Find the average rate of change of the function f(x)

f(x) = 10 from [2, 3].
x-4

Answer:

19.4

Step-by-step explanation:

cosФ=adjacent ÷hypotenuse

cos72° =6/x

0.309016994=6/x

∴x=6/0.31

   =19.35

   =19.4

Answer:

1. Draw a coordinate plane with a circle on it somewhere

2. B. and C.

Step-by-step explanation:

A function is a set of points that has a specific input (x-value) and a specific output (y-value). Let's take the example of y = 2x. Let's start by plugging in 1 for x. 1 will be our input value, and 2• 1 = 2 will be our y-value because the x-value was changed to get to our output, the y-value.

In a function, it is possible to have the same y-value for different x-values; take the example of y = x^2. X can have 2 values, but because it is squared, it will give the same y-value. However, a function that has the same x-values for one y-value is not a function. For example, take a circle, with the equation x^2 + y^2 = 0. This is not a function, because, for 2 y-values, it will equal the same x-value. For your answer, you can draw a coordinate plane with a circle on it. IMPORTANT: 2 x-values cannot equal one y-values in a function.

A linear function is a function that has an x and y-value, as well as sometimes a coefficient to either variable and a constant. For example, the equation y = 5x +4 is a linear function because there is one y and one x-value, a coefficient (even though it is not necessary), and a constant (even though it is not necessary). It doesn't matter where the coefficients are, but there has to be one y-value and one x-value. Since there can be only one x and y, equations like y = x^2 does not work, because there are 2 x's (in the x^2). Using this information, we can figure out the correct solutions:

A. doesn't work, because there are 3 y-values.

B. works because there is one x and y, and a coefficient (although it isn't necessary)

C. works because like b, it has only one x and y, a coefficient (although it isn't necessary)

D. doesn't work because there is only one y-value and no x-value.

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The measure of length MN is 31.

The measure of length KN is 45.

The measure of m∠K is 61⁰.

The measure of m∠L is 119⁰.

A parallelogram is a four-sided plane figure in which opposite sides are parallel and congruent (having the same length) and opposite angles are congruent (having the same measure). In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.

The properties of a parallelogram include:

So the length MN = Length KL = 31

Length KN = Length LM = 45

Angle K = angle M = ( 180 - 119) = 61⁰

Angle L = angle N = 119⁰

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Answer:

The chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.

Step-by-step explanation:

Let's call the amount of the first alloy used "x" and the amount of the second alloy used "y". We can set up a system of two equations based on the amount of gold and lead needed in the final alloy:

Equation 1: 0.10x + 0.40y = 57 (the amount of gold in the first alloy is 10%, and in the second alloy is 40%)

Equation 2: 0.20x + 0.30y = 94 (the amount of lead in the first alloy is 20%, and in the second alloy is 30%)

We can then solve for x and y using any method of solving systems of equations. One way is to use substitution:

Therefore, the chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.

Answer:

x= infinite or -5/2 or 1, + infinite

Step-by-step explanation:

Answer:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Step-by-step explanation:

tan(19°) = 7425/d1

tan(37°) = 7425/d2

Solving for d1 and d2, we get:

d1 = 7425/tan(19°) ≈ 22977.6 feet

d2 = 7425/tan(37°) ≈ 13060.2 feet

Therefore, the distance the plane traveled from point A to point B is:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Answer:

x = 2 or x = 4

Step-by-step explanation:

The equation:

Has two solutions:

The values of x can be found by graphing the two functions ([tex]y = 2^{x}[/tex] and [tex]y = x^{2}[/tex]) and finding their points of intersection, or you can use numerical methods to solve the equation.

To check our work, we can simply insert 2 and 4 in as y.

For 2:

You can see that it is the same.

For 4:

They are also the same.

Therefore, x can equal either 2 or 4.

The linear equation that passes through (-9, -9) and has the slope m = 0 is:

y = -9

A general linear equation can be written in slope-intercept form as.

y = m*x + b

Where m is the slope and b is the y-intercept.

