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egoroff_w [7]
2 years ago
9

Based on the diagram, which expresses all possible lengths of segment AB?

Mathematics
2 answers:
Amiraneli [1.4K]2 years ago
8 0
B It should be the second answer choice
lukranit [14]2 years ago
4 0

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)

So

1) AC+BC > AB

27+54 > AB\\ 81 > AB\\ AB < 81

2) 27+AB > 54

AB > 54-27\\ AB > 27

3) 54+AB > 27

AB > 27-54\\ AB > -27

therefore

the answer is

27 < AB < 81


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Emily went to the movie theater for her birthday. A mix of adults and children attended, making a total of 22 people. Each adult
viktelen [127]

Answer:

13 children and 9 adults if the total cost is $152.5

Step-by-step explanation:

Let x children and y adults

x + y = 22 (1)

5.5x + 9y = 125.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 125.5

5.5x + 198 - 9x = 125.5

-3.5x = 125.5 - 198

-3.5x = -72.5

x = 20.7

y = 22 - x = 1.3

Which is not possible

If the total cost is $152.5

x + y = 22 (1)

5.5x + 9y = 152.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 152.5

5.5x + 198 - 9x = 152.5

-3.5x = 152.5 - 198

-3.5x = -45.5

x = 13

y = 22 - 13 = 9

3 0
2 years ago
How much heat is required to raise the temperature of
Elina [12.6K]

Answer:

The amount of heat required to raise the temperature of liquid water is 9605 kilo joule .

Step-by-step explanation:

Given as :

The mass of liquid water = 50 g

The initial temperature = T_1 = 15°c

The final temperature = T_2  = 100°c

The latent heat of vaporization of water = 2260.0 J/g

Let The amount of heat required to raise temperature = Q Joule

Now, From method

Heat = mass × latent heat × change in temperature

Or, Q = m × s × ΔT

or, Q =  m × s × ( T_2 - T_1 )

So, Q = 50 g × 2260.0 J/g × ( 100°c - 15°c )

Or, Q =  50 g × 2260.0 J/g × 85°c

∴   Q = 9,605,000  joule

Or, Q =  9,605 × 10³ joule

Or, Q = 9605 kilo joule

Hence The amount of heat required to raise the temperature of liquid water is 9605 kilo joule . Answer

4 0
2 years ago
What is the value of 7P7? <br><br> A. 1<br> B. 14<br> C. 49<br> D. 5040
sp2606 [1]
The answer is
D. 5040
3 0
2 years ago
isco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence
maks197457 [2]

Answer:

0.8894 is the probability that the test result comes back negative if the disease is present .

Step-by-step explanation:

We are given the following in the question:

P(Disco Fever) = P( Disease) =

P(D) = \dfrac{1}{2}\times 1\% = 0.5 \times 0.01 = 0.005

Thus, we can write:

P(No  Disease) =

P(ND) =1 - P(D)= 0.995

P(Test Positive given the presence of the disease) = 0.99

P(TP | D ) = 0.99

P( false-positive) = 4%

P( TP | ND) = 0.04

We have to evaluate the probability that the test result comes back negative if the disease is present, that is

P(test result comes back negative if the disease is present)

By Bayes's theorem, we can write:

P(ND|TP) = \dfrac{P(ND)P(TP|ND)}{P(ND)P(TP|ND) + P(D)P(TP|D)}\\\\P(ND|TP) = \dfrac{0.995(0.04)}{0.995(0.04) + 0.005(0.99)} = 0.8894

0.8894 is the probability that the test result comes back negative if the disease is present .

5 0
2 years ago
What is the sum of StartRoot negative 2 EndRoot and StartRoot negative 18 EndRoot?
Crank

Answer:

<h2>B. 4 StartRoot 2 EndRoot i </h2>

Step-by-step explanation:

Given the surd function √-2 and √-18, we are to fund the sum of both values.

Taking the sum:

= √-2 + √-18

= (√2 * √-1)+ (√18 *√-1)

from complex numbers, √-1) = i

The expression becomes

= √2 i+ √18 i

= √2 i+ √9*2 i

= √2 i+ 3√2 i

= 4 √2 i

= √-2 + √-18 = 4 √2 i

The result is 4 StartRoot 2 EndRoot i

8 0
2 years ago
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