A bike trail is 5 1/10 long. Jade rides 1/4 of the trail before stopping for a water break. How many miles does jade ride before stopping?

The critical numbers of f are x = -5 and x = 5.

(A) To find the derivative f'(x), we differentiate f(x) = x³ - 75x - 2 with respect to x:
f'(x) = 3x² - 75

(B) There are no partition numbers for f' as partition numbers are related to integer partitions, which are not applicable in this context.

(C) To find the critical numbers of f, we set f'(x) equal to 0 and solve for x:
3x² - 75 = 0
x² = 25
x = ±5

So the critical numbers of f are x = -5 and x = 5.

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Answer:

72.5 square inches

Step-by-step explanation:

See attachment.

The areas of the 2 shapes are in blue, but when added together:

60+12.5=72.5

Hope this helps!

Answer: Box and whisker plots are plots on number lines with a box and two lines off the edges, called whiskers. The box has a line at the upper quartile(1), one at the lower quartile(2), and one in the center of the box at the median(3). The two lines go to the ends of the data, one at the minimum(4) and one at the maximum(5).

  4     2     3       1             5

   |-----[___|____]-----------|

₀__₁__₂__₃__₄__₅__₆__₇__₈

I hope this helps.

The number of solutions that are there for the pair of equations for lines Q and S is zero solution (no solution) because the lines are parallel with no point of intersection.

In Mathematics and Geometry, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

This ultimately implies that, a system of equations would have no solution when the line representing each of the equations are parallel lines and have the same slope i.e both sides of the equal sign are the same and the variables cancel out.

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Optimize crate cost by expressing material cost in terms of x and y, calculating cost of all four sides, and finding minimum cost. Optimal dimensions: x = 16 ft, y = 48 ft. Minimum cost: $8704.

To find the dimensions of the crate that will minimize the total cost of material, we need to use optimization techniques, we need to express the cost of materials in terms of x and y then calculate the cost of all four sides, then find the minimum cost.
Let's start by defining the variables we need to work with:

Let x be the length of one side of the square base (in feet),  Let y be the height of the crate (in feet).
From the given volume, we know that:
V = x^2 * y = 12288 ft^3
We can use this equation to solve for one of the variables in terms of the other:
y = 12288 / (x^2)
Now we need to express the cost of materials in terms of x and y.
The area of the bottom is x^2, so the cost of the bottom is:
[tex]C_b = 10 * x^2[/tex]
The area of each side is x * y, and there are four sides, so the cost of the sides is:
[tex]C_s = 4 * 2 * x * y = 8xy[/tex]
The area of the top is also x^2, so the cost of the top is:
[tex]C_t = 2 * x^2[/tex]
The total cost of materials is the sum of these three costs:
[tex]C = C_b + C_s + C_t = 10x^2 + 8xy + 2x^2[/tex]
Now we can substitute y = 12288 / (x^2) into this equation:
[tex]C = 10x^2 + 8x * (12288 / x^2) + 2x^2[/tex]
Simplifying this expression, we get:
[tex]C = 12x^2 + 98304 / x[/tex]
To find the minimum cost, we need to find the value of x that minimizes this expression. We can do this by taking the derivative of C with respect to x and setting it equal to zero:
C' = 24x - 98304 / x^2 = 0
Solving for x, we get:
x = 16 ft
Now we can use this value of x to find y:
y = 12288 / (16^2) = 48 ft
Therefore, the dimensions of the crate that will minimize the total cost of material are:
- Length of one side of the square base = x = 16 ft
- Height of the crate = y = 48 ft
To check that this is indeed the minimum cost, we can plug these values back into the expression for C and calculate the cost:
C = 10 * 16^2 + 8 * 16 * 48 + 2 * 16^2 = 8704
Therefore, the minimum cost of material for the crate is $8704.

