Find the distance between the two points in simplest radical form.
(-5, 8) (-3, 1)

(y2-y1)/(x2-x1)

19-10=9

6-3=3

9/3=3

slope: 3

y-int: 1

y=3x+1

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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The graph illustrates the supply and demand curves on a single graph to represent the equilibrium point in a market. The equilibrium point is where the quantity demanded equals the quantity supplied, resulting in a balance between buyers and sellers.

This point determines the market price and quantity exchanged in the market. The graph demonstrates the interplay between supply and demand, showcasing how changes in these factors can impact the equilibrium point and market outcomes.

The equilibrium point is the intersection of the supply and demand curves on the graph. At this point, the quantity demanded by buyers matches the quantity supplied by sellers. The equilibrium price is determined by the vertical position of the equilibrium point on the graph, while the equilibrium quantity is determined by the horizontal position.

If the market price is above the equilibrium price, there is excess supply, leading to a surplus. Sellers will be motivated to decrease prices to sell their goods, which, in turn, increases the quantity demanded. Conversely, if the market price is below the equilibrium price, there is excess demand, resulting in a shortage. Buyers will be incentivized to bid higher prices, increasing the quantity supplied by sellers.

The equilibrium point represents a state of market balance where the forces of supply and demand are in harmony. It reflects the price and quantity at which both buyers and sellers are satisfied, maximizing the efficiency of resource allocation in the market.

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Answer:

Point Form:  ( 4 , − 5 )

Equation Form:  x  =  4 ,  y  =  - 5

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:  ( 4 , − 5 )

Equation Form:  x  =  4 ,  y  =  - 5

Answer:

(4, - 5)

Step-by-step explanation:

3x - 4y = 32 ........ (1)

5x + 2y = 10 ....... (2)

(2) × 2 + (1)

13x = 52 ⇒ x = 4

3(4) - 4y = 32 ⇒ y = - 5

(4, - 5)

Answer:

-9,0

Step-by-step explanation:

Counterclockwise in math most likely relates to something being negative mean while clockwise most likely relates to something being positive. So if were making a 90 degree turn counterclockwise(negative) then all we need to do is flip the x and y cordinants and make them negative to put it simply.

Answer:

B.(4,20)

Step-by-step explanation:

Given: \(x^2 -24x = -80\)

To solve the quadratic equation by completing the square, we follow these steps.

Step 1: Divide the coefficient of x by 2

\(-\dfrac{24}{2}=-12\)

Step 2: Square your result fro Step 1

\((-12)^2\)

Step 3: Add the result form step 2 to both sides of the equation

\(x^2 -24x+(-12)^2 = -80+(-12)^2\)

Step 4: Rewrite the Left hand side in the form \((x+k)^2\)

\((x-12)^2=-80+144\\(x-12)^2=64\)

Step 5: Take square roots of both sides

\(x-12=\pm \sqrt{64}\)

Step 6: Solve for x

\(x=12\pm \sqrt{64}\\=12\pm8\\x=12+8$ or x=12-8\\x=20 or x=4.\)

Therefore, the solution set of the equation is (4,20).

Answer:

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Answer:

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The probability that the trade balance is greater than 0 is 1 - 0.1056 = 0.8944, or 89.44%.

Here is the breakdown-

The probability that the trade balance is greater than 0 can be determined using the given information.

To solve this, we need to find the probability that exports minus imports is greater than 0.

Let's denote X as exports and Y as imports. The trade balance is defined as X - Y.

To find the probability that the trade balance is greater than 0, we need to find the probability that X - Y > 0.

We know that the correlation between exports and imports is +0.70.

Using this information, we can calculate the covariance of X and Y as:

Cov(X, Y) = correlation * standard deviation of X * standard deviation of Y

\(Cov(X, Y) = 0.70 * sqrt(900) * sqrt(625)\)

= 0.70 * 30 * 25

= 525

Now, we can calculate the standard deviation of the trade balance as:

Standard deviation of trade balance = sqrt(variance of X + variance of Y - 2 * Cov(X, Y))

Standard deviation of trade balance = sqrt(900 + 625 - 2 * 525)

= sqrt(400)

= 20

Now, we can standardize the trade balance by subtracting the mean of the trade balance and dividing by the standard deviation:

Z = (trade balance - mean of trade balance) / standard deviation of trade balance

Z = (0 - (100 - 125)) / 20

= -25 / 20

= -1.25

Finally, we can find the probability that the trade balance is greater than 0 by finding the area under the standard normal distribution curve to the right of Z = -1.25:

Probability = 1 - cumulative distribution function (CDF) of Z at -1.25

Using a standard normal distribution table or calculator, we find that the CDF at -1.25 is approximately 0.1056.

Therefore, the probability that the trade balance is greater than 0 is 1 - 0.1056 = 0.8944, or 89.44%.

