A room is 18 feet long and 12 feet wide. At $13.25 per square yard, what will be the cost for wall-to-wall
carpeting?

Okay, let's break this down step-by-step:

U = {x | x < 20, x is a natural number}

A = {x | 3 < x < 15}

B = {x | 1 < x < 15}

C = {x | x is an odd number, x is a natural number}

(a) A n B' (using De Morgan's law: A n B' = A' U B')

= {x | x ≥ 15 or x ≥ 3}

= {16, 17, 18, 19}

(b) B C' U A

= B U (C' U A)

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} U {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

(c) (A' n C ')

= (A' C') (by De Morgan's law)

= {x | x > 15 and x is even, x is a natural number}

= {16, 18}

The Venn diagram would be:

U A B C

_____|_____|_____|_____

| | | |

| | | |

| | ___|_____|___

| | | |

| | | 16, 17, 18, 19

| | | |

| | |_____|_____|___

| | | | |

| | | ___|_____|___

| | | | 16, 18

| | | |_____|_____|___

Does this make sense? Let me know if you have any other questions!

If Lily took a survey of 80 students of 7th grade and 150 students of 8th grade, then there are 64 "7th" grade students, and 90 "8th" grade students who like music.

First we find the the number of students who like music in "7th-grade".

Number of 7th grader students that are being surveyed = 80,

Percent of 7th graders who like country music = 80%,

So, Number of 7th graders who like country music are

⇒ 80% of 80 = 0.8 × 80 = 64

So, 64 out of the 80 students in 7th grade like country music.

For 8th graders;

Number of "8th-grader" students that are being surveyed = 150,

Percent of 8th graders who like country-music = 60%,

So, Number of 8th graders who like country music

⇒ 60% of 150 = 0.6 × 150 = 90,

Therefore, 90 out of the 150 students in 8th grade like country music.

Learn more about Percent here

https://brainly.com/question/13744961

#SPJ1

The given question is incomplete, the complete question is

Lily took a survey of 80 students on 7th grade and 150 students in 8th grade she found that 80% of the 7th graders like country music while only 60% of the 8th graders like it. Find the number of students from each grade who like music.

The equation of the transformed function is y = -f(x + 6)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x

On simplifying , we get

Reflecting over the x-axis: To reflect a function over the x-axis, we multiply the function by -1. This changes the sign of the y-coordinate of each point on the graph of the function. So, the function after reflection over the x-axis would be y = -f(x).

Translating 6 units left: To translate a function 6 units to the left, we replace x with (x + 6). This shifts the graph of the function horizontally to the left by 6 units. So, the function after translation 6 units left would be y = -f(x + 6)

Hence , the function is y = -f(x + 6)

To learn more about transformation of functions click :

https://brainly.com/question/26896273

#SPJ1

The steps of "hypothesis-testing" for papers bought home are stating the Null and Alternate Hypothesis, find level-of-significance, collecting data, determining p-value, and making decision.

The "Hypothesis-Testing" is defined as a statistical method used to make inferences about a population based on a sample of data. It involves making a assumption about a population parameter (such as its mean or proportion) and then collecting data to test whether the hypothesis is likely to be true or false.

The steps of hypothesis testing are:

Step 1: State the "Null-Hypothesis"

The null hypothesis (H₀) is = average number of papers brought home by the kids at Little Kids Elementary School is the same as the average for the general population, which is 13.

⇒ H₀: µ = 13,

Step 2: State the alternative hypothesis

The "Alternative-Hypothesis" (Hₐ) is = average number of papers brought home by the kids at Little Kids Elementary School is different from 13.

⇒ Hₐ: µ ≠ 13,

Step 3: Determine the level of significance

Let "significance-level" be "α = 0.05". This means we accept a 5% chance of making a "Type I Error"

Step 4: Collect the data and calculate test-statistic

The sample mean of the number of papers brought home by the kids at Little Kids Elementary School is:

⇒ x' = (14 + 12 + 18 + 8 + 11)/5 = 12.6,

The sample standard deviation is:

⇒ s = √[((14-12.6)² + (12-12.6)² + (18-12.6)² + (8-12.6)² + (11-12.6)²)/4] ≈ 3.71

The "test-statistic" ⇒ t = (x' - µ)/(s/√n);

where n = sample size = (5),

⇒ t = (12.6 - 13)/(3.57/√5) = -0.25,

Step 5: Determine of "p-value",

The "degrees-of-freedom" = 4,   ..because 5 - 1 = 4,

We know that "p-value" for t = -0.63 with 4 "degrees-of-freedom" is approximately 0.8103.

Step 6: Making decision and interpreting results

The p-value is 0.8103 which is greater than "significance-level" of (0.05),

So we fail to reject the null hypothesis. and say that there is not enough evidence to conclude that the average number of papers brought home by the kids at Little Kids Elementary School is different from the population mean of 13.

