3.1 In the diagram below, O is the centre of the circle. Chord AB is perpendicular to diameter DC. CM: MD= 4:9 and AB = 24 units. B 3.1.1 Determine an expression for DC in terms of x if CM-4x units. 3.1.2 Determine an expression for OM in terms of x 3.1.3 Hence, or otherwise, calculate the length of the radius of the circle (1) (2)
​

Answer:

54.88cm

Step-by-step explanation:

For shaded region perimeter, subtract the circle perimeter from the rectangle

perimeter

= (10*8) - (2 * 3.14 * 8/2)

= 80 -  25.12

= 54.88cm

The minimum height of the cone is 17.87 in (approx)

In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.  

Total surface area, A = 2πr²+ 2πrh square units

The volume of the Cylinder, V = πr²h cubic units

Here we have

A cylindrical can with an open top is to be constructed so that

The volume of the cone is 167 in³  

As we know volume of cone = (1/3) πr²h

=> (1/3) πr²h = 167

=> h = 501/πr²  

As we know Surface Area of the cone = 2πrh + 2πr²  

Substitute h = 501/πr² in Surface Area of cone  

=> SA = 2πr(501)/πr² + 2πr²  

=> SA = 1002r⁻¹+ 2πr²        

Differentiate SA with respect to r

=> SA' = (-1) 1002r⁻²+ 4πr  

=> SA' = - 1002r⁻² + 4πr  

Here  - 1002r⁻² + 4πr = 0

=>  - 501r⁻² + 2πr = 0  

=>  - 501/r² + 2πr = 0  

=>  [-501 + 2πr³ ]/r² = 0

=>  [-501 + 2πr³ ] = 0  

=>  2πr³ = 501

=>  πr³ = 250.5

=>  r³ = 79.70

=>  r = 8.92  (approx)

Hence the height of the cone, h = 501/πr²    

= 501/π(8.92)

= 17.87 (approx)

Therefore,

The minimum height of the cone is 17.87 in (approx)  

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Answer:

i think it is b i am not sure

Step-by-step explanation:

Seen can close the lid on the cube container with a 6 in. marker inside it which has the side length of 4 inches.

The cube shape is the three-dimensional solid which has 6 equal side. The diagonal of a cube can be calculated with the following formula;

d=6∛a

Here, (a) is the length of the side of the cube.

Sean has a plastic container which is in the shape of a cube. The side lengths of the cube container is 4 in. Thus, the diagonal of the cube is,

d=6∛a

d=6∛(4)

d=6 x 1.587

d=9.522 inches.

The diagonal of the cube container is 9.522 inches, which is more than the length of the marker.

9.522 in >6 in

Hence, Seen can close the lid on the cube container with a 6 in. marker inside it, which has the side length of 4 inches.

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For the three rectangular prisms, the measurements are -

A = 6 in × 2 in × 5 in

B = 5 in × 3 in × 4 in

C = 10 in × 2 in × 3 in

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

The volume of each rectangular prism is 60 in³.

For the rectangular prism A -

The measurement of width is - 2 inches

The measurement of height is - 5 inches

The formula for volume of a rectangular prism is -

Volume = length × width × height

Substitute the values into the equation -

60 = length × 2 × 5

60 = length × 10

length = 60/10

length = 6 inches

Therefore, the measurement of length is 6 inches.

For the rectangular prism B -

The measurement of length is - 5 inches

The measurement of height is - 4 inches

The formula for volume of a rectangular prism is -

Volume = length × width × height

Substitute the values into the equation -

60 = 5 × width × 4

60 = width × 20

width = 60/20

width = 3 inches

Therefore, the measurement of width is 3 inches.

For the rectangular prism C -

The measurement of length is - 10 inches

The measurement of width is - 2 inches

The formula for volume of a rectangular prism is -

Volume = length × width × height

Substitute the values into the equation -

60 = 10 × 2 × height

60 = height × 20

height = 60/20

height = 3 inches

Therefore, the measurement of height is 3 inches.

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Answer:

In 48 hours the ice cream factory can make 1,680 quarts.

Step-by-step explanation:

Multiply UNIT RATE 35 by 48 to answer your first question.

