If the volume of the region bounded above by z = a² - x² - y², below by the xy-plane, and lying outside x² + y² = 1 is 32 phi units and a > 1, then a =? a. 2 b. 3
c. 4 d.5 e. 6

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

Element  Frequency Cumulative Frequency

15                   3              3

16                   6              9

17                   1              10

18                   6             16

20                   6            22

24                   5            27

25                   6            33

27                   2            35

28                   4            39

30                   1             40

Step-by-step explanation:

Find out how many times an element(data value) appears. That will be the frequency(column 2). The cumulative frequency is the total of all frequencies prior to that element plus the current element frequency

Cumulative frequency for first element is same as its frequency

Cumulative frequency for element 16 is 3 + 6 = 9

Cumulative frequency for element 17 = 3 + 6 + 1 = 9 + 1=10. Basically it is the sum of the previous element cumulative frequency + the current frequency

Answer:

3 1/4

Step-by-step explanation:

3x+5=7x-8

Subtract 5 from both sides

3x=7x-13

Subtract 7 from both sides

-4x= -13

Divide by -4

X= 13/4

SIMPLIFIED: 3 1/4

The air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second is 1011.5 millibars.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

In a hurricane,

the mean sustained wind velocity v (in meters per second) can be modeled by v(p) = 6.3/(1013-p)

The mean sustained wind velocity = 54.5 M/s

To find the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second:

That means,

the equation

54.5 = 6.3/(1013-p)

63 = (1013 - p)54.5

63 = 55208.5 - p54.5

p = 55145.5 / 54.5

p = 1011.844

Therefore, the air pressure is 1011.844 millibars.

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The linear representation is a proportional relationship.

What is proportional relationship?

Proportional relationships are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportionate relationship. The "constant of proportionality" is the name given to this variable.

We know that in a proportional relationship the ratios are equal i.e.

\(\frac{y_{1}}{x_{1} } = \frac{y_{2} }{x_{2} } =\frac{y_{n} }{x_{n} }\)

So,

-16/4 = -12/3 = -8/2 = -4/1 = -4

Since, the ratios of the linear representation are equal, therefore, it is a  proportional relationship.

Hence, the linear representation is a proportional relationship.

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The inverse Laplace transform of 1/s(s^2 + 36) using the convolution theorem is (1/6)sin(6t) + (1/6)cos(6t).

First, we need to find the Laplace transform of the given function 1/s(s^2 + 36). We can use the table of Laplace transforms to find that L{1/s(s^2 + 36)} = (1/6)sin(6t).

Next, we need to find the Laplace transform of the function f(t) = cos(6t)u(t), where u(t) is the unit step function. Using the table of Laplace transforms, we find that L{cos(6t)u(t)} = (s)/(s^2 + 36).

Now, we can apply the convolution theorem, which states that the inverse Laplace transform of the product of two functions in the frequency domain is equal to the convolution of their inverse Laplace transforms in the time domain.

The convolution of (1/6)sin(6t) and (s)/(s^2 + 36) is given by the integral of (1/6)sin(6(t - τ)) * (s)/(s^2 + 36) dτ from 0 to t.

To solve the integral, we can use partial fraction decomposition. We can express (s)/(s^2 + 36) as (A/s) + (B(s)/(s^2 + 36)), where A and B are constants to be determined.

Solving for A and B, we get A = 1/6 and B(s) = -s/6.

Substituting A and B(s) back into the integral and evaluating the integral, we get (1/6)sin(6t) + (1/6)cos(6t).

Therefore, the inverse Laplace transform of 1/s(s^2 + 36) using the convolution theorem is (1/6)sin(6t) + (1/6)cos(6t).

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Answer:  b

Step-by-step explanation:

I think

Answer:

y = 1/4x - 8

Step-by-step explanation:

Given

y + 2 = 1/4 ( x - 24 )

Arranging in slope intercept form; y = mx + c

y + 2 = 1/4x - 24 /4

y+ 2 = 1/4x - 6

y = 1/4x - 6 - 2

y = 1/4x - 8

Hope it will help :)

Answer:

y=1/4×-8

Step-by-step explanation:

say thanks if you like

na

it wants you to factor a 3, and you could get that comon x out of there but it only wants 3, out of that

it would go like this

divide that left side by 3

write it on the right side so it multiplies the 3 back in

3x^2 + 15x = 3(x^2 + 5x)

see how when you distribute that 3 into the right side, you get back the left side?

if you need more help just ask me bro

Hope this helps,

- Jeron :- )

The work done by the gas during the isothermal expansion is 331.32 J.

Isothermal Expansion refers to a process in which the temperature of a system stays constant while the volume increases. In this process, an ideal gas expands from 1.1 m³ to 1.8 m³, and the gas constant is R = 8.314 J/(mol K).

