In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems? There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen matters. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen matters. There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen does not matter. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.

The probability that a single randomly selected value is greater than 31.9 is 0.511.

The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.

Probability that a single randomly selected value is greater than 31.9:

z = (31.9 - 32) / 3.9 = -0.026

We can find the probability:

P(X > 31.9) = P(Z > -0.026) = 0.511

Also, μ = 32, σ = 3.9, n = 66

z = (31.9 - 32) / (3.9 / √66) = -0.363

Using a standard normal distribution table or calculator, we can find the probability:

P(M > 31.9) = P(Z > -0.363) = 0.641

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The amount of grams that is equivalent to 3/10 of a kg is given as follows:

300 grams.

The amount of grams that is equivalent to 3/10 of a kg is obtained applying the proportions in the context of the problem.

The amount of kg is 3/10 of a kilogram is given as follows:

3/10 = 0.3kg.

(conversion of a fraction to decimal, divide the numerator by the denominator).

Each kg is composed by 1000 grams, hence the amount of grams in 0.3 kg is given as follows:

0.3 x 1000 = 300 grams.

(proportion applied to obtain the conversion).

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Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.

Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.

Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.

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When a cylinder is cut parallel to its base, the plane section that results is a circle. This circle will have the same radius as the cylinder's base. The center of the circle will be located at the center of the cylinder's base. This type of cut will create a circular cross-section that is parallel to the base of the cylinder.

Answer:

Step-by-step explanation:

The standard parametric equations for a circle with center (h, k) and radius r are:

x = h + r cos(theta)

y = k + r sin(theta)

Here, center is (−2, −3) and the radius is 6. Therefore, we have:

h = -2

k = -3

r = 6

Substituting these values into the standard equations, we get:

x = -2 + 6 cos(theta)

y = -3 + 6 sin(theta)

So the set of parametric equations for the circle is:

x(t) = -2 + 6 cos(t)

y(t) = -3 + 6 sin(t)

where t = theta.

4w+6.

The perimeter is just the summation of the length of all sides of a shape. In the case of a circle, the perimeters is its circumference length. So for this case, all we need to do is add up all the sides in a single expression that will represent the perimeter.

So perimeter for this triangle should be:

Side 1 + Side 2 + Side 3.

Where:

Side 1= w+4;

Side 2= 2w+2;

Side 3= w.

Then, perimeter is:

(w+4)+(2w+2)+(w)

Adding up all the like terms:

(w+2w+w)+(4+2)

(4w)+(6)

4w+6.

If a, b, c are in Harmonic Progression, b+ca+ca+b ac' ab bc are in Arithmetic Progression.

Given a, b, c are in H.P.:

1/a + 1/b = 2/c

Multiplying both sides by abc:

bc + ac = 2ab

Adding c to both sides:

bc + ac + c = 2ab + c

Rearranging the terms:

c + ab = ac + bc

Adding the terms b + ca and ca + b to both sides:

b + ca + ca + b + ac' + ab + bc = ac + bc + b + ca + ca + b

Simplifying:

b + ca + ca + b + ac' + ab + bc = 2ac + 2b

Dividing both sides by 2:

(b + ca + ca + b + ac' + ab + bc)/2 = ac + b

Hence, b+ca+ca+b ac' ab bc are in A.P.

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In the given diagram, the areas of the figures are as follows:

Area of the rectangle is 1/6 cm²

Area of the parallelogram is 12 m²

From the question, we are to calculate the areas of the given plane shapes

From the diagram, we have a rectangle and a parallelogram

The area of a rectangle is given by the formula

Area = l × w

Where l is the length

and w is the width

From the given information,

l = 1/2 cm

w = 1/3 cm

Thus,

Area = 1/2 cm × 1/3 cm

Area = 1/6 cm²

Hence, the area of the rectangle is 1/6 cm²

For the parallelogram

The area of a parallelogram is given by the formula

Area = b × h

Where b is the base length

and h is the perpendicular height

From the given information,

b = 6 m

h = 2 m

Thus,

Area = 6 m × 2 m

Area = 12 m²

Hence, the area of the parallelogram is 12 m²

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So it would take A 10 days to do the whole job alone.

An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.

Here,

Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:

In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).

If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.

We can simplify the second equation by multiplying out the brackets and collecting like terms:

8a + 2b = 1

Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:

5(a + b) = 1

5b = 1 - 5a

b = (1/5) - a

Now we can substitute this expression for "b" into the second equation:

8a + 2b = 1

8a + 2((1/5) - a) = 1

8a + (2/5) - 2a = 1

6a = (3/5)

a = (1/10)

So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:

time = amount of work / rate

Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:

time = 1 / (1/10)

= 10 days

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The meauser of center is the most appropriate answer for table two is the mean.

Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.

Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean

It is the mean because all of the data points are fairly close and there aren't any outliers (extreme values).

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The rocket will hit the ground after 19.09 seconds.

a) The height of the rocket can be describe as:

h(t) = -16t² + 210t + 75

where

t = time in seconds

h(t) = height of the rocket in feet

b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:

t = -b/(2a)

where

a = -16

b = 210

Substituting these values, we get:

t = -210/(2(-16)) = 6.5625 seconds

To find the maximum height, we substitute this value of t back into the equation for h(t):

h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet

This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.

c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:

-16t² + 210t + 75 > 721

-16t² + 210t - 646 > 0

Solving for t using the quadratic formula, we get:

t < 2.975 or t > 14.038

Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.

d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:

-16t² + 210t + 75 = 0

Solving for t using the quadratic formula, we get:

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

a = -16, b = 210, c = 75

t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]

t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]

t = [tex]\frac{-210 \± 149}{-32}[/tex]

t = 2.53125 or t = 13.53125

Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:

t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds

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Answer:

Each of these functions is a transformation of the parent function f(x) = |x|. The transformations include shifting the graph up or down, stretching or compressing the graph vertically, reflecting the graph across the x-axis, and shifting the graph left or right. The vertex of each graph is located at a different point.

Step-by-step explanation:

- The function f(x) = |x| - 3 is a transformation of the parent function f(x) = |x|. The "-3" at the end of the function shifts the graph 3 units down. This means that the vertex, or lowest point, of the graph is at (0, -3) instead of (0, 0).

- The function f(x) = -|x - 4| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-4" inside the absolute value function shifts the graph 4 units to the right. This means that the vertex of the graph is at (4, 0) instead of (0, 0).

- The function f(x) = (1/3)|x| is a transformation of the parent function f(x) = |x|. The "1/3" in front of the absolute value function stretches the graph vertically by a factor of 1/3. This means that the graph is narrower and closer to the x-axis than the parent function. However, because the absolute value function is symmetrical, the graph is still centered at (0, 0).

- The function f(x) = -2|x - 1| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-1" inside the absolute value function shifts the graph 1 unit to the right. The "2" in front of the absolute value function stretches the graph vertically by a factor of 2. This means that the graph is narrower and closer to the x-axis than the parent function, and it is also reflected across the x-axis. The vertex of the graph is at (1, 0).

Answer:

it is 0.94 miles

Step-by-step explanation:

that is because to make a mile you need 63,360 but since you have 60,000 it is not technically a mile

The calculated measure of the angle Y is 38°

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

The angle S and angle Y are corresponding angles

This means that the angles are congruent

So, we have

Y = S

Substitute the known values in the above equation, so, we have the following representation

Y = 38°

Hence, the measure of the angle Y is 38°

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Complete question

Lines MN and GH are parallel. If mS is 38°, then what is mY?

See attachment for figure

Answer:

[tex] \sqrt{( {3 - 2)}^{2} + {( - 2 - 6)}^{2} } [/tex]

[tex] \sqrt{ {1}^{2} + {( - 8)}^{2} } [/tex]

[tex] \sqrt{1 + 64} = \sqrt{65} [/tex]

a

1.5/4

b

0.5/4

c

0.5/4

because half of 3 is 1.5

Answer:

I'm pretty sure the answer is B(

The number of times more high school football players were there is 500.

Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.

Here, the number of times more high school football players were there

= 1×10⁶/2×10³

= 1×10³/2

= 1000/2

= 500

Therefore, the number of times more high school football players were there is 500.

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"Your question is incomplete, probably the complete question/missing part is:"

In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?​

Answer:

D.

x = 31; m∠ROS = 62°

Step-by-step explanation:

we know that a right angle is always 90 degrees, so we subtract 90° by ∠QOR:

[tex]90 - 28 = 62[/tex]

Then we insert the 62 with the (2x)

[tex]62 = 2x[/tex]

we divide both sides by 2 and we get:

[tex]31 = x[/tex]

so the answer is D

x is equal to 31 and we can multiply 31 by 2 and we can get 62°

Answer:

Step-by-step explanation:

To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.

We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's find the length of each side of the triangle:

AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34

BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136

CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170

Now, let's check if the Pythagorean theorem is satisfied:

AC² = AB² + BC²

170 = 34 + 136

Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.

