Find the values of A and B in each triangle
Show your work

Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

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A definite integral is said to be improper if one or both of the limits of integration are infinite, or if the integrand function has a vertical asymptote within the interval of integration.

In other words, an improper integral is one that cannot be evaluated using the usual techniques of integration, such as the fundamental theorem of calculus, because it involves infinite limits or a function that is not integrable over the interval.

For example, the definite integral of f(x) = 1/x from 1 to infinity is an improper integral because the upper limit of integration is infinity, which is not a finite number. Similarly, the definite integral of f(x) = ln(x) from 0 to 1 is an improper integral because the lower limit of integration is 0, and the function has a vertical asymptote at x=0.

To evaluate improper integrals, we use limit processes to determine whether the integral converges (has a finite value) or diverges (has an infinite value). If the integral converges, we can find its value by taking the limit of a related integral as one or both of the limits of integration approach infinity or zero.

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Answer:

600 square feet

Step-by-step explanation:

I notice it says "Estimate" in bold. Therefore, you would round all of the measurements. They're all pretty simple to round (to the nearest tens place). From here, you subtract the length of the large room from the length of both rooms. So, 50 - 30 = 20. This is the length of the small room. We now multiply this by the width of the small room (since area of a rectangle is length * width) and we get:

20 * 30 = 600, our final answer

Hope it made sense. I would appreciate Brainliest, but no worries.

If f = q (v x b) and v is perpendicular to b, then the direction of b will be perpendicular to both f and v.

The cross product, also known as the vector product, is a mathematical operation performed between two vectors in three-dimensional space. The result of the cross product is another vector that is perpendicular to both original vectors.

If we have the cross product (v x b) v is perpendicular to b, then the direction of b will be perpendicular to both f and v. This is because the cross product of two vectors, v x b, will result in a vector that is perpendicular to both of the original vectors. Therefore, the direction of b will be in a direction that is perpendicular to both f and v.

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when both are mixed and left to settle, they separate into two layers with oil on top and water underneath.

When a scientist pours two liquids into a flask and swirls the flask to combine the liquids, and then places the flask on a laboratory workbench, after a few seconds, the liquids separate into two layers.

This phenomenon is possible if the two liquids are immiscible.

The contents of the flask can be classified as immiscible liquids.

Immiscible liquids are liquids that do not mix to form a homogenous solution.

They separate into distinct layers instead. When two immiscible liquids are mixed together and then left to settle, they create a two-layer system, with one layer on top of the other.

In general, two liquids are said to be immiscible if the free energy change in mixing them is positive or if the entropy change in mixing them is negative.

A practical example of immiscible liquids is oil and water.

They are unable to mix with each other since oil is nonpolar while water is polar.

As a result, when both are mixed and left to settle, they separate into two layers with oil on top and water underneath.

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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(a) The distance traveled by motorcycle is 1548 ft.

(b) The distance traveled by motorcycle is 1512 ft.

(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.

What is velocity?

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.

Given table is:

t (s)        0       12      24     36     48      60

v (ft/s)   30      28     25     21      25      27

The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:

12(30 + 28 + 25 + 21 + 25)

=12 × 129

= 1548 ft

The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:

12(28 + 25 + 21 + 25 + 27)

=12 × 126

= 1512 ft

The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.

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The constant average rate of change is the slope of the line which can be used to write the linear function.

What is a Data Table ?

A table of data is linear if there is a constant average rate of change between all pairs of points.

Testing for Linearity

Finding a Function from a Table that is Linear

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Answer:

38 degrees

Step-by-step explanation:

By the Law of Cosines,

5² = 3² + 7² - 2(3)(7) cos A

5² - 3² - 7² = -2(3)(7) cos A

-33 = -42 cos A

cos A = 33/42

A = arccos(33/42), which is about 38 degrees.

The option B is correct answer which is ba-r(X) +/- 4.6.

What is Ma-rgin Er-ror?

The ma-rgin of er-ror is a statistic that describes how much ran-dom sa-mpling error there is in survey results. One should have less fa-ith that a p-oll's findings would accurately reflect those of a popu-lation census the higher the ma-rgin of er-ror.

If the ma-rgin of er-ror in an interval esti-mate of μ is 4.6, the interval esti-mates equals to ba-r(X) +/- 4.6.

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The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).

To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.

Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:

∂F/∂x = 3x² - 12

∂F/∂y = 3y² + 6y - 9

To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:

3x² - 12 = 0 --> x² = 4 --> x = ±2

3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1

Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).

To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:

∂²F/∂x² = 6x

∂²F/∂y² = 6y + 6

Now, let's evaluate the second partial derivatives at each critical point:

At (-2, -3):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.

At (2, -3):

∂²F/∂x² = 6(2) = 12 (positive)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.

At (-2, 1):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(1) + 6 = 12 (positive)

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.

Therefore, the critical points are classified as follows:

Local maximum: (-2, -3)

Saddle points: (2, -3) and (-2, 1)

Local minimum: (2, 1)

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d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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The probability that a student has a cat given that they do not have a dog is 2/29.

Let's call the event of having a cat "C" and the event of having a dog "D". We want to find the probability that a student has a cat given that they do not have a dog, which can be written as P(C | not D).

To find this probability, we first need to calculate the total number of students who do not have a dog. From the table, we can see that 7 students have a dog, so the total number of students who do not have a dog is:

Total number of students who do not have a dog = Total number of students - Number of students who have a dog

= 3 + 7 + 6 + 13

= 29

Next, we need to find the number of students who have a cat but do not have a dog. From the table, we can see that 6 students do not have a cat, so the number of students who have a cat but do not have a dog is:

Number of students who have a cat but do not have a dog = Number of students who have a cat - Number of students who have both a cat and a dog

= 3 - 1

= 2

Finally, we can use Bayes' theorem to calculate the probability of having a cat given that the student does not have a dog:

P(C | not D) = P(C and not D) / P(not D)

= 2 / 29

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The fraction that satisfies the problem is 20/24.

Equivalent fractions are fractions that have the same value, but different numerators and denominators.

If the fraction is equivalent to 5/6, then the numerator and denominator of the fraction is a multiple of 5 and 6, respectively.

Let x be the factor

fraction = 5x / 6x

If the sum of my numerator and my denominator is 44, then:

5x + 6x = 44

11x = 44

x = 4

fraction = 5x / 6x = 20/24

The final statement says that the sum of the digits in the denominator is 6.

2 + 4 = 6

Hence, the fraction is 20/24.

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The quantity of energy moved or transformed per unit of time is referred to as power. The amount of energy that is consumed by the hairdryer in 15 minutes will be 0.3 kWh.

The quantity of energy moved or transformed per unit of time is referred to as power.

Formula: Power = Energy / Time

Units: kW = kWh / hour

The power of electric equipment is given by the formula,

P = E/t

where E is the energy consumed in kWh and t is the time in hours.

Given the power of the hairdryer is 1.200 kW while the time for which it is kept on is 15 minutes, therefore, 0.25 hours. Now, the energy consumed by the dryer in 15 minutes will be,

1.200 kW = E / 0.25

0.3 kWh = E

Hence, the amount of energy that is consumed by the hairdryer in 15 minutes will be 0.3 kWh.

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Answer:

14

Step-by-step explanation:

always subtract the highest number from the lowest and I believe that is your range

Answer:

14

Step-by-step explanation:

The critical value for a left-tailed test of a population mean at the α = 0.01 level of significance, based on a sample size of n = 15, is -2.624.

To determine the critical value(s) for a left-tailed test of a population mean at the α = 0.01 level of significance based on a sample size of n = 15, we need to refer to the t-distribution table or use statistical software.

Since the sample size is small (n = 15) and the population standard deviation is unknown, we use the t-distribution instead of the standard normal distribution.

For a left-tailed test at the α = 0.01 level of significance, we need to find the critical t-value that corresponds to an area of 0.01 in the left tail of the t-distribution with n-1 degrees of freedom (df = 15 - 1 = 14).

Using a t-distribution table or statistical software, the critical t-value for a left-tailed test at the α = 0.01 level of significance with 14 degrees of freedom is approximately -2.624.