The dimensions are;

Length = 7 meters

Width = 5 meters

The area of a rectangle is expressed as;

Area = length × width

From the information given, we have that;

Length = 2w - 3

Area = 65

Substitute the values

65 = (2w - 3)w

expand the bracket

65 = 2w² - 3w

solve the quadratic equation;

2w² + 13w - 10w - 65

Factorize the terms

w(2w + 13) - 5(2w + 13)

w = 5

Substitute the value

Length = 2w - 3 = 2(5) - 3 = 7

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Using the properties of similar triangles and ratio and proportion we get the vale of x as 2.8 units.

In the given figure the triangle ΔKFG and ΔFJH

KG is parallel to JH

Hence ΔKFG is similar to ΔFJH

Now using the property of similarity and proportion we can say that:

FG/FH = KF/JF

putting the values in the above proportion we get:

7 /(7+x) = 5/ 7

or, 49 = 35 +5 x

or, 14 = 5x

or, x =14/5

or, x = 2.8

The majority of ratio and percentage explanations involve using fractions.

A proportion states that two variables are equal, whereas a ratio is a fraction that is written as a:b. The two ratios given are equal to one another, as demonstrated by the proportional equation.

Hence the value of x is 2.8 units.

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Answer:

h

Step-by-step explanation:

uwuwuwuuwu2u2u2uuwuwuwuwuwuwuwuwu

Answer:

The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function.

Answer:

-5/4

Step-by-step explanation:

slope = rise/run

Start at the lower right point. Go up 5. The rise = 5. Go left 4. The run -4.

slope = 5/-4 = -5/4

The equation of the tangent line at point P (-5, -53) is y = 75x + 322.

To find the slope of the curve at the given point P (-5, -53) for the equation y = x^3, we need to find the derivative of the function and evaluate it at x = -5.

A. The slope of the curve at the point P:

We differentiate y = x^3 with respect to x:

dy/dx = 3x^2

Substituting x = -5 into dy/dx:

dy/dx = 3(-5)^2

dy/dx = 3(25)

dy/dx = 75

Therefore, the slope of the curve at the point P (-5, -53) is 75.

B. Equation of the tangent line at point P:

We can use the point-slope form of a line to find the equation of the tangent line.

The point-slope form is given by:

y - y1 = m(x - x1)

Substituting the values of the point P (-5, -53) and the slope m = 75:

y - (-53) = 75(x - (-5))

y + 53 = 75(x + 5)

y + 53 = 75x + 375

y = 75x + 322

Therefore, the equation of the tangent line at point P (-5, -53) is y = 75x + 322.

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a) He will start 900 feet from the edge

b) 16 Round trips are needed to cover the field.

Because Mr. Johns intends to check a wheat field 960 feet wide for weeds so he will distribute a 60-foot wide strip using a high clearance sprayer that has two 30-foot booms.

a) 960 foot - 60 foot = 900 foot

Therefore, he should start 900 feet from the edge.

b) 960 foot / 60 foot = 16 Trips.

Therefore, 16 round trips are needed to cover the field.

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Number of measurements that must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm is 16

To estimate the diameter with an uncertainty of 0.5 mm, we need to reduce the uncertainty to that level. Let's call the number of measurements we need to make "N". We can use the formula for the standard deviation of the mean

σ_mean = σ / sqrt(N)

where σ is the standard deviation of the individual measurements. In this case, the uncertainty of each measurement is given as 1.4 mm, which we can assume is the standard deviation.

To reduce the uncertainty to 0.5 mm, we need

0.5 = 1.4 / sqrt(N)

Solving for N, we get

N = (1.4 / 0.5)^2 = 15.68

≈ 16

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The maximum number of sheets of paper that can fit in the tray is 625 of a printer paper tray is 5 cm deep one sheet of paper is 8x10 to the power of -3 cm thick

To determine the maximum number of sheets of paper that can fit in the tray, we need to find the total thickness of the paper.

