For 127 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 5 bottles. The average across all 635 bottles (127 days, 5 bottles per day) was 54 degrees Fahrenheit. The standard deviation across all bottles was 1.1 degree Fahrenheit. When constructing an X-bar chart, what would be the center line?

Because of this, we need to choose 16 integers in such a way that we can ensure that when they are divided by 15, at least two of them will provide the same residual.

This is further explained below.

Generally,  If you divide a number by 15, the result is a fraction. There are 15 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14.

That is to say, if we choose one number and divide it by 15, there is a chance that the remainder may be any of the 15 (0 reminders 14). Therefore, if we choose 15 numbers, we will have the opportunity to pick 15 unique reminders, ranging from 0 to 14.

In conclusion, if we select one more integer, that is we pick 16 integers, then at least two of them would have the same reminder since there are only 15 reminders and 16>15, and by the pigeonhole principle.

Because of this, we need to choose 16 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 15.

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Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.

Answer: last option.

Answer:

c

Step-by-step explanation:

a) 75.80 percentage of students will be scoring below 550 in a typical year.

b) 22.2 marks should be set by the engineering school setas a comparable standard on ACT math test.

Here we have been mentioned that in the recent years, sat maths exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.

a) The percentage of the students scoring below 550 marks in a typical year is calculated as follows:

Let x be the SAT score

So, x follows normal distribution

Given above,

mean (μ) = 480

standard deviation (σ) = 100

we will find P ( x < 550)

We will use the excel function NORM.DIST to find the required probability

P(x < 550) = NORM.DIST\((550, 480, 100, TRUE)\)

= 0.7580

= 75.80%

Hence the percentage of the students who are scoring below 550 in a typical year = 75.80%

b) We calculate the score to be set by the engineering school as a comparable standard on the ACT math test as follows:

Let Z be the ACT score

Z follows the normal distribution

Given above, μ = 18 and σ = 6

Let Z' be the ACT score comparable to the standard set for SAT

Then we need to find Z' such that P(Z < Z') = 75.80% = 0.758

From standard normal tables we get Y' such that

Z' = NORM.INV\((0.758, 18, 6)\)

= 22.2

The ACT score that needs to be set by the college = 22.2 marks

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The amount of aspirin that will be present in the patient's body after two hours is 281.25 milligrams.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For this case, we have:

Amount of aspirin in a person's body (in milligrams) after t hours of taking the medicine is:

\(a = 500\times(\dfrac{3}{4})^t\) (in milligrams)

For t = 2 hours, we get:

\(a = 500\times(\dfrac{3}{4})^2 = 281.25 \: \rm milligrams\)

Thus, the amount of aspirin that will be present in the patient's body after two hours is 281.25 milligrams.

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Using the z-distribution, the sample sizes required are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Then, the margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

We have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

Item a:

The estimate is of \(\pi = 0.26\), hence we solve for n when M = 0.03.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2\)

n = 821.2

Rounding up, a sample of 822 is needed.

Item b:

No prior estimate, hence \(\pi = 0.5\), which is when the largest sample size is needed.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2\)

n = 1067.11

Rounding up, a sample of 1068 is needed.

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The cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

The formula for converting currencies is Original Currency / New Currency = Exchange Rate.

Given:

Cost of 7 t-shirts at a special deal = $97.93

Now, she wants to purchase 5 t-shirts for her family members at this special rate.

Total Cost of 5 shirts in dollars = (97.93 * 5)/7 = $69.95

The exchange rate of the currency is 1 U.S. Dollar = 8.6964 Krona

So, $69.95 = (69.95 * 8.6964)/1 = 608.313 Krona

Therefore, the cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

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The surface area of the square pyramid is 45.

Given data :

H = 6ft.)

W = 3ft

L = 3ft.

2 × b × s +b. Volume of a Square Pyramid

= 45ft

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Step-by-step explanation:

The polynomial has a zero 3i, then it must have another zero -3i. Thus in all there would be 3 zeros -1,3i,-3i. The polynomial would be equivalent of (x+1)(x-3i)(x+3i) , or

x3+x2 +9x+ 9

Answer link

The value of 'x' for the two given complementary angles is 6.5⁰.

To resolve this issue, we must understand complimentary views.  

The angle that can create another angle has to have a value of 90⁰ and is known as the complimentary angle. One way to spell it is as

A + B = 90⁰

In which the corresponding angles A and B are.

The parameters are as follows, based on the question above:

A = 32⁰

B = (12x - 20)⁰

We may determine the x value by inserting the provided inputs.

