Please help I will give brainliest.

Given:

The two points are (-1,10) and (2,4).

To find:

The equation of line which passes though the given points.

Solution:

If a line passes through two points, then the equation of line is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

The line passes through (-1,10) and (2,4). So, the equation of line is

\(y-10=\dfrac{4-10}{2-(-1)}(x-(-1))\)

\(y-10=\dfrac{-6}{2+1}(x+1)\)

\(y-10=\dfrac{-6}{3}(x+1)\)

\(y-10=-2(x+1)\)

Using distributive property, we get

\(y-10=-2x-2\)

Adding 10 both sides, we get

\(y=-2x-2+10\)

\(y=-2x+8\)

Therefore, the required equation of line is \(y=-2x+8\).

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

\(\textsf{C.} \quad \dfrac{3}{4x^{\frac{1}{4}}\left(1+x^{\frac{3}{2}}\right)}\)

Step-by-step explanation:

To find the derivative of the given function, we can use the inverse tangent differentiation rule.

\(\boxed{\dfrac{\text{d}}{\text{d}x}\; \tan^{-1}(g(x))=\dfrac{g'(x)}{1+(g(x))^2}}\)

Given function:

\(f(x)=\tan^{-1}\left(x^{\frac{3}{4}}\right)\)

\(\textsf{Therefore, let $g(x)=x^{\frac{3}{4}}$}.\)

First, differentiate the part in the brackets by using the rule for differentiating xⁿ:

\(\boxed{\begin{minipage}{4.5 cm}\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}\)

\(\begin{aligned}g(x)=x^{\frac{3}{4}} \implies g'(x)&=\dfrac{3}{4}x^\left({\frac{3}{4}-1}\right)\\\\g'(x)&=\dfrac{3}{4}x^{-\frac{1}{4}}\\\\g'(x)&=\dfrac{3}{4x^{\frac{1}{4}}}\end{aligned}\)

Now apply the inverse tangent differentiation rule:

\(\begin{aligned}f'(x)&=\dfrac{\dfrac{3}{4x^{\frac{1}{4}}}}{1+\left(x^{\frac{3}{4}}\right)^2}\\\\&=\dfrac{3}{4x^{\frac{1}{4}}\left(1+\left(x^{\frac{3}{4}}\right)^2\right)}\\\\&=\dfrac{3}{4x^{\frac{1}{4}}\left(1+x^{\frac{6}{4}}\right)}\\\\&=\dfrac{3}{4x^{\frac{1}{4}}\left(1+x^{\frac{3}{2}}\right)}\\\\\end{aligned}\)

Answer:

i) The probability of getting 50 cent coin is 5/18, or approximately 28%

ii) To scale the numbers up to let us have 65 fifty cent coins, there would be a total of 234 coins

Step-by-step explanation:

We are told the probability of choosing ten and 20 cent coins, and from that we can work out the probability for the 50 cent coin.  All we need to do is add up the other two probabilities and subtract them from 1.

\(p = 1 - (\frac{1}{3} + \frac{7}{18})\\p = 1 - (\frac{6}{18} + \frac{7}{18})\\p = 1 - \frac{13}{18}\\p = \frac{5}{18}\\\)

So the chance of getting a 50 cent coin is five eighteenths, or approximately 28%

For the second question We are asked to find the total number of coins if there are 65 fifty cent coins. (I can't see the text below that, but presumably it's saying that the ratios will stay the same).

We can solve this by comparing the two ratios, with x as the total, and solving for x:

\(\frac{5}{18} = \frac{65}{x}\\5x = 65 * 18\\x = 13 * 18\\x = 234\)

So to keep the same ratios and have 65 fifty cent coins, we would need a total of 234 coins.

Answer:

Step 1!

Step-by-step explanation:

I dont know if this is correct but she is supposed to add the numbers on top for a new top number in step two.

( 9 + 2(the top number) x 4)

Hope this helps!

Sorry if its wrong :(

Answer:

step 2................

Based on the information given, the amount that he'll be expected to save in 30 years will be $83.

From the question given, since Buzz had $47 and had been saving for 17 years, the amount saved per year will be:

= $47/17

= $2.7647

Therefore, the amount that'll be saved in 30 years will be:

= 30 × $2.7647

= $82.941

= $83

The amount saved will be $83.

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Answer: where is the figure tot he right???

Step-by-step explanation:

Answer:

I believe it is: P(F|B) = 0.51; given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.

Step-by-step explanation:

26/51=0.509

Round up to 0.51

The conditional order P(A|B) means that given that A is occurring, what's the probability that B occurs. Thus giving me answer A. Given that B is the preferred brand, what's the probability of freestyle being the strongest stroke. 0.51

P(F|B) = 0.51 Given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.

In order to create scientific investigations, sample surveys, medical clinical trials, and environmental research, applied statistics uses mathematical principles and techniques. In many businesses, analysis and forecasting are made possible by the application of mathematical models of variation.