Here we want to find the equation of a line that passes through (-9, -9) and that has the slope m = 0.

Repplacing the slope we will get:

y = 0*x + b

And no we want it to pass throug (-9, -9), replacing these values we will get:

-9 = 0*-9 + b

-9 = b

Then the linear equation is:

y = -9

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Answer:

143 degrees

Step-by-step explanation:

angles on a straight line add up to 180 degrees

[tex]x + y = 180 \\ 37 + y = 180 \\ y = 180 - 37 \\ y = 143 \: degrees[/tex]

Answer:

Step-by-step explanation:

o prove the first associative law of set theory, we need to show that for any sets A, B, and C:

A ∪ (B ∪ C) = (A ∪ B) ∪ C

To do this, we need to show that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa.

First, let's consider an arbitrary element x.

If x ∈ A ∪ (B ∪ C), then x must be in A, or in B, or in C (or in two or more of these sets).

If x ∈ A, then x ∈ A ∪ B, and so x ∈ (A ∪ B) ∪ C.

If x ∈ B, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.

If x ∈ C, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.

Therefore, we have shown that if x ∈ A ∪ (B ∪ C), then x ∈ (A ∪ B) ∪ C.

Next, let's consider an arbitrary element y.

If y ∈ (A ∪ B) ∪ C, then y must be in A, or in B, or in C (or in two or more of these sets).

If y ∈ A, then y ∈ A ∪ (B ∪ C), and so y ∈ (A ∪ B) ∪ C.

If y ∈ B, then y ∈ A ∪ B, and so y ∈ A ∪ (B ∪ C), which means that y ∈ (A ∪ B) ∪ C.

If y ∈ C, then y ∈ (A ∪ B) ∪ C.

Therefore, we have shown that if y ∈ (A ∪ B) ∪ C, then y ∈ A ∪ (B ∪ C).

Since we have shown that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa, we can conclude that:

A ∪ (B ∪ C) = (A ∪ B) ∪ C

This proves the first associative law of set theory.

Answer:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

n this case, we have the points (3, 1) and (-2, 1), so we can plug in the values:

slope = (1 - 1) / (-2 - 3)

slope = 0 / -5

slope = 0

Therefore, the slope between the points (3, 1) and (-2, 1) is 0. This means that the line passing through these points is a horizontal line, since the y-coordinate of both points is the same and the slope is 0 (i.e., there is no change in the y-coordinate as we move along the line).

0.08 rounded for the nearest hundredth

The equation for solving the side length of a cube is s = ∛V, where s is the side length of the cube, and V is the volume.

The equation for solving the side length of a cube can be expressed as s = ∛V, where s is the side length of the cube, and V is the volume. This equation can be used to calculate the side length of a cube when the volume is known. For example, if the volume of a cube is 125 cubic units, the side length can be calculated by substituting 125 for V and solving the equation: s = ∛125 = 5. This means that the side length of the cube is 5 units.

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Answer:

144,000

Step-by-step explanation:

you multiply 18,000 by 8 since its after one year and you get 144,000.

Answer:

Step-by-step explanation:

To calculate the reorder level of component X, we need to find out the average weekly consumption of X.

Average consumption of X per unit of 'RED' = 0.4 kg

Average weekly production of 'RED' = 400 units

Average weekly consumption of X for producing 400 units of 'RED' = 0.4 kg/unit x 400 units/week = 160 kg/week

Assuming lead time of 3 weeks for delivery of X, the reorder level of X would be:

Reorder level of X = Average weekly consumption of X x Lead time for delivery of X

Reorder level of X = 160 kg/week x 3 weeks = 480 kg

To calculate the maximum level of X, we need to take into account the economic order quantity and the maximum storage capacity.

Economic order quantity of X = Square root of [(2 x Annual consumption of X x Ordering cost per order) / Cost per unit of X]

Assuming 52 weeks in a year:

Annual consumption of X = Average weekly consumption of X x 52 weeks/year = 160 kg/week x 52 weeks/year = 8,320 kg/year

Ordering cost per order of X = 600

Cost per unit of X = 1

Economic order quantity of X = Square root of [(2 x 8,320 kg x 600) / 1] = 2,771.28 kg (approx.)

