The doubling period of a bacterial population is 20 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0?
Find the size of the bacterial population after 3 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount in the account = x

Amount deducted every month = $14

The change in the account after 7 months.

= x - 7 x 14

= x - 98

Thus,

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

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Answer:7,800

Step-by-step explanation:

Answer:

Option B (3,510ft) would be correct.

Step-by-step explanation:

The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm3, m3 and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.

The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.

The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as

[tex](\frac{1}{4^{-3 } } )^{2}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)

Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]

using law of indices,

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]

4⁻⁶  = 1 / 4⁶ = 1 / 4096

Hence,

1 / 4096 = 0.00024414062

Therefore,  the value is less than 1.

Let's change one sign to make the expression greater than 1.

Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]

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a) The amount of money in the account at the beginning is $222,222.222.

b) The total amount of money withdrawn from the account is $400,000.

c) The amount of interest earned is $177,777.778.

It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".

A = $20,000*20 = $400,000

Let the amount of money in the account at the beginning be represented by the variable "P".

A = P*R*T

400,000 = P*0.09*20

400,000 = P*1.8

P = 222,222.222

The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".

I = A - P = $400,000 - $222,222.222 = $177,777.778

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The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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Answer:

1-5+171

Step-by-step explanation:

Stock used to sell for $105.81 ten years ago.

[tex]CAGR = ((\frac{EV}{BV} )^{\frac{1}{n}}-1)*100[/tex]

Here, CAGR = Compounded Annual Growth Rate = -2.3%

               EV = Ending Value = x

               BV = Beginning Value = $83.80

                  n = No. of years = 10

Putting the values in the equation,

[tex]-2.3 = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)*100[/tex]

[tex]\frac{-2.3}{100} = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)[/tex]

[tex]\frac{-2.3}{100}+1 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{100-2.3}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{97.7}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]0.977 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex](0.9777)^{10} = \frac{83.80}{x}[/tex]

[tex]\frac{83.80}{x}=0.792[/tex]

[tex]x = \frac{83.80}{0.792}[/tex]

x = 105.81

Hence, the beginning value is $105.81.

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The credit sale after state and local tax payable is 2562$.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The credit sale before sales taxes = 2800$,

The rate of state sale tax = 6%,

And rate of local sale tax = 2.5%

The sale after state tax = 2800-2800×6/100=2800-168=2632,

The sale after local tax=2800-2800×2.5/100=2800-70=2730

The credit sale after state and local tax= 2800-168-70=2562.

The required credit sale =2562$.

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The value of WV is 9x - 10

A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.

From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.

We have;

This is represented as;

WV + VY = WY

Then;

WV = WY - VY

substitute the values

WV = 5x + 19 - (29 - 4x)

expand the bracket

WV = 5x + 19 - 29 + 4x

collect like terms

WV = 9x - 10

Hence, the value is  9x - 10

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Answer:

X=-27

Step-by-step explanation:

X/-9 = 3

(-9) * X/-9  =(-9) * 3

X=(-9) * 3

X=-27

Answer:

x=-27

Step-by-step explanation:

x/-9=3

Multiply each side by -9

x=-27

That's it!

Answer:

Joseph's present age=3 yrs

David's present age=9 yrs

Step-by-step explanation:

Let Joseph's present age be x.

David's present age=3x

__________________

Ater 3 yrs,

Joseph's age=x+3

David's age=2(x+3)

Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.

Now, balance them.

3x+3=2(x+3)

3x+3=2x+6

x=3

D"s prsent age=9

J's present age=3

Answer:

The difference is the what the sum of 2+x is

Step-by-step explanation:

suppose x=3 2+3 = 5

the difference between 5 and 2 is 3

The equation that could be used to determine x, the number of purses Paula must sell to pay for the new equipment is;

A. 5.00x - 2.25x = 5000

We are told the materials costs $2.25 per purse.

She sells the materials for $5 each.

If the number of materials she purchased was x, it means that;

Selling price - Cost price = 5.00x - 2.25x

Now, we are told that she wants to invest $5000 for some new equipment. This means that she must realize at least $5000 in profit from the sales she is making of the materials.

Since the formula for profit is;

Profit = Selling Price - Cost Price

Then, we will have;

5.00x - 2.25x = 5000

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Answer:  5.00x - 2.25x = 5000

Step-by-step explanation:

The equation of the parabola which passes through the point (-3, -8) as described and has x-intercepts -7 and -4 as described is; y = -2 (x + 4) (x + 7).

It follows from the task content that the equation of the parabola whose x-intercepts are -7 and -4 and has the point, (-3, -8) on it be determined.

Since the equation of a parabola in the factored form usually takes the form;

y = a (x - f) (x - g) in which case when f and g are x-intercepts of the parabola.

Therefore, we have; y = a (x - (-4)) (x - (-7))

y = a (x + 4) (x + 7)

Hence, to find the value of a, we set y = -8 and x = -3 so that we have;

-8 = a (-3 + 4) (-3 + 7)

-8 = 4a

a = -2.

Therefore, the equation of the parabola is; y = -2 (x + 4) (x + 7).

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The probability that a single lottery has one correct number, using the hypergeometric distribution, is of:

0.4159 = 41.59%.

The probability mass function of the hypergeometric distribution is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the function are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

N = 40, k = 7, n = 7.

The probability that a single lottery has one correct number is P(X = 1), hence x = 1 and the calculation is as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,40,7,7) = \frac{C_{7,1}C_{33,6}}{C_{40,7}} = 0.4159[/tex]

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If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current  is 4km/h  and no current is 5km/h.