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Answer:

-4 = 5

0 = -1

2 = -4

4 = -7

(-4, 5)

(0, -1)

(2, -4)

(4, -7)

Step-by-step explanation:

First, let's identify what each term represents.

y-intercept: -1

slope: 3/2

Then, fill out the table.

x = -4

-1 - (3/2 · -4)

-1 - (-12/2)

-1 - (-6)

-1 + 6

y = 5

x = 0

-1 - (3/2 · 0)

-1 - 0

y = -1

x = 2

-1 - (3/2 · 2)

-1 - (6/2)

-1 - (3)

y = -4

x = 4

-1 - (3/2 · 4)

-1 - (12/2)

-1 - (6)

y = -7

Then, plot the points in the function on the graph.

(-4, 5)

(0, -1)

(2, -4)

(4, -7)

Answer:p(x)=3x+5

Step-by-step explanation:

f(x)=2x+3

g(x)=x+2

p(x)=(2x+2)+(x+2)= 3x+5

Answer:

p(x)=ax + b

Step-by-step explanation:

Answer: it will need to be rewritten so that the variable is only on one side of the equation

Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator

As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.

A number line is a visual representation of numbers placed in order on a straight line. It is a graphical tool used to represent the real numbers, starting from negative infinity on the left side and extending to positive infinity on the right side. The number line is divided into equal intervals, and each point on the line corresponds to a specific value or number. The distance between any two points on the number line represents the numerical difference between the corresponding numbers. The number line is a fundamental tool in mathematics for understanding the order and magnitude of numbers, as well as for performing operations such as addition, subtraction, and comparison.

As you approach zero from the left on a number line, the integers become increasingly negative, but the absolute values of those integers remain positive.

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Answer:

D

Step-by-step explanation:

Answer:

A, C, F

Step-by-Step:

The amplitude is whatever the coefficient is behind the trig function

The triangle that will always have the same area, no matter how it is drawn, is a right triangle that has two 45° angles. The correct answer is option A

This is because any right triangle with two 45° angles is a special type of triangle called an isosceles right triangle. In an isosceles right triangle, the two legs are congruent, which means they have the same length. Therefore, no matter how the triangle is drawn, its area will always be the same.

To see why this is true, let's use the formula for the area of a right triangle:

Area = (base x height) / 2

In an isosceles right triangle, the base and height are congruent, so we can write:

Area = (leg x leg) / 2

Simplifying this expression, we get:

Area = (leg^2) / 2

Since the legs of an isosceles right triangle are congruent, we can substitute leg for both legs in the formula:

Area = (leg^2) / 2 = (leg x leg) / 2

No matter how the triangle is drawn, the legs will have the same length, so the area of the triangle will always be the same.

Therefore, the correct answer is option A, a right triangle that has two 45° angles.

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Answer:

1

1

1

2

2

2

2

Step-by-step explanation:

The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.


1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).

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The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.

To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.

The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:

where C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.

Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:

Simplifying, we get:

Therefore, the antiderivative of h(x) is:

We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:

where C is the constant of integration. Thus, the final answer is:

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The decay factor corresponding to each percent decrease is 0.87. The correct option is c. The customer would save a total of $17.35, or 17.35% off the original price.

To determine the decay factor corresponding to each percent decrease, we need to use the formula:

decay factor = (100% - percent decrease)/100%

For the first discount of 13%, the decay factor would be:

decay factor = (100% - 13%)/100% = 0.87

For the additional neighborhood discount of 5%, the decay factor would be:

decay factor = (100% - 5%)/100% = 0.95

So the correct answer is option C, with a decay factor of 0.87 for the 13% discount and 0.95 for the neighborhood discount.

These decay factors represent how much of the original price is left after the discount has been applied. For example, if the original price was $100, after the 13% discount, the price would be:

price after first discount = $100 x 0.87 = $87

Then, after the additional 5% discount, the final price would be:

final price = $87 x 0.95 = $82.65

So the customer would save a total of $17.35, or 17.35% off the original price.

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Answer:

Step-by-step explanation:

The possible outcomes of rolling a fair six-sided die are the numbers 1, 2, 3, 4, 5, and 6, each of which has an equal probability of $\frac{1}{6}$ of appearing.

