If the half-life of a radioactive isotope is 3 million years,
what percent of the isotope is left after 6 million years?
- 50
- 25
- 12.5
- 6.75

Answer: B

Step-by-step explanation:

 In the systems of equation it already gives you the solution for x  which is -2 so all you have to do is substitute -2 into the first equation and solve for y.

y= 2/3x + 3    

x= -2

Substitute x for -2

y = \(\frac{2}{3}* \frac{-2}1} + 3\)  

y= \(\frac{-4}{3}\) + \(\frac{3}{1}\)    

y = \(\frac{5}{3}\)  

so now you have the solution like this \((-2,\frac{5}{3})\)

Answer:

7.28 units

Step-by-step explanation:

Using the Pythagorean theorem, \(a^{2} + b^{2} = c^{2}\), we get:

\(2^{2}+7^{2}=c^{2}\\4+49=c^{2}\\53=c^2\\\sqrt{53}=c\\c=\sqrt{53}\)

\(\sqrt{53}\) ≈ 7.28

The sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value of the t-distribution with (n - 1) degrees of freedom.

For the given case, the most appropriate confidence interval would be the t-interval for the population mean. Confidence interval: A confidence interval refers to the range of values that are likely to include the population parameter. Confidence intervals provide us with a range of values where the true mean lies with some degree of certainty. The formula to calculate a confidence interval for the mean with a known population standard deviation is as follows

\(:\[\overline{x}-z\frac{\sigma }{\sqrt{n}}\text{ }\le \text{ }\mu \text{ }\le \text{ }\overline{x}+z\frac{\sigma }{\sqrt{n}}\]Where, \[\overline{x}\]\) is the sample mean, σ is the population standard deviation, z is the critical value of the normal distribution and n is the sample size.

Now, since the population standard deviation is unknown, a t-distribution must be used instead of the normal distribution. Thus, the formula to calculate a confidence interval for the mean with an unknown population standard deviation is as follows:\(\[\overline{x}-t\frac{s}{\sqrt{n}}\text{ }\le \text{ }\mu \text{ }\le \text{ }\overline{x}+t\frac{s}{\sqrt{n}}\]\)

Where, s is the sample standard deviation, and t is the critical value of the t-distribution with n - 1 degrees of freedom. Given that the sample size is 55, the appropriate degrees of freedom to use would be (55 - 1) = 54.Since we are constructing a confidence interval for the true mean filling amount of DoubleStuf Oreos, the appropriate confidence level to use would depend on the desired level of certainty or the margin of error. Commonly used levels of confidence are 90%, 95%, and 99%. A 95% confidence level is usually preferred for most cases.

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Answer:

standard form is {Ax+By=c}

as mentioned above the given equation is not in {Ax+By=c}..

hence it's not in standard form

Answer:

ax+by=c so no

Step-by-step explanation:

Expected counts are calculated by the test of independence and also by using Homogeneity.

The main difference between a test of independence and a test of uniformity when analyzing voting results from a two-page table is how the expected count is calculated.

The test of independence calculates expected frequencies assuming no relationship between the two variables analyzed and is based on the marginal totals of the two-way table.

Independence tests are used to know whether there is a significant association between two variables or not.

Homogeneity tests, on the other hand, compute expected frequencies assuming that the two groups being compared have the same distribution for the variable being analyzed, based on the row sums of a two-way table.

Homogeneity tests are used to know whether there is a  difference in the distribution of a categorical variable between groups.

The number of columns and rows in the two-way table and the number of samples obtained are important factors to consider when performing both tests.

However, how the expected count is calculated is the main difference between the two tests. The degrees of freedom are also calculated differently for the two tests, but this is secondary. 

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The answer to your question is that the only way to demonstrate causation is to conduct a controlled experiment. This domain involves manipulating one variable and measuring the effect it has on another variable while holding all other variables constant.

correlation simply shows a relationship between two variables, but it doesn't prove that one variable causes the other. There could be other factors at play that are influencing both variables. For example, there may be a correlation between ice cream sales and crime rates, but this doesn't mean that ice cream causes crime or vice versa. It's possible that a third variable, such as temperature, is influencing both ice cream sales and crime rates.

further into the complexities of establishing causation, such as the need for random assignment in experimental studies, the importance of replicating findings, and the challenges of applying experimental findings to real-world situations. However, the key point is that a controlled experiment is the most reliable method for establishing a causal relationship between variables.

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Answer:

=x^2 +4x+11

Step-by-step explanation:

f(x) = x^2 + 7,

Replace x with x+2

f(x+2) = (x+2)^2 + 7

         = (x+2)(x+2) +7

     FOIL

     = x^2 +2x+2x+4 +7

Combine like terms

    =x^2 +4x+11

Answer:

\(f(x+2)=x^2+4x+11\)

Step-by-step explanation:

In \(f(x)=x^2+7\), for all values of \(x\), we substitute \(x\) (what is in the parentheses) into \(x^2+7\) to output a \(y\) value.

In \(f(x+2)\), the term \((x+2)\) is in the parentheses. Therefore, substitute \((x+2)\) for \(x\) in \(x^2+7\) to find \(f(x+2)\):

\(f(x+2)=(x+2)^2+7\)

Expand using \((a+b)^2=a^2+2ab+b^2\),

\(f(x+2)=x^2+4x+4+7\)

Combine like terms:

\(\boxed{f(x+2)=x^2+4x+11}\)

To express the condition that x1 must be at most 75% of the blend of x1, x2, and x3, a constraint can be formulated using inequalities.

Let's denote the blend of x1, x2, and x3 as B. To express that x1 must be at most 75% of B, we can write the constraint as:
x1 ≤ 0.75B
This inequality ensures that x1 is less than or equal to 75% of the blend. If x1 exceeds this limit, it violates the constraint. By formulating the constraint in this way, it explicitly specifies the relationship between x1 and the blend and provides an upper bound for x1.
It's worth noting that additional constraints may be required depending on the specific problem and the values and ranges of x1, x2, and x3. The above constraint addresses the condition that x1 must not exceed a certain proportion of the blend, but further constraints may be necessary to define the lower and upper bounds of x1, x2, and x3 or any other relevant constraints related to the problem at hand.

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Answer:

There are approximately 82 inches

Step-by-step explanation:

Here, we want to calculate the circumference of the wheel

To do this, we are going to use the formula for the circumference of a circle

C = 2 * pi * r

C = 2 * pi * 13

= 26 * pi

C = 81.7 inches which is approximately 82 inches

The correct answer is, the most powerful test is the test least likely to result in a Type II error.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

In terms of hypothesis testing, the power of a test is given by the probability of rejecting a null hypothesis when it is actually false.

Also, we know that we commit a type II error when we don't reject the null hypothesis when it is actually false.

So, combining these two facts, we can infer that the most powerful test is the test where we have a high probability of rejecting a null hypothesis when it is actually false. This means that the most powerful test is given by the test that will have almost no or absolutely no type II error.

Hence, the most powerful test is the test least likely to result in a Type II error.

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Answer:

I'm pretty sure the answer would be 3.

Step-by-step explanation:

I'm not super sure but that makes sense

Answer:

X=6

Step-by-step explanation:

Hope this helps.

Answer:

x = K

Step-by-step explanation:

If,

x = 6

and 6 = k

=> x = 6 = k

=> x = k

The Transitive Property of Equality states the same fact as:

"If two units are equal to each other and the second unit is equal to a third unit, then the first unit is also equal to the third unit."

The user cost of capital for that machine over one year is \(\$1,700.\)

The user cost of capital represents the economic cost incurred by a company for using a machine or capital asset. It takes into account both the opportunity cost of the capital invested and the depreciation of the asset over time.

In this scenario, the machine initially costs \(\$10,000\) in constant dollars, which means it is the real price adjusted for inflation. The real rate of interest is given as \(12\%\), which represents the cost of borrowing or the opportunity cost of using the capital for other investments.

The machine is expected to increase in price by \(2\%\) due to inflation, and the rate of depreciation is \(5\%\) which represents the decrease in the value of the machine over time.

To calculate the user cost of capital over one year, we add the real rate of interest and the rate of depreciation, and multiply it by the initial machine value:

\(User cost of capital = (0.12 + 0.05) * \$10,000 = 0.17 * \$10,000 = \$1,700\)

Therefore, the user cost of capital for that machine over one year is \(\$1,700.\)

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Answer:

159.4

Step-by-step explanation:

I'm assuming that it's supposed to be 15x^3-12x^2 because when you copy and paste the "^" gets cut out

15*2.5^3 - 12*2.5^2 = 234.375 - 75 = 159.375

rounded is 159.4

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Right answer but i am not conform

x = - 85

y = 52

Answer:

(4,19)

Step-by-step explanation:

Cuz if u substitute these values in for the x and y in the equation, the equation would be true:

1.) 19 = 7(4) - 9

2.) 9 ≠ 7(54) - 9

3.) 30 ≠ 7(-3) - 9

4.) 15 ≠ 7(2) - 9

As you can see, 1st equation is the only equation that's true.

Hope this helps!

Answer:

There are 400 Students.

Answer:

It would be 12.

Step-by-step explanation:

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

P”Q=3PQ

Step-by-step explanation:

Cost of goods sold (COGS) is an important accounting calculation that measures the costs associated with selling a company’s goods or services. Therefore, the cost of goods sold for the month ended is $600.

Cost of Goods Sold (COGS) is a measure of the cost of goods sold during the accounting period. It is calculated by subtracting the beginning inventory from the cost of goods purchased during the accounting period and then adding the ending inventory. For Dig the Dogs, Inc., the cost of goods sold for the month ended is calculated as follows: Beginning Inventory = 0 Cost of Goods Purchased = $900 Ending Inventory = $300 .COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory  = 0 + 900 - 300   = $600 Therefore, the cost of goods sold for the month ended is $600.

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Hello!

Total brownies: 16 (so that's the denominator of the fraction)

Brownies with nuts: 6 (that's the numerator of our fraction)

The fraction is:

\(\bf{\displaystyle\frac{6}{16}}\)

Divide the numerator (6) and denominator (16) by 2:

\(\bold{\displaystyle\frac{3}{8}}\)

That's the answer.

I hope everything is clear.

Let me know if you have any questions!

#KeepLearning :-)

Answer:

\(\frac{3}{8}\)

Step-by-step explanation:

⇒ Given:

Conner made 16 brownies.

Put nuts on 6 brownies.

⇒ To Find:

Write the simplified fraction of the brownies that had nuts.

⇒ Solution:

Since Conner made 16 brownies:

16 brownies is the total also known as denominator of a fraction.

Since, Conner put nuts on 6 brownies:

6 brownies is the ones that has nuts also known as numerator of a  fraction.

Thus, the fraction is \(\frac{6}{16}\).

It a even number thus, we can simplify:

\(\mathrm{Factor\:the\:number:\:}\:6=2\cdot \:3\)

\(=\frac{2\cdot \:3}{16}\)

\(\mathrm{Factor\:the\:number:\:}\:16=2\cdot \:8\)

\(=\frac{2\cdot \:3}{2\cdot \:8}\)

\(\mathrm{Cancel\:the\:common\:factor:}\:2\)

\(=\frac{3}{8}\)

Therefore, the simplify fraction of the brownies that had nuts is \(\frac{3}{8}\)

`~lenvy~`

The most direct way to measure how dispersed a set of scores is, is by using the range. The range is calculated by subtracting the lowest score from the highest score in the dataset, which gives a quick and easy measure of the spread of the scores.

However, the range can be influenced by extreme scores and may not provide a complete picture of the variability. Other measures of variability, such as the standard deviation and variance, take into account the variability of all scores in the dataset and provide a more robust measure of variability.

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here is your answer 4msquare. I hope you get it.. if you didn't understand..be sure to ask any doubt for any inconvenience

The height of the cylinder is 4 cm.

Given,

The volume of a cylinder is 36π cm³ and a base with a radius of 3 cm.

We need to find the height of the cylinder.

The volume is given by:

V = π r² h

Find the volume of the cylinder.

We have,

V =  36π cm³

r = 3 cm

V = π r² h

36π cm³ = π 3²cm² h

Find the height of the cylinder.

We have,

36π cm³ = π 3²cm² h

Divide both sides by π

36 cm³ = 9 cm² h

Divide both by 9cm².

4 cm = h

h = 4 cm.

Thus the height of the cylinder is 4 cm.

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Answer:

сенпай

Step-by-step explanation:

яьхз что это

лвдыдыжыжыжжыжыжыжжвжвжжвжв

Answer:

3

Step-by-step explanation:

The correct answer is A.\(\((5 \frac{1}{\overline{9}}) \times (-0.\overline{3})\)\), as it involves the multiplication of two rational numbers, resulting in a rational number.

Therefore, the product of these two rational numbers in option A will yield a rational number.

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