Mr. Mann asked his class to form a number pattern using the rules:

Use the number 6 as the first term.

To find the other term, subtract 2 from the previous term, then multiply by 2.

The first two numbers in the pattern are 6 and 8.

What is the fourth number in the pattern?

The image of point K after GHK is rotated 90° counterclockwise about point G is (1,8).

What is counterclockwise ?

Counterclockwise is a rotational direction opposite to the direction that the hands on a clock move. It is also known as anticlockwise or counter-clockwise. In mathematical contexts, counterclockwise usually refers to a rotation direction in a Cartesian coordinate system where the positive direction of rotation is opposite to the positive direction of the x-axis.

According to the question:
To rotate point K 90° counterclockwise about point G, we can follow these steps:

Translate the image so that the center of rotation is at the origin (0,0). We can do this by subtracting the coordinates of G from each point:

G' = (1-1, 3-3) = (0,0)

K' = (6-1, 3-3) = (5,0)

H' = (6-1, 0-3) = (5,-3)

Rotate the image 90° counterclockwise. This can be done using the following formula for a 2D rotation:

(x', y') = (-y, x)

So, for each point:

K'' = (-0, 5) = (0,5)

Translate the image back to its original position by adding the coordinates of G:

K''' = (0+1, 5+3) = (1,8)

Therefore, the image of point K after GHK is rotated 90° counterclockwise about point G is (1,8).


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The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.

The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.

For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:

Summing up these values gives us:

1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5

Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.

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The total cost of repayment over 5 years is $23,300.

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

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Answer:

I'm not reallu sure.. but 5

Step-by-step explanation:

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Answer:

1.

7 x 30  is equal to 3 tens-

9 x 200 is equal to 2 hundreds-

2 x 5,000 is equal to 5 thousands-

6 x 7,000 is equal to 7 thousands-

Step-by-step explanation:

30/10 = 3

200/100 = 2

5,000/1,000 = 5

7,000/1,000 = 7

I love you it's gonna be okay :)

Answer: K is greater than or equal to 18

Step-by-step explanation:

Answer:k>=-18

Step-by-step explanation:

Rewrite so k

is on the left side of the inequality.

2/5⋅(k−2)≥−8

Multiply each term in

2/5⋅(k−2)≥−8 by 5/2 to eliminate the fractions.

k−2≥−20

Move all terms not containing

k to the right side of the inequality.

k≥−18

The result can be shown in multiple forms.

Inequality Form:

k≥−18

The equation of the plane is 12y - 48z = 0. It is a vertical plane parallel to the x-axis and intersects the y-z plane at y = 0 and z = 0. The plane extends infinitely in the x-direction and has a constant value of x.

The equation 12y - 48z = 0 can be rewritten as y - 4z = 0 by dividing both sides by 12. This equation represents a plane in three-dimensional space. To sketch the plane, we can start by considering points that satisfy the equation.

When y = 0 and z = 0, the equation is satisfied, giving us a point (0, 0, 0) on the plane. We can also choose other values for y and z to find additional points. For example, when y = 4 and z = 1, the equation is still satisfied, giving us another point (4, 4, 1) on the plane.

Since the coefficient of x is zero, the value of x can be any real number. This means the plane extends infinitely in the x-direction. The plane is parallel to the x-axis and intersects the y-z plane at y = 0 and z = 0, forming a line on the y-z plane.

In summary, the plane defined by the equation 12y - 48z = 0 is a vertical plane parallel to the x-axis. It intersects the y-z plane at y = 0 and z = 0, and extends infinitely in the x-direction, maintaining a constant value of x.

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We know that :

\(\sf{\bigstar \ \ Cos\theta = \dfrac{Adjacent \ Side}{Hypotenuse}}\)

From the figure, We can notice that :

Ф   Adjacent side length = 8

Ф  Hypotenuse length = 11

\(\sf{\implies Cosx^{\circ} = \dfrac{8}{11}}\)

\(\sf{\implies x^{\circ} = Cos^{-1}\bigg(\dfrac{8}{11}\bigg)}\)

\(\sf{\implies x^{\circ} = 43.34}\)

Answer:

It’s ain’t no function

Step-by-step explanation:

Answer:

2 gallons

Step-by-step explanation:

Answer:

2 gallons for 5.98$

Step-by-step explanation:

for two gallons.

1/4g milk = 12.92

1/2g milk= 8.36

1g milk= 8.50

The value of y when x is 1 is -2

Linear also interpretes as straight and a graph is a diagram which shows a connection or relation between two or more quantity.

We can also define straight graph which is drawn on a plane connecting the points on x and y coordinates. It is a graph of a linear equation.

To calculate any value of x or y we can use the graph to determine the value of x if y is given and the value of y if x is given

Therefore from the graph;

when x is 1 , the reading of y to the straight line is -2. Therefore the value of y is -2.

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The range of values (lower bound, upper bound) that corresponds to this confidence interval is $144 to $158. The confidence interval is expressed in the form of "estimate ± margin of error.

What is the range of values (lower bound, upper bound) that corresponds to this confidence interval?

To determine the range of values (lower bound, upper bound) that corresponds to this confidence interval, we need to use the formula of confidence interval.

