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4 years ago

Solve the equation 7-2log3(1/4x)=11

Mathematics

1 answer:

valentina_108 [34]4 years ago

4 0

Answer:

$\large\boxed{x=\dfrac{4}{9}}$

Step-by-step explanation:

$Domain:\dfrac{1}{4}x>0\to x>0\\\\Use\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\\\\a^{-n}=\dfrac{1}{a^n}\\=======================\\\\7-2\log_3\left(\dfrac{1}{4}x\right)=11\qquad\text{subtract 7 from both sides}\\\\-2\log_3\left(\dfrac{1}{4}x\right)=4\qquad\text{divide both sides by (-2)}\\\\\log_3\left(\dfrac{1}{4}x\right)=-2\iff\dfrac{1}{4}x=3^{-2}\\\\\dfrac{1}{4}x=\dfrac{1}{3^2}\\\\\dfrac{1}{4}x=\dfrac{1}{9}\qquad\text{multiply both sides by 4}\\\\x=\dfrac{4}{9}\in D$

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Need help with dividing integer questions

lord [1]

8/2 is 4 and -10 + -2 is -12 because your adding two negatives

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3 years ago

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Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an lg sm

GuDViN [60]

Answer: 0.951%

Explanation:

Note that in the problem, the scenario is either the adult is using or not using smartphones. So, we have a yes or no scenario involved with the random variable, which is the number of adults using smartphones. Thus, the number of adults using smartphones follows the binomial distribution.

Let x be the number of adults using smartphones and n be the number of randomly selected adults. In Binomial distribution, the probability that there are k adults using smartphones is given by

$P(x = k) = \frac{n!}{k!(n-k)!}p^k (1-p)^{n-k}$

Where p = probability that an adult is using smartphones = 54% (since 54% of adults are using smartphones).

Since n = 12 and k = 3, the probability that fewer than 3 are using smartphones is given by

$P(x \ \textless \ 3) = P(x = 0) + P(x = 1) + P(x = 2)
\\ \indent = \frac{12!}{0!(12-0)!}(0.54)^0 (1-0.54)^{12-0} + \frac{12!}{1!(12-1)!}(0.54)^1 (1-0.54)^{12-1} + \\ \indent \frac{12!}{2!(12-2)!}(0.54)^2 (1-0.54)^{12-2}
\\
\\ \indent = \frac{12!}{(1)(12!)}(0.46)^{12} + \frac{12(11!)}{(1)(11!)}(0.54)(0.46)^{11}+ \frac{12(11)(10!)}{(2)(10!)}(0.54)^2(0.46)^{10}
\\
\\ \indent = (1)(0.46)^{12} + (12)(0.54)(0.46)^{11}+ (66)(0.54)^2(0.46)^{10}
\\ \indent \boxed{P(x \ \textless \ 3) \approx 0.00951836732 }
$

Therefore, the probability that there are fewer than 3 adults are using smartphone is 0.00951 or 0.951%.

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4 years ago

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3 years ago

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What is the quotient of 4 1/4 / 2 1/5

Snezhnost [94]

The quotient for the given mixed fraction is 1.9318

Step-by-step explanation:

Step 1; First we must convert the mixed fractions into improper fractions. To do that the whole number is multiplied with the denominator and add with it the numerator while the denominator does not change. To convert this fraction $4\frac{1}{4}$ we multiply 4 with 4 and then add 1 and keep the 4 as the fraction's denominator so we get $\frac{17}{4}$ . Similarly, we get the improper fraction $\frac{11}{5}$ for converting the mixed fraction $2\frac{1}{5}$ .

Step 2; After conversion, it's just a matter of division. The fraction $\frac{17}{4}$ equals 4.25 while the denominator $\frac{11}{5}$ equals 2.2. Dividing 4.25 by 2.2 we get 1.9318.

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4 years ago

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Fed [463]

Answer:

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Step-by-step explanation:

1^1 = 1

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3 years ago