use the product rule to find the derivative of the given function. b. find the derivative by expanding the product first.

The  days needed are 5 days

The reduction in radioactive nuclei per unit of time is the rate of decay, or activity, of a sample of a radioactive substance.

The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a given time t and dN is the amount by which the population decreases in time dt.

Exponential decay is the opposite of exponential growth; it has a constant multiplier that is less than 1 when a quantity decreases by the same amount over equal intervals of time. This quantity also referred to as the decay factor, can be written as (1-r).

From the above question

B= 7.8+10.8sin((2pi/63)t)

B=13=7.8+10.8 sin((2pi/63)t)

sin((2pi/63)t)=13/27

(2pi/63)t=sin(13/27)=0.502344 radians

t=5 days

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Answer:



Step-by-step explanation:

GraphA shows the quadratic equation with complex roots.

Answer:

Step-by-step explanation:

Answer: x<-7 or x>-3

Step-by-step explanation: Tell me if its wrong ill fix it

answer:

x>-7, x>-3

step-by-step explanation:

- the first step would to be to add five to both sides: x^2+10x+21>0

- then you can solve be grouping which results in: (x+7)(x+3)>0

- the final answer will be: x>-7, x>-3

hope that helps!

Answer: y=−16.309691adqrsux+16.309691adqrsu+3

Let's solve for y.

y=((((((((−3(x−1))(2))(s))(q))(u))(a))(r))(2.718282))(d)+3

This is the best I could come up with

The conversion factor you should use to adjust your recipe for the new amount is 6.

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.

Given: original serving = 50                        8-ounce serving            

required new serving = 200                     12-ounce serving

Original serving = 50×8 ounce = 400 ounce

Required serving = 200×12 ounce                          

 = 2400 ounce

As we know, conversion factor = {Required Yield} ÷ {Original Yield}

∴ Conversion factor =2400 ÷ 400

∴  Conversion factor = 6

Conversion factor is greater than 1 when required yield is supposed to be greater than original yield and conversion factor is less than 1 when required yield is less than original yield.

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By using the vertical line test we will see that the relation that is a function is the one in the top left graph.

Here we ave the graphs of some relations, and we want to see which one of these represents a function.

To check that, we need to do the vertical line test.

The test says that if we draw a vertical line on the coordinate axis, and that line intercepts the graph of the relation more than one time, then the relation is not a function.

With that test we can see that the only relation that is a function is the one in the top left graph, is the only one that passes the vertical line test.

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Answer:

:Equation of line is[tex]y=1.2x+3.8[/tex]To find:The equation of line that passes through the point (5, 0) and parallel to the given line.

Step-by-step explanation:

For symmetric distributions without outliers, the mean should be used to get the measure of center.

What are the Center and Spread of the data?

The spread in the data measures how far the numbers in the data set are away from the mean and the center in the data measures the standard deviation.

To determine the measure of center for symmetric distributions without outliers, one should use the mean. They should use the median to determine the measure of center in all other situations. The range is a suitable metric for determining the spread of a distribution.

However, the interquartile range should be used when using the median as the measure of center, and the standard deviation should be used when using the mean as the measure of center.

Hence, For symmetric distributions without outliers, the mean should be used to get the measure of center.

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Answer:

A) y=0.5x+10 C) 17.5 dollars (don't forget your units)

Step-by-step explanation:

a) 0.5 is the price paid per song, or x, and 10 is the price that does not change for a month, so we can say that y=0.5x+10

c) to download 15 songs, we substitute x by 15

y=0.5(15)+10

y=7.5 + 10

y=17.5

and for b, im sorry but I cannot graph here.

For the triangle to be true, the square of the hypothenuse is equal to sum of the square of the leg and the sum of the angles is equal to 180 degrees

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC² = AB² + AC2​². Here, ​​​​AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

In this case, for the triangle to be true,

1. The sum of square of two sides (s) and (r) must be equal to the square of t

t² = s² + r²

2. The sum of angles in the right angle triangle must be equal to 180 degrees

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The correct answer is b that is the probability that the mean of their test scores is greater than 78 is 0.0008.

The field of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number that lies between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is calculated on dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas where odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

mean, μ = 73
standard deviation σ =7.8

η = 24

P (X*=78)

P( Z>3.1403)

Hence, the probability that the mean of their test scores is greater than 78 is 0.0008.

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Temperature of ch4 will be 150K

given :-

[tex]\sqrt{2} speed of 02 = 448.8[/tex]

u.avg. = [tex]\sqrt{8rt/\pi m} \\[/tex]

u.avg ch4 = [tex]\sqrt{8rt1/\pi 16}[/tex]

hence , mass of ch4 = 12 +4 = 16

Methane (US: MEH-thayn, UK: MEE-thayn) is a chemical compound with the chemical formula CH4 (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas.

The molar mass of oxygen atom  O

O

 is 15.99

This is only the mass of 1 oxygen atom so the molar mass of oxygen molecule  O is 15.99

is double the number, i.e. approximately 32

u.avgO2 = [tex]\sqrt{8r(300)/\pi (32)}[/tex]

u.avgch4 = u.avgo2

[tex]\sqrt{8rt1/\pi 16}[/tex] = [tex]\sqrt{8r(300)/\pi (32)}[/tex]

==> t1/16 = 300/32

==> t1 = 150 K

They have same average velocity when the temperature of CH4 is 150 K

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The statistic's bias is a quality that the statistic does not display, according to the Central Limit Theorem for proportions.

Central limit theorem:

According to the central limit theorem in statistics, samples will be normally distributed and their means will be roughly equal to those of the entire population when the big sample size has a finite variance.

Given,

A certain statistic The population parameter d is being estimated using the function d. D's predicted value is not the same as D.

Find the property that does d display in this case.

According to the Central Limit Theorem, the following is true for a proportion p in an n-person sample:

Value anticipated, μ = p

Standard deviation: s = √p(1 - p) /n

Therefore,

The statistic is biased because the expected value in this case differs from the expected.

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Answer:

Step-by-step explanation:

first, you have to divide the total cost of the passes by the number of teachers and students combined. Then you must multiply the individual cost of the pass by the number of students. Finally, you have to take the total cost for student passes and add it to the cost of the lunches, then you answer.

Answer:

b

Step-by-step explanation:

Answer:

y ≈ 16.12452

Step-by-step explanation:

Pythagorean theorem = a² + b² = c²

In this example, 14 = a, 8 = b, and y = c

14² = 196, 8² = 64

196 + 64 = 260 = y²

y² = [tex]\sqrt{260}[/tex] ≈ 16.12452

Answer: 5/3 or 1.67

Step-by-step explanation:

Answer:

y = -3x + 13

Step-by-step explanation:

Assuming the line is linear, you can use the point-slope equation of a line.

(y - y) = m (x - x)

The y and x variables come from the points on the line. Points are written in the form (x, y). In the point (2,7), 2 is x and 7 is y.

1. Plug your points in.

(7 - - 2) = m (2 - 5)

2. Solve for m (the slope)

(7 + 2) = m (2 - 5)

(9) = m (-3)

9 = -3m

m = -3

3. Write an equation of the line with the slope you found.

You can write this equation in different forms, but I'll use the slope-intercept form.

y = mx + b

You'll have to find b, the y-intercept. You can plug one of your points in for x and y as well as your slope, m, and solve for b.

7 = -3(2) + b

7 = -6 + b

b = 13

Therefore, the equation is y = -3x + 13

Answer:

The answer should be (8,0)

Answer:

"Broadly speaking, an oligarchy is a form of government characterized by the rule of a few persons or families. More specifically, the term was used by Greek philosopher Aristotle in contrast to aristocracy, which was another term to describe rule by a privileged few."

Step-by-step explanation: I hope this helps with something

Answer: y = 16807

Step-by-step explanation:

7 * 7 * 7 * 7 * 7 * 7 = 117649

7^16807 = 117649

The percentage of 39/100 can be written as 39% as given in the question.

A percentage is a figure or ratio stated as a fraction of 100. The abbreviations "pct.", "pct," and "pct" are also used. A% is a dimensionless (pure) number with no unit of measurement.

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento. The "cento" symbol was developed from two circles divided by a horizontal line.

As money denominations expanded in the Middle Ages, computations with a denominator of 100 were increasingly prevalent, to the point where it became normal for mathematics texts to incorporate such computations from the late 15th to the early 16th centuries

We write 39/100 in the percentage as 39%

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Answer: 4(x + y) = 4x + 4y 2(3x + 4) = 2(3x) + 2(4) = 6x + 8

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

y2-y1/x2-x1

-10-(-3)/9-(-5)=-7/14=-1/2

The probability that they each win six games is 0.225.  

Given : A computer chess game and a human chess champion are evenly matched. They play twelve games.

To find : The probability that they each win six games?

Applying binomial distribution,

Here n=12 and p=0.5

(a) They each win seven games. P =

[tex]P(X=k)=\frac{n !}{k !(n-k) !} \times p^k \times(1-p)^{n-k}[/tex]

The probability that they each win six games is k=6.

(b) The human chess champion wins eleven games. P =

[tex]\begin{aligned}& P(X=6)=\frac{12 !}{6 !(12-6) !} \times 0.5^6 \times(1-0.5)^{12-6} \\& P(X=6)=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 !}{6 \times 5 \times 4 \times 3 \times 2 \times 6 !} \times 0.015625 \times 0.015625 \\& P(X=6)=11 \times 2 \times 3 \times 2 \times 7 \times 0.015625 \times 0.015625 \\& P(X=6)=0.225\end{aligned}[/tex]

(c) The computer wins at least eleven games. P =

Therefore, The probability that they each win six games is 0.225.

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t-distribution in the bank or restaurant to get the customer arrival time is a b) normal distribution.

The t-distribution is defined by degrees of freedom. These are related to sample size. The t distribution is most useful when the sample size is small, the population standard deviation is unknown, or both. As the sample size increases, the t-distribution will become more normal.

The t distribution is the continuous probability distribution of z scores when the estimated standard deviation is used in the denominator instead of the true standard deviation. The purpose of the t-test is to compare a specific characteristic that describes the groups, and the means will be representative of the populations that are normally distributed.

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To complete the square of the quadratic function x² + 10x + 4 we need to add 21

Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. In simple words, we can say that completing the square is a process where consider a quadratic equation of the ax² + bx + c = 0 and change it to write it in the form a(x + p)² + q = 0. This method is generally used to find the roots of a quadratic equation.

Completing the square formula is a technique or method to convert a quadratic polynomial or equation into a perfect square with some additional constant. A quadratic expression in variable x: ax² + bx + c, where a, b and c are any real numbers but a ≠ 0, can be converted into a perfect square with some additional constant by using completing the square formula or technique

The equation given is

x² + 10x + 4 = 0

Take 4 to right side

x² + 10x = -4

rewrite in (x + a)² = b form

(x + 5)² = 21

x + 5 = ±√21

x = √21 - 5

x = -√21 - 5

To complete the square, we need to add 21

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