Show work please for number 2

Answer:

30w+200=1000

Step-by-step explanation:

Given

Then, (f-g)(x) can be found as,

The average rate of change for the number of bacteria from 0 to 8.5 hours is 130 bacteria per hour and the average rate of change for the number of bacteria from 11.9 to 13.6 hours is 360 bacteria per hour.

We know that,

Average rate of change for the number of bacteria from 0 to 8.5 hours =

(Number of bacteria at 8.5 hours - Number of bacteria at 0 hours)/(8.5 - 0)

= (2105 - 1000)/8.5 = 1105/8.5 = 130 bacteria per hour.

Also,

Average rate of change for the number of bacteria from 11.9 to 13.6 hours =

(Number of bacteria at 13.6 hours - Number of bacteria at 11.9 hours )/(13.6 - 11.9) = (3992 - 3380)/1.7 = 612/1.7 = 360 bacteria per hour.

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Figure 2 is the image of Figure 1 after rotation by an angle of 90degrees counter-clockwise

Step 1: Write out the coordinates of EFGH and the coordinates of KLMN,

Step 2: Write out the formula for the rotation of a point (x,y) by 90° counter-clockwise

Step 3: Show that the points KLMN are the images of R on EFGH

Hence, Figure 2 is the image of Figure 1 on Rotation by 90 degrees counter-clockwise

Since rotation preserves the shape of a figure, then the measures of corresponding angles are equal.

Therefore,

m

The third Choice is correct

Answer:

5220

Step-by-step explanation:

Answer:

Step-by-step explanation:

eq of line perpendicular to 3x+5y=10 is

5x-3y=a

where a is constant.

it passes through (3,2)

5(3)-3(2)=a

a=15-6=9

reqd. eq. is 5x-3y=9

or

3y=5x-9

y=5/3 x-3

gradient=5/3

y-intercept=-3

or

5y=-3x-10

y=-3/5 x-2

slope=-3/5

slope of reqd. line=-1/(-3/5)=5/3

eq. of line through (3,2) is

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

3y-6=5x-15

3y=5x-15+6

3y=5x-9

y=5/3 x-3

Answer:

40.49

Step-by-step explanation:

First term: a         n term: aₙ        common ratio: r     sum of first n term: sₙ

a + (ar) = a(r+1) = 36

a * ar² = 9 * ar  .... divide ar both side

ar = 9   ... 2nd term

a + (ar) = a + 9 = 36

a = 27  ... first term

r = 9/27 = 1/3

sₙ = a (1 - rⁿ) / (1-r)      n=8

s₈ = 27 * (1 - 1/3⁸) / (1 - 1/3)

   = 27 * (1 - 1/6561) / 2/3

   = 27 * (6560/6561) / 2/3

   = 27 * 3280/2187

   = 3280/81

   = 40.49

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

By using Orbit-Stabilizer Theorem, we can prove that the number of G-subsets of X is 2n, where n is the number of distinct orbits in X

The Orbit-Stabilizer Theorem states that, for any element x in a G-set X, the number of elements in the orbit of x is equal to the number of elements in the stabilizer of x, multiplied by the number of orbits in X. In other words, if G is a group and X is a finite G-set, then the following equation holds:

|G| = |Orbit(x)| * |Stabilizer(x)|

where |G| is the number of elements in G, |Orbit(x)| is the number of elements in the orbit of x, and |Stabilizer(x)| is the number of elements in the stabilizer of x.

A subset is a set of objects or elements that are contained within another set.

we can use the Orbit-Stabilizer Theorem. This theorem states that, for any element x in a G-set X, the number of elements in the orbit of x is equal to the number of elements in the stabilizer of x. The orbit of x is the set of all elements that can be obtained from x by applying the action of G, and the stabilizer of x is the set of all elements of G that leave x unchanged.

Since each element of X belongs to exactly one orbit, there are a total of n orbits in X. For each orbit, we can either include all of the elements in the orbit in our G-subset or exclude all of the elements in the orbit. This gives us 2 options for each of the n orbits, so the total number of G-subsets of X is 2^n = 2n.

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Answer:

a. c = 5.5n

b. Continuous

c. $33

Step-by-step explanation:

A store sells assorted nuts for $5.50 per pound.

a) Write a function in equation form to represent the total cost (c) of any number of pounds of nuts (n)

For every n, 5.5 is added to c. Thus, c = 5.5n

b) Will the graph of this function be continuous or discrete?

Continuous domains are ones that continue on in between intervals. For example, the height of someone would be continuous, because it could, for example, be between 50 inches and 70 inches. On the other hand, discrete domains are ones that can only be a set of given numbers. An example would be how much food you need to feed to a number of cats (for example, each cat needs to eat 0.5 pounds of food). Because you cannot have half a cat, the domain needs to have whole numbers.

Because you can buy 0.5 or 0.2 (or any amount of nuts), the domain is continuous.

c) What would the total cost be for 6 pounds of nuts?

Using the function from a), we know that the cost is 5.5n, where n is the amount of nuts you buy, in pounds. So, plug in "6"

5.5n = 5.5 * 6 = 33

Cost is $33

I hope this helps! Feel free to ask any questions!

