A nutritionist would like to estimate the number of times adults exercise each week. To collect information, the nutritionist emails the members of the local fitness center. Which of the following describes the bias that may arise from the results?
A- This is a convenience sample and likely overestimates the frequency of exercise.
B- This is a convenience and likely underestimated the frequency of exercise.
C- This is a voluntary response sample and likely overestimates the frequency of exercise.
D- This is a voluntary response sample and likely underestimates the frequency of exercise.

Answer: (−∞,8)∪(8,∞),{y|y≠8}

Step-by-step explanation:

Answer: The range of a function is the set of all possible output values (y-values) for a given function.

For the function y = 3/x+8, we can find the range by analyzing the domain of the function. The domain of a function is the set of all input values (x-values) for which the function produces a valid output value.

The range of this function is all real numbers, since the denominator x+8 can't be equal to zero.

However, we can't express the range of the function as a specific set of numbers because the range is defined as all real numbers. The answer would be R

It's worth noting that if we change the function for example to y = 3/x-8, the domain would be x≠8 and the range would be y<-8/3

Step-by-step explanation:

Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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The trigonometric function that models the temperature T in the South Pole in March t hours after midnight is given as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

The lowest temperature is of -54ºC, while the highest is of -50ºC, with a difference of 4ºC, hence the amplitude is given as follows:

2a = 4

a = 2.

A function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -54 and -50, hence the vertical shift is given as follows:

d = -50.

The period is of 24 hours, hence:

2π/B = 24

24B = 2π

B = π/12.

The highest value of the cosine function should be assumed at t = 0, but it is assumed at t = 14(2 p.m.), hence the phase shift is given as follows:

c = 14.

Thus the function is defined as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

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Answer:

Add '-2b' to each side of the equation.

a + 2b + -2b = 12 + -2b

Combine like terms: 2b + -2b = 0

a + 0 = 12 + -2b

a = 12 + -2b

Simplifying

a = 12 + -2b

Answer: b= 6-a/2

Step-by-step explanation:

Always try to isolate what you are looking for.

a+ 2b=12 (subtract a)

2b= 12-a (divide by 2 to isolate b)

b= 12-a/2 (divide both numbers by 2 to get the smallest fraction)

b= 6-a/2 [b is now isolated :) ]

Answer:

y = x-2

Step-by-step explanation:

Pick two points on the line

(0,-2) and (2,0)

We can find the slope

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

   = (0--2)/(2-0)

   = (0+2)/(2-0)

   2/2

  =

We know the y intercept is -2 (  where it crosses the y axis)

y = mx +b is the slope intercept form of the equation  where m is the slope and b is the y intercept

y = 1x -2

y = x-2

Answer: \(y=x-2\)

Step-by-step explanation:

I explained the other problem you asked, why couldnt you apply that info to this one? Either way, Ill explain it again.

We can see the slope intercept is -2, so b = -2

To get the slope, just from visualization. Look at the y value and x value direction for which you gotta take to get to the next coords. From the y-intercept, you go up 1 and then right 1. 1/1 = 1

Therefore, sin(0) = -√305/41 when 0 is an angle in quadrant IV.

Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles. It is used to solve problems in many fields, including engineering, physics, astronomy, and architecture. Trigonometry involves the use of functions such as sine, cosine, and tangent to relate the angles and sides of a right triangle. It also includes the study of trigonometric identities, equations, and graphs, as well as applications of trigonometry in real-world situations.

Here,

If 0 is an angle in quadrant IV, then cosine is positive and sine is negative. We can use the Pythagorean identity to find the value of sin(0):

sin²(0) + cos²(0) = 1

sin²(0) = 1 - cos²(0)

sin(0) = -√(1 - cos²(0))

substituting the given value of cos(0):

sin(0) = -√(1 - (4√47/41)²)

sin(0) = -√(1 - (16*47/41))

sin(0) = -√(1 - 736/41)

sin(0) = -√(305/41)

sin(0) = -(√305)/√(41)

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Answer:

d no more than two questions correct

The true statement is his friend's tank can hold almost twice as much water as Julian's tank.

