To determine which student is most likely to win the student council election, 100 students from the school are randomly asked who they intend to value for. This experimental design is using a _____ to gather its results.

A.confounding variable
B. Sample survey
C. Simulated model
D. Census

The triangle after the reflection over the line y = x has image points: (x'k), (5,-2), and (-6,-1). The corresponding preimage points are: (3,4), (4,3), and (-2,5).

The given information describes a triangle undergoing a transformation with a reflection over the line y = x. Let's analyze the preimage and image points to determine the transformation.

Preimage points: (3,4), (4,3), and (-2,5)

Image points: (x'k), (5,-2), and (-6,-1)

Since we know the reflection is over the line y = x, we can determine the image points by swapping the x and y coordinates of the preimage points. Therefore, the reflection can be represented by the transformation: (x, y) -> (y, x).

Applying this transformation to the preimage points, we get the image points as follows:

(3,4) -> (4,3)

(4,3) -> (3,4)

(-2,5) -> (5,-2)

Now we can check if the image points match the given image points:

(4,3) matches (x'k)

(3,4) matches (5,-2)

(5,-2) matches (-6,-1)

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Answer:

g(12) = 10

Step-by-step explanation:

To find g(12)

here t = 12 and lies in the range 6 ≤ t ≤ 12

so we use g(t) = [tex]\frac{5t}{6}[/tex]

⇒ g(12) = [tex]\frac{5*12}{6}[/tex]

= 5*2

= 10

g(12) = 10

The population increases by 1200 people each year starting from the base population of 28,000 in 2003.

To write an equation for the population, P, years after 2003, we can use the information given about the population growth.

We know that in 2003, the population was 28,000. Since the population has been growing linearly by 1200 people each year, we can express the growth rate as 1200 people per year.

Let's denote the number of years after 2003 as 'x'. Since the growth rate is constant, we can use the slope-intercept form of a linear equation to represent the population:

P = mx + b

Where:

P represents the population

m represents the slope (growth rate)

x represents the number of years after 2003

b represents the y-intercept (population in the base year)

In this case, the slope, m, is 1200 people per year, and the y-intercept, b, is 28,000 people in 2003.

Plugging in the values, the equation for the population, P, years after 2003 becomes:

P = 1200x + 28000

This equation represents the linear growth of the town's population, where the population increases by 1200 people each year starting from the base population of 28,000 in 2003.

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The probability that a data value in a normal distribution is between a z-score of 1.65 and a z-score of 2.24 is approximately 6.9%.

To calculate the probability, we need to use the standard normal distribution table or a statistical calculator.

Look up the cumulative probability for the lower z-score (1.65):

From the standard normal distribution table or a statistical calculator, we find that the cumulative probability for a z-score of 1.65 is approximately 0.9505.

Look up the cumulative probability for the higher z-score (2.24):

Similarly, the cumulative probability for a z-score of 2.24 is approximately 0.9875.

Calculate the probability between the two z-scores:

To find the probability between the two z-scores, we subtract the cumulative probability of the lower z-score from the cumulative probability of the higher z-score.

Probability = Cumulative probability (Higher z-score) - Cumulative probability (Lower z-score)

Probability = 0.9875 - 0.9505

Probability = 0.037

Convert the probability to a percentage:

Multiply the probability by 100 to express it as a percentage.

Probability (in percentage) = 0.037 × 100

Probability (in percentage) = 3.7%

Rounded to the nearest tenth of a percent, the probability that a data value in a normal distribution is between a z-score of 1.65 and a z-score of 2.24 is approximately 6.9%.

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The simplified form of the expression (-3x² + x + 5) - (4x² - 2x) is -7x² + 3x + 5.

To simplify the expression (-3x² + x + 5) - (4x² - 2x)

you will have to perform the subtraction of the two polynomials.

This can be done by first removing the brackets by applying the negative sign of the second polynomial.

After removing the brackets, you can combine like terms.

Hence;

(-3x² + x + 5) - (4x² - 2x)

= -3x²+ x + 5 - 4x²+ 2x (applying negative sign)

= -3x² - 4x² + x + 2x + 5 (combining like terms)

= -7x² + 3x + 5

Therefore, the simplified form of the  given expression is -7x² + 3x + 5.

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The second coordinate of the given first coordinate is determined as;

f(0) = 1

(1) = 6.06.

The second coordinate of the given first coordinate is calculated by applying the following method as follows;

The given function;

F(x) = [tex]4^{1.3x}[/tex]

The value of f(0) is calculated as;

f (0) = [tex]4^{1.3 \times 0}[/tex] = 4⁰ = 1

The value of f(1) is calculated as;.

f (1) = [tex]4^{1.3 \times 1} = 4^{1.3}[/tex] = 6.06

Thus, the second coordinate of the given first coordinate is determined by applying the appropriate substittue of the function as shown above.

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Answer: B. 6x + 4y ≤ 50 x + y ≥ 10

Step-by-step explanation: To represent this situation with a system of inequalities, we need to consider two constraints: the budget and the number of guests.

The budget constraint is that the total cost of the party favors should not exceed $50. Since each stuffed animal costs $6 and each toy truck costs $4, the total cost can be expressed as 6x + 4y, where x is the number of stuffed animals and y is the number of toy trucks. To satisfy the budget constraint, we need 6x + 4y to be less than or equal to 50. This gives us the first inequality: 6x + 4y ≤ 50.

The number of guests constraint is that Laura wants to provide at least one party favor per person to at least 10 guests. This means that the total number of party favors should be greater than or equal to 10. Since each party favor is either a stuffed animal or a toy truck, the total number of party favors can be expressed as x + y, where x and y are the same as before. To satisfy the number of guests constraint, we need x + y to be greater than or equal to 10. This gives us the second inequality: x + y ≥ 10.

Therefore, the system of inequalities that represents this situation is:

6x + 4y ≤ 50 x + y ≥ 10

Hope this helps, and have a great day! =)

The desired minimum revenue is $3. See the reason below.

Charge= b, Customer= c, Revenue= r

r= bc, currently, r= 16*10= $160

We know that: b+1 ⇒ c-2  and the target is r ≥ 130

So, this will all be reflected as -

b=10+x ⇒ c= 16-2x

(10+x)(16-2x) ≥ 130

160 -20x +16x - 2x² ≥ 130

-2x² - 4x + 30 ≥ 0

x² + 2x -15 ≤ 0

(x+1)² ≤ 4²

x+1 ≤ 4 (negative value not considered)

x ≤ 3

As we see the max increase amount is $3, when the revenue will be  -

(10+3)*(16-3*2)= 13*10= $130

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.

The factors of the original expression, u and v to produce a sum of simpler terms, the derivative of y with respect to x is: y' = -2x⁴ - x² - 10x + 15

Given the expression y = (3 - x²) (x³ - 5x + 5),

We need to find the derivative of y with respect to x.

We can find y' using two methods:

Method 1: Applying the Product RuleIf y = uv, then we know that y' = u'v + uv'Applying this formula to the given expression, We get:

y = (3 - x²) (x³ - 5x + 5)u = (3 - x²) and v = (x³ - 5x + 5)

Differentiating u and v, we get:u' = -2x and v' = 3x² - 5

Substituting these values into the formula for y', we get:

y' = u'v + uv' = (-2x) (x³ - 5x + 5) + (3 - x²) (3x² - 5)

Simplifying this expression, we get:

y' = -2x⁴ + 10x² - 10x - 3x² + 15 = -2x⁴ - x² - 10x + 15

Method 2: Multiplying the Factors to Produce a Sum of Simpler Terms to Differentiate

Expanding the given expression, we get:

y = 3x³ - 15x + 15 - x⁵ + 5x³ - 5x - 3x² + 15x² - 15x

Differentiating this expression, we get: y' = 9x² - 15 + 0 - 5x⁴ + 15x² - 5 - 6x + 30x - 15

Simplifying this expression, we get:

y' = -2x⁴ - x² - 10x + 15

Therefore, the derivative of y with respect to x is:y' = -2x⁴ - x² - 10x + 15

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The expression that is equivalent to the composite function (f ° g) (5) is; Option A: f (5) times g (5)

A composite function is defined as an operation where two functions say f and g, generate a new function say h in such a way that h(x) = g(f(x)). It means here that function g is said to be applied to the function of x. So, this basically,l tells us that a function is applied to the result of another function.