Maximum storage capacity of X = Economic order quantity of X + Safety stock - Average weekly consumption x Maximum lead time

Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:

Maximum storage capacity of X = 2,771.28 kg + (0.2 x 2,771.28 kg) - (160 kg/week x 3 weeks) = 2,815.82 kg (approx.)

To calculate the maximum level of Y, we follow the same approach as for X:

Annual consumption of Y = Average weekly consumption of Y x 52 weeks/year

Average consumption of Y per unit of 'RED' = 0.6 kg

Average weekly consumption of Y for producing 400 units of 'RED' = 0.6 kg/unit x 400 units/week = 240 kg/week

Annual consumption of Y = 240 kg/week x 52 weeks/year = 12,480 kg/year

Economic order quantity of Y = Square root of [(2 x Annual consumption of Y x Ordering cost per order) / Cost per unit of Y]

Ordering cost per order of Y = 1,000

Cost per unit of Y = 1.5

Economic order quantity of Y = Square root of [(2 x 12,480 kg x 1,000) / 1.5] = 915.65 kg (approx.)

Maximum storage capacity of Y = Economic order quantity of Y + Safety stock - Average weekly consumption x Maximum lead time

Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:

Maximum storage capacity of Y = 915.65 kg + (0.2 x 915.65 kg) - (240 kg/week x 3 weeks) = 732.52 kg (approx.)

Answer:

x = 432.

Step-by-step explanation:

We know that 24 x 18 and x x 1 are in proportion, which can be written as:

(24 x 18) / (x x 1) = k, where k is a constant of proportionality.

Simplifying the left-hand side, we get:

24 x 18 = 432

x x 1 = x

Substituting these values, we get:

432 / x = k

To solve for x, we need to find the value of k. We can do this by using the fact that the two ratios are in proportion. That is:

24 x 18 : x x 1 = 432 : k

Simplifying the left-hand side, we get:

(24 x 18) / x = 432 / k

Multiplying both sides by x and k, we get:

24 x 18 k = 432 x

Dividing both sides by 24 x, we get:

18 k / 1 = 18

Solving for k, we get:

k = 1

Substituting k = 1 into the equation 432 / x = k, we get:

432 / x = 1

Multiplying both sides by x, we get:

432 = x

Therefore, x = 432.

Answer:

Step-by-step explanation:

The statement that describes the function f(x) = 4x^3 + 8 is:

A. The function does not have an inverse function because f(x) fails the vertical line test.

To see why this is the correct answer, let's first define what the vertical line test and the horizontal line test are.

Vertical line test: A function passes the vertical line test if any vertical line intersects the graph of the function at most once. This means that no two points on the graph have the same x-coordinate.

Horizontal line test: A function passes the horizontal line test if any horizontal line intersects the graph of the function at most once. This means that no two points on the graph have the same y-coordinate.

Now, let's look at the function f(x) = 4x^3 + 8. We can graph this function by plotting points or by using a graphing calculator. The graph of the function looks like a curve that goes up and to the right.

If we draw a vertical line anywhere on the graph, we can see that it intersects the graph at most once, which means that f(x) passes the vertical line test. However, if we draw a horizontal line on the graph, we can see that it intersects the graph at more than one point. This means that f(x) fails the horizontal line test.

The fact that f(x) fails the horizontal line test tells us that there are some values of y that correspond to more than one value of x. This means that f(x) is not a one-to-one function, and therefore it does not have an inverse function.

Therefore, the correct statement that describes the function f(x) is:

A. The function does not have an inverse function because f(x) fails the vertical line test.

To find out how long it will take for the arrow to hit the enemy on the bridge, we need to find the time when the height of the arrow is 45 feet (the height of the enemy's head above the ground).