Since one sheet of paper is 8x10^-3 cm thick, if we have n sheets of paper, the total thickness will be:

total thickness = n * 8x10^-3 cm

And since the tray is 5 cm deep, the maximum number of sheets of paper that can fit in the tray is given by:

n = 5 / (8x10^-3) = 5 / 0.008 = 625

So, the maximum number of sheets of paper that can fit in the tray is 625.

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The two statements that are true about the company's Market share going from 50 to 65 percent of the total market . The initial market share and multiply by 100, which gives 30 percent. Option B is correct answer.

The two statements that are true about the company's market share going from 50 to 65 percent of the total market are:

The company's market share increased by 30 percent: The difference between the initial market share of 50 percent and the final market share of 65 percent is 15 percentage points. To calculate the percentage increase, we can divide the difference by the initial market share and multiply by 100, which gives (15/50) x 100 = 30 percent.

The company's relative market position improved: With a market share of 65 percent, the company now holds a greater proportion of the total market than before. This means that its relative market position has improved compared to its competitors, who have a smaller share of the market. This could translate into increased bargaining power, profitability, and other benefits for the company.

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a company’s market share went from 50 to 65 percent of the total market. of the following choices, which two statements about the company's market shares are true?
A) 40

B) 30

C) 35

D) 45

Answer:

$21.8

Step-by-step explanation:

Carlos is buying a shirt that costs $20 the sales tax is 9% what is the total

Given data

Cost= $20

Tax= 9%

Amount of tax=

9/100*20

0.09*20

1.8

Total amount

=1.8+20

=$21.8

False. Cronbach's alpha is a measure of internal consistency reliability, not a measure of the correlation between scale items.

It assesses the extent to which the items in a scale or questionnaire are measuring the same underlying construct.

Cronbach's alpha is calculated based on the inter-item correlations among the items in a scale. It provides a measure of the average correlation between all possible pairs of items in the scale. The range of Cronbach's alpha is between 0 and 1, with higher values indicating greater internal consistency or reliability.

Essentially, Cronbach's alpha quantifies the extent to which the items in a scale are consistently measuring the same construct or concept. It assesses how well the items "hang together" as a reliable measurement tool.

While correlation between scale items is related to internal consistency, Cronbach's alpha specifically measures the degree to which the items are interrelated and provides a single coefficient that reflects the overall reliability of the scale. It does not directly indicate the extent of item-item correlations or the strength of individual item contributions to the scale.

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The relation "r" defined on the set of people, where xry if x is older than y, is not a partial ordering. The first paragraph will provide a summary of the answer, and the second paragraph will explain why the relation fails to satisfy the properties of a partial ordering.

Reflexivity: For every person x, x must be older than or equal to themselves. In this case, the relation holds true since a person is always older than or equal to themselves.

Antisymmetry: If x is older than y and y is older than x, then x and y must be the same person. However, in this case, the relation does not satisfy antisymmetry because two different people can have different ages. For example, person A can be older than person B, and person B can be older than person C, but person A and person C can still be different individuals.

Transitivity: If x is older than y and y is older than z, then x must be older than z. In this case, the relation satisfies transitivity since if person A is older than person B and person B is older than person C, then person A is older than person C.

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Answer:

The answer would be: -145.125

Step-by-step explanation:

:)

Answer:

there are different answers for this

-1161/8

-145.125

-145 1/8

Step-by-step explanation:

why-

Answer:

m=y = 2x + 4.

y intercept is 4

Step-by-step explanation:

Based on the normal probability table, the value of x corresponding to the random number U = 0.9 is approximately 1.28.

a. In the graphical version of the inverse transform method, the random number U represents a point on the y-axis of the graph of the normal cumulative distribution function (CDF). The CDF of a standard normal distribution ranges from 0 to 1. Since the given random number U = 0.9 is close to the upper end of the range, it is expected that the corresponding x value will be positive.

b. To determine the value of x using a normal probability table, we need to find the z-score that corresponds to the cumulative probability of 0.9. In this case, we are using a standard normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1.

Looking up the cumulative probability of 0.9 in a normal probability table, we find that the closest value is 0.8997. The corresponding z-score is approximately 1.28.

To find the value of x, we can use the formula: x = μ + (z * σ). Since μ = 0 and σ = 1, the formula simplifies to x = z.

