Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression below.

Answer:

-45

Step-by-step explanation:

2/3x - 11 = x + 4

2/3x = x + 15

-1/3x = 15

x = -45

Answer:

-45.

Step-by-step explanation:

2/3 x - 11 = x + 4

2/3 x - x = 4 + 11

-1/3x = 15

x = 15 * -3

x = -45.

Answer:

15 and 25

Step-by-step explanation:

15+25=40

10+20=30+5+5=10+30=40

Answer:one number is 15 and the other number is 25

Step-by-step explanation:

Let x represent one of the numbers.

Let y represent the other number.

There are 2 numbers and the sum of those numbers are 40. This means that

x + y = 40 - - - - - - - -1

The difference of those numbers is 10. This means that

x - y = 10 - - - - - - - - -2

We would eliminate x by subtracting equation 2 from equation 1, it becomes

2y = 50

y = 50/2 = 25

Substituting y = 25 into equation 1, it becomes

x + 25 = 40 - 25 = 15

Jose will spend 18 minutes on his science homework.

Step-by-step explanation:

Given,

Time Jose have to spend on homework = 5/6 hour

We know that 1 hour = 60 minutes

Therefore;

[tex]\frac{5}{6}\ hour = \frac{5}{6}*60\ minutes\\\\\frac{5}{6}\ hour = 50\ minutes[/tex]

Time Jose have to spend on homework = 50 minutes

Time spent on math home work = [tex]\frac{1}{3}\ of\ his\ time[/tex]

Time spent on math home work = [tex]\frac{1}{3}*50=16.66\ minutes[/tex]

Rounding off to nearest whole minute;

Time spent on math homework = 17 minutes

Time spent on reading homework = 15 minutes

Total time spent = Mathematics + Reading + Science

50 = 17+15+Science

50 = 32 + Science

Science = 50-32 = 18 minutes

Jose will spend 18 minutes on his science homework.

Keywords: addition, fraction

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Answer:

H(160)=150  means that  Kana's height is 150 cm when she is 160 months old

Step-by-step explanation:

According to the model described in the question:

H(t)=X where

Thus H(160)=150 states

Answer:

When Kana was 160 months old, her height was equal to 150 centimeters.

Step-by-step explanation:

Answer:

C. There were 6,27 times as many people who visited the aquarium on the seventh day as on the first day.

Explanation:

[tex]\displaystyle 1,3^7 = 6,2748517 ≈ 6,27[/tex]

I am joyous to assist you anytime.

The power developed in the first crane will be twice the power developed in the second crane.

Given information:

Two construction cranes are used to lift identical 1200-kilogram loads of bricks at the same vertical distance.

The first crane lifts the bricks in 20 seconds and the second crane lifts the bricks in 40 seconds.

Now, the load is the same and the vertical lift is also the same. So, the work done W by both the lifts will also be the same.

The power developed by first crane will be,

[tex]P_1=\dfrac{W}{20}[/tex]

The power developed by second crane will be,

[tex]P_2=\dfrac{W}{40}[/tex]

So, the ratio of power developed in two cranes will be,

[tex]P_1:P_2=\dfrac{W}{20}:\dfrac{W}{40}\\P_1:P_2=2:1[/tex]

Therefore, the power developed in the first crane will be twice the power developed in the second crane.

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Final answer:

The power developed by the first crane is twice as great as the power developed by the second crane because it lifts the bricks in half the time.

Explanation:

To compare the power developed by the first crane with the power developed by the second crane, we can use the formula:

Power = Work / time

Since both cranes are lifting identical 1200-kilogram loads of bricks the same vertical distance, the work done by both cranes is the same. Therefore, the power developed by the first crane is twice as great as the power developed by the second crane. This is because the first crane lifts the bricks in 20 seconds, which is half the time it takes the second crane to do the same work in 40 seconds.

