The number of bacteria in a colony increases by 10% every 2 hours. What is the overall percent increase after 4 hours?

[tex]Here, h=41,0.25,y=1+x21

[/tex]

[tex]x     y101.020.25     0.9413 0.250.94140.750.64510.5

[/tex]

[tex]By Simpson's Rule:

[/tex]

[tex]∫011+x2dx=4×31

[/tex]

[tex][(1+0.5)+4(0.941+0.941+0.64)+2(0.8)]

[/tex]

[tex]=121[9.424]=0.785

[/tex]

Answer:

a= $10.00

Step-by-step explanation:

It's very simple. Move /8 to the other side of the equation. It should give you $1.25 x 8. Solve the multiplication and you should get $10.00.

If I didn't make my explanation clear enough, please comment. I sometimes don't even explain myself very well.

Answer:

a = 10

Step-by-step explanation:

a/8 = 1.25

multiply both sides by 8 to isolate a.

(8)(a/8) = 1.25(8)

which gives you

a = 1.25(8)

which simplifies to

a = 10

Answer:

In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the or the and define the length and width of the rectangle.

We can break one large of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the or quotient.

To multiply two 2-digit numbers, using the area model, follow the given steps:

Write the multiplicands in expanded form as tens and ones.

For example, 27 as 20 and 7, and 35 as 30 and 5.

Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.

Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.

On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.

Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.

write the product in the cell

Finally, add all the partial products to get the final product.

Here, for example, the area model has been used to multiply 27 and 35.

area model multiplication

Let us see how to find the product of 3-digit number by a 2-digit number using the area model.

Find the Product using Area Model

Let us now use the area model for the division. Here, we divide 825 by 5.

Area Model Division 1

Area Model Division 2

Fun Facts

The area model is also known as the box model.

The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.

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Step-by-step explanation:

Measure the width, length and height of the shipping box in inches. Multiply the width, length and height of the box to calculate its volume in cubic inches. For example, if the box is 20 inches wide, 24 inches long and 16 inches high, then the volume is (20)(24)(16) = 7,680 cubic

Answer:

The volume of the shipping box would be 36 9/16

Step-by-step explanation:

One method to find the volume of the shipping box would be (l)(w)(h)

one we plug in our dimensions the equation would become 3 1/4 x 3 x 3 3/4

To simplify this we would first

Multiply

3 1/4 x 3 x 3 3/4 = 39/4 x 3 3/4

The bolded parts are the pieces we are working on

3 1/4 as an improper fraction is 13/4

13/4 x 3 = 13 x 3/4 = 39/4

- The second step would be to

Convert the mixed number to an improper fraction.

3 3/4  = ( 3 × 4 ) / 4 + 3/4 = 12 + 3 / 4 = 15/4

Now we have to Multiply

39/4 x 15/4 =  39 x 15 / 4 x 4 = 585/16

Lastly, we have to simplify

585/16 = 36 9/16

9514 1404 393

Answer:

  x² -22 = 0

Step-by-step explanation:

The roots are opposites, so the equation is pretty simple.

  x = ±√22

  x² = 22 . . . . . square both sides

  x² -22 = 0 . . . . your quadratic equation in standard form

Answer:

192

Step-by-step explanation:

geometric mean theorem :

with p and q being the segments of the Hypotenuse, then

h = x = sqrt(p×q)

p = 144

q = 400-144 = 256

h = x = sqrt(144×256) = 12×16 = 192

9514 1404 393

Answer:

  none

Step-by-step explanation:

Multiplying the second equation by -3 gives ...

  6x -3y = -24

Values of x and y that satisfy this equation cannot also satisfy the first equation ...

  6x -3y = 5

There are no solutions to this system of equations.

__

The equations describe parallel lines. There is no point of intersection.

Answer:

3. 6a+60

5. 25+5w

7. 90-10t

11. 4.5-12c

13. f-2

15. 12z+1.5

Step-by-step explanation:

3.

6(a+10)

Multiply 6 by both factors in the parentheses, in this case, a and 10.

