Solve the equation for a, when b=4 and c=5

\(17+2b-4c=4(a-7)-3\)

The probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are 5 classic rock CDs and 4 country music CDs in the bag.

To calculate the probability, we multiply the probability of pulling a classic rock CD (5/17) by the probability of pulling a country music CD from the remaining CDs (4/16). (5/17) * (4/16) = 0.0735. Rounded to the nearest hundredth, the probability is approximately 0.07.

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Answer:

\( x = 20 \)

Step-by-step explanation:

\( \frac{3}{5}x - \frac{1}{4}x = 7 \)

The LCD is 20, so multiply both sides of the equation by 20.

\( 20(\frac{3}{5}x - \frac{1}{4}x) = 20 \times 7 \)

\( 4 \times 3x - 5 \times x = 140 \)

\( 12x - 5x = 140 \)

\( 7x = 140 \)

\( x = 20 \)

The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.

It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.

Given;

Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.

The addition of the internal angles of triangle is 180

So, let vertex angle be x

The other two sides will be x+10,

x+x+10+x+10=180

3x+20=180

x=160/3

x=53.3

Therefore, the vertex angle of the triangle will be 53.3degrees.

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As per the unitary method, there are 16 boys and 8 girls.

Unitary method.

Unitary method is the way of a method of determining the answer to a problem by first determining the value of a single unit and then multiplying the single unit value by the essential value.

Given,

Hillary and 23 of her friends went on a hayride. There are 8 more boys than girls on the ride.

Here we need to find the number of boys and girls in the ride.

While looking at the question, the total number of peoples went for the ride is 24 including Hillary.

So, let us consider b represents the number of boys and g represents the number of girls.

According to the given condition,

We know that,

b = g + 8 -----------(1)

As per total, the equation is

b + g = 24 --------------(2)

Apply the value of b on the equation (2),

Then we get,

g + 8 + g = 24

2g + 8 = 24

2g = 16

g = 8

Therefore, the value of b = 8 + 8 = 16.

Therefore, there are 8 girls and 16 boys in the ride.

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Answer:

I don’t know

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Since it is an isosceles triangle the two sides are equal

Answer:

answer will be the integer only which was added to zero

The solution for t > 2 is:

q(t) = e^(-t/2)*((1 - sqrt(t^2/4 - 1))/sqrt(t^2/4 - 1)*e^(sqrt(t^2/4 - 1)*t/2) - (1 + sqrt(t^2/4 - 1))/sqrt(t^2/4 - 1)*e^(-sqrt(t^2/4 - 1)*t/2))

To solve for q(t) in a series LRC circuit with time-dependent resistance, we need to use Kirchhoff's voltage law and the equation for the voltage across a capacitor:

v_R + v_L + v_C = 0

v_C = q/C

v_L = L(di/dt)

v_R = iR(t)

where di/dt is the time derivative of the current i, and q is the charge on the capacitor.

Substituting the expressions for the voltages and simplifying, we get:

L(d^2q/dt^2) + Rdq/dt + q/C = 0

We can rewrite this as a second-order linear differential equation with variable coefficients:

d^2q/dt^2 + R(t)/(LC) dq/dt + 1/(LC) q = 0

Plugging in the given values of L = C = 1 and R(t) = t, we get:

d^2q/dt^2 + tdq/dt + q = 0

This is a homogeneous linear differential equation with constant coefficients, which we can solve using the characteristic equation:

r^2 + tr + 1 = 0

The roots of this equation are given by:

r = (-t ± sqrt(t^2 - 4))/2

Depending on the value of t, the roots can be real or complex. Let's consider the three cases separately:

t < 0: In this case, both roots are complex and given by r = -t/2 ± i*sqrt(1 - t^2/4). The general solution of the differential equation is then:

q(t) = e^(-t/2)(c1cos(sqrt(1 - t^2/4)) + c2sin(sqrt(1 - t^2/4)))

Using the initial conditions i(0) = 1 and q(0) = 0, we can determine c1 and c2 as follows:

c1 = 0

c2 = i

Therefore, the solution for t < 0 is:

q(t) = e^(-t/2)*sin(sqrt(1 - t^2/4))

0 ≤ t ≤ 2: In this case, the roots are real and given by r = -t/2 ± sqrt(1 - t^2/4). The general solution of the differential equation is then:

q(t) = c1e^(r1t) + c2e^(r2t)

where r1 and r2 are the two roots. Using the initial conditions i(0) = 1 and q(0) = 0, we can determine c1 and c2 as follows:

c1 = (i - sqrt(3))/2

c2 = (i + sqrt(3))/2

Therefore, the solution for 0 ≤ t ≤ 2 is:

q(t) = e^(-t/2)((i - sqrt(3))/2e^(-sqrt(3)t/2) + (i + sqrt(3))/2e^(sqrt(3)*t/2))

t > 2: In this case, the roots are real and given by r = -t/2 ± sqrt(t^2/4 - 1). The general solution of the differential equation is then:

q(t) = c1e^(r1t) + c2e^(r2t)

where r1 and r2 are the two roots. Using the initial conditions i(0) = 1 and q(0) = 0, we can determine c1 and c2 as follows:

c1 = (1 - sqrt(t^2/4 - 1))/sqrt(t^2/4 - 1)

c2 = -(1 + sqrt(t^2/4 - 1))/sqrt(t^2/4 - 1)

