Find the gradient of a line perpendicular to the longest side of the triangle formed by A(-3,4),B(5,2) and C(0,-3)

Answer:

  0.13

Step-by-step explanation:

You want the probability that a point in the figure lies in the red shaded area.

The desired probability is the ratio of the red area to the entire area.

The red area is half a 4×4 square, so is (4×4)/2 = 8 square units.

The area of the whole figure is that of an 8×8 square, so is (8×8) = 64 square units.

The ratio of the areas is ...

  red/whole = 8/64 = 1/8 = 0.125 ≈ 0.13

The probability that a randomly selected point falls in the red area is about 0.13.

<95141404393>

Answer:

Step-by-step explanation:

dior dior

To find the equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3), follow these steps: 1. Find the derivative of the function: dy/dx r,

Represents the slope of the tangent line at any point (x, y) on the curve.
y = 9x - (6/x)
dy/dx = d(9x)/dx - d(6/x)/dx

Using the power rule for the first term and the quotient rule for the second term:
dy/dx = 9 - (-6/x^2)
dy/dx = 9 + 6/x^2

2. Find the slope of the tangent line at the given point (1, 3) by plugging x = 1 into the derivative:
m = 9 + 6/1^2
m = 9 + 6
m = 15

3. Use the point-slope form of a linear equation to find the equation of the tangent line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (1, 3) and m is the slope:
y - 3 = 15(x - 1)

4. Solve for y to get the equation of the tangent line:
y = 15(x - 1) + 3
y = 15x - 15 + 3
y = 15x - 12

The equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3) is y = 15x - 12.

To know more about derivative click here

brainly.com/question/29096174

#SPJ11

Answer:

If this is the full question, 60x

Step-by-step explanation:

Let x = # of liters leaked per minute.  There are 60 minutes in an hour.

If this isn't the full question and you forgot to write the # of liters leaked per minute, just multiply that number by 60.

The constant of proportionality is expressed as a fraction in reduced terms as: k = 1/9.

The constant of proportionality is a constant which represents the rate at which one variable vary directly with another variable, proportionately.

For example, if x and y are the two variables, and y is dependent on x, therefore:

Constant of proportionality (k) = y/x.

The table given as shown in the attachment shows a relationship between v and w. Therefore, we have:

Constant of proportionality (k) = 16/144 = 7/63 = 4/36

Constant of proportionality (k) = 1/9

Learn more about Constant of proportionality on:

https://brainly.com/question/1835116

#SPJ1

Answer:

504

Step-by-step explanation:

use pemdas

multiply 8 and 7 first then u have 56 so multiply it by 9

The expression 9x (8x7) can be rewritten as (9x8) x7 or 72x7 by using the associative law of multiplication. This law states that the way numbers are grouped doesn't affect the result of multiplication.

The question asks to rewrite 9x (8x7) using the associative law of multiplication. The associative law of multiplication, in basic terms, states that the way in which numbers are grouped in multiplication does not change the result.

To apply this law to the given expression, we just need to change the grouping of the numbers. Instead of grouping (8x7) together, we could group (9x8) together. So, the content loaded rewrite of 9x (8x7) using the associative law of multiplication would be: (9x8) x7 or we can write it as 72x7.

This does not change the result of the multiplication, thus demonstrating the associative property. This is a helpful principle to understand, as it is commonly applied in a variety of mathematical operations and can simplify complex equations.

https://brainly.com/question/35585926

#SPJ2

The measure of <1 is 80 and <2 is 100 degree.

we have,

m<1 (4 x + 12)° and m <2 = (6x - 2)°

As, <1 and <2 are in linear pair then

m<1 + m<2 = 180

4x+ 12 + 6x -2= 180

10x + 10 = 180

10x= 170

x= 170/10

x= 17

Thus, the measure of each angle is

m <1 = 4x+ 12 = 68 + 12=  80

m<2= 6x-2 = 102-2= 100

Learn more about  Linear Pair here:

https://brainly.com/question/17525542

#SPJ1

To mitigate this risk, the algorithm is often run multiple times with different starting points, and the solution with the highest likelihood is chosen.

The EM algorithm is an iterative method for maximum likelihood estimation when some of the data is missing or unobserved. The algorithm works by alternately updating estimates of the unobserved data and the model parameters until convergence.

It can be proven that the EM algorithm monotonically increases the likelihood of the data at each iteration. This means that the likelihood of the data cannot decrease as the algorithm progresses, and therefore the algorithm is guaranteed to converge to a local maximum of the likelihood function.

