10. The time it takes to drain a swimming pool varies inversely with the amount of water being
pumped per hour. If a large pool takes 12 hours to empty at 400 gallons an hour, how many
hours faster can the pool be drained if the pumping rate is increased to 500 gallons per hour?
(teal)

we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.

How to solve the problem ?

The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.

To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.

Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.

Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.

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The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56

what is synthetic division ?

Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).

In the given question,

To use synthetic division to rewrite the fraction, we first set up the problem like this:

   -3 | 4    17    14    -3    0    2

       |     -12    -15    3   0

       +----------------------------------

          4     5    -1     0    0    2

The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.

We then proceed to perform synthetic division as follows:

Bring down the first coefficient, which is 4, and write it under the horizontal line.

Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.

Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.

Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.

Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.

Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.

Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.

The result of the synthetic division is:

4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56

Therefore, we have rewritten the fraction in the desired form:

4x⁵+17x⁴+14x³-3x²+2

---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)

         x+3

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Step-by-step explanation:

[tex]3 ln(2x) = 12[/tex]

[tex] ln(2x) = 4[/tex]

Let both sides be a power of a base e.

[tex]e {}^{ln(2x)} = e {}^{4} [/tex]

The e and ln would just cancel out so

[tex]2x = e {}^{4} [/tex]

[tex]x = \frac{ {e}^{4} }{2} [/tex]

The given operation of the matrix is expressed as: -9y + 2z = 12

Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.

The simultaneous equations formed by the matrix are:

x + 2y + z = -5

    4y - 2 = 3

4x - y + 6 = -8

We are told to Multiply row 1 by -4 and this gives us:

-4x - 8y - 4z = 20

Adding it to row 3 gives us:

-9y + 2z = 12

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The median number of newspapers sold is 202 newspaper. So, correct option is C.

To find the median, we need to arrange the given data in ascending or descending order.

The given data in ascending order: 71, 81, 113, 202, 242, 248, 269

Since there are 7 data points, the median will be the fourth value in the sorted list. Therefore, the median number of newspapers sold is 202.

Hence, the correct answer is option C, which states that the median number of newspapers sold is 202.

The median is the middle value of a dataset when arranged in order, and it's a measure of central tendency that is less affected by outliers than the mean. In this case, the median value represents the value at which half the data points are below it and half are above it.

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Complete question is:

A store manager kept track of the number of newspaper sold each week over a seven week period. the result were as fellows 71,81,202,113,269,248,242​

Find the median number of newspapers sold.

A. 175 newspapers

B. 113 newspapers

C. 202 newspapers

D. 242 newspapers

Answer:$909.03

Step-by-step explanation:he new balance on Guadalupe's credit card is calculated as follows:

First, we calculate the interest charged on the previous balance. Since the APR is 23%, the monthly interest rate is 23%/12 = 1.92%. So the interest charged on the previous balance for the month is:

Interest = Previous balance x Monthly interest rate

= $900.00 x 1.92%

= $17.28

Next, we add the finance charge, which is calculated as 1% of the previous balance plus any new charges. So the finance charge for the month is:

Finance charge = 1% x (Previous balance + New charges)

= 1% x ($900.00 + $0.00)

= $9.00

The total amount due is the sum of the previous balance, the interest charged, and the finance charge:

Total amount due = Previous balance + Interest + Finance charge

= $900.00 + $17.28 + $9.00

= $926.28

The minimum payment due is 2% of the total amount due, which is:

Minimum payment = 2% x Total amount due

= 2% x $926.28

= $18.53

If the minimum payment is less than $25, the minimum payment due is $25. So in this case, the minimum payment due is $25.

Guadalupe made a payment of $18.00, which is less than the minimum payment due, so she will be charged a late fee in addition to the interest on the unpaid balance.

The principal paid is the difference between the payment made and the interest charged, which is:

Principal paid = Payment - Interest

= $18.00 - $17.28

= $0.72

The new balance is the sum of the previous balance, any new charges, and the interest charged, minus the payment made, plus any finance charge and late fee:

New balance = Previous balance + New charges + Interest - Payment + Finance charge + Late fee

= $900.00 + $0.00 + $17.28 - $18.00 + $9.00 + $0.75

Answer:

2y - 3> 9 it is not y + 6< 10

Answer:

x = 5

Step-by-step explanation:

To solve the equation 4x-8 + 4 = 16, we first combine the constants on the left-hand side:

4x-8+4 = 16

4x-4 = 16

Next, we add 4 to both sides to isolate the variable on one side:

4x-4+4 = 16+4

4x = 20

Finally, we divide both sides by 4 to solve for x:

4x/4 = 20/4

x = 5

Therefore, the solution to the equation 4x-8 + 4 = 16 is x = 5.

the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,

B) 10x + 10x + 20 - 5.

Given that;

The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.

We can simplify this expression by factoring out the common factor of 5: = 20x + 15

= 5(4x + 3)

Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.

