Suppose that So, S1, S2,... is a sequence of subsets of N. Which one of the following sets is guaranteed to be different from all sets in the sequence? (a) S = {n | n & Sn²} (b) S = {n | n² & Sn²} (c) S = {n²| n & Sn²} (d) S = {n² | n² & Sn} (e) S = {n² | n & Sn} Explain why your chosen set is guaranteed not to be in the sequence So, S1, S2, ...

Answer:

2

Step-by-step explanation:

To evaluate the expression substitute t = 4 into the expression, that is

8/t = 8/4 =2

Answer:8/2=4

Step-by-step explanation:

The reasonable estimate would be 25

We have to solve this using the rule of 3

9 out of 30 members said that they run more than 5 days a week.

We will form the equations

when 9 ran = 30 menbers

when n ran = 84 members

we will then cross multiply

84 x 9 = 30 x n

n = 25.2

When we round this, the reasonable estimate would be 25

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Complete question

Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.

There are 84 Freemont Run Club members.

Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?

The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

The null hypothesis (H₀): The company's heaters have a mean lifespan of 5 years or more.

The alternative hypothesis (H₁): The company's heaters have a mean lifespan of less than 5 years.

In hypothesis testing, the null hypothesis represents the claim or assumption that is being tested. In this case, the null hypothesis assumes that the mean lifespan of the company's heaters is equal to or greater than 5 years. The alternative hypothesis, on the other hand, challenges this claim and suggests that the mean lifespan is less than 5 years.

To determine which hypothesis is supported by the evidence, statistical analysis would need to be conducted using appropriate data and methods. The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

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Answer: 12 packages can be made.

Step-by-step explanation:

It takes three packages to make 2 ounces and 3×4=12

Answer:

Section 4-1 Day 5 Translating Parabolas Key.pdf

Step-by-step explanation:

The statement is true because 4 × 30%=120

In the first month, the price of the avocado is said to have been raised by 30 percent.

While already raised by 30 percent, another 30 percent raise would make the increase to be 60 percent.

While is at 60 percent, the third month the raise would be = 90 percent because 30 * 3 = 90

Then at 90 percent if there is another raise of 30 percent, the increase would grow to be 120 percent.

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Step-by-step explanation:

=x^2+2x+4+9-6x+x^2

=2x^2-4x+13

the d1 = 2A/d2 and d2 = 2A/d1 are correct options.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

The given A=a equals Start Fraction one-half End d1, d2, 2d1d2 where d1 and d2 are the lengths of the diagonals.

So the correct options are

d1 = 2A/d2

d2 = 2A/d1

Hence the d1 = 2A/d2 and d2 = 2A/d1 are correct options.

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Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

Step-by-step explanation:

(15.4*102)*(2.8*10-4)

(1,570.8)*(28-4)

(1,570.8)*(24)

37,699.2

Answer:

D. Obtuse

Step-by-step explanation:

Answer:

You typed that incorrectly.  That first angle should be 113 degrees.

It would be an obtuse triangle.

Step-by-step explanation:

The surface area and volume of the second cylinder are given in square millimeters and cubic millimeters, V =

The given dimensions for cylinders are:

r = 1.75 in, h = 2.2 in Surface Area of Cylinder:

S = 2πr² + 2πrh

The surface area formula of a cylinder is  S = (2 * pi * \(r^2\)) + (2 * pi * r * h).

S = (2 * 3.14 * 1.75²) + (2 * 3.14 * 1.75 * 2.2)

= 44.33 + 38.49

= 82.82 square inches.

Volume of Cylinder: V = πr²h

The formula to calculate the volume of a cylinder is given by V = pi * \(r^2\) * h.

Volume = 3.14 * 1.75² * 2.2 = 20.28 cubic inches.

Volume = π(1.75)²(2.2)

Volume ≈ π(3.0625)(2.2)

Volume ≈ 6.7375π cubic inches

The given dimensions for cylinders are: d = 4.3 mm, h = 2 mm

Surface Area of Cylinder: S = 2πr² + 2πrhS = (2 * 3.14 * 2.15²) + (2 * 3.14 * 2.15 * 2) = 67.65 square millimeters.

Volume of Cylinder: V = πr²hV = 3.14 * 2.15² * 2 = 28.33 cubic millimeters.