To see why the likelihood of the data increases at each iteration, consider the E-step and the M-step of the algorithm. In the E-step, the algorithm estimates the expected value of the unobserved data given the observed data and the current estimates of the model parameters. In the M-step, the algorithm updates the estimates of the model parameters based on the expected values of the unobserved data.

The likelihood of the data is a function of the model parameters, and it can be shown that the expected value of the log-likelihood function increases at each iteration of the EM algorithm. This is because the E-step maximizes the expected value of the log-likelihood function with respect to the unobserved data, and the M-step maximizes the expected value of the log-likelihood function with respect to the model parameters. Since the expected value of the log-likelihood function is a lower bound on the actual log-likelihood function, the likelihood of the data increases at each iteration.

The monotonically increasing property of the EM algorithm has important implications for its convergence. Since the likelihood of the data is guaranteed to increase at each iteration, the algorithm is guaranteed to converge to a local maximum of the likelihood function. However, the algorithm may converge to a suboptimal local maximum, depending on the starting point of the algorithm and the shape of the likelihood function. To mitigate this risk, the algorithm is often run multiple times with different starting points, and the solution with the highest likelihood is chosen.

To learn more about implications visit:

https://brainly.com/question/14410475

#SPJ11

The surface area of the cylinder with radius of 3.2 in and height of 7 in is 205 in²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The surface area of a cylinder is:

Surface area = (2π * radius * height) + (2π * radius²)

The radius is 3.2 inches and the height is 7 inches, hence:

Surface area = (2π * 3.2 * 7) + (2π * 3.2²) = 205 in²

The surface area of the cylinder is 205 in²

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Boolean algebra, truth tables, and logic diagrams are the three methods of Boolean functions.

The three methods to express the logical behavior of Boolean functions are:

1. Boolean algebra: This method uses algebraic expressions with binary variables and operators such as AND, OR, and NOT to represent the logical behavior of a Boolean function.

2. Truth tables: A truth table is a tabular representation of all possible input combinations and their corresponding output values for a given Boolean function. Each row in the table represents a unique input combination, and the corresponding output value is the result of applying the Boolean function to that input.

3. Logic diagrams: Also known as logic gates or circuit diagrams, these graphical representations use symbols to illustrate the logical relationships between input and output variables. Common symbols include AND, OR, and NOT gates, which represent the fundamental Boolean operations.

By utilizing these methods, you can effectively express and analyze the logical behavior of Boolean functions in a variety of scenarios.

Learn more about boolean functions here:

https://brainly.com/question/7581378

#SPJ11

The main difference between sequential and combinational circuits is that sequential circuit have internal memory and state, while combinational circuits do not.

Sequential circuit and combinational circuits are both types of digital circuits that are used in electronics and computer engineering. The main difference between the two is that sequential circuits use feedback and memory elements to store and propagate information, while combinational circuits do not.

Combinational circuits are made up of logic gates that are connected together to perform a specific function, such as addition or subtraction. The output of a combinational circuit depends only on the current inputs, and there is no internal memory or state.

In contrast, sequential circuits use feedback to store and propagate information, and the output of a sequential circuit depends not only on the current inputs but also on the past inputs and the internal state of the circuit. Sequential circuits include flip-flops, registers, and counters, which are used to store and manipulate data over time.

In summary, the main difference between sequential and combinational circuits is that sequential circuits have internal memory and state, while combinational circuits do not.

Learn more about circuit here:

https://brainly.com/question/14213253

#SPJ11

The probability that the team will have exactly 8 turnovers during a game is approximately 0.035 or 3.5%.

Given that the number of turnovers per game follows the Poisson distribution and the team averaged 18 turnovers per game, we can use the Poisson distribution formula to find the probability of the team having exactly 8 turnovers during a game.

The Poisson distribution formula is: P(X = x) = (e^-λ * λ^x) / x!, where λ is the average number of turnovers per game and x is the number of turnovers we want to find the probability for.

a. Using the given information, we have: λ = 18 and x = 8.

Plugging these values into the formula, we get:

P(X = 8) = (e^-18 * 18^8) / 8!

