What are the values of x and b? Inscribed Angles A) x=121, b=76 B) x=45, b=90 c) x=14, b=45 d)x=38, b=90

The solution to each equation is:

1. a = 5

2. x = 3

3. y = -1

4. z = 5

5. b = 6

To find the solution, we have to isolate the variable in each equation to one side.

1. 3(2a +5) +4(3a +1) = 109

Expand the brackets:

6a + 15 + 12a + 4 = 109

Collect like terms:

18a + 19 = 109

Subtract 19 from both sides:

18a = 90

Divide both sides by 18:

a = 5

2. 5(2x +3) +3(5x -2) = 84

Expand the brackets:

10x + 15 + 15x - 6 = 84

Collect like terms:

25x + 9 = 84

Subtract 9 from both sides:

25x = 75

Divide both sides of the equation by 25:

x = 3

3. 4(5y +3) -5(3y +1) = 2

Expand the brackets:

20y + 12 - 15y - 5 = 2

Collect like terms:

5y + 7 = 2

Subtract 7 from both sides:

5y = -5

Divide both sides by 5:

y = -1

4. 6(3z -2) +4(z -5)= 78

18z - 12 + 4z - 20 = 78

Collect like terms:

22z - 32 = 78

22z = 110

z = 5

5. 3(6b -1) -7(2b +3)=0​

18b - 3 - 14b - 21 = 0

4b - 24 = 0

4b = 24

Divide both sides by 4:

b = 6

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The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Answer:

16

Step-by-step explanation:

The figure shown is a trapezoid

Area of a trapezoid = 1/2(bottom base length + top base length) × height

Bottom base length = 7 units

Top base length = 1 unit

Height = 4 units

So area = 1/2 ( 7 + 1 ) × 4

==> add 7 and 1

Area = 1/2 (8) × 4

==> multiply 1/2 and 8

Area = 4 × 4

==> multiply 4 and 4

Area = 16

The number of one-liter bottles she can fill from 5 gallons is A = 19

Given data ,

Aisha brings 5 gallons of a sports drink to a game

Now , 1 liter≈ 4.2 cups

And , 1 gallon is approximately equal to 3.78541 liters.

So, 5 gallons is approximately equal to 5 * 3.78541 = 18.92705 liters

On simplifying the equation , we get

Now, we divide the total liters by 1 liter (the capacity of each bottle) to find the number of bottles Aisha can fill:

Number of bottles = 18.92705 liters / 1 liter ≈ 18.93

Hence Aisha can fill approximately 19 one-liter bottles with 5 gallons of sports drink

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Using the Integral Test, the correct choice is B. Since the integral ∫(k+7)dx diverges, the series also diverges.

We are supposed to use Integral Test to determine the convergence or divergence of the series, ∑(k+7)dx.

We can use the Integral Test to test for the convergence of series if the function in the series is continuous, positive, and decreasing for all x greater than or equal to some value N.

The Integral Test states that a series converges if and only if the integral of the series term is convergent, i.e. if the integral of u(x)dx is convergent. Also, if the integral of u(x)dx diverges, the series is divergent.

So we need to check whether the function in the given series is continuous, positive, and decreasing for all x greater than or equal to some value N.

If we integrate the series, ∑(k+7)dx, we get:∫(k+7)dx= ∫k

dx + ∫7dx= (k²/2) + 7x+ C

where C is the constant of integration.

Since the value of C is not given, we cannot say anything about the exact value of the integral.

However, the value of the constant of integration does not matter in this case as we only need to determine whether the integral converges or diverges.

Therefore, we can use the Integral Test to determine the convergence or divergence of the series.

Using the Integral Test, the correct choice is B.

Since the integral ∫(k+7)dx diverges, the series also diverges.

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Answer:

y=-3x+10

Step-by-step explanation:

slope = y2-x2/y1-x1

4-(-5)/2-5

9/-3

-3

y=-3x+b

Plug in 2,4:

4=-3(2)+b

4=-6+b

10=b

y=-3x+10

Hope this helps plz hit the crown :D

a)-Digit numbers can be formed from the digits

b) The total number of odd numbers is  x  = .

c) The total number of numbers greater than  is  x  = .

The number of -digit numbers that can be formed from the digits is given by the formula n!/(n-r)!, where n is the number of digits and r is the number of digits in the desired number. In this case, n =  and r = , so the formula becomes !/(!) = . Therefore,  -digit numbers can be formed from the digits .

To find the number of odd numbers, we need to consider the last digit of the number. Since there are odd digits (, , , , and ), there are  ways to choose the last digit. For the remaining  digits, there are  ways to choose each one. So the total number of odd numbers is  x  = .

To find the number of numbers greater than , we need to consider the first digit of the number. There are  digits greater than  (, , , , and ), so there are  ways to choose the first digit. For the remaining  digits, there are  ways to choose each one. So the total number of  number greater than  is  x  = .