6*a = 6a

6*10 = 60

6(a+10) = 6a + 60

I only put the step- by- step explanation for #3, but you should be able to figure the rest out with that.

Answer:

40141

Step-by-step explanation:

Answer:

[tex]352\ yd^2[/tex]

Step-by-step explanation:

1. Approach

The surface area of a three-dimensional figure is the two-dimensional space around the figure. Simply put, if one was going to wrap the figure up in paper, the surface area is the amount of paper one would need to wrap the entirety of the figure. One can find the surface area of a figure by finding the area of each individual facet of the figure and then adding up the areas.

2. Finding the area of the triangular faces

The formula to find the area of a triangle is the following:

[tex]A_t=\frac{b*h}{2}[/tex]

Where (b) is the base of the figure, and (h) is the figure's height. Since there is only one type of triangular face, one only has to find the area of one triangular face and then multiply its measurement by four.

Triangle 1

[tex]A_t=\frac{b*h}{2}[/tex]

[tex]A_t=\frac{11*10.5}{2}[/tex]

[tex]A_1=\frac{115.5}{2}[/tex]

[tex]A_t=57.75[/tex]

3. Finding the area of the quadrilateral

The following formula can be used to find the area of a quadrilateral:

[tex]A_q=b*h[/tex]

Substitute the dimensions of the quadrilateral in and solve for its area:

[tex]A_q=b*h[/tex]

[tex]A_q=11*11[/tex]

[tex]A_q=121[/tex]

4. Find the total surface area of the figure

To find the total surface area of the figure, add up all of the area values of its faces. Remember the area of the triangular face is multiplied by four because there are four triangular faces.

[tex]4(A_t)+(A_q)=A[/tex]

[tex]4(57.75)+121=A[/tex]

[tex]231+121=A[/tex]

[tex]352=A[/tex]

Answer:

$.08 per mile

Step-by-step explanation:

$2.25          gallon

------------ * ---------------

gallon          28 miles

$2.25

-------------

28 miles

$.080357143 per mile

Rounding to the nearest cent

$.08 per mile

Answer:

incomplete question

Step-by-step explanation:

that is what is wrong with your question

Answer:

r = 4.3%

Step-by-step explanation:

6810= 6000(x)^3

6810/6000=  (x)^3

x = 1.043114431

r = 043114431

Answer:

7 ans-HCF is y

Step-by-step explanation:

soln

first expression=X and y

second expression=l and y

so HCF means common so the Ans is y

Answer:

48degrees

Step-by-step explanation:

From the circle geometry shown, traingle BDC is an isosceles triangle which shows means that their base angels are the same. Hence;

<B = <C

<CBD + <BCD + <D = 180

<BCD + <BCD + <D =180

2<BCD + <BDC = 180

Get <BCD;

<BCD+ <ECB = 90

<BCD + 48 = 90

<BCD = 90 - 48

<BCD = 42degrees

Get <BDC

2<BCD + <BDC = 180

2(42)+ <BDC = 180

84 + <BDC = 180

<BDC = 180 - 84

<BDC = 96

Since angle at the centre is twice that at the circumference, then;

<BAC = 1/2(<BDC )

<BAC = 96/2

<BAC = 48degrees

Answer:

The final price of the textbook rounded to the nearest dollar is $167

Step-by-step explanation:

To solve this problem, we need to find out what 13.5% of $147 equals.

13.5% = 0.135

0.135 x $147 = $19.845

$147 + 19.845 = 166.845

Round to the nearest dollar to get $167

Answer:

Cost of 1kg tomato=rs.75

Cost of 14kg tomato=(75×14)

rs.1050

9514 1404 393

Answer:

  4.8 years

Step-by-step explanation:

Solving the compound interest formula for the number of years gives ...

  t = log(A/P)/(n·log(1 +r/n))

where principal P invested at rate r compounded n times per year produces value A after t years.

  t = log(24805/22000)/(365·log(1 +0.025/365)) ≈ 4.800

The loan was for 4.8 years.