We want to find (f ° g) (5)

This simply means f(5) × g(5)

The composite function definition demands that must be the expression of the the question and as such option A is the only correct option.

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Answer:

f(5) x g(5)

Step-by-step explanation:

(fg)(5) = (f x g)(5) = f(5) x g(5)

a. The spring's displacement when t = 0 is 12 cm.

The spring's displacement when t = π/3 is 6 cm.

The spring's displacement when t= 3π/4 is -6√2 cm.

b. The spring's velocity when t = 0 is 0 cm/sec.

The spring's velocity when t = π/3 is -6√3 cm/sec

The spring's velocity when t= 3π/4 is -6√2 cm/sec.

a. When t = 0, the spring's displacement can be calculated by using the given displacement equation:

x = 12cost

x(0) = 12cos(0)

x(0) = 12 cm.

When t = π/3, the spring's displacement can be calculated by using the given displacement equation:

x = 12cost

x(π/3) = 12cos(π/3)

x(π/3) = 12 × 1/2 = 6 cm.

When t = 3π/4, the spring's displacement can be calculated by using the given displacement equation:

x = 12cost

x(3π/4) = 12cos(3π/4)

x(3π/4) = 12 × -√2/2 = -6√2 cm.

Part b.

In order to determine the spring's velocity, we would have to take the first derivative of the displacement equation with respect to time;

v(t) = dx/dt = -12sint

When t = 0, the spring's velocity can be calculated as follows:

v(0) = -12sin(0)

v(0) = 0 cm/sec.

When t = π/3, the spring's velocity can be calculated as follows:

v(π/3) = -12sin(π/3)

v(π/3) = -6√3 cm/sec.

When t = 3π/4, the spring's velocity can be calculated as follows:

v(3π/4) = -12sin(3π/4)

v(3π/4) = -6√2 cm/sec.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

8 x 6 is 48.

8 x 6 can also be written as eight 6s or six 8s.

So 8 + 8 + 8 + 8 + 8 + 8 or 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6.

A net is a two-dimensional pattern that can be folded into a three-dimensional shape. The figure you provided is a net for a right rectangular prism with dimensions 10 cm x 7 cm x 13 cm. It consists of six rectangles, where the two rectangles on the ends have dimensions of 10 cm x 7 cm, and the four rectangles in the middle have dimensions of 13 cm x 7 cm.

To create the right rectangular prism from the net, you would need to cut along the solid lines and fold along the dashed lines. The two rectangles with dimensions 10 cm x 7 cm would become the top and bottom faces of the prism, while the four rectangles with dimensions 13 cm x 7 cm would become the four side faces of the prism. When folded and glued or taped together, the prism would have a height of 10 cm, a width of 7 cm, and a length of 13 cm.

This method of approximation is derived from the mathematical concept of limits and the definition of the number e as the limit of (1 + 1/n)^n as n approaches infinity. By increasing the value of n, we approach closer and closer to the actual value of e.

To approximate the mathematical constant "e," you can use the expression (1 + 1/n)^n, where n is a large value. As n approaches infinity, this expression converges to the value of e. The larger the value of n, the closer the approximation will be to the actual value of e.

For example, let's substitute a large value, say n = 10,000, into the expression:

Approximation of e ≈ (1 + 1/10,000)^10,000

Calculating this expression, we get an approximation of e as approximately 2.7181459. Although it's not an exact value, it is a close approximation of the mathematical constant.

To use this approximation, choose a large value for "n", such as 10,000 or 100,000, and evaluate the expression (1 + 1/n)^n using a calculator or computer program. The result will be a close approximation of the value of "e". The larger the value of "n", the more accurate the approximation will be.

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Simplifying the given expression results to

To simplify the expression using PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right), we'll break it down step by step:

The expression is rewritten as, 1/2 (1/4 ÷ 1/3 - 1/4 - 3/4 + 1/2). hence we start we parenthesis.

Performing division results to

1/2 (3/4 - 1/4 - 3/4 + 1/2)

Performing addition results to

1/2 (3/4 - 1/4 - 5/4)

Performing subtraction results to

1/2 (-3/4)

Now we multiply

-3/8

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The solution to the multiplication of the decimals is; 39.15

One of the ways to multiply decimals is as follows;

To multiply decimals, first multiply as if there is no decimal.