Therefore, we can say that the digital work program did not have a statistically significant effect on the amount of papers brought home by the students at Little Kids Elementary School.

Learn more about Hypothesis here

https://brainly.com/question/30588452

#SPJ1

The values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.

The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.

We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):

μ[tex]= 7000/16,780 = 0.4168[/tex]

We can use μ as the value of λ in the Poisson distribution since they are equal.

To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:

P(x=3) = (e^(-λ) * λ^x) / x!

where x = 3.

Substituting the values we have:

[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]

Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:

[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]

[tex]P(x=3) ≈ 0.000305[/tex]

Therefore, the values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

To know more about poisson probability:

https://brainly.com/question/7283210

#SPJ1

The values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.

The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.

We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):

μ[tex]= 7000/16,780 = 0.4168[/tex]

We can use μ as the value of λ in the Poisson distribution since they are equal.

To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:

P(x=3) = (e^(-λ) * λ^x) / x!

where x = 3.

Substituting the values we have:

[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]

Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:

[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]

[tex]P(x=3) ≈ 0.000305[/tex]

Therefore, the values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

To know more about poisson probability:

https://brainly.com/question/7283210

#SPJ1

Answer:

First, we need to calculate Michael's daily interest rate:

0.1199 / 365 = 0.0003282

Then, we can calculate his daily finance charge:

327.50 x 0.0003282 = 0.1075

To find his monthly finance charge, we multiply his daily finance charge by the number of days in a month:

0.1075 x 30 = 3.225

So Michael's monthly finance charge will be $3.23 (rounded to the nearest cent).

A.) The length of the missing part of the triangle would be given as follows;

a = 4

b = 3

To calculate the missing part of the triangle, the sine formula should be used such as follows;

x /SinX = b/sinB

where;

x= 5

X = 90

b = ?

B = 37°

That is;

5/sin90 = b/sin37

make b the subject of formula;

b = 5× 0.601815023/1

= 3

a² = C²- b²

= 25-9

= 16

a = √16 = 4

Learn more about triangle here:

https://brainly.com/question/28470545

#SPJ1

Answer:

  -1

Step-by-step explanation:

You want the average rate of change of the function shown in the graph between x=-1 and x=2.

The y-value at x = -1 is 9.

The y-value at x = 2 is 6.

The graph changes by 6-9 = -3 units as x changes by 2 -(-1) = +3 units.

The average rate of change is ...

  (change in y) / (change in x) = -3/3 = -1

The average rate of change from x = -1 to x = 3 is -1.

<95141404393>

multiply each shapes by length x width

Step-by-step explanation:

an example:

5x3 is 15

then do that for all of the shapes in this photo then add all of your answer together to get you're area

hope this helps

Answer:

If the y value decreases while the x value remains the same over time, then the correct answer would be A. Y decreases and X decreases.

Step-by-step explanation:

Sure! A slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-coordinates (rise) by the change in the x-coordinates (run) between two points on a line. The formula for slope is m = (y2 - y1) / (x2 - x1).

In your question, if the y value decreases while the x value remains the same over time, it means that the change in y-coordinates (rise) is negative while the change in x-coordinates (run) is zero. This results in a vertical line with an undefined slope. Therefore, the correct answer would be A. Y decreases and X decreases.

The surface area of the pyramid is 128.2cm².

What is the surface area of the pyramid?

A pyramid is a three-dimensional building with triangular lateral faces and a polygonal base. A pyramid's surface area is simply the total area of all of its faces.

Here, we have

Given:  A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.

We have to find the surface area of the pyramid.

The rectangular base of the pyramid has a length of 7 centimeters and a width of 5 centimeters, so the area of the rectangular base is 35 cm².

The two large triangular faces have a height of 7.6 centimeters, so the area of each of these faces can be calculated as:

= (1/2)×7×7.6

= 26.6 cm²

Similarly, the two small triangular faces have a height of 8 centimeters, so the area of each of these faces can be calculated as:

= (1/2)×5×8

= 20cm²

The total surface area of the rectangular pyramid is:

= 35cm² + 2×26.6 cm² + 2×20 cm²

= 128.2cm²

Hence, the surface area of the pyramid is 128.2cm².

To learn more about the  surface area of the pyramid from the given link

https://brainly.com/question/22744289

#SPJ1

The highest temperature on Day 7 is equal to 60 degrees.

The day in which the highest temperature was 60 degrees is day 3.

Yes, the high temperature is a function of the day because it is dependent variable.

No, the day is not a function of the high temperature because it is an independent variable.

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter, scientist, or a researcher.

This ultimately implies that, an independent variable is always considered as the cause in an experiment and it is represented by the x-axis value on a graph.

