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m_a_m_a [10]
3 years ago
14

What is the range of possible sizes for side x

Mathematics
1 answer:
Xelga [282]3 years ago
3 0

Answer:

0.5 < x < 16.5

Step-by-step explanation:

For a triangle (by the triangular inequality theorem), we know that the sum of any two sides must be larger than the other side.

When we have a triangle and we know two sides, let's define the measures of these sides as S1 and S2.   (such that S2 > S1)

By the first property, we will have that S1 + S2 > S3

Where S3 is the third side, the one that we do not know.

But there is also a lower restriction, given by:

S2 - S1 < S3 < S1 + S2

This is because we also must have:

S1 + S3 > S2

and

S2 + S3 > S1

We can rewrite both of these to get:

S2 - S1 < S3

S1 - S2 < S3

Because S2 > S1, the first inequality is more restrictive, so we need to use that one.

Then we get the inequality:

S2 - S1 < S3 < S1 + S2

Ok, in this case, the shorter side is 8.0 then:

S1 = 8.0

And the longer side is 8.5, then:

S2 = 8.5

And the third side is x, S3 = x

Replacing those in our inequality, we get:

8.5 - 8.0 < x < 8.5 + 8.0

0.5 < x < 16.5

This is the range of possible sizes for side x.

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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 2 small boxes has a t
nikdorinn [45]

Each large box weighs 15 kilograms and each small box weighs 13.5 kilograms.

Step-by-step explanation:

Let,

Weight of large box = x

Weight of small box = y

According to given statement;

5x+2y=102      Eqn 1

3x+8y=153      Eqn 2

Multiyplying Eqn 1 by 4

4(5x+2y=102)\\20x+8y=408\ \ \ Eqn\ 3

Subtracting Eqn 2 from Eqn 3

(20x+8y)-(3x+8y)=408-153\\20x+8y-3x-8y=255\\17x=255

Dividing both sides by 17

\frac{17x}{17}=\frac{255}{17}\\x=15

Putting x=15 in Eqn 2

15(3)+8y=153\\45+8y=153\\8y=153-45\\8y=108

Dividing both sides by 8

\frac{8y}{8}=\frac{108}{8}\\y=13.5

Each large box weighs 15 kilograms and each small box weighs 13.5 kilograms.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/10541435
  • brainly.com/question/10666510

#LearnwithBrainly

4 0
3 years ago
HELP MARK BRANLIEST AND ALSO POINTS
Taya2010 [7]

Answer:

25 rides

Step-by-step explanation:

has $28.50

15.75 + 0.50r \leq 28.50

Subtract 15.75

0.50r \leq 12.75

r \leq 25.5

you can't have half rides, so 25 rides

4 0
3 years ago
Suppose a normal distribution has a mean of 62 and a standard deviation of
lutik1710 [3]

Answer:

62.5%

Step-by-step explanation:

(56 - 62) / 4 = -1.5 z score = 0.0668

(64 - 62) / 4 = 0.5 z score = 0.6915

0.6915 - 0.0668 = 0.6247

Rounded this becomes 62.5%

7 0
2 years ago
Luis made some trail mix .He mixed 4 2/3 cups of popcorn ,1 1/4 cups of peanuts ,1 1/3 cups of raisins ,and 3/4 cup of sunflower
erastova [34]
I would say the answer is A.
4 0
3 years ago
The Food and Drug Administration (FDA) produces a quarterly report called Total Diet Study. The FDA’s report covers more than 20
pav-90 [236]

Using the normal approximation to the binomial, it is found that:

  • The mean of X is of 52 samples.
  • The standard deviation of X is of 4.2661 samples.
  • 0.0017 = 0.17% probability that less than half without any traces of pesticide.

--------------------------------

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, with mean given by:  

E(X) = np

And standard deviation of:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution  

Z-score formula is used, which, in a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • Each z-score has an associated p-value, which measures the percentile of measure X.

--------------------------------

  • 65% of samples had no pesticide, thus p = 0.65
  • 80 samples, thus n = 80

The mean of X is of:

E(X) = np = 0.65(80) = 52

The standard deviation of X is of:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80(0.65)(0.35)} = 4.2661

Using the approximation and continuity correction, the probability is P(X < 40 - 0.5) = P(X < 39.5), which is the p-value of Z when X = 39.5. Thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{39.5 - 52}{4.2661}

Z = -2.93

Z = -2.93 has a p-value of 0.0017, thus:

0.0017 = 0.17% probability that less than half without any traces of pesticide.

A similar problem is given at brainly.com/question/24261244

8 0
2 years ago
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