Option A:

18x + 4x + 6 + 7 does not have a factor of 5,

so it cannot be the correct answer.

Option B:

10x + 10x + 20 - 5

= 20x + 15,

which is the same as the original expression.

Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.

Option C:

6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,

which does not have a factor of 5.

Therefore, Option C is not correct.

Option D:

3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,

which does not have a factor of 5.

Therefore, Option D is not correct.

Therefore, the correct answer is,

B) 10x + 10x + 20 - 5.

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Answer:

f(-1)=0

Step-by-step explanation:

To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :

[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]

[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0

Answer:

C. (x + 3)² + (y - 4)² = 9

Step-by-step explanation:

The equation for a circle is r² = (x - a)² + (y - b)² where "r" is the radius and (a, b) is the center.

We are given that (-3, 4) is the center and the radius is 3, so that means a = -3, b = 4, and r = 3. Insert the values to their respective places in the equation:

3² = (x - (-3))² + (y - 4)²

9 = (x + 3)² + (y - 4)²

Answer:

equation of a circle: (x-a)²+(y-b)²=r²

(x-(-3))²+(y-4)²=3²

(x+3)²+(y-4)²= 9

(x+6x+9)+(y-8y+16) =9

x+6x+9+y-8y+16=9

x+y+6x-8y+9+16-9=0

x+y+6x-8y+16 =0

The appropriate measure of variability for the data shown and its value is A. The range is the best measure of variability and equals 600.

The range is one of  the three measures of variability.

The range shows the difference between the highest value and the lowest value in a data set.

The other measures of variability are the IQR (Interquartile Range) and the the Standard Deviation.

Highest value = 800 m

Lowest value = 200 m

The range = 600 m (800 - 200)

IQR = 400 (600 - 200)

Mean = 567 (3,400 ÷ 6)

Median = 625 [(650 + 600) ÷ 2]

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The row of zeros at the bottom immediately lets us conclude "infinitely many solutions". This system is consistent and dependent. This is because we have 0x+0y+0z = 0 aka 0 = 0 which is always true for any choice of x, y, and z.

The second row of values lead to the equation 0x+0y+1z = 6, aka z = 6

The first row says: 1x+6y+0z = 1 which is the same as x+6y = 1

Let's say we isolate x

x+6y = 1

x+6y-6y = 1-6y

x = 1-6y

Then we have these three values or expressions

All of the infinitely many solutions are of the form (x,y,z) = (1-6y, y, 6)

A lot of textbooks will use a parameter such as t, so we could write it as (1-6t, t, 6).

The choice of the letter for the parameter does not matter. I think t is most popular because it represents time. Each (x,y,z) point could represent a particle's location at any given time.

and so on.

=============================

Conclusion:

There are infinitely many solutions of the form (x,y,z) = (1-6t, t, 6) where t is any real number.

This system is consistent and dependent.

1. The linear regression equation is y = -1.17x+ 10.69

2. The correlation coefficient is -0.982.

3. This means there is a strong negative correlation between the gallons and hours.

4. The number of gallons is decreasing as the hours are increasing.

Step 1: find slope.

Formula for slope m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)

Σx = 1 + 2 + 3 + 4 + 5 = 15

Σy = 9.2 + 8.4 + 7.7 + 6.1 + 4.5 = 35.9

Σ(xy) = (1 × 9.2) + (2 × 8.4) + (3 × 7.7) + (4 × 6.1) + (5 × 4.5) = 96

Σ(x²) = 1 + 4 + 9 + 16 + 25 = 55

n = 5

Therefore ∴

m = (5 × 96 - 15 × 35.9) / (5 × 55 - 15²) = -1.17

y-intercept b = (Σy - m × Σx) / n

b = (35.9 - (-1.17) × 15) / 5 = (53.15) / 5 = 10.63

Therefore the linear regression equation is y = -1.17x + 10.63

correlation coefficient (r): (n × Σ(xy) - Σx × Σy) / sqrt((n × Σ(x²) - (Σx)²) × (n × Σ(y²) - (Σy)²))

r = (5 × 96 - 15 × 35.9) / sqrt((5 × 55 - 15²) × (5 × 271.95 - 35.9²)) = -0.982

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If  landscaper worked 8-1/2 hours on Monday, 3-1/3 hours on Tuesday and 6-1/4 hours on Wednesday then  total of 18.08 hours worked.

To find the total number of hours worked, we need to add up the hours worked on each day.

On Monday, the landscaper worked for 8-1/2 hours, which is the same as 8.5 hours.

On Tuesday, the landscaper worked for 3-1/3 hours, which is the same as 3.33 hours

On Wednesday, the landscaper worked for 6-1/4 hours, which is the same as 6.25 hours.

To find the total hours worked, we add the hours worked on each day:

Total hours worked = 8.5 + 3.33 + 6.25

Total hours worked = 18.08

Therefore, the landscaper worked a total of 18.08 hours.

