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1 year ago

The rectangle ABCD shown in the diagram is reflected across the line y = 2. What

Mathematics

1 answer:

kobusy [5.1K]1 year ago

3 0

Answer:

Since you haven't attached the diagram here, I'll go over how to do this in general. In order to reflect the rectangle across the horizontal line drawn at y = 2, consider the number of units of each coordinate from this line of reflection. Now count the same number of units on the other side of the line to plot the coordinates of the reflected rectangle. For example, if point A was at (1, 5), the point A' would then be at (1, -1). Notice that the x-coordinate remains the same.

Hope that answers the question, have a great day!

You might be interested in

A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into t

Svet_ta [14]

Answer:

$F_w=9408\ N$

Weight of the truck=9408 N

Step-by-step explanation:

Boat is experiencing the buoyant force as it is in the water and is sinking

According to the force balance in y direction. As both is floating, two forces balance each other:

$F_b-F_w=0$

where:

$F_b$ is the buoyant force

$F_w$ is the weight=mg

$F_b=F_w$ Eq (1)

Buoyant force is equal to the mass of water displaced * gravitational acceleration.

$F_b=m_{water\ displaced}*g\\F_b=\rho Vg\\$

Taking density of water to be 1000 Kg/m^3

$F_b=1000*(6*4*4*10^{-2})*9.8\\F_b=9408 N$

From Eq(1):

$F_w=9408\ N$

Weight of the truck=9408 N

6 0

2 years ago

Customers are used to evaluate a preliminary product design. In the past, 95% of highly successful products received good review

Sever21 [200]

Answer:

a. 61.5%; b. About 61.8%; c. About 36.4%

Step-by-step explanation:

This is a kind of question that we can solve using the Bayes' Theorem. We have here all the different conditional probabilities we need to solve this problem.

According to that theorem, the probability of a selected product attains a good review is:

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$ (1)

In words, the probability that a selected product attains a <em>good review</em> is an <em>event </em>that depends upon the sum of the conditional probabilities that the product comes from <em>high successful product</em> P(G|H) by the probability that this product is a <em>highly successful product</em> P(H), plus the same about the rest of the probabilities, that is, P(G|M)*P(M) or the probability that the product has a good review coming from a <em>moderately successful</em> product by the probability of being moderately successful, and a good review coming from a poor successful product by the probability of being poor successful or P(G|P)*P(P).

<h3>The probability that a randomly selected product attains a good review</h3>

In this way, the probability that a randomly selected product attains a good review is the result of the formula (1). Where (from the question):

P(G|H) = 95% or 0.95 (probability of receiving a good review being a highly successful product)

P(G|M) = 60% or 0.60 (probability of receiving a good review being a moderately successful product)

P(G|P) = 10% or 0.10 (probability of receiving a good review being a poorly successful product)

P(H) = 40% or 0.40 (probability of being a highly successful product).

P(M) = 35% or 0.35 (probability of being a moderately successful product).

P(P) = 25% or 0.25 (probability of being a poor successful product).

Then,

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$

$\\ P(G) = 0.95*0.40 + 0.60*0.35 + 0.10*0.25$

$\\ P(G) = 0.615\;or\; 61.5\%$

That is, <em>the probability that a randomly selected product attains a good review</em> is 61.5%.

<h3>The probability that a new product attains a good review is a highly successful product</h3>

We are looking here for P(H|G). We can express this probability mathematically as follows (another conditional probability):

$\\ P(H|G) = \frac{P(G|H)*P(H)}{P(G)}$

We can notice that the probability represents a fraction from the probability P(G) already calculated. Then,

$\\ P(H|G) = \frac{0.95*0.40}{0.615}$

$\\ P(H|G) =\frac{0.38}{0.615}$

$\\ P(H|G) =0.618$

Then, the probability of a product that attains a good review is indeed a highly successful product is about 0.618 or 61.8%.

<h3>The probability that a product that <em>does not attain </em>a good review is a moderately successful product</h3>

The probability that a product does not attain a good review is given by a similar formula than (1). However, this probability is the complement of P(G). Mathematically:

$\\ P(NG) = P(NG|H)*P(H) + P(NG|M)*P(M) + P(NG|P)*P(P)$

P(NG|H) = 1 - P(G|H) = 1 - 0.95 = 0.05

P(NG|M) = 1 - P(G|M) = 1 - 0.60 = 0.40

P(NG|P) = 1 - P(G|M) = 1 - 0.10 = 0.90

$\\ P(NG) = 0.05*0.40 + 0.40*0.35 + 0.90*0.25$

$\\ P(NG) = 0.385\;or\; 38.5\%$

Which is equal to

P(NG) = 1 - P(G) = 1 - 0.615 = 0.385

Well, having all this information at hand:

$\\ P(M|NG) = \frac{P(NG|M)*P(M)}{P(NG)}$

$\\ P(M|NG) = \frac{0.40*0.35}{0.385}$

$\\ P(M|NG) = \frac{0.14}{0.385}$

$\\ P(M|NG) = 0.363636... \approx 0.364$

Then, the <em>probability that a new product does not attain a good review and it is a moderately successful product is about </em>0.364 or 36.4%.

8 0

1 year ago

Most everyday situations involving chance and likelihood are examples of ______. simple probability permutations conditional pro

Fynjy0 [20]

Answer:

Most everyday situations involving chance and likelihood are examples of simple probability.

Explanation:

The probability is the chance or likelihood of any event happening. In our everyday life, we unintentionally use the probability. For example, we say there is 70% chance that tomorrow will be rain, there is 50% chance that Brazil will win the world cup, there is less likelihood of he arriving today and soon. In all these concepts we are dealing with uncertainty and there is chance factor involved in all these examples. So in most everyday situations which involve chance and likelihood are actually examples of simple probability.

6 0

1 year ago

What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2

Margaret [11]

<u>Answer-</u>

$\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}$

<u>Solution-</u>

Given expression is $(x+2)^4$

Applying Binomial Theorem

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

Here,

a = x, b = 2 and n = 4

So,

$\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i$

Expanding the summation

$=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4$

$=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4$