Derek tried to solve an equation step by step. 8d=72 8d/8 = 72/8 d=8 Find Derek's mistake

Answer:  We can start by using algebra to represent the information given in the problem. Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.

We know that:

x + y = 45 (the total number of gallons consumed by both cars)

15x + 30y = 975 (the total number of miles driven by both cars, given the fuel efficiency of each car)

We have two equations and two unknowns, so we can use these equations to solve for the value of x and y.

From the first equation, we can solve for x:

x = 45 - y

We can substitute this expression of x into the second equation:

15(45 - y) + 30y = 975

Simplifying the left side of the equation:

675 - 15y + 30y = 975

Subtracting 675 from both sides:

15y = 300

And finally divide both sides by 15:

y = 20

So the second car consumed 20 gallons of gas that week.

We can substitute this value of y back into the equation x = 45 - y to find the value of x

x = 45 - 20 = 25

So the first car consumed 25 gallons of gas that week.

Step-by-step explanation:

The equation of a sphere with center (a, b, c) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 + (z - c)^2 = r^2[/tex]

Given the center (2,-6,4) and radius 5, we can substitute these values into the equation to find the equation of the sphere:

[tex](x - 2)^2 + (y + 6)^2 + (z - 4)^2 = 5^2[/tex]

So, the equation of the sphere is:

[tex](x-2)^2 + (y+6)^2 + (z-4)^2 = 25[/tex]

The sphere will intersect each of the coordinate planes in circles.

Intersection with the XY-plane:

The sphere intersects the XY-plane when z = 4.

Then, the equation of the circle on the XY-plane is [tex](x-2)^2 + (y+6)^2 = 5^2[/tex]

Intersection with the XZ-plane:

The sphere intersects the XZ-plane when y = -6.

Then, the equation of the circle on the XZ-plane is [tex](x-2)^2 + (z-4)^2 = 5^2[/tex]

Intersection with the YZ-plane:

The sphere intersects the YZ-plane when x = 2.

Then, the equation of the circle on the YZ-plane is [tex](y+6)^2 + (z-4)^2 = 5^2[/tex]

The sphere with center (2,-6,4) and radius 5 intersects each of the coordinate planes at circles.

These circles are defined by the equations [tex](x-2)^2 + (y+6)^2 = 25[/tex] on the XY-plane, [tex](x-2)^2 + (z-4)^2 = 25[/tex]  on the XZ-plane, and  [tex](y+6)^2 + (z-4)^2 = 25[/tex]  on the YZ-plane.

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Answer:

answer is B) 8 240 000

(: have a nice day

Answer:

B 8,240,000

Step-by-step explanation:

your welcome

Answer:

slope: 2 , y-int: (0, -5)

Step-by-step explanation:

The measure of ∠2 is [tex]54^{0}[/tex], ∠3 is [tex]23^{0}[/tex], ∠6 is [tex]121^{0}[/tex].

7.- The sum of the internal angles in a triangle equals 180°.

2x + 22 + 4x + 11 + [180- (9x - 15)] = 180

6x + 180 - 9x + 15 = 180 - 33

-2x = 147 - 180 - 15

-2x = -48

x = -48/-3

x = 16

∠X = 2(16) + 22

∠X = 54°                  

8. 8x - 31 + 6x - 8 + [180 - (10x + 17)] = 180

14x - 39 + 180 - 10x - 17 = 180

4x = 56

x = 56 / 4

x = 14

∠ ECD = 180 - 10(14) - 17

∠ECD = 180 - 140 - 17

∠ECD = 23°                          

9.- In ΔABC

m ∠C = m ∠A - 9

m ∠B = 4m∠A - 15

The sum of the internal angles in a triangle equals 180°.

∠A + ∠B + ∠C = 180°

∠A + 4∠A - 15 + ∠A - 9 = 180

6∠A = 180 + 24

6∠A = 204

∠A = 204 / 6 = 34

Then, ∠B = 4∠A - 15

∠B = 4(34) - 15

∠B = 121                  

10.- ∠XYZ = 2∠X - 9

m ∠W = 38°

38 + ∠X + [180 - (2∠X - 9)] = 180

38 + ∠X + 180 - 2∠X + 9 = 180

-1∠X = -47⇒∠X = -47/-1

∠X = 47

Then, ∠XYZ = 2(47) - 9

∠XYZ = 85°                

Therefore, the measure of ∠2 is [tex]54^{0}[/tex], ∠3 is [tex]23^{0}[/tex], ∠6 is [tex]121^{0}[/tex] and ∠XYZ is [tex]85^{0}[/tex].  

