Hunter needs 10 ounces of a snack mix that is made up of seeds and dried fruit. the
seeds cost $1.50 per ounce and dried fruit costs $2.50 per ounce. hunter has $22
to spend and plans to spend it all.
let x = the amount of seeds
let y = the amount of dried fruit
part 1: create a system of equations to represent the scenario. (2 points)
part 2: solve your system using any method. write your answer as an ordered pair. (2
points)

Answer:

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Step-by-step explanation:

Answer:

10/12

Step-by-step explanation:

(3/10)x=1/4

3x=10/4

x=10/12

The ratio to make the portrait proportional is width/42 = 5/8

From the question, we have the following parameters that can be used in our computation:

Photograph that is 5 inches wide by 8 inches high.

This means that

Ratio = width/height

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

Ratio = 5/8

Given that he wants the portrait to be proportional to the photograph and 42 inches high.

Then, we have

width/42 = 5/8

Hence, the ratio to make the portrait proportional is width/42 = 5/8

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Answer:

[tex]x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}[/tex]

Step-by-step explanation:

The center of the circle is the midpoint of its diameter.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given the endpoints of the diameter are (0, 3) and (0, -4), to find the coordinates of the center of the circle, substitute the two endpoints into the midpoint formula:

[tex]\text{Center}=\left(\dfrac{0+0}{2},\dfrac{-4+3}{2}\right)=\left(0,-\dfrac{1}{2}\right)[/tex]

As the x-values of the endpoints of the diameter are the same, the length of the diameter, d, is the absolute value of the difference in y-values of the endpoints:

[tex]d=|3-(-4)|=7[/tex]

Therefore, the diameter of circle Q is 7 units.

The radius, r, of a circle is half its diameter. Therefore:

[tex]r=\dfrac{d}{2}=\dfrac{7}{2}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Now we have determined the center and radius of circle Q, we can substitute these values into the equation of a circle to write the equation of circle Q in standard form:

[tex](x-0)^2+\left(y-\left(-\dfrac{1}{2}\right)\right)^2=\left(\dfrac{7}{2}\right)^2[/tex]

[tex]x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}[/tex]

Therefore, the equation of circle Q in standard form is:

[tex]\boxed{x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}}[/tex]

The number of miles remaining in Mr. Ramos's monthly allowance is 191.1 miles.

To find out how many miles remain in Mr. Ramos's monthly allowance after the trip, let's first calculate the total miles he drove:

1. For the 10 days at 8 miles per day: 10 days * 8 miles/day = 80 miles
2. For the 3-day trip, sum up the miles driven each day: 156.1 + 240.8 + 82.0 = 478.9 miles

Now, add the miles from both parts: 80 miles + 478.9 miles = 558.9 miles

Finally, subtract this total from Mr. Ramos's monthly allowance of 750 miles:

750 miles - 558.9 miles = 191.1 miles

After the trip, 191.1 miles remain in Mr. Ramos's monthly allowance.

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the slope of   [tex]6.5[/tex] in this equation indicates that for each additional year of age, the median height of boys increases by approximately 6.5 cm. Thus, option D is correct.

The statement that best interprets the slope in the context of the problem is "The slope is 6.5, this means that each year boys grow approximately  [tex]6.5[/tex]  cm."

The slope of a linear equation represents the rate of change, or the amount by which the dependent variable (in this case, median height) changes for each unit increase in the independent variable (in this case, age).

Therefore, the slope of  [tex]6.5[/tex] in this equation indicates that for each additional year of age, the median height of boys increases by approximately [tex]6.5[/tex] cm.

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x = 0, π, 2π, 3π, 4π, 5π, 6π, π/3, 5π/3

These are the exact solutions of the given equation on the interval [0, 21). To find all exact solutions of the equation sec(x) sin(x) - 2 sin(x) = 0 on the interval [0, 21), we will use the factoring method:

First, we can factor out the sin(x) term:

sin(x) (sec(x) - 2) = 0

Now, we have two separate equations to solve:

1) sin(x) = 0
2) sec(x) - 2 = 0

For equation (1), sin(x) = 0 at x = nπ, where n is an integer. We need to find the values of n that give solutions in the range [0, 21):

0 ≤ nπ < 21
0 ≤ n < 21/π
n = 0, 1, 2, 3, 4, 5, 6

x = 0, π, 2π, 3π, 4π, 5π, 6π

For equation (2), sec(x) - 2 = 0, or sec(x) = 2. We know that sec(x) = 1/cos(x), so:

1/cos(x) = 2
cos(x) = 1/2

The values of x for which cos(x) = 1/2 in the range [0, 21) are x = π/3 and x = 5π/3.

