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Statistics Chapter 11: Simulation Practice

The incorrect phrases in the paragraph are as follows:

Since ∠AMC is a right angle,  ∠BMC and  ∠CMD are complementary.

Since  ∠BMD is a right angle,  ∠AMB and  ∠BMC are complementary.

To identify the wrong phrases, note that a right angle is an angle that forms 90° when inclined to another line. Also, complementary angles are those whose sum is 90°.

A close look at the angles will show that ∠BMD is a right angle but ∠BMC and  ∠CMD are complementary. Also, the following is correct: ∠AMC is a right angle,  ∠AMB and  ∠BMC are complementary.

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Answer:

π(2^2 - .75^2) = 55π/16 m² = 10.8 m²

D is the correct answer.

Answer: C

Step-by-step explanation:

the x - 2 means go right 2

the +3 means go up 3

Answer:

x = 1 or

x = 1/2

Step-by-step explanation:

2x² - 5 = 3x - 6

⇒ 2x² - 5 - 3x + 6 = 0

⇒ 2x² - 3x + 1 = 0

Using quadratinc formula, the roots are

[tex]\frac{-b \pm\sqrt{b^{2} -4ac } }{2a}[/tex]

where, a = 2, b = -3 and c = 1

sub in the formula,

[tex]\frac{-(-3) \pm\sqrt{(-3)^{2} -4(2)(1) } }{2(2)}\\\\= \frac{3 \pm\sqrt{9 -8 } }{4}\\\\= \frac{3 \pm\sqrt{1 } }{4}\\\\= \frac{3 \pm 1 }{4}\\\\= \frac{3+1}{4} \;or\; \frac{3-1}{4}\\ \\=\frac{4}{4} \; or\; \frac{2}{4} \\\\= 1 \; or \; \frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

To interchange Row 1 and Row 2 of the given matrix, the indicated row operation can be performed as follows:

Original matrix:

8 -2 1 7

2

9

4 5

1

4

-4 9

Interchanging Row 1 and Row 2:

2

8 -2 1 7

9

4 5

1

4

-4 9

The transformed matrix after interchanging Row 1 and Row 2 is:

2

8 -2 1 7

9

4 5

1

4

-4 9

The calculated equation of the line is y = -2x + 3

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(1, 1) and (0, 3)

The equation of the line is calculated as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the points, we have

m + 3 = 1

So, we have

m = -2

This means that

y = -2x + 3

Hence, the equation of the line is y = -2x + 3

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The central angle of the sector is 540°.

The area of the sector formula is A = (1/2) r² θ Where, A = Area of sector r = Radius of sectorθ = Central angle of sector Given that the radius of the sector is 10mm and area is 40/3 pie mm²

To find the measure of central angle θ, plug the given values in the formula as shown; A = (1/2) r² θ40/3 pie = (1/2)(10)² θ40/3 pie = (1/2)100 θ40/3 pie = 50θ (multiply by 3/40)θ = (3/40) × 40πθ = 3π.

So, the measure, in degrees, of the central angle of the sector is;θ = (180/π) × 3πθ = 540°Therefore, the central angle of the sector is 540°.

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Answer:

Not parallelogram

Step-by-step explanation:

points A(-4, 1), B(1,3), C(8, -1) and D(4, -3).

The slope of a line can be found using the following formula:

Slope  [tex]m= = \frac{(y_2 - y_1) }{(x_2 - x_1)}[/tex]

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Using the formula above,

Side AB: Slope =[tex]\frac{3-1}{1-(-4)}=\frac{2}{5}[/tex]

Side BC: Slope =[tex]\frac{-1-3}{8-1}=\frac{-4}{7}[/tex]

Side CD: Slope =[tex]\frac{-3 - (-1)}{4 - 8}= \frac{1}{2}[/tex]

Side DA: Slope =[tex]\frac{-3 - 1}{4 - (-4)}= \frac{-1}{4}[/tex]

Since The slopes of opposite sides are equal,

Therefore ABCD is not Parallelogram:

The probability of randomly selecting either a diamond or a 3 from the bag is 100%.

Random selection refers to the process of selecting elements from a group with equal probability of selection.

Probability is a measure of the likelihood of an event occurring, which is usually expressed as a fraction or a decimal.

When it comes to random selection of a diamond or 3, we can use probability to determine the likelihood of either event occurring.

For instance, suppose we have a bag containing 10 numbered balls: 5 of them are diamonds and 5 are threes.