Therefore, the solution for t > 2 is:

q(t) = e^(-t/2)*((1 - sqrt(t^2/4 - 1))/sqrt(t^2/4 - 1)*e^(sqrt(t^2/4 - 1)*t/2) - (1 + sqrt(t^2/4 - 1))/sqrt(t^2/4 - 1)*e^(-sqrt(t^2/4 - 1)*t/2))

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Answer:

(f ￮ g)(0) = 3

Step-by-step explanation:

evaluate g(0) then substitute the value obtained into f(x)

g(0) means what is the value of g(x) when x = 0

from the graph g(0) = 2 , then

f(2) , that is what is the value of f(x) when x = 2

from the graph  f(2) = 3

then

(f ￮ g)(0) = 3

The classical errors-in-variables (CEV) assumptions require that the measurement error in tv hours is not related to the true value of television viewing.In other words, the error should be random and not correlated with the actual amount of time spent watching TV.

Additionally, the CEV assumptions require that the measurement error has a mean of zero and a constant variance. Whether or not the CEV assumptions are likely to hold in this application depends on several factors. One important consideration is the accuracy of the survey instrument used to collect data on tv hours.

If the survey is poorly designed or administered, it may introduce systematic measurement error that is correlated with the true value of television viewing.

Another important factor is the population being surveyed. If the population is highly diverse with respect to television viewing habits, it may be difficult to ensure that the CEV assumptions hold for all subgroups.

Overall, while it is possible that the CEV assumptions hold in this application, it is also possible that they do not. Researchers should carefully consider the potential sources of measurement error and take steps to minimize them if possible.

Additionally, sensitivity analyses can be conducted to explore the robustness of study results to violations of the CEV assumptions.

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Answer:

The answer to the question provided is 5 units.

Answer:

The answer is 5 divided by 8, or answer A.

Answer:

Answer A, because 5 divided by 8 is the same as 5/8

Step-by-step explanation:

Answer: 26, 28, 30

Explanation:

Let's define a variable x to represent the least of the three consecutive even integers. This means that the three integers are x, x + 2, and x + 4.

We can write the given information as an equation:

3 * (x + 4) = 2 * x + 38

We can solve for x by moving all the terms with x to one side of the equation and all the other terms to the other side:

3 * (x + 4) - 2 * x = 38

Then we can distribute the 3 and the -2 to get:

3 * x + 12 - 2 * x = 38

And then we can combine like terms on each side of the equation:

x + 12 = 38

Finally, we can subtract 12 from both sides to solve for x:

x = 26

Therefore, the three consecutive even integers are 26, 28, and 30.

We can check our solution by substituting these values back into the original equation and verifying that it holds true:

3 * (26 + 4) = 2 * 26 + 38

3 * 30 = 52 + 38

90 = 90

The equation holds true, so our solution is correct.

Answer:

No it does not apply to this problem because the submarine starts at a depth of 100 feet below sea level.

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Answer:

x=23

Step-by-step explanation:

1/6 as a decimal is 0.16666667 but i rounded it to 0.2

so the equation is the 0.2(3x-9)-9=3

then i did 0.2 times 3x =0.6x

then 0.2 times -9= -1.8

so the equation now looks like this:

0.6x-1.8x-9=3

so i add 1.8 and 9 to 3 which gives you 13.8

then the equation looks like this:

0.6x=13.8

then you do 13.8 divided by 0.6 which equals 23.

hope this helps

tell me if i got it right or wrong

Answer:

5x+4y-40=0

Step-by-step explanation:

The value of circumferences of both circles to the nearest hundredth are 28.27 ft and 44ft.

Since, We know that;

The circumference of a form is the space surrounding its edge. Find the circumference of various forms by summing the lengths of their sides.

Given two coincide circles, the Radius of the smaller circle is 4.5ft.

Since the diameter is 9 ft.

Since, the bigger circle is 2.5 ft wider than the smaller circle,

Thus, the radius of the bigger circle = 4.5 + 2.5

Hence, the radius of the bigger circle = 7

From the formula for the circumference of a circle:

Circumference = 2π × radius

Thus,

The circumference of the yellow(bigger) circle is about = 2 x pi x 7

The circumference of the yellow(bigger)  circle is about = 44 ft

The circumference of the purple(smaller) circle is about = 2 x pi x 4.5

The circumference of the purple(smaller) circle is about = 28.274 ft

therefore, The circumference of the yellow circle is about 44 ft. The circumference of the purple circle is about 28.27ft.

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The Circumference of the yellow circle is about 44 ft.

The circumference of the purple circle is about 28.27ft.