The volume of the friend's tank 1 1/4 x 1 1/4 x 300

5/4 x 5/4 x 300 = 468.75

Ratio of the friend's tank to Julian's tank = 468.75 / 300 = 1.56

Here is the complete question:

One of Julian's friends also has a rectangular aquarium. The dimensions of his friend's tank are each exactly 1 1/4 times the dimensions of Julian's tank.

If the area of the rectangular base of Julian's tank is approximately 300 square inches, which of the following statements is true?

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Answer:

x^7/12

Step-by-step explanation:

The question asks what is x^1/3 * x^1/4

x^1/3 * x^1/4

Now with those exponents we can already see that we have the same BASE (x)!! That saves a lot of time.

From there all we do is add the exponents

x ^(1/3 +1/4)

common denominator

x ^(4/12 + 3/12)

x^(7/12)

Answer:

Step-by-step explanation:

Before we do anything, we need to write this question from written form into expression form.

"The product of the cube root of x squared times the 4th root of x cubed" is:

\((\sqrt[3]{x^{2}})(\sqrt[4]{x^{3} } )\)

The best way to solve this is if you know the properties of exponents. The first thing to do is to convert these square roots and squares into exponents using the fractional exponent rule:

\(a^{\frac{m}{n} } =\sqrt[n]{a^{m} }\)

\(= (x^{\frac{2}{3} } )(x^{\frac{3}{4} } )\)

Now, we can combine these two using the product rule:

\((a^{m} )(a^{n} )=(a^{m+n} )\)

\(= x^{\frac{2}{3} } + x^{\frac{3}{4} } = x^{\frac{17}{12} } or \sqrt[12]{x^{17} }\)

Answer:

B is correct because there cannot be negative people in a cafeteria.

Step-by-step explanation:

Answer

Cut out the shapes, and then multiply them.

Step-by-step explanation:

The object was 334 feet in the air 9 seconds after it was launched.

The height of an object launched from the top of a hill can be modeled by the function h(t) = -16t² + 170t + 100, where t represents the number of seconds after the launch.

This function gives the height of the object in feet at any time t after the launch.

To find the height of the object 9 seconds after it was launched,

Substitute 9 for t in the function h(t) to calculate the height of the object at that time. This gives us the equation :

⇒ h(9)  = -16(9)² + 170(9) + 100

⇒ h(9)  = -16(81) + 1530 + 100

⇒ h(9)  = -1296 + 1530 + 100

⇒ h(9)  = 334 feet.

Therefore, 9 seconds after being launched, the object had reached a height of 334 feet.

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A) The probability that a piece of toast lands butter side down when dropped from a 2.5-foot high table is 0.81 means that out of all possible outcomes of dropping a piece of toast from that height, 81% of the time it will land with the butter side facing down.

B) No, it does not mean that exactly 81 out of 100 pieces of toast will land butter side down. The probability of a single piece of toast landing butter-side down is 0.81, so when 100 pieces of toast are dropped, we can expect around 81 of them to land butter-side down on average, but the actual number may vary due to randomness.

C) Maria may or may not be surprised, depending on her expectations and the level of significance she sets for her test. To carry out a simulation, we can use a random number generator to simulate dropping 10 pieces of toast with a probability of 0.81 of landing butter side down. We can repeat this simulation multiple times, say 1000 times, and count the number of times the simulation yields 4 or fewer pieces of toast landing butter side down. If this rarely happens (e.g., less than 5% of the time), we can say that Maria should be surprised.