Therefore, the critical value for a left-tailed test of a population mean at the α = 0.01 level of significance, based on a sample size of n = 15, is -2.624.

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Answer:

12

Step-by-step explanation:

The number of particles in 1 mol of substance is given by the Avogadro's constant. Its value is: \(N_A\)= 6.02214076×10²³ mol⁻¹

The definition of Avogadro's constant is:

The Avogadro constant is the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in that sample. Its SI unit is the reciprocal mole, and it is defined exactly as

\(N_A\)= 6.02214076×10²³ mol⁻¹. (per mol).

Thus, the number of particles in 1 mol of substance is given by the Avogadro's constant. Its value is: \(N_A\)= 6.02214076×10²³ mol⁻¹

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The total amount get as a gross pay is $1,129.46.

It is required to find the gross pay.

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given that:

Gross pay is the total of basic salary plus any other payments such as bonuses, commissions, and overtime.

Regular salary = $984  per month

Overtime  rate= $10.39 per hour  x 14 hours

=$145.46

Gross pay =  $984 + $145.46

=$1,129.46

So, the total amount get as a gross pay is $1,129.46.

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Answer:

p = 12

Step-by-step explanation:

p ÷ 3 = 4

p = 12

Answer:

y = 4x - 16

Step-by-step explanation:

Plug in the slope and point into y = mx + b, and solve for b:

y = mx + b

-8 = 4(2) + b

-8 = 8 + b

-16 = b

Then, plug in b and the slope into y = mx + b

y = 4x - 16 is the equation in point slope form

9514 1404 393

Answer:

  y +8 = 4(x -2)

Step-by-step explanation:

Point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . line of slope m through point (h, k)

Filling in the given point and slope, you have ...

  y -(-8) = 4(x -2)

  y +8 = 4(x -2)

Answer:

C

Step-by-step explanation:

A triangle is 180 degrees so 120+40 is 160

180-160=20

(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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The Wald test is a statistical test that can be used to test the significance of a group of coefficients in a multiple regression model.

The test statistic is calculated as the ratio of the estimated coefficient to its standard error. If the test statistic is significant, then the null hypothesis that the coefficient is equal to zero can be rejected.

Suppose we have a multiple regression model with three independent variables: age, gender, and education. We want to test the hypothesis that the coefficients for age and education are both equal to zero. The Wald test statistic would be calculated as follows:

Test statistic = (Estimated coefficient for age) / (Standard error of estimated coefficient for age) + (Estimated coefficient for education) / (Standard error of estimated coefficient for education)

If the test statistic is significant, then we can reject the null hypothesis that the coefficients for age and education are both equal to zero. This would mean that there is evidence that age and education are both associated with the dependent variable.

The Wald test is a powerful tool that can be used to test the significance of a group of coefficients in a multiple regression model. However, it is important to note that the test statistic is only valid if the assumptions of the multiple regression model are met. If the assumptions are not met, then the p-value of the Wald test may be inaccurate.

Here are some of the assumptions of the multiple regression model:

* The independent variables are independent of each other.

* The dependent variable is normally distributed.

* The errors are normally distributed.

* The errors have constant variance.

If any of these assumptions are not met, then the Wald test may not be accurate.

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When a figure is rotated and reflected, the new figure will be congruent to the original one, but different coordinate axis. When a figure is translated, reflected and dilated the image will be similar, but the scales will be different.

The original figure we transform is the pre-image and after transformation it is called image. Rotation is the transformation of an image when it is rotated through the Centre of axis. Reflection creates a mirror image of the original figure/ pre-image. Translation means the image is moved to a certain distance in the coordinate axis. Dilation is making an image bigger or smaller, the sides will be in ratio and thee will be a scale factor.

So if a image is rotated, reflected and translated, there will be changes in the coordinate plane, but no change in the size of the image. During dilation the size is varied.

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Answer:

355 miles

Step-by-step explanation:

Figure out how far the car travelled in 1 hour - 3 hours can be divided by 3 for 1 hour, so do the same for the miles - 213 / 3 = 71 miles.

So we know the car travelled 71 miles in 1 hour.

Now just multiply the miles by 5 to figure out the answer - 71 * 5 = 355 miles

:)