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Use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle. Show all work for full credit.

diamong [38]

Answer: The given triangle LMN is an obtuse-angled triangle.

Step-by-step explanation: We are given to use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle.

From the figure, we note that

in ΔLMN, LM = 5 units, MN = 13 units and LN = 14 units.

We know that a triangle with sides a units, b units and c units (a > b, c) is said to be

(i) Right-angled triangle if $b^2+c^2=a^2,$

(ii) Acute-angled triangle if $b^2+c^2>a^2,$

(iii) Obtuse-angled triangle if $b^2+c^2$

For the given triangle LMN, we have

a = 14, b = 13 and c = 5.

So,

$b^2+c^2=13^2+5^2=169+25=194,\\\\a^2=14^2=196.$

Therefore, $b^2+c^2$

Thus, the given triangle LMN is an obtuse-angled triangle.

5 0

2 years ago

A basketball is rolling with a velocity of 0.5 meters/second relative to the ground and due north. A tennis ball is rolling with

RSB [31]

Ok so let me help you like this: We need to understand first that The basketball has a higher speed, that means that the tennis ball will never catch up. so what we need to use is the formula
Vr=Vb--Vt
=0.5-0.25=0.25
So the speed is 0.25m/s
Hope this is useful

5 0

2 years ago

A study is being conducted in which the health of two independent groups of ten policyholders is being monitored over a one-year

uysha [10]

Answer:

46.91% probability that at least nine participants complete the study in one of the two groups, but not in both groups

Step-by-step explanation:

We use two binomial trials to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

Probability of at least nine participants finishing the study in a group.

0.2 probability of a students dropping out. So 1 - 0.2 = 0.8 probability of a student finishing the study. This means that $p = 0.8$ .

10 students, so $n = 10$

We have to find:

$P(X \geq 9) = P(X = 9) + P(X = 10)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{10,9}.(0.8)^{9}.(0.2)^{1} = 0.2684$

$P(X = 10) = C_{10,10}.(0.8)^{10}.(0.2)^{0} = 0.1074$

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.2684 + 0.1074 = 0.3758$

0.3758 probability that at least nine participants complete the study in a group.

Calculate the probability that at least nine participants complete the study in one of the two groups, but not in both groups?

0.3758 probability that at least nine participants complete the study in a group. This means that $p = 0.3758$

Two groups, so $n = 2$

We have to find P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,1}.(0.3758)^{1}.(0.6242)^{1} = 0.4691$

46.91% probability that at least nine participants complete the study in one of the two groups, but not in both groups

5 0

2 years ago

Read 2 more answers

Cheese costs $4.40 per pound. Find the cost per kilogram. (1kg = 2.2lb)

MakcuM [25]

Answer:

The cost is $9.70 per kilogram.

Step-by-step explanation:

This can be solved by a rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In this problem, the measures are the weight of the cheese and the price. As the weight increases, so does the price. It means that this is a direct rule of three.

Solution:

The problem states that cheese costs $4.40 per pound. Each kg has 2.2 pounds. How many kg are there in 1 pound. So:

1 pound - xkg

2.2 pound - 1 kg

$2.2x = 1$

$x = \frac{1}{2.2}$

$x = 0.45$ kg

Since cheese costs $4.40 per pound, and each pound has 0.45kg, cheese costs $4.40 per 0.45kg. How much does is cost for 1kg?

$4.40 - 0.45kg

$x - 1kg

$0.45x = 4.40$

$x = \frac{4.40}{0.45}$

$x = 9.70$

The cost is $9.70 per kilogram.

6 0

2 years ago

Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.

butalik [34]

(a) Data with the eight day's measurement.
Raw data: [60,58,64,64,68,50,57,82],
Sorted data: [50,57,58,60,64,64,68,82]
Sample size = 8 (even)
mean = 62.875
median = (60+64)/2 = 62
1st quartile = (57+58)/2 = 57.5
3rd quartile = (64+68)/2 = 66
IQR = 66 - 57.5 = 8.5

(b) Data without the eight day's measurement.
Raw data: [60,58,64,64,68,50,57]
Sorted data: [50,57,58,60,64,64,68]
Sample size = 7 (odd)
mean = 60.143
median = 60
1st quartile = 57
3rd quartile = 64
IQR = 64 -57 = 7

Answers:
1. The average is the same with or without the 8th day's data. FALSE
2. The median is the same with or without the 8th day's data. FALSE
3. The IQR decreases when the 8th day is included. FALSE
4. The IQR increases when the 8th day is included. TRUE
5. The median is higher when the 8th day is included. TRUE

8 0

2 years ago

Read 2 more answers