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I hope this helps you with your question.

Answer:

m∠A=  115

Step-by-step explanation:

The required measure of the angle A is 115°.

Given that,
Two corresponding equal angles are given,
A = 4x - 13 and B = 3x + 19 all are in degrees.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is the angle?

The angle can be defined as the one line inclined over another line.

Here,
A = 4x - 13

B = 3x + 19

A = B
4x - 13 = 3x + 19
4x - 3x = 19 + 13
x = 32

Now the measures,
A = 4x -13

A = 4 * 32 - 13
A = 128 - 13
A = 115

Thus, the required measure of the angle A is 115°.

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Answer:

0.4

Step-by-step explanation:

Answer:

a. 1.00 minute (rounded to 2 decimal places)

b. 0.7568 (rounded to 4 decimal places)

c. 0.2432 (rounded to 4 decimal places)

Step-by-step Explanation:-

a. To calculate the expected arrival time, we multiply the total time range (3.7 minutes) by the probability of the elevator arriving at any given time within that range. Since the arrival time is equally likely at any time, the probability is uniformly distributed. Thus, the expected arrival time is:

Expected arrival time = (3.7 minutes) * (1/3.7) = 1.00 minute (rounded to 2 decimal places)

b. To find the probability that the elevator arrives in less than 2.8 minutes, we divide the desired time range by the total time range:

Probability = (2.8 minutes) / (3.7 minutes) = 0.7568 (rounded to 4 decimal places)

c. To find the probability that the wait for an elevator is more than 2.8 minutes, we subtract the probability from 1 since it is the complement event:

Probability = 1 - 0.7568 = 0.2432 (rounded to 4 decimal places)

Therefore, the probability that the wait for an elevator is more than 2.8 minutes is 0.243 (rounded to 3 decimal places).

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Answer:

B. 5x+3y=325

Step-by-step explanation:

the total value of the strawberries and blueberries sold is equal to 325. we have to multiple the variable for each fruit with the amount its sold for in order to get this equation.

Answer:

∠ AOB

Step-by-step explanation:

Answer:

Set 2 contains an outlier. The outlier would be 63. I would say the most affected measure of spread is the range.

Answer:

6^10

Step-by-step explanation:

We know that a^ -b = 1/ a^b

So 1/ a^-b = a^b

1/6^-10 = 6^10

Answer:

6¹⁰

Step-by-step explanation:

Whenever there is a negative exponent, switch its place between the vinculum (line). In this case, since there is a negative exponent in the denominator, move it up to the numerator and make the exponent positive.

Therefore, the answer is \(6^{10}\).

Consider a simulation that uses random numbers to represent inputs. the reason why confidence intervals are used to analyze simulation output is A. Because process output will vary randomly.

The output data that is obtained from a simulation model is analyzed for obtaining a valid statistical inference. The inference is obtained from the initial as well as the long-term behaviour of the system. The average is obtained from n number of replicate simulation runs. The analysis of the data that is generated by the simulation run is called “output analysis”. The analysis can be used for predicting the performance of the system or for comparing the performance of multiple system designs. Multiple simulation runs are required and necessary for stochastic simulation.

The output data that is obtained from the simulation runs exhibits random variability. It is produced when the random number generators are deployed. For instance, when two different and random number streams are used there will be two different sets of outputs. The confidence interval can be used for finding out the average (or mean) in such a scenario. The confidence interval will provide information between the expected value of a certain parameter (when the simulation is run infinite times) and the actual or real value/statistic obtained for a certain simulation.

The question is incomplete. The complete question is:

"Consider a simulation that uses random numbers to represent inputs. the reason why confidence intervals are used to analyze simulation output is:

A. Because process output will vary randomly.

B. Because the simulation code may not be 100% accurate for representing the process flow.

C. All of these reasons reasons

D. To account for inaccuracies in the simulation code."

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Answer:

y = 2

Step-by-step explanation:

Given

\(\sqrt[3]{3y+2}\) + 4 = 6 ( subtract 4 from both sides )

\(\sqrt[3]{3y+2}\) = 2 ( cube both sides )

3y + 2 = 2³ = 8 ( subtract 2 from both sides )

3y = 6 ( divide both sides by 3 )

y = 2

Answer:

|n - 1| + 1 = 0

|n - 1| = -1

no solution

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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Approximately 16% of the design is black.

Since the radius of each circle increases by 2 inches, the diameter of each circle increases by 4 inches. Thus, the diameter of the largest circle is 2 + 4(5) = 22 inches.

The area of each circle is proportional to the square of its radius, so the area of the smallest circle is π(\(2^2\)) = 4π square inches. The area of the second circle is π(\(4^2 - 2^2\)) = 12π square inches, the area of the third circle is π(\(6^2 - 4^2\)) = 20π square inches, and so on.