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The amount you will have in the account in 30 years is $22836.77

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:

Amount = P * (1 + r)^t

Where

P = Principal = 3000

r = Rate = 7%

t = time = 30

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

Amount = 3000 * (1 + 7%)^30

Evaluate

Amount = 22836.77

Hence, the amount is 22836.77

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Answer:

-9

Step-by-step explanation: Definitely correct

The volume of the new object is approximately 439.3 cubic inches

To find the volume of the new object, we need to first know the volume of the prism before the cylinder is removed hence we do this:

The volume of a cylinder: = πr²h

where:

r = radius

h  = height

Note that the volume of a rectangular prism is :  = lwh

l = length

w = width

h = height

Assumption: In the above case, we will  assume that the dimensions of the rectangular prism because the cylinder can be cut out from the center of one of the faces.

Hence the length and width of the prism will be taken to be twice the radius of the cylinder, that is 16 inches, and the height will be taken to be same as the radius of the cylinder, that ia 8 inches.

So  V_prism = lwh

 = 16 × 16 × 8

= 2048 cubic inches

V_cylinder = πr²h

= π × 8² × 8

= 512 π cubic inches

Hence To get  the volume of the new object, we need to subtract the volume of the cylinder from the volume of the prism:

V_new = V_prism - V_cylinder

= 2048 - 512π

= 2048  - 1608.70

= 439.3 cubic inches

Hence, the volume of the new object is about 439.3 cubic inches

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Answer:

Less than 180

Step-by-step explanation:

Minor: Less than 180

Major: More than 180

Answer:

10 wax cubes

Step-by-step explanation:

the volume of the square pyramid can be found by using the following formula:

[tex]V = \frac{1}{3} * B * h[/tex]

where b is the base of the pyramid and h is the height of the pyramid

The area of the base of the pyramid is given as 12 in * 12 in = 144 in^2

So, the volume of the pyramid is:

V = (1/3) * 144 in^2 * 14 in = 2,016 in^3

Each wax cube has a volume of 6 in * 6 in * 6 in = 216 in^3.

To find the number of wax cubes needed, we can divide the volume of the pyramid by the volume of each wax cube:

Number of wax cubes = Volume of pyramid / Volume of each wax cube

Number of wax cubes = 2,016 in^3 / 216 in^3

Number of wax cubes = 9.33 (rounded to two decimal places)

Since we can't have a fraction of a wax cube, Josiah will need to use 10 wax cubes to make the candle.

Answer:

B

Step-by-step explanation:

the answer is B because I know it

The area in square yards of the athletic field at IDEA Brentwood would be 170. 24 yards ²

The shape of the athletic field at IDEA Brentwood is shown to be a rectangle with two semi - circles attached.

The area of the athletic field at IDEA Brentwood is the sum of the areas of these shapes.

Area of rectangle :

= 15 x 8

= 120 yards ²

The area of the two semi - circles would be:

= π x radius x radius

= π x ( 8 / 2 ) x ( 8 / 2 )

= 50. 24 yards ²

The area of the athletic field at IDEA Brentwood is :

= 50. 24 + 120

= 170. 24 yards ²

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The error is in step 2 based on the given statement.

The given statement is[tex]cos(2x) = 1-2sin^2(x),[/tex] and it is not appropriate to simply let 2x = 0.

By doing this, you are only considering a specific case where x = 0, rather than proving the statement for all values of x.

To properly prove the given statement, you should consider using trigonometric identities or double-angle formulas to establish the equivalence between cos(2x) and 1-2sin²(x) for all x.

Thus, the error is in Step 2

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Answer:113

Step-by-step Explanation:

To create an equation to predict the number of seats in any row, we need to start by defining a few variables:

Let's call the number of seats in the first row "a".

Let's call the number of additional seats in each row after the first row "d".

Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:

d = 6

We also know that the first row has 11 seats, so we can set a equal to 11:

a = 11

To find the number of seats in any row, we can use the following formula:

number of seats in a given row = a + (n - 1) * d

Where "n" is the number of the row we are interested in.

Using this formula, we can find the number of seats in row 18:

number of seats in row 18 = 11 + (18 - 1) * 6

= 11 + 102

= 113

Therefore, there are 113 seats in row 18.

The equation of the axis of symmetry of the given quadratic function is x = -2. So, correct option is C.

The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. For a quadratic function in the form y = ax² + bx + c, the equation of the axis of symmetry is given by x = -b/(2a).

In the given equation, y = 2x² + 8x - 3, the coefficients of x² and x are a = 2 and b = 8, respectively. Substituting these values in the equation of the axis of symmetry, we get:

x = -b/(2a)

x = -8/(2*2)

x = -8/4

x = -2

This means that the parabola is symmetric about the vertical line x = -2. So the correct answer is x=-2.

So, correct option is C.

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