In this problem, there are two different values of P(F|B) 0.51 and 0.58 as per the option given below. we will solve both and find the most preferable. Since the Strongest stroke is directly proportional to the P(F|B) so the value of stoke when P(F|B) is 0.58 will be lesser than the value of stoke at 0.51. Hence we will solve this for 0.51

26/51=0.509

Round up to 0.51

Therefore, The conditional order P(A|B) means that given that A is occurring. Thus giving me answer A. Given that B is the preferred brand. the probability of freestyle being the strongest stroke is 0.51.

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Using the concepts of Application of derivative, we got that 1657.92inches³/sec rate  of the  volume of the cone changing when the radius is 40 inches and the height is 40 inches for a right circular cone.

We know that volume of right circular cone is given by =(1/3πr²h)

We are given rate of change of radius(dr/dt) and rate of change of the height(dh/dt)

Therefore ,differentiating the volume with respect to time and applying the chain rule.

dV/dt = [(1/3)πr²×(dh/dt)+ (1/3)π·2·r·(dr/dt)·h]

=>dV/dt=[(1/3)× π×r × [(r×dh/dt)+2h×(dr/dt)]]

We are given that dr/dt=2inc/sec and dh/dt= -5inc/sec

So, on putting the values, we get

=>dV/dt=[ ( (1/3)×3.14×40)×[40×(-5)+2×40×2]]

=>dV/dt=[0.33×3.14×40×[-200+160]

=>dV/dt=[0.33×3.14×40×(-40)]

=>dV/dt= -1657.92inches³/sec(negative sign denote volume is decreasing)

Hence, if the radius of a right circular cone is increasing at the rate of 2 inches per second and its height is decreasing at the rate of 5 inches per second.  the rate of  the volume of the cone changing when the radius is 40 inches and the height is 40 inches is 1657.92inches³/sec.

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The point which is located on the ray PQ as required in the task content given that the points M, N, O, P, Q, R, S are collinear is; point R.

It follows from the task content that the point which is located on the ray PQ is to be identified among the given answer choices.

Since all points given are said to be contained on a line, it can therefore be inferred that the points are collinear.

Also, by the definition of a ray; it follows that the ray PQ is one which starts from P and goes through Q and continues in the direction of Q.

Ultimately, the point which is located on such ray as described above among the answer choices is the point R.

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Answer:

Point R

Step-by-step explanation:

The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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Answer: C. cosx/2

Step-by-step explanation:

Answer:

cos x/2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

-2^4-5(5)+2(-2-3)^2

16-25+2(25)

16-25+50

41

Answer:

x = -2

y = -4

Step-by-step explanation:

The way systems of equations  work is that you have to substitute to solve for a variable *(only one of the 2 ways to figure this out)*

so, we will use addition property of equality in a form to add the two equations together, since +5y and -5y added together will cancel out.

that would leave

5x = -10

divide both sides by 5

x = -2

Now that we know x = -2, we can plug in -2 into one of the equations to find y.

2 ( -2)  + 5y = -24

-4 + 5y = -24

-4 + 4 + 5y = -24 + 4

5y = -20

y = -4

x = -2

y = -4

To create the masshaul diagram and calculate the cuts and fills, we need additional information about the reference plane or benchmark level.

Additional data or a reference level is needed to accurately calculate cuts and fills and create the masshaul diagram based on the given stake values and ground heights.

The given data provides the ground height at various stake values, but without a reference point, it is not possible to determine the actual elevation changes and calculate the cuts and fills accurately.

Please provide the reference level or any additional data necessary for calculating the elevation differences.

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Answer:

z =  4.90131578

Step-by-step explanation:

Answer:

9.8z + 113.3

Step-by-step explanation:

Combine like terms!

12.5z - 2.7z = 9.8z

19.4 + 93.9 = 113.3

Given that the test result is positive, we need to find the probability that the person actually has cancer. Let's denote the event of having cancer as C and the event of a positive test result as T. We want to find P(C|T), the conditional probability of having cancer given a positive test result.

According to the problem, the probability of a positive test result given that a person has cancer is P(T|C) = 0.95. The probability of a positive test result given that a person does not have cancer is P(T|C') = 0.1.

To calculate P(C|T), we can use Bayes' theorem, which states that:

P(C|T) = (P(T|C) * P(C)) / P(T)

P(C) represents the probability of having cancer, which is given as 0.003 in the problem.

P(T) represents the probability of a positive test result, which can be calculated using the law of total probability:

P(T) = P(T|C) * P(C) + P(T|C') * P(C')

P(C') represents the complement of having cancer, which is 1 - P(C) = 1 - 0.003 = 0.997.

Substituting the given values into the equations, we can find P(T) and then calculate P(C|T) using Bayes' theorem.

P(T) = (0.95 * 0.003) + (0.1 * 0.997)

Finally, we can find P(C|T) by substituting the values of P(T|C), P(C), and P(T) into Bayes' theorem.

P(C|T) = (0.95 * 0.003) / P(T)

By performing the necessary calculations, we can determine the probability that the person actually has cancer given a positive test result.

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Answer:

-5

Step-by-step explanation:

9+6-2*10

15-20

= -5

The scale factor for the model of the elephant is 1 : 30 (option A).

A scale drawing is either a smaller or a larger version of an original image. For example, a map is a smaller version of a city, country or area.

