labor charge per square yard. For the downstairs area, the labor charge would be

110.18 * $3.82 = $420.58.

For the halls, it would be

31.18 * $3.82 = $119.12,

and for the bedrooms upstairs, it would be

161.28 * $3.82 = $616.34.

To find the total cost, we add up the costs of the carpet, foam padding, and labor charges for each area. The total cost for the downstairs area would be

$1,583.83 + $349.37 + $420.58 = $2,353.78.

Similarly, for the halls, the total cost would be

$447.65 + $98.62 + $119.12 = $665.39,

and for the bedrooms upstairs, the total cost would be

$2,318.64 + $511.80 + $616.34 = $3,446.78.

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The complete question is:

Randi went to Lowe's to buy wall-to-wall carpeting. She needs 110.18 square yards for downstairs, 31.18 square yards for the halls, and 161.28 square yards for the bedrooms upstairs. Randi chose a shag carpet that costs $14.37 per square yard. She ordered foam padding at $3.17 per square yard. The carpet installers quoted Randi a labor charge of $3.82 per square yard.

If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other. the given statement is True.

If the dot product of two vectors is equal to zero, it means that the two vectors are orthogonal or perpendicular to each other.A dot product of two nonzero vectors is zero when the cosine of the angle between the two vectors is 90 degrees or pi/2 radians.

Since the cosine of pi/2 radians is zero, any two vectors that are orthogonal will have a dot product of zero, and this applies to nonzero vectors as well.

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Arthur is planning to put a tile floor in his room. The dimensions of the tiles are 1 foot on each side. Half of the tiles that will be used are dark brown, costing 58 cents per tile. The other half of the tiles are light brown, on sale for 49 cents per tile. We need to calculate the cost of tiles that will be needed to cover the entire floor of the room.

The total cost of the floor can be calculated as:Total Cost = (Cost of Dark Brown Tiles x Number of Dark Brown Tiles) + (Cost of Light Brown Tiles x Number of Light Brown Tiles)We can calculate the number of tiles needed by calculating the area of the floor that needs to be covered and dividing that area by the area of each tile. The area of the room is not given in the problem, so we cannot calculate the exact number of tiles needed or the total cost of the floor.In order to provide an estimate, let us assume that the room is 10 feet by 10 feet.

This means that the area of the floor is 100 square feet. Since the tiles are 1 foot on each side, they have an area of 1 square foot. This means that we will need 100 tiles to cover the entire floor.Assuming that half of the tiles are dark brown, we will need 50 dark brown tiles. Similarly, we will need 50 light brown tiles.

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