Second step is to count the number of digits after the decimal in each factor.

Last step is to put the same number of digits behind the decimal in the product.

Now, we want to multiply the decimals given as;

8.7 × 0.45

Converting them to fractions gives us;

(87/10) × (45/10)

= 3915/100

= 39.15

Thus, that is the solution to the multiplication of the decimals.

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Answer: 1/4

Step-by-step explanation:

Answer:

Your correct

Step-by-step explanation:

The transversal,a, creates right angles for line b, c, and d. This they are parallel

The correct answer is that Alan mixed up the positions of 8 and 25 in the equation (8)(x) = (25)(200). This mistake led to incorrect calculations and the wrong answer.

Alan's error lies in mixing up the positions of 8 and 25 in the equation (8)(x) = (25)(200). In the original proportion, the correct equation is (x/200) = (8/25).

However, Alan mistakenly wrote it as (8)(x) = (25)(200), reversing the positions of 8 and 25. This error leads to incorrect calculations and ultimately an incorrect answer of x = 625.

Let's break down Alan's steps to understand his mistake:

StartFraction x over 200 EndFraction = StartFraction 8 over 25 EndFraction.

Alan correctly writes down the proportion.

(8)(x) = (25)(200).

Here is where Alan's error occurs. Instead of multiplying 8 by x and 25 by 200, he mistakenly swaps their positions. This mistake results in incorrect products.

8x = 5,000.

Alan multiplies incorrectly and obtains 5,000 as the product of 25 and 200.

StartFraction 8x over 8 EndFraction = StartFraction 5,000 over 8 EndFraction.

Alan divides both sides of the equation by 8, which is the correct step.

x = 625.

Alan divides 5,000 by 8 to find the value of x, which is his final incorrect answer. So, the correct option is he mixed up the positions of 8 and 25 in the equation (8) (x) = (25) (200).

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Answer:

Since segments AC and BD are diameters of Circle E, angle ACD is a central angle that intercepts arc ACD, and angle BCD is also a central angle that intercepts arc ACD. Therefore, arc ACD is divided into two equal arcs, arc CDB and arc CAB, by the diameter CD.

Since arc ACD is 326 degrees, each of arc CDB and arc CAB is 326/2 = 163 degrees.

Therefore, arc CDB equals 163 degrees.

The points in the graph of the system of inequalities are:

(-2, 0) --> not a solution.

(5, 0) --> not a solution.

(7, 0) --> not a solution.

(0, 7) --> solution.

Here we can see the graph of a system of inequalities, and there we have the points:

(-2, 0)

(5, 0)

(7, 0)

(0, 7)

You can see that all the points lie on the lines (these are solid lines, meaning that the points on the lines are solutions for the corresponding inequality)

Now, a point is a solution of a system of inequalities only if it solves both of them at the same time.

The only point that is a solution of both inequalities at the same time is point (0, 7).

So the points are:

(-2, 0) --> not a solution.

(5, 0) --> not a solution.

(7, 0) --> not a solution.

(0, 7) --> solution.

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Answer:

[tex]\huge\boxed{\sf b = 4/3}[/tex]

Step-by-step explanation:

[tex]9^2 \times b^2 = 12^2[/tex]

So,

81 × b² = 144

b² = 144 / 81

b² = (12 × 12) / (9 × 9)

b² = 12² / 9²

√b² = √(12²/9²)

b = 12 / 9

[tex]\rule[225]{225}{2}[/tex]

Answer:

50 minutes

Step-by-step explanation:

28 cents = $0.28

Let the call be for x minutes

Total cost = connection fee + x*cost per minute

14.85 = 0.85 + 0.28x

14.85 - 0.85 = 0.28x

0.28x =  14

x = 14/0.28

x = 50

Answer:

50 min

Step-by-step explanation:

Let the call be for x minutes

14.85 = 0.85 + 0.28x

0.28x = 14

x = 14/0.28 = 50

The contrapositive of the sentence is this: Jose isn't going for a bike ride if and only if he doesn't wake up early.

A contrapositive is a statement that challenges both the predicate and the subject of a given sentence. In the above sentence, the statement is that Jose wakes up early if and only if he is going for a bike ride.

The contrapositive now challenges the subject's action of waking up early and going for a bike ride. The hypothesis and conclusion are disputed.

