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Anastaziya [24]
3 years ago
6

If f(x) is a parabola with vertex (2,−1) whose equation isf(x) =ax2+bx+c, what are the values of a, b, c if the graph off inters

ects the y-axis at the point (0,3).

Mathematics
1 answer:
Masja [62]3 years ago
6 0

Answer:

(a, b, c) = (1, -4, 3)

Step-by-step explanation:

In vertex form, the equation is ...

... f(x) = a(x -2)² -1

This has a y-intercept of ...

... f(0) = a(0 -2)² -1 = 4a -1

We want that value to be 3, so we can find "a" as ...

... 4a -1 = 3 . . . . . set f(0) = 3

... 4a = 4 . . . . . . . add 1

... a = 1 . . . . . . . . divide by 4

Then ...

... f(x) = (x -2)² -1 = x² -4x +3

The coefficients are a=1, b=-4, c=3.

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It is correct to state that a bit can be in one of 2 states, either 1 or 0.

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A bit is is a single binary digit. A bit can either be "1" or "0".

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We stated that It is correct to indicate that a bit can be in one of 2 states, either 1 or 0. This indicates that 2ⁿ strings must be created in total. The string must then be processed twice.

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Simplify 36*3.<br> O A. 35<br> B. 36<br> O C. 37<br> O D. 96<br> HELP ME
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Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam
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Answer:

P(A) = \frac{30}{100}

P(B) = \frac{77}{100}

P(A\ n\ B) = \frac{22}{100}

P(A\ u\ B) = \frac{85}{100}

Step-by-step explanation:

Given

See attachment for proper format of table

n = 100 --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

In this row:

Yes = 22 and No = 8

So, we have:

n(A) = Yes + No

n(A) = 22 + 8

n(A) = 30

P(A) is then calculated as:

P(A) = \frac{n(A)}{Sample}

P(A) = \frac{30}{100}

Solving (b): P(B)

Here, we only consider data in the Yes column.

In this column:

(1) = 22    (2) = 25 and (3) = 30

So, we have:

n(B) = (1) + (2) + (3)

n(B) = 22 + 25 + 30

n(B) = 77

P(B) is then calculated as:

P(B) = \frac{n(B)}{Sample}

P(B) = \frac{77}{100}

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

This cell is: [Supplier 1][Yes]

And it is represented with; n(A n B)

So, we have:

n(A\ n\ B) = 22

The probability is then calculated as:

P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}

P(A\ n\ B) = \frac{22}{100}

Solving (d): P(A u B)

This is calculated as:

P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)

This gives:

P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}

Take LCM

P(A\ u\ B) = \frac{30+77-22}{100}

P(A\ u\ B) = \frac{85}{100}

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