Combining both sets of solutions, we have:

x = 0, π, 2π, 3π, 4π, 5π, 6π, π/3, 5π/3

These are the exact solutions of the given equation on the interval [0, 21).

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It will take Josh about 66.67 minutes to easy the cafeteria alone.

Let's anticipate that the amount of work required to easy the cafeteria is 1 unit.

In a single minute, Josh can easy 1/x of the cafeteria (in which x is the number of mins it takes Josh to do the task alone), and Draven can clean 1/40 of the cafeteria in one minute.

When they work together, they could easy the cafeteria in 25 minutes, so in one minute they are able to easy 1/25 of the cafeteria.

The use of the fact that their combined rate is the sum in their individual rates, we are able to installation an equation:

1/x + 1/40 = 1/25

Multiplying each facets through the least common more than one of the denominators (40 * 25 * x), we get:

25 * 40 + x * 40 = x * 25

1000 + 40x = 25x

15x = 1000

x = 66.67

Therefore, it'd take Josh about 66.67 minutes to easy the cafeteria alone.

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Answer:

6

Step-by-step explanation:

The distance between both those points are 6

The price of the stereo system after the discount and markup is $691.20.

The markup price represents the price after adding a percentage of the discounted price.

The markup can be determined using the markup factor, which increases 100% by the markup percentage.

The discount offered on the stereo system = 20%

Original sales price of the system = $720

Discount factor = 0.8 (1 - 0.2)

Discounted price = $576 ($720 x 0.8)

Markup percentage after the discount = 20%

Markup factor = 1.2 (1 + 0.2)

Marked up price = $691.20 ($576 x 1.2)

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Answer:

Approx 67.24%

Step-by-step explanation: If the Atlanta Hawks' free-throw percentage is 82%, the probability that a player will make one free throw is 0.82.

To find the probability that a player will make two free throws in a row, we can use the multiplication rule of probability which states that the probability of two independent events occurring together is the product of their individual probabilities.

Therefore, the probability of a player making two free throws in a row can be calculated as follows:

P(making two free throws in a row) = P(making first free throw) x P(making second free throw)

P(making two free throws in a row) = 0.82 x 0.82

P(making two free throws in a row) = 0.6724 or 67.24%

Therefore, the probability that a player for the Atlanta Hawks will make two free shots in a row is approximately 67.24%

Answer:

1)55,44

2)6,4

3)49,8

4)11,7

5)12,444

6)23,04

7)12,46

8)15,06

9)31,68

10)30,4

Step-by-step explanation:

Recheck them and make sure there are no mistakes

The image of  WXYZ moves two unit to the right and 5 unit down. The coordinate is (x+2, y-5).

The polar system of coordinates is a coordinate system with two dimensions in which the location of each point can be determined by its distance from the origin, a fixed point, and its angle from the polar axis, also known as the polar axis of rotation. A ray beginning at the origin and extending outward at a set angle, typically 0 degrees or horizontal, is how the polar axis is typically depicted. The image of  WXYZ moves two unit to the right and 5 unit down. The coordinate is (x+2, y-5).

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The magnitude of the resultant force is approximately 60.28 newtons. The angle between the resultant force and the smaller force is approximately 50.5 degrees.

To find the magnitude of the resultant force, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the two forces are acting at right angles, so we can treat them as the sides of a right triangle:

resultant force^2 = (39n)^2 + (46n)^2

resultant force^2 = 1521n^2 + 2116n^2

resultant force^2 = 3637n^2

resultant force = sqrt(3637n^2) = 60.28n

So the magnitude of the resultant force is approximately 60.28 newtons.

To find the angle that the resultant force makes with the smaller force, we can use trigonometry.

