Consider the function f(x)=2(3)x.

What are the coordinates of the y-intercept of the function?

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

A fraction is a value representing a part of a whole.

We have,

Supporters for the Home team = 4/9

Supporting for the away team = 1 - 4/9 = 5/9

Now,

Male supporters from the away team = 3/5 x 5/9 = 1/3

So,

Female supporters from the away team = (1 - 3/5) x  5/9 = 2/5 x 5/9 = 2/9

Thus,

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

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Therefore when the Triangle PQR is rotated a Triangular prism will be generated, option D is the correct answer.

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces.

The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases.

The bases are also called the top and the bottom (faces) of the prism.

The properties of a triangular prism help us to identify it easily. Listed below are a few properties of a triangular prism:

A triangular prism has 5 faces, 9 edges, and 6 vertices.

It is a polyhedron with 3 rectangular faces and 2 triangular faces.

The two triangular bases are congruent to each other.

Any cross-section of a triangular prism is in the shape of a triangle.

When the Triangle PQR is rotated a Triangular prism will be generated.

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The sum of the given series ∑ n=2∞ n5n xn is 2⁵x2 + 3⁵x3/5 + 4⁵x4/25 + 5⁵x5/125 + …. [We know that ∑ n=0∞ xnrn= x/(1-r), for |r|<1]

Here, we can use the same formula, but there is a modification. We need to multiply the formula with a factor of r.

∑ n=2∞ n5n xn = ∑ n=1∞ (n+1)5(n+1) xn+1 5(x2 + 3x3/5 + 4x4/25 + 5x5/125 + …. )

= 5(x2 + 3x3/5 + 4x4/25 + 5x5/125 + …. ) + 5(x3 + 3x4/5 + 4x5/25 + …. ) + 5(x4 + 3x5/5 + …. ) + 5(x5 + ….)

This is of the form, S1 + S2 + S3 + S4 + ….where Sn = 5(xn + xn+1/5 + xn+2/5² + …)

Using the formula for the sum of an infinite geometric progression with a common ratio of r, we get:

Sn = 5(xn/(1-1/5)) = 25/4 xn

Hence, the sum of the given series is 5(x2 + 3x3/5 + 4x4/25 + 5x5/125 + …. ) + 25/4 (x2 + x3 + x4 + x5 + …)

The series is expressed in the form of Sn and using the formula for the sum of an infinite series of this form, we obtained the simplified form. Hence, the above problem can be concluded that the summation of an infinite series is an interesting and important concept in Mathematics.

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Answer:

48,841,380.8

Step-by-step:

find 12% of 14,365,112= 1,723,813.44

then find 1,723,813.44×20= 34,476,268.8

then 34,476,268.8+14,365,112=48,841,380.8

To increase a number by 12% means to multiply it by 1.12. If you do this repeatedly over the years, you're multiplying \(n\) times by 1.12, i.e. you're multiplying by \(1.12^n\).

So, in 20 years, the population will be

\(12365112\cdot (1.12)^{20}\approx 119277494\)

Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

Substitute 8 for x in the equation to ontain the value of f(8).

So answer is f(8)=79.

Answ

Step-by-step explanation:

Answer:

B. 6.3

D. 5.9

F. 8.2

Step-by-step explanation:

B. 6.3

D. 5.9

F. 8.2

Those are the only answer choices that when added to negative 5.8 will equal a positive number.

Hope this helps!

Please mark as brainliest if correct!

If we add the extra vertex E at the center of the square, we can construct a minimum-weight spanning tree with a total weight of 600, which is less than the 300 weight achieved without the additional vertex.

We start by adding a vertex at the center of the square and label it  E, we can create a minimum-weight spanning tree as follows:

1. We connect Connect E to each of the vertices A, B, C, D.

2. Connect the remaining vertices with the minimum-weight edges.

This construction creates additional edges in the spanning tree, reducing the total weight. The additional edges will be :

Half of the square's side length, or 50, is required to reach any vertex (A, B, C, or D). Therefore, each of these extra edges has a 50 weight.

Total weight = Weight of AB + Weight of BC + Weight of CD + Weight of DA + Weight of EA + Weight of EB + Weight of EC + Weight of ED

= 100 + 100 + 100 + 100 + 50 + 50 + 50 + 50

= 600

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slope is

9-(-1)/-2-3

10/(-5)

=-2

slope is -2

\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

     What is the slope of the line containing (-2, 9) and (3, -1)?

\(\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

We can find the slope using the following formula:-

\(\boxed{\frac{y_2-y_1}{x_2-x_1}}\)

\(\bigstar\) substitute the numbers in lieu of the letters:-

\(\boxed{\frac{-1-9}{3-(-2)}}\)

\(\dagger\) On simplification,

\(\boxed{\frac{-10}{3+2}}\)

\(\dagger\) On further simplification,

\(\boxed{\frac{-10}{5}}\)

\(\dagger\) Which simplifies to

\(\boxed{Slope=-2}\)

\(\rule{300}{1}\)

The inverse Laplace transform of 1/(s^4-36) is (1/6)sin(6t).

