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2 years ago

Help me please!!!!!!!!!!!!!

Mathematics

2 answers:

Virty [35]2 years ago

5 0

Hiiiiiii

The answer is 1 1/9

Arada [10]2 years ago

4 0

Your answer is 1 1
9

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How to solve logarithmic equations as such

Serga [27]

$\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \log_2(x-1)=\log_8(x^3-2x^2-2x+5) \\\\\\ \log_2(x-1)=\log_{2^3}(x^3-2x^2-2x+5) \\\\\\ \log_{2^3}(x^3-2x^2-2x+5)=\log_2(x-1) \\\\\\ \stackrel{\textit{writing this in exponential notation}}{(2^3)^{\log_2(x-1)}=x^3-2x^2-2x+5}\implies (2)^{3\log_2(x-1)}=x^3-2x^2-2x+5$

$\bf (2)^{\log_2[(x-1)^3]}=x^3-2x^2-2x+5\implies \stackrel{\textit{using the cancellation rule}}{(x-1)^3=x^3-2x^2-2x+5} \\\\\\ \stackrel{\textit{expanding the left-side}}{x^3-3x^2+3x-1}=x^3-2x^2-2x+5\implies 0=x^2-5x+6 \\\\\\ 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}$

5 0

3 years ago

Angelo is making a rectangular floor for a clubhouse with an area of 84 square feet. The length if each side of the floor is a w

Alexxandr [17]

Answer:

L=1 ft and B=84 ft

L=2 ft and B=42 ft

L=4ft and B=21ft

L=6ft and B=14 ft

L=7ft and B=12ft

L=12 ft and B=7ft

L=14ft and B=6 ft

L=21 ft and B=4 ft

L=42 ft and B=2 ft

L=84 ft and B=1 ft

Step-by-step explanation:

We are given that

Area of rectangular floor=84 square feet

We have to find the possible length and width of for Angelo's clubhouse.

Area of rectangle= $length\times breadth$

Using the formula

Area of rectangular floor for clubhouse=84 square feet

$Length(L)\times breadth(B)=84$

Factor of 84 are

1,2,4,6,7,12,14,21,42,84

Therefore, possible dimension of rectangular floor

$1ft\times 84ft,2ft\times 42ft,4ft\times 21ft,6ft\times 14ft,7ft\times 12ft,12ft\times 7ft,14ft\times 6ft,21ft\times 4ft,42ft\times 2ft,84ft\times 1ft$

L=1 ft and B=84 ft

L=2 ft and B=42 ft

L=4ft and B=21ft

L=6ft and B=14 ft

L=7ft and B=12ft

L=12 ft and B=7ft

L=14ft and B=6 ft

L=21 ft and B=4 ft

L=42 ft and B=2 ft

L=84 ft and B=1 ft

5 0

2 years ago

OC and OR are similar. Find the length of QP.

Elena L [17]

Given:

Circle C and circle R are similar.

The length of arc AB is $s = \frac{22 \pi}{9}$

The radius of circle C (AC) = 4 unit

The radius of circle R (QR) =6 unit

To find the length of arc QP.

Formula

The relation between s, r and $\theta$ is

$arclength = 2\pi r \frac{\theta}{360}$

where,

s be the length of the arc

r be the radius

$\theta$ be the angle.

Now,

For circle C

Taking r = 4

According to the problem,

$2 \pi r \frac{\theta}{360} = \frac{22 \pi}{9}$

or, $2r \frac{\theta}{360} = \frac{22}{9}$ [ eliminating $\theta$ from both side]

or, $\theta = \frac{(22)(360)}{(9)(2)(4)}$

or, $\theta = 110^\circ$

Again,

For circle R

Taking, r = 6 and $\theta = 110^\circ$ we get,

The length of arc QP is

$arc length = 2\pi (6)(\frac{110}{360} )$

or, $arclength = \frac{11 \pi}{3}$

Hence,

The length of QP is $\frac{11 \pi}{3}$ . Option C.

5 0

2 years ago

Suppose that a recent poll found that 49% of adults believe that the overall state of moral values is poor. Complete parts (a)

Lunna [17]

Answer:

The mean of X is 122.5 and the standard deviation is 7.9.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they believe that the overall state of moral values is poor, or they do not believe this. The probability of an adult believing this is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$