We know that the two forces are at right angles, so the angle between the resultant force and the smaller force is the same as the angle between the resultant force and the larger force. Let's call this angle θ. Then we have:

tan θ = (larger force) / (smaller force)

tan θ = 46n / 39n

θ = tan^-1(46/39) = 50.5°

Therefore, the angle between the resultant force and the smaller force is approximately 50.5 degrees.

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0.626 liters of water is needed to fill the container to its brim.

The volume of the rectangular container can be found by multiplying the area of the base (length x width) by the height:

Volume of rectangular container = length x width x height

Since the base is a square with a side of 12 cm, the area of the base is:

Area of base = 12 cm x 12 cm = 144 cm^2

Converting the height to cm, we have:

Height = 16.5 cm

So the volume of the container is:

Volume = 144 cm^2 x 16.5 cm = 2376 cm^3

To convert the volume from cubic centimeters to liters, we divide by 1000:

Volume = 2376 cm^3 ÷ 1000 = 2.376 liters

Since there is already 1.75 liters of water in the container, the amount of water needed to fill the container to its brim is:

Amount of water needed = 2.376 liters - 1.75 liters = 0.626 liters

Therefore, 0.626 liters of water is needed to fill the container to its brim.

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The total interest on a 20-year, 5.26% loan with a principal of $50,000 is $52,600.

From the information,

Principal: $50,000

Interest rate: 5.26%

Loan duration: 20 years

Total Interest = (Principal x Interest Rate x Loan Duration) / 100

Plugging in the values we have, we get:

Total Interest = (50,000 x 5.26 x 20) / 100

Total Interest = $52,600

The interest is $52600.

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If the slope is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), then the slope would depend on how the dependent variable and independent variable are measured.

Assuming that the dependent variable y is some form of economic outcome (e.g., consumption, savings, investment) and the independent variable x is income, then the slope of the relationship would depend on the units in which income is measured.

If income is measured in thousands of dollars, then a one-unit change in income would correspond to a $1,000 change. Therefore, the slope would reflect the change in the economic outcome associated with a $1,000 change in income.

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The possible maximum value of the expression is (d) None

From the question, we have the following parameters that can be used in our computation:

a = bq + r

The above expression is an Euclid's Division statement

The Euclid's Division Algorithm states that "For any two positive integers a, b there exists unique integers q and r such that:"

a = bq + r

where 0 ≤ r < b.

From the question, we have

q = 4

Max r = 4

Using 0 ≤ r < b, we have

Minimum b = 5

So, we have

a = bq + r

This gives

Min a = 5 * 4 + 4

Min a = 24

The above represents the minimum value of a

The maximum value cannot be calculated because as b increases, the value of the expression also increases

Hence, the possible maximum value is (d) None

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Answer: 8.9

Step-by-step explanation:

This is pythagoras.

[tex]a^{2} + b^{2} = c^{2}\\6.4^{2} + 6.2^{2} = c^{2}\\40.96 + 38.44 = 79.4\\\sqrt{79.4} = 8.91066776398[/tex]

8.91066776398 = 8.9 (nearest tenth)

When we multiply (2x - 1) and (x + 2) using FOIL method, we get:

(2x - 1)(x + 2) = 2x(x) + 2x(2) - 1(x) - 1(2)

= 2x² + 4x - x - 2

= 2x² + 3x - 2

Therefore, the product of (2x - 1) and (x + 2) is 2x² + 3x - 2.

The financing option that will likely lead to the lowest monthly payment is:

$3000 down payment, 6% interest, 84 months

The longer loan term (84 months) will spread out the payments over a longer period of time, resulting in a lower monthly payment. The down payment will also help to reduce the monthly payment amount.

The 6% interest rate is relatively low, so it won't have a significant impact on the monthly payment compared to the loan term.

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The only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.

A function is even if it satisfies the property g(-x) = g(x) for all x.

Checking each of the given functions:

g(x) = (x - 1)^2 is not even, because g(-x) = (-x - 1)^2 = x^2 + 2x + 1, which is not equal to g(x) = (x - 1)^2.

g(x) = 2x^2 is even, because g(-x) = 2(-x)^2 = 2x^2 = g(x) for all x.

g(x) = 4x^2 is even, because g(-x) = 4(-x)^2 = 4x^2 = g(x) for all x.

g(x) = 2x is odd, because g(-x) = 2(-x) = -2x = -g(x) for all x.

