Solve for x and y in the equation log(x-1) + 2logy = 2log3, log x + log y =log 6​

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 \(min^{-1}\)is the rate constant of the nucleus

To solve this problem, we use

N(t) = \(N_{0}\)e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 \(N_{0}\) = 0.25\(N_{0}\)

We can substitute this in the decay equation:

0.25\(N_{0}\) =\(N_{0}\) e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 \(min^{-1}\)

t = -1.3863 /2.5 x 10^-2 \(min^{-2}\)

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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Answer:

4

Step-by-step explanation:

4y+1=5y-3

-1y=-4

y=4

Answer:

The measures of this complementary angles is:

45°

Step-by-step explanation:

Complementary angles sum 90°

∡A + ∡B= 90°

∡A = ∡B

Then:

∡A + ∡A = 90°

2∡A = 90°

∡A = 90/2

∡A = 45°

∡B = 45°

Answer:

27

Step-by-step explanation:

Let x = ten's digit

Let y = units' digit

Given: the units of a two-digit numeral means

that our final answer will be a 2 digit number (xy)

Given: 5 more than the tens digit  means

y is 5 more than x (y = x + 5)

Given: the number is three times the sum of its digits.

xy is 3 times x + y

A two digit positive integer can be written as 10x + y, where x is the tens digit and y is the ones digit

y = x + 5 and 10x + y = 3(x + y)

x - y = -5

7x - 2y = 0

Multiply the first equation by -2:

-2x + 2y = 10

7x - 2y = 0

Add the equations to get 5x = 10

So, x = 2 and y = x + 5 = 7

Reminder:

Let x = ten's digit

Let y = units' digit

The number is 27

Answer:

try the first, fourth, and last one

Step-by-step explanation: when you read the question it say select all that apply to form the equation so all you have to do is select the numbers and the variables that are in the equation above.

the ratio of the number of men to the total number of persons is 7:18.

The ratio of the number of men to the total number of persons can be calculated by dividing the number of men by the total number of persons.

Number of men: 112

Total number of persons: 288

Ratio of men to total persons = Number of men / Total number of persons

                            = 112 / 288

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 16 in this case.

112 / 288 = (112 ÷ 16) / (288 ÷ 16)

          = 7 / 18

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Answer:

200g oats

0.96l milk

72g sugar

Step-by-step explanation:

250/5 * 4 = 50 *4 = 200g oats

1.2/5 * 4 = 0.96l milk

90/5 * 4= 18*4 = 72g sugar

Answer:

221

Step-by-step explanation:

Take it portion by portion, we can do two at a time

Let's start with 34.76 and 170

34.76+170= 204.76

Now we can take our answer and add 16.24

204.76+16.24 = 221

If you break down a problem into smaller parts it'll be a lot easier to solve.

I hope this helps :)

The probability of the event occuring is 29/51

When we talk about probability, we are essentially trying to measure the likelihood of an event occurring. One way to do this is by using the ratio of the number of favorable outcomes to the total number of outcomes.

In this case, the odds for a certain event are given as 29 to 22. This means that for every 29 favorable outcomes, there are 22 unfavorable outcomes. So, the total number of outcomes can be calculated as the sum of the favorable and unfavorable outcomes, which is 29 + 22 = 51.

To calculate the probability of the event occurring, we need to divide the number of favorable outcomes by the total number of outcomes. In this case, the number of favorable outcomes is 29, so the probability can be calculated as:

Probability = 29 / 51

This can be simplified by dividing both the numerator and denominator by the greatest common factor, which is 1 in this case. So the final answer is:

Probability = 29/51

This means that if we were to repeat the event many times, we would expect the event to occur approximately 29/51 or 56.86% of the time.

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Answer:

D.

Step-by-step explanation:

5(-4 +10) × 4.8 ÷ \(\frac{3}{4}\)

5(6) × 4.8 ÷ \(\frac{3}{4}\)

30 × 4.8 ÷ \(\frac{3}{4}\)

30 × 4.8 × \(\frac{4}{3}\)

_________________________________

Hope this helps!!

If I have made a mistake, please let me know; I enjoy leaning from them:)

Answer:

Step-by-step explanation:

Using classical probability, we found that the chance of one minority candidate getting hired is 2/5.

What is meant by probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The degree to which something is likely to happen is basically what probability means.

Given,

  Number of total candidates = 5

Number of candidates from minority = 2

a) Probability that one of the minority candidates is hired

= number of favourable events/total events = 2/5

b) Classical probability is used.

   This is because since the candidates are selected by lottery, each candidate has an equal chance of getting selected. So the classical probability is used.

Therefore using classical probability, we found that the chances of one minority candidate getting hired is 2/5.

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Answer:

-2 to 0.8 seems to be like than..

Answer:

the first one i think sorry it im wrong

Step-by-step explanation:

Answer:63.75 :)

Step-by-step explanation:

Answer:

$63.75

Step-by-step explanation:

85 x 75/100

85/1 x 3/4

255/4 - > $63.75

- You should already know how to do this yourself as this is very easy and basic question.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{y})\qquad B(\stackrel{x_2}{1}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ 10= \sqrt{(~~ 1- (-5) ~~)^2 + (~~ 2- y ~~)^2} \implies 10^2= (~~ 1 +5 ~~)^2 + (~~ 2 -y ~~)^2 \\\\\\ 100=36+(4-4y+y^2)\implies 100=y^2-4y+40 \\\\\\ 0=y^2-4y-60\implies 0=(y-10)(y+6)\implies y= \begin{cases} 10\\ -6 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-5~~,~~10)\hspace{5em}(-5~~,~-6)~\hfill\)

There is a 16% probability that the individual actually had the disease given a positive test result.

