In circle P, chord is 3 inches from the center and chord is 5 inches from the center. Chord CD is
than chord AB.

The mean absolute deviation of 4 in data set is -7

First, we need to determine the value of the mean

We have from the information given that;

6, 22, 14, 9, 11, 4​

Mean = sum of the given set of data/number of the data given

Substitute the values, we have that;

Mean = 6 + 22 + 14 + 9 + 11 + 4/6

add the values, we get

Mean = 66/6

Divide the values

Mean = 11

Mean absolute deviation = data value - mean

Mean absolute deviation = (4 -11) = -7

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Answer:

=4(2x-5y)-3x    first we multiply 4(2x-5y)⇒4(2x) and 4(5y) =8x-20y    then it becomes,

=8x-20y-3x   collect like term (8x & -3x)

=8x-3x-20y        8x-3x=5x  so,

=5x-20y

The transformation applied to the triangle is a rotation.

Here we have a transformation that maps the blue triangle into the orange one.

Remember that neither a translation nor a dilation change the orientation of the figure, so we can discard these two.

If it was a reflection, we should be able to find a line of symmetry between the two figures, and we can't do that here, then we can conclude that the transformation applied was a rotation.

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The parabola intersects the x-axis at the point (4.5, 0), and the x-intercept is 4.5.

To find the x-intercepts of a parabola, we need to determine the values of x where the graph intersects the x-axis. At the x-intercepts, the y-coordinate is always 0.

Given the information about the parabola falling from the left, passing through the point (3, 2), rising to the right, and passing through the point (6, 2), we can determine the equation of the parabola.

Since the parabola is symmetric, we can find the axis of symmetry (x-coordinate of the vertex) by taking the average of the x-values of the two given points:

x-coordinate of the vertex = (3 + 6) / 2 = 4.5

Now, we know the vertex of the parabola is (4.5, 0).

The equation of the parabola can be written in vertex form as follows:

y = a(x - h)^2 + k

where (h, k) represents the vertex. Since the vertex is (4.5, 0), we have:

y = a(x - 4.5)^2 + 0

Simplifying, we get:

y = a(x - 4.5)^2

To find the value of 'a', we can substitute one of the given points on the parabola. Let's use the point (3, 2):

2 = a(3 - 4.5)^2

2 = a(-1.5)^2

2 = 2.25a

a = 2 / 2.25

a = 8/9

Therefore, the equation of the parabola is:

y = (8/9)(x - 4.5)^2

To find the x-intercepts, we set y = 0:

0 = (8/9)(x - 4.5)^2

Setting each factor equal to zero, we get:

(x - 4.5)^2 = 0

Taking the square root of both sides, we find:

x - 4.5 = 0

Solving for x, we get:

x = 4.5

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All of the given equations y = |x| + 3, y = x^2 + 3x, y = 2x + 1, and y = x^2 - 5x represent functions because they meet the criteria of assigning a unique output value to each input value.

A function is a mathematical relation that assigns a unique output value to each input value. To determine which of the given equations represent functions, we need to analyze if there is a unique output for each input.

(1) y = |x| + 3: This equation represents a function. For every input value of x, the absolute value of x is taken and then added to 3, resulting in a unique output value for each input.

(2) y = x^2 + 3x: This equation represents a function. The variable x is squared, multiplied by 2, and then 3 is added to it. Again, this process ensures that for each input value of x, there is a unique output.

(3) y = 2x + 1: This equation represents a function. It is a linear equation where the output (y) is determined by multiplying the input (x) by 2, then adding 1. The process guarantees a unique output for each input.

(4) y = x^2 - 5x: This equation represents a function. The input value of x is squared and then multiplied by x, and the result is subtracted from 5x. This equation follows the definition of a function, providing a unique output for every input.

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The surface area of the triangular prism is 77 units²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is calculated by adding all the area of the surfaces.

area of the two triangles = 2( 1/2 bh)

= bh

= 3 × 4 = 12 units

area of the two squares =2 l²

= 2(5²) = 50 units

area of the rectangle = l× w

= 5 × 3

= 15 units

The surface area of the prism

= 12 + 50 +15

= 77 units²

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The y-intercept is 40.5 the machine starts with 40.5 ounces of diet soda.

Option B is the correct answer.

We have,

From the graph plot,

We see that,

The y-intercept is when x = 0.

This means,

At 0 hours, the amount of diet soda is 40.5.

Now,

y = 40.5 means the machine starts with 40.5 ounces of diet soda.

Thus,

The y-intercept is 40.5 the machine starts with 40.5 ounces of diet soda.

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Kennedy will pay $46.58 to mail all four packages.

Given that; Kennedy wants to mail three packages that each weigh 2.25 pounds.

Hence:

The weight of packages is:

3 × 2.25 pounds per package = 6.75 pounds

He also wants to mail another package that weighs 1.75 pounds. Therefore, the total weight of all the packages is:

6.75 pounds + 1.75 pounds = 8.5 pounds

To determine the total cost of mailing all four packages, we need to multiply the total weight by the cost per pound.

Since the cost per pound is given as $5.48.

Therefore, the total cost will be:

Total cost = 8.5 pounds × $5.48 per pound

Total cost = $46.58

Therefore, the total cost of mailing all the packages is $46.58.

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Answer:

m∠6 = 50°

Step-by-step explanation:

We know that angles 3 and 6 are same side interior angles.  Whenever a traversal cuts through two parallel lines (AB and CD), the sum of the same side interior angles is always 180.

Thus, we can find the measure of ∠6 by subtracting the measure of ∠3 from 180:

m∠6 + m∠3 = 180°

m∠6 + 130° = 180°

m∠6 = 50°

Answer:

8 3/4

Step-by-step explanation:

First convert mixed number into improper fraction

3 3/4= multiply whole number by denominator, then add the numerator 3*4+3= 15/4

2 1/3= 2*3+1= 7/3

15/4*7/3= 8 3/4

When Suzi stuck two lumps of coal in Mr Snowman's face He exclaimed "I can see!"

Suzi was a little and yet mischievous girl who came to play with Mr. Snowman who lived in the snowy wonderland. He however had no eyes and Suzi noticed this.

So, Suzi decided that she would make Mr. Snowman capable of seeing and so found two lumps of coal and stuck them in Mr. Snowman's face. Mr. Snowman exclaimed in a deep, booming voice, "I can see!" Suzi was surprised and delighted to hear the snowman talk.

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Introducing numeracy to young children can be done through various types of equipment and resources that engage their senses and make learning math concepts more interactive and enjoyable.

Here are some different types of equipment commonly used to introduce numeracy to young children:

Thus, by incorporating a variety of equipment and resources, educators and parents can create a rich learning environment that supports children's numeracy development and fosters a positive attitude towards math.

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Answer:

40 slices

Step-by-step explanation:

I rounded 38 to 40 and divided by 8

The side length of the given square having an area of 81 cm² is 9cm.

Given side length of the square (c) = ?

The square with side length 'c' having an area of = 81 cm²

From the above line, we have given an equation. It is

c² = 81 cm²

We know that, the area of the square = side length²

So, to find out the side length of the square we have to find the "c" value.

C² = 81 cm²

C = √81 cm²

C = 9 cm.

From the above analysis, we can conclude that the given square is having a side length of 9cm.

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Given question is not having clear information. I am attaching the clear question below:

The solution to the inequality is x < 3/14.

To solve the inequality -14x > -3 need to isolate the variable x on one side of the inequality sign.

We can start by dividing both sides by -14.

Since we are dividing by a negative number need to flip the inequality sign to maintain the direction of the inequality:

-14x/-14 < -3/-14

x < 3/14

The solution to the inequality is x < 3/14.

The solution by noting that 3 and 14 do not have any common factors so 3/14 is already in its simplest form.

The solution tells us that x is less than 3/14 means any value of x that is less than 3/14 will make the inequality true.

x = 0 x = -1 and x = -0.5 are all values that satisfy the inequality since they are less than 3/14.

We divide both sides of an inequality by a negative number need to flip the direction of the inequality sign.

This is because dividing by a negative number flips the sign of the inequality and we need to maintain the direction of the inequality to ensure that our solution is correct.

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We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer:

1837.711 feet

Step-by-step explanation:

sin (86.03)= 183.27 over x H degrees

183.27/sin (86.03)

which = 1837.711 feet

Answer:

384.67

Step-by-step explanation:

The margin of error for the 99% confidence interval for the true mean monthly salary of all former students can be calculated using the formula:

Margin of error = z * (standard deviation / sqrt(sample size))

where z is the z-score associated with the desired confidence level (in this case, 99%), standard deviation is the population standard deviation (given as $550), and sqrt(sample size) is the square root of the sample size (15).

The z-score for a 99% confidence level can be found using a standard normal distribution table or calculator, and it is approximately 2.576.

Plugging in the values, we get:

Margin of error = 2.576 * ($550 / sqrt(15))

                ≈ $384.67

Therefore, the margin of error of the 99% confidence interval for the true mean monthly salary of all former students is approximately $384.67.

The solution is:

Perimeter = 4 units

Explanation:

here, we have,

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

we have,

The perimeter of a figure is the measures of the distance around it.

Now in our case EFGH is a square with side length 1.

Since a square has 4 side lengths, its perimeter is

1 + 1 + 1 + 1 = 4

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complete question:

What is the perimeter of square EFGH?Perimeter = ____ units

Answer:

  (0, -4)  and  (6, 0)

Step-by-step explanation:

You want two solutions to 2x -3y = 12.

Each intercept is the value of the variable when the other is zero. Here, they are easy to find by dividing the constant by the variable's coefficient:

  x-intercept: 2x = 12   ⇒   x = 12/2 = 6 . . . . point (6, 0)

  y-intercept: -3y = 12   ⇒   y = 12/-3 = -4 . . . . point (0, -4)

__

Additional comment

The intercepts can be used as two points on the line when you want to graph it. They can also be used to estimate the quadrant of the solution when you are working with a system of two equations.

For example, these intercepts tell you there will be no solutions in quadrant II. Any solutions in the first quadrant will have x-values greater than 6. Any in the third quadrant will have y-values less than -4.

If you want other solutions, it is convenient to choose x-values that are multiples of 3, and/or y-values that are multiples of 2. These will ensure integer solutions.

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a. The events A and B are independent

b. The events A and B are independent

a. The events A and B are independent because the outcome of one event does not affect the outcome of the other event.

After selecting a penny, there are still dimes in the jar, and the probability of selecting a dime does not change.

b. The events A and B are independent because the day of the week does not affect the choice of shoe color.

The probability of selecting red shoes is the same for any day of the week.

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The value of x from the given figure is 8/3

Perimeter of a parallelogram

The sum of all the ides of the parallelogram is perimeter.

According to the given figure;

2(3x-8)+2(16) = 32.2

Expand to have:

6x-16 + 32 = 32.2

6x + 16 = 32.2

Subtract 16 from both sides

6x = 16

x = 16/6

x = 8/3

Hence the value of x from the given figure is 8/3

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complete question;

The perimeter of the parallelogram below is 32.2. What equation would you set up to solve for x? What is the value of x?

The length of the rectangle is 4 units.

We have,

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Let n be the length of the rectangle.

The width of a rectangle is the length minus 2 units.

The width = n - 2

The area of the rectangle is 8 square units.

The area of the rectangle = length x width

8 = n (n-2)

n²-2n - 8 = 0

n²-4n+2n - 8 = 0

n(n-4)+2(n-4) = 0

(n+2)(n-4) = 0

n = 4 and -2.

So the length is 4 units.

Therefore, 4 units are the length of the rectangle.

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complete question:

The width of a rectangle is the length minus 2 units. The area of the rectangle is 8 square units. What is the length, in units, of the rectangle?

The monthly payment is approximately $95.63.