To find the probability of randomly selecting a diamond, we divide the number of diamonds by the total number of balls: P(Diamond) = Number of diamonds/ Total number of balls = 5/10 = 0.5 or 50%

This means that the probability of randomly selecting a diamond from the bag is 50%.

To find the probability of selecting either a diamond or a 3, we add the probability of selecting a diamond to the probability of selecting a 3, since the events are mutually exclusive: P(Diamond or 3) = P(Diamond) + P(3) = 5/10 + 5/10 = 1

This means that the probability of randomly selecting either a diamond or a 3 from the bag is 100%.

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Answer:

34.63

Step-by-step explanation:

The 2 in 34.6285 marks the hundredths place

We can round by seeing what number is to the right of it which is 8.

Since 8 is larger than 5, we round up by 1.

Thus, 34.63 is our answer

The answer is:

34.63

Work/explanation:

Rounding to the nearest hundredth means rounding to 2 decimal places (DP).

So we have 2 decimal places, and the 3rd one matters too because it will determine the value of the 2nd DP.

The third DP is 8. Since it's greater than 5, then the value of the 2nd DP will be rounded up. I will add 1 to it.

Remember that we round up when the digit that we're rounding to is followed by another digit that is greater than or equal to 5.

So we round :

[tex]\bf{34.6285 =\!=\!\!\! > 34.63}[/tex]

Answer:

f(0) = 1

f(1) = 21.1

Step-by-step explanation:

Do as the problem says:

[tex]f(0)=4^{2.2(0)}=4^0=1\\f(1)=4^{2.2(1)}=4^{2.2}\approx21.1[/tex]

Answer:

[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]

The solutions to the absolute value equations are:

1. b. x = 1, -19.      2. a. no solution.     3. c. x = 5, -9.

1. |3x+9| = 30

To solve this equation, we isolate the absolute value expression by considering two cases: 3x+9 = 30 and -(3x+9) = 30. Solving both equations, we find x = 7 and x = -19, respectively. Thus, the answer is b. x = 1, -19.

2. |2x+11| = -13

An absolute value cannot be negative, so there is no solution to this equation. The answer is a. no solution.

3. |x + 2| + 4 = 11

To solve this equation, we isolate the absolute value expression by subtracting 4 from both sides, resulting in |x + 2| = 7. Considering two cases: x + 2 = 7 and -(x + 2) = 7, we solve for x and find x = 5 and x = -9, respectively. Thus, the answer is c. x = 5, -9.

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Step-by-step explanation:

Let the statement be:

The converse of a statement is:

Let's try it for each statement and see if the converse is true.

a) The converse is:

It is true.

b) The converse  is:

It is true.

c) The converse is:

It is false, since not all rhombus have four right angles.

d) The converse is:

It is false, since it could be a square.

a. Converse: If the interior angles sum to 180°, then my shape is a triangle. (Converse is not true)

b. Converse: If alternate interior angles are equal, then the lines are parallel. (Converse is true)

c. Converse: If I have a Rhombus, then I also have a Square. (Converse is not true)

d. Converse: If I have a shape with four right angles, then I have a rectangle. (Converse is true)

a. Converse: If the interior angles of a shape sum to 180°, then the shape is a triangle.

The converse of this statement is not true. There are many shapes other than triangles whose interior angles sum to 180°, such as quadrilaterals and polygons with more than four sides.

b. Converse: If alternate interior angles of two lines are equal, then the lines are parallel.

The converse of this statement is true. If the alternate interior angles of two lines are equal, then the lines are parallel. This is a property of parallel lines and can be proven using the corresponding angles postulate.

c. Converse: If I have a Rhombus, then I also have a Square.

The converse of this statement is not true. While all squares are rhombuses (a square is a special type of rhombus), not all rhombuses are squares. A rhombus is a quadrilateral with all sides of equal length, but its angles can be anything other than 90°.

d. Converse: If I have a shape with four right angles, then I have a rectangle.

The converse of this statement is true. If a shape has four right angles, then it is a rectangle. This is a defining characteristic of rectangles, as all rectangles have four right angles.

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The complete question is :

Write the converse of each statement and determine if the converse is true.

a. If my shape is a triangle, then the interior angles sum to 180°.

b. If two lines are parallel, then alternate interior angles are equal.

c. If I have a Square, then I also have a Rhombus.

d. If I have a rectangle, then I have a shape with four right angles.

=================================================

Explanation

I'll use the distance formula.