So, we can set h(t) equal to 45 and solve for t:

h(t) = − 16t²+60t + 9.5

45 = −16t² + 60t + 9.5

Rearranging the equation, we get:

16t² - 60t - 35.5 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b² - 4ac)) / 2a

where a = 16, b = -60, and c = -35.5

Plugging in the values, we get:

t = (-(-60) ± sqrt((-60)² - 4(16)(-35.5))) / 2(16)

Simplifying the expression inside the square root, we get:

t = (60 ± sqrt(3600 + 2272)) / 32

t = (60 ± sqrt(5872)) / 32

t ≈ 0.81 or t ≈ 3.69

Since we're looking for the time when the arrow hits the enemy, we need to choose the positive solution: t ≈ 3.69 seconds.

Therefore, it will take approximately 3.69 seconds for the arrow to hit the enemy on the bridge with a perfect headshot.

The possible values of ∠L are 118.9 degrees (rounded to 10th of a degree).

A polygon with three sides and three angles is a triangle. It is one of the simplest geometric shapes.

To find the measure of angle L in ΔLMN, we can use the fact that the sum of the angles in a triangle is 180 degrees:

∠L + ∠M + ∠N = 180

We know that ∠N = 61 degrees, so we can substitute that value in and simplify:

∠L + ∠M + 61 = 180

∠L + ∠M = 119

We also know that the length of LM is 150 inches and the length of LN is 890 inches. We can use the Law of Cosines to find the measure of angle M:

cos M = (150² + 890² - LM²) / (2 × 150 × 890)

cos M = 0.999989 (rounded to 6 decimal places)

M = cos⁻¹(0.999989)

M ≈ 0.00114 radians

M ≈ 0.0655 degrees (rounded to 10th of a degree)

Now we can substitute the value of M into the equation we derived earlier and solve for angle L:

∠L + 0.0655 + 61 = 180

∠L = 118.9345

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Answer:

Let the total number of cows in the herd be represented by "x". Then, according to the problem:

The first son received half the herd, or (1/2)x cows.

The second son received one fourth of the herd, or (1/4)x cows.

The third son received one fifth of the herd, or (1/5)x cows.

The fourth son received 48 cows.

We can write an equation to represent the total number of cows in the herd:

(1/2)x + (1/4)x + (1/5)x + 48 = x

To solve for "x", we can start by simplifying the fractions:

5/10x + 2/10x + 2/10x + 48 = x

Combining like terms, we get:

9/10x + 48 = x

Subtracting 9/10x from both sides, we get:

48 = 1/10x

Multiplying both sides by 10, we get:

x = 480

Therefore, the original herd had 480 cows.

Answer:

A. To graph the linear relation representing the school's cost for up to 200 bottles of water, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the cost, x is the number of bottles of water, m is the slope, and b is the y-intercept.

The y-intercept is the fixed cost of renting the coolers, which is $25. The slope represents the additional cost per bottle of water, which is $0.65. Therefore, the equation is:

y = 0.65x + 25

To graph the line, we can plot the y-intercept at (0, 25), and then use the slope to find additional points. For example, when x = 50, y = 0.65(50) + 25 = 57.50, so we can plot the point (50, 57.50) and draw a line through the points.

B. To graph the linear relation representing the school's income from selling up to 200 bottles of water, we can also use the slope-intercept form of a linear equation: y = mx + b, where y is the income, x is the number of bottles of water, m is the slope, and b is the y-intercept.

The y-intercept is the revenue from selling 0 bottles of water, which is $0. The slope represents the revenue per bottle of water, which is $1.25. Therefore, the equation is:

y = 1.25x + 0

To graph the line, we can plot the y-intercept at (0, 0), and then use the slope to find additional points. For example, when x = 50, y = 1.25(50) + 0 = 62.50, so we can plot the point (50, 62.50) and draw a line through the points.

C. The equation for the school's cost is y = 0.65x + 25, and the equation for the school's income is y = 1.25x + 0.

D. To find the coordinates of the point where the lines cross, we can set the two equations equal to each other and solve for x:

0.65x + 25 = 1.25x + 0

0.6x = 25

x = 41.67

Then we can plug in x = 41.67 into either equation to find y:

y = 0.65(41.67) + 25 = 52.08

Therefore, the point where the lines cross is (41.67, 52.08).