We can use Theorem 7.2.1 to find the inverse Laplace transform of 1/(s^4-36). According to this theorem, if F(s) has partial fraction expansion F(s) = (A/(s-p1)) + (B/(s-p2)) + ... + (N/(s-pn)), where p1, p2, ..., pn are distinct complex numbers and A, B, ..., N are constants, then the inverse Laplace transform of F(s) is given by:

ℒ^(-1){F(s)} = Aℒ^(-1){1/(s-p1)} + Bℒ^(-1){1/(s-p2)} + ... + Nℒ^(-1){1/(s-pn)}

In this case, the denominator s^4-36 can be factored as (s^2+6)(s^2-6). We can rewrite the expression 1/(s^4-36) as 1/[(s^2+6)(s^2-6)]. The roots of s^2+6 are ±i√6, and the roots of s^2-6 are ±√6.

To find the inverse Laplace transform, we need to calculate ℒ^(-1){1/(s^2+6)} and ℒ^(-1){1/(s^2-6)} separately.

ℒ^(-1){1/(s^2+6)} = (1/√6)sin(√6t)

ℒ^(-1){1/(s^2-6)} = (1/√6)sin(√6t)

Using Theorem 7.2.1, the inverse Laplace transform of 1/(s^4-36) is given by:

ℒ^(-1){1/(s^4-36)} = (1/√6)sin(√6t) + (1/√6)sin(√6t)

Simplifying the expression, we get:

ℒ^(-1){1/(s^4-36)} = (2/√6)sin(√6t)

Further simplifying, we find:

ℒ^(-1){1/(s^4-36)} = (1/6)sin(6t)

Therefore, the inverse Laplace transform of 1/(s^4-36) is (1/6)sin(6t).

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I think 100 grams per box

Answer:

Step-by-step explanation:

X = 64.

x^(1/2) = 8

\(\sqrt{x} = 8^{2}\)

Therefore, x = 64

Answer:

D. 64

Step-by-step explanation:

x^1/2 = 8

√x = 8

√64 = 8

x = 64

An exponential function has the form:

Where A is the initial value, r is the ratio that is applied for each period of time and x is the time since the initial A in the same unit as the period of r.

The initial value of the population was 15500, so:

It decreases 3% per year, so x is the time since the population was 15500 in years and, since it is a 3% decrease, this means that after each year there are just 97% left, so the ratio is 97% or, in the decimal form, 0.97.

So, the function is:

To graph the function, we can first plot some points.

Let's plot one point per 10 year until we pass the value of 8000.

For x = 0:

For x = 10:

For x = 20:

Now that we are close, let's do 2 years:

For x = 22:

So, ploting the points and graphing, we have:

The dotted line is the y = 8000. We can see that in the 21th year, the population is still above 8000, but at year 22 the population went belowe 8000.

So, the population will drop below 8000 by the 22th year since the initial population of 15500.

Answer:

-8-5m

Step-by-step explanation:

Based on the given autocorrelations, an ARMA(2,1) model may be appropriate for the series.

From the given information, we know that the series has a length of 169 and that the autocorrelations decrease in magnitude as the lag increases. This suggests that the series may be stationary and that an ARMA model may be appropriate.

From the ACF data, we can see that the autocorrelations decay slowly, suggesting that the series may have a long memory. However, there are significant spikes at lags 1, 2, and 3, suggesting that there may be some autoregressive structure in the data.

From the PACF data, we can see that the partial autocorrelations are significant at lags 1 and 2, but not at higher lags. This suggests that an ARMA(2,0) model may be appropriate.

However, since the autocorrelations decay slowly, we may want to consider a model with a moving average component as well. A reasonable starting point would be an ARMA(2,1) model, which includes two autoregressive terms and one moving average term.

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SOLUTION:

Given;

(a) At the end of the first year;

ANSWER: $5,100

(b) At the end of two years;

ANSWER: $5,202

hello

let's get the data from this question

the conversion formula for Celcius (C) to Fahrenheit (F) is given as

2.

the tempreture in Fahrenheit is

The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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Answer:

\(AB = 8\)

Step-by-step explanation:

Given

\(x = 60\)

\(BC = 4\)

See attachment

Required

Find AB

From the attachment, using cosine rule:

We have:

\(cos\ x = \frac{BC}{AB}\)

Make AB the subject

\(AB = \frac{BC}{cos\ x}\)

Substitute values for BC and x

\(AB = \frac{4}{cos\ 60}\)

\(AB = \frac{4}{0.5}\)

\(AB = 8\)

Step-by-step explanation:

I assume you mean

y = 28(1.01)^x

if I multiply something by a number that is even slightly larger than 1, the result will be bigger than the original "something" (except for 0, of course. where the result will be 0 again).

if I multiply by a number between 0 and 1, then the result will be smaller.

so, with growing x y will also grow.

and with every increase of x by 1 we multiply the previous result by 1.01.

1 represents 100%.

0.01 represents 1/100 of 100% = 1%

1.01 = 100% + 1%

the the percentage rate of increase is 1%.

1) 1000 AA Batteries in one Case.

2) 10,000 AA Batteries in One carton.

3) 100,000 AA Batteries in 10 cartons.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The Store sells AA batteries in the order below:

⇒ 10 batteries in 1 packages

⇒ 10 packages in 1 box

⇒ 10 boxes in 1 case

⇒ 10 cases in 1 Carton

1) We want to determine how many AA batteries are in 1 Case;

Using Multiplication

Number of AA Batteries in 1 Case = 10 Batteries × 10 package × 10 box

                                                    = 1000 AA Batteries

2) We want to determine how many AA batteries are in 1 Carton;

From Part (a),

There are 1000 AA Batteries in 1 Case.

Since, There are 10 Cases in 1 carton.

Number of Batteries in 1 carton = 10 × 1000

                                                = 10,000 AA Batteries

3) 10 Cartons

⇒ 1 carton = 10000 AA Batteries

Therefore, We get;

⇒ 10 Cartons = 10 × 10000

                     = 100,000 AA Batteries

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The missing value in the equation 3(y - 2) = 18 using the properties of equality is 6.

Given that 3(y - 2) = 18. To solve for y, use the properties of equality and fill the missing value as follows: 3(y - 2) = 18. The first step is to simplify the left side of the equation by multiplying 3 to the brackets.

3 * y - 3 * 2 = 183y - 6 = 18

Add 6 to both sides of the equation to isolate the term 3y on one side.

3y - 6 + 6 = 18 + 63y = 24

Finally, divide both sides of the equation by 3 to obtain the value of y.

3y/3 = 24/3y = 8

Therefore, the solution for y is 8.

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Answer:

The first number is -3, the second number is 8

Step-by-step explanation

Let x = the first number

exceeded means add, so the second number is x+11

sum means add, so the equation is x+x+11=5

combine like terms to get 2x+11=5

subtract 11 on both sides, 2x=-6

divide by 2 on both sides, x= -3

second number was x+11, so -3+11 = 8

We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

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Answer:

Step-by-step explanation:

No, this is not correct.

Step 1: Find the directional distance from every vertex on the blue image to  the center, Point C.

Point A is 1 unit left and 4 units upwards to Point C.

Point B is 4 units right and 5 units upwards to Point C.

Point C is the center of the dilation, so that point will not change.

Step 2: Apply the scale factor to the directional distances to know the distances of the new images.

The scale factor is 2 so

Point A' should be 2 units left and 8 units upwards to Point C.

Point B' should 8 units right and 10 units upwards to Point C.

Step 3:  Move the point in respect to Point C.

The new image should have the these points.

One point that is 2 units left and 8 units upwards to Point C.

Another point that is Point B' should 8 units right and 10 units upwards to Point C.

One point that coincides  with  Point C.

Answer:

do u have the radius ?

Step-by-step explanation:

112/360 * (2πr)

Answer:

A a pair of intersecting lines

Step-by-step explanation:

i got it right on the test bub

Answer: a pair of intersecting lines

Step-by-step explanation: i had many people help me know this is right

The two solutions of the equation sin(theta) = 0.5 within the range of 0 to 2pi radians are approximately 0.524 radians and 6.166 radians.

To find two solutions of an equation, we need to solve the equation for the given range of theta. Since the question specifies that theta should be in radians and between 0 and 2pi, we will find two solutions within this range.
Let's consider an example equation to demonstrate the steps. Suppose we have the equation:
sin(theta) = 0.5
1: Identify the equation and the trigonometric function involved. In this case, the equation is sin(theta) = 0.5, and the trigonometric function is sine.

2: Solve for theta algebraically. To solve the equation, we need to find the values of theta that make the equation true. In this example, we can use the inverse sine function (also known as arcsin) to solve for theta. Applying the inverse sine function to both sides of the equation, we get:
theta = arcsin(0.5)

3: Calculate the value of theta using the inverse sine function. The inverse sine function gives us the angle whose sine is equal to 0.5. In this example, the inverse sine of 0.5 is approximately 0.524 radians (or 30 degrees).

4: Find a second solution within the given range. To find a second solution, we can add the period of the sine function to the first solution. The period of the sine function is 2pi radians. Adding 2pi to the first solution, we get:
theta = 0.524 + 2pi
Simplifying, we find that the second solution is approximately 6.166 radians (or 354 degrees).

Therefore, the two solutions of the equation sin(theta) = 0.5, within the range of 0 to 2pi radians, are approximately 0.524 radians (or 30 degrees) and 6.166 radians (or 354 degrees).

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