Nine times the product of two numbers a, and b less five times a third number c, divided by a fourth number d

An expression for the number of bacteria after t hours is \(N(t) = e^{(10 + 2t)}\).

To find an expression for the number of bacteria after t hours, given that a bacteria culture starts with e¹⁰ bacteria and grows at a rate proportional to its size, we can use the exponential growth formula:
\(N(t) = N(0) * e^{(kt)}\)
where N(t) is the number of bacteria after t hours, N(0) is the initial number of bacteria, k is the growth constant, and t is the time in hours.

First, we are given that after 3 hours there are e¹⁶ bacteria.

Let's use this information to find the growth constant k:
\(e^{16} = e^{10} * e^{(3k)} \\e^{6} = e^{(3k)}\)

Now, we can find k by dividing both sides by 3:
6 = 3k
k = 2

Now that we have the growth constant k, we can plug it into the exponential growth formula:
\(N(t) = e^{10} * e^{(2t)}\)
which is equivalent to:
\(N(t) = e^{(10 + 2t)}\)

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The given sets are

The given question is

This means we need to list the comment elements in both sets

Since the common letters are t and a, then

Answer:

70

Step-by-step explanation:

280×25%=70 pages per night

Answer:

70

Step-by-step explanation:

Answer:

inequality

Step-by-step explanation:

Emphasis on in because that is the part that negates the equality.

Inequalities fit the description of all of the following.

1) 2 Linear Expressions: 2x ? 5y (EXAMPLE)

Linear expressions are expressions that have a variable to the first power.

2) OR Linear Expression and a Constant: 2x ? 5

A constant is a fixed value. For example, a variable is NOT a constant because if the variable changes, the value changes.

3) Are not equal: >, <, \(\geq\), \(\leq\)

Greater than, less than, greater than or equal to, and less than or equal to, are NOT equality.

Answer:

6

Step-by-step explanation:

Trust the process

The function f represents the cost of renting the tractor, is f(x) = 40x + 100 and the function g represents the cost if the hourly rate were doubled is g(x) = 80x + 100

The slope of the graph g is double of the graph f, and difference of y intercept of both the graph is multiple of 40.

A function is defined as a relation between a set of inputs having one output each.

Given that, The cost of renting a landscaping tractor is a $100 security deposit plus the hourly rate is $40/hour

According to question,

Function f representing total cost for x hours is f(x) = 40x + 100

Function g representing total cost for x hours is g(x) = 80x + 100

Comparing with y = mx + c we get

Slope for f(x) = 40

Slope for g(x) = 80

Hence, The slope of the graph g is double of the graph f, and difference of y intercept of both the graph is multiple of 40, also The function f represents the cost of renting the tractor, is f(x) = 40x + 100 and the function g represents the cost if the hourly rate were doubled is g(x) = 80x + 100

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The probability of drawing a green Skittle, replacing it, and then drawing another green Skittle is 1/36

The distribution of the Skittle is given as:

Red = 6

Orange = 4

Yellow = 7

Purple = 3

Green = 4

The total number of skittle is:

Total = 6 + 4 + 7 + 3 + 4

Evaluate

Total = 24

The probability of selecting a green skittle is:

P(Green) = 4/24

So, the probability of selecting 2 green skittles is:

P = 4/24 * 4/24

Evaluate

P = 1/36

Hence, the probability of drawing a green Skittle, replacing it, and then drawing another green Skittle is 1/36

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To find the critical numbers of the function provided , we need to determine the values of x at which the derivative of g(x) equals zero or does not exist.

First, let's find the derivative of g(x). Applying the product rule and chain rule, we have:

\(g'(x) = 8e^{(8x)cosh(10x) + e^(8x)(10sinh(10x))}\\ = e^{(8x)(8cosh(10x) + 10sinh(10x))\)

Now, to find the critical numbers, we set g'(x) equal to zero and solve for x:

\(e^{(8x)(8cosh(10x) + 10sinh(10x)) = 0\)

8cosh(10x) + 10sinh(10x) = 0

\(8((e^{(10x) + e^(-10x))/2) + 10((e^(10x) - e^(-10x))/2) = 0\)

on simplifying and combining like terms , will get:

\(9e^{(10x) }+ e^{(-10x) = 0\)

Dividing both sides by \(e^{(-10x)\), we obtain:

\(9e^{(20x)\) = -1

Taking the natural logarithm of both sides, we have:

ln(9) + 20x = ln(-1)

However, ln(-1) is undefined since the natural logarithm is only defined for positive values. Therefore, there are no critical numbers for the function g(x) = \(e^{8x)}cosh(10x).\)

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Answer:

Standard deviation gets smaller

Step-by-step explanation:

No. of students = 45

The class had an average of 56 words per minute (WPM) with a standard deviation of 7 WPM.