E. The significance of this point is that it represents the breakeven point, where the school's cost equals its revenue. If the school sells fewer than 41.67 bottles of water, it will not cover its costs. If it sells more than 41.67 bottles of water, it will make a profit.

Step-by-step explanation:

Answer:2 4/9

Step-by-step explanation:

Answer: I gave you two answers if you can try them both :)

Step-by-step explanation:

If his weight on Earth is 126lb and only 21lb on moon, you can divide  to see what is the ratio of those weights.

It means that your weight on moon will be 6 times less than on Earth.

Now we have to multiply 31lb which is weight of the person on moon by 6 to get his weight on Earth

On moon our mass becomes 1/6 of actual mass so if you weigh 60 kg then your mass on moon will be 10 kg..

Similarly if your mass on moon is 31 lbs then your mass on earth will be 31*6=186 lbs.

0.24 gallons of oil should be mixed with 12 gallons of gasoline.

Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.

Step-by-step explanation:

a. To calculate the amount of oil needed, we need to know the ratio of gas to oil in terms of units. Since 50 parts of gas are mixed with 1 part of oil, we have:

1 gallon of gas / 50 = x gallons of oil

To find x, we substitute the given value of gas (12 gallons) and solve for x:

1 gallon of gas / 50 = x gallons of oil

12 gallons of gas / 50 = x

0.24 gallons of oil = x

Therefore, 0.24 gallons of oil should be mixed with 12 gallons of gasoline.

b. To convert gallons to fluid ounces, we multiply by 128:

0.24 gallons of oil * 128 fluid ounces/gallon = 30.72 fluid ounces of oil

Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.

Answer:

B. 120o

Step-by-step explanation:

A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.

t + 2t = 180

3t = 180

t = 180/3 = 60

m∠Z  = 2t = 2(60) = 120

If any number is divided by zero. the result is indeterminate.

Therefore, zero is the non-permissible replacement for x.

The probability that the mean weight of the sample of 25 cartons is greater than 7.19 ounces is given as follows:

0.0571 = 5.71%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 7, \sigma = 0.6, n = 25, s = \frac{0.6}{\sqrt{25}} = 0.12[/tex]

The probability that the mean weight is greater than 7.19 ounces is one subtracted by the p-value of Z when X = 7.19, considering the standard error s, hence:

Z = (7.19 - 7)/0.12

Z = 1.58

Z = 1.58 has a p-value of 0.9429.

Hence:

1 - 0.9429 = 0.0571 = 5.71%.

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Answer:

Step-by-step explanation:

To calculate the volume of sand needed to fill the long jump pit to a depth of 0.07 meters, we need to know the length and width of the pit.

Assuming that the long jump pit is a rectangular prism, we can use the formula:

Volume = length x width x depth

Let's say the length of the pit is 8 meters and the width is 3 meters. Then the volume of sand needed to fill the pit to a depth of 0.07 meters would be:

Volume = 8m x 3m x 0.07m

Volume = 1.68 cubic meters

Therefore, we would need 1.68 cubic meters of sand to fill the long jump pit to a depth of 0.07 meters.

Answer:

Step-by-step explanation:

[tex]\tt y=x+2\\3x+3y=6[/tex]

Substitute y= y=x+2 into 3x+3y=6

Solve for x :-

Cancel 6 from both sides:-

Divide both sides by 6:-

Now, Let's solve for y:-

Substitute x = 0 into y=x+2

Therefore, x = 0 and y = 2.

_________________

Check:-

To check a system of equations by substitution, we plug the values for x and y into the equations, If both simplified are true then your answer is correct.

Equation 1 :-

y = x + 2

Equation 2 :-

3x+3y=6

__________________________

Hope this helps!

Answer:

[tex]\frac{1}{-125}[/tex]

x = -125

Step-by-step explanation:

It shows the steps in the pic you attached so I didn't add those steps.

(-5)(-5)(-5) = -125