The general formula for the confidence interval of a population mean is: \text{CI}=\text{sample mean}±\text{margin of error}\ \left(\text{ME}=z\frac{\text{SD}}{\sqrt{\text{n}}}\right)

Where: CI is the Confidence IntervalSD is the Standard Deviationn is the sample sizeme is the Margin of Errorz is the z-score.

For a 95% confidence interval, the corresponding z-value is 1.96 (we use the z-value because we know the sample size is greater than 30).

Let’s substitute the known values into the formula.

\text{CI}=\text{sample mean}±\text{margin of error}$$$$\text{CI}=151±7$$

Lower bound of the confidence interval:

\text{CI}=151-7$$$$\text{CI}=144$$

Upper bound of the confidence interval:

\text{CI}=151+7$$$$\text{CI}=158

Thus, the range of values (lower bound, upper bound) that corresponds to this confidence interval is $144 to $158.

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Answer:

The internship pays $7.5 an hour.

Step-by-step explanation:

From the information given, the equation would indicate that the amount the student earns per hour at the intership for two plus seven would be equal to 22:

2x+7=22

Now, you can solve for x:

2x=22-7

2x=15

x=15/2

x=7.5

According to this, the answer is that the internship pays $7.5 an hour.

The percentage of adult spiders that have carapace lengths exceeding a certain value is equal to the area under the standard normal curve that lies to the right of that value.

This is because the normal distribution is symmetric around its mean, and the area to the right of a certain value represents the proportion of data points that are greater than that value. Therefore, by calculating the area under the standard normal curve to the right of a certain value, we can determine the percentage of adult spiders with carapace lengths exceeding that value.

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The output of the following code snippet will be 1, 2, 3, and 4.

The reason is that the while loop runs infinitely until the break statement is executed. The break statement terminates the loop if the value of x is divisible by 5. However, the value of x is incremented at each iteration of the loop before checking the condition. Here is the step-by-step explanation of how this code works:

Step 1: Assign 1 to x.x = 1

Step 2: Start an infinite loop using the while True statement.

Step 3: Check if the value of x is divisible by 5 using the if x % 5 == 0 statement.

Step 4: If the value of x is divisible by 5, terminate the loop using the break statement.

Step 5: Print the value of x to the console using the print(x) statement.

Step 6: Increment the value of x by 1 using the x += 1 statement.

Step 7: Repeat steps 3-6 until the break statement is executed.

Therefore, the output of the code will be: 1 2 3 4.

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Answer:

x = 25

Step-by-step explanation:

Using the formula a²+b²=c², you can easily find out the hypotenuse of the triangle (which is the long side of it, and is the x in this problem.)

If we substitute the side lengths for the question in a²+b²=c², you'll get

20²+15²=x²

Simplifying the numbers and squaring them, you get

400+225=625²

Since you want the value of the x side, you'll need to root 625.

√625=25

Therefore, x = 25

Answer:

x = 25

Step-by-step explanation:

To find the side lengths of a right triangle, we can use the Pythagorean Theorem, a² + b² = c². a and b are the legs, and c is the hypotenuse, the longest side. In this figure, x is the hypotenuse, c.

Plug in our values for a and b and solve for x.

\(a^2+b^2=c^2\)

\(20^2+15^2=c^2\)

\(400+225=c^2\)

\(625=c^2\)

\(\sqrt{625}\) = \(\sqrt{c^2}\)

\(25=c\)

c, or x is equal to 25. The missing sidelength is 25 units.

Good luck ^^

Answer:

Putting -7 in place of x

Step-by-step explanation:

h(x) = 5.7 −19x

h(-7)= 5.7 - 19(-7)

         5.7 + 133

         138.7

The value of the function at -7 is 138.7.

x + y = 11

Putting -7 in place of x

-7 + y= 11

y = 18

Answer:

587.18 in²

Step-by-step explanation:

In the above question, we are given the following values

Diameter = 11 inches

Radius = Diameter/2 = 11 inches/2 = 5.5 inches

Slant height = 28.5 inches.

We were asked to find how many square inches of paper will she need to cover the ENTIRE cone.

To solve for this, we would use formula for Total Surface Area of a Cone

Total Surface Area of a Cone = πrl + πr²

= πr(r + l)

Using 3.14 for π

Total Surface Area of a Cone

= 3.14 × 5.5( 5.5 + 28.5)

= 3.14 × 5.5 × (34)

= 587.18 in²

Therefore, Anita will need 587.18 square inches of paper to cover the entire cone.

Answer:

B

Step-by-step explanation: Just trust me bro

The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."

The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.

The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.

The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).

Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.

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We can see that the measure that changes the most when the value of 82° is changed to 94° is the mean. The new mean temperature is 82.3°

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Before the change, the measures are:

IQR = 105 - 61 = 44°

Range = 105 - 57 = 48°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 81.4°

Median = the middle value, which is 84°

After the change, the list becomes:

58, 61, 71, 77, 91, 100, 105, 102, 95, 94, 66, 57

IQR = 102 - 61 = 41°

Range = 105 - 57 = 48°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 94 + 66 + 57) / 12 = 82.3°

Median = the middle value, which is still 84°

Hence, we can see that the measure that changes the most when the value of 82° is changed to 94° is the mean. The new mean temperature is 82.3°

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Answer:

  (d)  Median 84°

Step-by-step explanation:

You want to know the effect on various statistics of changing the value 82 to 94 in the data ...

  {57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105}

Changing a middle value in the list will have no effect on either the range or the IQR.

Changing a value from 82 to 94 adds 12 to the total of the 12 data values. This will increase the mean by 12/12 = 1 degrees to about 81.4.

The median value is currently the average of 77 and 82. Replacing 82 with 94, changes the order so that the median will be the average of 77 and 91. That is the median will increase by 9/2 = 4.5 degrees.

The measure that changes the most is the median. Its new value is 84°, choice D.

<95141404393>

Answer:2.94642857143

Step-by-step explanation:

Answer:

c<1

Step-by-step explanation:

If you needed c by itself this would be c<1

Therefore, the change in profit is approximately 0.60 and the percent change in profit is approximately 0.81%.

The given function is P = 100xe–x/400, where is sales.

The change in profit as sales increase from x = 115 to x = 120 units is to be determined.

To find the change in profit, we need to calculate the profit at x = 115 and x = 120 and then find the difference between them.

P(115) = 100 * 115e^(–115/400) ≈ 73.99

P(120) = 100 * 120e^(–120/400) ≈ 73.39

The change in profit = P(120) - P(115) ≈ 0.60

Approximate percent change in profit as sales increase from

x = 115 to x = 120 units = (change in profit / initial profit) × 100%≈ (0.60/73.99) × 100%≈ 0.81%.

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Surface area of old cube

Side of new cube

Surface area

Difference

Answer:

A)  6(x + y)² = 6x² + 12xy +6y²

B)  12xy +6y²

Step-by-step explanation:

Surface area of a cube = 6s²  (where s is the side length)

Part A

Given:

⇒ Surface area of the original cube = 6x²

If the side length of the cube is increased by y, then:

⇒ Surface area of the new cube = 6(x + y)²

Expand and simplify:

⇒ 6(x + y)²

⇒ 6(x + y)(x + y)

⇒ 6(x² + xy + xy + y²)

⇒ 6x² + 12xy +6y²

Part B

To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:

⇒ SA of new cube - SA of original cube

⇒ 6x² + 12xy +6y² - 6x²

⇒ 12xy +6y²

Answer:

-29.8

Step-by-step explanation:

4 (-1.2-4-4.75) +1+(-3)²

4 (-1.2-4-4.75) +1+(-3)²

4 (-9.95) +1+9

4 (-9.95) +1+9

-39.8 +1+9 = -29.8

Given:

The red figure dilated with a scale factor of \(s=\dfrac{1}{3}\) and the center of dilation is at the point (4,2) to get the green figure.

To find:

The coordinates of C' and A.

Solution:

If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

\((x,y)\to (k(x-a)+a,k(y-b)+b)\)

In given problem, the scale factor is \(\dfrac{1}{3}\) and the center of dilation is at (4,2).

\((x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)\)            ...(i)

Let the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

\(C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)\)

\(C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)\)

\(C(-2,11)\to C'(-2+4,3+2)\)

\(C(-2,11)\to C'(2,5)\)

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

\(A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)\)

From the given figure it is clear that the image of point A is (8,4).

\(A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)\)

On comparing both sides, we get

\(\dfrac{1}{3}(m-4)+4=8\)

\(\dfrac{1}{3}(m-4)=8-4\)

\((m-4)=3(4)\)

\(m=12+4\)

\(m=16\)

And,

\(\dfrac{1}{3}(n-2)+2=4\)

\(\dfrac{1}{3}(n-2)=4-2\)

\((n-2)=3(2)\)

\(n=6+2\)

\(n=8\)

Therefore, the coordinates of point A are (16,8).

Answer:

Step-by-step explanation:

Answer:

f(x) = 3.56(2.04)^x

Step-by-step explanation:

Put x as 2, to see whether the output will be close to 16.

116.4 - 42.8 ln(2) = 86.733301

2.04(3.56)^2 = 25.854144

3.56(2.04)^2 = 14.815296

-42.8 + 116.4 ln(2) = 37.882332

Put x as 3, to see whether the output will be close to 30.

116.4 - 42.8 ln(3) =69.379394

2.04(3.56)^3 = 92.040753

3.56(2.04)^3 = 30.223204

-42.8 + 116.4 ln(3) = 85.07847

Put x as 6, to see whether the output will be close to 271.

116.4 - 42.8 ln(6) = 39.712695

2.04(3.56)^6 = 4152.69615

3.56(2.04)^6 = 256.584846

-42.8 + 116.4 ln(6) = 165.760802

Put x as 7, to see whether the output will be close to 522.

116.4 - 42.8 ln(7) = 33.115046

2.04(3.56)^7 = 14783.598295

3.56(2.04)^7 = 523.433085

-42.8 + 116.4 ln(7) = 183.703941

The exponential function that models the data is f(x) = 3.56(2.04)^x.

If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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