A scale factor provides information on the relationship that exists between the scale drawing and the actual image. The scale factor shows the rate of reduction or enlargement of the original image.

Scale factor = actual length of the elephant / length of the elephant in the model

216 / 7.2 = 30

The scale factor is 1 : 30

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A:  10x + 8 = 3(x – 2)

    10x + 8 = 3x – 6

    7x =  – 14

    x = -2

The teacher's goal in introducing students to a card game where they must find the missing addend could be to develop and enhance their algebraic reasoning skills.

By presenting the problem as a puzzle or game, the teacher aims to engage the students in a fun and interactive way while fostering their ability to think critically and solve mathematical problems. The game helps students practice identifying the missing addend and applying algebraic thinking to find the solution. Additionally, it promotes the development of problem-solving strategies, logical reasoning, and the ability to generalize mathematical patterns, which are foundational skills in algebraic reasoning.

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Answer:

B. Corresponding Angles

Step-by-step explanation:

If it's asking for just one answer, this is the right answer.

The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).

In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.

A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.

When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.

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Answer:

x = 75.7 cm

Step-by-step explanation:

sin = opp/hyp

sin63 = x/85

multiply both sides by 85

85 * sin63 = x

Use calculator

75.735554556011268 = x

Rounded

x = 75.7 cm

If A = PDP⁻¹ = , Then  \(A^k = (PDP^{-1})^{k}\)  

                   =  \(PDP^{-1} PDP^{-1} .... PDP^{-1}\) = \(PD^{k}P^{-1}\)

since P⁻¹ P = I, the identity matrix.

The term identity matrix is ​​also widely used, but the term identity matrix is ​​now standard. The term identity matrix is ​​ambiguous, as it is also used for any unit of a matrix and ring of all n × n matrices.

In some fields, such as group theory or quantum mechanics, the identity matrix is ​​sometimes shown in bold, or called "id" (short for identity). Less commonly, some math books use U or E for identity matrix, which stands for "identity matrix" and the German word Einheitsmatriks, respectively.

So for A = PDP⁻¹ is given by:

\(\left[\begin{array}{ccc}a&0&\\7(a-b)&b&\ \end{array}\right] = \left[\begin{array}{ccc}1&0&\\7&1&\\\end{array}\right] \left[\begin{array}{ccc}a&0&\\0&b&\ \end{array}\right] \left[\begin{array}{ccc}1&0&\\-7&1&\\\end{array}\right]\)

we have

\(\left[\begin{array}{ccc}a&0&\\7(a-b)&b&\ \end{array}\right] ^k = \left[\begin{array}{ccc}1&0&\\7&1&\\\end{array}\right] \left[\begin{array}{ccc}a&0&\\0&b&\ \end{array}\right] ^k \left[\begin{array}{ccc}1&0&\\-7&1&\\\end{array}\right]\)

                               = \(\left[\begin{array}{ccc}1&0&\\7&1&\\\end{array}\right] \left[\begin{array}{ccc}a^k&0&\\0&b^k&\ \end{array}\right] \left[\begin{array}{ccc}1&0&\\-7&1&\\\end{array}\right]\)

Then computing the matrix multiplication, we have:

\(\left[\begin{array}{ccc}1&0&\\7&1&\\\end{array}\right] \left[\begin{array}{ccc}a^k&0&\\0&b^k&\ \end{array}\right] \left[\begin{array}{ccc}1&0&\\-7&1&\\\end{array}\right] = \left[\begin{array}{ccc}a^k&0&\\7a^k&b^k&\\\end{array}\right] \left[\begin{array}{ccc}1&0&\\-7&1&\\\end{array}\right]\)

                                                              = \(\left[\begin{array}{ccc}a^k&0&\\7a^k-7b^k&b^k&\\\end{array}\right] = A^k\)

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The distance between two raisins will increase by a factor of the square root of 2.

As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.

However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.

This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.

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A(v1 + v2) = [56, 7].

We are given that the eigenvectors of the matrix A are v1 = [-2, 3] and v2 = [3, 2] and the eigenvalues of the matrix are λ1 = -4 and λ2 = 3 respectively.

To find the value of A(v1 + v2), we need to first find v1 + v2 and then substitute it into the equation A(v1 + v2).

So, v1 + v2 = [-2, 3] + [3, 2] = [1, 5]

Now, we can substitute this value into the equation A(v1 + v2) as follows:

A(v1 + v2) = A([1, 5])= A(1[-2, 3] + 5[3, 2])

Using the properties of matrix multiplication, this can be written as follows:

A(v1 + v2) = 1A[-2, 3] + 5A[3, 2] = -2A[1, 0] + 3A[0, 1] + 15A[1, 0] + 10A[0, 1]

Now, since v1 and v2 are eigenvectors of A, we know that A(v1) = λ1v1 and A(v2) = λ2v2

Substituting these values, we get:

A(v1 + v2) = -2λ1v1 + 3λ2v2 + 15v1 + 10v2 = -2(-4)[-2, 3] + 3(3)[3, 2] + 15[-2, 3] + 10[3, 2]= [56, 7]

Hence, A(v1 + v2) = [56, 7].

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