A bag contains 5 purple marbles and 5 orange marbles. Rahul reaches into the bag and draws one marble without looking. Then he replaces the marble and repeats the experiment. If he repeats the experiment 120 times, how many times should he expect to pull out an orange marble? Please someone help me I need to finish this soon

The hypotenuse of the paper is 2√106 cm.

What is Pythagorean theorem ?

Hypotenuse ² = Height ² + Width ²

Know more about Pythagorean theorem,

The Pythagorean Theorem, also known as the Pythagoras Theorem, explains the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. Pythagorean triangles are the name given to the sides of a right triangle. Let's learn about Pythagorean theorem, formula, derivation and examples in detail.

The history of the Pythagorean theorem goes back to the ancient Babylonian and Egyptian era. The Greek mathematician Pythagoras of Samos introduced the Pythagorean theorem. Pythagoras was born in 570 BC. The Greek philosopher studied with other monks and formed a group of people; he finally stated the Pythagorean theorem. Even before Pythagoras, the ratio was shown on a Babylonian tablet 4000 years ago, but the theorem is published under the name of Pythagoras.

Here given, a triangle shaped paper’s height is 18 cm and width is 10 cm.

We want find the hypotenuse of the paper ?

Here, height of the paper = 18 cm and width of the triangle = 10 cm.

[tex] = {18}^{2} + {10}^{2} \\ = 324 + 100 \\ = 424[/tex]

So,

[tex]hypotenuse = \sqrt{424} \\ = \sqrt{2 \times 2 \times 2 \times 53} \\ = 2 \sqrt{2 \times 53} \\ = 2 \sqrt{106} \: cm[/tex]

Therefore,the hypotenuse of the paper is 2√106 cm.

Pythagoras theorem related one more question:

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Answer:

d. [tex]-15x^3y^7[/tex]

Step-by-step explanation:

By the binomial theorem,

[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r} q^r[/tex]

Where,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Thus,

[tex](\frac{1}{2}x-y)^{10}=(\frac{x}{2}+(-y))^{10})=\sum_{r=0}^{n} ^10C_r (\frac{x}{2})^{10-r} (-y)^{r}[/tex]

For the 8th term, r = 7,

Thus, the 8th term would be,

[tex]^{10}C_7 (\frac{x}{2})^{10-7} (-y)^{7}[/tex]

[tex]=\frac{10!}{7!(10-7)!} (\frac{x}{2})^3 (-y)^7[/tex]

[tex]=-\frac{10\times 9\times 8}{3\times 2\times 1}\times \frac{x^3}{8}\times y^7[/tex]

[tex]=-\frac{720x^3y^7}{48}[/tex]

[tex]=-15x^3y^7[/tex]

Hence, option 'D' is correct.

Answer: the number is x = 1 + 21/52

Step-by-step explanation:

we have

(5 + 5/12) - x = (6 + 1/6) - (2 + 2/13)

this means that x is smaller than 5 + 5/12 by the same amount as (2 + 2/13) is smaller than (6 + 1/6)

We can solve it directly, first solve the parentheses, put the whole numbers at one side and the fractions in the other side:

5 - 6 + 2 - x = -5/12 + 1/6 - 2/13

1 - x = -5/12 + 2/12 - 2/13

1 - x = -3/12 - 2/13 = -1/4 - 2/13 = -13/(4*13) - (2*4)/(4*13) = -21/52

x = 1 + 21/52

Answer:

73/52

Step-by-step explanation:

This problem can be solved using equivalent fractions. The first step in resolving this problem is to realize that fractions are best compared when they both have the same denominator.  In this case, I will choose to make that common denominator 100. There is no need to rewrite the fraction [tex]\frac{21}{100}[/tex] as the denominator for this fraction is already 100. The fraction [tex]\frac{1}{5} =\frac{20}{100}[/tex] . This is achieved by multiplying both the numerator and denominator by 20. Now that the two fractions have the same denominator, we can easily see that [tex]\frac{21}{100}[/tex] is greater than [tex]\frac{1}{5}[/tex] because it is greater than its equivalent fraction.

The common ratio of the given geometric sequence is [tex]-\frac{1}{2}[/tex], as each term is half the value and opposite in sign of the previous term.

The common ratio of a geometric sequence can be found by dividing any term by the previous term. In the given sequence, -96, 48, -24, 12, -6,..., let's divide the second term by the first term:

Common ratio (r) = [tex]\frac{48 }{-96} = -\frac{1}{2}[/tex]

This ratio will be consistent throughout the sequence. For example, dividing the third term by the second term also gives [tex]-\frac{24 }{ 48} = -\frac{1}{2}[/tex], confirming that the common ratio is indeed [tex]-\frac{1}{2}[/tex].

Answer: B. 38,273 + 51,425 = 89,798

Step-by-step explanation:

Let's check all the sum by adding their corresponding places.

A. [tex]46,371 + 32,618 = 78,989[/tex]

Its correct.

B. [tex]38,273 + 51,425 =89698\neq 89,798[/tex]

Here when we add the digits on the hundredth place we get 6 not 7.

Hence, it is the example of an error of addition by one.

Its correct.

C. [tex]13,246 + 84,631 = 97,877[/tex]

Its correct.

D. [tex]52,634 + 25,145 = 77,779[/tex]

Its correct.

The points that are solutions to the system of inequalities is ( -12,0), (-10,1), the correct option is A and C.

The system of Inequalities are the set of inequalities that have a common solution.

The solution of the set of Inequalities can be obtained by plotting a graph and finding the common area.

The solution to the system of inequalities is shown in the graph.

The points that are solutions to the system of inequalities is

( -12,0)

(-10,1)

To know more about System of Inequalities

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Answer:

If a step is "at least" 8 inches high, the minimum number of steps is theoretically 1, because that 1 step could be a 10-foot high step.

Step-by-step explanation:

Answer:

12 minutes

Step-by-step explanation:

Just took the test and got it right

The mistake is in Step 4 of Honi's calculation. The correct actual distance between Niceville and Live Oak should be 200 miles instead of the 250 miles that was stated in the original steps.

The student's question pertains to setting up and solving a proportion to find the actual distance between two places using a map scale. The map scale given is  ¼ in. = 20 miles. Honi measures a distance of 2.5 inches on the map. The steps to find the actual distance, using a proportion, should be evaluated for accuracy.

To set up the proportion correctly, we use the ratio of the map scale and compare it to the ratio of the measured distance to the actual distance (x). The correct proportion should be: (1/4 in.) / 20 miles = 2.5 in. / x miles.

Step 1 is correct, setting up the proportion based on the scale and measured distance. Step 2 involves cross-multiplying to find the relationship between the scale and the actual distance, which should yield (1/4) * x = 2.5 * 20. Step 3 should simplify this equation correctly, which would give us x = 2.5 * 20 * 4 = 200 miles. Therefore, Step 4 has a mistake because the solution provided should be 200 miles, not 250 miles as given.

Answer:

32.27

Step-by-step explanation: