Permutation/combination In how many ways can five people line up to get on a bus? (Hint: all 5 people are lining up)

Answer:

x = 3/2 or 1.5

Step-by-step explanation:

Let the unknown number be x.

Translating the word problem into an algebraic expression, we have;

2 - x = 5 + x

Rearranging the equation, we have;

x + x = 5 - 2

2x = 3

x = 3/2

x = 1.5

The maximum value of the original data set is 109.

To determine the maximum value of the original data set from the given stemplot, we need to look at the rightmost digits in each stem and identify the highest value.

Looking at the stemplot:

O 10 | 0 0 8 9 8 9 0 0 0

0 20 | 5 4 7 9 6

0 30 | 1 4 6 7 7 9 7

0 40 | 0 0 2 5 5 7 7 9 9 8

0 50 | 1 2 2 2 3 4 5 5 7 8 9 9

0 60 | 0 0 0 3 3 3 3 6 8

The rightmost digits in each stem represent the original data values. We can see that the highest value occurs in the stem "10" with a rightmost digit of "9".

Therefore, the maximum value of the original data set is 109.

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Answer:  37.68 feet

Step-by-step explanation:

Answer:

The circumference equals 18.85 when rounded and 18.84 when not rounded

Step-by-step explanation:

Have a nice day/night :)

Answer:

-5 is the answer

Hope it will be helpfull....

The values of the composite functions f(g(x)) and g(f(x)) are (x/4) and (4x - 9),respectively.

We are given two functions, f(x) and g(x). The function f(x) is defined as 1/(x - 3). The function g(x) is defined as (4/x) + 3. A function connects an input to an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. We need to find the composition of the functions.

The first composition is f(g(x)). The composite function is solved below.

f(g(x)) = f((4/x) + 3)

f(g(x)) = 1/([(4/x) + 3] - 3)

f(g(x)) = 1/(4/x)

f(g(x)) = x/4

The second composition is g(f(x)). The composite function is solved below.

g(f(x)) = g(1/(x - 3))

g(f(x)) = (4/[1/(x - 3)]) + 3

g(f(x)) = 4(x - 3) + 3

g(f(x)) = 4x - 12 + 3

g(f(x)) = 4x - 9

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Answer:

The selections are dependent.

Yes, they can be treated as independent (less than 5% of the population).

Step-by-step explanation:

Since the selections are made without replacement, each selection affects the outcome of the next selection and, therefore, the selections are dependent.

Although they are dependent, the selections can be treated as independent if the sample size is no more than 5% of the total population. In this case, the sample size is 1235 adults out of a population of 15,958,866 adults. The percentage represented by the sample is:

\(P=\frac{12,345}{15,958.866}*100\\ P=0.077\%\)

Thus the selections can be treated as independent for the purposes of calculations.

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

Step-by-step explanation:

nth term = 3*(2n - 1 )

n =1  ;    first term = 3*( 2*1 - 1) = 3* (2-1)  = 3*1 = 3

n = 2 ; second term = 3*( 2*2 - 1) = 3* (4-1)  = 3*3 = 9

n = 3 ;  third term = 3*( 2*3 - 1) = 3* (6-1)  = 3*5 = 15

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer: c(m),coffee=minutes

Step-by-step explanation:

I hope this answers your question

Slope=Δy/Δx=(y2-y1)/(x2-x1)

The points are (7,-4) and (7,0)

So slope= [ 0 -( -4 ) ] / [ 7 -7 ] = 4/0 =undefined

We know this is the vertical line of x=7 and vertical lines have undefined (or infinite) slope

Answer:

G

Step-by-step explanation:

The linear equation perpendicular to x - 6y = 5 that passes through (0, -6) is:

y = -6x - 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is -1.

We want to find a linear equation perpendicular to:

x - 6y = 5

We can rewrite that as:

6y = -5 + x

y = (1/6)*x - 5/6

Then the slope of our line must be such that:

a*(1/6) = -a

a = -6

So our line is something like:

y = -6x + b

And we want this line to pass through the point (0, -6), replacing these values we will get:

-6 = -6*0 + b

-6 = b

So the linear equation is:

y = -6x - 6

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A must be an acute angle that is less than π/2. The obtuse angle A is approximately 2.533 radians or 145.38 degrees.

An angle is the figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. The angle is typically measured in degrees or radians, and it represents the amount of rotation between the two rays.

a) When we calculate the sine of an angle, the result is always between -1 and 1. If sin A = 0.607103, then A must be between arcsin(0.607103) and π - arcsin(0.607103), since sine is positive in the first and second quadrants.

Since A is obtuse, it must be in the second quadrant (where sine is positive), but it cannot be larger than π/2 (which is a right angle) since that would make it acute. Therefore, A must be an acute angle that is less than π/2.

b) To calculate the obtuse angle that has a sine of 0.607103, we need to use the inverse sine function (arcsin) and the fact that sine is negative in the third and fourth quadrants. We can write:

sin A = 0.607103

A = arcsin(0.607103) or π - arcsin(0.607103)

Since we want the obtuse angle, we choose the larger of the two solutions:

A = π - arcsin(0.607103)

A = 2.533 radians (rounded to three decimal places)

Therefore, the obtuse angle A is approximately 2.533 radians or 145.38 degrees.

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Distance is the total length covered by an object.

Displacement is the distance between the final point and the initial point.

The distance of the helicopter's flight is 150 m

The displacement of the helicopter's flight is zero.

Displacement is the distance between the final point and the initial point.

We have,

A helicopter lifts 75m vertically into the air and then comes back down to the ground.

Distance is the total length covered by an object.

Distance of the helicopter's flight.

= 75m + 75m

= 150 m

Displacement of the helicopter's flight.

= Final point - Initial point

= 0 - 0

= 0  

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Answer:

Step-by-step explanation:

sina=12/20=0.6

cosa=16/20=0.8

tana=0.6/0.8=0.75

The statements that are true about the graph of y < 2x+1 include the following:

C. The area below the line is shaded.

D. A solution to the inequality is (2, 3).

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided, we have the following equation (inequality);

y < 2x + 1

The slope of the above equation (inequality) is 2 and the y-intercept of the boundary line is (1, 0). Additionally, the area below the dashed line must be shaded because the inequality symbol is less than (<).

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L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

L,M,N are midpoints altitude to ac​

a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

Convert this back to function form:

The equation is f(x) = 1(x - 4.5)² - 6.25.

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

For the given triangles ΔABC ≈ ΔXYZ, the length of the side AB is, 24

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

One triangle, ΔABC

Another triangle , which is ΔXYZ

Triangle ΔABC and ΔXYZ similar,

So, we can say ΔABC ≈ ΔXYZ

And it is known that

for similar triangles, ratio of lengths of sides are equal for similar triangles

so, AB/BC = XY/ZY

⇒   X/18   =  16/12

⇒   X   =  24

Hence, the value of x is 24

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Answer:

b

Step-by-step explanation:

just because not 100% sure but if i remember correctly how to do it its b

Answer: B

Step-by-step explanation:

Add 47.6 and 7.32 to get 54.92.

Add 54.92 and 0.0574 to get 54.9774.

Add 54.9774 and 6 to get 60.9774.

We conclude that the correct option is alternative "B".

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

The slope is undefined.

Step-by-step explanation:

They used the formula correctly. However, you cannot divide any number by zero.

Graphically, you can also plot both points. (see attached)

Vertically lines have undefined slopes.

Answer:

..

Step-by-step explanation:

Answer:

$8,000

Step-by-step explanation:

8,375.79 < 8,500 so it will round to 8,000

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