\(Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\56=\frac{Sum}{45}\\56 \times 45=Sum\\2520=Sum\)

The teacher realized that the data from one student who typed 55 WPM was not entered.

So, new sum = 2520+55

New sum =2575

So, new mean =\(\frac{2575}{45}\)

New mean =57.22

Standard deviation is the measure of distance between observation and mean

So, if number gets closer to mean , Standard deviation gets smaller . if the numbers get bigger , Standard deviation gets bigger.

Since 55 is closer to 57.22

So, Standard deviation gets smaller

Answer:

smaller

Step-by-step explanation:

edg

The vertical asymptotes for the function are x = 2 and x = -2, and the horizontal asymptote is y = 3.

To find the vertical and horizontal asymptotes of the function f(x) = (3x²) / (x² - 4), we can analyze the behavior of the function as x approaches infinity or negative infinity and as x approaches the values that make the denominator equal to zero.

Vertical Asymptote:

To find the vertical asymptote(s), we need to determine the values of x that make the denominator of the function equal to zero.

x² - 4 = 0

Factoring the denominator, we get:

(x - 2)(x + 2) = 0

Setting each factor equal to zero, we find:

x - 2 = 0 or x + 2 = 0

x = 2 or x = -2

Therefore, the vertical asymptotes are x = 2 and x = -2.

Horizontal Asymptote:

To find the horizontal asymptote(s), we examine the behavior of the function as x approaches infinity or negative infinity.

As x approaches infinity or negative infinity, the highest power terms in the numerator and denominator dominate the function. In this case, the highest power terms are both x².

The coefficient of x² in the numerator is 3, and the coefficient of x^2 in the denominator is 1.

Therefore, the horizontal asymptote is determined by the ratio of these coefficients, which is:

y = 3/1 = 3

Thus, the horizontal asymptote is y = 3.

In summary, the vertical asymptotes for the function are x = 2 and x = -2, and the horizontal asymptote is y = 3.

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Complete question =

What are the vertical and horizontal asymptotes for the function f (x) = StartFraction 3 x squared Over x squared minus 4 EndFraction? horizontal asymptote: y = –2, y = 2 vertical asymptote: x = 3 horizontal asymptote: y = –4, y = 1 vertical asymptote: x = 3 horizontal asymptote: y = 3 vertical asymptote: x = –4, x = 1 horizontal asymptote: y = 3 vertical asymptote: x = –2, x = 2

The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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Answer:

A. It is 140° because It is supplementary to 40°

It is 140° because it is supplementary to 40°. Then the correct option is A.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Angle ∠A and angle 40° are supplementary angles. Then the equation is given as,

∠A + 40° = 180°

∠A = 140°

The proportion of point ∠A will be 140°. It is 140° in light of the fact that it is strengthening to 40°. Then the right choice is A.

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Answer:

\((4+4n)+(7+2a) = 11+4n+2a\)

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

mx+b=y   --> m=slope

if m is slope of a line.... -m is the slope of a line perp to the first

y=-2/3x+5/3

slope m=-2/3

slope perp to m ->   -m = 2/3

Answer:4.1

Step-by-step explanation:

Step-by-step explanation:

15X - 4Y when X=7 Y=8

=15*(7) - 4*(8)

= 105 - 32

=73

Answer:

60,600,2400

Step-by-step explanation:

12 x 5=60, 50 x 12=600, 200 x 12=2400.

Answer: A) y= -1/2x+5

Step-by-step explanation: If the line is perpendicular to the original, the  new "m" (coefficient  of x) has to be the negative reciprocal of the original "m"

Answer:

64/3

Step-by-step explanation:

The equation of a direct proportion is:

y = kx

When x = 3, y = 8.

8 = k × 3

k = 8/3

This equation of direct proportion is:

y = 8/3 x

When x = 8,

y = 8/3 × 8

y = 64/3

Answer: 64/3

Answer:

Answer: 64/3

Step-by-step explanation:    

The equation of a direct proportion is:  

y = kx  

When x = 3, y = 8.  

8 = k × 3  

k = 8/3  

This equation of direct proportion is:  

y = 8/3 x  

When x = 8,  

y = 8/3 × 8  

y = 64/3  

Answer: 64/3

The answer to your question would be B. 10/15 and 14/21.

10/15 in simplest form is 2/3

14/21 in simplest form is 2/3

By applying standard deviation concept, it can be concluded that all the students had the same score.

The mean is the average of all the scores. It is calculated by adding up all the scores and dividing them by the number of scores.

The standard deviation is a measure of how spread out the scores are. It is calculated by finding the difference between each score and the mean, squaring those differences, finding the average of those squared differences, and then taking the square root of that average.

If all the scores are the same, then the difference between each score and the mean will be 0. This means that the standard deviation will also be 0. Therefore, the correct answer is "all the students had the same score."

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Answer:

12

Step-by-step explanation:

The Least Common Multiple (LCM) of some numbers is the smallest number that the numbers are factors of. Like the LCM of 3 and 4 is 12, because 12 is the smallest number that 3 and 4 are both factors for.

Answer:

The least common multiple is 12.

Step-by-step explanation:

Multiples of 3:

3, 6, 9, 12, 15, 18

Multiples of 4:

4, 8, 12, 16, 20

The simplified expression, with r and t written only once, is:\((r^2^m t^2)^(^1^/^n^) / (t^2^m r^1^/^n^)^m\)

To simplify the given expression, let's break it down step by step:

Step 1: Simplify the numerator.

The numerator contains two terms: r³m and \(r^-^mt^4^n\). To simplify, we combine the terms with the same base, r.

r³m / \(r^-^mt^4^n\) can be rewritten as \(r^(^3^m^ -^ (^-^m^)t^4^n\), which simplifies to \(r^4^m t^4^n\).

Step 2: Simplify the denominator.

The denominator contains two terms: \(r^1^/^n and t^2^/^m.\) To simplify, we combine the terms with the same base, t which simplifies to\(r^-^m^/^n / t^-^2^m^/^m\).

Simplifying further, we have \(r^-^m^/^n / t^-^2\), which can be rewritten as \(r^-^m^/^n / 1 / t^2\), and finally as \(r^-^m^/^n t^2\).

Step 3: Combine the numerator and denominator.

We now have \((r^(^4^m^) t^(^4^n^))^(^1^/^n) / (r^(^-^m^/^n) t^2)\).

To simplify further, we can apply the exponent rule for raising a power to a power. When we raise a power to another power, we multiply the exponents.

In the numerator, \((r^(^4^m^) t^(^4^n^))^(^1^/^n^)\) simplifies to \(r^(^4^m^/^n^) t^(^4^n^/^n^)\), which becomes \(r^(^4^m^/^n^) t^4\).

In the denominator, \(r^(^-^m^/^n^) t^2\) remains the same.

Putting it all together, the simplified expression is:

\(r^(^4^m^/^n^) t^4 / (r^(^-^m^/^n^) t^2)\).

Therefore, the simplified expression with r and t written only once is \((r^2^m t^2)^(^1^/^n^) / (t^2^m r^1^/^n^)^m\)

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As the number of people visiting each day is the same 404 people visited on Sunday.

We have,

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday and the number of people who visited on each day is the same.

As the number of visitors is same on each day and the total number of days is three each they the number of people visited is,

= (1212/3).

= 404.

So, On Sunday 404 visitors were there.

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complete question:

The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday. If the same number of people visited each day, how many visitors were there on Sunday

Answer:

1/3

Step-by-step explanation:

= y2-y1/x2-x1

3-2/1+2

1/3

Answer:

slope = \(\frac{1}{3}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1,3) and (x₂, y₂ ) = (4, 4) ← 2 points on the line

m = \(\frac{4-3}{4-1}\) = \(\frac{1}{3}\)

SOLUTION

Step 1 :

In this question, we were told that A cosmetics company tested a new lotion.

Of the 2,500 people tested, 15 had an allergic reaction.

What percent of the people tested did not have an allergic reaction to the new lotion?

Step 2 :

Answer:

1.yeah

2.no

Step-by-step explanation:

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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