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umka21 [38]
4 years ago
14

Which is the function represented by the table? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, neg

ative 1, 0, 1. Column 2 is labeled f (x) with entries negative 8, negative 4, 0, 4.
Mathematics
1 answer:
Serggg [28]4 years ago
7 0

Answer:

f(x)=4x

Step-by-step explanation:

Given: See the attached image

To find: the function represented by the table

Solution:

A function is a relation in which every element of the domain has a unique image in the co-domain.

f(-2)=-8=4(-2)\\f(-1)=-4=4(-1)\\f(0)=0=4(0)\\f(1)=4=4(1)

Here, -2,-1,0,1 are elements in the domain and -8,-4,0,4 are elements in the co-domain.

Therefore, the table represents the function f(x)=4x

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If the graph of y=f(x) passes through the point (0,1), and dy/dx=xsin(x^2)/y, then f(x)= ?
Zigmanuir [339]

The differential equation

d<em>y</em>/d<em>x</em> = <em>x</em> sin(<em>x</em> ²) / <em>y</em>

is separable as

<em>y</em> d<em>y</em> = <em>x</em> sin(<em>x</em> ²) d<em>x</em>

Integrate both sides:

∫ <em>y</em> d<em>y</em> = ∫ <em>x</em> sin(<em>x</em> ²) d<em>x</em>

∫ <em>y</em> d<em>y</em> = 1/2 ∫ 2<em>x</em> sin(<em>x</em> ²) d<em>x</em>

∫ <em>y</em> d<em>y</em> = 1/2 ∫ sin(<em>x</em> ²) d(<em>x</em> ²)

1/2 <em>y</em> ² = -1/2 cos(<em>x</em> ²) + <em>C</em>

Solve for <em>y</em> implicitly:

<em>y</em> ² = -cos(<em>x</em> ²) + <em>C</em>

Given that <em>y</em> = 1 when <em>x</em> = 0, we get

1² = -cos(0²) + <em>C</em>

1 = -cos(0) + <em>C</em>

1 = -1 + <em>C</em>

<em>C</em> = 2

Then the particular solution to the DE is

<em>y</em> ² = 2 - cos(<em>x</em> ²)

Solving explicitly for <em>y</em> would give two solutions,

<em>y</em> = ± √(2 - cos(<em>x</em> ²))

but only the one with the positive square root satisfies the initial condition:

√(2 - cos(0²)) = √1 = 1

-√(2 - cos(0²)) = -√1 = -1 ≠ 1

So the unique solution to this DE is

<em>y</em> = √(2 - cos(<em>x</em> ²))

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Keiko sold 3 less than three-fourths of his sister's sales. Which expression represents what Keiko sold?
lisov135 [29]

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Step-by-step explanation:

Let his sister's sale be represented by x.

Since we are informed that Keiko sold 3 less than three-fourths of his sister's sales, the expression that represents what Keiko sold will be:

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Consider random samples of size 58 drawn from population A with proportion 0.77 and random samples of size 70 drawn from populat
fredd [130]

Answer:

Step-by-step explanation:

a) The formula for determining the standard error of the distribution of differences in sample proportions is expressed as

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where

p1 = sample proportion of population 1

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n1 = number of samples in population 1,

n2 = number of samples in population 2,

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n1 = 58

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Standard error = √{(0.77 - 0.67)/[(0.77)(0.23)/58) + (0.67)(0.33)/70}

= √0.1/(0.0031 + 0.0032)

= √1/0.0063

= 12.6

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Answer:

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Step-by-step explanation:

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