f
is inversely proportional to
√
g
.
When
f
=
12
,
g
=
64

Work out
f
when
g
=
16

Answer:

(16*15) + 2*(0.5*8*5)

240 + 40

280 cm2

Answer:

95% is 1700 customers

Step-by-step explanation:

JK i actually dont know but thnks for the points BTW

The mean time it takes Diane and her three friends to complete the obstacle course is approximately 45.75 seconds.

To find the mean of the times it takes Diane and her three friends to complete the obstacle course, we need to add up the times and then divide by the number of people who completed the course.

Let's assume that the times (in seconds) it took each person to complete the course were:

Diane: 42 seconds

Friend 1: 55 seconds

Friend 2: 39 seconds

Friend 3: 47 seconds

To find the mean, we add up all of the times and then divide by the total number of people who completed the course (in this case, four people):

Mean time = (42 + 55 + 39 + 47) / 4

= 183 / 4

= 45.75 seconds

It's important to note that the mean can be impacted by outliers or extreme values in the data set. In this case, if one person had a much longer time to complete the course, it could significantly impact the mean time. It's important to consider the distribution and range of the data in addition to the mean when analyzing data.

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Answer:

It requires of two equations

Step-by-step explanation:

example:

2x +7y = 12

Answer:

y = 6

Step-by-step explanation:

Awnser: y=38.50

Step-by-step explanation:

7 times 2y and 7 times 10

7 times 2y - 70

add 70 to 14

7 times 2y = 84

84 minus 7 =77

77 divided by 2 =38.50

Answer:

2k-8

Step-by-step explanation:

3k +9 -k-17

Combine like terms

3k -k    +9-17

2k         -8

Answer:Simplifying

3k + 9 + -1k + -17 = 0

Reorder the terms:

9 + -17 + 3k + -1k = 0

Combine like terms: 9 + -17 = -8

-8 + 3k + -1k = 0

Combine like terms: 3k + -1k = 2k

-8 + 2k = 0

Solving

-8 + 2k = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '8' to each side of the equation.

-8 + 8 + 2k = 0 + 8

Combine like terms: -8 + 8 = 0

0 + 2k = 0 + 8

2k = 0 + 8

Combine like terms: 0 + 8 = 8

2k = 8

Divide each side by '2'.

k = 4

Simplifying

k = 4

Step-by-step explanation:

In any rhombus, the four sides are the same length.

Because of this, we know that

Furthermore, AC = AC due to the reflective property

Those three facts then allow us to prove triangle ACD is congruent to triangle ACB through the SSS congruence property. Then from CPCTC, we then know that  angle DAC = angle BAC,  which is enough to show that AC bisects the angle shown. The term "bisect" means "cut in half".

opposit side of parallelogram are equal and opposit angles are also equal

Answer:

C: 5 3/8

Step-by-step explanation:

The length of each straw half is 5.375

A= 6.25

B = 5.65

C = 5.375

D = 5.125

The option "b. all events are equally likely in any probability procedure" is not a principle of probability. In reality, events can have different probabilities assigned to them based on various factors and conditions.

The principle of equal likelihood states that in certain cases, when no information is available to distinguish between outcomes, all outcomes are considered equally likely. However, this principle does not apply universally to all probability procedures.

The principle of equal likelihood, stated in option "b," is not a universally applicable principle of probability. While it holds true in some specific scenarios, it does not hold for all probability procedures.

Probability is a measure of the likelihood of an event occurring. It is based on the understanding that events can have different probabilities assigned to them, depending on various factors and conditions. The principles of probability help to establish the foundation for calculating and understanding these probabilities.

The other three options listed—options "a," "c," and "d"—are recognized principles of probability. Firstly, option "a" states that the probability of an impossible event is 0. This principle reflects the notion that if an event is deemed impossible, it has no chance of occurring and therefore has a probability of 0.