The probability of rolling a number greater than 1 is $\frac{5}{6}$, since there are five out of six possible outcomes that satisfy this condition (namely, 2, 3, 4, 5, and 6).

The probability of rolling a number less than 3 is $\frac{2}{6}=\frac{1}{3}$, since there are two out of six possible outcomes that satisfy this condition (namely, 1 and 2).

To find the probability of both events happening (rolling a number greater than 1 and then rolling a number less than 3), we can multiply their respective probabilities:

$\frac{5}{6}\cdot\frac{1}{3}=\frac{5}{18}$

Therefore, the probability of rolling a number greater than 1 and then rolling a number less than 3 is $\boxed{\frac{5}{18}}$.

The profit is maximized at $16,400 when the ticket price is $12.

To find the ticket price that maximizes the profit, we used the fact that the maximum or minimum value of a quadratic function occurs at its vertex. For a quadratic function in the form of P(x) = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / 2a.

In this case, we were given the function [tex]P(x) = -100x^2 + 2400x - 8000,[/tex]where x represents the price per ticket. The coefficient of [tex]x^2[/tex] is negative, which tells us that the graph of this function is a downward-facing parabola. The vertex of this parabola represents the maximum value of the function.

Using the formula x = -b / 2a, we found the x-coordinate of the vertex to be x = -2400 / 2(-100) = 12. This means that a ticket price of $12 will maximize the profit.

To verify that this is indeed the maximum profit, we substituted x = 12 into the profit function P(x):

[tex]P(12) = -100(12)^2 + 2400(12) - 8000 = 16,400[/tex]

We can see that the profit is maximized at $16,400 when the ticket price is $12.

In summary, to find the ticket price that maximizes the profit, we used the formula x = -b / 2a to find the x-coordinate of the vertex of the quadratic function representing the profit from selling tickets to a musical. The maximum profit occurs at the ticket price that corresponds to the x-coordinate of the vertex.

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Answer:We can start by resolving the forces acting on the ornamental star in the vertical direction and in the horizontal direction. Since the star is stationary, these forces must balance each other out.

Let's call the tension in the higher chain T1 and the tension in the lower chain T2. We can use trigonometry to find the vertical and horizontal components of each tension force.

For T1:

The vertical component is T1cos(40°) and the horizontal component is T1sin(40°).

For T2:

The vertical component is T2cos(30°) and the horizontal component is T2sin(30°).

Now, resolving the forces in the vertical direction, we have:

T1cos(40°) + T2cos(30°) - mg = 0

where m is the mass of the star and g is the acceleration due to gravity.

Substituting the values:

T1cos(40°) + T2cos(30°) - (40 kg)(9.81 m/s^2) = 0

T1cos(40°) + T2cos(30°) = 392.4 N

Next, resolving the forces in the horizontal direction, we have:

T1sin(40°) = T2sin(30°)

Now we have two equations with two unknowns:

T1cos(40°) + T2cos(30°) = 392.4 N

T1sin(40°) = T2sin(30°)

Solving these equations simultaneously, we get:

T1 = 266.4 N

T2 = 205.1 N

Therefore, the tension in the higher chain (T1) is 266.4 N and the tension in the lower chain (T2) is 205.1 N.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's given that, The height of three basketball players is 210 cm, 220 cm and 191 cm.

h₁ = 210 cm

h₂ = 220 cm

h₃ = 191 cm

Total number of observations = 3.

Average = Sum of all observations/Total number of observations.

↠ Average = h₁ + h₂ + h₃/3

↠ Average = 210 +220 + 191 /3

↠ Average = 430 + 191/3

↠ Average = 621/3

↠ Average = 207

Therefore, The required average height is 207 cm.

The quadratic equation given the points (6,0), (-1,0), and (7,4).

The correct answer is h(x) = 1/2(x + 1)(x - 6).