We know that,

the distance between two points=√(x2-x1)²+(y2-y1)²

∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²

                                                                         =√(9+25)

                                                                         = √(34)

∴ The length of side AB = √(34)

Again,

The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]

                                                                      = √(100+36)

                                                                      = √136

∴ The length of side BC =√136

Also,

The distance between points A and D, AC= √(-8-5)²+(3-2)²

                                                                      = √(169+1)

                                                                      = √170

∴ The length of side AC=√170

Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170

Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,

AC²=170

BC²=136

AB²=34

Clearly, 170=136+34

or, AC²=AB²+BC²

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Answer:

$10,359.73.

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the specified time

P = the principal amount (the initial amount of money)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $4,000.00

r = 15% = 0.15

n = 1 (compounded annually)

t = 6 years

Substituting into the formula, we get:

A = 4000(1 + 0.15/1)^(1*6)

A = 4000(1.15)^6

A ≈ $10,359.73

Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.

The statement that is not true is: C. The translation of a line is a pair of parallel lines.

In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.

Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.

In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.

The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.

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Answer:

A!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

Step-by-step explanation:

To solve this expression, we need to first combine the integer part of -2 and -1, which gives us -3. Then, we need to combine the fractional parts of -1 and 3/7.

To do this, we find a common denominator, which is 7, and convert -1 to an equivalent fraction with denominator 7 by multiplying both the numerator and denominator by 7, which gives us -7/7.

Now we can add -7/7 and 3/7 to get -4/7.

Therefore, -2 - 1 3/7 = -3 - 4/7, which can also be written as -3 4/7 or -23/7 in improper fraction form

a)There is higher variability of Y with larger values of X.

b) There is non linear relation between X and Y.

a) Based on the given figure, we can make the following observations:

Therefore, the correct statement is There is higher variability of Y with larger values of X.

b) Based on the features, it is likely that a linear model may not be suitable for these data, and a non-linear model or other regression techniques may be more appropriate to capture the relationship between X and Y accurately.

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Answer:

All lines are parallel

Step-by-step explanation:

Get each equation in Slope-Intercept form:

 1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]

 2. No change

 3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]

Notice:

a. All slopes are -4/3, AND

b. All y-intercepts are different

Answer:

Step-by-step explanation:

Observation of the real life and way of life of the peoples of Oceania are intertwined in them with local myths.

The State Cash Flow Statement using the direct method.

                                                         OP                       INV                  FIN

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets                          100,000

Purchase of marketable securities                           50,000

Purchase & construction of fixed assets                  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts                                            100,000

Grants & subventions from NGO                                                     200,000

Proceeds from loan & other borrowings                                         300,000

Dividends received                                                                           100,000

                                            12,234,000             -450,000              500,000  

  Net Cash Flow for the year ended 31 December 2006: 12,284,000  

To prepare the State Cash Flow Statement using the direct method, we'll classify cash flows into three categories: Operating Activities (OP), Investing Activities (INV), and Financing Activities (FIN). Then, we'll calculate the net cash flow for each category and add them together to find the net cash flow for the year.

Operating Activities:

(-2,000,000 - 1,000,000 + 20,000,000 + 200,000 + 100,000 + 10,000,000 - 15,000,000 + 50,000 - 36,000 - 20,000 - 10,000) = 12,234,000

Investing Activities:

(100,000 - 50,000 - 500,000) = -450,000

Financing Activities:

(-100,000 + 200,000 + 300,000 + 100,000) = 500,000

Net Cash Flow for the year ended 31 December 2006:

12,234,000 (Operating Activities) - 450,000 (Investing Activities) + 500,000 (Financing Activities) = 12,284,000

The above answer is in response to the question below;

The following information has been extracted from the records of WELFARE STATE of Nigeria for the year ended 31 December 2006:

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets  100,000

Purchase of marketable securities  50,000

Purchase & construction of fixed assets  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts      100,000

Grants & subventions from NGO               200,000

Proceeds from loan & other borrowings       300,000

Dividends received                                       100,000

You are required to:

Prepare the State Cash Flow Statements for the year ended 31 December 2006 using the direct method approach (ICAN May 2008)

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Using trigonometric ratio, the value of x in the figure is 2.61 units

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In this problem, we have the adjacent side and we need to find the opposite side.

The ratio that gives us room to find this is the tangent to the angle

tanθ = opposite / adjacent

tan 43 = x / 2.8

x = 2.8 * tan 43

x = 2.61

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