There are 7 children that are taking turns using the swing on a playground. How many different ways are there in which they each can use the swing where everyone gets exactly one turn? roscoe has 15 books on his summer reading list. He wants to choose 6 books to read in order from first to last. In how many ways can he do this? the student council has 15 students. They need to choose a president, vice president, secretary and treasurer for student council. In how many ways can the 4 different positions be appointed from the 15 students? thomas is creating a 7 digit passcode using the digits 0 through 9. How many 7 digit passcodes are possible if the numbers cannot be repeated?

Answer:

incomplete question friend

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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The letters of the alphabet that have a symmetry group with four elements are I, O, H, X. The four symmetries are Identity symmetry, 90-degree rotation symmetry, 180-degree rotation symmetry, and 270-degree rotation symmetry.

The letter H has two lines of symmetry, that is, one horizontal and one vertical. The letter I has one line of symmetry, that is, a vertical line that runs through its center point. The letter O has rotational symmetry. The letter X has two lines of symmetry, that is, a diagonal line that runs from the top left to the bottom right, and a diagonal line that runs from the top right to the bottom left.

Identity symmetry is the symmetry where the letter remains unchanged after rotation by 0 degrees.

90-degree rotation symmetry is the symmetry where the letter is rotated 90 degrees clockwise. After this rotation, the letter looks exactly the same as it did in its initial orientation.

180-degree rotation symmetry is the symmetry where the letter is rotated 180 degrees clockwise. After this rotation, the letter looks exactly the same as it did in its initial orientation.

270-degree rotation symmetry is the symmetry where the letter is rotated 270 degrees clockwise. After this rotation, the letter looks exactly the same as it did in its initial orientation.

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Answer:

12t - 1

Step-by-step explanation:

(9t+5) + (3t-6)

9t + 5 + 3t - 6

12t - 1

Answer:

A. Yes

B. The triangles are similar

C. The corresponding sides are proportional

D. The slope of ΔABC = tanθ₁ = tanθ₂ = The slope pf ΔDEF, therefore, the slope of any two points on the line are congruent by similar triangles

E. The rate of proportionality = 2

Step-by-step explanation:

A. From the given graph, given that the angles are formed between the transversal and lines parallel to the R-value axis and the transversal and lines parallel to the thickness axis, the angle formed by the transversal and each parallel lines are corresponding angles and are therefore congruent

The tan of one of the angles on each triangle are

On the uppermost triangle, tanθ₁ = (9.42 - 3.14)/(3 - 1) = 3.14

On the other triangle, tanθ₂ =(25.12 - 12.56)/(8 - 4) = 3.14

tanθ₁ = tanθ₂

∴ θ₁ = θ₂

ΔABC and ΔDEF are right triangles, therefore, all the angles of ΔABC and ΔDEF  are congruent

B. Given that the interior angles of the triangles formed by the line the graph are congruent, the triangles are similar by AA similarity postulate

C. Given that the triangles are similar, the length of the corresponding  sides of the triangles are proportional

D. Given that the slope is the tangent of the angle between the line of the graph and the Thickness axis, and that the angle is the same for both triangles, (∠θ₁ and ∠θ₂) the slope or the rise-to-run ratio is constant for the two triangles and also for any two points on the line

E. The Unit of proportionality is found using any two points as follows;

Using points used to show the proportional relationship on triangle ΔABC are (8, 25.12) and (4, 12.56) and on triangle ΔDEF, the two points used to show proportional relationship are (3, 9.42), and (1, 3.14)

The ratio of the corresponding sides on ΔABC and ΔDEF are

\(\overline {AC}\)/\(\overline {DF}\) = (25.12 - 12.56)/(9.42 - 3.14) = 2

\(\overline {BC}\)/\(\overline {EF}\) = (8 - 4)/(3 - 1) = 2

Therefore, the unit rate of proportionality which is the scale factor = 2.

Answer:

w= A / l

Step-by-step explanation:

A = lw

Where,

A= Area of a rectangle

l= Length of a rectangle

w= width of a rectangle

Area of a rectangle = length × width

Solve the formula(equation) for width(w).

A= lw

Divide both sides by l

A / l = lw / l

A / l = w

Width = Area of the rectangle / length of the rectangle

Example: Find the width of the rectangle with length of 6 inches and Area of 12 square inches.

A= 12 square inches

l= 6 inches

w= x inches

A= lw

w= A / l

= 12 / 6

= 2

w = 2 inches

Answer:  

I would think 15c+5= 35 because it is the one answer that makes the most sense.  If you get this wrong I am so sorry.

Answer:its the last choice

Step-by-step explanation: im sorry if i get this wrong lol

Answer:

\(16^{\frac{1}{2} }\)

Step-by-step explanation:

something to the power of 1/2 is sqauer root of it

\(16^{\frac{1}{2} }\) = 4

Answer:

V ≈ 68.63 cm³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = \(\frac{4}{3}\)πr³

the volume of a hemisphere is half the volume of a sphere, so

V = \(\frac{1}{2}\) × \(\frac{4}{3}\) πr³ = \(\frac{2}{3}\) πr³ , then

V = \(\frac{2}{3}\) π × 3.2³

  = \(\frac{2}{3}\) π × 32.768

  ≈ 68.63 cm³ ( to 2 dec. places )

Answer:

Logic puzzles use grids to help you make eliminations based on deciphering the truth in the clues provided.