Using a calculator, we can simplify this to:

P(X = 8) ≈ 0.035

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

The calculated amount paid by Leroy is 4.75

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

Ticket = 5

Reduction = A quarter

using the above as a guide, we have the following:

Amount paid = 5 - A quarter

Evaluate

Amount paid = 4.75

Hence, the amount paid = 4.75

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

Therefore, the probability of observing 8 occurrences of the event in a 10-minute interval is about 10.49%.

The Poisson distribution with a mean of 5.1 occurrences over a 10-minute interval can be used to model the number of occurrences of an event in that interval. The probability of observing k occurrences in this interval is given by the following formula:

[tex]P(X=k) = (e^(-λ) * λ^k) / k![/tex]

where λ is the mean number of occurrences over the interval.

In this case, we want to find the probability of observing 8 occurrences in 10 minutes, so we can plug in λ=5.1 and k=8 into the formula above:

[tex]P(X=8) = (e^{(-5.1)} * 5.1^8) / 8![/tex]

Using a calculator or software, we can evaluate this probability to be approximately 0.1049, or about 10.49%.

To know more about poisson random variable,

https://brainly.com/question/29350065

#SPJ11

"A researcher is curious about the average IQ of all currently registered voters in the state of Iowa. If the average could be attained, it would be an example of a population parameter."

In statistical terms, a population parameter refers to a characteristic of a whole population. In this case, the researcher is interested in the average IQ of all registered voters in Iowa, which would be a population parameter. The researcher would need to gather IQ data from every registered voter in the state and calculate the mean IQ to obtain the population parameter.

However, it's important to note that obtaining the true population parameter is often impractical or impossible due to logistical constraints, so researchers typically rely on samples to estimate population parameters with a certain level of confidence.

This question should be provided as:

Learn more about population parameter: https://brainly.com/question/28175212

#SPJ11

Once the activity is completed, facilitate a discussion among the students to analyze the differences between their predictions and the actual results. This will help reinforce the concept of probability and its properties in their minds.

The teacher should take the following approach with the students who opted to skip the prediction step:

1. Remind the students of the importance of making predictions in the context of probability and its properties. Predictions help them understand the expected outcomes and compare them with the actual results.

2. Instruct the students to pause their coin flipping and return to the prediction step. Ask them to predict the outcomes of the 10 flips, considering the possible results (HH, HT, TH, or TT).

3. After the students have made their predictions, encourage them to resume flipping the coins and recording their findings in a frequency chart.

To learn more about probability visit;

https://brainly.com/question/30034780

#SPJ11

Since the p-value is less than the significance level of 0.08, we reject the null hypothesis and conclude that there is enough evidence to show that the proportion of Australians in November 2013 who believe unemployment would increase is lower than the proportion who felt it would increase in July 2013 at the 8% level of significance.

To determine if there is enough evidence to show that the proportion of Australians in November 2013 who believe unemployment would increase is lower than the proportion who felt it would increase in July 2013, we need to perform a hypothesis test.

Let p1 be the proportion who thought unemployment would increase in July 2013 and p2 be the proportion who thought unemployment would increase in November 2013.

The null hypothesis is that there is no difference between the two proportions: p1 = p2. The alternative hypothesis is that the proportion in November 2013 is lower than the proportion in July 2013: p2 < p1.

We can use a two-sample z-test to test this hypothesis, since we have two independent samples and the sample sizes are large enough.

The test statistic is calculated as:

z = (p1 - p2) / √(p * (1 - p) * (1/n1 + 1/n2))

where p = (x1 + x2) / (n1 + n2) is the pooled proportion, x1 and x2 are the number of people who thought unemployment would increase in July 2013 and November 2013, respectively, and n1 and n2 are the sample sizes.

Using the given data, we have:

p1 = 0.47

p2 = 338/800 = 0.4225

n1 = n2 = 800

p = (8000.47 + 8000.4225) / (800 + 800) = 0.44625

z = (0.47 - 0.4225) / √(0.44625 * (1 - 0.44625) * (1/800 + 1/800))

= 3.373

Using a standard normal distribution table or calculator, we find that the p-value for a one-tailed test with a z-score of 3.373 is less than 0.01.