D) The dot plot displaying the results of 50 simulated trials of dropping 10 pieces of toast can provide some information about the variability of the outcomes. If most of the dots are clustered around 8 or 9 (which would correspond to 80% or 90% of the pieces of toast landing butter side down), then Maria's result of only 4 out of 10 pieces landing butter side down would be considered unusual, and she should be surprised. However, if the dots are spread over a wide range, it would suggest that getting 4 out of 10 is not that uncommon, and Maria should not be surprised.

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Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

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

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

Answer:

166

Step-by-step explanation:

multiply the 6 by 2 and then multiply 13 by 10

to get 166

Solution

- The quadratic equation given is:

Question 1:

- To know which direction a parabola opens, we follow the these rules:

- The value of a given is -1 < 0.

- Thus, the parabola opens downwards

Question 2:

- The y-intercept of the function is the coordinate of where the graph crosses the y-axis.

- In other words, this is also seen as the point where x = 0. Thus, substituting x = 0 into the equation given to us should readily reveal the y-value of the y-intercept.

- That is,

- Thus, the y-intercept is (0, 5)

Question 3:

- The factorization of the function is given below:

- Thus, the factorized form is:

Question 4:

- Thus, the vertex of the parabola is (-2, 9)

Question 5:

- The vertex form of the parabola is given by:

- The equation of the vertex is

The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Quantity of electricity used in kilowatts is;

1000 watts = 1 kilowatts

2,500 watts = 2.5 kilowatts

Given that Number of hours Val runs AC per day = 5 hours

Number of days = 30 days

Cost of electricity = $0.18 kilowatts per hour

The Cost of Val’s AC to run for a summer month of 30 days can be calculated as;

= Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity

= 2.5 × 5 × 30 × 0.18

= $67.5

The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.

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Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

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

you did not provide enough information to answer the question

Answer:

$16.10

Step-by-step explanation:

He spent $16.10 in total. Because 3.5 x 4.6 feet = 16.1

Answer:

$16.10

Step-by-step explanation:

3.50 x 4.6 = 14 + 2.10

Using an exponential function, it is found that the Tequesta settlement is 1845 years old.

The exponential equation for a decaying amount of a substance is given by:

\(A(t) = A(0)e^{-rt}\)

In which:

Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.

\(A(t) = A(0)e^{-rt}\)

\(0.5A(0) = A(0)e^{-5730r}\)

\(e^{-5730r} = 0.5\)

\(\ln{e^{-5730r}} = \ln{0.5}\)

\(5730r = -\ln{0.5}\)

\(r = -\frac{\ln{0.5}}{5730}\)

\(r = 0.00012096809\)

Hence, the equation is:

\(A(t) = A(0)e^{-0.00012096809t}\)

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).

\(A(t) = A(0)e^{-0.00012096809t}\)

\(0.8A(0) = A(0)e^{-0.00012096809t}\)

\(e^{-0.00012096809t} = 0.8\)

\(\ln{e^{-0.00012096809t}} = \ln{0.8}\)

\(-0.00012096809t = \ln{0.8}\)

\(t = -\frac{\ln{0.8}}{0.00012096809}\)

\(t = 1845\)

The Tequesta settlement is 1845 years old.

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The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60

(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.

Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200

Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments

Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]

Total amount paid = $1,300 + $13,200 + $14,041.60

Total amount paid = $28,541.60

Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.

(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.

Total interest paid = Total amount paid - Total amount borrowed - Down payment

Total interest paid = $28,541.60 - $13,200 - $1,300

Total interest paid = $14,041.60

Therefore, the amount of interest Debra paid on the loan was $14,041.60.

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The possible values for the discriminant include the following:

A. -1

D. -18

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.

Discriminant, D = b² - 4ac

In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.

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Complete Question:

The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.

A. -1

B. 3

C. 0

D. -18

Answer:

D

Step-by-step explanation:

Volume of cylinder = Base x height

Base = πr^2 = 25π

Volume = 25π x 10 = 250π

Volume of cone = 1/3 Base x height

= 1/3 x 25π x 5 = 125π/3

Volume of silo = cylinder + cone + cone

= 250π + 125π/3 + 125π/3

= 785.4 + 130.9 + 130.9

= 1047.2

a) The linear programming model is 0.45x + 0.58y.

b) An optimal solution is  $32.26.

c) The shadow price for special sauce is $0.10

d) The new solution is $0.22

Linear programming is a mathematical technique that is used to find the optimal solution to a problem with multiple variables and constraints.

a) Develop a linear programming model:

Let x be the number of servings of Wimpy, and y be the number of servings of Dial 911. Then, the objective function to be maximized is:

0.45x + 0.58y

The profit on one serving of Wimpy is $0.45, and on one serving of Dial 911, it is $0.58.

The constraints are:

0.25x + 0.25y ≤ 20 (available beef)

0.25x + 0.4y ≤ 15 (available onions)

0.05x + 0.02y ≤ 88 (available special sauce)

0.05y ≤ 60 (available hot sauce)

x, y ≥ 0 (non-negativity)

b) Find an optimal solution:

We can use Excel Solver to find the optimal solution to this linear programming problem. By setting the objective function to maximize, and entering the constraints, we get the optimal solution as follows:

Number of servings of Wimpy = 52

Number of servings of Dial 911 = 18

Maximum profit = $32.26

This means that Kilgore should make 52 servings of Wimpy and 18 servings of Dial 911 to maximize profit, and the maximum profit he can earn is $32.26.

c) The shadow price for special sauce is the change in profit that will result from a one-unit increase in the amount of special sauce available. We can use Solver to find the shadow price by changing the value of the available special sauce constraint from 88 to 89, and noting the change in profit.

The shadow price for special sauce is $0.10.

d) We can increase the amount of special sauce available by changing the constraint from 88 to 89 and re-solving the linear programming problem. The new optimal solution we get is:

Number of servings of Wimpy = 54

Number of servings of Dial 911 = 15

Maximum profit = $32.48

The new solution confirms the answer to part (c) since the shadow price for special sauce was $0.10, and the profit has increased by $0.22 with an additional ounce of special sauce.

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The margin of error for 16 eggs with sample means 2 ounce and standard deviation as 42 ounces is   18.407   .

In the question ,

it is given that ,

the number of eggs = 16

the sample means weight is = 2 ounce .

the standard deviation is = 42 ounces .

we have to find the margin of error .

degree of freedom is 16 - 1 = 15 .

and the t score for the 90% confidence interval is

t₁₅,₀.₀₅ = 1.753

So , the margin of error is =  t₁₅,₀.₀₅×(standard deviation/√n)

Substituting the values ,

we get ,

= 1.753×(42/√16)

On simplifying further ,

we get ,

= 18.407

Therefore , the margin of error is = 18.407 .

The given question is incomplete , the complete question is

A sample of 16 eggs yields a sample mean weight of 2.00 ounces and a sample standard deviation = 42.0 ounces, find the margin of error in estimating a confidence interval estimate at the 90% level of confidence. Round your answer to three decimal places. You may assume that egg weights are normally distributed .

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Answer:

1 sheet of card is 24.5mm thick. I think the keyword here is thick

Step-by-step explanation:

245/10=24.5

We can see here that the data set approximately periodic. The period and amplitude is: Periodic with a period of 4 and an amplitude of about 30.

The size or magnitude of a wave or vibration is measured by its amplitude in physics. It describes the greatest deviation of a wave from its equilibrium or rest state, or the greatest intensity of an electromagnetic or sound wave.

When referring to waves, amplitude is commonly calculated as the distance between a wave's peak or trough and its resting position.

We can deduce that the values are being repeated at regular interval of four (4).

For the amplitude:

\(Amplitude: \frac{140 - 74}{2}\)

Amplitude = 33 ≈ 30.

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Answer:

tanA = sinA / cosA = 3/5 / 4/5 = 3/4.