We have,

Radius of the smaller circle is 4.5ft

and radius of the bigger circle = 4.5 + 2.5 = 7 ft

Now, Circumference of Bigger circle (yellow) = 2 x π x r

= 2(3.14)(7)

= 44 ft

and, Circumference of Smaller circle (Purple) = 2 x π x r

= 2(3.14)(4.5)

= 28.274 ft

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In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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Answer:

A. x = -2,500.

Step-by-step explanation:

sqrt(-4x) = 100

(sqrt(-4x)^2 = (100)^2

-4x = 10,000

4x = -10,000

x = -2,500

Check your work...

sqrt(-4(-2,500))

= sqrt(4 * 2,500)

= sqrt(10,000)

= plus or minus 100

A. x = -2,500 is your answer.

Hope this helps!

Answer:

The answer would be A, x=-2500

Explanation:

To remove the radical on the left side of the equation, square both sides of the equation.

√ − 4 x^ 2 = 100^ 2

Simplify each side of the equation.

− 4 x = 10000

Divide each term by  

−4

and simplify.

x = -2500

Answer:

23+11

Hope that helps  :)

Answer:

31+3

Step-by-step explanation:

2,3,5,7,11,13,17,19,23,27,29,31

31+3=34

Using a 92% learning curve rate, the estimated manual labor hours required to build the 5th house would be 1,034 hours, the 10th house would be 692 hours, and all 18 houses combined would require 3,046 hours. Additionally, if the learning curve rates are 70%, 75%, and 80%, the estimated manual labor hours for all 18 houses would be 5,177, 4,308, and 3,636 hours, respectively.

The learning curve formula is given by \(Y = a * X^b\), where Y represents the cumulative average time per unit, X represents the cumulative number of units produced, a is the time required to produce the first unit, and b is the learning curve exponent.

In this case, the learning curve rate is 92%, which means the learning curve exponent (b) is calculated as log(0.92) / log(2) ≈ -0.0833.

a. To estimate the time required to build the 5th house, we can use the learning curve formula:

\(Y = a * X^b\)

\(Y(5) = 3500 * 5 ^ (-0.0833)\)

Y(5) ≈ 1034 hours

b. Similarly, the time required to build the 10th house can be estimated:

\(Y(10) = 3500 * 10^(-0.0833)\)

Y(10) ≈ 692 hours

c. The cumulative time required to build all 18 houses can be estimated by summing the individual estimates for each house:

\(Y(18) = 3500 * 18^(-0.0833)\)

Y(18) ≈ 3046 hours

d. To calculate the manual labor estimates for all 18 houses using different learning curve rates, we can apply the respective learning curve exponents to the formula. The results are as follows:

- For a 70% learning curve rate: Y(18) ≈ 5177 hours

- For a 75% learning curve rate: Y(18) ≈ 4308 hours

- For an 80% learning curve rate: Y(18) ≈ 3636 hours

In conclusion, using the given learning curve rate of 92%, the estimated time required to build the 5th house is 1034 hours, the 10th house is 692 hours, and all 18 houses combined would require 3046 hours. Additionally, different learning curve rates yield different manual labor estimates for all 18 houses.

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Answer:

Slope = 5

Step-by-step explanation:

A slope of any parallel line has the same slope since the two lines never touch.

Step-by-step explanation:

Answer:

it's b on edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

To work out the value of k, we can use the given information that fg(2) = 12. We know that fg(x) is the composition of two functions f and g, so we can write fg(x) = f(g(x))

In this case, fg(2) = f(g(2)) = f(k*2^2) = f(4k)

We know that fg(2) = 12. So we can substitute this value into the equation above:

12 = f(4k)

Since we are only interested in the value of k, we can set the equation equal to 12 and solve for k.

12 = 4k

k = 12/4

k = 3

Therefore, k = 3 is the value of k in the function g(x) = kx^2

Answer:

$15

Step-by-step explanation:

Answer

Use division, how many times will 14 go into 210?

210÷14=15

$15

Or you can also multiply 15x14=210

The coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

From the data, we can draw a triangle as shown in the attached picture.

Let the coordination of B is at (0, 0)

The coordinate of point A:

A(x, y):

a = (x + 0)/2

x = 2a

y = 2b

A(x, y): (2a, 2b)

The coordinate of point C:

C(X, Y):

2a = (X + 2a)/2

4a = X + 2a

X = 2a

b = (Y + 2b)/2

Y = 0

Thus, the coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.

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The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds

To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.

Given the starting altitude of the balloon, we know:

h(0) = 1200 feet

The rate of change of the altitude, or the speed at which the altitude is changing, is given as:

dh/dt = −712 feet/second

This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:

h(t) = h(0) + dh/dt * t

We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:

310 = 1200 + (−712) * t

This equation can be solved for t by isolating t on one side and then dividing both sides by −712:

t = (1200 - 310) / −712

t = (890) / (−712)

t = 1.25 seconds.

So it will take 1.25 seconds for the balloon to drop below 310 feet.

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