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The internal rate of return (IRR) is a financial metric used to evaluate the profitability of an investment project. It is the discount rate that makes the net present value (NPV) of the project equal to zero. In other words, it is the rate at which the present value of the cash inflows equals the present value of the cash outflows.

To determine whether Nadia should accept the investment in the new factory, we need to compare the IRR of the project with the required rate of return, which is 14.25 percent in this case.

If the IRR is greater than or equal to the required rate of return, then Nadia should accept the investment. This means that the project is expected to generate a return that is at least as high as the required rate of return.

If the IRR is less than the required rate of return, then Nadia should reject the investment. This suggests that the project is not expected to generate a return that is high enough to meet the required rate of return.

So, to determine whether Nadia should accept the investment, we need to calculate the IRR of the project and compare it with the required rate of return. If the IRR is greater than or equal to 14.25 percent, then Nadia should accept the investment. If the IRR is less than 14.25 percent, then Nadia should reject the investment.

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Answer:

Step-by-step explanation:

This rotation would create a sphere.

If a semi-circle is rotated about the y-axis of the graph, then the resulting three-dimensional shape will be a sphere.

A semicircle is a half-circle formed by a one-dimensional locus of points.

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space.

If a semi-circle is rotated about the y-axis of the graph, then the resulting three-dimensional shape will be a sphere. This is because of the fact that when the semi-circle will be rotated about the y-axis then all the points will be at equal distance in all the directions from the centre.

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Answer:

416.84 m

Step-by-step explanation:

First Step:

Multiple 312.63 by 1/3

312.63*1/3=104.21

Second Step:

Add 312.63 to 104.21

312.63+104.21=416.84

\(✤ \: \underline{ \underline{ \frak{Understanding~the~question : - }}} \\ \\ \)

In this question, we have been provided that Evan swims 1/3 times farther than Drake, thus, the total distance covered by Evan will be equal to the sum of 312.63 m and the 1/3rd of 312.63 m. Thus, at first we will calculate the one third of the distance and then add them up to get our final answer.

⠀

\(✤ \: \underline{ \underline{ \frak{Given:-}}} \\ \\ \)

⠀

\(✤ \: \underline{ \underline{ \frak{To~Find :-}}} \\ \\ \)

⠀

\(✤ \: \underline{ \underline{ \frak{Solution :-}}} \\ \\ \)

Calculating the one - third,

\( \sf \longrightarrow \dfrac{1}{3} \: of \: 312.63 \: m \\ \\ \\ \sf \longrightarrow \dfrac{1}{3} \times 312.63 \: m \\ \\ \\ \sf \longrightarrow \dfrac{1}{ \cancel3} \times \cancel{312.63} \: m \: \\ \\ \\ \sf \longrightarrow 1 \times 104.21 \: m \: \: \\ \\ \\ \sf \longrightarrow 104.21 \: m \: \: \: \: \: \: \: \: \: \: \\ \\ \)

Thus,

⠀

\( \sf \longrightarrow Distance~covered~by~Evan =312.63 \: m + 104.21 \: m \\ \\ \\ \sf \longrightarrow Distance~covered~by~Evan =416.84 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \)

Thus, the distance covered by Evan is 416.84 m.

⠀

\(\underline{\rule{227pt}{2pt}} \\ \\ \)

Answer: A. The compromise allowed California to join the United States as a free state but would allowed slavery in the southwestern territories.

Step-by-step explanation:

As the abolitionist North and the pro-slavery South saw their rivalry intensify with the lobbying by the South that slavery should be allowed in the western territories, Congress decided to pass the compromise of 1850 which was several acts that would calm both sides for the time being.

With this compromise, California was allowed to join the United States as a free state but in return, the Southwestern territories were allowed to decide their slavery status in an election which meant that if the territories so pleased, they could allow slavery in their territories.

Answer: 50% I think

Step-by-step explanation: blue and orange are both good colors so I think it would be a 50/50 chance. blue isn't better then orange and orange isn't better then blue.

The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

According to the statement

we have given that the some data of the marks of 18 students and we have to make the plot of that data.

So, For this purpose, we have given that the

A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.

And it is used to find the median and the lower value and the maximum value.

So, The median become:

median = n /2

median = 18/2

median = 9th term and

median value is 71.

And then the lower value of the data is a 53.

And the upper value of the data is a 89.

So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.

So, The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

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Answer:

._________________________*___*___________________

Answer:

45 Tiles

Step-by-step explanation:

7 1/2 × 13 1/2 = 101 1/4

Area = 101 1/4

1 1/12 × 1 1/2 = 2 1/4

Tile Area = 2 1/4

101 1/4 ÷ 2 1/4 = 45

good luck, i hope this helps :)

Considering the data in the table, it is found that:

a) The scatter plot is given by the image at the end of the answer.

b) The correlation of the scatter plot is negative, as when the input increases the output decreases.

c) The estimate for the depth at 15 seconds is of 50.37 cm.