Therefore, the only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.

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For series Σ a(-1)^(k+1)k!, convergence depends on the limit of |a(k+1)/a(k)|. For series Σ ka sin(2), it diverges.

Consider the series Σ a(-1)^(k+1)k!, where a is a sequence of real numbers.

To determine the convergence of this series, we can use the ratio test

lim┬(k→∞)⁡〖|a(k+1)(-1)^(k+2)(k+1)!|/|ak(-1)^(k+1)k!| = lim┬(k→∞)⁡〖(k+1)|a(k+1)|/|a(k)||〗

If this limit is less than 1, then the series converges absolutely. If the limit is greater than 1, the series diverges. If the limit is equal to 1, then the test is inconclusive.

Let's evaluate the limit

lim┬(k→∞)⁡〖(k+1)|a(k+1)|/|a(k)||〗 = lim┬(k→∞)⁡〖(k+1)!/(k!k)|a(k+1)/a(k)||〗 = lim┬(k→∞)⁡〖(k+1)/(k)|a(k+1)/a(k)||〗

Since lim┬(k→∞)⁡〖|a(k+1)/a(k)||〗 exists, we can apply the ratio test again:

if the limit is less than 1, the series converges absolutely.

if the limit is greater than 1, the series diverges.

if the limit is equal to 1, the test is inconclusive.

Therefore, we can classify the series Σ a(-1)^(k+1)k! as either absolutely convergent, conditionally convergent, or divergent depending on the value of the limit.

Consider the series Σ ka sin(2), where a is a sequence of real numbers.

To determine the convergence of this series, we can use the alternating series test, which states that if a series Σ (-1)^(k+1)b(k) is alternating and |b(k+1)| <= |b(k)| for all k, and if lim┬(k→∞)⁡〖b(k) = 0〗, then the series converges.

In this case, we have b(k) = ka sin(2), which is alternating since (-1)^(k+1) changes sign for each term. We also have

|b(k+1)|/|b(k)| = (k+1)|a|/k < k|a|/k = |b(k)|/|b(k-1)|

Therefore, |b(k+1)| <= |b(k)| for all k. Finally, we have

lim┬(k→∞)⁡〖b(k) = lim┬(k→∞)⁡〖ka sin(2)〗 = ∞〗

Since the limit does not exist, the series diverges.

Therefore, we can classify the series Σ ka sin(2) as divergent.

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E = 0.01(0.0005(30)^2 + 0.38(30) + 35)(2*0.0005(30) + 0.38) ≈ 0.63

Interpretation: The income elasticity of demand is 0.63, which means that for every 1% increase in household income, the fraction of children attending a live musical performance increases by 0.63%.
At a family income level of $30,000, the fraction of children attending a live musical performance is increasing by 0.63% per 1% increase in household income.
To compute the income elasticity of demand E at an income level of $30,000, we need to find the derivative of q with respect to x, and then evaluate it at x=30. The derivative of q with respect to x is:

dq/dx = 0.01(0.001x + 0.38)
Now, let's evaluate this derivative at x=30:
dq/dx = 0.01(0.001(30) + 0.38) = 0.004
To calculate the income elasticity of demand E, we use the formula:
E = (dq/dx)(x/q)
First, let's find q at x=30:
q = 0.01(0.0005(30)^2 + 0.38(30) + 35) = 0.178
Now, we can find E:
E = (0.004)(30/0.178) ≈ 0.67

Interpret the result:
At a family income level of $30,000, the fraction of children attending a live musical performance is increasing by approximately 67% per 1% increase in household income.

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The event that has a probability of 0 is selecting a yellow marble

Other probabilities are listed below

The items in the jar are given as

6 black, 4 brown, 8 white, and 2 blue.

These items are the sample space of this event

Hence, the sample space is 6 black, 4 brown, 8 white, and 2 blue.

For the probability Julie will draw a white marble, we have

P(White) = White/Total

So, we have

P(White) = 8/20

Simplify

P(White) = 2/5

For the event that is more likely to happen, we have

P(black marble) = 6/20

P(brown or blue marble) = (4 + 2)/20

P(brown or blue marble) = 6/20

The probabilities are equal

So, both events have equal likelihood

The event that has a probability of 0 could be the probability of selecting a yellow marble

This is because the jar has no yellow marble

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The amount of water in the tank can be calculated by multiplying 3/4 to the volume of the tank: 3/4 x V = (3/4)L x W x H.