[tex](x_1,y_1) = (1,3) \text{ and } (x_2, y_2) = (-2,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-2))^2 + (3-7)^2}\\\\d = \sqrt{(1+2)^2 + (3-7)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

The distance is 5 units.

Answer:

5

Step-by-step explanation:

The difference quotient of the function f(x) = 12x + 1 is 12.

The difference quotient of a function measures the average rate of change of the function between two points. To find the difference quotient of the function f(x) = 12x + 1, we can follow these steps:

Select two points on the function, let's call them x and x + h, where h is a small positive value.

Evaluate the function at those two points to get the corresponding y-values. For f(x) = 12x + 1, we have:

f(x) = 12x + 1

f(x + h) = 12(x + h) + 1

Calculate the difference quotient by subtracting the values and dividing by h:

[f(x + h) - f(x)] / h

= [(12(x + h) + 1) - (12x + 1)] / h

= [12x + 12h + 1 - 12x - 1] / h

= (12h) / h

= 12

In this case, since the function is linear with a slope of 12, the difference quotient is constant and equal to the slope of the function. This means that for every unit increase in x, the function f(x) increases by 12.

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Answer:

The valid prediction about the continuous function f(x) is : f(x) ≥ 0 over the interval [5, ∞).

Step-by-step explanation:

Answer:

Based on the values in the table, it can be observed that changing the radius of the sphere has a direct effect on the surface area of the sphere. As the radius increases, the surface area also increases.

Step-by-step explanation:

In general, multiplying the radius of a sphere by a factor of x will result in the surface area of the sphere being multiplied by a factor of x^2. This is because the surface area of a sphere is given by the formula:

Surface Area = 4πr^2

When the radius is multiplied by a factor of x, the new radius becomes xr. Substituting this into the formula, we get:

New Surface Area = 4π(xr)^2

= 4πx^2r^2

= x^2(4πr^2)

Therefore, the surface area of the sphere is multiplied by a factor of x^2 when the radius is multiplied by a factor of x. This relationship shows that the surface area increases at a faster rate than the radius.

The correct linear inequality represented by the graph is:

y < -2x + 3. Option D

To determine which linear inequality is represented by the graph of the dashed straight line with a negative slope and going through (0, 3) and (2, -1), we can start by finding the slope of the line.

The slope of a line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1).

Using the coordinates (0, 3) and (2, -1), we have:

m = (-1 - 3) / (2 - 0),

m = -4 / 2,

m = -2.

So, we know that the slope of the line is -2.

Next, we need to determine the y-intercept of the line. To do this, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

Using the point (0, 3), we can substitute the coordinates into the equation and solve for b:

3 = -2(0) + b,

3 = b.

Therefore, the y-intercept is 3.

Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:

y = -2x + 3.

Since we are shading everything to the left of the line, we want the region where y is less than the line. Option D is correct.

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The probability of taking the smallest ball at least once during 4 tries can be calculated as 1 minus the probability of not taking the smallest ball in any of the 4 tries. Since each try is independent and the probability of not taking the smallest ball in a single try is 9/10, the probability of not taking it in all 4 tries is (9/10) * (9/10) * (9/10) * (9/10) = 0.6561. Therefore, the probability of taking the smallest ball at least once during 4 tries is 1 - 0.6561 = 0.3439, or approximately 34.39%.

To find the probability of not taking the smallest ball in any of the 4 tries, we need to calculate the probability of not selecting the smallest ball in each try and then multiply them together.

In each try, there are 9 balls remaining that are not the smallest ball, out of a total of 10 balls. Therefore, the probability of not taking the smallest ball in a single try is 9/10.

Since the tries are independent events, we can multiply the probabilities together to find the probability of not taking the smallest ball in all 4 tries.

After calculating this probability, we subtract it from 1 to obtain the probability of taking the smallest ball at least once during the 4 tries.

In this case, the probability of not taking the smallest ball in all 4 tries is (9/10) * (9/10) * (9/10) * (9/10) = 0.6561.

Finally, subtracting this value from 1 gives us the probability of taking the smallest ball at least once, which is 1 - 0.6561 = 0.3439, or approximately 34.39%.