Therefore, based on the normal probability table, the value of x corresponding to the random number U = 0.9 is approximately 1.28.

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As per the given curvature, the value of PC is 1785.68 and PT is 1787.55

Curvature:

In statistics, curvature means amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.

Given,

PI is at station (20 00), the radius of curvature is 800 feet, and the angle of curvature is 30 degrees.

Here we need to determine the value of PC and PT.

According to the given value, the tangent distance is calculated as,

=> T = 800 x tan (30/2)

=> T = 800 x 0.2679

=> T = 214.32

Now, the value of PC is calculated as,

PC = PI - T

=> PC = 2000 - 214.32

=> PC = 1785.68

And the value of PT is calculated as,

PT =  PC + L

=> PT = 1785.68 + (100 x (30/1600))

=> PT = 1785.68 + 1.875

=> PT = 1787.55

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Answer: since [B]^-1[B] = I.

Step-by-step explanation:

To find the matrix for T relative to B, we need to find the coordinates of the vectors T(b), T(b^2), and T(b^3) with respect to the basis B.

We have:

T(b) = 6T(b^2) + 1T(b^3) = b, -5b^2

T(b^2) = 1T(b^2) + 0T(b^3) = 7b, -3b^2

T(b^3) = 0T(b^2) - 2T(b^3) = 0, 4b^2

To find the matrix [T], we write the coordinates of T(b), T(b^2), and T(b^3) as columns:

[T] = [b, 7b, 0; -5b^2, -3b^2, 4b^2]

To check this matrix, we can apply it to the basis vectors and see if we get the same coordinates as the vectors T(b), T(b^2), and T(b^3):

[T][b] = [b, 7b, 0][1; 0; 0] = [b; -5b^2]

[T][b^2] = [b, 7b, 0][0; 1; 0] = [7b; -3b^2]

[T][b^3] = [b, 7b, 0][0; 0; 1] = [0; 4b^2]

These are the same as the coordinates we found for T(b), T(b^2), and T(b^3), so our matrix [T] is correct.

To find ITIB, we first need to find the inverse of the matrix [B] whose columns are the basis vectors b, b^2, and b^3. We can do this by row reducing the augmented matrix [B | I]:

[1 0 0 | 1 0 0]

[0 1 0 | 0 1 0]

[0 0 1 | 0 0 1]

So [B] is already in reduced row echelon form, and its inverse is just I:

[B]^-1 = [1 0 0; 0 1 0; 0 0 1]

Therefore,

ITIB = [B]^-1[T][B] = [T]

since [B]^-1[B] = I.

Answer:

D. the subtraction property of equality was not applied.

Step-by-step explanation:

Step 1: Listed the statement

Step 2: applied the addition property of equality

Step 3: Simplified

Step 4: Applied the multiplication property of equality

Step 5: Simplified

~

60 to the negative 3 power

Answer:

-60

Step-by-step explanation:

Answer:

"Y" will be at ( 7 , 8 )

Step-by-step explanation:

"R" is moved up 4, to the right 1.

Doing this to "Y" leads to the answer.

Answer:I’m not able to see your Image

Step-by-step explanation:

Answer:

only the inverse is a function

Answer:

it's correct good job :)

Answer:

Step-by-step explanation:

Answer:  Fortunately, you don’t have to prove that x or y must be 1 or -1 in order for x*y to not be an element of G.

You only need to prove that x*y is an element of G for any x,y in G.  (That’s what it means for * to be an operation on G.)

I haven’t thought yet about how to prove that, but let me give you some thoughts off the top of my head.

We know -1 < x, y < 1.  We must show -1 < (x + y) / (xy + 1) and (x + y) / (xy + 1) < 1.

First, let’s show that -1 < (x + y) / (xy + 1).

I want to multiply xy + 1 to both sides, but we need to know whether it’s positive or not, so we know whether to reverse the inequality.

Well, -1 < x, y < 1 implies that xy > -1, which implies that xy +1 > 0.

So we must show that -(xy + 1) < x + y.

That is, let’s show that 0 < x + y + xy + 1.  (I don’t know if this is going anywhere useful; I’m just playing around with algebra.)