Y = X - 39 and Y = 9 + 5X

The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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Answer:

y-2=0

Step-by-step explanation:

In y=mx+b

m=(y2-y1)/(x2-x1) [2]

Or another way of thinking about it is rise over run.

define point (-1,2) as x1,y1

define point (5,2) as x2,y2

substitute into formula [2]

m=(2-2)/(5-(-1))

We know that 2-2=0 therefore the slope (m) is 0

y=0x+b

Or simply

y=b

to solve for b we substitute into the formula any of the points

2=b for y1

or 2=b for y2

b=2

therefore y=2

to convert it into general form make the equation equal 0

y-2=0

Answer:

cos 2.78 = 1

Step-by-step explanation:

The domain will be (-∞, ∞). The range will be (-1, 1]. The function will be increasing during the intervals (0, π/2) and (3π/2, 2π), and will be decreasing at the interval (π/2, 3π/2). It will be constant only at x=0 and not at any interval.

We are given a graph in the question and we have to determine its domain, range, and the intervals over which the defined function is increasing, decreasing, and constant. If we observe this graph, we can see that this is a sin(x) graph.

The domain of this graph will be from -\(\infty\) to \(\infty\) as we can see in the graph that it is a repeating pattern. The range for this graph will lie between -1 and 1 as it is a sin x graph. The sin x graph increases at the intervals  (0, π/2) and (3π/2, 2π) and decreases at the interval  (π/2, 3π/2). As we can see from the graph, it is constant only at a point where x = 0 and there is no interval at which this graph is constant.

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Answer:

f(-3) = 11

Step-by-step explanation:

f(x) = -x² + x - 5

f(-3) = -(-3)² + (-3) - 5

f(-3) = 9 - 3 + 5

f(-3) = 11

Answer:

33% or 33.3% or 33.33%

Step-by-step explanation:

1/3 as a decimal is 1 divided by 3 which ends up being an infinite number: 0.33333333333333333333333...

But you can write it as 33% or 33.3% or 33.33%

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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Answer:

C) y =-4x-6

The equation of the line y = -4x-6

Step-by-step explanation:

Step(i):-

Given point (-3,6)

Given line is y = -4x +5

The equation of the parallel line a x+ b y + k=0

Given straight line is y = -4x+5

                    4x + y -5=0

Step(ii):-

The equation of the parallel line 4x+  y + k=0 is passes through the point (-3,6)

    4x+  y + k=0

   4(-3) +6 +k=0

     -12 +6 +k = 0

             k = 6

Final answer:-

The equation of the parallel line 4x+  y + 6 =0

The equation of the parallel line     y = - 4x -6                                                

So on solving the provided question we can say that - the equation will be y = -120x^2 - 2500x + 80,000; x = 0 so, y = 80000

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

y = -120x^2 - 2500x + 80,000

x = 0

so, y = 80000

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Answer:

\(\frac{-4}{3}\)

Step-by-step explanation:

a rational number is expressed as

\(\frac{a}{b}\) where a and b are integers , then

- 1 \(\frac{1}{3}\) = \(\frac{-4}{3}\)

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer:

235.6 units^3

Step-by-step explanation:

The formula for the volume of the oblique cone is the same as for the volume of a right circular cone:  V = (1/3)(base area)(height).

Here that comes to        V = (1/3)(π)(5 units)^2*(9 units), or

V = 75π units^3, or approximately 235.6 units^3

Answer:

235.5 cubic units

Step-by-step explanation:

Answer i think is 395 km

Step-by-step explanation:

Answer: The correct answer is C

x-1/8y^2=0

Step-by-step explanation: i took the test and got it right

Using distributive property, the equivalent expression is 45 - 16x

To find the equivalent expression of 13 - 8(2x - 4), we need to simplify the expression using the distributive property and then combine like terms.

First, we distribute the -8 to the terms inside the parentheses:

13 - 8(2x - 4) = 13 - 16x + 32

Next, we combine the constant terms:

13 - 16x + 32 = 45 - 16x

Therefore, the equivalent expression of 13 - 8(2x - 4) is 45 - 16x.

Overall, finding the equivalent expression of an algebraic expression can help simplify calculations and make solving equations easier.

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The correct options include:

b. In the fifth year Mariah's balance will be higher than Colton's

c. Mariahs beginning balance was 400 and coltons beginning balance was 500.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, from the table

(0, 500), (1, 550), (2, 600), (3, 650) and (4, 700)

The equations for the given points is y=500+50t

Put t=0, 1, 2, 3, 4 in f(t)=400(1.15)t

When t=0, f(0)=$0

When t=1,

f(1)=400×1.15×1

= $460

When t=2,

f(2)=400×1.15×2

= $920

When t=3,

f(3)=400×1.15×3

= $1380

When t=4,

f(4)=400×1.15×4

= $1840

Fifth year:

The balance in Mariah account is

f(t)=400(1.15)t

⇒ f(5)=400×1.15×5

= $2300

The balance in Colton account is

y=500+50t

⇒ y=500+50(5)

= $750

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The upper bound of a 99% confidence interval is found as 57.07.

A random sample of size 18.

Normal population gives 36.5.

Explain the term upper confidence bound (UCB)?

Whenever a machine is often used frequently than other machines, the border shrinks.

