All categories

3 years ago

Two sides of a triangle have lengths 11 and 18. Write an inequality to represent the possible lengths for the third side, x.

Mathematics

2 answers:

Hitman42 [59]3 years ago

6 0

Answer: $7$

Step-by-step explanation:

The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

Given: Two sides of a triangle have lengths 11 and 18.

The third side is represented by x.

So by triangle inequality, we have the following inequality:

$x\leq11+18\\\\\Rightarrow\ x\leq29$

Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

$\Rightarrow18-11$

Thus, the inequality to describe the possible side length for the third side is

$7$

KatRina [158]3 years ago

3 0

<span>Side inequality of triangle states that the sum of any two sides of a triangle should be greater than the third side so the sum of two sides

In this case, 11 + 18 = 29 > 3rd side So 29 > 3rd side or we can say 3rd side < 29

Also, the third side cannot be smaller than the difference of the given two sides so the third side has to be greater than 18-11 = 7 so 3rd side > 7 so if length of 3rd side is represented by x, then 7 < x < 29</span>

You might be interested in

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random

g100num [7]

Answer:

97.4% probability

Step-by-step explanation:

Since there is only two possible outcome of inspecting the catridge : either defective or not, we can solve the problem using the binomial probability distribution (approximated to normal).

To approximate the binomial probability to normal, we find the expected value and the standard deviation of the probability of exactly x sucesses on n repeated trials with p probability

Expected values E(X) = np

Standard deviation √V(X) = √np(1-p)

using the z-score formula (X - μ)/σ, we can solve normally distributed problem.

Where μ is the mean and σ is the standard deviation. The Z-score is is the measure of how much a sample is from the mean. The p-value associated with this z-score which is the probability that the value of the measure is smaller than X can be checked on the z-score table.

FOR THIS QUESTION,

a random sample of 200 cartridges is selected

n = 200

Therefore If there are more than 0.02 × 200 = 4 defective, the sample will be returned.

To determine the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05

μ = E(X)

= 0.05 × 200 = 10

σ = √V(X) = √np(1-p)

= √200 × 0.05 × 0.95

= 3.08

This probability is 1 subtracted by the pvalue of Z when X =4

Z = (X - μ)/σ

Z= (4 - 10)/3.08

Z = -1.95

Z = -1.95 has a P-value of 0.026 (on the z-score table)

This means that there is a 1 - 0.026 = 0.974

= 97.4% probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05.

6 0

3 years ago

The difference of two numbers is equal to 0.6. Their quotient is also 0.6. What are the numbers? There are 4

Makovka662 [10]

Let the two numbers be represented by x and y. The problem statement gives rise to two sets of equations.
x - y = 0.6
y/x = 0.6 . . . . . . . assuming x is the larger of the two numbers
or
x/y = 0.6 . . . . . . . assuming y has the larger magnitude

The solution of the first pair of equations is
(x, y) = (1.5, 0.9)

The solution of the first and last equations is
(x, y) = (-0.9, -1.5)

The pairs of numbers could be {0.9, 1.5} or {-1.5, -0.9}.

8 0

3 years ago

1) On a standardized aptitude test, scores are normally distributed with a mean of 100 and a standard deviation of 10. Find the

Musya8 [376]

Answer:

A) 34.13%

B) 15.87%

C) 95.44%

D) 97.72%

E) 49.87%

F) 0.13%

Step-by-step explanation: