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4 years ago

Express 16=2x as a logarithmic equation

Mathematics

1 answer:

Andrews [41]4 years ago

6 0

Convert the exponential equation to a logarithmic equation using the logarithm base

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of the right side

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equals the exponent

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log

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<img src="https://tex.z-dn.net/?f=7%20%7Bx%7D%5E%7B3%7D%20%20%2B%204x%20-%205%20%2B%208%20%7Bx%7D%5E%7B5%7D%20" id="TexFormula1"

elixir [45]

Answer:

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of a term within the polynomial.

Given

7x³ + 4x - 5 + 8 $x^{5}$

The term with the largest exponent is 8 $x^{5}$ with exponent 5

Thus the polynomial is of degree 5 → D

3 0

3 years ago

Josea went out to dinner to an Indian restaurant. The total bill was $38 .she wanted to leave a 20% tip

jekas [21]

Answer:

$20?

Step-by-step explanation:

6 0

3 years ago

What is the sum of the interior angles of a nonagon?

SSSSS [86.1K]

To find the sum of the interior angles of a nonagon, divide it up into triangles... There are seven triangles... Because the sum of the angles of each triangle is 180 degrees... We get

7 * 180 = 1260°

So, the sum of the interior angles of a nonagon is 1260 degrees.

3 0

3 years ago

Read 2 more answers

Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In p

Bingel [31]

Answer:

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is significant difference between in drug resistance between the two states

B)

The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance

Rejected H₀

There is a significant difference in drug resistance between the two states.

P - value = 0.0066

P - value = 0.0066 < 0.02

D)

1) Reject H₀

There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 174

Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant.

First sample proportion

$p_{1} = \frac{x_{1} }{n_{1} } = \frac{11}{174} = 0.0632$

Given second sample size n₂ = 375

Given data Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant

Second sample proportion

$p_{2} = \frac{x_{2} }{n_{2} } = \frac{7}{375} = 0.0186$

Step(ii):-

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is significant difference between in drug resistance between the two states

Test statistic

$Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

Where

$P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }$

$P = \frac{174 (0.0632) + 375 (0.0186) }{174+375 } = \frac{17.9718}{549} = 0.0327$

Q = 1 - P = 1 - 0.0327 = 0.9673

Step(iii):-

Test statistic

$Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

$Z = \frac{0.0632-0.0186 }{\sqrt{0.0327 X 0.9673(\frac{1}{174 }+\frac{1}{375 } ) } }$

Z = 2.7261

Level of significance = 0.02 or 0.98

The z-value = 2.054

The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance

Reject H₀

There is a significant difference in drug resistance between the two states.

P- value

P( Z > 2.7261) = 1 - P( Z < 2.726)

= 1 - ( 0.5 + A (2.72))

= 0.5 - 0.4967

= 0.0033

we will use two tailed test

2 P( Z > 2.7261) = 2 × 0.0033

= 0.0066

P - value = 0.0066 < 0.02

Reject H₀

There is a significant difference in drug resistance between the two states.

8 0

3 years ago

Find two positive numbers whose product is 25 and whose sum is a minimum. (if both values are the same number, enter it into bot

pshichka [43]

Let xy = 25, x and y > 0.

$y = \frac{25}{x}$
$\text{Denote S as: } x + y$
$S(x) = x + \frac{25}{x}$

$\text{Minimum: }S'(x) = 0, S''(x) > 0$
$S'(x) = 1 - \frac{25}{x^{2}}$
$1 - \frac{25}{x^{2}} = 0$
$x^{2} = 25$
$x = 5 (x > 0)$

$S''(x) = \frac{50}{x^{3}} > 0, (x > 0)$

Thus, at x = 5, there lies a minimum summation, and this forms a square with side length of 5.

4 0

4 years ago