Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–10, 13) and Q (–20, 7)

Anwser 52 degrees

Step-by-step explanation:

first you figure out the 2 angles the triangle is missing so 28-90 would be 62

then to find the other unknown angle you solver for the larger triangle

so 90+48=138

180-138=42

42+62=104

104+2y-30=180

add 30

104+2y=210

-104

2y=106

divide by 2

y=53

I did it wrong :) don't pay attention to this comment XP

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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The probability that in a given ten-minute interval, 15 cars arrive at the booth, and 10 of these are japanese imports = 0.0002

We know that the conditions for the Poisson distribution.

1) The occurrence of one event does not affect the probability another event will occur. i.e., the events are independent events.

2) The average rate i.e., the ratio events per time period is constant.

3) Two events cannot occur at the same time.

and the formula for the Poisson distribution is:

\(P(X = k)=\frac{e^{-\lambda}\times {\lambda}^k}{k!}\)

Here, the cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.

We need to find the probability tthat in a given ten-minute interval, 15 cars arrive at the booth, and 10 of these are japanese imports.

Here, we need to multiply the Binomial probability of 10 out of 15 cars being Japanese with the Poisson probability of 15 cars arriving in a 10 minute period.

The Binomial probability of 10 out of 15 cars would be:

P₁(x = 10) = ¹⁵C₁₀ (0.6)¹⁰ (0.4)¹⁵⁻¹⁰

P₁ = 0.18594

And the Poisson probability of 15 cars arriving in a 10 minute period.

So we use λ = 30.

P₂(X = 15) = \(\frac{e^{-30}\times {30}^{15}}{15!}\)

P₂ = 0.0010

So, the required probability would be:

P = P₁ × P₂

P =  0.18594 ×  0.001

P = 0.00018594

P= 0.0002

Therefore, the required probability is 0.0002

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The complete question is:

Cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.

b) Of the cars arriving at the both, it is known that over the long run 60% are Japanese imports. What is the probability that in a given ten-minute interval. 15 cars arrive at the booth, and 10 of these are Japanese imports? State your assumptions clearly.

The diameter of the circle pen for the sheep of the farmer is 68 yards.

The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.

Thus,

circumference = 213.52 yards

The formula for the calculation of the circumference of circle is,

circumference = 2πr,

In which,

π = 3.14  and radius r.

Thus,

213.52 = 2πr

r = 213.52 / 2π

r = 34

Diameter = 2 x radius

Diameter = 2 x 34

Diameter = 68 yards.

Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.

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Answer:

[9 - 2 = 7 x 4] = {28}

[ ] =expression { } answer

Answer:

∠A = 116°

∠B = 116°

∠C = 64°

Step-by-step explanation:

since it is an isosceles trapezoid, ∠C = ∠D = 64°

∠A would be same side interior to ∠D so it would be 180° - 64° = 116°

∠B = ∠A = 116°

The  measure of each angle in the isosceles trapezoid are; ∠A = 116°

∠B = 116° and ∠C = 64°

Due to the figure being isosceles trapezoid, it is symmetric.

Isosceles trapezoid has its two rest sides(which aren't necessary parallel) are of equal length.

Since it is an isosceles trapezoid, ∠C = ∠D = 64°

Here we can use the  symmetric property of the isosceles trapezoid and the fact that a triangle has sum of its angles as 180°

We have ∠A that would be same side interior to ∠D

Thus, it would be 180° - 64° = 116°

∠B = ∠A = 116°

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Answer:

50 m

Step-by-step explanation:

We find the perimeter by adding all the sides of our figure.

The initial figure has perimeter :

P = 2 + 5 + 1 + 3 + 3 + 1 + 5

P = 20 m

The dilated figure with the scale factor of 2.5 has perimeter:

P = (2 + 5 + 1 + 3 + 3 + 1 + 5 ) · 2.5

P = 20 * 2.5 = 50 m

Charlie is correct.

The rate at which the sales are changing when the number of units sold is 1,900 is approximately $4,358 per month.

The correct answer is A. $4,358.899/month.

Here, we have,

To find how fast the sales are changing when the number of units sold is 1,900, we need to determine the rate of change of sales with respect to time.

The rate of change of sales can be found using the chain rule.

Given that the profit generated by the product is P(x) = 2√x, where x is the number of units sold, we can express the profit as a function of time, P(t), where t is the time in months.