We can use the method to solve a logic puzzle is;

''Logic puzzles use grids to help you make eliminations based on deciphering the truth in the clues provided.''

Here,

We have to find a method to solve the logic puzzle.

What is Logic puzzle?

A problem that can be solved through the deductive reasoning is called Logic puzzle.

Now,

To solve a logic puzzle we can use grids which help to make eliminations based on deciphering in providing the truth in the clues.

Hence,

We can use the method to solve a logic puzzle is;

⇒ 'Logic puzzles use grids to help you make eliminations based on deciphering the truth in the clues provided.'

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Answer:

∠ P = 45°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

∠ P + 45° + 90° = 180° , that is

∠ P + 135° = 180° ( subtract 135° from both sides )

∠ P = 45°

Answer:

√17 is not a rational number

Step-by-step explanation:

The reason why √17 is not a rational number is because it doesn't repeat, nor terminate.

Answer:

Step-by-step explanation:

2x - y = -8

3x + y = -2

5x = -10

x = -2

3(-2) + y = -2

-6 + y = -2

y = 4

(-2, 4)

Answer: (-2, 4)

Good luck!

(a) The unit vector in the same direction as -3i+5j is:

\(u = (-3i+5j) / \sqrt(34)\)

(b) The unit vector in the opposite direction is:

\(V = -v = (-15i + 10j - 10k) / (5\sqrt(6))\)

(c) The unit vector in the same direction as AB is:

\(w = AB / \sqrt(11) = (3/ \sqrt(11))i + (1/ \sqrt(11))j - (1/ \sqrt(11))k\)

(a) To find a unit vector in the same direction as -3i+5j, we divide this vector by its magnitude:

\(|-3i+5j| = \sqrt((-3)^2 + 5^2) = \sqrt(34)\)

So, a unit vector in the same direction as -3i+5j is:

\(u = (-3i+5j) / \sqrt(34)\)

(b) To find a unit vector in the opposite direction to 15i - 10j + 10k, we first find a unit vector in the same direction and then multiply it by -1:

\(|15i - 10j + 10k| = \sqrt(15^2 + (-10)^2 + 10^2) = 5\sqrt(6)\)

So, a unit vector in the same direction as 15i - 10j + 10k is:

\(v = (15i - 10j + 10k) / (5\sqrt(6))\)

And a unit vector in the opposite direction is:

\(V = -v = (-15i + 10j - 10k) / (5\sqrt(6))\)

(c) To find a unit vector in the same direction as the vector from A(-1,0,2) to B(2,1,1), we first find this vector:

AB = <2 - (-1), 1 - 0, 1 - 2> = <3, 1, -1>

Then, we divide it by its magnitude:

\(|AB| = \sqrt(3^2 + 1^2 + (-1)^2) = \sqrt(11)\)

So, a unit vector in the same direction as AB is:

\(w = AB / \sqrt(11) = (3/ \sqrt(11))i + (1/ \sqrt(11))j - (1/ \sqrt(11))k\)

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It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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Imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year.

There are several possible explanations for the finding that people who used sunscreen were more likely to have been sunburned in the past year.

However, without additional context or data, it is difficult to determine the most likely explanation definitively. Here are a few possible explanations to consider:

1. Ineffective or improper use of sunscreen: It is possible that the individuals who reported using sunscreen did not apply it correctly or did not reapply it as recommended.

Inadequate application or failure to follow proper sunscreen usage guidelines could result in insufficient protection from the sun's harmful rays, leading to sunburn.

2. Self-selection bias: It is possible that individuals who have previously experienced sunburns may be more likely to use sunscreen. They may be more aware of the potential risks and take precautions, including using sunscreen.

This could create an association between sunscreen use and sunburn, even though sunscreen itself is intended to prevent sunburn.

3. Recall bias: The survey responses may be subject to recall bias, where individuals may inaccurately remember or report their sunscreen use and sunburn experiences.

Memory limitations or subjective perceptions of sunburn severity could influence the reported data and the observed association between sunscreen use and sunburn.

4. Confounding factors: There may be other factors or variables at play that are related to both sunscreen use and sunburn. For example, individuals who engage in activities that increase sun exposure or who have certain skin types may be more likely to both use sunscreen and experience sunburn.

It is important to note that further investigation, including more detailed surveys, data collection and statistical analysis, would be necessary to determine the most likely explanation for the observed association between sunscreen use and sunburn.

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The parameters of the sinusoidal function, y = -3·cos(π·(π - 2)) - 4, obtained from the equation of the function are;

(a) a) 2

b) 4 units down

c) 2 units left

(b) d) Please find attached the graph of the function showing the period created with MS Excel.

A sinusoidal function is a periodic sine or cosine based function.

