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Agata [3.3K]
3 years ago
11

Write the expression 44(4–7)(4) using a single exponent.

Mathematics
2 answers:
Ghella [55]3 years ago
8 0
<h3>The given expression as single exponent is:</h3>

4^4 \times 4^{-7} \times 4 = 4^{-2}

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

4^4 \times 4^{-7} \times 4

In exponents,

When the base is same, exponents can be added

Which means,

a^m \times a^n = a^{m+n}

Therefore,

4^4 \times 4^{-7} \times 4 = 4^{4-7+1}\\\\Simplify\\\\4^4 \times 4^{-7} \times 4 = 4^{-3+1} \\\\4^4 \times 4^{-7} \times 4 = 4^{-2}

Thus the given expression as single exponent is:

4^4 \times 4^{-7} \times 4 = 4^{-2}

jek_recluse [69]3 years ago
5 0

Answer:

D). 4^-2

Step-by-step explanation:

Just did it on edge.

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Find the value of x. 50 points
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Suppose that the functions q and r are defined as follows.
satela [25.4K]

Answer:

(r o g)(2) = 4

(q o r)(2) = 14

Step-by-step explanation:

Given

g(x) = x^2 + 5

r(x) = \sqrt{x + 7}

Solving (a): (r o q)(2)

In function:

(r o g)(x) = r(g(x))

So, first we calculate g(2)

g(x) = x^2 + 5

g(2) = 2^2 + 5

g(2) = 4 + 5

g(2) = 9

Next, we calculate r(g(2))

Substitute 9 for g(2)in r(g(2))

r(q(2)) = r(9)

This gives:

r(x) = \sqrt{x + 7}

r(9) = \sqrt{9 +7{

r(9) = \sqrt{16}{

r(9) = 4

Hence:

(r o g)(2) = 4

Solving (b): (q o r)(2)

So, first we calculate r(2)

r(x) = \sqrt{x + 7}

r(2) = \sqrt{2 + 7}

r(2) = \sqrt{9}

r(2) = 3

Next, we calculate g(r(2))

Substitute 3 for r(2)in g(r(2))

g(r(2)) = g(3)

g(x) = x^2 + 5

g(3) = 3^2 + 5

g(3) = 9 + 5

g(3) = 14

Hence:

(q o r)(2) = 14

8 0
2 years ago
Refer to the previous exercise. The researchers wanted a sufficiently large sample to be able to estimate the probability of pre
Maru [420]

Answer:

<em>The large  sample n = 117.07</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the estimate error (M.E) = 0.08

The proportion (p) = 0.75

q =1-p = 1- 0.75 =0.25

Level of significance = 0.05

Z₀.₀₅ = 1.96≅ 2

<u><em>Step(ii):-</em></u>

The Marginal error is determined by

M.E = \frac{Z_{0.05} \sqrt{p(1-p)}  }{\sqrt{n} }

0.08 = \frac{2 X \sqrt{0.75(1-0.75)}  }{\sqrt{n} }

Cross multiplication , we get

\sqrt{n}  = \frac{2 X \sqrt{0.75(1-0.75)}  }{0.08 }

√n = \frac{2 X0.4330}{0.08} = 10.825

squaring on both sides , we get

n = 117.07

<u><em>Final answer:-</em></u>

<em>The large  sample n = 117.07</em>

6 0
2 years ago
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