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valkas [14]
2 years ago
5

3

Mathematics
1 answer:
dem82 [27]2 years ago
8 0

Answer:

y = 2x - 19

Step-by-step explanation:

Slope-intercept form: y = mx + b

y = (x , y) = 1

m = slope = 2

x = (x , y) = 10

b = y-intercept

Plug in the corresponding numbers to the corresponding variables:

1 = 2(10) + b

First, simplify, and then isolate the variable, b. Note the equal sign, what you do to one side, you do to the other.

First, multiply 2 with 10:

1 = (2 * 10) + b

1 = 20 + b

Next, subtract 20 from both sides of the equation:

1 = b + 20

1 (-20) = b + 20 (-20)

1 - 20 = b

b = -19

Plug in 2 for m, and -19 for b.

y = 2x - 19 is your slope-intercept form.

~

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First option: 14.0 cm^2

Area of semicircle + area of triangle
1/2(pi)(r^2) + 1/2(b)(h)
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Answer:

6.2

Step-by-step explanation:

Although there's multiple ways to solve this problem, my method will be to simply find the area for the full triangle (the empty + orange triangles) and subtract the area of the smaller, empty triangle.

Now, you that area for a triangle is 1/2*base*height.

To find the measurements for the full triangle, you must add up the bases for the two smaller triangles:

Base_{total}  = Base_{empty} + Base_{orange}  \\Base_{total} = 1.9ft + 3.1 ft\\Base_{total} = 5 ft

Height is the same for both triangles so Height total = 4 ft.

Now the total area can be calculated:

Area total= 1/2* base_total * height_total

Area total = 1/2 * 5ft * 4 ft  

Area total = 20 / 2 = 10 ft squared

Lastly, subtract the area of the empty triangle from the total triangle to find the orange triangle.

Area Empty Triangle = 1/2 * base_empty * height_empty

Area Empty Triangle = 1/2 * 1.9ft * 4 ft = 7.6 ft / 2 = 3.8 ft squared

Area total - Area empty = 10ft^2 - 3.8ft^2 = 6.2 ft squared

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3 years ago
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A frog moves in a sequence of unit steps. Each step is N, S, E or W with equal probability. It starts at the origin. Find the pr
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The answer is 067.

It takes an even number of steps for the object to reach (2,2), so the number of steps the object may have taken is either 4 or 6 .

If the object took 4 steps, then it must have gone two steps $\mathrm{N}$ and two steps E, in some permutation. There are $\frac{4 !}{2 ! 2 !}=6$ ways for these four steps of occuring, and the probability is $\frac{6}{4^{4}}$.

If the object took 6 steps, then it must have gone two steps N and two steps E, and an additional pair of moves that would cancel out, either N / S or W/E. The sequences N, N, N, E, E, S can be permuted in $\frac{6 !}{3 ! 2 ! 1 !}=60$ ways. However, if the first four steps of the sequence are N, N, E, E in some permutation, it would have already reached the point (2,2) in four moves. There are $\frac{4 !}{2 ! 2 !}$ ways to order those four steps and $2 !$ ways to determine the order of the remaining two steps, for a total of 12 sequences that we have to exclude. This gives $60-12=48$ sequences of steps. There are the same number of sequences for the steps N, N, E, E, E, W, so the probability here is $\frac{2 \times 48}{4^{6}}$.

The total probability is $\frac{6}{4^{4}}+\frac{96}{4^{6}}=\frac{3}{64}$, and $m+n=067$.

What is probability?

  • Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one.
  • Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur.
  • This is the fundamental probability theory, which is also utilized in probability distribution, in which you will learn about the possible results of a random experiment.
  • To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

To learn more about probability visit:

brainly.com/question/11234923

#SPJ4

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