To know more about proportion,

https://brainly.com/question/16454354

#SPJ11

Answer:

no

Step-by-step explanation:

We can get a common denominator to compare fractions

19 * 2 = 38

1/2 * 19/19 = 19/38

This means the fractions are not equal

Answer: no

Step-by-step explanation:

No because 17/38 cannot be reduced to 1/2

Reduced meaning divided by same on top and bottom

17/34 is 1/2   because both top 17 and bottom 34 can be divided by 17 and reduced down to 1/2

25. If point A is the incenter then point A is the point of concurrence of the  angle bisectors of a triangle

26. ST = 15

27. x = 8

28. ∠ QRT = 24 degrees

29. ∠ RPT = 31 degrees

This is a point where the angle bisectors of the triangle intersect. The incenter is also the center of the circle

since incenter is the center of the triangle therefore

ST = WT = UT = 16

The incenter is meeting point of angle bisectors too hence we have that

∠ QRT = ∠ PRT = 24 degrees.

Also, ∠ RPT = ∠ RPQ / 2 = 62 / 2 = 31 degrees

Learn more about incenter at

https://brainly.com/question/1831482

#SPJ1

Answer: )Step-by-step explanation:

When you say that the matrices form a basis for the linear space, I assume you mean that they form a basis for the vector space of matrices with the same dimensions.

To write the matrix of the linear transformation relative to the given basis, follow these steps:

1. Identify the basis matrices for the linear space.
2. Apply the linear transformation to each basis matrix.
3. Express the transformed matrices as linear combinations of the basis matrices.
4. Write the coefficients of these linear combinations as columns in the matrix of the linear transformation.

By following these steps, you will have the matrix of the linear transformation relative to the given basis. Note that I cannot provide specific numbers or examples since no specific matrices or transformations were provided in your question.

To learn more about coefficients visit;

https://brainly.com/question/28975079

#SPJ11

2x - 8 = 2(2x - 15) and 11 are the correct equation and answer respectively.

The given diagram is a triangle. From the figure, the triangles QLK is similar to triangle QRP.

Hence, the correct expression to solve for x will be:
RP = 2LK

Substitute the expression given

RP = 2x - 8

LK = 2x - 15

Substitute to have:

2x - 8 = 2(2x - 15)

Simplify to have:

2x - 8 = 4x - 30

2x - 4x = -30 + 8

-2x = -22

x = 11

Hence the correct equation and answer to solve for x using the triangle are 2x - 8 = 2(2x - 15) and 11 respectively.

Learn more on similar triangles here: https://brainly.com/question/30104125

#SPJ1

In this context, a type I error would occur if the null hypothesis was rejected when it is actually true, meaning that the patient does not have the disease but is diagnosed with it.

This would be a false positive result. It is important to note that a type I error is related to the level of significance chosen for the hypothesis test, and it represents the probability of rejecting the null hypothesis when it is true.

In this case, if the level of significance was set at 0.05, for example, there would be a 5% chance of making a type I error. It is also important to consider the consequences of making a type I error in a medical context, as it could lead to unnecessary treatments or interventions that could harm the patient.

Therefore, it is crucial to carefully design hypothesis tests and choose appropriate levels of significance to minimize the risk of making such errors.

Learn more about error here:

https://brainly.com/question/30524252

#SPJ11

The amount of fabric needed to make the tent is given as follows:

C. 18,350 sq. in.

The amount of fabric needed is given by the surface area of the figure presented in this problem.

The surface area is given by the sum of all areas that compose the figure in the context of the problem.

The figure is composed as follows:

Hence the surface area is given as follows:

S = 198 x 75 + 2 x 0.5 x 50 x 70

S = 18,350 sq. in.

More can be learned about the surface area of a figure at https://brainly.com/question/29183306

#SPJ1

Answer:

Step-by-step explanation:

2(6-x)³ when x = 4

[tex]\mathrm{2\left(6-\left(4\right)\right)^3}[/tex]

Follow the PEMDAS order of operations:-

1) Parentheses:-

[tex]\mathrm{2\cdot \:2^3}[/tex]

2) Exponents:-

[tex]\mathrm{2\cdot \:8}[/tex]

3) Multiply:-

________________________

Hope this helps! :)

The amount of glass needed to cover the entire pyramid is given as follows:

144.53 ft².

The amount of glass needed to cover the entire pyramid is given by the surface area of the pyramid.

The surface area of any prism is given by the sum of the areas of all the parts of the prism.

The pyramid in this problem is composed as follows:

The areas are calculated as follows:

Hence the surface area of the pyramid is given as follows:

S = 7 x 6 + 2 x 0.5 x (7 x 7.79 + 6 x 8)

S = 144.53 ft².

More can be learned about the surface area of a pyramid at https://brainly.com/question/22744289

#SPJ1

The coordinates of the vertices of the dilated image, ΔR'S'T' include the following: A. R' (4, 12), S' (12, 12), T' (8, 4).