The specified sinusoidal function can be presented as follows;

y = -3·cos(π·(x - 2)) - 4

The general form of a sinusoidal function is; y = A·cos(B·(x + C)) + D

(a) a) The period of a sinusoidal function is T = 2·π/|B|

A comparison with the general form of a sinusoidal function indicates;

A = 3, B = π, C = -2, D = -4

B = π

Therefore; T = 2·π/π = 2

The period, T = 2

b) The vertical shift of the function, D = -4

c) The horizontal shift of the function, C = -2

(b) d) Please find attached the graph of the function created with MS Excel

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The equations in the slope-intercept form are

p = 3b + 2 and p = (5/2)b + 15/2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

From the table and scatter plot;

(a). The line for 'Build it' passes through (1, 10) and (3, 15),

then the equation of the line is,

p = (5/2)b + 15/2

Similarly, the equation of the line-'All things home' is,

p = 3b + 2.

(b) the graphs of the lines are given in the attached image.

(c) The equation in the slope-intercept form;

p = 3b + 2 and p = (5/2)b + 15/2.

(d) When b = 65,

then p = 3(65) + 2 and p = (5/2)(65) + 15/2.

So, p = 197 and p = 170

Therefore, all the required values are given above.

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Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Answer:

A

Step-by-step explanation:

To find the area of a rectangle, it is length times width (10*3x), and if it equals 40, you could just write that after the equation, and then find out that "x" would equal \(\frac{4}{3}\)

Answer:

30x = 40 ; x ≈ 1  

Step-by-step explanation:

\(A^{}\) = \(l^{}\) \(w^{}\)

\(l^{}\) = 10 inch.

\(w^{}\) = 3x

10(3x) = 40

30x = 40 ; x = \(1\frac{1}{3}\) ≈ 1

Ethan's total weekly pay T is given by T = 16d + 135.

Linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Let T represent  Ethan's total weekly pay for d deliveries.

Ethan is paid $16 per delivery. Hence:

He made 5 deliveries, and his total pay was $215, hence:

Ethan's total weekly pay T is given by T = 16d + 135.

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Answer:

Step-by-step explanation:

Add together:  2 2/3 hrs and 2 3/4 hrs:

First determine the LCD of these two fractions.  The LCD here is 3*4 = 12.

Rewrite the given times using this LCD:

2 8/12 + 2 9/12

Adding 2 and 2 results in 4; adding 8/12 and 9/12 results in 17/12, or 1 5/12.

The final result is 4 + 1 5/12, or 5 5/12.

The movie and dinner together lasted 5 5/12 hrs.

If movie and dinner started at 3:00, dinner would have finished at

3:00 + 5:5/12, or

8:25 p.m. (since 5:5/12 is the same as 5:25).

Finished eating at 8:25 p.m.

Answer:

Finished eating at 8:25 and both lasted 5:25 hours in total

Step-by-step explanation:

In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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Answer:

Step-by-step explanation:

P(both) = 4/7 * 3/7 = 12 / 49

Answer:

1 hour and 8 minutes

Step-by-step explanation:

After travelling 1 hour you’ve reached 60 miles. So you go 1 mile/ minute.

You have then 8 miles left. You get: 8 minutes. Which gives us the answer:

1 hour and 8 minutes.

a. The minimum sample size needed is 601.

b. The minimum sample size needed using a prior study is 304.

c. The difference between the results from parts (b) and (a) shows that a preliminary estimation of the population proportion can lower the necessary minimum sample size.

The signed, fractional number of standard deviations above the mean value that an event is above is expressed by the dimensionless variable known as the z-score. Among other names, it is also referred to as the normal score, z-value, and standard score. Z-scores are indicative of values that are higher than the mean and lower than the mean.

(a) To find the minimum sample size needed assuming that no prior information is available, we can use the formula:

n = (Zα/2)² *\(\hat p \hat q\)/ E²

where Zα/2 is the z-score corresponding to the desired level of confidence (90% confidence corresponds to a z-score of 1.645), \(\hat p\) is the sample proportion (unknown), \(\hat q = 1 - \hat p\), and E is the maximum error of estimation (2% of the true proportion, or 0.02).

Plugging in the values, we get:

n = (1.645)² * 0.5*0.5 / 0.02² ≈ 601

Consequently, 601 is the required minimum sample size.

(b) To find the minimum sample size needed using a prior study that found that 42% of the respondents said they think Congress is doing a good or excellent job, we can use the formula:

n = (Zα/2)² * \(\hat p \hat q\) / E²

where now we have a preliminary estimate of the population proportion, \(\hat p = 0.42, and \hat q = 1 - \hat p.\)

Plugging in the values, we get:

n = (1.645)² * 0.42*0.58 / 0.02² ≈ 304

Therefore, the minimum sample size needed using a prior study is 304.

(c) The result from part (b) is smaller than the result from part (a), indicating that having a preliminary estimate of the population proportion can reduce the minimum sample size needed. This is because a preliminary estimate can provide a starting point for the sample size calculation, and reduce the variability of the sampling distribution.

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Answer:

Quadrant III yw :3

Step-by-step explanation: