9. A rectangle is inscribed in a circle.
a. Calculate the area of the circle.

b. Calculate the area of the rectangle.

c. Calculate the area of the shaded region.

SOLUTION

This is a right-triangle problem.

We will use the SOHCAHTOA principle.

In this triangle, we will relate the opposite side and the hypotenuse side to get the value of x. That will be the CAH relationship.

The final answer is 73.87 degrees.

Solution

We have the following data:

0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5

And the mean would be:

Mean = 2.958

And the median

Median = 4

Then if we add a 5 then the median would be the same 4

And the mean = 3.04

then the solution is:

The mean would increase

And for the other part of the question

we have:´

4+3+1+2 = 10 people made 3 or less trips to the movie

the answer is 1 1/4 cups of vinegar

Step-by-step explanati

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side thus bisecting that side.

Hence, Median best describes the line.

Option A is the correct option,

Given data:

The given principal is P=$3,300.

The given rate of interest is r=3.3%.

The given time is t=20 years.

The expression for the final amount of money is,

Substitute the given values in the above expression.

Thus, the final amount after 20 years is 5,478.

The slope of the line passing through the y intercept and the vertex of the quadratic  x²+10x-5 is 5.

The provided quadratic equation is,

y = x²+10x-5

The vertex of a quadratic equation,

(-b/2a, -D/4a)

Where,

a = 1,

b = 10,

c = -5,

D = (b²-4ac)

D = (10²-4(-5)(1))

D = 100+20

D = 120,

Putting all the values to find the vertex of the equation,

(-10/2,-120/4)

(-5,-30)

So, the vertex are now known,

To find the y intercept, putting x = 0 and solving the equation for y,

y = (0)²+10(0)-5

y = -5

The y intercept is,

(0,-5)

If there are two points on the line, let say (a,b) and (c,d), then the slope of the line is,

M = (d-b)/(c-a)

Now, we know two points,(-5,-30) and (0,-5).

We can now find the slope of line,

M = (-5+30)/(0+5)

M = 25/5

M = 5

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Answer:

Step-by-step explanation:

The answer is  B!

k=12

1) Gathering the data, and setting this table:

Blocks | Pounds

5 60

6 72

7 84

8 96

2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx

Then we can write:

y =12x

3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.

5 x 12 = 60

6 x 12 =

The correct answer is the figure

the equation for the circle with radius, r = 4 units and center =(4,-7)

will be (x-4)² + (y+7)² = (4)².

When the center and radius of a circle are known, how do you determine its equation?

Use the formula (x-a) ² + (y-b) ² = r ² to determine a circle's equation when you are aware of its radius and center. Here, stands for the circle's center, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.

In this question,

we are given the center of our circle to be,

(4,-7) ≈ (a,b)

thus we are given,

a = 4

and b = -7

and we are given the radius to be 4units

substituting these values in the above equation,

(x-4)² + (y-(-7))² = (4)²

= (x-4)² + (y+7)² = (4)²

Hence the equation for the circle with radius, r = 4 units and center =(4,-7)

will be (x-4)² + (y+7)² = (4)².

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The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

Given that,

equation of given line with a slope of m = 3

y=3x-5​

A line perpendicular to that line will have a slope that is the negative reciprocal of 3.

The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.

Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).

y = mx + b

4 = (-1/3)(6) + b      

(we've set up the equation with only one unknown, b, that we can now solve for)

4 = -2 + b

b = 6

With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:

y = (-1/3)x + 6

Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .

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We have two parallel lines intersected by other line.

We have to relate the angles.

We will take the angle with measure 17° as reference (red angle).

The angle <1 has a measure that is supplementary to the red angle, as <1 is supplementary to the <4, which is a corresponding angle to the red angle.

It has no direct relationship with the red angle.

The angle <2 is supplementary to <1, so it will have the same measure as the red angle (m<2 = 17°).

The relationship with the red angle is that they are alternate exterior angles.

Angle <3 has no direct relationship with the red angle. As it is vertical with <1 it has the same measure (m<3 = 163°) and is supplementary to the red angle.

Angle <4 and the red angle are corresponding angles.

They have the same measure, so they are congruent.

Angle <5 and the red angle form a linear pair, so they are supplementary. The measure of <5 is then m<5 = 163°.

Angle <6 and the red angle are vertical angles, so they have the same measure.

Angle <7 and the red angle form a linear pair, so they are supplementary. The measure of <7 is then m<7 = 163°.

Answer:

Angle <1:

Measure = 163°

Relationship: No name for relationship and supplementary.