To calculate the amount of water in the aquarium's fish tank in the shape of a prism,

you would need to know the dimensions of the tank and then multiply the volume of the tank by 3/4.

Let's assume that the aquarium has a rectangular prism shape,

the amount of water in the tank would depend on the dimensions of the tank.

Let's assume the tank has a length of L, a width of W, and a height of H.

The volume of the tank can be calculated by multiplying the length, width, and height together: V = L x W x H.

If the tank is 3/4 full of water, the volume of water in the tank would be 3/4 of the total volume of the tank.

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Tim's truck has a volume of (6.5 feet) x (5 feet) x (7 feet) = 227.5 cubic feet. Each box of papers has a volume of (2 feet) x (2 feet) x (2 feet) = 8 cubic feet. To determine how many boxes of papers Tim can pack into the truck, we need to divide the total volume of the truck by the volume of each box:

227.5 cubic feet ÷ 8 cubic feet per box = 28.44 boxes

Since we can't pack a fraction of a box, Tim can pack a maximum of 28 boxes of papers into his truck. However, this assumes that there is no wasted space due to irregular shapes of the boxes or other items in the truck.

In reality, Tim may be able to pack slightly fewer boxes depending on how he arranges them in the truck.

Hence, Tim's truck has a volume of 227.5 cubic feet. Each box of papers has a volume of 8 cubic feet.

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Using the  Pythagorean theorem we get , the  height of the TV screen is approximately 15.4 inches to the nearest tenth of an inch.

The screen of a 32-inch high definition television has a diagonal length of 31.5 inches. If the TV screen is 27.5 inches wide, you need to find the height of the screen to the nearest tenth of an inch. To do this, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides (width and height).

1. Let the height of the TV screen be h inches.
2. According to the Pythagorean theorem, (width)^2 + (height)^2 = (diagonal)^2.
3. Substitute the given values: (27.5)^2 + (h)^2 = (31.5)^2.
4. Calculate the squares: 756.25 + h^2 = 992.25.
5. Subtract 756.25 from both sides: h^2 = 236.
6. Find the square root of 236: h ≈ 15.4 inches.

The height of the TV screen is approximately 15.4 inches to the nearest tenth of an inch.

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DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.

    D

   / \

  /   \

 /     \

E-------F

Given that XF = 10, YF = 5, and EF = 13, we need to find DY.

We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:

EF / ED = EY / EJ  (where J is the intersection of XY and DF)

EF / DF = EJ / EY

Substituting the given values, we get:

13 / ED = EY / EJ

13 / DF = EJ / (13 - EY)

Multiplying the above two equations, we get:

13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)

169 / (ED * DF) = EY / (13 - EY)

Substituting the values of XF = 10 and YF = 5, we get:

169 / (ED * DF) = 5 / 8

ED / DF = 135 / 169

Using the Pythagorean theorem on triangles DEX and DFY, we get:

ED^2 = EX^2 + DX^2

DF^2 = FY^2 + DY^2

Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:

ED^2 = EX^2 + (13 - EX)^2

ED^2 = 2EX^2 - 26EX + 170

Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:

DF^2 = FY^2 + DY^2

DF^2 = 170 - 26EY + EY^2 + DY^2

Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:

(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170

DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)

DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX)   (Substituting XF = 10)

Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:

FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY)   (Substituting YF = 5)

DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2

Substituting the given values, we get:

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

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To find the slope of the secant line connecting two points on a curve, we can use the formula: slope of secant line = (change in y) / (change in x).

In this problem, we are given the function f(x) = x^3 - 5x on the closed interval [-1, 3), and we need to find the slope of the secant line connecting (-1, f(-1)) and (3, f(3)). To do this, we first need to find the y-coordinates of these points by plugging the given x-values into the function f(x). Then, we can use the formula for the slope of a secant line to find the slope of the line connecting these two points.

The slope of a secant line is an important concept in calculus and is used to approximate the instantaneous rate of change of a function at a particular point.

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