Stat 2300 a survey was conducted that asked randomly selected students nationwide if they traveled outside the country for spring break. a 99% confidence interval for the proportion of all students who traveled outside the country is (0.0994, .1406). how many students were surveyed

The function will be continuous at x = 3 for any values of a and b.

f(x) = ax + b to be continuous at x = 3

A function is continuous at a point x = c if:

1. f(c) is defined

2. The limit of f(x) as x approaches c exists

3. The limit of f(x) as x approaches c is equal to f(c)

For f(x) = ax + b to be continuous at x = 3:

1. f(3) is defined:

f(3) = a(3) + b

2. The limit of f(x) as x approaches 3 exists.

3. The limit of f(x):

lim (x->3) (ax + b) = a(3) + b

There are no specific values for a and b that must be satisfied. The function will be continuous at x = 3 for any values of a and b.

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Answer:

$9.50

Step-by-step explanation:

Divide the total earnings by total hours.

If John has to buy 10 "2-Liter" bottles of soda, then the inequality representing this situation is "10(1.50) + 7.50p ≤ 150" and greatest number of pizzas he can buy is 18, Correct option is (d).

Let "p" denote the number of "large-pizzas" that John can buy.

One "2-liter" bottle of soda cost is = $1.50,

So, the cost of the 10 bottles of soda is : 10 × $1.50 = $15,

one "large-pizza's cost is = $7.50,

So, the cost of p large pizzas is : $p × $7.50 = $7.50p,

The "total-cost" of the soda and pizza must be less than or equal to $150, so we can write the inequality as :

10(1.50) + 7.50p ≤ 150

Simplifying the left-hand side of the inequality,

We get,

15 + 7.50p ≤ 150

7.50p ≤ 135

p ≤ 18

Therefore, John can buy at most 18 large pizzas with his remaining budget, the correct option is (d).

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The given question is incomplete, the complete question is

John is planning an end of the school year party for his friends he has $150 to spend on soda and pizza.

Soda (2-liter) costs $1.50;

large pizza cost $7.50;

He knows he has to buy 10 "2-Liter" bottles of soda.

Choose the inequality and calculate the greatest number of pizzas he can buy.

(a) 10(1.50) + 7.50p ≥ 150; 54 pizzas

(b) 10(7.50) + 1.50p ≤ 150; 53 pizzas

(c) 10(7.50) + 1.50p ≥ 150; 19 pizzas

(d) 10(1.50) + 7.50p ≤ 150; 18 pizzas

The product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.

To represent the product of a complex number and a real number on the complex plane:

We multiply the real part and the imaginary part of the complex number by the real number.

The magnitude (or length) of the resulting complex number is multiplied by the absolute value of the real number.

The angle (or argument) of the resulting complex number is the same as the angle of the original complex number.

For the product of 2−4i and 3:

We multiply the real part (2) and the imaginary part (-4i) of the complex number by the real number (3), to get:

3(2) + 3(-4i) = 6 - 12i

The magnitude of the resulting complex number is:

|6 - 12i| = √(6² + (-12)²) = √180 = 6√5

The angle of the resulting complex number is the same as the angle of the original complex number (2-4i), which can be found using the inverse tangent function:

tanθ = (imaginary part) / (real part) = (-4) / 2 = -2

θ = atan(-2) ≈ -1.107 radians or ≈ -63.43 degrees

Therefore, the product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.

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The equation which most accurately represents the word problem,  is (b) 68 = 2L + 2(9).

The word problem states that the perimeter of a rectangle is 68 inches, and the perimeter equals twice the length (L) plus twice the width (9). We can represent this relationship by using the equation as :

We know that, the perimeter of rectangle is : 2(length + width),

Substituting the value,

We get,

⇒ 68 = 2(L + 9);

⇒ 68 = 2L + 2(9); and this statement is represented by Option(b).

Therefore, the correct equation is (b) 68 = 2L + 2(9).

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The given question is incomplete, the complete question is

Select the equation that most accurately depicts the word problem.

"The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches".

