An epidemiologist is observing the growth pattern of a pathogenic bacteria. She starts with 20 bacteria that grow at a rate of 90% per hour. She will check on the bacteria in 16 hours. How many bacteria will she find? Round your answer to the nearest whole number.

Answer:

125 cm

Step-by-step explanation:

If you separate the shape, you get an area of 50, 50, and 25. you then add these together to get 125

Step-by-step explanation:

please type the question properly

Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

Step-by-step explanation:

HJ+5=20

HJ=20-5

HJ=15

Answer:

1

Step-by-step explanation:

To find this, you simply need input points.

The given equation is y=-2/3x +{}. You can plug in the given point, (0,1). This would make the equation 1 = -2/3·0 +{}. To solve this, you simplify the equation. You then get 1 = {}. Hence, The missing number is 1.

Answer: -8, 0. 2, -10, 15

Step-by-step explanation:

4x+6 > 3x-9

x + 6 > -9

x > -15

So the answers are -8, 0. 2, -10, 15.

Answer:

Step-by-step explanation:

To derive the differential equation that describes the amount of salt in the tank, we need to use the law of conservation of mass. The rate of change of the amount of salt in the tank is given by the difference between the rate of salt entering the tank and the rate of salt leaving the tank. The rate of salt entering the tank is the product of the concentration of the solution and the flow rate of the solution, while the rate of salt leaving the tank is the product of the concentration of salt in the tank and the flow rate of the draining solution. Therefore, we get:

dy/dt = (0.6 kg/L x 7 L/min) - (y(t)/100 L x 5 L/min)

where y(t) is the amount of salt (in kilograms) in the tank after t minutes.

To find the amount of salt in the tank after 30 minutes, we can solve the differential equation we derived in part 1 using separation of variables:

dy/dt = 4.2 - 0.05y

dy/y - 4.2/0.05 dt = 0

Integrating both sides, we get:

ln|y| - 84t + C = 0

where C is the constant of integration. Solving for C using the initial condition that y(0) = 0, we get:

C = 84 ln(6)

Substituting back, we get:

ln|y| - 84t + 84 ln(6) = 0

ln|y| = 84t - 84 ln(6)

|y| = e^(84t - 84 ln(6))

Since y is the amount of salt, it must be positive, so we take the absolute value off and get:

y = e^(84t - 84 ln(6))

Plugging in t = 30, we get:

y = e^(84(30) - 84 ln(6)) ≈ 37.86 kg

Therefore, there is approximately 37.86 kg of salt in the tank after 30 minutes.

Answer: the Ferris Wheel

Step-by-step explanation:

The minimum amount of plastic wrap needed to completely wrap 8 containers is  794. 4 in². Option D

The area of each circular end is:

A = πr²

A = 3.14 × (2.75)²

A = 23.68in²

The area of the rectangular side is:

A = h * circumference

circumference = 5.5in * π

circumference = 17.27in

Using the given height of 3 inches, we get:

A = 3in * 17.27

A = 51.81in²

Therefore, the total surface area of each container is:

A = 2 * 23.68 + 51.81

A = 98.17in²

To wrap 8 containers, we need to multiply the surface area of each container by 8:

Total surface area = 8 × 98.17

Total surface area = 794. 4 in²

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Answer:

12

Step-by-step explanation:

Answer:

A) 3.94

B) 12.40

Step-by-step explanation:

Refer to the work image. You also need the radius to calculate A and B.

Answer:

-25

Step-by-step explanation:

Answer:

I think you forgot to include the model

Good luck:)

The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Step-by-step explanation:

the answer to your question is a

Answer: $12 for one ticket.

Step-by-step explanation:

simply divide 48 by 4, that's how you find the price for one ticket.

Answer: They found 14 dollars.

Step-by-step explanation: Jose and his best friend together count as 2 people. Since they split the money even between 2 people, it means that  you would have to add the money they each got based on the number of people there are. In this case, there are 2 people who each get 7 dollars, so you add 7 dollars two times. 7+7=14!

Answer:

The probability that the student answers at least seventeen questions correctly is \(8.03\times 10^{-10}\).

Step-by-step explanation:

Let the random variable X represent the number of correctly answered questions.

It is provided all the questions have five options with only one correct option.

Then the probability of selecting the correct option is,

\(P(X)=p=\frac{1}{5}=0.20\)

There are n = 20 question in the exam.

It is also provided that a student taking the examination answers each of the questions with an independent random guess.

Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.

The probability mass function of X is:

\(P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...\)

Compute the probability that the student answers at least seventeen questions correctly as follows:

\(P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)\)

\(=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}\)

Thus, the probability that the student answers at least seventeen questions correctly is \(8.03\times 10^{-10}\).

Using equations, the time for the main engine 14.4 seconds and 21.6 seconds for the auxiliary engine

Let's call the time each engine takes to consume its allotted fuel supply as "t₁" for the main engine and "t₂" for the auxiliary engine.