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Answer:

x=60

Step-by-step explanation:

Answer:

Diagonals are perpendicular

1 diagonal bisects the other

Opposite angles are congruent

The gauge pressure, or the difference between the inner pressure and the external pressure p0, is what the pressure gauge on a gas cylinder measures. Give the gauge pressure the letter pg.

The gas in the cylinder weighs mi at pgi gauge pressure when it is full. We can apply the ideal gas formula, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, assuming the cylinder's temperature stays constant.

We can assume that the product nRT is constant because the temperature is constant. Consequently, we can write:

(pgf + p0) = (pgi + p0)(Vi) (Vf)

where Vi is the cylinder's initial volume and Vf is the cylinder's final volume when the pressure is pgf.

We also know that the gas's mass, m, is determined by multiplying the number of moles, n, by the molar mass, M, or m = nM.

The ideal gas law can be used to express the number of moles in terms of volume and pressure:

m/M = P(V/RT) = n

Thus, mf = pgf(Vf/RT).

M equals (pgf + p0)(Vf/RT).

(Vi/RT) Mi (pgi + p0)

where mf is the mass of gas still present in the cylinder at pgf pressure.

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The rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

Oil is spilled onto a kitchen floor. The function A, where A(t) is measured in square centimeters and t is measured in seconds, gives the area covered by the oil at time t.

Given that the region that was covered in oil at time t = A(t)

We must differentiate A(t) with respect to time t in order to calculate the rate of change in the area covered by the oil over time.

By differentiation:

[tex]\frac{dA}{dt}=A'(t)[/tex]

The rate at which the oily area is transforming is t = 10

[tex]\frac{dA}{dt}|_{t=10}=A'(t)|_{t=10}[/tex]

[tex]\frac{dA}{dt}=A'(10)[/tex]

Hence, the rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

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The equation for the graph will be

[tex]y=1 cos(3x)[/tex]

The function y = cos(2x + π/4) is a cosine function where the independent variable x is multiplied by 2 and then has π/4 added to it before the cosine is applied. The amplitude of this function is 1 and the period is π.

In this question

[tex]we assume, \\y=acos(bx)\\\\when x=0y=1\\\\y=acos(bx)\\\\1=acos0\\\\a=1\\so y=cos(bx)\\\\when x=\pi/3 y=-1\\y=cos(b.\pi/3)\\-1=cos1b.pi/3=cos(pi)\\b=3[/tex]

[tex]y=acosbx[/tex]

[tex]so, y=1.cos(3x)[/tex]

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Answer:

A

Step-by-step explanation:

Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].

The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].

When 62.5 pairs of jeans are sold, the price is $112.50.

Based on the information, the store should discount $112.50 from the price to maximize its revenue.

To calculate the amount of discount that the store must make to maximize its profits we must perform the following mathematical operation:

First we have to analyze the available data which are:

According to the above information, the problem could be answered with the following mathematical formula:

(175 - x)(40 + 0.8x)

x = 175

x = -50

x = 62.50.

According to the above, the correct answer is $112.50 (option A).

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The z-score for the given values is - 0280, -1.08, 0.49, 0.147 respectively.

The z-score of a data point defines this precise distance in terms of standard deviations above or below the mean.

This formula is used to determine a z-score:

mean standard deviation for each data point

Means of the data points with a standard deviation of z

Below is the same equation in symbol form:

z= x−μ / σ

Here are some noteworthy z-score details:

When the z-score is high, the data point is.

A negative z-score indicates that a data point is below average.

If the z-score is close to 0.00, the data point is thought to be around average.

For the given data set,

14 9 19 18 5 8

Mean of the data =sum of observations / no. of observations =  73/6 = 12.16

Mean of the data is 12.16

Standard deviation = √∑(x - μ)² / n-1

= ​5.70

a) The z- score of 12 is

z=  x−μ / σ

z = 12 - 12.16 / 5.70

z = - 0280

b) x = 6,

z = 6 - 12.16/5.70

z = -1.08

c) x = 15

z = 15 - 12.16/5.70

z = 0.49

d) x = 13

z = 13 - 12.16 / 5.70

z = 0.147

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Answer:

3.53%

Step-by-step explanation:

annual 3.5%

So half a year =1.75% and compound twice a year.

equivalent annual rate is (1+1.75%)^2 -1 =.0353 =3.53%

If two friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. The expression to represent how much more Jaxson spent is :5.1 +p.

P = price of the cherries per pound

Price of cherries bought by Jaxson= $3p

Total amount spent by Jaxson =  $8.25 + $ 3p

Price of cherries bought by Tim = $2p

Total amount spent by Tim = $3.15 + $ 2p

Now let find how much more Jaxson spent.

8.25 + 3p - 3.15 + 2p

5.1 + 3p - 2p

Combine like terms

5.1 +1p

Multiply by 1

5.1 + p

Therefore the expression to represent how much more Jaxson spent is :5.1 +p.

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Answer:

The equation [tex]\frac{csc x -1}{cot x} = \frac{cot x}{csc x + 1}[/tex] can be simplified by cross-multiplying the fractions and then solving for x. This will result in the equation [tex]csc^2 x - 1 = 0[/tex], which can be simplified to [tex]csc x = 1[/tex], and thus [tex]x = \frac{\pi}{2} + n\pi[/tex], where n is any integer.

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The break-even points at which the sum of the fixed and variable costs (40,800 + (1/3)·x + 222) is equivalent to the revenue (1946·x - (2/3)·x²) are; x = 21, 2897

The break-even point in cost accounting is the point where the total cost of production is equivalent to the total revenue from the sale of the products.

The fixed cost of the company = $40,800

The variable cost = (1/3)·x + 222 Dollars

x = The total number of units sold

The selling price of the product = 1946 - (2/3)·x Dollars

A possible question, obtained from a similar question is the value of the number of units sold at break even point

The break even point where the cost and revenue are equivalent, can be found as follows;

Revenue = Selling price × Number of units sold, therefore;

Revenue = (1946 - (2/3)·x) × x = 1946·x - (2/3)·x²

At the break even point, we get;

Sum total of the cost = Revenue

Therefore;

Fixed cost + Variable cost = Revenue

40,800 + (1/3)·x + 222 = 1946·x - (2/3)·x²

1946·x - (2/3)·x² - (40,800 + (1/3)·x + 222) = 0

(-2·x² + 5837·x - 123066)/3 = 0

x = (-5837 ± √(5837² - 4×(-2)×(-123066)))/(2×(-2))

x = (-5837 ± √(33086041))/(-4)

x ≈ 21 or x ≈ 2897

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The correct answer is Unit Price, Units in Stock, Units on Order, and Reorder Level.

The unit price is the cost of a single item or unit of a product or service. It is usually expressed as a monetary value, such as dollars per item. It can be calculated by dividing the total cost of a product or service by the number of units.

Units in stock refer to the number of items or units of a product or service that are currently available for purchase. It is used to track inventory levels and to manage the replenishment of products or services.

Units on order refer to the number of items or units of a product or service that have been ordered by a company but have not yet been received. It is used to track expected inventory levels and to manage the replenishment of products or services.

The reorder level, also known as the reorder point, is the point at which a company needs to replenish its inventory of a particular product or service. It is determined by calculating the lead time (the time it takes to receive new inventory after placing an order) and the average daily usage of the product or service.

Therefore, The correct answer is Unit Price, Units in Stock, Units on Order, and Reorder Level.

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Given matrix equation as a vector equation:

[tex]\begin{bmatrix}c_1 & c_2 & c_3 & c_4 & c_5\\d_1 & d_2 & d_3 & d_5 & d_5\end{bmatrix}~\begin{bmatrix}v_1\\ v_2\\v_3\\ v_4\\v_5\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]

We know tha a matrix equation is nothing but the equation of the form Av = b,

where A is m × n matrix, ( It is called the coefficient matrix),

v is n × 1 column vector,

and b is m × 1 column vector.

A matrix equation is also called a matrix–vector equation.

Consider given matrix equation.

[tex]\begin{bmatrix}-3 & 5 & -4 & 9 & 7\\5 & 8 & 1 & -2 & -4\end{bmatrix}~\begin{bmatrix}-3\\ 2\\4\\ -1\\2\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]

We need to write the this matrix equation as a vector equation, using symbols v₁, v₂, v₃, . . . for vectors and c₁, c₂ and c₃, . . . for scalars.

We can observe that the first matrix is 2 × 5 matrix and the solution matrix is also 2 × 1

So, it can be rewritten as c₁, c₂, c₃, c₄ and c₅ for the first row and for the second row of matrix d₁, d₂, d₃, d₄ and d₅

Then we multiply those rows with vector v₁, v₂, v₃, v₄ and v₅ we'll get the resultant matrix.

So, we get a vector equation as:

[tex]\begin{bmatrix}c_1 & c_2 & c_3 & c_4 & c_5\\d_1 & d_2 & d_3 & d_5 & d_5\end{bmatrix}~\begin{bmatrix}v_1\\ v_2\\v_3\\ v_4\\v_5\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]

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Find the complete question below.

Answer:

m=12b

Step-by-step explanation:

m (money raised) is equal to 12b, or 12 tickets per b (b = people)

The change in height divided by the change in time yields the firework's average speed from t=1 to t=3 seconds.