Option "c" states that the probability of any event is between 0 and 1 inclusive. This principle indicates that probabilities range from 0, indicating impossibility, to 1, indicating certainty. Probabilities cannot exceed 1, as that would imply a greater than certain chance of occurrence.

Lastly, option "d" states that the probability of an event that is certain to occur is 1. This principle recognizes that if an event is certain, it has a probability of 1, meaning it will happen with absolute certainty.

In contrast, the principle of equal likelihood, mentioned in option "b," is not universally applicable because events can have different probabilities based on various factors such as prior knowledge, available data, and underlying distributions. Probability is determined by analyzing these factors, and events are not always equally likely in all probability procedures.

Overall, while options "a," "c," and "d" are recognized principles of probability, option "b" does not hold as a general principle and should be considered as the answer to the question posed.

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Answer:

you have to × 3.14 to 10cm

=3.14×10cm

after you will get your answer correctly

The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is \(f(x,y,z) =xyz^{2} + e^{\pi }\)   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = \((yz^{2} )i + (xz^{2} )j + (2xyz)k\) ,

So , we can write the partial derivatives function of potential function as :

\(\frac{\partial f}{\partial x} = yz^{2}\) ; \(\frac{\partial f}{\partial y} = xz^{2}\) ; \(\frac{\partial f}{\partial z} = 2xyz\),

On Antidifferentiating any of the above three partial derivatives ,

we get ; \(f=xyz^{2} + C\) , here the constant C can take any value ,

so , we take C as \(e^{\pi }\) .

Therefore , the potential Function is \(f(x,y,z) =xyz^{2} + e^{\pi }\) .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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The compositions between functions f(x) = 3 · x - 2 and g(x) = x + 1 are f[g(x)] = 3 · x + 1 and g[f(x)] = 3 · x - 1, respectively.

Let be f(x) and g(x) functions, there is a composition of the form f[g(x)], when the independent variable of function f is substituted by function g. That is to say:

f ° g(x) = f [g(x)]

First, define functions f(x) and g(x):

f(x) = 3 · x - 2

g(x) = x + 1

Second, perform the required compositions and simplify the expressions:

f[g(x)] = 3 · (x + 1) - 2

f[g(x)] = 3 · x + 1

g[f(x)] = (3 · x - 2) + 1

g[f(x)] = 3 · x - 1

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The general solution of the differential equation d²y/dx² - 36y = cosh(3x) is: \(C_1e^(^6^x^) + C_2e^(^-^6^x^) - (1/27) cosh(3x)\)

We have the following information from the question is:

The differential equation is given as:

d²y/dx² - 36y = cosh(3x)

Now, we have to solve by using the method of undetermined coefficients, we assume a particular solution of the form:

yₙ = A cosh(3x) + B sinh(3x)

where A and B are constants to be determined.

We have to find the second order derivatives of \(y_p\) with respect to x:

yₙ' = 3A sinh(3x) + 3B cosh(3x) y_p'' = 9A cosh(3x) + 9B sinh(3x)

Substituting these derivatives into the original differential equation,

we get:

(9A cosh(3x) + 9B sinh(3x)) - 36(A cosh(3x) + B sinh(3x)) = cosh(3x)

Simplify the equation, we get :

(9A - 36A) cosh(3x) + (9B - 36B) sinh(3x) = cosh(3x)

This leads to the following system of equations:

-27A = 1

-27B = 0

When solving above two equation we get the value of A and B:

The value of A and B are -1/27 and 0 respectively

Therefore, the particular solution is

yₙ = (-1/27) cosh(3x)

To find the general solution, we need to find the complementary solution, he solution to the homogeneous equation is d²y/dx² - 36y = 0.

The characteristic equation is r² - 36 = 0, which has roots r = ±6.

Hence, the complementary solution is:

\(y_a = C_1e^(^6^x^) + C_2e^(^-^6^x^)\)

where C₁ and C₂ are arbitrary constants.