(a) 68 = 9(L + 2)

(b) 68 = 2L + 2(9)

(c) 68 = 2(L - 9)

(d) 68 = 9L + 2

(e) 68 = 2/L + 2/9

(f) 68 = L/2 + 2(9)

The value of the scale factor for the similar figures is 1/4

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

The similar figures

The corresponsing sides of the similar figures are

Original = 8

New = 2

Using the above as a guide, we have the following:

Scale factor = New /Original

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

Scale factor = 2/8

Evaluate

Scale factor = 1/4

Hence, the scale factor for the similar figures is 1/4

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The value of angle HCI is determined as 244⁰.

The value of angle HCI is calculated by applying intersecting chord theorem as follows;

The intersecting chord theorem, also known as the secant-secant theorem, states that when two chords intersect inside a circle, the products of the segments of one chord are equal to the products of the segments of the other chord.

From the diagram, the value arc CUH is equal to the value of angle HCI.

Thus, angle HCI = 244⁰

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If the surface area of a can with a particular volume is minimized when the height of the can is 22 cm, we would expect the radius of the can to be the same as the height, given that a cylinder has the smallest surface area when its height and radius are equal.

The surface area of a can with height h and radius r can be given by the formula:

A = 2πr² + 2πrh

The volume of the can is given by:

V = πr²h

If we differentiate the surface area with respect to r and equate it to zero to find the critical point, we get:

dA/dr = 4πr + 2πh(dr/dr) = 0

Simplifying this expression, we get:

2r + h = 0

Since we know that the height of the can is 22 cm, we can substitute h = 22 in the equation to get:

2r + 22 = 0

Solving for r, we get:

r = -11

Since the radius of the can cannot be negative, we discard this solution. Therefore, the radius of the can should be equal to its height, which is 22 cm.

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The expression that explains what happened to the price of the jacket is 0.85(1.4s), which represents a 40% increase in price followed by a 15% discount.

The expression 0.85(1.4s) represents the current selling price of the jacket, which includes two price changes.

To explain what happened to the price of the jacket, we can break down the expression into two steps:

1. The first change was an increase by 40%, which can be represented as multiplying the original price "s" by 1.4 (100% + 40% = 140% or 1.4). So, the price after the first change is 1.4s.

2. The second change was a discount of 15%, which can be represented as multiplying the price after the first change by 0.85 (100% - 15% = 85% or 0.85). So, the price after both changes is 0.85(1.4s).

So, the expression that explains what happened to the price of the jacket is 0.85(1.4s), which represents a 40% increase in price followed by a 15% discount.

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To find the derivative of y = cos(sin(14x-13)), we will use the chain rule.

Let's start by defining two functions:

u = sin(14x-13)
v = cos(u)

We can now apply the chain rule:

dy/dx = dv/du * du/dx

First, let's find dv/du:

dv/du = -sin(u)

Next, let's find du/dx:

du/dx = 14*cos(14x-13)

Now we can put it all together:

dy/dx = dv/du * du/dx
dy/dx = -sin(u) * 14*cos(14x-13)

But we still need to substitute u = sin(14x-13) back in:

dy/dx = -sin(sin(14x-13)) * 14*cos(14x-13)

So the derivative of y = cos(sin(14x-13)) is:

dy/dx = -14*sin(sin(14x-13)) * cos(14x-13)

To find the derivative of the function y = cos(sin(14x - 13)), we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Let u = sin(14x - 13), so y = cos(u). Now we find the derivatives:

1. dy/du = -sin(u)
2. du/dx = 14cos(14x - 13)

Now, using the chain rule, we get:

dy/dx = dy/du × du/dx

dy/dx = -sin(u) × 14cos(14x - 13)

Since u = sin(14x - 13), we can substitute back in:

dy/dx = -sin(sin(14x - 13)) × 14cos(14x - 13)

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The smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.

To find the measure of both angles in a right triangle with the given conditions, we will use the information provided:

Let x be the measure of the smallest angle. The problem states that the measure of one of the small angles is 30 less than 7 times the smallest angle, which can be written as:

Other non-right angle = 7x - 30

Since this is a right triangle, the sum of the two small angles must be 90 degrees (because the other angle is 90 degrees, and the sum of angles in a triangle is 180 degrees). So, we can set up the following equation:

x + (7x - 30) = 90

Now, solve for x:

8x - 30 = 90
8x = 120
x = 15

So, the smallest angle is 15 degrees. Now, we can find the measure of the other non-right angle:

Other non-right angle = 7x - 30 = 7(15) - 30 = 105 - 30 = 75 degrees

In summary, the smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.

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The measures of central tendencies changed as mode remained the same, the median increased and the mean increased.

To determine how the data set would've changed if she entered the competition, we simply need to work on the mean, median and mode of the data.

Given data;

35, 22, 31, 23, 35, 22, 30, 35, 40

Rearranging this data;

22, 22, 23, 30, 31, 35, 35, 35, 40

The mean of this data will be

mean = 30.3

The mode = 35

The median = 31

When her weight is added, the measures of central tendencies change to;

mean = 31.5

median = 33

mode = 35

The median decreases, the mode remains the same and the mean increases

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The combined time if Mike and Nancy worked together is approximately 1.71 hours.

To answer your question, we can use the concept of work rates. Mike can mop McDonald's in 3 hours and Nancy can do it in 4 hours. To find the combined work rate, we can use the formula:

1/Mike's rate + 1/Nancy's rate = 1/combined rate

1/3 + 1/4 = 1/combined rate

To solve for the combined rate, we can find a common denominator for the fractions:

(4 + 3) / (3 × 4) = 1/combined rate

7/12 = 1/combined rate

Now we can find the combined time by inverting the combined rate:

Combined time = 12/7

So, if Mike and Nancy worked together, they would mop McDonald's in 12/7 hours, which is approximately 1.71 hours.

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Main answer:

Working together, Mike and Nancy can mop the McDonald's in 12/7 hours or approximately 1.71 hours (rounded to two decimal places).

Explanation:

To solve the problem, we can use the following formula:

time = work / rate

where time is the time it takes to complete the job, work is the amount of work to be done (which in this case is mopping the McDonald's), and rate is the rate of work, or the amount of work done per unit of time.

Let's let x be the time it takes for Mike and Nancy to mop the McDonald's together. Then, we can set up two equations based on the given information:

x = work / (Mike's rate of work)

x = work / (Nancy's rate of work)

To solve for x, we can use the fact that the amount of work to be done is the same in both equations. So we can set the two equations equal to each other:

work / (Mike's rate of work) = work / (Nancy's rate of work)

Simplifying this equation by multiplying both sides by (Mike's rate of work)*(Nancy's rate of work), we get:

work * (Nancy's rate of work) = work * (Mike's rate of work)

We can cancel out the work on both sides, and then solve for x:

x = 1 / [(1/Mike's rate of work) + (1/Nancy's rate of work)]

Substituting in the given rates of work, we get:

x = 1 / [(1/3) + (1/4)] = 12/7

Therefore, it takes Mike and Nancy 12/7 hours, or approximately 1.71 hours (rounded to two decimal places), to mop the McDonald's together.

The measurements are x = 7 and ∠NJK = 51°

Given is a rectangle, we need to find the asked measurement,

So,

Since we know that the diagonals of a rectangle bisect each other,

So,

JN + JN = JL

4x+4+4x+4 = 5x+29

8x+8 = 5x+29

3x = 21

x = 7

And,

The vertex angle is 90° so,

∠NMJ + ∠NML = 90°

∠NML = 51°

Also,

∠NML = ∠NJK because they are alternate angles,

So, ∠NJK = 51°

Hence x = 7 and ∠NJK = 51°

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function f(x,y) = 2 + y

The minimum value are f(√5, √5) = 2 + √5.