A + B = 90⁰

32⁰ + (12x - 20)⁰ = 90⁰

12x = 90 - 32 + 20

12x = 78

x = 6.5⁰

Thus, the value of 'x' for the two given complementary angles is 6.5⁰.

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The correct answer is option (a) n < 27. By dividing both sides of the inequality by -3, we get n > -27.

To solve the inequality -3n < 81, we divide both sides by -3. Remember that when dividing by a negative number, the direction of the inequality sign changes. Dividing both sides by -3 gives us n > -27. So, the correct answer is option (d) n > -27.

The reasoning behind this is that dividing by -3 reverses the inequality sign, which means that the less than ("<") sign becomes a greater than (">") sign.

Option (a) n < 27 is incorrect because dividing by -3 changes the direction of the inequality. Option (b) is stated to be wrong. Option (c) n = 27 is incorrect because the original inequality is strict ("<") and not an equality ("=").

Therefore, By dividing both sides of -3n < 81 by -3, we get n > -27. Therefore, the correct answer is option (a) n < 27.

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Answer:

a+11b/3

Step-by-step explanation:

Answer:

3 and 2/3b + 1a

Step-by-step explanation:

Simplifying b:

4b - 1/3b = 11/3b = 3 and 2/3b

Simplifying a:

-5a + 6a = 1a

Answer:

answer is y = -2x + 18

Step-by-step explanation:

D, ive done this worksheet yesterday actually! lol

Answer:

y = -2x + 18

Step-by-step explanation:

m = -2, (2,14)

y - 14 = -2(x - 2)

y - 14 = -2x +4

y = -2x + 18

The probability that a five-card poker hand does not contain the queen of hearts is 47/52.

We have been given that,

Total card to choose = 5

Total cards in a deck = 52

We need to find the probability that a five-card poker hand does not contain the queen of hearts.

The total ways of choosing 5 cards from a deck of 52 cards = \(^{52}C_5\)

The number of queens of hearts in a deck = 1

The number of cards excluding queens of hearts = 52 - 1

                                                                                  = 51

The total ways of choosing 5 cards from 51 cards = \(^{51}C_5\)

Now we find the required probability.

\(\Rightarrow P= ^{51}C_5 \times ^{52}C_5\\\\\Rightarrow P=\frac{51!}{5!(51-5)!} ~\times \frac{52!}{5!(52-5)!}\\\\\Rightarrow P=\frac{47}{52}\)

Therefore, the probability that a five-card poker hand does not contain the queen of hearts is 47/52.

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Answer:

Curl ups

Step-by-step explanation:

I'm not 100% sure, but it seems like the most logical answer to me.

Answer:

Trunk Lift

Step-by-step explanation:

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

Pattern B

A quadratic relationship is characterized by constant second differences.

Pattern A

Sequence: 0, 2, 4, 6

First Differences: 2, 2, 2 . . . . constant indicates a 1st-degree (linear, arithmetic) sequence

__________________________________________________________

Pattern B

Sequence: 1, 2, 5, 10

First Differences: 1, 3, 5

Second Differences: 2, 2 . . . . constant indicates a 2nd-degree (quadratic) sequence

__________________________________________________________

Pattern C

Sequence: 1, 3, 9, 27

First Differences: 2, 6, 18

Second Differences: 4, 12 . . . . each set of differences has a common ratio, indicating an exponential (geometric) sequence

__________________________________________________________

Pattern B shows a geometric relationship between step number and dot count.

Reflection and rotation will not alter the perimeter of the quadrilateral

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformations has basically classifications

Non rigid transformation are the transformation where the dimension or size of the object will be different going from preimage to the image, example is dilation

In rigid transformation, the dimensions of the object is maintained or not altered through out the transformation process. instance of rigid transformations are

Because the transformation used are all rigid transformations then all the sides will remain same and the perimeter conserved

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Answer:

4 shirts

Step-by-step explanation: 150 - 49.5 = 100.5 / 22.99 = 4.3

Answer:

4shirt thats is correct i research it

Answer:

3 7/8

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

first multiply like terms,

-4 x -5 = 20 [Multiplying two negative signs equal to positive]

3 x 20= 60

If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,

Part a

He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery

Part b

He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery

The payment at the grocery store per hour = $20

The payment at the nursery per hour = $21

Part a

Number of hours he works at the grocery store = 13 hours

Number of hours he works at nursery = 9 hours

Total pay = 13×20 + 9×21

= 260 + 189

= $449

Part b

Number of hours he works at the grocery store = g hours

Number of hours he works at nursery = n hours

Total pay = 20g + 21n

Hence, If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,

Part a

He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery

Part b

He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery

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The number of bundles to be used to make one block of cardboard is 8 bundles.

