State the coordinates of the point after the reflection across each axis.
1. (5,2)
2. (-6, 12)
3. (2,-7)
4. (-4,-2)
5. (0,-2)
Reflect across
the x-axis
Reflect across
the y-axis

g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.

Option C is the correct answer.

We have,

To find the transformation that maps f(x) to g(x), we need to determine how the points of g(x) relate to the points of f(x).

First, we can see that the two functions have the same x-coordinates (1 and 4). This means that the transformation only affects the y-coordinates of the points.

At x = 1,

f(x) has a y-value of 4, and g(x) has a y-value of 2.

This means that g(x) is f(x) after vertical compression by a factor of 1/2.

At x = 4, f(x) has a y-value of 8, and g(x) has a y-value of 4.

This means that g(x) is f(x) after vertical compression by a factor of 1/2.

Therefore,

g(x) can be expressed as a transformation of f(x) by vertical compression by a factor of 1/2.

i.e

g(x) = (1/2) f(x)

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The values with Charged Chip model are

9 + (-4) = 5.

9-(-4)=13

-9+4=-5

-9-(-4)=-5

To solve 9 + (-4), we start with 9 positive chips and take away 4 negative chips. We can represent this as:

[+][+][+][+][+][+][+][+][+]

[-][-][-][-]

When we combine the chips, we end up with 5 positive chips remaining:

[+][+][+][+][+]

Therefore, 9 + (-4) = 5.

To solve 9 - (-4), we start with 9 positive chips and add 4 negative chips. We can represent this as:

[+][+][+][+][+][+][+][+][+]

[-][-][-][-]

When we combine the chips, we end up with 13 positive chips remaining:

[+][+][+][+][+][+][+][+][+][+][+][+][+]

Therefore, 9 - (-4) = 13.

Similarly -9+4 value is -5

-9-(-4) value is -5

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Answer:

The answer is D

Step-by-step explanation:

8× the number

let the number be n

8×n=8n

Answer:

8n

Step-by-step explanation:

whenever a number is attached to a variable, that means multiplication. 8n is the correct answer.

have a great day and thx for your inquiry :)

Answer:

B is correct. Angle 7 measures 125°.

Step-by-step explanation:

Parallel lines intersected by a transversal form congruent alternate interior angles. Therefore, angles 4 and 5 are congruent, meaning angle 5 measures 55°. Angles 5 and 7 are supplementary angles, so angle 7 measures 125°. B is the correct answer.

The equation of each parabola with the given focus and directrix is:

y = (1/6)x² - (2/3)x - 11/6

Here, we have,

To derive the equation of the parabola, let (x , y) be a point in the parabola. Its distance from the focus should be equal to its distance from the directrix.

we will show here how to do  an equation of each parabola with the given focus and directrix.

1.)  focus: (2, -1); directrix: y = -4​

                      d (point to focus) = d (point to directrix)

                        sqrt ((x - 2)² + (y + 1)²) = (y + 4)

Squaring both sides gives us,

                                 (x - 2)² + (y + 1)² = (y + 4)²

Simplifying gives,

                      x² - 4x + 4 + y² + 2y + 1 = y² + 8y +16

Simplifying leads to,

                                       6y = x² - 4x -11

This leads to our final answer of

                                  y = (1/6)x² - (2/3)x - 11/6

Hence, The equation of each parabola with the given focus and directrix is: y = (1/6)x² - (2/3)x - 11/6

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The Surface Area is 11.075 square m and Volume is 2.15625 cubic m.

we have,

Length = 2.3 m

width= 1.25 m

height = 0.75 m

So, Surface Area

= 2 (lw + wh + lh)

= 2( 2.875 + 0.9375 + 1.725)

= 11.075 square m

Now, Volume = l w h

= 2.3 x 1.25 x 0.75

= 2.15625 cubic m

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Answer:

The correct option is A. Parallel line.

The y-intercept represents the base price of $200 for airfare from NYC.

The slope represent a cost of $0.30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.

In Mathematics, the slope-intercept form of the equation of any straight line is modeled by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this trip, an equation that represents the situation is given by;

y = mx + c

y = 0.30x + 200

When x = 2000 miles, the price of airfare (y) can be calculated as follows;

y = 0.30(2000) + 200

y = $800.

When y = $500, the distance traveled (x) can be calculated as follows;

500 = 0.30x + 200

300 = 0.30x

x = 1000 miles.

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We would need to randomly sample at least 1067 people to estimate the proportion of Americans who ate breakfast this morning with a margin of error of 3 percentage points and a 95% confidence interval.

The formula to calculate the sample size required to achieve a desired margin of error and confidence interval is:

n = (Z² x p x (1-p)) / E²

where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population who ate breakfast, and E is the desired margin of error as a decimal (0.03 in this case).

To determine the estimated proportion of Americans who ate breakfast this morning, we could use data from previous studies or surveys. Let's assume that previous studies have found that approximately 60% of Americans eat breakfast regularly. Therefore, we can use p = 0.60 in our formula.

Substituting the values into the formula, we get:

n = (1.96² x 0.60 x 0.40) / 0.03²

n ≈ 1067

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The true statement about the given ones is:

"The 4 is the x-coordinate and indicates movement parallel to the x-axis."

A general point in 2D is written as (x-coordinate, y-coordinate). The x-axis is the horizontal axis, and the y-axis is the vertical one. With information we can graph the point.

Here we have the point (4, 9), then:

4 = x-coordinate.

9= y-coordinate.

And to graph these, just move these number of units along (or parallel to) the correspondent axis.

The only true statement from the given one is:

"The 4 is the x-coordinate and indicates movement parallel to the x-axis."

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The mistake done in the solution is while finding the distance from mean we have not taken the absolute value

To find the MAD (Mean Absolute Deviation), first find the mean of the data set:

mean = (2 + 3 + 4 + 7 + 9 + 11) / 6 = 6

Then, calculate the absolute deviation of each data point from the mean:

|2 - 6| = 4

|3 - 6| = 3

|4 - 6| = 2

|7 - 6| = 1

|9 - 6| = 3

|11 - 6| = 5

Next, find the average of these absolute deviations:

(4 + 3 + 2 + 1 + 3 + 5) / 6 = 2.67

While find the distance from mean we have to use the absolute value or positive value

Hemce, the MAD of the data set {2, 3, 4, 7, 9, 11} is 2.67.

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The translation matrix is,

[tex]\left[\begin{array}{ccc}2&2&2\\-1&-1&-1\end{array}\right][/tex]

The coordinates of the triangle as a coordinate matrix is

-2 0 0

0 0 1.

Here the triangle has been translated 2 units right and 1 unit down.

Translating the triangle 2 units to the right means that each x -coordinate increases by 2.

Translating the triangle 1 unit down means that each y -coordinate decreases by 1.

So the translation matrix is,

[tex]\left[\begin{array}{ccc}2&2&2\\-1&-1&-1\end{array}\right][/tex]

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The volume of the object made up of 3 cubes of 1 inch each is 3 cubic inches.

To find the volume of the object made up of 3 cubes, we need to know the dimensions of the object in terms of the length, width, and height.

If each cube has a length, width, and height of 1 inch, then the object made up of 3 cubes will have a length of 3 inches, a width of 1 inch, and a height of 1 inch.

Therefore, the volume of the object is:

Volume = Length x Width x Height

Volume = 3 inches x 1 inch x 1 inch

Volume = 3 cubic inches

So, the volume of the object made up of 3 cubes is 3 cubic inches.

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--The given question is incomplete, the complete question is given

" The object is of 3 cubes is made up of 1 inch cubes what is the volume of the object"--

The value of KL and LMJ in the pie chart are 54 degrees and 198 degrees respectively

The pie chart is an important type of data representation. It contains different segments and sectors in which each segment and sector of a pie chart forms a specific portion of the total(percentage). The sum of all the data is equal to 360°. The total value of the pie is always 100%.

To find the value of angle KL and LMJ, we can proceed as;

a. angle KL;

KL = 15 / 100 = x / 360

KL = 0.15 = x / 360

x = 360 * 0.15

x = 54°

KL = 54°

Let's find LMJ

LMJ = 24 + 31 = 55%

55 / 100 = x / 360

0.55 = x / 360

x = 360 * 0.55

x = 198°

LMJ = 198°

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Surface area  of Maya's deck box  is 11.075 square meter and Volume is 2.15625 cubic meters

The dimensions of Maya's deck box are length is 2.3 m, width is 1.25m and height is 0.75m

Surface area =2lw+2lh+2hw.

=2(2.3×1.25) + 2(2.3×0.75) + 2(0.75×1.25)

=2(2.875) + 2(1.725)+2(0.9375)

=5.75+3.45+1.875

=11.075 square meter

Volume = Length×width×height

=2.3×1.25×0.75

=2.15625 cubic meters

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Answer:

[tex]-\frac{9}{1}[/tex]

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

The value of angle x is 48.07 degree.

Given that,

ΔSTU is right angle triangle

TU = 7

SU = 9.4

Since sinx = opposite/hypotenuse

                 = TU/SU

                 = 7/9.4

                 = 0.744

⇒ sinix = 0.744

Take inverse of sinx both sides

⇒ x = 48.07 degree

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Answer:

7 schools have fewer than 50 classrooms.

The probability that a person will be exposed to more than 5.20 mrem of cosmic radiation on a flight across the US is 0.0745, or 7.45%.

We want to find the probability that a person will be exposed to more than 5.20 mrem of cosmic radiation on such a flight.

