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kow [346]
1 year ago
8

Given that line CD is a perpendicular bisector of triangle ABC, if side AB has a length of 11 and side AC has a length of 14 wha

t is the length of side CD? Write your answer to the
nearest hundredth

Mathematics
1 answer:
nalin [4]1 year ago
4 0

Answer:

12.87

Step-by-step explanation:

Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.

As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5

We now know two values of our equation, and thus we can solve for the missing third value.

5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
\sqrt{165.75} = b
b = 12.87

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Answer:

0.0076 = 0.76% probability that all five plants emerged from treated seeds

Step-by-step explanation:

The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

6 + 6 = 12 seeds, which means that N = 12

6 treated, which means that k = 6

Five sprouted, which means that n = 5

What is the probability that all five plants emerged from treated seeds?

This is P(X = 5). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076

0.0076 = 0.76% probability that all five plants emerged from treated seeds

3 0
3 years ago
What is the solution set of -x^2-6<0 ?
natita [175]

Answer:

All real numbers

Step-by-step explanation:

Let's solve your inequality step-by-step.

−x2−6<0

Let's find the critical points of the inequality.

−x2−6=0

−x2−6+6=0+6(Add 6 to both sides)

−x2=6

−x2

−1

=

6

−1

(Divide both sides by -1)

x2=−6

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3 years ago
3. Identify each following representation as a function or nonfunctional and explain your reasoning.
Vaselesa [24]

Answer:

1.1

Step-by-step explanation:

I think it.

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3 years ago
Read 2 more answers
A company is producing a new product. Due to the nature of the​ product, the time required to produce each unit decreases as wor
balu736 [363]

Answer:

The total time to produce units 1 through 10 = 21.762 hours

The total time to produce units 30 through 40 = 22.187 hours

Step-by-step explanation:

Function for the learning process is T(x) = 2 + 0.6(1/x)

Time required to produce 1st unit = 2.6

Time required to produce 2nd unit = 2.3

Time required to produce 3rd unit = 2.2

Time required to produce 4th unit = 2.15

Time required to produce 5th unit = 2.12

Time required to produce 6th unit = 2.1

Time required to produce 7th unit = 2.09

Time required to produce 8th unit = 2.075

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The total time required for a new worker to produce units 1 through 10 is the sum of the above times. The total time to produce units 1 through 10 = 21.762

Function for the learning process is T(x) = 2 + 0.6(1/x)

Time required to produce 30th unit = 2.02

Time required to produce 31st unit = 2.019

Time required to produce 32nd unit = 2.0188

Time required to produce 33rd unit = 2.018

Time required to produce 34th unit = 2.0176

Time required to produce 35th unit = 2.017

Time required to produce 36th unit = 2.0167

Time required to produce 37th unit = 2.016

Time required to produce 38th unit = 2.0158

Time required to produce 39th unit = 2. 0154

Time required to produce 40th unit = 2. 015

The total time required for a new worker to produce units 30 through 40 is the sum of the above times. The total time to produce units 30 through 40 = 22.187

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3 years ago
Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a true-false e
Gemiola [76]

Answer:

2^26

Step-by-step explanation:

For a true - false examination ; number of options or possible outcomes = 2

Number of questions = 26

Using the counting principle ; the number of elements in the sample space ;

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This is equivalent to : 2^26

2^26 = 67108864

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2 years ago
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