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3 years ago

2x-8y=-24 6x+4y=68 Using elimination method

1 answer:

4 0

6(2x-8y=-24)
-2 (6x+4y=68)
12x-48y=-144
-12x-8y=-136
-56y=-280

-280÷-56=5
y=5

2x-8 (5)=-24
2x-40=-24
+40. +40
2x=16
16÷2=8
×=8

y=5
x=8
hope this helps, if needed a picture for better understanding,please comment.

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Find the surface area of the regular pyramid

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24ft^2 I think this is right :)

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3 years ago

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"What is the probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice? Assume you’re throwing a single d

dem82 [27]

Answer:

There is a 51.61% probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice.

Step-by-step explanation:

For each throw, there are only two possible outcomes. Either it is a '3', or it is not. This means that we solve this problem using the binomial probability distribution.

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 combinatios 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.

In this problem we have that:

There are 6 possible outcomes for the dice. This means that the probability that it is a '3' is $\frac{1}{6} = 0.167$

There are 10 throws, so $n = 10$ .

Probability of throwing AT LEAST two ‘3’s on the dice?

Either you throw less than two, or you throw at least two. The sum of the probabilities of these events is 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$ .

In which

$P(X < 2) = P(X = 0) + P(X = 1)$ .

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

$P(X = 0) = C_{10,0}.(0.167)^{0}.(0.833)^{10} = 0.1609$

$P(X = 1) = C_{10,1}.(0.167)^{1}.(0.833)^{9} = 0.3225$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.1609 + 0.3225 = 0.4834$ .

Finally:

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4839 = 0.5161$ .

There is a 51.61% probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice.

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3 years ago

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4 years ago

Given the following sequence, find the 23rd term: 3, 5, 7, 9, 11, . . .

sashaice [31]

Answer:

B. 47

Step-by-step explanation:

The formula for an arithmetic sequence is

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a1 =3 (it is the first term)

We can find the common difference by taking the second term and subtracting the first term

5-3 =2

d=2

n = the term number we are looking for

an = 3 + 2(n-1)

We are looking for the 23rd term so n=23

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A rectangle has length x and width x – 3. The area of the rectangle is 10 square meters. Complete the work to find the dimension

Tamiku [17]

Answer:

Step-by-step explanation:

Area of rectangle = Length × Width

The given rectangle has a length if x meters

The width of the triangle is (x-3) meters

The area of the rectangle is given as 10 square meters.

Area if rectangle = x(x-3) = 10

Multiplying each term in the parentheses,

x^2 -3x = 10

x^2 -3x -10 = 0

This is a quadratic equation

We will look for two numbers such that when they are multiplied, it will give us -10x^2 and when they are added, it will give -3x. It becomes

x^2 + 2x - 5x -10 = 0

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The length of the rectangle cannot be negative so the length is 5 meters

Widith = x+3 = 5-3 = 2 meters

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