Use the circle shown below to determine the following:



What is the measure of the central angle?

central angle = ______ degrees

Solve an equation for x.

x = ________

What is the measure of the angle that bisects the minor arc?

bisecting angle = ________ degrees

Determine the measure of the major arc.

Major arc = _______ degrees

(45 points will give brainiest for efort)

Answer:

-72

Step-by-step explanation:

Because -32 + (2 - 6)(10). is -72

Answer:

Step-by-step explanation:

You want the equations for the lines shown on the graph.

The slope-intercept form of the equation for a line is ...

  y = mx + b

where m is the slope, and b is the y-intercept.

The slope of a line is the ratio of its "rise" to its "run". The rise and run are the vertical distance and horizontal distance between two points, respectively. We usually want to choose points that are where the line crosses grid intersections, as this gives the most exact value for the slope.

Red line: There is no rise for any value of run. The slope is ...

  m = rise/run = 0/1 = 0

Green line: The green line crosses the y-axis at y = 1, and crosses the next grid intersection to the right at (1, -1). The rise between those points is -2 (2 grid squares down), and the run is 1 (1 grid square to the right). The slope is ...

  m = -2/1 = -2

Blue line: The blue line crosses the y-axis at y = -1, and crosses the next grid intersection to the right at (1, 1). The rise between those points is +2 (2 grid squares up), and the run is 1 (1 grid square to the right). The slope is ...

  m = 2/1 = 2

Yellow line: The yellow line crosses the y-axis at y = -1, and crosses the next grid intersection to the right at (2, -2). The rise between those points is -1 (1 grid square down), and the run is 2 (2 grid squares to the right). The slope is ...

  m = -1/2

Y-Intercept.

The y-intercept is the value of y where the line crosses the y-axis. In the slope-intercept form equation (y=mx+b), this is the value of 'b'. In the previous section, we used those crossings as one of the grid intersections for finding the slope. They are ...

Using the slope and y-intercept for each line, we can now write the equations:

__

Additional comment

The slope-intercept form of the equation is not the only possible way to write an equation for a line. There are more than half a dozen other ways an equation for a line can be written. Each will have its use.

Other forms include ...

  ax +by = c . . . . . . . standard form

  ax +by -c = 0 . . . . . general form

  x/a +y/b = 1 . . . . . . . intercept form

  y -k = m(x -h) . . . . . point-slope form

Intercept forms don't work well when one of the intercepts is missing. For the red line, the x-intercept is missing. Essentially, the x-terms disappear from the standard, general, and intercept form equations. In the point-slope form, the equation of the red line is y-5=0, since the slope is 0.

Answer: (440-308) ÷ 22 = The cost of each tool kit is 6 dollars

Step-by-step explanation:

The original price of the field trip was $308 after the price fof each tool kit was added the price was $440.

The total costs of all the tool kits was 132

440-308=132

the total cost of the tool kits divided by the number of kids will get the price of each tool kit

132÷22 =

K=

The vertical measurement of the structure corresponds to an estimated value of 119.53 feet.

The dimensions of the building can be represented by the variable h, whereas the proximity of Jeanna to the building in her initial stance can be identified as x. Utilizing the principles of trigonometry, it is feasible to express the following:

The trigonometric function involving the angle of 35 degrees and its corresponding acute triangle can be written as an equation in the form of tan(35) = h/x, which is denoted as equation 1.

Upon moving a distance of 100 feet from her initial position, Jeanna's distance from the building can be represented as x - 100. Additionally, the angle at which she must look up to view the top of the building is now 40 degrees. Through the application of comparable trigonometric reasoning, it is possible to articulate the following statement:

Equation 2 can be expressed as tan(40) = h/(x - 100), where h and x represent the height and horizontal distance, respectively.

Equation 1 can be manipulated in such a way as to express the variable x in terms of h. The value of x is obtained by dividing h by the tangent of 35 degrees.

The substitution of the given expression for variable x in equation 2 leads to the following result:

The equation tan(40) = h/(h/tan(35) - 100) is amenable for rephrasing in a more academic style of writing.

Upon performing reduction on this mathematical expression, it results in:

The given mathematical equation can be represented in an academic manner as follows: The equation tan(40) = tan(35)h/(h - 100tan(35)) holds true, where h denotes the height of an object located at an angle of 40 degrees to the horizontal plane. This equation specifies the relationship between the tangent values of two distinct angles, 40 degrees and 35 degrees, and the height of the object.

The present equation can be expressed in a more formal academic style as follows: "The function h is defined as the difference between the tangent of 40 degrees and the tangent of 35 degrees, i.e., h = tan(40) - tan(35). This formula can be simplified, resulting in h = -100tan(35)tan(40)."