To find the quadratic equation given the points (6,0), (-1,0), and (7,4), we can use the general form of a quadratic equation, which is [tex]h(x) = ax^2 + bx + c.[/tex]

First, let's substitute the coordinates of the given points into the equation to create a system of equations:

For the point (6,0):

[tex]0 = a(6)^2 + b(6) + c ---- (1)[/tex]

For the point (-1,0):

[tex]0 = a(-1)^2 + b(-1) + c ---- (2)[/tex]

For the point (7,4):

[tex]4 = a(7)^2 + b(7) + c ---- (3)[/tex]

We now have a system of three equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.

Solving the system of equations (1), (2), and (3), we find:

a = 1/2

b = -3/2

c = 0

Thus, the quadratic equation that satisfies the given points is:

h(x) = 1/2(x + 1)(x - 6).

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After solving the word problem, the large bag contains enough sugar to make 40 cakes

Since the large bag is 2.5 times larger than the small bag, and the small bag contains enough sugar to make 9 cakes, the large bag contains enough sugar to make:

2.5 * 9 = 22.5 cakes

However, since there are only 30 cups of sugar in the large bag, and we don't know how much sugar is needed to make a single cake, we cannot determine the exact number of cakes that can be made with a large bag of sugar.

As for the small bag, if it had enough sugar to make 9 cakes and there are 0.75 cups of sugar remaining, then each cake requires:

(sugar in bag - remaining sugar) / number of cakes

= (9 - 0.75) / 9

= 0.75 cups of sugar

Therefore, the large bag contains enough sugar to make:

30 cups / 0.75 cups per cake

= 40 cakes

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The volume of the resulting solid is estimated 4,128.38 cubic units.

The volume of the ball isgitten as:

V_ball = (4/3)πr^3

r is the radius of the ball. In this scenario

r = 11, so:

V_ball = (4/3)π(11)^3

V_ball = (4/3)π(1331)

V_ball = 4,396.46 cubic units

The volume of the hole is gotten as :

V_hole = (4/3)πr^3

r is the radius of the hole.

In thisscenario, r = 4, so:

V_hole = (4/3)π(4)^3

V_hole = (4/3)π(64)

V_hole = 268.08 cubic units

In conclusion, the volume of the resulting solid is:

V_resulting_solid = V_ball - V_hole

V_resulting_solid = 4,396.46 - 268.08

V_resulting_solid = 4,128.38 cubic units

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The correct options are:

Option B:  The football is thrown from 6 feet off the ground.

when t = 0

h(t) = 6 * 75 * 0 + 16 * 0

= 6 feet

Option C : - 16t² represents the effect of gravity

we have

[tex]h = ut - \frac{1}{2}gt^2[/tex]

[tex]\frac{1}{2}gt^2=-16t^2[/tex]

F. The vertex of the graph of h gives the maximum height of the foot

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Answer:

If Mandy completed 70% of her walk in 3 hours, then we can find her walking rate as follows:

Let's assume that the entire walk takes t hours. Then, 70% of the walk would take 0.7t hours. We know that Mandy completes 70% of her walk in 3 hours, so we can set up the following equation:

0.7t = 3

Solving for t, we get:

t = 3 ÷ 0.7 ≈ 4.29

So, the entire walk will take approximately 4.29 hours. Since Mandy has already walked for 3 hours, the remaining time she needs to complete her walk is:

4.29 - 3 = 1.29 hours

Therefore, the answer is closest to option A, 3 4/5 hours.

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Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job

To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.

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The area of the quadrilateral can be found by dividing it into two triangles and finding the sum of their areas. The line connecting points B and D divides the quadrilateral into two triangles ABD and BCD. The area of triangle ABD is 1/2 * base * height = 1/2 * 6 * 6 = 18 square units. The area of triangle BCD is 1/2 * base * height = 1/2 * 3 * 8 = 12 square units. Therefore, the area of the quadrilateral is 18 + 12 = 30 square units.

The rewritten expression of 12 using the distributive property is 3(2 + 2)

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

12 distributive property

This means that

12

Express as 6 + 6

So, we have

12 = 6 + 6

Factor out 3 from the equation

So, we have

12 = 3(2 + 2)

The above equation has been rewritten using the distributive property.

Hence, the rewritten expression using the distributive property is 3(2 + 2)

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