To find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 using Lagrange multipliers,

we first set up the Lagrangian function:

L(x,y,λ) = f(x,y) - λ(xy - 5)

Taking partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 0 = -λy
∂L/∂y = 1 - λx
∂L/∂λ = xy - 5

Solving for λ from the first equation and substituting into the second equation, we get:

x/y = 0/λ
1 - λx = 0
xy - 5 = 0

From the first equation, we see that either x = 0 or y = 0. But since xy = 5, neither x nor y can be zero.

Therefore, we have:

λ = 0
1 - λx = 0
xy - 5 = 0

Solving for x and y from the last two equations, we get:

x = 5/y
y = ±√5

We take the positive root for y since we are looking for a minimum value of the function.

Substituting y = √5 into x = 5/y, we get x = √5.

Therefore, the minimum value of f(x,y) = 2 + y subject to the constraint xy=5 is:
f(√5, √5) = 2 + √5.

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The function 1/[tex]r^2[/tex] can be expressed in terms of the spherical Bessel functions of the first kind, which are a family of solutions to the spherical Bessel differential equation.

The expansion involves a combination of the delta function and the first two spherical Bessel functions, j_0(r) and j_1(r). Specifically, the expansion can be written as (1/2)*[pi * delta(r) + (1/r)*d/d(r)(r * j_0(r)) + (1/[tex]r^2[/tex])*d/d(r)[[tex]r^2[/tex] * j_1(r)]]. This expansion is valid for all values of r except for r=0, where the first term dominates. The spherical Bessel functions are commonly used in physics, particularly in the context of scattering problems and wave propagation.

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The probability of picking an odd number and then picking an even number 5/18

The probability of picking an odd number on the first card is 1/2 since there are 5 odd cards out of 10 total cards. After picking an odd card, there are now 4 odd cards and 5 even cards left out of a total of 9 cards. So the probability of picking an even card on the second draw is 5/9.

To find the probability of both events happening, we multiply the probabilities:

P(odd and even) = P(odd) * P(even | odd)

= (1/2) * (5/9)

= 5/18

Therefore, the probability of picking an odd number and then picking an even number is 5/18.

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If sales increase by 66,000, income will increase by 220,000.00

Net operating income 37,200.00

The margin of safety is 14.01%

Statement showing Computations  

particulars Amount Per unit

Sales 628,000.00 40.00

Variable Expenses 439,600.00 28.00

Contribution Margin 188,400.00 $ 12.00

Fixed Expenses 151,200.00

Net operating income 37,200.00

'

1)  BEP in unit sales = 151,200/12 12,600.00

.BEP in sales $ = 12,600 * 40 504,000.00

2)  Total Contribution margin at BEP = Fixed costs 151,200.00

3)a Target Profit $ 64,800.00

Fixed Expenses 151,200.00

Desired Contribution 216,000.00

3b. No of units to be sold = 216,000/12 18,000.00

Sales 720,000.00

Variable Expenses 504,000.00

Contribution Margin 216,000.00

Fixed Expenses 151,200.00

Net operating income 64,800.00

4)  Margin of safety = 628,000.00-540,000.00 88,000.00

MOS in % = 88,000/6280001 14.01%

5)CM Ratio = 188,400/628,000 0.3

If sales increase by 66,000, income will increase by 220,000.00

66,000/0.3

=220,000.

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The subscriptions of magazines you need to sell is at least 7

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

Using the above as a guide, we have the following:

f(x) = 130x + 90

In order to make at least $1000.00 each week, we have

130x + 90 = 1000

So, we have

130x = 910

Divide by 130

x = 7

Hence, the number of orders is 7

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Answer:

(5,725)1.045^5

Step-by-step explanation:

(5,725)1.045^5

5,725 is the original amt of $

1.045 is the % of interest

5 is the # of years

Solve this and round the nearest

cent.

The quotient of 6 and 1/4 is 24.

We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.

We can represent this condition in either of the two ways.

Denominator < Numerator

(Or)

Numerator > Denominator

We are given a numerical expression which is 6÷ 1/4 and we have to solve this.

To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.

The reciprocal of 1/4 is 4.

Therefore,

6÷ 1/4

= 6 × 4

= 24

Therefore, the quotient of 6 and 1/4 is 24.