Answer:An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Step-by-step explanation:

[tex]\\ \Large\sf\longmapsto h(t)[/tex]

[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]

[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]

[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]

[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]

[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]

[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]

9514 1404 393

Answer:

  16.9

Step-by-step explanation:

The marked sides are the hypotenuse and the one opposite the angle. The relevant trig function is ...

  Sin = Opposite/Hypotenuse

Multiplying by the hypotenuse gives an equation for the opposite side.

  x = 22·sin(50°)

  x ≈ 16.9

Answer:

0.235 = 0.24

13.467 = 13.47

0.24+13.47=13.71

Answer:

GHC22.5

Step-by-step explanation:

90/3=30

30=0.75

30×0.75

=22.5

Answer:

Option C. √5/3

Step-by-step explanation:

We'll begin by simplifying √15 / 3√3. This can be obtained as follow:

√15 / 3√3

Rationalise

√15 / 3√3 × (√3 /√3)

(√15 × √3) / (3√3 × √3)

√45 / (3 × 3)

√45 / 9

Recall:

√45 = √(9 × 5) = √9 × √5 = 3√5

Thus,

√45 / 9 = 3√5 / 9

√45 / 9 = √5 / 3

Therefore,

√15 / 3√3 = √5 / 3

Thus, option C gives the right answer to the question.

Answer:

[tex]P(C'\ and\ H') =0. 2178[/tex]

Step-by-step explanation:

Let

[tex]C \to[/tex] Student with cat

[tex]H \to[/tex] Student has HBO sub

[tex]P(C) = 66\% \\ P(H) = 37\%[/tex]

Required

[tex]P(C'\ and\ H')[/tex]

This is calculated as:

[tex]P(C'\ and\ H') = P(C') * P(H')[/tex]

Using complement rules, we have:

[tex]P(C'\ and\ H') = [1 - P(C)] * [1 - P(H)][/tex]

So, we have:

[tex]P(C'\ and\ H') = [1 - 66\%] * [1 - 37\%][/tex]

[tex]P(C'\ and\ H') = [33\%] * [66\%][/tex]

[tex]P(C'\ and\ H') =0. 2178[/tex]

Answer: [tex]10,000\ lb.ft[/tex]

Step-by-step explanation:

Given

Initial weight of the bucket is [tex]145\ lb[/tex]

It is lifted at constant rate and rate of sand escaping is [tex]0.5\ lb/ft[/tex]

At any height weight of the sand is [tex]w(h)=145-0.5h[/tex]

Work done is given by the product of applied force and displacement or the area under weight-displacement graph

from the figure area is given by

[tex]\Rightarrow W=\int_{0}^{80}\left ( 145-0.5h \right )dh\\\\\Rightarrow W=\left | 145h-\dfrac{0.5h^2}{2} \right |_0^{80}\\\\\Rightarrow W=\left [ 145\times 80-\dfrac{0.5(80))^2}{2} \right ]-0\\\\\Rightarrow W=11,600-1600\\\\\Rightarrow W=10,000\ lb.ft[/tex]

Answer:

(8x²+7y²–z²+2yz+3xz–5xy) × ( 2x–3y)

= (16x³+14xy²–2z²x+4yzx+6x²z–10x²y –24yx²–21y³+3z²y–6y²z–9xzy+15xy²)

=( 16x³+29xy²–2z²x–5xyz+6x²z–34x²y–21y³+3z²y–6y²z)

[tex] = 16 {x}^{3} - 21 {y}^{3} - 2 {z}^{2}x + 3 {z}^{2} y - 5xyz - 6 {y}^{2} z + 6 {x}^{2} z - 34 {x}^{2} y+ 29x {y}^{2} [/tex]

I hope I helped you^_^

Answer:

Stratified sampling

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

People divided by groups, for each group(<100, >100<500, >500), a number(not all) is selected, so stratified sampling.

Answer:

The numbers that 430 is divisible by are 1, 2, 5, 10, 43, 86, 215, and 430.