Answer:

A) 14 cm² per sec

B) 0 cm per sec

C) -28 cm per sec

Step-by-step explanation:

We know that,

If l = length of a rectangle and w = width of the rectangle

A) Area of a rectangle,

[tex]A=l\times w[/tex]

Differentiating with respect to t ( time )

[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex]

We have,

[tex]l=12\text{ cm}, w=5\text{ cm}, \frac{dw}{dt}=2\text{ cm per sec}, \frac{dl}{dt}=-2\text{ cm per sec}[/tex]

[tex]\frac{dA}{dt}=12\times 2+5\times -2[/tex]

[tex]\frac{dA}{dt}=24-10[/tex]

[tex]\frac{dA}{dt}=14\text{ square cm per sec}[/tex]

B) Perimeter of the rectangle,

[tex]P=2(l+w)[/tex]

Differentiating with respect to t ( time ),

[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})=2(-2+2)=0[/tex]

C) Length of the diagonal,

[tex]D=\sqrt{l^2+w^2}[/tex]

[tex]D^2 = l^2 + w^2[/tex]

Differentiating with respect to t ( time ),

[tex]2D\frac{dD}{dt}=2l\frac{dl}{dt}+2w\frac{dw}{dt}[/tex]

Since, if l = 12 cm, w = 5 cm,

[tex]D=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\text{ cm}[/tex]

[tex]\implies 2\times 13 \frac{dD}{dt}=2(12)(-2)+2(5)(2)[/tex]

[tex]26\frac{dD}{dt}=-48+20=-28\text{ cm per sec}[/tex]

Using implicit differentiation, it is found that:

a) The rate of change of the area of the rectangle is: 14 cm²/sec.

b) The rate of change of the perimeter of the rectangle is: 0 cm/sec.

c) The rate of change of the lengths of the diagonal of the rectangle is: [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.

Item a:

The area of a rectangle of length l and width w is given by:

[tex]A = lw[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt}[/tex]

For this problem, the values are:

[tex]w = 5, \frac{dl}{dt} = -2, l = 12, \frac{dw}{dt} = 2[/tex]

Then:

[tex]\frac{dA}{dt} = 5(-2) + 12(2)[/tex]

[tex]\frac{dA}{dt} = 14[/tex]

The rate of change of the area is of 14 cm²/sec.

Item b:

The perimeter is given by:

[tex]P = 2l + 2w[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dP}{dt} = 2\frac{dl}{dt} + 2\frac{dw}{dt}[/tex]

Then

[tex]\frac{dP}{dt} = 2(-2) + 2(2) = 0[/tex]

The rate of change of the perimeter is of 0 cm/sec.

Item c:

The diagonal is the hypotenuse of a right triangle in which the sides are the length and the width, then, applying the Pythagorean Theorem:

[tex]d^2 = l^2 + w^2[/tex]

The value of the diagonal is:

[tex]d^2 = 5^2 + 12^2[/tex]

[tex]d^2 = 169[/tex]

[tex]d = \sqrt{169}[/tex]

[tex]d = 13[/tex]

The rate of change is:

[tex]2d\frac{dd}{dt} = 2l\frac{dl}{dt} + 2w\frac{dw}{dt}[/tex]

Then

[tex]26\frac{dd}{dt} = -48 + 20[/tex]

[tex]26\frac{dd}{dt} = -28[/tex]

[tex]\frac{dd}{dt} = -\frac{14}{13}[/tex]

The rate of change of the lengths of the diagonals of the rectangle  is of [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.

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Answer:

we have 448 ways of putting them.

Step-by-step explanation:

For the first piece we have no restrictions, so we have 8*8 = 64 ways of puting it. For the second piece we have 7 ways to put it in the same row and 7 ways of put it in the same column, so we have 14 ways.

This gives us a total of 14*64 = 896 ways.

However, since the pieces are indistinguishable, we need to divide the result by two, because we were counting each possibility twice, (if we swap the pieces, then it counts as the same way), thus we have 896/2 = 448 of putting two pieces on the board.