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Answer:

264 degree angle

Step-by-step explanation:

The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

Answer: y= 1/3 x + 5/3

Step-by-step explanation:

1= 1/3(-2) + b where b is the y intercept

  1=   -2/3 + B

+2/3   +2/3

B = 5/3

so we know the slope and the y- intercept

y= 1/3x + 5/3   check:   1=1/3(-2) +5/3

                                    1 =1

Slope intercept form: y = mx + b

m = slope

b = y-intercept

Since we know the slope and one point, we can solve for the y-intercept.

y = 1/3x + b

1 = 1/3(2) + b

1 = 2/3 + b

1 - 2/3 = 2/3 - 2/3 + b

1/3 = b

Now, put the final equation together.

y = 1/3x + 1/3

Best of Luck!

Answer:

you'll know bc your fridge will be broken

Step-by-step explanation:

Answer:

When there is footprints in the butter.

Step-by-step explanation:

Its the first one i believe

Answer: 21 is the least common denominator

Step-by-step explanation:

The least common denominator of 7 and 6 is 42, but will be simplified.

The fractions would turn into 30/42 and 28/42.

Now simplify.

15/21 and 14/21

This cannot be simplified any further without losing the common denominator

Answer:

The least common denominator is 21.

Step-by-step explanation:

Put the fractions out of a denominator of 42

5/7 = 30/42          4/6 = 28/42

Divide both fractions by 2

35/42 = 15/21       4/6 = 14/21

Problem 10

The error occurs in line 2. Notice how in the previous line, the variable d doesn't have an x attached to it. So we can't factor out x from it if it doesn't exist there.

Instead, the expression ax+bx+d would become x(a+b)+d and not x(a+b+d). You can verify this by distributing the x back through.

Put another way: if we distributed the x in x(a+b+d), then we'd get ax+bx+dx; however there isn't supposed to be an x attached to the d.

Here's how we should solve for x.

\(k = ax+bx+d\\\\k-d = ax+bx\\\\k-d = x(a+b)\\\\x = \frac{k-d}{a+b}\)

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

Problem 11

---------------------

Explanation:

Any time we have the same number on both sides, this means we have infinitely many solutions. If both sides are different, then we have no solutions. For either case, this only applies once the variables are completely gone.

Consider something like x+x = 2x. Both sides turn into 2x and we can subtract 2x from both sides to get 0 = 0. No matter what we plug in for x, it will be a true statement. Therefore, this equation has infinitely many solutions.

For an example that has no solutions, try something like 2x+1 = 2x. Subtracting 2x from both sides yields 1 = 0 which is always false. So 2x+1 = 2x is always false regardless of what you pick for x.

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

Problem 12

Answers:

Both of those values are exact.

---------------------

Explanation:

Let's say point A is the starting point and B is the delivery point. The truck goes from A to B, then back to A again. Let's call the one-way distance d. So we can think of it like saying "the length of segment AB is d miles" even though technically the two cities aren't connected with a straight line road.

When going from A to B, the speed is 55 mph. The time it takes to drive this is

\(\text{distance} = \text{rate}*\text{time}\\\\d = r*t\\\\d = 55t\\\\t = \frac{d}{55}\\\\\)

Through similar logic, the time to drive back at 35 mph is \(t = \frac{d}{35}\\\\\) because the truck driver is driving the same distance (assume she takes the same roads).

The total time spent driving is \(\frac{d}{55}+\frac{d}{35}\). This total drive time is 9 hours, which means we have this equation we need to solve

\(\frac{d}{55}+\frac{d}{35} = 9\)

Let's multiply both sides by the LCD 385 to clear out the denominators

That will help us isolate the variable d.

\(\frac{d}{55}+\frac{d}{35} = 9\\\\385*\left(\frac{d}{55}+\frac{d}{35}\right) = 385*9\\\\385*\left(\frac{d}{55}\right)+385*\left(\frac{d}{35}\right) = 3465\\\\7d+11d = 3465\\\\18d = 3465\\\\d = 3465/18\\\\d = 192.5\\\\\)

The distance from A to B is exactly 192.5 miles.

We can then say:

These two results are time values in hours.

So it takes exactly 3.5 hours to go from A to B. Then it takes exactly 5.5 hours to go from B to A. The second leg of the trip is longer in duration as expected due to the slower average speed.

As a check,

3.5+5.5 = 9

which confirms our answers.

The length of AD is 1 unit.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let us solve the question

In Δ ABC

∠B is a right angle

BD is perpendicular to the hypotenuse AC

(AB)² = AD × AC ⇒ rule

AB = 3 units

AC = 9 units

Let AD = x

Substitute them in the rule above

(3)² = x × 9

9 = 9x

Divide both sides by 9

x=1

Hence, the length of AD is 1 unit.

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Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)

For the sample size of 20, the 95% confidence interval is (-4.87, 27.16), which is narrower than the previous interval due to the larger sample size.

In statistics, mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total number of values in the set. Mean is also commonly referred to as the arithmetic mean. It is a commonly used statistical measure in many fields including finance, economics, social sciences, and more.

Here,

To calculate the z-scores associated with each student, we first need to calculate the sample mean and standard deviation for the Distance to Work variable:

Sample mean: (0+0+5+10+15+30+32)/7 = 10.71

Sample standard deviation: √(((0-10.71)² + (0-10.71)² + (5-10.71)² + (10-10.71)² + (15-10.71)² + (30-10.71)² + (32-10.71)²)/6) = 10.72

Now we can calculate the z-scores for each student:

Student 1: (0 - 10.71) / 10.72 = -0.94

Student 2: (0 - 10.71) / 10.72 = -0.94

Student 3: (5 - 10.71) / 10.72 = -0.53

Student 4: (10 - 10.71) / 10.72 = -0.07

Student 5: (15 - 10.71) / 10.72 = 0.40

Student 6: (30 - 10.71) / 10.72 = 1.80

Student 7: (32 - 10.71) / 10.72 = 1.98

Student 8: (8 - 10.71) / 10.72 = -0.25

Student 9: (36 - 10.71) / 10.72 = 2.37

Student 10: (9 - 10.71) / 10.72 = -0.16

Student 11: (22 - 10.71) / 10.72 = 1.05

Student 12: (10 - 10.71) / 10.72 = -0.07

Student 13: (15 - 10.71) / 10.72 = 0.40

Student 14: (28 - 10.71) / 10.72 = 1.54

Student 15: (12 - 10.71) / 10.72 = 0.12

Student 16: (6 - 10.71) / 10.72 = -0.44

Student 17: (0 - 10.71) / 10.72 = -0.94

Student 18: (10 - 10.71) / 10.72 = -0.07

Student 19: (30 - 10.71) / 10.72 = 1.80

Student 20: (0 - 10.71) / 10.72 = -0.94

To identify potential outliers, we can look for z-scores that are more than 2 standard deviations away from the mean (i.e., greater than 2 or less than -2). From the list above, we can see that Students 6, 7, 9, and 19 have z-scores greater than 2, indicating that they may be potential outliers.

For the second sample of seven data points (0, 0, 5, 10, 15, 30, 32), the mean is 11.14 and the standard deviation is 12.05. Using a t-distribution with 6 degrees of freedom (n-1), the 95% confidence interval is (-7.54, 29.82).

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Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:

f(x) = λ.\(e^{-\lambda.x}\)

and the cumulative distribution function, which describes the probability distribution of a random variable X, is:

F(x) = 1 - \(e^{-\lambda.x}\)

(a) Probability of distance at most 100m, with λ = 0.0143:

F(100) = 1 - \(e^{-0.0143.100}\)

F(100) = 0.76

Probability of distance at most 200:

F(200) = 1 - \(e^{-0.0143.200}\)

F(200) = 0.94

Probability of distance between 100 and 200:

F(100≤X≤200) = F(200) - F(100)

F(100≤X≤200) = 0.94 - 0.76

F(100≤X≤200) = 0.18

(b) The mean, E(X), of a probability distribution is calculated by:

E(X) = \(\frac{1}{\lambda}\)

E(X) = \(\frac{1}{0.0143}\)

E(X) = 69.93

The standard deviation is the square root of variance,V(X), which is calculated by:

σ = \(\sqrt{\frac{1}{\lambda^{2}} }\)

σ = \(\sqrt{\frac{1}{0.0143^{2}} }\)

σ = 69.93

Distance exceeds the mean distance by more than 2σ:

P(X > 69.93+2.69.93) = P(X > 209.79)

P(X > 209.79) = 1 - P(X≤209.79)

P(X > 209.79) = 1 - F(209.79)

P(X > 209.79) = 1 - (1 - \(e^{-0.0143*209.79}\))

P(X > 209.79) = 0.0503

(c) Median is a point that divides the value in half. For a probability distribution:

P(X≤m) = 0.5

\(\int\limits^m_0 f({x}) \, dx\) = 0.5

\(\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx\) = 0.5

\(\lambda.\frac{e^{-\lambda.x}}{-\lambda}\) = \(-e^{-\lambda.x} + e^{0}\)

\(1 - e^{-\lambda.m}\) = 0.5

\(-e^{-\lambda.m}\) = - 0.5

ln(\(e^{-0.0143.m}\)) = ln(0.5)

-0.0143.m = - 0.0693

m = 48.46

Answer:

y < - 12

Step-by-step explanation:

y + 15 < 3 ( subtract 15 from both sides )

y < - 12

Answer:

Step-by-step explanation:

There is an infinite number of solutions

but I'll go with the most obvious way:

Answer:

The forecasted sale for the month of November is $1,675.

Step-by-step explanation:

A moving average can be described as a series of averages of different subsets that is calculated from the full data set.

Using the 4-period moving averages to calculate the forecasted sale of ice cream in the month of November therefore implies the average of sale of ice cream in the 4 months preceding November. And these 4 months are July, August, September, and October.

Therefore, we have:

Forecasted sale for the month of November = (Sales in July + Sales in August + Sales in September + Sales in October) / 4 = ($2,200 + $1,800 + $1,500 + $1,200) / 4 = $6,700 / 4 = $1,675

Answer:

The resin materials cost per foot of finished product for June is $0.53

Option a) $0.53 is the right answer

Step-by-step explanation:  

Given the data in the question;

                                                       May                  June                          uly

Resin pounds input

into the process                        470,000            700,000                 650,000  

Price per pound                         X$1.50               X$1.50                    X$1.50

Plastic material costs             $493,000         $640,000                 $677,000

Conversion costs                    $80,000           $120,000                 $115,000

Conduit output from

the process (feet)                   800,000           1,200,000                 1,130,000

Assuming that there is one-half pound of resin per foot of the finished product, determine the resin materials cost per foot of finished product for June.

Now;  

Materials cost for June = $640,000

Number of Feet produced as output in June =  1,200,000    

so

Material Cost per feet of finished product will be;

= $640,000 / 1,200,000

= $0.5333 ≈ $0.53

Therefore, the resin materials cost per foot of finished product for June is $0.53

Option a) $0.53 is the right answer

Answer:

Step-by-step explanation:

Step 1

Step 2

Step 3

Answer:

0.21

Step-by-step explanation:

The simplification of the following expression is

Given that

(0.0245 × 1.2) ÷ (0.08 × 1.75)

Here first we do multiply and after that divided with each other

= 0.0294 ÷ 0.14

= 0.21

Hence, the answer to simplifying the above expression is 0.21

The same would be considered and relevant too

Graph 1 represents the inverse of the function \(f(x)=\sqrt{x+1} -2\)

What is the inverse of a function?

The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.

The inverse of \(\sqrt{x+1} -2\) is \(x^{2} +4x+3\).

Plotting the inverse, we get the graph to be option 1.

Therefore, graph 1 represents the inverse of the function \(f(x)=\sqrt{x+1} -2\)

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The inverse function of the function given as f(x) = \(\sqrt{x+1}\) - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.

The steps for finding the inverse function, the steps to be followed are:

The given function is f(x) = \(\sqrt{x+1}\) - 2  

Consider the given function as f(x) = y ⇒ y =  \(\sqrt{x+1}\) - 2

Then, on rewriting the function for x, we get

y + 2 =  \(\sqrt{x+1}\)

⇒ (y + 2)² = (x + 1)

⇒ x = y² + 4y + 4 - 1

⇒ x = y² + 4y + 3

Interchanging the variables y to x and x to y we get

y = x² + 4x + 3

Thus, the inverse of the given function is obtained. I.e,

f⁻¹(x) = x² + 4x +3

To identify the graph, the point that satisfies the given function is

f(x) = \(\sqrt{x+1}\) - 2; for x = -1,

f(-1) = -2

So, the point is (-1, -2).

Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).

From the given graphs, graph 1 shows this point on it. So, that is the required option.

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Answer:

-290

Step-by-step explanation:

(-260) +(-30)

=-260-30

=-290

Answer:

the answer is -290

Step-by-step explanation:

it is telling us to add so we can see that both the numbers have the same sign which is negative

when the signs are all the same, we can add and we got -290