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Elden [556K]
3 years ago
5

Suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. If 83 babies ar

e sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams?
Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
5 0

Answer: 0.129

Step-by-step explanation:

Let \overline{X} denotes a random variable that represents the mean weight of babies born.

Population mean : \mu= \text{3316 grams,}

Standard deviation: \text{324 grams}

Sample size = 83

Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :

P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}

hence, the required probability =  0.129

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What is the factorization of 729x15 1000? (9x5 10)(81x10 – 90x5 100) (9x5 10)(81x5 – 90x10 100) (9x3 10)(81x6 – 90x6 100) (9x3 1
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The factors of the equation are \rm (9x^4+10)(81x^{10} -90x^5 + 100).

Given

Equation; \rm  729x^{15 }+ 1000.

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots  is given by:

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Where a is the leading coefficient.

The factors of the equation are;

\rm (9x^5 + 10)(81x^{10} -90x^5 + 100)\\\\ 729x^{15}-810x^{10}+900x^5+810x^{10}-900x^5+1000\\\\9x^5(81x^{10} -90x^5 + 100)+10(81x^{10} -90x^5 + 100)\\\\ (9x^4+10)(81x^{10} -90x^5 + 100)

Hence, the factors of the equation are \rm (9x^4+10)(81x^{10} -90x^5 + 100).

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4 0
2 years ago
Find the value of x and y to the nearest tenth
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The value of 'x' is 24.2 and the value of 'y' is 46.5.

To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
    cos30° = b/34 [adjacent over hypotenuse]
    b = 34cos30° [cross-multiply]
    b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
     l² + l² = hyp²
     29.4² + h² = 34²
     h² = 1156 - 864.36
     √h² = √291.64
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<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.     
  Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
     x = 17.1 × √2
     x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u />     y = a + b
     y = 17.1 + 29.4
     y = 46.5

And there you have it! <em>Hope this helps.</em>
     <em>
</em>
5 0
3 years ago
PLEASE HELP ASAP!!! 7th Grade Math.​
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Answer:

1,300

Step-by-step explanation:

First, we need to substitute all the variable with the given number.

To figure out the 2 equivalent squares, do 20 x 20 , which is 400.

Then, the 3rd triangle, do 28 x 25 , equaling 700.

Lastly, for the 2 triangles, 20 x 20 / 2 , leading to the solution of 200.

Now, putting everything together by adding 400+700+200, the final answer is 1,300.

I hope this helped!!

~ Penny

7 0
3 years ago
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