Answer:

With the given zeros x=-2,1,4 the polynomial function is [tex]x^3-3x^2-6x-8[/tex]

Step-by-step explanation:

Given zeros are x=-2,1,4

Now to find the polynomial function:

With the given zeros we can write it as below:

x=-2  implies that x+2=0

x=-1  implies that  x-1=0

x=4  implies that  x-4=0

Then we can the zeros or factors by (x+2)(x-1)(x-4)

Now expanding the zeros or factors:

[tex](x+2)(x-1)(x-4)[/tex]

[tex](x+2)(x-1)(x-4)=(x^2-x+2x-2)(x-4)[/tex]  ( multiply each term with each term of another factor)

[tex]=(x^2+x-2)(x-4)[/tex] ( adding the like terms)

[tex]=x^3-4x^2+x^2-4x-2x+8[/tex]   ( multiply each term with each term of another factor)

[tex]=x^3-3x^2-6x+8[/tex]  ( adding the like terms)

[tex](x+2)(x-1)(x-4)=x^3-3x^2-6x+8[/tex]

Therefore the polynomial function is [tex](x+2)(x-1)(x-4)=x^3-3x^2-6x+8[/tex]

With the given zeros x=-2,1,4 the polynomial function is [tex]x^3-3x^2-6x-8[/tex]

Answer:

The product of 'x' and 'y' is [tex]\boxed 8[/tex].

Step-by-step explanation:

Given:

[tex]\log_{5\sqrt5}125=x\\\\\log_{2\sqrt2}64=y[/tex]

We need to determine the product of 'x' and 'y'.

Using the following logarithmic property:

[tex]\log_ab=\frac{\log b}{\log a}[/tex]

Here, [tex]a=5\sqrt5\ and\ 2\sqrt2[/tex]

[tex]b=125\ and\ 64[/tex]

So, [tex]log_{5\sqrt5}125=\frac{\log 125}{\log 5\sqrt{5}}\\\\log_{5\sqrt5}125=\frac{\log 5^3}{\log 5\times5^{1/2}}.......[\sqrt5=5^{1/2}][/tex]

[tex]log_{2\sqrt2}64=\frac{\log 64}{\log 2\sqrt{2}}\\\\log_{2\sqrt2}64=\frac{\log 2^6}{\log 2\times2^{1/2}}.......[\sqrt2=2^{1/2}][/tex]

Now, we use another property of log and exponents.

[tex]\log a^m=m\log a\\a^m\times a^n=a^{m+n}[/tex]

[tex]log_{5\sqrt5}125=\frac{3\log 5}{\log 5^{1+{1/2}}}=\frac{3\log 5}{\log 5^{\frac{3}{2}}}=\frac{3\log 5}{\frac{3}{2}\log 5}=2\\\\\\\\log_{2\sqrt2}64=\frac{6\log 2}{\log 2^{1+{1/2}}}=\frac{6\log 2}{\log 2^{\frac{3}{2}}}=\frac{6\log 2}{\frac{3}{2}\log 2}=\frac{12}{3}=4[/tex]

So, [tex]x=2\ and\ y=4[/tex]

The product of 'x' and 'y' = [tex]2\times 4=8[/tex]

Therefore, the product of 'x' and 'y' is 8.

Using the mean formula and the data given, the fifth participant’s time to complete the memory task must be 13 seconds to result in a mean (M) of 9 seconds for all five participants.

To find the fifth time recorded when four participants took 7, 8, 8, and 9 seconds to complete a memory task and the mean (M) time is 9 seconds, we need to use the formula for the mean of a sample which is the sum of all values divided by the number of values.

Here's the equation based on the data provided:
(7 + 8 + 8 + 9 + x) / 5 = 9

First, calculate the sum of the times we know:
7 + 8 + 8 + 9 = 32 seconds

Now, insert this sum into the equation and solve for x, where x represents the fifth time:
(32 + x) / 5 = 9
32 + x = 45
x = 45 - 32
x = 13 seconds

The fifth participant must have taken 13 seconds to complete the memory task to have a mean time of 9 seconds.

Answer: Coefficient

Step-by-step explanation:

When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the coefficient.

A coefficient is a number preceding any variable in a function for example, given the function 4x, the variable is 'x' and the number preceding it is 4. This number preceding the variable is what we call 'coefficient' of the variable 'x'

Answer:

  8

Step-by-step explanation:

There are two choices for each digit, and 3 digits, so 2^3 = 8 possible numbers. Here's a list:

  222, 225, 252, 255

  522, 525, 552, 555

Answer:

8

Step-by-step explanation:

The first digit has two possibilities; it can either be a 2 or a 5.  

The second digit has two possibilities; it can either be a 2 or a 5.

The third digit has two possibilities; it can either be a 2 or a 5.

2 x 2 x 2 = 8 integers.

(Here are the numbers listed out):

222

225

252

255

522

525

552

555

Answer:

a. x = primes.difference(odds)

Step-by-step explanation:

Given the list of numbers primes and odds, the list x is made subtracting odds to primes. To do that in a object oriented language you use: x = primes.difference(odds) which is equivalent to x = primes  - odds

The correct line of code that will result in x containing {1} is option b: x = odds.difference(primes). This provides the set of elements in the 'odds' set that are not in the 'primes' set, which is {1}.

The question revolves around the concept of set operations in mathematics. Specifically, it focuses on the difference and intersection operations between two sets named primes and odds. To find the set containing only the number {1}, we should look for the difference between the odds and primes sets because 1 is in the odds but not in the primes.

Answer option a, x = primes.difference(odds), would result in a set that contains elements present in primes but not in odds, which would be {2}. However, that's not what we are looking for.

Answer option b, x = odds.difference(primes), is correct. It would result in a set containing elements that are in odds but not in primes, which is exactly {1}.

Answer options c and d, which refer to the intersection of the two sets, would result in the set {3, 5}, which are elements common to both primes and odds, and therefore not the correct answer.

For visual representation, you could draw a Venn diagram with two circles, one for primes containing {2, 3, 5, 7} and another for odds containing {1, 3, 5, 7}. The number 1 would be in the part of the odds circle that does not overlap with the primes circle.

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Answer:

He needs to walk 41 mins or 2,76 miles to burn 150 calories.

If he increases the speed of walking or eats snack with less calories, he will spend less time for walking.

Step-by-step explanation:

The person is burning

[tex]5,1*60=306[/tex]

calories per hour.

He needs to burn 150 calories plus 60 calories that comes from the snack. In total 210 calories to burn.

[tex]210/306=0,69[/tex]

He needs to walk 0,69 hours (aprrox. 41 mins) to burn 210 calories

[tex]0,69*4=2,76[/tex]

In total he need to walk 2,76 miles to burn 210 calories.

Final answer:

A 150-pound person must walk approximately 17.65 minutes at 4 mph to burn at least 150 calories, after accounting for a 60-calorie snack. To decrease walking time, they can increase activity intensity or choose lower-calorie snacks.

Explanation:

To calculate the time required for a 150-pound person to burn at least 150 calories at a rate of 5.1 calories per minute while walking at 4 miles per hour, we must account for the 60-calorie snack they consumed. We first subtract the 60 calories from the 150-calorie goal, which leaves 90 calories to be burned through exercise. Dividing 90 calories by the 5.1 calories burned per minute gives us the time needed in minutes.

Calculation:
Total calories to burn = 150 - 60 (from snack) = 90 calories
Calories burned per minute = 5.1
Time (in minutes) = Total calories to burn ÷ Calories burned per minute = 90 ÷ 5.1 = 17.65 minutes

So, the person must walk approximately 17.65 minutes to burn at least 150 calories, minus the calories from the snack. To reduce the time spent walking, the person could increase their walking speed, engage in a more vigorous exercise, or consume a lower-calorie snack.

Answer:

Credit the buyer $1,776 and debit the seller $1,776.

Step-by-step explanation:

In accounting books the buyer will be credit from $1,776 and seller will be debit from $1,776.

Answer:

1) Credit the buyer $1,776 and debit the seller $1,776.

Step-by-step explanation:

For this, we are to simply understand and follow the calculation of proration. Proration is the allocation or dividing of certain money items at the closing.

The buyer pays:

Total taxes = $ 9540

Total Time Span before closing took place = 2 months and 7 days

Per month charge = [tex]\frac{9540}{12}[/tex] = $795 per month

Charges per day =  [tex]\frac{795}{30}[/tex] =$ 26.5 per day

2 months charge = 795 x 2 = $1590

Charges for 7 days = 7 x 26.5 = $185.5

Total Charges = 1590 + 185.5 = $ 1775.5 ≈ $1776 (Rounding off)

As the property's taxes were paid for by the buyer and the seller was responsible for the day of closing, and buyer paid for the arrears too of the previous 2 months and 7 days, the buyer gets a credit and seller gets a debit. The seller owes the buyer $1776.

Hence,

The buyer gets a credit of $1,776 and Seller gets a debit of $1,776

Step-by-step explanation:

Given data:

Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%.

During the first month, Tran charged $450 and paid $150 of that in his billing cycle.

The expression which will find the amount of interest Tran will be charged after the first month is (0.012)(300)

Here 0.01 because it is 1 month tax.

300 is remaining amount as Tran used $450 but paid $150.

Answer:

its 0.01 [300]

Step-by-step explanation:

Question is incomplete, complete question is given below.

Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 3 cm. B) A rectangle with a length of 20 cm and a width of 10 cm. C) A rectangle with a length of 18 cm and a width of 9 cm. D) A rectangle with a length of 27 cm and a width of 3 cm.

Answer:

A) A rectangle with a length of 9 cm and a width of 3 cm.

Step-by-step explanation:

Given,

Length = 21 cm       Width = 7 cm

[tex]Ratio = \frac{Length}{Width}\\\\Ratio = \frac{21}{7}=3:1[/tex]

For the similarity of rectangle the ratio of length to width of any two rectangles should be equal.

So we have four options given;

A) A rectangle with a length of 9 cm and a width of 3 cm.

[tex]Ratio =\frac{9}{3}=3:1[/tex]

Here the ratio is equal as of rectangle A. So this rectangle is similar to rectangle A.

B) A rectangle with a length of 20 cm and a width of 10 cm.

[tex]Ratio =\frac{20}{10}=2:1[/tex]

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

C) A rectangle with a length of 18 cm and a width of 9 cm.

[tex]Ratio =\frac{18}{9}=2:1[/tex]

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

D) A rectangle with a length of 27 cm and a width of 3 cm.

[tex]Ratio =\frac{27}{3}=9:1[/tex]

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

Thus the correct option is A) A rectangle with a length of 9 cm and a width of 3 cm.

Answer:

40%

Step-by-step explanation:

135 of 225 is equal to 60%. Therefore, the remaining percent, which should equal to 100, did not wear spirit shirts. 100 - 60 = 40. Therefore, 40% of students did not wear spirit shirts on Friday.

The percentage of students who did NOT wear spirit shirts on Friday is 40%

To find the percentage of students who did NOT wear spirit shirts on Friday, we subtract the number of students who wore spirit shirts from the total number of students and divide by the total number of students.

Then, multiply by 100 to get the percentage.

Number of students who did NOT wear spirit shirts = Total number of students - Number of students who wore spirit shirts = 225 - 135 = 90.

Percentage of students who did NOT wear spirit shirts = (90 / 225) x 100 = 40%

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I've attached the correct image to this answer, just in case they're scrambled.

To match the equation 5x-4y=20 with its graph, convert it to slope-intercept form to identify a positive slope of 5/4 and a y-intercept of -5. Look for a graph with these features in the provided pictures.

To match the equation with its graph for 5x-4y=20, we first need to rewrite it in slope-intercept form, which is y=mx+b. By isolating y, we get 4y = 5x - 20, or y = (5/4)x - 5. This equation signifies a line with a slope (m) of 5/4, meaning for every increase of 4 units in x, y increases by 5 units. The y-intercept (b) is -5, indicating where the line crosses the y-axis. Now, looking at the provided pictures, we should find a graph with a positive slope of 5/4 and a y-intercept of -5.

The correct graph will rise more than it runs since the slope is greater than 1, and will cross the y-axis below the origin at -5. Without seeing the actual images, we are unable to definitively identify which picture corresponds to the given equation. Typically, you would examine each graph to see which one matches these characteristics.

Answer:

The expression representing the Total Cost of the item is  [tex]P + 0.07P[/tex].

Step-by-step explanation:

Given:

Price of Certain item = 'P' dollars

Sales tax =7%

We need to find the expression for Total Cost of the item when tax is applied.

we will first find the Amount deducted in tax;

Amount deducted in Tax is equal to Percentage of sales tax multiplied by Price of Certain item and then divide by 100

Framing in equation form we get;

Amount Deducted in Tax  = [tex]\frac{7}{100}\times P = 0.07P[/tex]

Now Total Cost of the item is equal to sum of Price of Certain item and Amount deducted in tax.

Expressing in expression form we get;

Total Cost of item = [tex]P + 0.07P[/tex]

Hence The expression representing the Total Cost of the item is  [tex]P + 0.07P[/tex].

The cost will be the same when 1 shirt is ordered.

Cost Comparison

Option 1: Cost = $41 (setup fee) + $10 (shirt price)

Option 2: Cost = $36 (setup fee) + $15 (shirt price)

Let's assume the number of shirts is 'x'.

Equating the costs of both options:

$41 + $10x = $36 + $15x

$5x = $5

x = 1

Therefore, the cost will be the same for 1 shirt.

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Answer:

Outer perimeter of the resulting 2-dimensional shape will be 18.84 units

Step-by-step explanation:

From the figure, we could see

AE =  FB = 1

And  minor arc EF  

=> [tex]\frac{2 \pi (1) }{6}[/tex]  

=>[tex]= \frac{2 \pi}{ 6}[/tex]

=>[tex]= \frac{ \pi}{ 3}[/tex]

So by symmetry the perimeter  is

=>[tex]3(2 + \frac { \pi}{3} )[/tex]

=>[tex]3(\frac {6 \pi}{3} )[/tex]

=>[tex]6 \pi[/tex]

=> [tex]6 \times 3.14[/tex]

=> 18.84 units

Answer:

6+pi or 9.14

Step-by-step explanation:

Answer:

A. 6 188

B. 749 398

C. 6 188

D. 52 975

E. 20 349

F. 11 316

Explanation:

(a) The shop has 6 types of croissants of which a dozen(12) has to be selected

Therefore n=6, r=12

Repetition of croissants is permitted

And C(n+r-1, r)

C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188

(b) The shop has 6 types of croissants of which three dozen(36) has to be selected

Therefore n=6, r=36

Repetition of croissants is permitted

And C(n+r-1, r)

C(6+36-1, 12) = C(41, 36) = 41!÷ 36!(41-36)! = 41!÷36! 5! = 749 398

(c) The shop has 6 types of croissants of which two dozen(24) has to be selected

Let us first select 2 of each kind which 12 croissants in total. Then we still need to select the remaining 12 croissants

Therefore n=6, r=12

Repetition of croissants is permitted

And C(n+r-1, r)

C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188

(d) The shop has 5 types of croissants of which two dozen(24) has to be selected

Therefore n=5, r=24

Repetition of croissants is permitted

And C(n+r-1, r)

C(5+24-1, 24) = C(28, 24) = 28!÷ 24!(28-24)! = 28!÷24! 4! = 20 475

This problem involves calculating the number of combinations with repetition where the order of choosing croissants does not matter and requires applying the combinatorics formula for such scenarios.

The question asked is concerning the number of ways to choose different quantities of croissants from a croissant shop that has six different types. This is a classic example of a combinatorics problem which falls under the category of counting the number of combinations with repetition.

The counting principle states that if there are 'n' ways to do one thing, and 'm' ways to do another, then there are n * m ways to do both. However, when choosing with repetition where the order does not matter, we use the formula for combinations with repetition: (n + r - 1)! / r!(n - 1)!, where 'n' is the number of types and 'r' is the number of items to be chosen.

Kira runs a total of 144 miles in 9 weeks.

Step-by-step explanation:

Given,

Distance covered on Monday = 2.5 miles

Distance covered on Wednesday = 5.75 miles

Distance covered on Friday = 7.75 miles

Total distance covered per week = 2.5+5.75+7.75 = 16 miles

Total distance in 9 weeks = Distance per week * 9

Total distance in 9 weeks = 16*9 = 144 miles

Kira runs a total of 144 miles in 9 weeks.