Therefore, the general solution of the given differential equation is

y = yₙ + yₐ = \(C_1e^(^6^x^) + C_2e^(^-^6^x^) - (1/27) cosh(3x)\)

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The given question is incomplete, complete question is:

Find the general solution for the following differential equation using the method of undetermined coefficients d²y/dx - 36 y = cosh3x.

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Yes. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001.

1. Yes, it is likely that the changes in the gateway course had an impact on the DFW rate, as the rate decreased from 42.1% in Year 1 to 19.4% in Year 3.

2. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate, while the alternative hypothesis is that the changes did have a significant impact on the rate.

3. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001. This indicates that there is a significant relationship between the year the course was given and the DFW rate, providing evidence to reject the null hypothesis in favor of the alternative hypothesis that the changes made to the course had a significant impact on the DFW rate.

The p-value of less than 0.001 indicates strong evidence against the null hypothesis, as it is less than the significance level of 0.1.

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Answer:

6/25

Step-by-step explanation:

Answer:

6/25

Step-by-step explanation:

100 divided by 25 is 4 and 4 multiplied by 6 is 24

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

54

Step-by-step explanation:

The variable m equals -2, so what you would do is plug it into the equation.

4(-2+5)+42

Next you would distribute the 4 into -2 & 5.

(-8+20) + 42

Add what's in the parenthesis.

12 + 42

Once you add that you will be left with your answer which is 54.

Hope this helped!

The equation of the circle is x² - 24x + y² + 14y + 144 = 0

We have,

The center of the circle is at (12, -7), so the coordinates of the center give us the values of h and k in the equation of the circle:

(x - h)² + (y - k)² = r²

where (h,k) is the center and r is the radius.

Substituting the given values, we get:

(x - 12)² + (y + 7)² = r²

The diameter of the circle is 14, so the radius is half of that, or 7.

Substituting this value into the equation above, we get:

(x - 12)² + (y + 7)² = 7²

Expanding the left side and simplifying, we get:

x² - 24x + 144 + y² + 14y + 49 = 49

Combining like terms, we get:

x² - 24x + y² + 14y + 144 = 0

Therefore,

The equation of the circle is x² - 24x + y² + 14y + 144 = 0

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The length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the length c by application of the trigonometric ratio of sine for the angle 50°.

sin 50° = 5/c {opposite/hypotenuse}

by cross multiplication

c = 5/sin 50°

c = 6.5270

Therefore, the length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.

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a) The probability of extinction occurring in the first generation is (0.5).

b) The probability of extinction occurring in the second generation is 0.25

c) The probability of extinction occurring in the third generation is 0.125

d) The probability of extinction occurring in the fourth generation is 0.0625

e) The probability of extinction occurring in the fifth generation is 0.03125

In a branching process, each individual can either have zero offspring or one offspring with a probability of 0.5. The probability of extinction occurring at each generation is the probability that all individuals have zero offspring, which is equal to \((0.5)^n\), where n is the generation number.

Therefore, the probability of extinction occurring by a certain generation can be calculated by raising 0.5 to the power of the generation number.

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Answer:

A

Step-by-step explanation:

i want it now

There is no solution to the problem (x)=x+3!

Sorry, Love~ :(

Answer:

f −^1( x ) = x − 3

Step-by-step explanation:

The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Answer:

| - 6 |

Step-by-step explanation:

the absolute value function always gives a positive value , that is

| - a | = | a | = a

then

| - 6 | = | 6 | = 6

| - 11 | = | 11 | = 11

since 6 < 11 , then

| - 6 | is the smaller of the 2 given numbers

The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.

The complete question is attached below.

Suppose that the given function is

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'

The function is given below.

f(x) = (1/4)x – 12

Then the inverse function of the function f(x) will be

(1/4)f⁻¹(x) - 12 = x

            f⁻¹(x) = 4x + 48

Then the correct option is D.

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