By dividing each side of the equation by (tan(40) - tan(35)), we are able to obtain the following result:

The following expression denotes the value of h, computed using mathematical operations: h = -100tan(35)tan(40)/(tan(40) - tan(35)).

The value of h is approximately equal to 119.53 feet.

Hence, the vertical measurement of the structure corresponds to an estimated value of 119.53 feet.

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Answer:

441cm^2

Step-by-step explanation:

84 divided by 4 is 21

21cm*21cm is 441cm^2

Answer:

0.506

0.516

0.609

0.615

Step-by-step explanation:

Psychologist requires a sample size of at least 126 SI scores.

We may use the following calculation to get the minimal sample size required to estimate the mean SI score of smokers with a margin of error of 12 and a 90% confidence level:

[tex]n = [Z * (\sigma / E)]^2[/tex]

Where:

Z = the z-score associated with the confidence level (90%), which can be found using a z-score table or calculator.

For a 90% confidence level, Z is approximately 1.645.

σ = the population standard deviation (82)

E = the desired margin of error (12)

Plugging in the values, we get:

n = [1.645 * (82 / 12)]^2

n = 126.2

We round up to the closest integer as the sample size must be a whole number in order to guarantee that the sample size is sufficient to fulfill the required confidence level and margin of error.

Thus, n = 126 is the required minimum sample size.

In order to estimate the mean SI score of smokers with 90% confidence that the estimate is within 12 of the actual population mean, the psychologist requires a sample size of at least 126 SI scores.

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Answer:

C. The items have different y-intercepts and different rates of change

Step-by-step explanation:

Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.

Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.

Thus, we know that the rates of change are different and the y-intercepts are different for both functions.

Answer:

52

Step-by-step explanation:

80% of 65 is 65 x 0.80

65 x 0.80 = 52

Therefore 52 seeds were planted.

Answer:

1:2

Step-by-step explanation:

The synthetic division of (x³ - 12x² + 15x + 7) / (x +4) gives Quotient

x² + 8x -17.

We have to divide.

(x³ - 12x² + 15x + 7) / (x +4)

Now, performing the division we get

              (x + 4) | x³ - 12x² + 15x + 7 | x² + 8x -17

                           x³ - 4x²

                         ________

                                  8x² + 15x

                                   8x² + 32x

                               ___________

                                             -17x + 7

                                               -17x -68

                                             __________

                                                          61

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Answer: Let's start by finding out the time it takes for Gerald to jog from Point A to Point B. We can use the formula:

distance = rate x time

to do this. Since the distance between Point A and Point B is 24 km and Gerald's speed is 6 km/h, we have:

24 = 6t

where "t" is the time it takes for Gerald to jog from Point A to Point B. Solving for "t", we get:

t = 4

So Gerald takes 4 hours to jog from Point A to Point B.

Now, let's look at Shaun's journey. We know that he starts 30 minutes after Gerald and reaches Point A 30 minutes earlier than Gerald. This means that the time it takes for Shaun to travel from Point B to Point A is 3.5 hours (i.e., 4 hours - 0.5 hours + 0.5 hours).

Using the formula distance = rate x time again, we can find out Shaun's average speed:

24 = rate x 3.5

simplifying, we get:

rate = 6.857 km/h

So Shaun's average speed is 6.857 km/h (or approximately 6.86 km/h rounded to two decimal places).

Answer:

  8 km/h

Step-by-step explanation:

You want to know Shaun's average speed on a 24 km jogging track if Gerald jogged at 6 km/h for the distance, while Shaun left half and hour later and arrived half an hour earlier than Gerald.

The time it took Gerald to complete the distance is found from ...

  time = distance/speed

  time = (24 km)/(6 km/h) = (24/6) h = 4 h

Shaun left half an hour later than Gerald, and completed the trip half an hour before Gerald did. Shaun's time was 1 hour less than Gerald's, so was ...

  4 h -1 h = 3 h

Shaun's average speed can be found from ...

  speed = distance/time

  speed = (24 km)/(3 h) = 8 km/h

Shaun's average speed was 8 km/h.

The number of cups of sugar that are there for each cup of flour would be = 1/2 cup of sugar.

The recipe contains sugar of = 3 cups

The recipe contains flour of = 6 cups

If 3cups sugar = 6 cups of flour

X cups sugar = 1 cup of flour

make X the subject of formula;

X = 3×1/6

X = 3/6 = 1/2

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The distance from the center are equal,

x = 6

The value of x is solved using the relationship existing between chords and the bisectors.

It will be noted that the line from the center

In the figure, since the chords are equal and the line from the center are perpendicular bisectors then the line from the center are equal.

we can therefore say that x = 6

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Answer:

L = (14x^2 - x - 3) / (2x - 1)

Step-by-step explanation:

The area of the rectangular lane is given as 14x^2 - x - 3 square feet.

Let's assume that the length of the lane is L feet. Then the formula for the area of a rectangle is:

Area = Length x Width

Substituting the values given in the question, we have:

14x^2 - x - 3 = L x (2x - 1)

To find an expression for the length of the lane, we can rearrange the equation to solve for L:

L = (14x^2 - x - 3) / (2x - 1)

Therefore, the expression that represents the length of the lane is:

L = (14x^2 - x - 3) / (2x - 1)

The number of more points that Owen must earn to meet his goal would be = 31 points.

The total number of point expected to be scored by Owen = 50 points

The total amount of points that Owen has earned so far = 19 point.

The amount of points that Owen should earn more to meet up with the points expected of him = 50-19= 31 points.

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Answer:

45% = 0.45

(you do this by bringing the decimal over 2 places)

multiply $55 and 0.45 to get $24.75

final answer = $24.75

Answer:

Here are two example data sets that meet the given conditions:

Data Set 1:

Values: 10, 12, 14, 16, 18, 20

Mean: (10+12+14+16+18+20) / 6 = 15

MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|10-15| + |12-15| + |14-15| + |16-15| + |18-15| + |20-15|)/6) = 2.5

Story: This dataset may have originated from measuring the time taken to complete a series of tasks by a group of skilled workers. The values represent the time taken in seconds, and the low MAD value indicates that the workers' performance was consistent. The mean value of 15 seconds suggests that the workers were efficient, completing the tasks quickly and accurately.

Data Set 2:

Values: 3, 5, 7, 9, 11, 13

Mean: (3+5+7+9+11+13) / 6 = 8

MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|3-8| + |5-8| + |7-8| + |9-8| + |11-8| + |13-8|)/6) = 2.5

Story: This dataset may have originated from measuring the height of a group of plants grown under different conditions. The values represent the height in inches, and the low MAD value indicates that the plants' growth was consistent across all conditions. The mean value of 8 inches suggests that the conditions were not optimal for plant growth, as the mean height is lower than the expected average for this type of plant.

Both data sets have a similar MAD value of 2.5, indicating that the variation in the data is relatively low, and the differences in the mean values suggest that they came from different sources. In both cases, the means are more than one MAD apart, indicating that there are significant differences between the values in each set.

The equation of the third linear function is:

y = (-1/3)x + (8/3)

To find a linear function with a rate of change between Function A and Function B, we need to calculate the rates of change for each function.

For Function A, the rate of change is:

(2 - (-4)) / (6 - (-1)) = 6/7

For Function B, we find the rate of change by selecting any two points on the graph, such as (2, 6) and (-4, 7):

(6 - 7) / (2 - (-4)) = -1/6

So the rate of change for Function A is 6/7, and the rate of change for Function B is -1/6.

To find a linear function with a rate of change between these two values, we can select any value between 6/7 and -1/6. Let's choose a rate of change of -1/3.

We can use the point-slope form of a linear equation to write the equation of the line with a rate of change of -1/3 and passing through the point (2, 6):

y - 6 = (-1/3) * (x - 2)

y = (-1/3)x + (8/3)

In conclusion, the equation of the third linear function is:

y = (-1/3)x + (8/3)

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Answer:

(½,0),(1,0)

...............

Answer:

Step-by-step explanation:

To find the x-intercepts of a function, we set y = 0 and solve for x.

For the function 2x² - 3x + 1:

2x² - 3x + 1 = 0

We can use the quadratic formula to solve for x:

x = [ -(-3) ± sqrt( (-3)² - 4(2)(1) ) ] / (2*2)

x = [ 3 ± sqrt(1) ] / 4

x = 1/2 or x = 1

Therefore, the x-intercepts are (1/2, 0) and (1, 0).

For the function y = 2x² + 8x + 6:

2x² + 8x + 6 = 0

We can simplify this equation by dividing both sides by 2:

x² + 4x + 3 = 0

This equation factors as:

(x + 3)(x + 1) = 0

So the solutions are x = -3 and x = -1.

Therefore, the x-intercepts are (-3, 0) and (-1, 0).

For the coordinates (0.5, [?]).

To find the y-coordinate of the point (0.5, [?]), we can substitute x = 0.5 into the equation for the function:

y = 2(0.5)² + 8(0.5) + 6

y = 2(0.25) + 4 + 6

y = 5.5

Therefore, the coordinates are (0.5, 5.5).

For the coordinates ([ ], [ ]).

Without knowing the specific function, we cannot determine the x-intercepts or any other information about the graph. We would need to know the equation of the function or have additional information about the graph.