To find the monthly payment, we need to calculate the balance after the upfront payment and then determine the monthly payment required to finance that balance over 24 months with 10% interest.

The upfront payment is 40% of $3499.58:

Upfront payment = 40% * $3499.58 = $1399.83

The balance to be financed is the remaining amount after the upfront payment:

Balance = $3499.58 - $1399.83 = $2099.75

To calculate the monthly payment, we can use the formula for monthly payments on a loan:

m = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount (balance)

r = Monthly interest rate

n = Number of monthly payments (24)

The monthly interest rate is 10% divided by 12 (for 12 months in a year):

r = 10% / 12 = 0.10 / 12 = 0.00833333 (rounded to 8 decimal places)

Plugging in the values:

m = ($2099.75 * 0.00833333 * (1 + 0.00833333)^24) / ((1 + 0.00833333)^24 - 1)

Evaluating the expression:

m ≈ $95.63 (rounded to 2 decimal places)

Therefore, the monthly payment is approximately $95.63.

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The new function in terms of g(x) is g(x) = -2|x - 3).The correct answer is option B.

To understand why, let's break down the transformation step by step:

1. Translation Down by 3 Units: This means shifting the graph of the function downward by 3 units. To achieve this, we subtract 3 from the original function's expression, resulting in f(x) - 3 = |x| - 3.

2. Vertical Stretch by a Factor of -2: A vertical stretch affects the magnitude of the function's output. When we stretch a function vertically by a factor of a, we multiply the function's expression by that factor.

In this case, the factor is -2. Multiplying the translated function from step 1 by -2, we get -2(|x| - 3), which simplifies to -2|x - 3|.

Therefore, the new function, in terms of g(x), is g(x) = -2|x - 3).

Option B correctly represents this transformation by subtracting 3 inside the absolute value and multiplying the entire expression by -2.Option A does not incorporate the vertical stretch factor of -2, while option C includes an additional unnecessary shift. Option D represents a different linear function, not the translated and stretched absolute value function.

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Answer:

Can you add more context?

Step-by-step explanation:

The equation of the parabola is y= 1/255 (x+4)² -8.

Since the parabola opens up, the general equation of the parabola is of the form [tex]$y = a(x-h)^2 + k$[/tex], where the vertex is (h, k).

So, substituting the given vertex (h,k)=(-4,-8), we have y=a(x+4)²-8.

Since the focal diameter is 16, the distance from the vertex to the focus is [tex]$\frac{1}{4}$[/tex] times the length of the focal diameter. Thus, the focus is at a point [tex]$(h,k+p)$[/tex] where [tex]$p = \frac{16}{4} = 4$[/tex]

The equation of the directrix is y = k-p = -8-4 = -12.

Using the formula for the distance between a point (x,y) and the directrix y = k-p, we get:

|y- (k-p)| / √(1+a²)

= |y+ 12|/ (√1+a²)

= |x-h|

Since the focus is on the parabola, the distance from the focus to any point (x,y) on the parabola is given by:

[tex]$$\sqrt{(x-h)^2 + (y-k-p)^2} = |4p(x-h)|$$[/tex]

Substituting the values of (h, k,p), we get:

[tex]$$\sqrt{(x+4)^2 + (y+4)^2} = 16|x+4|$$[/tex]

Squaring both sides and simplifying, we get:

[tex]$$(y+4)^2 = 256(x+4)^2 - (x+4)^2 = 255(x+4)^2$$[/tex]

[tex]$$(y+4)^2 = \frac{1}{255}(x+4)^2$$[/tex]

[tex]$$y+4 = \pm\frac{1}{\sqrt{255}}(x+4)$$[/tex]

Finally, substituting [tex]$y=a(x+4)^2-8$[/tex] and solving for a, we get:

a= (y+8)/ (x+4)²

Substituting this value of a in[tex]$y=a(x+4)^2-8$[/tex], we get:

y= (y+8)/ (x+4)²  (x+4)² -8

= 1/255 (x+4)² -8.

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