The work done by the gas during the isothermal expansion can be calculated as follows:Answer:During an isothermal process, the change in internal energy of the system is zero since the temperature remains constant.

Therefore,ΔU = 0The first law of thermodynamics is given by:ΔU = q + w

where q is the heat absorbed by the system, and w is the work done on the system.Since ΔU = 0 for an isothermal process, the above equation reduces to:w = -q

During an isothermal process, the heat absorbed by the system is given by the equation:q = nRTln(V₂/V₁)Where, n is the number of moles, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.

Substituting the given values, we have:q = (1 mol) × (8.314 J/(mol K)) × (293 K) × ln(1.8 m³ / 1.1 m³)q = 331.32 J

Therefore, the work done by the gas during the isothermal expansion is given by:w = -qw = -(-331.32 J)w = 331.32 J

Thus, the work done by the gas during the isothermal expansion is 331.32 J.

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Step-by-step explanation:

j = jana's age

m = mom's age = 2.5 j

g = grandma's age = 5.25 j      summed, they equal 149 IN THREE YEARS

j+3       +     2.5j +3     +    5.25 j + 3 = 149

8.75 j  + 9 = 149

8.75 j = 140

j = 16  y/o

   mom = 2.5 j = 40 y/o

         g-ma = 5.25 j = 84 y/o

The reason for statement (3) ∠1 ≅ ∠5 and ∠3 ≅ ∠6 is alternate interior angles.    

From the following attached diagram.

ABC is a triangle with line y is parallel to line z.

We can observe that side AC of triangle ABC is a transversal.

Here ∠1 and ∠5 are alternate interior angles.

⇒ ∠1 ≅ ∠5

Similarly, side AB of triangle ABC is a transversal.

Here ∠3 and ∠6 are alternate interior angles.

⇒  ∠3 ≅ ∠6

So, ∠1 = ∠5 and   ∠3 = ∠6         ............(from definition of congruence)

m∠1 + m∠2 + m∠3 = m∠LAM     ........(angle addition postulate)

m∠1 + m∠2 + m∠3 = 180°    ........(definition of straight angle)

m∠5 + m∠2 + m∠6 = 180°    ........(substitution)

Therefore, the two column proof is presented as follows:

      Statement                                            Reason

1. ABC is a triangle                                      Given

2. lines y and z are parallel                         Given

3. ∠1 ≅ ∠5 and ∠3 ≅ ∠6                        alternate interior angles.

4. m∠1 = m∠5; m∠3 = m∠6                  By definition of congruency

5. m∠1 + m∠2 + m∠3 = m∠LAM          By angle addition Postulate

6. m∠1 + m∠2 + m∠3 = 180°                Angles on a straight line

7. m∠5 + m∠2 + m∠6 = 180°                 Substitution (property)

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Find the complete question below.

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Statements Reasons 1. ABC is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅ 5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution Which could be the missing reason in Step 3? alternate interior angles are congruent alternate exterior angles are congruent vertical angles are congruent corresponding angles are congruent

Answer: y = \(\frac{5}{3}\)x + 14 \(\frac{5}{3}\)

Step-by-step explanation:

      First, we will transform the given equation into slope-intercept form. To do this, we will isolate the y-variable.

             -5x + 3y = 6

             3y = 5x + 6

             y = \(\frac{5}{3}\)x + 2

      A parallel line will have the same slope as the given line. To solve for the y-intercept, we will input the given coordinate point and solve.

             y = \(\frac{5}{3}\)x + b

             (14) = \(\frac{5}{3}\)(-1) + b

             (14) = -\(\frac{5}{3}\) + b

             14 \(\frac{5}{3}\) = b

             y = \(\frac{5}{3}\)x + 14 \(\frac{5}{3}\)

      We can also graph the two lines and the given coordinate point. You can see the equation we wrote goes through the coordinate point (-1, 14) and is parallel to -5x + 3y = 6.

Answer:

  5x -3y = -47

Step-by-step explanation:

You want the equation of the line through point (-1, 14) that is parallel to -5x +3y = 6.

The equation of a parallel line can be found by leaving the x- and y-coefficients alone, and finding the constant that makes the equation be true at the given point. Substituting the point coordinates for x and y, we have ...

  -5(-1) +3(14) = 5 +42 = 47

Making the constant be 47 will give the desired equation:

  -5x +3y = 47

The equation is written in standard form when the leading coefficient is positive:

  5x -3y = -47 . . . . . . multiply the above equation by -1

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The cost of three points for the homebuyers is $739.80.

To calculate the cost of three points for the homebuyers, we need to determine the value of each point and then multiply it by three.

Given:

Loan amount: $137,000

Interest rate without points: 5.05%

Interest rate with points: 4.87%

The difference between the two interest rates is the value of one point.