Angle <2:

Measure = 17°

Relationship: Alternate exterior and congruent.

Angle <3:

Measure = 163°

Relationship: No name for relationship and supplementary.

Angle <4:

Measure = 17°

Relationship: Corresponding and congruent.

Angle <5:

Measure = 163°

Relationship: Linear pair and supplementary.

Angle <6:

Measure = 17°

Relationship: Vertical and congruent.

Angle <7:

Measure = 163°

Relationship: Linear pair and supplementary.

Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.

As given in the question,

Total number of students enrolled in Blue Bear High School =175

Number of students train in karate = 25

Number of students compete with other school in karate =35

Number of students practice martial arts but not karate=100

Number of students qualify for a karate tournament if they train and compete at Blue Bear High School

= 25 + 35

= 60

Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.

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Answer: -11270

Step-by-step explanation:

14xy = -11270   x=-23   y=35

14(-23)(35) = -11270

SOLUTION:

Case: System of equations

Given: A table of value of snacks and drinks for Sidney and Erica

Required: Write a system of equations to determine the price of each candy and each drink.

Method:

Step 1: Assume the price of snacks be represented by s and drinks by d

Step 2: Equation for Sidney

Step 3: Equation for Erica

Final answer:

The system of equations is:

The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (-2,-3)

h = -2

k = -3

P in this problem, is the distance between the vertex and the directrix

P = -3 - -5 = -3 + 5 = 2

p = 2

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -2)² =  4 * 2 (y - -3)

(x + 2)² =  8 (y + 3)

rearranging the equation

8 (y + 3) = (x + 2)²

y + 3 = 1/8 (x + 2)²

y = 1/8 (x + 2)² - 3 (standard vertex form)

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Answer:

[tex]x=\frac{-1}{7}[/tex]

Step-by-step explanation:

[tex]8=x/7+9\\[/tex]

Subtract 9 from both sides

[tex]-1=x/7[/tex]

Multiply both sides by 7

[tex]\frac{-1}{7} =x[/tex]

Swap the order because you're a smart person

[tex]x=\frac{-1}{7}[/tex]

Answer:

I don't know if it is the answer

12x^3

Name: Monomial , because it has only 1 term

Degree: 3, exponent of the monomial

The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches ​if the standard deviation is 2.52.

To proceed we, find the z-score of 65 in the distribution, we make use of the formula;

x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.

inserting these values, we have;

The problem now boils down to finding the probability of the z-score greater than 0.043

From z-score tables. the probability of the z-score greater than 0.043;

Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285

When the linear correlation coefficient is 1 there is a perfect positive linear relation between the two variables. Scatter diagram would contain points that all lie on a line with a positive slop.

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.

A correlation coefficient is a metric that expresses a correlation, or a statistical link between two variables, in numerical terms. Two columns of a specific data set of observations, sometimes referred to as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.

The strength and direction of the linear links between two sets of variables are evaluated using correlation coefficients. Use Pearson's correlation coefficient if both variables are regularly distributed; otherwise, use Spearman's correlation coefficient.

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The value of a nickel is 5 cents

The value of the quarter is 25 cents

Since Priam has a total of 9.30 dollars = 930 cents, then

Simplify the equation by dividing all terms by 5

Since he has 6 nickels less than 3 times the quarters, then

Substitute n in equation (1) by equation (2)

Add the like terms on the left side

Add 6 to both sides

Divide both sides by 8

The number of quarters is 24

Substitute q by 24 in equation 2 to find n

The number of nickels is 66

He has 66 nickels and 24 quarters

The current amount of the sale is 96

The sale is 120

It was decreased by 20%

20/100 × 120

= 0.2 × 120

= 24

The amount of the current sale is

120-24

= 96

Hence the amount of the current sale which is calculated by subtracting 24 from 120 is 96

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Answer:

Step-by-step explanation:

A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.

a. All positive integers are greater than 0,

we can express this as a set which positive integers less than 8, A = {1, 2, 3, 4, 5, 6, 7}.

This is a Finite Set.

b. The number 12353888 has a set of digits, 1, 2, 3, 5 and 8 and can be expressed as C = {1, 2, 3, 5, 8}

This is also a Finite Set.

c. The set of courses you are enrolled depends on the number of courses. We can express this as

D = {course1, course2, course3, ...}

This is Universal Set.

The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;

The answer is 10.82 inches, to 2 decimal places

According the question

Side AC of the triangle = 16

Side BC = 14

The opposite side of the triangle is AC = 14

The adjacent side of the triangle is BC = 16

Using SOH CAH TOA