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Step-by-step explanation:

Can you provide an image please?

Answer:

C

Step-by-step explanation:

Answer:

6 by 36 is the answer.....

Answer:

A.

Step-by-step explanation:

New x-coordinate = (-4) * (4/5) = -16/5 = -3.2

New y-coordinate = 6 * (4/5) = 24/5 = 4.8

that's the only option with a -3.2 for A

Answer:

#5 - [tex]x=-2[/tex]

#6 - [tex]x=-4[/tex]

#7 - [tex]x=2[/tex]

#8 - [tex]x=10[/tex]

Step-by-step explanation:

Solve the following multi-step equations.

#5 - [tex]-10-7x=-3x-2[/tex]

#6 - [tex]-13-4x=x+7[/tex]

#7 - [tex]x-2=10-5x[/tex]

#8 - [tex]3x-1=4x-11[/tex]

[tex]\hrulefill[/tex]

I will use the SCAM method to solve these multi-step equations.

[tex]\mathbb{S}\text{implify each side of the equation} \\\\\\\mathbb{C}\text{ombine like terms, collect variables on one side }\\\\\\\mathbb{A}\text{dd and/or subtract}\\\\\\\mathbb{M}\text{ultiply and/or divide}[/tex]

What is our goal when solving equations?

Our goal is to isolate the variable.

Remember when solving equations, whatever you do to one side of the equation you must do to the other.  [tex]\hrulefill[/tex]

Now solving #5,

[tex]-10-7x=-3x-2[/tex]

Observing the equation, we notice on either side of the equation we cannot simplify using the distributive property or order of operations ("PEMDAS"). Well will skip to the "C" in SCAM.

Add "7x" to each side of the equation.

[tex]\Longrightarrow -10-7x+7x=-3x-2+7x\\\\\\\Longrightarrow -10=4x-2[/tex]

The variable "x" now appears on one side of the equation. Now we are on the "A" in SCAM.

Add the value of "2" to each side of the equation.

[tex]\Longrightarrow -10+2=4x-2+2\\\\\\\Longrightarrow -8=4x[/tex]

Now on the "M" in SCAM.

Divide both sides of the equation by the value of "4."

[tex]\Longrightarrow \dfrac{-8}{4}=\dfrac{4}{4}x\\\\\\\Longrightarrow -2=x\\\\\\\therefore \boxed{x=-2}[/tex]

Thus, problem #5 is solved.

[tex]\hrulefill[/tex]

For the rest of the problems I will simply show the operations I am doing.

Now solving #6,

[tex]-13-4x=x+7\\\\\\\Longrightarrow -13-4x+4x=x+7+4x\\\\\\\Longrightarrow -13=5x+7\\\\\\\Longrightarrow -13-7=5x+7-7\\\\\\\Longrightarrow -20=5x\\\\\\\Longrightarrow \dfrac{-20}{5}= \dfrac{5}{5}x\\\\\\\Longrightarrow-4=x\\\\\\\therefore \boxed{x=-4}[/tex]

Thus, problem #6 is solved.

[tex]\hrulefill[/tex]

Now solving #7,

[tex]x-2=10-5x\\\\\\\Longrightarrow x-2+5x=10-5x+5x\\\\\\\Longrightarrow 6x-2=10\\\\\\\Longrightarrow 6x-2+2=10+2\\\\\\\Longrightarrow 6x=12\\\\\\\Longrightarrow \dfrac{6}{6}x=\dfrac{12}{6}\\\\\\\therefore \boxed{x=2}[/tex]

Thus, problem #7 is solved.

[tex]\hrulefill[/tex]

Now solving #8,

[tex]3x-1=4x-11\\\\\\\Longrightarrow 3x-1-3x=4x-11-3x\\\\\\\Longrightarrow -1=x-11\\\\\\\Longrightarrow -1+11=x-11+11\\\\\\\Longrightarrow 10=x\\\\\\\therefore \boxed{x=10}[/tex]

The variable x as the subject​ of the equation is x = n(w - 2)

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

x/n + 2 = w

Subtract 2 frm both sides of the equation

So, we have

x/n = w - 2

Next, we have

x = n(w - 2)

Hence, the solution is x = n(w - 2)

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