Since the profit is changing at a rate of $200 per month, we have:

dP/dt = 200

To find dx/dt, the rate of change of sales with respect to time, we need to relate P(x) and x. We can rewrite the profit equation as:

P(x) = 2√x

x = (P(x)/2)²

Now, we differentiate both sides with respect to time, t:

dx/dt = d/dt((P(x)/2)²)

Applying the chain rule, we have:

dx/dt = 2(P(x)/2)(dP/dt)(1/2)(1/x)

= P(x) * dP/dt * (1/2) * (1/x)

Substituting the given values, P(x) = 2√x and dP/dt = 200, we have:

dx/dt = 2√x * 200 * (1/2) * (1/x)

= 200/√x

Now, we can substitute x = 1,900 into the equation to find the rate of change of sales at that point:

dx/dt = 200/√(1,900)

= 200/√(1900)

≈ 200/43.58899

≈ 4.587

Rounding the answer to the nearest dollar per month, we get approximately $4,358.

Therefore, the rate at which the sales are changing when the number of units sold is 1,900 is approximately $4,358 per month.

The correct answer is A. $4,358.899/month.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

5 nickles in a quator.

Step-by-step explanation:

Answer:

5 nickels

Step-by-step explanation:

The value of a nickel is 5 cents and the value of a quarter is 25 cents.

The equation we can use for this is 5 times x = 25

From here, you can divide 25 By 5 and get 5 as your final answer.

Hope this helps, have a good day!

Answer:

Below

Step-by-step explanation:

the  exterior angle measurement  is equal to half the difference of the measure of intercepted arcs.

? = (152-50)° / 2 = 51°

Answer:

all are in the picture I attached

Step-by-step explanation:

hope this helps

P₂ = (-3, 10)

The midpoint, (a, b) = (-5, 3)

The starting point, P₁ = (x₁, y₁) = (-7, 4)

Let P₂ = (x₂, y₂)

The formulae for the coordinates of the midpoint are:

To solve for x₂, substitute a = -5, x₁ = -7 into the formula

To solve for y₂, substitute b = 3, y₁ = -4 into the formula

Therefore, P₂ = (-3, 10)

Answer:

250 $3 tickets and 100 $2 tickets were sold.

37

Step-by-step explanation:

they're are three adults so multiply 3 by 7 which is 21

and 4 kids so multiply 4 by 4 to get 16

to get the total add 16 and 21 to get 26

Answer:

C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The arrow is pointing to the right which means its greater than, and the circle is open so it doesn't include 4

The area of the region enclosed by the graphs y ≠ tan(x), y = -3 tan(x), and x = 4 is 4 ln (0.25). This represents the definite integral of the absolute difference between the two curves over the specified interval.

To determine the area of the region enclosed by the graphs of y ≠ tan(x), y = -3 tan(x), and x = 4, we need to evaluate the definite integral of the difference between the two curves.

The two curves intersect at points where y = tan(x) and y = -3 tan(x). Setting these two equations equal to each other, we get tan(x) = -3 tan(x).

This equation has solutions at x = -π/4 and x = 3π/4.

To determine the area, we integrate the absolute difference between the two curves over the interval from x = -π/4 to x = 3π/4.

A = ∫[(-π/4), (3π/4)] |tan(x) - (-3 tan(x))| dx

Simplifying the integrand,

we get |4 tan(x)|.

Now, we can integrate the absolute value of 4 tan(x) over the interval.

A = ∫[(-π/4), (3π/4)] 4 tan(x) dx

Evaluating this integral gives:

A = 4 ln |sec(x)| |[(-π/4), (3π/4)]

Substituting the limits of integration, we get:

A = 4 ln |sec(3π/4)| - 4 ln |sec(-π/4)|

Simplifying further, we have:

A = 4 ln |1/√2| - 4 ln |√2|

A = 4 ln (1/√2) - 4 ln (√2)

A = 4 ln (1/2) - 4 ln (2)

A = 4 ln (0.5) - 4 ln (2)

A = 4 ln (0.5) - 4 ln (2)

A ≈ 4 ln (0.25)

Therefore, the area of the region enclosed by the graphs is approximately 4 ln (0.25).

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Each individual result of a probability experiment is called an "outcome" (d).

An outcome refers to a specific result or occurrence that can happen when conducting a probability experiment. It represents the different possibilities or potential results of an experiment.

For example, when flipping a fair coin, the possible outcomes are "heads" or "tails." In this case, "heads" and "tails" are the two distinct outcomes of the experiment.

Similarly, when rolling a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, or 6. Each number represents a different outcome that can occur when rolling the die.