Average change speed is equal to (h(3) – h(1)) (3 - 1)

h(3) = 16*32 + 105*3 + 10 = 536

h(1) = 16*12 + 105*1 + 10 = 126

Average speed = (536 - 126)/(3 - 1) = 410/2 = 205 ft/sec

h(t) = 16r2 + 105t + 10 models the height of a firework t seconds after it is released. We must determine the change in height divided by the change in time in order to get its average speed between t=1 and t=3 seconds.

By entering t = 3 into h(t), we can determine the height at 3 seconds, which gives us h(3) = 16*32 + 105*3 + 10 = 536. We can figure out the height.

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With constant of proportionality= 0.45 the New Hamsphire would have 51 golf courses.

What is a constant of proportionality?

The constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.

Direct Variation: The equation for direct proportionality is y = kx,  which shows as x increases, y also increases at the same rate. Example: The cost per item(y) is directly proportional to the number of items(x) purchased, expressed as y ∝ x

Inverse Variation: The equation for the indirect proportionality is y = k/x, which shows that as y increases, x decreases and vice-versa. Example: The speed of a moving vehicle (y) inversely varies as the time taken (x) to cover a certain distance, expressed as y ∝ 1/x

In both cases, k is constant. The value of this constant is called the coefficient of proportionality. The constant of proportionality is also known as the unit rate.

Now,

As given Georgia has 401 golf courses with a population of 10, 736, 059 while New Hampshire has 113 golf courses with a population of 1, 371, 246.

So Georgia have 1 golf course for 26773 people and New hamsphore have 1 golf course for 12135 people.

that means they have constant of proportionality= 0.45 with respect to population/golf course ratio .

population/golf course ratio for georgia=26773

population/golf course ratio for new hamsphire=12135

and For new hamsphire to have same ratio for population/golf ratio as georgia it will need 113*0.45=51 golf courses

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Answer: One way to calculate the percent increase in Robin's monthly bill is to use the following formula:

% increase = (new amount - original amount) / original amount x 100

In this case, the original amount is $120 and the new amount is $150. So, the calculation would be:

% increase = (150 - 120) / 120 x 100 = 30 / 120 x 100 = 0.25 x 100 = 25

Therefore, the percent increase in Robin's monthly bill is 25%.

Another way to calculate the percent increase is to use the formula:

(New amount - original amount) / original amount

In this case: (150-120)/120 = 0.25, and multiply by 100 to get 25%

So, both formula gives the same answer 25%

Step-by-step explanation:

The typical increase in speed from 40 to 70 seconds The magnitude is lower than the initial acceleration and is positive.

The velocity change's average acceleration is referred to as this. To calculate any object's average acceleration, we divide the change in velocity by the amount of time that has passed. As a result, it is clear that the average acceleration is defined as the ratio of the change in velocity to the change in time over a certain interval.

The average acceleration is the velocity change divided by the time that has passed. A marble's average acceleration is 20 cm/s, for instance, if its velocity increases from 0 to 60 cm/s in three seconds. The marble's speed will increase by 20 cm/s every second as a result. The ball will therefore have an upwards-moving terminal velocity of 20 m/s after two seconds.

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Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.

A quadrilateral is a four-sided closed shape, where sum of the interior angles equals 180°.

Here,
For the quadrilateral there are only two quadrilaterals where diagonals bisect each other at 90° and will be of equal length of measure are square and rhombus.

Thus, Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.

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Answer: Bird A's top speed is 1428 MPH.

Step-by-step explanation: 238x6 = 1428

Answer:

Train 1: 130 km/h

Train 2: 108 km/h

Step-by-step explanation:

Let train 1 be the faster train.

Train 1:

distance = d

speed = s

time = 2 hours

Train 2:

distance = 476 - d

speed = s - 22

time = 2 hours

speed = distance/time

distance = speed × time

Train 1:

d = 2s

Train 2:

476 - d = 2(s - 22)

d = 2s

476 - d = 2s - 44

d = 2s

476 - 2s = 2s - 44

520 = 4s

s = 130

s - 22 = 108

Train 1: 130 km/h

Train 2: 108 km/h

Any square-free integer can be expressed as the product of a square-free integer (which has no square  factors) and a perfect square (which has only square factors). This product is unique for any given square-free integer.

Any square-free integer can be expressed as the product of a square-free integer and a perfect square. This is because a square-free integer has no square factors, so the product of a square-free integer and a perfect square would have only square factors, and thus be square-free. To show that this product is unique for any given square-free integer, we can use the fact that any integer can be expressed as the product of its prime factors and that a square-free integer has no square factors. This means the prime factors of the square-free integer are all distinct, and thus the product of the square-free integer and the perfect square can be expressed as the product of the prime factors of the square-free integer and the prime factors of the perfect square. Since the prime factors of the perfect square are all the same, the product is uniquely determined by the prime factors of the square-free integer. Thus, the product of a square-free integer and a perfect square is unique for any given square-free integer.

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