The probability that the individual had the disease can be calculated as follows:

Let A = Event of testing positive and actually having the disease

Let B = Event of testing positive but not actually having the disease

We are looking for P(A|B), which is the probability of actually having the disease given a positive test result.

Using Bayes' Theorem, we have:

P(A|B) = P(A) * P(B|A) / P(B)

Bayes' theorem is a mathematical formula used in probability theory to calculate the probability of an event based on prior knowledge of conditions that might be related to the event.

It states that the conditional probability of an event A given event B is equal to the product of the probability of event B and the conditional probability of event A given event B, divided by the probability of event B. The formula is represented as P(A|B) = P(B|A) * P(A) / P(B).

Where:

P(A) = 1/500 (probability of having the disease)

P(B|A) = 0.95 (probability of a correct positive result given that the individual has the disease)

P(B) = P(B|A) * P(A) + P(B|A') * P(A') (probability of a positive test result)

= 0.95 * 1/500 + 0.01 * 499/500 (probability of a false positive result given that the individual does not have the disease)

Plugging in the values, we have:

P(A|B) = (1/500) * 0.95 / [0.95 * 1/500 + 0.01 * 499/500] = 0.16 or 16%

Therefore, there is a 16% probability that the individual actually had the disease given a positive test result.

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Answer:

1 1/2 - 1/2 = 2/2

Step-by-step explanation:

2/2 is fraction form and is equal to 1

Answer:

1

Step-by-step explanation:

it cant go in fraction form

Answer: (18,2)

Step-by-step explanation:

Martha had 8 2/3 yards of material left to make matching throw pillows. Martha started with 12 2/3 yards of material. She used 4 yards of it to make drapes for her family room. To find out how much material she has left, we need to subtract the amount used from the total amount.

To do this, we can convert the mixed number 12 2/3 into an improper fraction:

12 2/3 = (12 x 3 + 2) / 3 = 38/3

Next, we can subtract the 4 yards used for the drapes from the total amount:

38/3 - 4 = (38 - 12) / 3 = 26/3

Finally, we can convert the improper fraction 26/3 back into a mixed number:

26/3 = 8 2/3

Therefore, Martha has 8 2/3 yards of drapery material left to make matching throw pillows.

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Answer:

Option 4

Step-by-step explanation:

Equating given length and width to the area :

Finding the dimensions :

Answer:

1:8

Step-by-step explanation:

You subtract 19 and 8, and you get 11 then you put them in ration form

Step-by-step explanation:

Answer:

2.15500

Step-by-step explanation:

hope it's help

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# PHILIPPINES

Answer:

By using the pythsgorean theorem! simple

Answer:\(\sqrt{155}\)

Step-by-step explanation:

Oh god pythagorean triples got thrown out the window for this one. This will be a bit ugly.

First, we find the other side length of the rectangle using the pythagorean theorem.

Then, we use that side length in ANOTHER pythagorean theorem to get our answer.

Well, we know that the side length is \(\sqrt{5^{2}+9^{2} }\)

We'll use whatever that number is, let's call it x for now, in our other expression:

\(\sqrt{x^{2}+7^{2}}\)

So we can do this in one clean equation by substituting our first equation as x in the second one.

Or do them separately. Your choice.

Anyways, try to solve this one now that you know what to do. If you need more help then message.

Answer:

1359.6

Step-by-step explanation:

To determine when the next 100-hour inspection is due, we need to add 100 hours to the current tachometer reading of 1259.6.

1259.6 + 100 = 1359.6

Therefore, the next 100-hour inspection is due when the tachometer reading reaches 1359.6.

\(y=x^2-4x+6\\y'=2x-4\)

To find the slope/gradient of the curve at the specific point, we use the derivative.

Then substitute x = 3 in y' = 2x-4

\(y'=2(3)-4\\y'=6-4\\y'=2\)

Therefore, the slope/gradient of y = x²-4x+6 at (3,3) is 2.

The answer is: 1.25

Remember: Keep the first fraction, Change the Sign, Flip the second fraction.

KEEP - 5/28

CHANGE - division to multiplication

FLIP - 7/1

Answer:

5/4 or 1 1/4 or 1.25

(5/28) / (1/7) =

5/28 * 7 =

5/4

The value of the expression, that is, 20.5 – (2 * 8.1) is 4.3

We have been given the expression 20.5 – (2 * 8.1).

To solve this problem we apply BODMAS rule, where each letter stands for

              B = Bracket

              O = of

              D = Divide

              M = multiply

             A = Addition

              S = Subtraction

When any equation is given where there is more than one operation, we solve them according to the BODMAS rule which tells us to solve the order of operation to be followed while solving expression in mathematics.

Now solving the expression we get,

           = 20.5 – (2*8.1)

First solve the bracket expression

          = 20.5 – 16.2

          = 4.3

Hence the answer for the expression is 4.3

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between 20 and 5000 characters

Answer:

(x^4) - 64x

Step-by-step explanation:

zeros at 4 and 0 are the roots so can be factor as x*(x-4) and the multiplicity tels to what power you have to raise those factors

\(x^{1} *(x-4)^{3}\) becuase multiplicity of 1 for root at 0, and multiplicity of 3 at root 4

now to write this in standard form

\(x*(x-4)^{3} = \\x*(x-4)(x^{2} +4x+16)= \\(x^{2} -4x)(x^{2} +4x+16) = \\x^{4} +4x^{3} +16x^{2} -4x^{3} -16x^{2} -64x = \\x^{4} -64x\)