In summary, an outcome is a specific result or occurrence that can happen during a probability experiment. It is essential to understand outcomes as they form the basis for calculating probabilities and analyzing the likelihood of different events occurring.

Thus, each individual result of a probability experiment is called an "outcome" (d).

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Answer:

If they are the lengths of the sides of a right triangle then yes it is a right triangle.

Step-by-step explanation:

21.6²+28.8²=36.2

L=466.56+829.44+1296

R=1296

L=R

The weight of an object with a mass of 2 kg would be 6 N on this planet, assuming the direct variation relationship holds.According to the given information, the weight of an object varies directly with its mass.

This implies that there is a constant of proportionality between weight and mass. Let's denote this constant as k.

From the given data, we have:

Mass = 5 kg

Weight = 15 N

Using the direct variation equation, we can write:

Weight = k * Mass

Substituting the given values, we have:

15 N = k * 5 kg

To find the value of k, we divide both sides of the equation by 5 kg:

k = 15 N / 5 kg = 3 N/kg

Now that we know the constant of proportionality, we can find the weight of an object with a mass of 2 kg:

Weight = k * Mass = 3 N/kg * 2 kg = 6 N.

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To find the height of the rocket after 2.5 seconds,

you'll need to plug in t = 2.5 into the given equation h(t) = 160t - 16t².

h(2.5) = 160(2.5) - 16(2.5)²
h(2.5) = 400 - 100
h(2.5) = 300 meters

The height of the rocket after 2.5 seconds is 300 meters.

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The required experimental probability that the next batter will get a hit is 2/11.

A number that indicates how likely an event is to occur is called its probability. It is communicated as a number in the reach from 0 and 1, or, utilizing rate documentation, in the reach from 0% to 100 percent. The higher the probability, the more likely the event is to occur.

The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials or events.

In this case, we are given that 4 out of 22 batters have gotten a hit so far. Therefore, the experimental probability that the next batter will get a hit is:

P(hit) = Number of hits / Total number of batters

P(hit) = 4/22

Simplifying:

P(hit) = 2/11

Therefore, the experimental probability that the next batter will get a hit is 2/11.

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Equation of a Line

The slope-intercept form of a line is:

y = mx + b

Where m is the slope.

We are given the equation of a line:

24x - 2y = 38

Subtracting 24x:

-2y = -24x + 38

Dividing by -2:

y = (-24/-2)x + 38/(-2)

Operating:

y = 12x - 19

We can see that b = 12, thus the slope of the graph is 12

Answer:

D. 12

A sensible original hypothesis that suggests a positive relationship between two variables could be: "Hypothesis: Increased physical exercise is positively associated with improved cardiovascular health."

The hypothesis suggests that there is a positive relationship between increased physical exercise and improved cardiovascular health. This means that as the level of physical exercise increases, it is expected to result in an improvement in cardiovascular health.

To explain further, the hypothesis is based on the understanding that physical exercise has various beneficial effects on the cardiovascular system. Regular exercise can lead to improvements in heart function, increased blood flow, lower blood pressure, improved cholesterol levels, and better overall cardiovascular fitness.

By proposing this hypothesis, we are suggesting that individuals who engage in more physical exercise will experience greater improvements in their cardiovascular health compared to those who engage in less or no exercise. This hypothesis can be tested through research studies, where data on exercise habits and cardiovascular health measures are collected and analyzed to determine if a positive relationship exists between the variables.

It is important to note that while the hypothesis suggests a positive relationship, further research is needed to provide concrete evidence and establish a causal link between increased physical exercise and improved cardiovascular health.

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Answer:

Graph attached →

Step-by-step explanation:

The correct option among the options provided in the question is option C.

The derivative of f(x) at x = a equals the slope of the function at x=a.

In mathematics, the derivative is defined as the rate of change of a function with respect to the variables it depends upon. It is used to find the slope of a curve at a given point. The slope of a curve is defined as the change in y coordinate per unit change in the x coordinate.

In calculus, the relationship between the slope and the derivative of f(x) at x-a is explained by the fact that the derivative of f(x) at x - a equals the slope of the function at x = a. This means that the rate of change of the function f(x) with respect to the variable x at x - a is equal to the slope of the curve at that point.

The derivative of a function f(x) at a point x = a is given by f'(a), which is defined as the limit of the ratio Δy/Δx as Δx approaches zero. The slope of the function at x = a is given by the tangent line to the curve at that point. This means that the slope of the curve at x = a is equal to the derivative of f(x) at x = a, which can be written as f'(a).

Thus, the derivative of f(x) at x = a equals the slope of the function at x = a.

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