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3 years ago

PLEASE HELP 25 POINTS

Mathematics

1 answer:

Monica [59]3 years ago

8 0

Answer:

Step-by-step explanation:

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What is the value of x in 2(5x) = 14? A. 0.34 B. 1.15 C. 1.21 D. 219.33

viva [34]

Answer:

C. 1.21 I think

Step-by-step explanation:

8 0

3 years ago

Jamiah bought two 125 ounce bags of flour for baking. He used up 32 ounces of flour to bake a batch of brownies. How much flour

V125BC [204]

Answer: its 218

Step-by-step explanation: you just have to subtract 250 minus 32

7 0

1 year ago

Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is t

Aneli [31]

Answer:

Not sufficient information

Step-by-step explanation:

Probability of white ball: P(W)

Probability of even number: P(E)

Probability of white ball or even number: P(W∨E) is asked

Considering case (1):

Probability of white ball and even number: P(W∧E) = 0

And we know that,

P(W∨E) = P(W) + P(E) - P(W∧E) = P(W) + P(E) - 0 = P(W) + P(E)

It is not sufficient to calculate the desired probability.

Considering case (2):

P(W) - P(E) = 0.2

Here, it is possible for P(W) and P(E) to get multiply values.

So P(W∨E) cannot be determined.

Considering cases (1) & (2):

P(W∧E) = 0 and P(W) - P(E) = 0.2

So, P(W∨E) = P(W) + P(E) = P(E) + 0.2 + P(E) = 2P(E) + 0.2

Again multiple answers are possible.

Such as, for P(E) = 0.4 (10 even balls) ⇒ P(W∨E) = 1

but for P(E) = 0.2 (5 even balls) ⇒ P(W∨E) = 0.6

So, the information are not sufficient.

3 0

3 years ago

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$