Keywords: addition, multiplication

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Answer:angle DAB will be equal to angle CAB

Step-by-step explanation:

AC is a straight line and forms one of the sides of triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

The measure of angle DAB will be congruent to angle CAB if AB and CD are parallel and right angles to AC and AD. The relationship changes as point D moves along AC, with angle DAB diminishing if DE remains parallel to AB.

If point D is placed on AC, the measure of ∠DAB will relate to the measure of ∠CAB based on several geometric principles. If AB is parallel to CD and D moves along AC, with DE remaining constantly parallel to AB, the angle at D (∠DAB) will diminish as D moves away from A. If AB and CD maintain parallels and AC makes equal angles with them, then accordingly ∠DAB will also equal ∠CAB at the point where the two angles are bisected by AC.

Moreover, if AB and CD are right angles to AC and AD, as described by the circle theorem stating that angles inscribed in the same arc are congruent, then ∠DAB will be congruent to ∠CAB.

Answer:

a) P({a, b, {a, b}})=[tex] 2*2*2=8[/tex]

b) P({∅, a, {a}, {{a}}})=[tex] 2*2*2*2=16[/tex]

c) P(P(∅))=P(P{∅})=2

Step-by-step explanation:

Previous concepts

For this case we need to remember the concpts of subset and the power set.

A is a subset of B if every element of A is an eelement if B and we write [tex]A \subseteq B[/tex]

The power set of a set R is th set of all the possible subsets of R and we writ this as P(R)

Solution to the problem

Part a

P({a, b, {a, b}}) as we can see this set contains 3 elements a,b and {a,b}

And since the power set contains all the possible subsets of the elements. For this case for each element we have 3-1 = 2 options in order to combine, then the number of possible subsets would be equal to the product of possible options and we got:

P({a, b, {a, b}})=[tex] 2*2*2=8[/tex]

Part b

P({∅, a, {a}, {{a}}}) as we can see this set contains 4 elements ∅,a,{a} and {{a}}

And since the power set contains all the possible subsets of the elements. For this case for each element we have 3-1 = 2 options in order to combine, then the number of possible subsets would be equal to the product of possible options and we got:

P({∅, a, {a}, {{a}}})=[tex] 2*2*2*2=16[/tex]

Part c

P(P(∅)) for this case we need to remember that P(∅) have all the possible subsets empty, but the power set for the empty set is also empty.

P(∅)={∅}

And we see that this last one set have just one element.

For this special case we have again 2 options since we can have the element in the subset or the element that is not on the subset, so then we have this:

P(P(∅))=P(P{∅})=2

The number of elements of the set are 8, 16, and 2.

It should be noted that the objects in a set are known as the elements or members of the set.

The number of elements in the set will be calculated thus:

P({a, b, {a, b} = 2³ = 2 × 2 × 2 = 8

P({∅, a, {a}, {{a}}) = 2⁴ = 16

P(P(∅)) = 2¹ = 2

In conclusion, the correct options are 8, 16, and 2.

Learn more about set theory on:

https://brainly.com/question/13458417

Answer:

Option D.

Step-by-step explanation:

Form the given line plot, first we need to find the data set. So, our data set is

24, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 28, 30, 30, 30, 32, 32, 32, 35

Divide the data in two equal parts.

(24, 26, 26, 26, 27, 27, 27, 28, 28), 28, (28, 28, 30, 30, 30, 32, 32, 32, 35)

Divide each of the parenthesis in two equal parts.

(24, 26, 26, 26), 27, (27, 27, 28, 28), 28, (28, 28, 30, 30), 30, (32, 32, 32, 35)

Now, we get

Minimum value = 24

First quartile = 27

Median = 28

Third quartile = 30

Maximum value = 35

It means the box lies between 27 and 30. The line inside the box at 28. Left point of the line isi 24 and right point of the line 35.

This description represented by the box plot in option D.

Hence, the correct option is D.