In this context, we can reasonably infer and logically deduce that time measured in days represent the independent variable while the highest temperature measured in degree Fahrenheit represent the dependent variable.

Read more on independent variable here: brainly.com/question/82796

#SPJ1

Step-by-step explanation:

We can use the binomial distribution to compute the probability that exactly 91 out of 153 registered voters will vote in the presidential election, assuming that the probability that any given registered voter will vote in the presidential election is 59%.

The probability mass function of the binomial distribution is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

- n is the number of trials (in this case, the number of registered voters)

- k is the number of successes (in this case, the number of registered voters who will vote in the election)

- p is the probability of success on any individual trial (in this case, the probability that a given registered voter will vote in the election)

Using this formula, we can calculate:

P(exactly 91 out of 153 voters will vote) = (153 choose 91) * 0.59^91 * (1 - 0.59)^(153 - 91)

= 0.037

Therefore, the probability that exactly 91 out of 153 registered voters will vote in the presidential election is approximately 0.037, or about 3.7%.

The total surface area of the pyramid from the net is 286 square cm

To calculate the total surface area of a pyramid from its net, you need to add up the areas of all its faces.

The net of a pyramid is a two-dimensional representation of the pyramid, where the edges of the net represent the edges of the pyramid.

In this case, the nets are

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

Area = 10 * 7 + 2 * (1/2 * 10 * 12.5 + 1/2 * 7 * 13)

Evaluate

Area = 286

Hence, the surface area is 286 square cm

Read more about surface area at

https://brainly.com/question/26403859

#SPJ1

Answer:

The two triangles are related by Angle-Angle-Side (AAS), so the triangles are congruent.

Answer:     <ABC =  <GHI     transitive property

Step-by-step explanation:

<ABC =  <GHI     transitive property

this is because if you have <B=<E and <H=<E   then <B=<H

thisis a tranisitive property

Using a proof by contraposition we can see that the sum must be even.

Here we know that x and y are odd integers, then we can write thes two numbers as:

x = 2n + 1

y = 2m + 1

Where n and m are integers.

If we use the proof by contraposition, then we will assume that the outcome is also an odd number 2k + 1

Then we can write:

2n + 1 + 2m + 1 = 2k + 1

We can simplify this to get:

2n + 2m + 1= 2k

2(n + m) + 1 = 2k

So there we have an odd number is equal to an even number, that does not make sense, thus, the outcome of the sum can't be odd.

Learn moer about proof by contraposition

https://brainly.com/question/30426179

#SPJ1

Answer:

17cm

Step-by-step explanation:

Perimeter is the sum of all the sides.

4.5+4.5=9

4+4=8

9+8=17

Peter’s new salary by the given data is $36,400.

We are given that;

Salary= 35000

Percentage= 4%

Now,

To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).

The amount of his raise is:

0.04 × 35000

= 1400

35000 + 1400

= 36400

Therefore, by the given percentage the answer will be $36,400.

Learn more about percentages;

brainly.com/question/24159063

#SPJ1

Peter’s new salary by the given data is $36,400.

We are given that;

Salary= 35000

Percentage= 4%

Now,

To find Peter’s new salary, we need to add the amount of his raise to his old salary. The amount of his raise is 4% of his old salary, which means we need to multiply his old salary by 0.04 (or 4/100).

The amount of his raise is:

0.04 × 35000

= 1400

35000 + 1400

= 36400

Therefore, by the given percentage the answer will be $36,400.

Learn more about percentages;

brainly.com/question/24159063

#SPJ1

It can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.

Therefore, X= 2.7532; T = 0.1203; P = 0.4524.

H0: ‘The mean class GPAs for a given course’ is equal to 2.75.

H1: ‘The mean class GPAs for a given course’ exceeds 2.75.

Our 'sample size' n = 50 and we calculate the ‘sample mean and sd’ with 'Excel', through its respective code ‘AVERAGE()’.

The resultant ‘sample mean’ xbar equals to 2.7532, while implementing the code ‘STDEV.S()’ gives us the ‘sample sd’ s being 0.188164.

The ‘hypothesized mean’ μ0 is again fixed at 2.75. Given that the ‘population sd is unknown’, we are obliged to perform a ‘t-test’ in order to receive our data.

Evaluating this test statistic provides us with-

T = (xbar-μ0)/(s/√n)

= (2.7532-2.75)/(0.188164/√50)

= 0.0032/0.0266

= 0.1203

Also, taking into account the 'degrees of freedom', which is (n-1), we figure out that it sums up to 49.

After conjuring a 'students t distribution', we get a P-value of 0.4524. Hereby, as the ‘P-value surpasses the significant level of 0.05’, the ‘null hypothesis fails to be dismissed’.

Consequently, it can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.

Therefore, X= 2.7532; T = 0.1203; P = 0.4524.