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The solution to the system is (b) (-2, 3, z) where z is any real number

From the question, we have the following parameters that can be used in our computation:

The augmented matrix

Where, we have

[tex]\left[\begin{array}{ccc|c}1&0&0&-2\\0&1&0&3\\0&0&0&3\end{array}\right][/tex]

From the above, we have the first two diagonals to be 1

And other elements to be 0

This means that

x = -2 and y = 3

For z, the value is infinitely many

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Answer:

379.2 in^2

Step-by-step explanation:

Each cylinder's side area is  pi *d * h = 43.98 in^2

  you need six    :     =263.89 in^2

each ned of the cylinder area = pi r^2 = 9.621 in^2

    and you have 12 ends  for 115.45 in^2

For total : 379.3  in^2       (slight difference due to the value of pi used and rounding)

Answer:

X intercepts: (-2, 0), (2, 0)

Y intercept: (0, 4)

Edited because I forgot to put in point form earlier. Depends on whether your teacher wants it in point form. If not, ignore the 0s.

Step-by-step explanation:

X intercepts are the points where a line crosses the x axis. Y intercepts are the points where a line crosses the y axis.

Answer:

A. x-intercept: (-2,0), (2,0)

A. y-intercept: (0,4)

Step-by-step explanation:

If you want to find the x and y-intercept of a line, you need to know its equation. But don't worry, it's not as hard as it sounds. Here are some tips to help you out.

One type of equation is y = mx + c, where m is the slope and c is the y-intercept. This means that the line crosses the y-axis at c. To find the x-intercept, just plug in y = 0 and solve for x. You'll get x = -c/m. Easy peasy!

For example, if the equation is y = 2x + 4, then the y-intercept is 4 and the x-intercept is -2.

Another type of equation is ax + by + c = 0, where a, b and c are constants. To find the x-intercept, plug in y = 0 and solve for x. You'll get x = -c/a. To find the y-intercept, plug in x = 0 and solve for y. You'll get y = -c/b. Piece of cake!

For example, if the equation is 3x + 2y - 6 = 0, then the x-intercept is 2 and the y-intercept is -3.

Now you know how to find the x and y-intercept of a line from its equation.Let us understand the calculations to find the x and y intercept, through the steps in the below table.

The expected return on the portfolio is approximately 13.465%.

To calculate the expected return on the portfolio, we need to consider the weights of each stock in the portfolio.

Let's denote the weight of Stock A as wA and the weight of Stock B as wB. The weight of a stock is the proportion of the total portfolio value that is invested in that stock.

Given that $3,000 is invested in Stock A and $4,100 is invested in Stock B, we can calculate the weights as follows:

wA = $3,000 / ($3,000 + $4,100) = $3,000 / $7,100

wB = $4,100 / ($3,000 + $4,100) = $4,100 / $7,100

Next, we need to calculate the weighted average of the expected returns of the two stocks using their respective weights:

Expected return on the portfolio = (wA * Return on Stock A) + (wB * Return on Stock B)

Expected return on the portfolio = (wA * 10%) + (wB * 16%)

Substituting the calculated weights into the equation:

Expected return on the portfolio = ($3,000 / $7,100 * 10%) + ($4,100 / $7,100 * 16%)

Simplifying the equation:

Expected return on the portfolio = (0.4225 * 10%) + (0.5775 * 16%)

Expected return on the portfolio = 0.04225 + 0.0924

Expected return on the portfolio = 0.13465 or 13.465%

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Answer:

y= -4

Step-by-step explanation:

To find the value of y when x = 6, we can substitute x = 6 into the equation and solve for y:

4(6) + y = 20

24 + y = 20

y = 20 - 24

y = -4

Therefore, when x = 6, y is equal to -4.

Jessica squeezed 235 cups of juice, Barry made 221 cups of juice, and the best estimate for the amount of juice Barry made is 198 cups.

Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. The best estimate for the amount of juice Barry made is 198 cups.

There are different ways to approach this problem, but one possible method is to use subtraction to find out how much juice Barry actually made, and then compare it to the estimated amount. If Jessica squeezed 235 cups of juice and Barry made 14 cups less, then Barry made 235 - 14 = 221 cups of juice.

This is the exact amount of juice that Barry made, but it may not be a convenient answer if we are looking for an estimate that is close to Barry's estimate of 212 cups of juice. One way to get such an estimate is to round 221 to the nearest ten or hundred. For example, if we round to the nearest ten, we get 220, which is only 8 cups away from Barry's estimate.

Alternatively, if we round to the nearest hundred, we get 200, which is only 12 cups away from Barry's estimate. Therefore, the best estimate for the amount of juice Barry made is 198 cups, which is obtained by rounding down to the nearest ten. This estimate is only 14 cups away from Barry's estimate, and it is also easy to compute mentally.

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