We shall convert the measurements to a consistent unit in order to estimate the number of bundles used to make one block of cardboard.

Now, we convert the height of the bundles and the block into the same unit like centimeters.

Given:

Height of each bundle = 150 mm = 15 cm

Height of one block = 1.2 meters = 120 cm

Next, we divide the height of the block by the height of each bundle to find the number of bundles:

Number of bundles = Height of block / Height of each bundle

Number of bundles = 120 cm / 15 cm = 8 bundles

Therefore, it takes 8 bundles to make one block of cardboard.

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Question completion:

Your question is incomplete, but most probably your full question was:

The 150mm bundles are stacked and tied into blocks that are 1.2 meters high. how many bundles are used to make one block of cardboard​

The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

Given that,

An octahedron is made by connecting the centers of the faces of the right rectangular prism in the illustration below.

We have to find what is the octahedron's volume.

The Greek term "Octahedron," which means "8 faces," is the source of the English word "octahedron." Eight faces, twelve edges, six vertices, and four edges that intersect at each vertex make up an octahedron, a polyhedron. It is one of the five platonic solids with equilateral triangle-shaped faces.

Since two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid. We can compute the volume of one pyramid, then multiply it by two to obtain the volume of an octahedron.

The pyramid's volume is equal to (Base area ×Height)/3.

Since the pyramid's base is square, its base area is equal to a².

Therefore, The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

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Answer:

  375

Step-by-step explanation:

You want to know the number of integers from 1 to 1000 that are multiples of 4 or 6.

Assuming the ends of the range are not multiples of interest, we can find the number of multiples of a given number by dividing the range by that number. Doing this for 4, 6, and (4×6), we find that in [1, 1000], there are ...

The number of multiples of 4 or 6 will be the total of multiples of 4 and multiples of 6, less the number of multiples of both 4 and 6. That is, the first sum counts those multiples of 24 twice.

  250 +166 -41 = 375

There are 375 multiples of 4 or 6 in the range 1 to 1000.

<95141404393>

676000 is the required total number of different identification codes.

The total number of possible combinations here is computed as:

= Product of the many ways to select each of the characters

= 262*103 = 676000 is the required number of total ways here.

Note that there are 26 possible ways to select each of the first 2 letters and there are 10 ways to select each of the 3 digits here.

Identification Code is a randomly generated set of alpha-numeric symbols supplied by the Bank at the time the Agreement was executed and used as a personal security measure to identify the Customer in communications between the Bank and the Customer via the Customer Service Desk.

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Mark has 5253 cups of sugar left after using 145 cups for a pie and 12/1 cups for his iced tea.

Mark has 5410 cups of sugar, and he used 145 cups for a pie and 12 of a cup in his iced tea. To find out how many cups of sugar he has left, we need to subtract the amount of sugar he used from the total amount of sugar he had:

Total amount of sugar = 5410 cups

Amount of sugar used for pie = 145 cups

Amount of sugar used for iced tea = 12/1 cups (since 12 of a cup is the same as 12/1 cups)

Total amount of sugar used = 145 cups + 12/1 cups = 157 cups

Amount of sugar left = Total amount of sugar - Total amount of sugar used

Amount of sugar left = 5410 cups - 157 cups

Amount of sugar left = 5253 cups

Therefore, Mark has 5253 cups of sugar left after using 145 cups for a pie and 12/1 cups for his iced tea.

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Answer:

To solve for the missing values in the equation Assets = Liabilities + Owner's Equity, we can use the fact that the sum of the assets must equal the sum of the liabilities and owner's equity.

Given:

Assets = $25,000 + $10,000 = $35,000

Owner's Equity = $21,000 + $11,000 = $32,000

We can use these values to solve for the missing liabilities:

Liabilities = Assets - Owner's Equity

Liabilities = $35,000 - $32,000

Liabilities = $3,000

Therefore, the missing values in the equation are:

Assets = $25,000 + $10,000 = $35,000

Liabilities = $9,000 + $3,000 = $12,000

Owner's Equity = $21,000 + $11,000 = $32,000

Answer:

No, a Celsius temperature is not proportional to its equivalent Fahrenheit temperature.

Step-by-step explanation:

The formula is

F=(9/5) C+ 32

F increases as C increases and F decreases as C decreases, but the relation is not a direct proportionality.

In mathematics, a direct proportion has the form

y=mx

where m is a constant.

If the formula had been F=(9/5) C, it would have been a direct proportion.

However, the addition of the + 32 term makes the formula no longer a direct proportion