For the stated question-

sample size n = 18

normal population mean x = 36.5

variance  s² = 1148; s = 33.88

z(α/2) for 99% confidence interval = 2.576

Thus, upper confidence bound (UCB) is estimated as;

UCB = \(x + z(\frac{\alpha}{2} )*\frac{s}{\sqrt{n} }\)

UCB = 36.5 + 2.576×33.88/√18

UCB = 36.5 + 20.57

UCB = 57.07

Therefore, the upper bound of a 99% confidence interval is found as 57.07.

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Answer:

\(P(F/E) = 0.6\)

Step-by-step explanation:

If we are given two dependent events \(A\) and \(B\) such that their chances of occurrence or the probabilities of the events are: \(P(A)\) and \(P(B)\).

Then the conditional probability that the event \(B\) will occur given that \(A\) has already occurred is given by the following formula:

\(P(B/A) = \dfrac{P(A \cap B)}{P(A)}\)

Here the two events given are \(E\) and \(F\).

\(P(E\ and\ F)\ or\ P(E\cup F) = 0.3\)

and \(P(E) = 0.5\)

As per the above formula that we have already discussed, the formula can be written as:

\(P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}\)

Answer:

im pretty sure its a

Step-by-step explanation:

Answer:

..........

Step-by-step explanation:

Answer

\(\large\pmb{\rm{x > 4}}\)

Further explanation

This is a two-step inequality. So we can do two steps and get our answer.

You solve an inequality just like you'd solve an equation, only instead of the equal sign you have "less than", "greater than", "less than or equal to" and "greater than or equal to" symbols.

Now, let's solve.

6x - 23 > 1

On each side, add 23.

6x > 1 + 23

6x > 24

Divide each side by 6.

x > 4

In conclusion, the solution to the inequality is x > 4.

n(A ∩ B ∩ C^c) = 15 there are 15 elements in the intersection of sets A and B but not in set C.

What is a circle?

A circle is a two-dimensional geometric figure that consists of all the points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius, which is denoted by the letter "r".

To find the cardinality of n(A∩B∩C^c), we need to know the number of elements that are in the intersection of A and B but not in C.

One way to approach this is to use the principle of inclusion and exclusion. This states that:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

We can rearrange this formula to solve for n(A ∩ B ∩ C^c):

n(A ∩ B ∩ C^c) = n(A ∩ B) - n(A ∩ B ∩ C) - n(B ∩ C) + n(A ∩ C) + n(B) + n(C) - n(A)

Plugging in the values we have been given, we get:

n(A ∩ B ∩ C^c) = 4 - 3 - 9 + 7 + 11 + 15 - 10

Simplifying this expression, we get:

n(A ∩ B ∩ C^c) = 15

Therefore, there are 15 elements in the intersection of sets A and B but not in set C.

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The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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The correct calculation of the standard deviation of the sampling distribution of p_hat subscript s - p_hat subscript p is 0.0934.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We are given that;

Percentage of students with laptop=68%

Percentage of professors with laptop=43%

p_s = 0.68 and p_p = 0.43.

Now,

The formula for the standard deviation of the sampling distribution of the difference between two sample proportions is:

sqrt[(p_s * (1 - p_s) / n_s) + (p_p * (1 - p_p) / n_p)]

where p_s and p_p are the population proportions of students and professors who have a laptop, respectively, n_s and n_p are the sample sizes of students and professors, respectively.

We are also given that 56 students and 31 professors were selected at random and asked if they have a laptop. Therefore, n_s = 56 and n_p = 31.

Substituting these values into the formula, we get:

sqrt[(0.68 * (1 - 0.68) / 56) + (0.43 * (1 - 0.43) / 31)]

sqrt[0.00367143 + 0.00505484]

= sqrt(0.00872627)

= 0.0934 (rounded to four decimal places)

Therefore, by standard deviation the answer will be 0.0934.

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Answer:

63

Step-by-step explanation:

180 -  143 = 37

80 + 37 + x = 180

117 + x = 180

x = 63

Answer:

The correct answer is 9

Step-by-step explanation:

I can assure you this is absolutely correct.

In this case appy the formular for :sine, tan and cosine of an angle

Given that the pole forms a 50 degrees angle with the ground, with the length of pole given as 12 feets and height the tip of the pole makes from the the ground also not given then the formula to apply will require a trial and error calculation.

Applying cosine of an angle where;

Where the angle theta is 50 degrees and H is the hypothenuse length equal to length of ladder and A is the length of base of pole from the house

Where

12*sin50 degrees = A

12*0.76604=A

9.1925 = A

9.19 feets (to the nearest tenth of a foot)

9.2 feet Answer choice D

The fraction of the total farm area is used to grow potatoes in its simplest form is 1/6.

Fraction of farm used in growing vegetables = 2/3

Fraction of farm used to grow potatoes = 1/4 of Fraction of farm used in growing vegetables

Fraction of the total farm area is used to grow potatoes = 1/4 × 2/3

= 2/12

= 1/6

Ultimately, 1/6 is the fraction of the total farm area used to grow potatoes.

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Answer:

In my screenshot

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

descartes rule of signs to test maximum positive and negative:

3x4 - 7x + 3

two sign changes, so maximum of 2 positive real zeroes

3x4 + 7x + 3

no sign changes, so maximum of 0 negative real zeroes

this means that we can have 2 or 0 real zeroes.

if we have 0 real zeroes, we will have 4 imaginary.

therefore the most possible number of complex roots is 4