Chantel counted 48 books on 6 shelves in the library, How many books would she expect to count on 12 shelves.

The equation that describes the length of the first leg of the right triangle, F, in terms of the length of the second leg, S, is F = √(S^2 - S^2/2).

To determine the equation, we consider the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the first leg (F), and the other two sides are the second leg (S) and the unknown side.

Using the Pythagorean theorem, we have F^2 = S^2 + S^2/2. Simplifying the equation, we get F^2 = 3S^2/2. Taking the square root of both sides, we find F = √(S^2 - S^2/2), which is the equation that describes the length of the first leg (F) in terms of the length of the second leg (S).

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To guarantee that the 3 team compositions (and team leads) are repeated, the professor would need to form groups a total of 3 times over the course of the semester. Each time the professor forms groups, there would be 3 possible team compositions (since the team lead can change within each group) and after 3 formations, all 3 compositions would have been used and repeated.

To determine the number of possible unique team compositions and team leads that can be formed.
1. First, we'll find the number of ways to choose team leads for each group:
There are 12 students and 3 team leads needed, so there are 12 choose 3 ways to pick the team leads, which is calculated as C(12,3) = 12! / (3! * (12-3)!) = 220.
2. Now, we'll calculate the number of ways to divide the remaining 9 students into 3 groups of 3 students each. We can use the multinomial coefficient formula, which is:
C(9,3,3,3) = 9! / (3! * 3! * 3!) = 1680
3. To find the total number of unique team compositions (including team leads), we multiply the results from steps 1 and 2 Total unique team compositions = 220 * 1680 = 369,600
4. The professor needs to form the groups 369,601 times in order to guarantee that the 3 team compositions (and team leads) will repeat.

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Answer:

A

Step-by-step explanation:

6/9=18/27

I just divided 27 by 3 which is 9

Answer:

Connor will earn more interest because he is getting compound interest.

Step-by-step explanation:

I have to assume in this case that the interest is 3.5% Per year:

Simple Interest = P(r + t)

{P = Principle, r = interest rate, t = time)

Wendy = $8,300 x (3.5% x 25)

Wendy = $7,262.50 (2 d.p)

Wendy = $8,300 + $7,262.50

Wendy = $15,562.50

Compound Interest = \(P (1 +r )^{t}\)

{P = Principle, r = interest rate, t = time)

Connor = $8,300 x \((1 + 0.035)^{25}\)

Connor = $19,614.93

Wendy's Interest = $15,562.50 - $8,300 = $7,262.50

Connor's interest = $ 19,614.93 - $8,300 = $11,314.93

Connor earned more interest by $4,052.43

___________________________________________________

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The correct answer is B.

Answer:

36

Step-by-step explanation:

Triangle BCD:

base = 15

height = BC = ?

area = 60

Solve for height.

area = base × height / 2

base × height = 2 × area

height = 2 × area / base

height = 2 × 60 / 15 = 8

height = BC = 8

Triangle BAD:

base = 9

height = BC = 8

area = base × height / 2

area = 9 × 8 / 2 = 36

Answer: 36

Answer:

C :3

Step-by-step explanation:

Whenever our simplification of a linear equation ends in a true statement, in this case 6=6, then our linear equation has infinitely many solutions.

Therefore, our answer is C.

even if we don’t know what x is we’ll still get an infinite amount of solutions

HOPE THIS HELPED :DDDD

Calvin needs to regroup  1 hundred into 10 tens to find the difference between 335 and 126.

After deciding if he needs to regroup, Calvin needs to subtract 2 tens from 3 tens to find the difference.The difference between 335 and 126 can be found as follows:335 - 126 = 209After regrouping 1 hundred into 10 tens, the units place will have 15 ones (5 ones from 335 and 10 ones from the regrouped hundred).

To subtract 6 ones from 15 ones, Calvin will need to regroup 1 ten from 2 tens and add it to the ones place, resulting in 13 ones (5 ones + 10 ones - 6 ones).Now, he can subtract 2 tens from 3 tens to get the tens place, which gives him 1 ten (3 tens - 2 tens). In the hundreds place, he simply subtracts 1 hundred from 2 hundreds, which gives him 1 hundred (2 hundreds - 1 hundred).Therefore, the difference between 335 and 126 is 209.