Interest rate difference = 5.05% - 4.87% = 0.18%

To find the value of one point, we calculate 0.18% of the loan amount:

Value of one point = 0.18% * $137,000

Value of one point = 0.0018 * $137,000

Value of one point = $246.60

Now, to determine the cost of three points, we multiply the value of one point by three:

Cost of three points = $246.60 * 3

Cost of three points = $739.80

The price of three points for the homebuyers is therefore $739.80.

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Answer: 4 hours

Step-by-step explanation:

21+2x=29

29-21=8/2=4 2x/2

Answer:

y=−1/2x−1

Step-by-step explanation:

I put it in slope intercept form as I assume that is what the question is asking.

Answer:

(-7, -1)

Step-by-step explanation:

The ratio is 1:4, the total is 1 + 5 = 5, so the partition is at 1/5 of the total length.

x2 - x1 = 25 - (-15) = 40

1/5 * 40 = 8

-15 + 8 = -7

x = -7

y2 - y1 = 15 - (-5) = 20

1/5 * 20 = 4

-5 + 4 = -1

y = -1

Answer: (-7, 1)

Answer:

Step-by-step explanation:

The formula of volume is length x width x height.

The amount Susan would get with each paycheck = $3222.57

For given question,

We need to find the amount Susan would get with each paycheck.

"Susan's annual salary is $56,000"

This means, we start with the number 56,000

"A total of $17,329.16 will be deducted for taxes and health insurance"

This means, It's the number we started with "deducted" (minus) 17,329.16

⇒ $56,000 - $17,329.16 = $38,670.84

"She will receive her paycheck monthly in 12 equal installments"

This means  the resulting number after above subtraction , number will be divided by 12.

⇒ $38,670.84 ÷ 12 = $3222.57

Therefore,  the amount Susan would get with each paycheck = $3222.57

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From the given data, we say a definite integral is improper if one endpoint is infinite, or if the integrand is infinite.

One endpoint is infinite, or if the integrand is infinite, the definite integral cannot be evaluated using the usual techniques. Instead, we must use the concept of a limit to find the value of the integral, if it exists. In the case where one endpoint is infinite, we take a limit as a variable approaches infinity. In the case where the integrand is infinite, we may need to split the integral into pieces or use some other method to deal with the singularity.

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Answer:

x=6 or x=−6

Step-by-step explanation:

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Answer:

24

Step-by-step explanation:

The probability of the spinner landing on 2 reds is P ( 2 Reds ) = 1/8

Given data ,

To find the probability of spinning two reds, we need to calculate the probability of spinning a red on the first spin and then multiply it by the probability of spinning a red on the second spin.

The probability of spinning a red on the first spin is 1/4 since there is one red section out of four equal sections.

Now , the value of P ( R ) = 1/4

when the spinner is spun twice ,

P ( A ) = P ( R ) P ( R )

P ( A ) = 1/4 ( 1/4 )

On simplifying , we get

P ( A ) = 1/8

Hence , the probability is P ( A ) = 1/8.

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Equation for the total cost of paint job 'y' with number of hours spent on paining 'x' is formed as:

y = 50 + 3x

y = 50 + 5x

Let the total cost of paint job be' 'y'.

Let 'x' be the number of hours spent on paining.

Then,

Total cost = supplies + hourly fee* number of hours.

Let the supplies cost be 'z'

140 = z + 3x

200 = z + 5x

Solving both equation.

2x = 60

x = 30

z = 50

Thus, equation for the  total cost of paint job 'y' with number of hours spent on paining 'x' is formed as:

y = 50 + 3x

y = 50 + 5x

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The equation of the line is x - 3y + 1 =0.

What is the meaning perpendicular line?

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle.

Given equation of line is

y=−3x + 5

Now compare the given equation with y = mx +c

m = -3 and c = 5.

The slope perpendicular line of the given line is = -1/m

= 1/3

The equation of line passes through the point (x₁, y₁) with slope m is

y - y₁ = m (x - x₁)

Putting m = 1/3, y₁ = 2, and x₁ = 5 in the above equation:

y - 2 = 1/3 (x - 5)

3y - 6 = x - 5

x - 3y + 1 =0

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Given the information on the circular graph, we have that Medicare & Medicaid has the 35%, then, in angles this is:

For the rest, we have the following:

Answer:

(2, 5 )

Step-by-step explanation:

Given the 2 equations

y = 3x - 1 → (1)

2x + 4y = 24 → (2)

Substitute y = 3x - 1 into (2)

2x + 4(3x - 1) = 24 ← distribute and simplify left side

2x + 12x - 4 = 24

14x - 4 = 24 ( add 4 to both sides )

14x = 28 ( divide both sides by 14 )

x = 2

Substitute x = 2 into (1) for corresponding value of y

y = 3(2) - 1 = 6 - 1 = 5

solution is (2, 5 )