Answer:

x = 8, y = 89/9

Step-by-step explanation:

Because of parallel lines, some angles are the same, see the attached image. That also means that (12x-28) + (9y-77) = 180 because they are half of an angle. So:

(12x-28) + (9y-77) = 180 ->

12x + 9y = 185.

Then,

(7x+12) = (12x-28) ->

x = 8.

We can plug that into the last equation:

12(8) + 9y = 185 ->

y = 89/9

:)

Answer:

look at the picture

Step-by-step explanation:

I'm not sure about the value of x but I believe it is -23

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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We can take Samanta's equation and rewrite it in such a way that we get Phil's equation, then the equations are equivalent.

Two equations are equivalent if we can rewrite one of them and get the other one.

We know that the equations are:

Samantha's equation: f(x)=(x+12)^2−16

Phil's equation: f(x)=(x+16)(x+8)

We can find the zeros of Samantha's equation by solving the quadratic equation:

(x+12)^2−16 = 0

(x + 12)^2 = 16

(x + 12) = ±√16

x + 12 = ± 4

x = ±4 - 12

Then the two zeros are:

x = (+4 - 12) = -8

x = (-4 - 12) = -16

Then we can factorize the quadratic function of Samantha as:

y = (x - (-8))*(x - (-16))

x = (x + 8)*(x + 16)

That is Phil's equation, then the equations are equivalent.

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the slope is

so, we need other point to calculate it

so, we have

the slope is 11/4

Step-by-step explanation:

in addition to a label what other piece of information must the axis on a graph include

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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a) The vertex of a quadratic function is a maximum point if the coefficient a is negative, and a minimum point if the coefficient a is negative.

b) A quadratic function in which the vertex is a maximum is given as follows: y = -2x².

c) A quadratic function in which the vertex is a minimum is given as follows: y = 2x².

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The leading coefficient a determines if the vertex of the quadratic function is a maximum point or a minimum point, as follows:

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We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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The equation represents the image of the line y = 3x +1 is y' = 3(x - 3) +1.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

The transformation that translates function y = f(x) by h units right and k units up is

y' = f(x -h) +k

We have y= 3x+ 1

So, After translating 3 units to x axis the function will become

y' = 3(x - 3) +1

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The total area of the regions between the curves is 4.5 square units

The graph is attached

From the question, we have the following parameters that can be used in our computation:

y = x² - 6x + 9 and y = x - 1

With the use of graphs, the curves intersect at

x = 2 and x = 5

So, the area of the regions between the curves is

Area = ∫x² - 6x + 9 - x + 1

This gives

Area = ∫x² - 7x + 10

Integrate

Area =  x³/3 - 7x²/2 + 10x

Recall that x = 2 and x = 5

So, we have

Area = [2³/3 - 7(2)²/2 + 10(2)] - [5³/3 - 7(5)²/2 + 10(5)]

Evaluate

Area = 4.5

Hence, the total area of the regions between the curves is 4.5 square units

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When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Case 1: SE = s / √500

Case 2: SE = s / √5,000

Case 3: SE = s / √50,000

To find the standard error of the mean in each of the given cases, we can use the formula:

Standard Error (SE) = population standard deviation / square root of sample size

However, since the population standard deviation is not provided, we'll need to use an estimated value. We'll assume the population standard deviation is unknown and use the sample standard deviation as an estimate.

Given that the sample size is 44 and the population mean (μ) is 8, we'll calculate the standard deviation for each case:

Case 1: Sample size (n) = 500

The sample size (500) is larger than 5% of the population (44), so we can assume it's a large enough sample. In this case, we'll use the standard formula for the standard error of the mean without the finite population correction factor:

SE = sample standard deviation / square root of sample size

= s / √n

Case 2: Sample size (n) = 5,000

Similar to Case 1, the sample size (5,000) is larger than 5% of the population (44), so we'll use the standard formula without the finite population correction factor:

SE = s / √n

Case 3: Sample size (n) = 50,000

In this case, the sample size (50,000) is much larger than the population size (44), which means we have a large enough sample. Therefore, we'll also use the standard formula without the finite population correction factor:

SE = s / √n

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Answer:

The answer to your query would be the Third Answer Choice.

Step-by-step explanation:

> First we need to find where the point (3,0) lies on the graph. We can do this by looking at the x coordinate, being 3, and the y, being 0. Keep in mind that the solution is where the two lines meet, not where the point on the graph is.

> This gets us to 3 on the x line, and no further. We then need to find which has an intersection of both lines on that point. If it is not (0,3), it is not the correct answer, which we are looking for.

> The first graph has a solution of (0, -1.5), as this is where the lines intersect. This is not (3, 0), so this is not our answer.

> The second graph’s lines intersect at (0,1), and since that is the solution of the graph, it is not the correct answer.

> The third graph’s lines intersect at (3, 0), and since this is it’s solution, it is the correct answer. Since we cannot be 100% sure, we still need to continue with checking the last graph.

> The fourth and last graph’s lines meet at (0,3), which is not what we are looking for, and is henceforth wrong.

> Once again, the correct answer is the Third Answer Choice. All the other graph’s have solutions on points other than (3,0), so they are not our answers.

> I hope this answered your query and any other questions you may have had on the subject. #LearningWithBrainly

The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

-------------

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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