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miskamm [114]
1 year ago
8

Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum dista

nces that the dog may be from the house can be found using the equation |x – 500| = 8. What are the minimum and maximum distances that Morgan’s dog may be from the house?
Mathematics
1 answer:
MAVERICK [17]1 year ago
4 0

Answer:

Max: 500

Min: 492

Step-by-step explanation:

Her dog is on an 8 meter leash but it doesn't necessarily take up the whole leash. The most is could be closer to her house than Morgan is 8 meters, the least is 0.

Most: 500-0=500

Min: 500-8=492

Please rate, thank, and mark branliest (not necessarily mine) Hope this helps :)

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What is the ninth term in the binomial expansion of (X-2y)^13?
vlada-n [284]

Answer:

329472\cdot x^5\cdot y^8  

Explanation:

Binomial expansion is:

(a+b)^n=a^n+n\cdot a^{n-1}{\cdot b}+\frac{n(n-1)}{2}\cdot a^{n-2}\cdot b^2+------+b^n

Here in given expression we have a=x , b=-2y and n = 13

general formula for binomial expansion is:

T_{r+1} =^nC_r\cdot a^{n-r}\cdot b^r

Since, T_{r+1}

r should be one number less than the term we need to find so it will become the number we need to find like here we have to find 9th term so, r=8

substituting the values in the genral formula we will get

^13C_8\cdot x^{13-8}\cdot (-2y)^8

After substituting the values we will get

\frac{13!}{8!\cdot 5!}\cdot x^5\cdot (-2y)^8}

After simplification we will get

329472\cdot x^5\cdot y^8  which will be the 9th term of the expansion



5 0
1 year ago
Read 2 more answers
the letters that spell Mississippi are each written on separate tiles lying face down on a table. a tile is selected at random,
Mars2501 [29]

Answer: The theoretical probability of choosing a tile with letter P =0.18


Step-by-step explanation:

Given word = MISSISSIPPI

Total number of letters in given the word = 11

Number of letter P in given word = 2

Let A be a event of choosing a tile with a letter P then

P(A) =Number of tiles with letter P / Total letters in given word

= 2 /11 = 0.18


6 0
1 year ago
A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the
Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

V_s=\frac{4}{3} \pi r^3

The radius is half the diameter. The diameter of the sphere is 10, thus:

r = d/2 = 10/2 = 5

5^3 = 5*5*5 = 25*5 = 125

V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125

The volume of a cylinder, which will be the shape of the increase in water, is the following:

V_c=\pi r^2 h

We know the radius r, as we know the diameter.

r=d/2=40/2=20

V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

V_s = V_c

\frac{4}{3} * 125 * \pi = 400 * h * \pi

We can get rid of pi by dividing both sides by pi:

\frac{4}{3} * 125 = 400 * h

And now divide both sides by 400:

\frac{4}{3} * \frac{125}{400}= h

Just reversing it and putting h to the left:

h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}

I see that I can divide both the numerator and the denominator by 4:

h =\frac{125}{3 * 100}= \frac{125}{300}

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

\frac{5}{12} ≈ 0.416666667 ≈ 0.42

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Suppose that a class contains 10 boys and 15 girls, and suppose that eight students are to be selected at random from the class
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Arte-miy333 [17]

Answer:

the answer is D

Step-by-step explanation:

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