A colony of bacteria doubles in population every hour. Approximately how many hours will it take until the colony is 32
size?

Answer:

Is there any more information than that? if there Is I might be able to help

$202.50 is your answer

Using arithmetic sequences, it is found that:

a) The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex].

b) 14 blocks will be needed to create the next figure.

c) The sequence means that the number of blocks start at 5 and increase by 3 each figure.

3) The 4th term of the sequence is of -3.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

From the figure, we have that:

Hence the first term and the common ratio are given as follows:

[tex]a_1 = 5, d = 3[/tex]

The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex], hence the sequence means that the number of blocks start at 5 and increase by 3 each figure.

For item b, the amount is:

[tex]a_4 = 5 + 3(4 - 1) = 14[/tex]

14 blocks will be needed to create the next figure.

For item 3, the sequence is given by:

[tex]a_n = 12 - 5(n - 1)[/tex]

Hence the 4th term is:

[tex]a_4 = 12 - 5(4 - 1) = -3[/tex]

The 4th term of the sequence is of -3.

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Answer:

Step-by-step explanation:

The simplified form of the expression (3/5)³  = 27/125

Step-by-step explanation:

The given expression is (3/5)³

3/5 is a proper fraction.

(3/5)³ can be written as,

(3/5)³ = 3³/5³

To find  3³ and 5³

3³ = 3*3*3 = 27

5³ =5*5*5 =125

Based on the results, the below  list shows a comparison of the overall performance of the portfolios, from best to worst:

Portfolio 2, Portfolio 3, Portfolio 1

What is weighted average ROR?

The weighted average ROR is the sum of rate of returns of the assets in the portfolio multiplied by the portion of the portfolio invested in each security

Portfolio 1:

total investment=$700+$2,575+$220+$1,000+$1,430

total investment=$5925

weighted average ROR=(-3.8%*$700/$5925+2.1%*$2575/$5925+11.3%*$220/$5925+5.8%*$1000/$5925+1.6%*$1430/$5925)

weighted average ROR=2.25%(third)

Portfolio 2:

total investment=$1,250+$1,700+$1,515 +$1,345+$1,675

total investment=$7485

weighted average ROR=(-3.8%*$1,250/$7485+2.1%*$1,700/$7485+11.3%*$1,515 /$7485+5.8%*$1,345/$7485+1.6%*$1,675/$7485)

weighted average ROR=3.53%(first)

Portfolio 3:

total investment=$1,025+$500+$790+$250+$2,500

total investment=$5065

weighted average ROR=(-3.8%*$1025/$5065+2.1%*$500/$5065+11.3%*$790/$5065+5.8%*$250/$5065+1.6%*$2,500/$5065)

weighted average ROR=2.28%(second)

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The amount Reiko invested in x shares is 1,700,000 based on 8% annual dividend

How do represent the amounts invested in each share?

The fact that Reiko invested 200,000 more on x shares means that if we assume that he invested Z on y shares then the amount invested in x shares is Z+200000

return on x shares=(Z+200,000)*8%

return on x shares=0.08Z+16000

return on y shares=Z*9%=0.09Z

total return=0.08Z+16000+0.09Z

total return=0.17Z+16000

total earnings=271000

271000=0.17Z+16000

271000-16000=0.17Z

255000=0.17Z

Z=255000/0.17

Z=1,500,000

Z+200,000=1,500,000+200,000=1,700,000

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Answer: 59

Step-by-step explanation:

Answer:

The slope is 1

Step-by-step explanation:

(3-0)/(3-0) = 3/3 = 1

Answer: 30

Step-by-step explanation:

Slope: y/x

y/x =

+60/+2=

60/2=30

The correct answer is 8 cm.

Given the surface area = 518 cm²

breadth of the cuboid = 11 cm

height of the cuboid = 9 cm

Now let l be the length of the cuboid,

The total surface area (TSA) of a cuboid is provided by the sum of the areas of its six rectangles, where l, b, and h are the length, width, and height, respectively

Cuboid's total surface area formula,

Thus the surface area of the cuboid = 2(lb+bh+lh)

518 = 2 ( l × 11 + 11 × 9 + l × 9 )

518 = 2 (11l + 99 + 9l)

259 = 11l +99 +9l

259 - 99 = 20 l

160/20 =l

length = 8 cm

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Using linear functions, it is found that:

1. The functions are given as follows:

2. They will have the same elevation after 18.4 minutes.

3. At that time, the elevation is of 18,150 feet.

A linear function is modeled in slope-intercept form by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence the functions are given as follows:

They will have the same elevation when:

E1(t) = E2(t)

28270 - 550t = 5270 + 700t

1250t = 23000

t = 23000/1250

t = 18.4.

They will have the same elevation after 18.4 minutes.

This elevation will be of:

28270 - 550(18.4) = 18150.

At that time, the elevation is of 18,150 feet.

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Answer:

I never took the lesson but il try!

Step-by-step explanation:

so if y is 34° and x should be 54° if I am being correct!

The probability of a random probability of a random student being chosen who is a female and is not between the ages of 18 and 20 will be 0.06.

From the information, 53% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 31% are both male and between the ages of 18 and 20.

Probability to females = 100% - 53% = 47%

Therefore, the probability of a random student being male or between the ages of 18 and 20 will be:

= 37% - 31%

= 6%

Therefore, the probability of a random student being female or between the ages of 18 and 20 will be 6%.

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Value of n is 4

The area of a rectangle is equal to the product of its length and width.

we know ,

the area of  rectangle, multiply the length, , and the width, ,

and set the product equal to the area.

area of rectangle        = length * width

            54                  = 3(n - 1) * (n + 2)

             54                 =( 3n - 3) * (n + 2)

multiply ( 3n - 3) with  (n + 2)

we get,

              54                = [tex]3n^{2} + 6n - 3n -6[/tex]

              54                = [tex]3n^{2} + 3n -6[/tex]

              54                = 3([tex]n^{2} + n -2[/tex])

             [tex]\frac{54}{3}[/tex]                  =  ([tex]n^{2} + n -2[/tex])

             18                 =  ([tex]n^{2} + n - 2[/tex])

 [tex]n^{2} + n - 2[/tex] - 18           = 0

 [tex]n^{2} + n - 20[/tex]                = 0

solve them

 [tex]n^{2} + 5n + 4n -20[/tex]       = 0

 n (n + 5) - 4 (n + 5)   = 0

(n + 5)(n -4)  

then we get,            

n = -5 , n = 4

value of n should not be negative . so value of n is 4

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area

Area of rectangle = Length x Breadth

A = lb

how to Factoring Quadratic Equation

Step 1: Consider the quadratic equation ax2 + b x + c = 0

Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.

(number 1)(number 2) = ac

(number 1) + (number 2) = b

Step 3: Substitute these two numbers in the formula given below:

(1/a) [a x + (number 1)]  [a x + (number 2)] = 0

Step 4: Finally simplify the above equation.

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Solution  : y = -7

One Variable in the linear equation :

The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equations in two variables, it has two solutions.

-6y+6= -2(4y + 4)

-6y = -8y -8 -6

-6y +8y = -14

2y = -14

y = -14/2

y = -7

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Answer: 3/-4

The slope is measured in terms of rise over run. Rise is how many units you go up or down from the point (0, 0). Run is how many units you go left to right from the point where rise left off.  For this question, we go up 3 and to the left 4. SO that's a 3 on top and a -4 on the bottom.

I hope this helps! :) I'm a huge Algebra nerd!!! I love Algebra. :)

The number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

Proportion can be defined as the mathematical comparison of two numbers.

It is also said to be an equation defining two given ratios as equivalent to each other.

From the information, we have that;

By recycling 1 ton of paper, 6, 953 gallons of water was saved

To determine the gallons of water that would be saved after recycling 4 tons of paper, we have to;

If 1 ton of paper = 6, 953 gallons of water

Then 4 tons of paper = x

cross multiply

x × 1 = 6953 × 4

multiply through

x = 27, 812 gallons

The number of gallons that would be saved after the recycling would be

27, 812 gallons

Thus, the number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812

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The length of AB is 11.40 units.

The length of two points can be calculated using the distance formulae.

The distance formulae comes under the Co-ordinate geometry section.

The distance between two points is measured by squaring  the sum of the difference between the x and y co-ordinates and then applying the square root to the result.

Here the two points given are A(-3,7) and B(6,14).

The length of the line segment AB is = √(-3-6)²+(7-14)²

                                                              = √(-9)²+(-7)²

                                                              = √81+49

                                                              = √130

                                                              = 11.40 units

So, the length of line segment AB is 11.40 units.

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Answer: Find [tex]2^{21} = (2y)^{3}[/tex] then the solution of [tex]y^{3}[/tex] = [tex]2^{7}[/tex]

Step-by-step explanation:

Given data,

                     [tex]2^{21}[/tex] = [tex](2y)^{3}[/tex]

[tex](a^{m)^{n} }[/tex] = [tex]a^{m*n}[/tex] says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it's the same as multiplying the number a by itself m * n times.

we can use formula,

                    [tex](a^{m)^{n} }[/tex] = [tex]a^{m} a^{n}[/tex]

So,

we can write,

                       [tex]2^{21}[/tex] = [tex]2^{3} y^{3}[/tex]

                        [tex](2^{7} )^{3}[/tex] = [tex]2^{3} y^{3}[/tex]

                          [tex]2^{7} 2^{3}[/tex] = [tex]2^{3} y^{3}[/tex]

cancel the [tex]2^{3}[/tex] in both sides,

Then,

                       [tex]2^{7}[/tex] = [tex]y^{3}[/tex]

Therefore,

                      [tex]y^{3}[/tex] = [tex]2^{7}[/tex]

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Answer:

y=x+6

Step-by-step explanation:

First, write out the slope intercept equation.

y=mx+b

Ok, the first step for finding a linear equation is finding the y-intercept. The line crosses the y-axis at 6, so the y-intercept is 6. Plug that into the slope-intercept Equation:

y=mx+6

Then, slope is rise over run, and the line goes up 1 and right 1 to get to the next point, so divide those numbers.

1/1=1

Then plug that into your slope intercept equation:

y=1x+6

Since the one won't do anything, it will just be this:

y=x+6

The equation that shows the amount Christa and Megan each had in sales in July is 630 + 0.03x = 609 + 0.035x

An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.

Let x represent the amount Christa and Megan each had in sales in July. Hence:

For Christa = 18(35) + 0.03x

For Megan = 21(29) + 0.035x

630 + 0.03x = 609 + 0.035x

The equation that shows the amount Christa and Megan each had in sales in July is 630 + 0.03x = 609 + 0.035x

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Using a transformation of the parent function y = x², the graph of f(x) = (x + 5)² is given at the end of the answer.

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

Examples of transformations are as follows:

For this problem, the parent function is given by:

f(x) = x².

Which has a parabolic graph with vertex at (0,0).

For f(x) = (x + 5)², we have that x -> x + 5, meaning that the function is shifted 5 units left, meaning that the parabola has a vertex at (0,-5), and the graph is given at the end of the answer.

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The solutions after rounding the numbers are;

a. 80

b. 190

c.780

d. 90

What is Rounding number?

Rounding means making a number simpler but keeping its value close to what it was.

The questions are given as;

a. -28 - 53

b. 514 + -321

c. -888 - - 111.

d. -61.1 + -29.3

Now, solve and rounding the numbers as;

a. -28 - 53 = 81

After rounding it we get;

81 ≈ 80

Hence, -28 - 53 = - 80

b. 514 + -321 = 514 - 321

                   = 193

After rounding it we get;

⇒ 193 ≈ 190

Hence, 514 + -321 ≈ 190

c. -888- - 111 = - 888 + 111

                  = - 777 ≈

After rounding it we get;

- 777 ≈ - 780

d. -61.1 + -29.3 = -61.1 - 29.3

                      = - 90.4

After rounding it we get;

- 90.4 ≈ - 90

So, The solutions are;

a. 80

b. 190

c.780

d. 90

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Answer:

A∩B = { 3 }

Step-by-step explanation:

A∩B means "the intersection of A and B" as in "all elements that appear in BOTH sets".

Only 3 appears in both sets.

Answer:

2/3 < 14/6

3/8 < 8/3

2 1/6 > 5/9

A quadratic function is one that has the formula f(x)=ax2+bx+c, where a, b, c, and an are all real values and a 0 a 0. The conventional form of a quadratic function is this form.

The quadratic function's graph is a U-shaped curve known as a parabola.

Below is a graph of the equation y=x2y=x2; it is a parabola.

The parabola rises if a>0a>0 in f(x)=ax2+bx+cf(x)=ax2+bx+c.  In this case, the vertex is the smallest or lowest point of the parabola.

The vertex of the y=x2y=x2 graph is (0, 0). (0,0).

The parabola opens downhill if a0a0 in f(x)=ax2+bx+cf(x)=ax2+bx+c is true. The maximal or highest point of the parabola in this instance is called the vertex.

The value of cc for an equation in standard form yields the graph's yy-intercept.

The axis of symmetry is the line that divides the parabola into two symmetric sections and runs through the vertex.

In the case of the graph y=ax2+bx+cy=ax2+bx+c, where a=0a=0, the equation for the axis of symmetry is x=b2ax=b2a.

The yy-axis, with x=0x=0, is the axis of symmetry in all of the graphs above. The axis of symmetry in the graphs below is different (marked in red.) As you can see, cc still provides the yy-intercept.

If you write a quadratic function like x=f(y)=ay2+by+cx=f(y)=ay2+by+c, instead of writing yy as a function of xx, you obtain a parabola with a horizontal axis of symmetry.

Hence, that the xx-intercept in this situation is cc. When aa is positive, the graph opens to the right; when aa is negative, it opens to the left.

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Based on the area of T, the area of U can be calculated to be 272 cm²

When you have an object that is enlarged and have the area of the object before it was enlarged, the area of the enlarged object is:

= Area of original object x Scale factor of enlargement ²

The scale factor is:

= Side of U / Corresponding side of T

= 12 / 3

= 4

The scale factor is 4.

The area of U is therefore:

= 17 x 4²

= 272 cm²

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Answer:

6 trips

Step-by-step explanation:

divide by 3

17/3

5.66666666

now round it off and say 6