Read more about t-statistic here:

https://brainly.com/question/29236955

#SPJ1

1) Percent of time that customers at the old store bought milk shakes is: 20%

2) Percent of time that customers at the new store bought milk shakes is:

26%

3) Percent of total sales that were ice cream is: 78%

4) Percent of new store sales of both shops is: 35%

We are given the following parameters:

Number of Servings of Icecream in Old store = 52100

Number of milk shakes in old store = 13400

Number of Servings of Icecream in New store = 25800

Number of milk shakes in new store = 9200

1) Percent of time that customers at the old store bought milk shakes is:

Percentage = [13400/(52100 + 13400)] * 100%

≈ 20%

2) Percent of time that customers at the new store bought milk shakes is:

Percentage = [9200/(25800 + 9200)] * 100%

≈ 26%

3) Percent of total sales that were ice cream:

Percentage = [(52100 + 25800)/(52100 + 25800 + 13400 + 9200)] * 100%

≈ 78%

4) Percent of new store sales of both shops is:

Percentage = (25800 + 9200)/(52100 + 25800 + 13400 + 9200)] * 100%

≈ 35%

Read more about percentage at: https://brainly.com/question/24877689

#SPJ1

It will take the acrobat 1/4 of a second to land safely on the net.

Velocity is a physical quantity that measures the rate at which an object moves in a particular direction. It is measured in terms of distance traveled per unit of time, usually expressed in terms of meters per second (m/s). Velocity is a vector quantity, meaning it has both a magnitude and a direction. It is an important concept in physics and is used to understand the motion of objects and forces.
The quadratic equation representing the height h of the acrobat t seconds after the jump can be written as follows: [tex]h=-16t^2+4t+25[/tex].
To find the time it takes for the acrobat to land safely on the net, we need to solve for t when h=5. We can do this by substituting 5 for h into the equation and solving for t:
[tex]h=-16t^2+4t+25\\\\5=-16t^2+4t+25\\\\=-16t^2+4t-20=0\\\\(4+\sqrt{64})/(-32)=t\\ \\t=(4+8)/(-32)\\\\t=1/4[/tex]
Therefore, it will take the acrobat 1/4 of a second to land safely on the net.
To know more about velocity click-
brainly.com/question/24445340
#SPJ1

Tom has jogged 9 29/30 miles in all.

Just add the values that tells us all the distamnce that he jogged

Write the values as improper fraction

(25/6) + (29/5)

To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 6 and 5. The LCM of 6 and 5 is 30. Now we can convert each fraction to an equivalent fraction with a denominator of 30:

(25/6) * (5/5) = 125/30

(29/5) * (6/6) = 174/30

Now, add the fractions:

(125/30) + (174/30) = (125 + 174) / 30 = 299/30

Now, let's convert this improper fraction back into a mixed number:

299 ÷ 30 = 9 (remainder 29)

So, the mixed number is 9 29/30.

Tom has jogged 9 29/30 miles in all.

Read more on distance here:https://brainly.com/question/7243416

#SPJ1

In the most recent reporting period, the amount of cash paid by Nike for property, plant and equipment was $4,904 million. The Option D is correct.

The cash payments under property, plant, and equipment (PP&E) are recognized in a company's financial statements when they represent actual expenditures for acquiring, constructing, or improving long-term assets.

Some examples of cash payments that could be recognized under PP&E include the purchase price of land or buildings, expenses related to preparing land for its intended use, costs incurred to construct new buildings or renovate existing ones, expenditures to install or upgrade equipment etc.

Read more about PPE

brainly.com/question/29764093

#SPJ1

The triangle presented in the diagram drawn is known as equilateral triangle.

A triangle with angle 60 degrees is known as equilateral triangle because the sum of angles in a triangle is 180 degrees.

So if the total angles in a triangles is 180 degrees, and two known angles are 60 degrees, then the remaining side will be 60 degrees.

In an equilateral triangle, each of the interior angle measures 60 degrees.

Thus, the triangle presented in the diagram drawn is known as equilateral triangle.

Learn more about equilateral triangle here: https://brainly.com/question/17264112

#SPJ1

The probability of pulling out a number which is divisible by 2 or 3 will be 7/10 which is not given here. So, option D will be the answer.

How do we find Probability?

The measurement through which we find the likelihood of an event to occur is called probability. We cannot predict a lot of events with total certainty. And thus, the chance of a event to occur (i.e. how likely they re going to happen) can be predicted using probability.

Probability of any event to happen can be find as: No of favorable outcomes/Total number of outcomes.

Here,

The total no of outcomes = 1,2,3,4,5,6,7,8,9,10

No of favorable outcomes ={2,3,4,6,8,9,10} = 7

Therefore, P(E) = 7/10

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1