In Mathematics and Geometry, a dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 4 centered at the origin as follows:

Ordered pair R (1, 3) → Ordered pair R' (1 × 4, 3 × 4) = R' (4, 12).

Ordered pair S (3, 3) → Ordered pair S' (3 × 4, 3 × 4) = S' (12, 12).

Ordered pair T (2, 1) → Ordered pair T' (2 × 4, 1 × 4) = T' (8, 4).

Read more on dilation and scale factor here: https://brainly.com/question/4421026

#SPJ1

The angle that has a cosine of 3/5 is: ∠A

The three main trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

The given fraction is actually 3/5. This can also be written as 6/10. Thus:

From the given triangle, we can say that:

cos A = 6/10

Thus, it represents angle A.

Read more about trigonometric ratios at: https://brainly.com/question/13276558

#SPJ1

-5, view below for what Maureen did wrong.

Given:

   -1.2+(-3.8)

A positive times a negative is a negative:

   -1.2-3.8

Subtract:

   -5

   Instead of distributing the positive sign into the -3.8 and subtracting, Maureen added 1.2 to -3.8, leading to -2.6 instead of -5.

Answer:

[tex]C.\quad \dfrac{\sqrt{17}}{6}[/tex]  

Step-by-step explanation:

We are given
[tex]\tan\theta = - \dfrac{\sqrt{19}}{\sqrt{17}} \\\\[/tex]

Square both sides
[tex]\tan^2\theta = \left(- \dfrac{\sqrt{19}}{\sqrt{17}} \right)^2 = \dfrac{19}{17}[/tex]

[tex]\tan \theta = \dfrac{\sin\theta}{\cos\theta}\\\\\tan^2 \theta = \dfrac{\sin^2\theta}{\cos^2\theta}\\[/tex]

Substituting for [tex]tan^2 \theta[/tex] and switching sides we get

[tex]\dfrac{\sin^2\theta}{\cos^2\theta} = \dfrac{19}{17}\\\\\text{Add 1 to both sides:}\\\\ \\ \dfrac{\sin^2\theta}{\cos^2\theta} + 1 = \dfrac{19}{17} + 1 \\\[/tex]

[tex]\dfrac{\sin^2\theta + cos^2\theta}{\cos^2\theta} = \dfrac{19 + 17}{17} = \dfrac{36}{17}[/tex]

[tex]\sin^2\theta + cos^2\theta = 1[/tex]

giving

[tex]\dfrac{1}{\cos^2\theta} = \dfrac{36}{17}[/tex]

[tex]\dfrac{17}{36} = \cos^2\theta\\\\ \cos^2\theta = \dfrac{17}{36}\\\\ \cos\theta = \sqrt{\dfrac{17}{36}}\\\\ \cos\theta = \dfrac{\sqrt{17}}{6} \\\\[/tex]

This is choice C. You had it right

(a) Therefore, the z-value for an area of 0.08 to the right of z is -1.41. (b) Therefore, the z-value for an area of 0.025 to the right of z is -1.96. (c) Therefore, the z-value for an area of 0.05 to the right of z is -1.64. (d) Therefore, the z-value for an area of 0.10 to the right of z is -1.28.

To answer this question, we need to use the standard normal distribution table (also called the z-table or appendix table). This table gives the area under the standard normal curve to the left of a given z-value.
(a) To find the z-value for an area of 0.08 to the right of z, we can subtract the area from 1 (since the total area under the curve is 1) to get the area to the left of z:
1 - 0.08 = 0.92
Using the standard normal distribution table, we can find the z-value that corresponds to an area of 0.92 to the left of z. This value is approximately 1.41.
(b) Following the same process, for an area of 0.025 to the right of z, we find:
1 - 0.025 = 0.975
Looking at the standard normal distribution table, we find that the z-value corresponding to an area of 0.975 to the left of z is approximately 1.96.
(c) For an area of 0.05 to the right of z, we get:
1 - 0.05 = 0.95

The z-value corresponding to an area of 0.95 to the left of z is approximately 1.64.
(d) Finally, for an area of 0.10 to the right of z, we have:
1 - 0.10 = 0.90
The z-value corresponding to an area of 0.90 to the left of z is approximately 1.28.

Learn more about standard normal distribution here:

https://brainly.com/question/31379967

#SPJ11