Let X be the amount of cosmic radiation exposure on a flight.

Then we need to find P(X > 5.20).

We need to standardize the random variable X by converting it to a standard normal variable Z with mean 0 and standard deviation 1, using the formula:

Z = (X - μ) / σ

Substituting the given values, we get:

Z = (5.20 - 4.35) / 0.59 = 1.44

Now we need to find the probability that a standard normal variable is greater than 1.44.

Using a standard normal distribution table or a calculator, we can find that this probability is approximately 0.0745.

Therefore, the probability that a person will be exposed to more than 5.20 mrem of cosmic radiation on a flight across the US is 0.0745, or 7.45%.

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Answer:

Step-by-step explanation:

The area of the kite is 47.25 square feet.

Given is a figure of Kite.

We know that the diagonal of a Kite divides the Kite into equal two triangles.

Here same things happened.

For the upper triangle, the length of the base is = 10.5 feet.

And the base of the height corresponding to that base = 4.5 feet.

So the area of the upper triangles = (1/2)*10.5*4.5 = 23.625 square feet.

Since the areas of the triangles are equal so the area of the bottom triangle is also 23.625 square feet.

Hence the area of Kite = sum of the areas of this triangles = 23.625 + 23.625 = 47.25 square feet.

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The probability that it ends up centered on the red color is 39/64.

Given that there are four concentric circles on the ice with radii of 4 inches, 3 feet, 5 feet, and 8 feet,

We need to find the probability that it ends up centered on the red color.

So,

The total area = 8²π = 64π

4 inches = 1/3 feet

So, the area of red part = (8²-5²)π = 39π ft²

So, the probability that it ends up centered on the red color = area of red part / total area

= 39/64

Hence the probability that it ends up centered on the red color is 39/64.

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Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

Answer:

Step-by-step explanation:

This data does not provide sufficient evidence that the level of radon in the country is unsafe at the 0.05 level of significance.

We have taken a random sample of 32 homes and we have measured the radon level in each. The sample mean is 4.9 with a standard deviation of 2.1. Using a significance level of 5 %, we have to determine whether this data provides convincing evidence that the mean radon level in the country is too high.

State:

H1: mu = 4

H2: mu > 4 (unsafe radon level)

The parameter is an acceptably safe radon level.

The significance level (alpha) = 0.05.

We will do a one-sample t-test with a random sample, large sample size (> 30), and sample size of less than 10% of the population

t-stat = (sample mean - population mean)/(sample standard deviation/square root(sample size)

= (4.9 - 4)/(2.1/[tex]\sqrt{32}[/tex]) = 2.42

p-value = P(t > 2.42) with 31 degrees of freedom is just above 0.1 (using table value for DOF = 30).

We will not reject H1 at 0.05 level of significance as

p-value > level of significance.

Therefore, we do not have sufficient evidence that the level of radon in the country is unsafe at the 0.05 level of significance.

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Answer:

The correct sequence of steps to use the offset command is:

1. Select the original object to be offset

2. Select the offset command

3. Add the distance of the offset

4. Select a point anywhere on the screen where you want to offset the object

5. Select the object from the original object

I hope that helps!

The logarithmic equation is equivalent to this exponential equation is x = log (8/25) (option c).

In this case, we are asked to find the logarithmic equation that is equivalent to the given exponential equation:

2,400 = 7,500(10)⁻ˣ

To solve for x, we need to isolate it on one side of the equation. We can start by dividing both sides by 7,500:

2,400/7,500 = (10)⁻ˣ

The choice of base for the logarithm doesn't matter, as long as we use the same base for both sides. Let's use base 10:

log(2,400/7,500) = log(10⁻ˣ)

Using the properties of logarithms, we can simplify the right-hand side:

log(2,400/7,500) = -x*log(10)

We know that log(10) = 1, so we can simplify further:

log(2,400/7,500) = -x

x = log(8/25) = log(8) - log(25) = 0.9031 - 1.3979 = -0.4948

So the only answer choice that gives us the same equation as the original exponential equation is (C) x = log (8/25).

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Complete Question:

Which logarithmic equation is equivalent to this exponential equation?

2,400 = 7,500(10)^(-x)

A. x= -log (25/8)

B. x = log(-25/8)

C. x = log (8/25)

D. x = -log (8/25)

The correct answer is:

C) Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

The student set up a hypothesis test to investigate whether there is evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The null hypothesis is that the proportion is 0.5, and the alternative hypothesis is that it differs from 0.5.

The student obtained a standardized test statistic of z = -0.80 and a P-value of 0.2119.

To make a conclusion, the student needs to compare the P-value to the significance level α.

The significance level is given as 0.10, which means that the student is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Since the P-value of 0.2119 is greater than α = 0.10, there is not convincing evidence to reject the null hypothesis. Therefore, the student cannot conclude that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

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