From the first piece of information, we know:

t₁ = (2/3)t₂

From the second piece of information, we know that the combined fuel consumption time for both engines is 36 seconds:

t₁ + t₂ = 36

Now we can substitute the first equation into the second:

t₁ + (2/3)t₂ = 36

Combining like terms:

t₂ = 21.6

Finally, substituting t₂ back into the first equation:

t₁ = (2/3)(21.6) = 14.4

So the main engine alone could be fired for 14.4 seconds and the auxiliary engine alone could be fired for 21.6 seconds.

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The odd one out in the set is "FOQZ." It deviates from the pattern  by the other sets, where the letters are arranged in Alphabetical order.

The set of letters "BCDEGPTV AJK FOQZ IY" seems to follow a specific pattern. If we examine the letters in each group, we can identify a difference that sets "FOQZ" apart from the others.

In the first group "BCDEGPTV," the letters are arranged in alphabetical order. Similarly, in the second group "AJK," the letters are also in alphabetical order. However, when we look at the third group "FOQZ," the letters do not follow alphabetical order.

Based on this pattern, we can conclude that the odd one out in the set is "FOQZ." It deviates from the pattern followed by the other sets, where the letters are arranged in alphabetical order.

It's worth noting that the pattern could be based on different criteria, such as the position of the letters in the alphabet or some other sequence. Without additional information or context, it is difficult to determine the exact pattern or reason for the deviation.

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well, the tax amount is simple, it was $71 and it went up to $86.45, that's a 15.45 difference, so that IS the tax amount.

now, if we take 71(origin amount) to be the 100%, what's 15.45 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 71 & 100\\ 15.45& x \end{array} \implies \cfrac{71}{15.45}~~=~~\cfrac{100}{x} \\\\\\ 71x=1545\implies x=\cfrac{1545}{71}\implies x\approx 21.76\)

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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M<2 + M<3 = 180 degrees, as this is the sum of all angles in a triangle.

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Answer:

The two statements are logically equivalent.

Step-by-step explanation:

Let X be the statement that Bob is a double math and computer science major.

Y be the statement that Ann is a maths major.

Z be the statement that Ann is a double maths and computer science major.

The two statements written in terms of X, Y and Z now

a. Bob is a double math and computer science major and Ann is a math major, but Ann is not a double math and computer science major.

(x and y) and not z

b. It is not the case that both Bob and Ann are double math and computer science majors, but it is the case that Ann is a math major and Bob is a double math and computer science major.

not (x and z) and (x and y)

Noting that for logical statements,

Negation is represented by ~

And is represented by conjunction sign Λ

Or is represented by disjunction sign V

(x and y) and not z

(x Λ y) Λ (~z)

not (x and z) and (x and y)

~(x Λ z) Λ (x Λ y)

We can then simplify the second statement to obtain the first statement and prove the equivalence of both sides

~(x Λ z) Λ (x Λ y)

Using DE MORGAN'S theory, ~(x Λ z) = (~x) V (~z)

~(x Λ z) Λ (x Λ y) = ((~x) V (~z)) Λ (x Λ y)

Then applying the distributive law to the expression, we can open the bracket up

((~x) V (~z)) Λ (x Λ y)

= ((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

Opening the first bracket up further

((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

= ((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

The NEGATION law shows that (~x Λ x) = c (where c is a negation law parameter for when two opposite statements are combined in this manner, it works like a 0 in operation)

((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

= (c Λ y) V ((~z) Λ (x Λ y))

But (c Λ y) = (y Λ c) = c (according to the UNIVERSALLY BOUND law, see how c works like a 0 now?)

(c Λ y) V ((~z) Λ (x Λ y))

= c V ((~z) Λ (x Λ y))

= ((~z) Λ (x Λ y)) V c (commutative)

And one of the foremost IDENTITY laws is that (any statement) V c = c

((~z) Λ (x Λ y)) V c

= ((~z) Λ (x Λ y))

= (x Λ y) Λ (~z)

Which is the same as the first statement!

PROVED!!!

Hope this Helps!!!

Answer:

Not 100% but I think they are equal logically.

y = 9x - 1/x

I like to rewrite 1/x as x^-1

y = 9x - x^-1

Taking the derivative

dy/dx = 9 - -1 x^-2

= 9 + 1/x^2

That is the first derivative

Now we do it again

dy^2/dx^2 = d/dx ( 9 + 1/x^2)

= d/dx( 9 + x^-2)

= 0 -2x^-3

=-2/x^3

The second derivative is -2 / x^3

Answer: \(40\sqrt{3}\)

Step-by-step explanation:

30-60-90 triangle- leg opposite 30 is x, leg opposite 60 is \(x\sqrt{3}\) and the hyp. is 2x

we need to figure out X

we also know that the leg opposite 60 is = 120

\(120=x\sqrt{3}\)

square everything

\(14400=3x^{2}\\4800=x^{2} \\\sqrt{4800} =x\\\sqrt{1600*3} =x\\40\sqrt{3} =x\)

Answer:

Step-by-step explanation:

To convert a mixed fraction into an improper fraction, we must multiply the whole number with the denominator, then add the numerator to the multiplication. The denominator of the mixed fraction will be the denominator of the improper fraction.

Hence, 2 3/8 is the answer.

Answer:

Ask you might know 63×32 is 2,016 so 630×32 is 2,016 just with a 0 added and so far on so 630×32 would be 20,160 and 6300×32 would be 201,600

You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.