The scatter plot is built inserting all the points in the table, which are in the following format:

(Time, Depth).

Hence the points are given as follows:

(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).

From both the table and the scatter plot given by the image at the end of the answer, as the input increases, the output decreases, hence the scatter plot has a negative correlation.

To make a prediction for a given input, the line of best fit has to be constructed using these points.

Inserting these points into a linear regression calculator, the line of best fit is:

y = -2.07x + 50.89.

At a time of 15 seconds = 0.25 minutes, the depth will be of:

y = -2.07 x 0.25 + 50.89 = 50.37 cm.

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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The  integral diverges, the series also diverges. Therefore, the series Σ 1/(5k+2), k=1, does not converge.

The integral test can be applied to a series if the following conditions are met:

1. The terms of the series are positive.
2. The terms of the series are decreasing.
3. The series has a continuous and positive function that can be integrated over the same interval as the series.

For the series Σ 1/(5k+2), k=1, all of these conditions are satisfied since:

1. The terms of the series are positive because the denominator is always greater than 0.
2. The terms of the series are decreasing because as k increases, the denominator increases and the overall fraction becomes smaller.
3. The function f(x) = 1/(5x+2) is continuous and positive on the interval [1, ∞).

Using the integral test, we can evaluate the convergence of the series by comparing it to the integral of the function f(x) over the same interval, as follows:

∫₁^∞ (1/(5x+2)) dx = (1/5) ln|5x+2| |₁^∞
= (1/5) lim┬(b→∞)⁡(ln|5b+2| - ln|7|) = ∞

Since the integral diverges, the series also diverges. Therefore, the series Σ 1/(5k+2), k=1, does not converge.
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Answer:

Infinite Solution

Step-by-step explanation:

We know that there are no variables on either die of the equation so the answer would be infinite because when you put a number for the variable it will always be true.

Hope this helps :)

Answer:

y = 1/2x + 3

Step-by-step explanation:

when X = 0, y = 3

when y = 0, 0 = kx + 3

k = 1/2

Answer:

29

Step-by-step explanation:

First make an equation that shows the relationship between x and y by finding what you need to do to x to get y:

-15 + ? = 12

? =  27

so the equation is : y = x + 27

now just plug in 2 for x:

y = 2 + 27

y + 29

The number of pastries baked by Katie is 40, and each pastry is shared by 5 people, making a total of 200 people served.

Let's define two variables to represent the number of pastries and the number of people per pastry:

p = number of pastries

pp = number of people per pastry

Then, the total number of pastries and the total number of people can be expressed as:

total pastries = p = 40

total people = p * pp = 200

We can solve for pp by dividing both sides by p:

pp = total people / p = 200 / 40 = 5

So, the algebraic expression to represent this situation is:

p = 40, pp = 5, total people = p * pp = 200

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The correct function to use when conducting an unpaired two-sample t-test with equal variances in Python is st.ttest_ind(var A, var B, equal_var=True).

The ttest_ind function from the scipy.stats module is used for independent two-sample t-tests. By setting the equal_var parameter to True, it assumes that the variances of the two samples are equal. This assumption allows for the use of the pooled variance estimate in the calculation of the test statistic.

The other options provided are incorrect:

sLttest_rel(var A, var B, equal_var=False): This function (sLttest_rel) does not exist in the scipy.stats module. Additionally, the ttest_rel function is used for dependent (paired) two-sample t-tests, not unpaired tests.

st.ttest_rel(var A, var B, equal_var=True): This function is used for dependent (paired) two-sample t-tests, where the two samples are related or matched. It is not suitable for unpaired t-tests.

suttest_ind(var A, var B, equal_var=False): This function (suttest_ind) does not exist in the scipy.stats module. Additionally, the correct parameter name for the equal_var argument is equal_var, not equal _var.

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A point estimate is the value of a statistic that estimates the value of a parameter. Question 2 is false and question 3 is true.

Question 1: A point estimate is the value of a statistic that estimates the value of a parameter.A point estimate is a single number that is used to estimate the value of an unknown parameter of a population, such as a population mean or proportion

Question 2: False

Mu (μ) is not used to estimate X. Mu represents the population mean, while X represents the sample mean. The sample mean, X, is used as an estimate of the population mean, μ.

Question 3: True

Beta (β) is indeed used to estimate the population proportion (p) when conducting hypothesis testing on a sample. Beta represents the probability of making a Type II error, which occurs when we fail to reject a null hypothesis that is actually false. By calculating the probability of a Type II error, we indirectly estimate the population proportion, p, under certain conditions and assumptions.

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Answer:

can you send a more clear photo its quite blurry

Answer:

17

Step-by-step explanation:

it's sufficient to set x=7

g(7)=2×7+3=14+3=17

Answer:

g(7)=2.7+3=17