The total area of the design is the sum of the areas of all the circles, which is:

4π + 12π + 20π + 28π + 36π = 100π

The black area in the design consists of four quarter circles, each with a radius of 4 inches. The area of a one-quarter circle is:

(1/4)π(\(4^2\)) = 4π

So the total black area is 4 times this, or 16π.

The percent of the design that is black is:

(16π / 100π) x 100% ≈ 16%

Therefore, approximately 16% of the design is black.

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Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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The final answer for the unit normal vector at point P(-3,-1,27) for the function f(x,y)=x^3 is N = <-1, 0, 0>.

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Answer:

432 cm²

Step-by-step explanation:

Diagonal of Square = √2a

=> 12√6 = √2a

=> a = 12√6 / √2

=> a = 12√3 ( because √6 can be written as √2 × √3 , so √2 and √2 cancel out)

Now the Area = a²

= (12√3)²

= 144 × 3

= 432 cm²

Answer:

Below in bold.

Step-by-step explanation:

The diagonal forms 2 right triangles in the square,

Applying the Pythagoras Theorem to a triangle:

(12√6)^2 = x^2 + x^2     where x is the side of the square.

144*6 = 2x^2

x^2 (which is the area of the square)

= 144*6 / 2

= 144*3

= 432 cm^2.

When one of the stars in a spectroscopic binary system is moving toward the Earth in its orbit, we observe a shift in its spectral lines towards shorter wavelengths, known as a blue shift.

The shift in the spectral lines towards shorter wavelengths is caused by the Doppler effect. This effect occurs when there is relative motion between the source of the waves (in this case, the star) and the observer (in this case, the Earth). When the star is moving towards the Earth, the waves are compressed and the wavelength is shortened, resulting in the blue shift.

Spectroscopic binary systems are a type of binary star system where the stars are too close together to be resolved visually, but their spectra can be observed separately. By measuring the spectral lines of the stars, astronomers can determine their velocities and orbital parameters. When one of the stars in a spectroscopic binary system is moving towards the Earth in its orbit, we observe a blue shift in its spectral lines. This blue shift is caused by the Doppler effect, which is a change in the wavelength of waves due to the relative motion between the source of the waves and the observer. In the case of a moving star, the waves are compressed as the star moves towards the Earth, resulting in a shorter wavelength and a blue shift.

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Replace x with 3. Then simplify

f(x) = 4x+1

f(3) = 4(3)+1

f(3) = 12+1

f(3) = 13

Answer:13

Step-by-step explanation:

You place 3 in place of x then multiply 4 and 3. You would get 12. Then you add 1. Which is 13.

Answer: A. 2x+2y

Step-by-step explanation:

Answer:

its d

Step-by-step explanation:

The required number is 94.

Let the digit on unit's place be 'x'

Digit on ten's place be 'y'

Therefore,

Original number = 10y + x

Given, the sum of the digits = 11

=> x + y = 11 →(I)

When the digits are reversed, new number = 10x + y

Therefore,

(10y + x) - (10x + y) = 63

10y + x - 10x - y = 63

9y - 9x = 63

=> y - x = 7 →(II)

Adding (I) and (II) we get

2y = 18

y = 9

Substituting the value of y in (I) we get

x + 9 = 11

x = 2

Therefore,

Original number = 10y + x = 10(9) + 4 = 94

The required number is 94.

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Given :

The square of a number, x, is 16 less than eight times the number.

To Find :

The value of x .

Solution :

The mathematical equation with all given data is :

\(x^2=8x-16\\\\x^2-8x+16=0\\\\x^2-4x-4x+16=0\\\\x(x-4)-4(x-4)=0\\\\(x-4)^2=0\\\\x=4\)

Therefore , the value of x is 4 .

Hence , this is the required solution .

The number is 4.

Given that,

Based on the above information, the calculation is as follows:

\(x^2 = 8x - 16\\\\x^2 - 8x + 16 = 0\\\\x^2 -4x - 4x + 16 = 0\\\\x (x - 4) - 4(x - 4) = 0\\\\(x - 4)^2 = 0\\\\x = 4\)

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Answer:

x= 1

Step-by-step explanation:

y= -2 + 1

3x - 2y = 5

substituting method:

substituting y= -2+1 in equ. 3x-2y=5

=> 3x - 2(-2 + 1) = 5

=> 3x +4 -2 = 5

=> 3x + 2 = 5

=> 3x = 5 -2

=> 3x = 3

=> x = 3/3

=> x = 1

From the diagram, we get that the height we are looking for is h₂*0.914. To compute h₂ we notice that it is equal to the tangent of the depression angle times 31 yds.

Therefore:

Answer: 9.21 meters.