Let b represent  the speed of the boat

Let c represent  the speed of the current

Downstream:

b + c = 9

Upstream:

b - c = 1

Subtraction

2c = 9-1

2c = 8

Divide both side by 2c

c = 8/2

c = 4 km/h (current)

No current

b = 9 - 4

b = 5 km/h

Therefore the speed is 4km/h and no current is 5km/h.

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The volume of liquid contained by cone is 105 inches cube.

What is volume?

It can be defined as the total content which can be held inside a container.

Main body:

the volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex]  , where r = radius and h = height of cone

diameter = 10 , so radius = d/2 = 5 inches

V = [tex]\frac{1}{3}\pi 5*5*4[/tex]

V = 3.14 *5*5*4*1/3

v≈105 inches cube

Hence the volume is 105 inches cube.

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A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.

The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.

From the given information, we get

x - y = 6 ...............(1)

"if five times the smaller number is two times the larger number"

from the above information, we get

5y = 4x + 2

5) To simplify the value of y:

y = (4x +2) / 5 ...............(2)

Substitute  y = (4x +2) / 5 in (1), then we get

x - (4x + 2) / 5 = 6

5x / 5 - (4x + 2) / 5 = 6

simplifying the above equation, we get

(5x - 4x - 2) / 5 = 6

x - 2 = 5 x 6

x -2 = 30

x = 32

Substitute the value of x in (2)

y = 4(32) + 2 / 5

simplifying the above equation, we get

y = 130 / 5

y = 26

From (1), we get

x - y = 6

substitute the value of x and y in the above equation,

32 - 26 = 6

6 = 6

6) T is the 10s digit

X is the one's digit

The two digit number is 10T + X

It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits

10T + X = 7(T+X)

By using distributive law

10T + X = 7T + 7X

10T + X - 7T - 7X = 0

simplifying the above equation, we get

3T - 6X = 0

3(T - 2X) = 0

T - 2X = 0

T = 2X

The tens digit is 3 more than the one's digits, so

T = X + 3

Then we have  

T = 2X = X  + 3

Subtracting X from both sides,

T - 3 = X  + 3 - 3

X = 3

The Tens digit is 6.

The number is 63.

The sum of the digits is 9.

9 × 7 = 63.

Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

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Answer:

Step-by-step explanation:

ABC = the draw of the square means that the angle is right

We can now say that the other two angles are acute because the sum of the interior angles of a triangle is 180 degrees

BCA = acute

CAB = acute

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?

f(x) = 1500(1.15)x

f(x) = 1500(115)x

f(x) = 1500(2.15)x

f(x) = 1500(215)x

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Correct answer is A 5

A golf club costs $342 at retail. The markup rate is 71.4% if the golf store has increased the price by $42.

Given,

The difference in prices is  $342 - $42 = $300

So, we need to find what percentage of 42 is 300

We do this by dividing: 300/42 = 7.14

which is 71.4 %.

So, the markup is  71.4 %.

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The value of TU is 21

From the question, we have

ST=3x+3 and TU=2x+9

ST = TU

3x + 3 = 2x + 9

3x - 2x = 9 - 3

x = 6

substituting the value, we get

TU = 2x + 9

= 2 (6) + 9

= 12 + 9

TU = 21

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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The values of the variables as represented in the right triangle are; (8√15)/3 and s = (4√15)/3.

It follows from the task content that the values of the variables in the right triangle are to be determined.

It follows from trigonometric ratios that;

Sin (∆) = opposite / hypothenuse

Cos (∆) = adjacent / hypothenuse

Tan (∆) = opposite / adjacent

It therefore follows from the attached image that;

Sin (60) = 4√5 ÷ p

p = 4√5 ÷ √3/2

p = (8√15)/3.

Also;

Tan (60) = 4√5 ÷ s

s = 4√5 ÷ √3

s = (4√15)/3

Therefore, the value of the variables are; p = (8√15)/3 and s = (4√15)/3.

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Answer:

given point is (-3,-2)

The rule for a rotation by 270° about the origin is (x,y)→(y,−x).

So,

(-3,-2)==============(-2,3).

there fore,

(-2,3) is the image point of (-3,-2)after the transformation r(x-axis) and rotation 270°.

The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

What is the scale factor?

A scale factor is Scaling the shape of an object. it means the shape of the object remains the same but the size of the object is either increased or decreased. A scale factor greater than 1 means size is increased and less than one means size is decreased

We are given a point (0,-4)

Which is to be scaled by the factor of 2 at the center position

As the value is greater than 1 the size increase

We multiply the coordinate to find the new coordinates

We get (0,-8)

Hence, The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

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Answer:

green 45 times or 40 a note

The possible roots for the given equation are, -1,3, -1-2i, -1+2i.

What do you mean by the roots of an equation?

The values of the variable that fulfill the equation are known as the roots of a quadratic equation. In addition, they are referred to as the "solutions" or "zeroes" of the quadratic equation. For instance, x = 2 and x = 5 satisfy the quadratic equation x2 - 7x + 10 = 0 and are hence the roots of the equation.

F(x) = x4-2x2-16x-15 has a root (zero) that you should find.

Finding x values for which F(x)=0 is the goal of the Polynomial Roots Calculator method set.

A tool from the list above is the rational roots test. Only numbers x that can be represented as the quotient of two integers, or rational roots, would be found.

According to the Rational Root Theorem, P and Q are factors of the Leading Coefficient and the Trailing Constant, respectively, if a polynomial zeroes for a rational number P/Q.

The Leading Coefficient is 1 and the Trailing Constant is -15 in this instance.

The component(s) are:

1 is the Leading Coefficient, while 1 is the Trailing Constant.

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Answer:

3

Step-by-step explanation:

y-intercept = b

The slope-intercept = y=mx+b

y=-2/5x+3

m=-2/5

b=3

If the equation was something like y=-2x-3, then the b would be -3 because you are subtracting 3.