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Answer:

option 3

Step-by-step explanation:

\(circumference = 2 \pi r\\30 \pi = 2 \pi r\\\\r = \frac{30 \pi }{2 \pi} =15mm\\\\Area = \pi r^2 = \pi 15^2 = 225 \pi \ mm^2\)

Answer:

C

Step-by-step explanation:

. .....................

On the basic of square peg sydney smith written point the probability that it is im-possible to fit a square peg in a round hole is equals to the zero.

Probability is defined as the number of chances of occurrence of an event. It is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Mathematical formula is written as, probability of an event, P(E) = (Number of favorable outcomes)/(Total possible outcomes). Now, we have specify that according to sydney smith written in on the conduct of the understanding about square peg that it is impossible to fit a square peg in a round hole. Let consider an event A of fit a square peg in a round hole. We have specify that it is impossible to fit a square peg in a round hole. So, the favourable possible outcomes for event A = 0. Therefore, the probability that to fit a square peg in a round hole, P(A) = 0

Hence, required probability value is zero.

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There are 8 feet³ of these sheets will Jill need to cover the floor.

We have to given that;

Plywood is sold in 1/4 inch thick sheets that have a length of 8 feet and a width of 4 feet.

Hence, The volume of for sheets are,

⇒ 1/4 × 8 × 4

⇒ 8 feet³

Therefore, There are 8 feet³ of these sheets will Jill need to cover the floor.

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Answer:

.................

Step-by-step explanation:

hmmm

?

Answer:

7 times however many lions they have

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

You have a right triangle, so use the Pythagorean theorem.

a² + b² = c²

5² + b² = 13²

25 + b² = 169

b² = 144

b = 12

Answer:

15 apples

Step-by-step explanation:

7×3=21

5×3=15

Answer:

15 apples

Step-by-step explanation:

hope I could help

Answer:

The question does not make a lot of sense to me but I think this is how its supposed to be done

so there are 15 shirts

2 are sold at 3.90, 2 x 3.90 = 7.8

15-2= 13 t shirts

13 sold at 4.70, 13 x 4.70 = 61.1

amount of money made is = 7.8 + 61.1

                                            = 68.9

Answer:

\(< -0.902, 0.431 >\)

Step-by-step explanation:

The unit vector of any vector is the vector that has the same direction as the given vector, but simply with a magnitude of 1. Therefore, if we can find the magnitude of the vector at hand, and then multiply \(\frac{1}{||v||}\), where ||v|| is the magnitude of the vector, then we can find the unit vector.

Remember the magnitude of the vector is nothing but the pythagorean theorem essentially, so it would be \(\sqrt{(-6.9)^{2} +(3.3)^{2} } ,\) which will be \(\sqrt{58.5}\). Now let us multiply the vector by 1 over this value, and rationalize to make your math teacher happy.\(< -6.9, 3.3 > * \frac{1}{\sqrt{58.5}} = < \frac{-6.9\sqrt{58.5} }{58.5} , \frac{3.3\sqrt{58.5}}{58.5} >\)

You can put those values into your calculator to approximate and get

\(< -0.902, 0.431 >\)

You can always check the answer by finding the magnitude of this vector, and see that it is equal to 1.

Hope this helps

A dilation with a scale factor of 1 will create an image and a pre-image that are similar figures

Given data ,

Let the figure be represented as A

Now , let the transformed image be represented as A'

Now , A dilation with a scale factor other than 1 would create an image and a pre-image that are similar figures, so the answer is either A or C.

Since a dilation with a scale factor of 1 would produce congruent figures, the correct answer is C, a dilation with a scale factor of 2.

Hence , the solution is a dilation with scale factor of 1

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The maximum of a graph is found on the y axis. Considering the given interval, the point on the y axis is 4. Thus, the maximum of the graph over the interval is 4.

Step-by-step explanation:

x will be 0

y will be -2

thats the answer babe

The maximum-likelihood estimates of the probabilities for clear, cloudy, and rainy summer days next year can be derived from this year's weather data. The estimates are given by the ratios of the number of days with each type of weather to the total number of days in the summer. The maximum-likelihood estimates are pclear = nclear/100, pcloudy = ncloudy/100, and prainy = nrainy/100.

To find the maximum-likelihood estimates of pclear, pcloudy, and prainy, we divide the number of days with each type of weather by the total number of days in the summer. Given that nclear = 62, ncloudy = 28, nrainy = 10, and the total number of days in the summer is 100, we can calculate the estimates as follows:

pclear = nclear/100 = 62/100 = 0.62

pcloudy = ncloudy/100 = 28/100 = 0.28

prainy = nrainy/100 = 10/100 = 0.1

These estimates represent the probabilities of each type of weather occurring on a summer day next year, based on the observed frequencies from this year's data. For example, the estimate of pclear suggests that there is a 0.62 (or 62%) chance of a summer day next year being clear.

It is important to note that these estimates assume that next summer's weather will follow the same pattern as this year's. However, weather patterns can vary, and other factors may influence the probabilities of different weather types. Therefore, these estimates provide a reasonable approximation based on the available data, but they may not accurately reflect the actual probabilities for next year's weather.

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Answer:

A

Step-by-step explanation:

Mulitply 3 by 7x and -8

21x - 24

The probability that exactly 3 homes will be sold tomorrow is A) 0.1809.

To solve this problem, we can use the Poisson distribution formula, which is:

P(x; μ) = (e^-μ) (μ^x) / x!

where P(x; μ) is the probability of x events happening in a given time period, μ is the mean number of events in that time period, e is the mathematical constant approximately equal to 2.71828, and x! is the factorial of x.

In this case, we want to find the probability of exactly 3 homes being sold tomorrow, given that the average number of homes sold is 2 per day. So, we plug in μ = 2 and x = 3 into the formula:

P(3; 2) = (e^-2) (2^3) / 3! = 0.1809

Therefore, the probability that exactly 3 homes will be sold tomorrow is 0.1809 or approximately 18.09%. This means that out of every 100 days, we can expect that around 18 of those days will have exactly 3 homes sold by Acme Realty Company.

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Answer:

4 seconds

Step-by-step explanation:

To integrate the function f(x, y) = (x + y + 3)^-2 over the given triangle with vertices (0,0), (4,0), and (0,8), we can set up the integral using symbolic notation and fractions.

The integral can be written as ∫∫R (x + y + 3)^-2 dA, where R represents the region of integration.

To evaluate this integral, we need to determine the limits of integration for x and y based on the triangle's vertices. Since the triangle is defined by the points (0,0), (4,0), and (0,8), we can set the limits as follows:

For x: 0 ≤ x ≤ 4

For y: 0 ≤ y ≤ 8 - (2/4)x

Now, we can rewrite the integral as ∫[0,4]∫[0,8-(2/4)x] (x + y + 3)^-2 dy dx.

Evaluating this integral will yield the exact value of the integral over the given triangle region.

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Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

\(2x^2+2x+4x+4=130\\2x^2+6x+4=130\\\)

Divide through by 2

\(x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63\)

Complete the square by adding the square of the half of the coefficient of x to both sides:

\((x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2\)

\((x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25\)

Take the square root of both sides

\(\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m\)

Hence the value of x is 6.58m

We can show that these data can be modeled using a linear function in the following manner:

a) We must compute the differences in the number of high school graduates in each year in order to model the data using a linear function. For instance, the difference between the 1993 and 1994 graduation rates is 5,479 - 5,410, or 69. This pattern of differences suggests that a linear function can be used to model the data.

The annual change in the number of graduates serves as the slope for the linear function. The slope, for instance, is 69 between 1993 and 1994 and 76 between 1994 and 1995. The slope for the linear function is, in general, the difference between the number of graduates in successive years, therefore it is the slope between graduates in consecutive years.

b) Y = mx + b, where y is the number of graduates, x is the year, m is the slope, and b is the y-intercept, is the formula for a linear function that represents the data. We need to know the values of m and b in order to calculate the formula for the linear function that describes the data.

We can use the slope between any two consecutive years to get the value of m. For instance, m = 69 since the slope from 1993 to 1994 is 69. The number of graduates in the first year of the data, which is the y-intercept, can be used to determine the value of b.

For instance, if the first year of the data is 1993 and that year had 5,479 graduates, then b = 5,479. Consequently, y = 69x + 5,479 is the equation for the linear function that models the data.

c) Functional notation can be used to indicate the number of high school graduates in 1994. The formula is y = 69x + 5,479, where x is the year and y is the total number of graduates. Therefore, y = 69(1994) + 5,479 = 137,123 is the total number of graduates in 1994. We may enter the numbers of x and b into the formula from section c to obtain y = 69 (1994) + 5,479 = 137,123.

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Answer:

s < 50

Step-by-step explanation:

s must be less than 50

s < 50