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Answer:

Sure, here are ten ordered pairs with the country as the first element and the capital as the second element:

1. (France, Paris)

2. (United States, Washington D.C.)

3. (China, Beijing)

4. (Mexico, Mexico City)

5. (Brazil, Brasília)

6. (Japan, Tokyo)

7. (Canada, Ottawa)

8. (Germany, Berlin)

9. (Australia, Canberra)

10. (India, New Delhi)

To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.

∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.

To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.

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a) It will take approximately 16.85 years for the rabbit population to double.

b) It will take approximately 37.28 years for the rabbit population to reach 1000.

The formula for calculating the population of rabbits in x years, starting with 100 rabbits and a natural growth rate of 4% per year, is given by:

f(x) = 100(1.04)ˣ

(a) To find out how long it will take for the rabbit population to double, we need to solve the following equation:

100(1.04)ˣ = 200

Dividing both sides by 100, we get:

(1.04)ˣ = 2

Taking the logarithm of both sides with base 1.04, we get:

x = log₁.₀₄ 2

Using a calculator, we get:

x ≈ 16.85

(b) To find out how long it will take for the rabbit population to reach 1000, we need to solve the following equation:

100(1.04)ˣ = 1000

Dividing both sides by 100, we get:

(1.04)ˣ = 10

Taking the logarithm of both sides with base 1.04, we get:

x = log₁.₀₄ 10

Using a calculator, we get:

x ≈ 37.28

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Answer:

image dosent load

Step-by-step explanation:

Answer:

a = 80°, b = 100°, c = 80°, d = 100°

Step-by-step explanation:

You know a + b + c + d = 360°.

Plugging b + c + d = 280° into the formula above:

a + 280° = 360°.

a = 80°.

You know a + d = 180° because of angles on a straight line. Solve for d:

80° + d = 180°.

d = 100°.

For the same reason, you know a + b = 180°. b must be equal to d, which is 100°.

Lastly, c + d = 180° because they make up the second line. Solve for c:

c + 100° = 180°.

c = 80°.

a = 80°, b = 100°, c = 80°, d = 100°.

The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.

To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:

Z = (X - μ) / σ

Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).

Z = (3.50 - 5.81) / 0.81 ≈ -2.84

Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.

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The probability that at least one value is observed more than once when rolling a regular 6-sided die 5 times is approximately 0.598.

The total number of possible outcomes when rolling a die 5 times is 6⁵ = 7776 (since there are 6 possible outcomes for each roll and there are 5 rolls). To calculate the number of outcomes where no value is repeated, we can use the permutation formula: P(6,5) = 6! / (6-5)! = 6! / 1! = 720, since there are 6 possible outcomes for the first roll, 5 for the second roll (since one outcome has been used), and so on.

So, the probability of not observing any repeated values is P(no repeats) = 720 / 7776 ≈ 0.0926. Therefore, the probability of observing at least one repeated value is P(at least one repeat) = 1 - P(no repeats) ≈ 0.9074.

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Statement 5 is True

Statement 1: (M ∧ ~R) ∨ (~S ∧ L)
T or F: T
Main Operator: ∨
Assuming the given truth values, Statement 1 is True.

Statement 2: (~S ↔ M) ∧ (L ∧ ~K)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 2 is False.

Statement 3: ~(R ∨ ~L) ∧ (~S ∨ S)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 3 is False.

Statement 4: ~ [(Q ∨ ~S) ∧ ~(R ↔ ~S)]
T or F: T
Main Operator: ~
Assuming the given truth values, Statement 4 is True.

Statement 5: (S ↔ Q) ↔ [(K ∧ ~M) ∨ ~(R ∧ ~L)]
T or F: T
Main Operator: ↔
Assuming the given truth values, Statement 5 is True.

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Answer:

310.2 cubic units

Step-by-step explanation:

since we know the diameter of the sphere (8.4), the radius is [tex]8.4/2 = 4.2[/tex]

The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]

Plugging in 3.14 as [tex]\pi[/tex] and 4.2 as r, we get 310.2