Answer:

There are 2598960 different ways to choose 5 cards from a standard 52-card deck.

Answer:

(52−5)5 = 2598960 different ways to choose 5 cards from the available 52 cards.

Step-by-step explanation:

Answer:

16.39 square units.

Step-by-step explanation:

The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.

To see this, we can use the Pythagorean identity for sine and cosine:

sin^2 t + cos^2 t = 1

Multiplying both sides by 9, we get:

9 sin^2 t + 9 cos^2 t = 9

Substituting x = sin t and y = 3 cos t, we get:

9 x^2 + y^2/3 = 9

This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.

The area of an ellipse is given by the formula:

Area = pi * a * b

Substituting the values of a and b, we get:

Area = pi * 3 * sqrt(3) ≈ 16.39

Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.

U is located in the plane or vector that A's columns span.

A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.

Part 1

To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.

Part 2

Why the answer in Part 1 is correct?

Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.

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Answer: (0,3)

x=0 ; y=3

Step-by-step explanation:

To solve the system of equations:

2x + 4y = 12

3x + y = 3

We can use the method of substitution or elimination. Here we will use the substitution method:

From Equation 2, we can isolate y:

y = 3 - 3x

We can substitute this expression for y into Equation 1:

2x + 4(3 - 3x) = 12

Simplifying and solving for x:

2x + 12 - 12x = 12

-10x = 0

x = 0

Now that we have found the value of x, we can substitute it back into either Equation 1 or Equation 2 to solve for y. Here we will use Equation 2:

3(0) + y = 3

y = 3

Therefore, the solution to the system of equations is (x, y) = (0, 3).

This means that the point (0, 3) is the intersection point of the two lines represented by the given equations. To verify this, we can substitute the values of x and y into both equations and see if they are true.

Answer:

[tex]f(x)=4(3)^x[/tex]

Step-by-step explanation:

The general equation for an exponential function is:

[tex]\boxed{f(x) = ab^x}[/tex]

where:

To find the values of a and b that satisfy the given conditions, we can use the two points (1, 12) and (3, 108) to form a system of equations:

[tex]\begin{cases}12 = ab^1\\108 = ab^3\end{cases}[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\dfrac{ab^3}{ab} = \dfrac{108}{12}[/tex]

[tex]b^2=9[/tex]

[tex]\sqrt{b^2}=\sqrt{9}[/tex]

[tex]b=3[/tex]

Substitute the found value of b into the first equation and solve for a:

[tex]12&=3a[/tex]

[tex]\dfrac{12}{3}=\dfrac{3a}{3}[/tex]

[tex]4=a[/tex]

[tex]a=4[/tex]

Therefore, the equation of the exponential function that passes through the points (1, 12) and (3, 108) is:

[tex]\boxed{f(x) = 4(3)^x}[/tex]

Answer:

Step-by-step explanation:

To find the equation of an exponential function passing through the given points (1,12) and (3,108),

we can use the standard exponential form y=a(b^x). We know that when x=1, y=12,

so we can substitute these values into the equation to find a.

So  12 = a(b^1). Similarly, when x=3, y=108, so 108 = a(b^3). We can divide the second equation by the first to eliminate a and get (108/12) = b^2, or 9 = b^2. Thus, b=3 (taking only the positive root). We can now substitute this value of b into either equation to find a. Using the first equation, we get 12 = a(3^1), so a=4. Therefore, the exponential function passing through the given points is y=4(3^x).

Part A: Number of servings  is  1.24 servings/person

Part A: To determine the number of complete servings of fruit salad, we need to divide the total amount of fruit salad Mrs. Harris made (31 cups) by the amount she wants each person to get (25 cup/person). Using the formula:

Number of servings = Total amount of fruit salad / Amount per serving

Number of servings = 31 cups / 25 cups/person

Number of servings = 1.24 servings/person

Since we cannot have a fraction of a serving, we round down to the nearest whole number, as we cannot serve a fraction of a fruit salad. Therefore, Mrs. Harris will be able to serve 1 complete serving of fruit salad with the amount she made.

art B:

If each cup of fruit salad contains 1/4 cup of fruit and each serving is 1/4 cup, then each serving contains 1 cup of fruit.

To calculate the number of bananas Mrs. Harris needs, we first need to determine how many cups of bananas are in 31 cups of fruit salad:

31 cups × 1/4 cup of banana per cup of fruit salad = 7.75 cups of bananas

Since each cup of banana contains 14 of a banana, we can multiply the number of cups of bananas by 14 to find the total number of bananas needed:

7.75 cups of bananas × 14 bananas per cup = 108.5 bananas

So Mrs. Harris needs to buy approximately 109 bananas for the fruit salad.

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