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2 years ago

Consider the diagram and proof by contradiction.

Mathematics

2 answers:

WARRIOR [948]2 years ago

8 0

by the converse of the triangle parts relationship theorem. ed2020

uranmaximum [27]2 years ago

5 0

The Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side.

The converse to the Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one angle of a triangle has a greater degree measure than another angle, then the side opposite the greater angle will be longer than the side opposite the smaller angle.

Thus, from the proof if AB > AC, then m∠C > m∠B by the converse of the triangle parts relationship theorem.

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The brass strip AB has been attached to a fixed support at A and rests on a rough support at B. Knowing that the coefficient of

Andre45 [30]

Answer:

Decrease in temperature = 4.6714°C

Step-by-step explanation:

We know that the formula fro deflection is:

δ = PL/AE + LαΔT

As deflection is equal to zero in this case, the formula becomes

ΔT = -P/αAE -------------- equation (1)

Now,

we see that only vertical force acting is weight

W = mg = 100*9.81

W = 981N = ∑ $F_{y}$ where 1N = 1kgm/s²

Now,

for horizontal forces

As we know that, Sum of all horizontal forces = 0

P - μN = 0

P - μW = 0

P = μW

P = 0.6 * 981

P = 588.8N or 589N

Now we need to calculate the area

area = width * thickness = 20 * 3

area = 60 mm²

Now by substituting all these values in equation 1, wee get

ΔT = -P/αAE = - 588.6/(20*10⁻⁶*60*10⁻⁶*105*10⁹)

ΔT = - 4.6714°C (negative sign indicates decrease)

7 0

2 years ago

The volume V (in cubic feet) of a right cylinder with a height of 3 feet and radius r (in feet) is given by V=3πr2. Solve the fo

makkiz [27]

Answer:

118. The radius is 118 feet.

Step-by-step explanation:

6 0

2 years ago

A really bad carton of eggs contains spoiled eggs. An unsuspecting chef picks eggs at random for his ""Mega-Omelet Surprise."" F

Dima020 [189]

Answer:

(a) The probability that of the 5 eggs selected exactly 5 are unspoiled is 0.0531.

(b) The probability that of the 5 eggs selected 2 or less are unspoiled is 0.3959.

Step-by-step explanation:

The complete question is:

A really bad carton of 18 eggs contains 8 spoiled eggs. An unsuspecting chef picks 5 eggs at random for his “Mega-Omelet Surprise.” Find the probability that the number of unspoiled eggs among the 5 selected is

(a) exactly 5

(b) 2 or fewer

Let X = number of unspoiled eggs in the bad carton of eggs.

Of the 18 eggs in the bad carton of eggs, 8 were spoiled eggs.

The probability of selecting an unspoiled egg is:

$P(X)=p=\frac{10}{18}=0.556$

A randomly selected egg is unspoiled or not is independent of the others.

It is provided that a chef picks 5 eggs at random.

The random variable X follows a Binomial distribution with parameters n = 5 and p = 0.556.

The success is defined as the selection of an unspoiled egg.

The probability mass function of X is given by:

$P(X=x)={5\choose x}(0.556)^{x}(1-0.556)^{5-x};\ x=0,1,2,3...$

(a)

Compute the probability that of the 5 eggs selected exactly 5 are unspoiled as follows:

$P(X=5)={5\choose 5}(0.556)^{5}(1-0.556)^{5-5}\\=1\times 0.05313\times 1\\=0.0531$

Thus, the probability that of the 5 eggs selected exactly 5 are unspoiled is 0.0531.

(b)

Compute the probability that of the 5 eggs selected 2 or less are unspoiled as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$=\sum\imits^{2}_{x=0}{{5\choose 5}(0.556)^{5}(1-0.556)^{5-5}}\\=0.0173+0.1080+0.2706\\=0.3959$

Thus, the probability that of the 5 eggs selected 2 or less are unspoiled is 0.3959.

(c)

Compute the probability that of the 5 eggs selected more than 1 are unspoiled as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-\sum\limits^{1}_{x=0}{{5\choose 5}(0.556)^{5}(1-0.556)^{5-5}}\\=1-0.0173-0.1080\\=0.8747$

Thus, the probability that of the 5 eggs selected more than 1 are unspoiled is 0.8747.

6 0

2 years ago

a water tank holds 24,000 gallons how many hours will it take for two thirds of the water to be used if the water is used at an

melomori [17]

In this question there are several important information's worth noting.Based on these information's the answer can be easily found. It is given that the total capacity of the tank is 24000 gallons. in 24 hours or in 1 day the amount of water used is 650 gallons. The question requires us to find the time it will take to use 2/3 rd of the water in the tank.
then
2/3 rd water in respect to total water in tank = (2/3) * 24000
= 16000
So 2/3 rd water of full tank is equivalent to 16000 gallons.
Now
650 gallons of water is used in = 24 hours
So
16000 gallons of water will be used in = (24/650) * 16000
= 590.77 hours
So it will take 590.77 hours to consume 2/3rd of the total water present in the tank.

6 0

2 years ago

Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately_______ .

Julli [10]

In this question , we have a graph given, and we have to find the x coordinate of the intersection point .

From the graph , the input value is approximately 3.3 .

In the graph,

$f(x) =3$