As células da bactéria Escherichia coli têm formato cilíndrico, com 8 x 10−7 metros de diâmetro. O
diâmetro de um fio de cabelo é de aproximadamente 1 x 10−4 metros. Dividindo-se o diâmetro de um fio
de cabelo pelo diâmetro de uma célula de Escherichia coli, obtém-se, como resultado

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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The required number of markers does Gerald has 56 markers.

Let's represent the number of markers that Gerald has with the variable "m", and the number of pens he has with the variable "p". We can set up two equations based on the information given:

m + p = 78 (equation 1)

(m + 11) + (p + 11) = 78 (equation 2)

In equation 2, we add 11 to both the number of markers and the number of pens, since Gerald has 11 more of each. We can simplify equation 2 by combining like terms:

m + p + 22 = 78

m + p = 56 (equation 3)

Now we have two equations with two variables. We can use either substitution or elimination to solve for one of the variables. Let's use substitution and solve for "m" in terms of "p" using equation 1:

m + p = 78

m = 78 - p

Now we can substitute this expression for "m" into equation 3:

m + p = 56

(78 - p) + p = 56

Simplifying the equation, we get:

78 - p + p = 56

78 = 56 + p

p = 22

Therefore, Gerald has 22 pens. To find the number of markers he has, we can substitute this value of "p" into equation 1:

m + 22 = 78

m = 56

So, Gerald has 56 markers.

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Answer:

x = -8 and x =1

Step-by-step explanation:

Given the equation

X^2+7x=8

X^2+7x-8 = 0

Factorize

x^2 - x +8x - 8 = 0

x(x-1)+8(x-1) = 0

(x+8)(x-1) = 0

x+8 = 0 and x-1 = 0

x = 0-8 and x = 0+1

x = -8 and 1

Hence the required solution is x = -8 and x =1

Answer:

80.78°

Step-by-step explanation:

When the 30 cm long string will be bent in the form of a sector it's two sides will be radii of the sector and lower part be the arc. Length of the arc can be found as given below.

Length of the string = 30 cm

radius of sector (r)= 8.8 cm

Length of the arc (l) = 30 - 2*8.8 = 30 - 17.6 = 12.4 cm

Let the sector makes \(\theta\) angle at the centre of the circle.

Formula for length of arc of a sector is given as:

\(\huge \red{l=\frac{\theta}{360\degree}\times 2\pi r}\)

Plugging the values of l and r in the above formula, we find:

\(12.4 = \frac{ \theta}{360 \degree} \times 2(3.14)(8.8) \\ \\\implies12.4 = \frac{ \theta}{360 \degree} \times 55.264 \\ \\ \implies \: \theta = \frac{12.4 \times 360 \degree}{55.264} \\ \\ \implies \: \theta =80.775 \degree \\ \\ \implies \: \theta \approx \: 80.78 \degree\)

To calculate the angles of a figure there are different strategies

In this case we can divide into different geometric shapes for example a square and a right triangle

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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The price of a gallon of milk relative to a pound of butter is 1.25.

The price of a loaf of bread relative to a gallon of milk can be calculated by finding the ratio of the price of a loaf of bread to the price of a gallon of milk.

This ratio can be calculated as follows:

Price of loaf of bread / Price of gallon of milk

= $1.50 / $3.00

= 0.5

Therefore, the price of a loaf of bread relative to a gallon of milk is 0.5.

The price of a gallon of milk relative to a pound of butter can also be calculated by finding the ratio of the price of a gallon of milk to the price of a pound of butter.

This ratio can be calculated as follows:

Price of gallon of milk / Price of pound of butter

= $3.00 / $2.40

= 1.25

Therefore, the price of a gallon of milk relative to a pound of butter is 1.25.

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Answer:

Step-by-step explanation:

The ratio of white loaves to brown loaves is 6:4

20 loaves per day divide 10 parts(6+4)

20/10=2  One part is 2 loaves

In one day, the baker makes 6x2=12 white loaves and 4x2=8 brown loaves

240 divided by 8 = 30 days.

The fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.

Given,

The area of the top side of a piece of sheet metal = 4 square feet

The sheet metal is submerged horizontally in 7 feet of water.

Fluid Force on the top side can be found as follows,

Formula used:

Fluid Force = weight-density × volume × depth of fluid

Fluid Force = 62.4 × volume × 7

As the sheet metal is completely submerged, the volume is equal to the area of the sheet metal.

Volume = Area × Depth

= 4 × 7

= 28

Fluid Force = 62.4 × 28 × 7

                   = 12441.6 lb

Thus, the fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.

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Therefore, the fluid force on the top side is 55838.08 lb.

Given, the area of the top side of a piece of sheet metal is 4 square feet and it is submerged horizontally in 7 feet of water.

The weight-density of water is 62.4 pounds per cubic foot.To find: the fluid force on the top side.Solution:Fluid force formula is given by,

F = ρ * g * V

Where, ρ is the density of the fluidg is the acceleration due to gravityV is the volume of the fluid displaced.Furthermore, the volume of fluid displaced is equal to the volume of the metal sheet submerged in the water.

Therefore,Volume of fluid displaced = Volume of metal sheet submerged in the water = area of metal sheet * depth submerged

Volume of metal sheet submerged in the water = 4 square feet * 7 feet

= 28 cubic feet

Now, calculate the fluid force on the top side of the metal sheet by using the fluid force formula.

F = ρ * g * V

Here, the density of water,

ρ = 62.4 pounds per cubic foot

g = 32.2 ft/s² (the acceleration due to gravity)

V = 28 cubic feet∴

F = 62.4 * 32.2 * 28 lb

= 55838.08 lb

Therefore, the fluid force on the top side is 55838.08 lb.

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Answer:

3

Step-by-step explanation:

x1y1 x2y2

(1,-1)+(5,-2)

0+3

3

Answer:

d.) y > 41

Step-by-step explanation:

33 < y - 8

41 < y

The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.

The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.

In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.

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Answer:

m<a is 32º

Step-by-step explanation:

4x-8=2x+12

   +8       +8

4x=2x+20

-2x     -2x

2x=20

÷2

x=10

4x-8

4(10)-8

40-8

32

Answer:

the answer u r looking for is 5 I might be wrong tho lol

Answer:

90

Step-by-step explanation:

Answer:

Option A 7,000+200+20+9 is equivalent expression of 7,229. Because after adding 7,000+200+20+9 we get 7,299.

The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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A good point estimate for the population proportion is 0.01714. Option D is correct.

A good point estimate to use for the population proportion to test the effectiveness of the flu vaccine can be calculated by dividing the number of people who got the flu (12) by the total number of participants in the study (700).

Point Estimate = Number of people who got the flu / Total number of participants

Point Estimate = 12 / 700

Using a calculator, the approximate value of the point estimate is 0.01714 (rounded to five decimal places).

Therefore, the good point estimate to use for the population proportion to test the effectiveness of the flu vaccine is 0.01714. Option D is correct.

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The angle X of the given triangle is equal to 83.0°.

This law is represented by the equation: C²=A²+B²-2ABcosθ, where: A,B and C are the sides of a triangle and θ=angle.

For solving this question, you should apply the Law of Cosines, where:

A=8ft

B=16ft

C=17 ft

θ=X

\(C^2=A^2+B^2-2*A*B*cos\theta \\ \\ 17^2=8^2+16^2-2*8*16*cosX\\ \\ 289=64+256-256*cosX\\ \\ 256cosX=256+64-289\\ \\ 256cosX=31\\ \\ cosX=\frac{31}{256}\)

Therefore, \(arccos(\frac{31}{256} )=83.0^{\circ \:}\).

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If n is a positive integer, then the expression is equivalent to option A) \(\sqrt[3]{n^2}\).

Rational exponents are numbers which are written in the form of \(x^\frac{p}{q}\), where x is the base with positive integer and p/q is the rational exponent and q ≠ 0.

The given expression is (\(\frac{1}{n}\))^\(^\frac{-2}{3}\).

A number in the form, 1/a can be written as a⁻¹.

So 1/n can be written as n⁻¹.

So,

(\(\frac{1}{n}\))^\(^\frac{-2}{3}\) = (n⁻¹)^\(^\frac{-2}{3}\)

We have a rule for exponent that (xᵃ)ᵇ = xᵃᵇ

Using the rule,

(\(\frac{1}{n}\))^\(^\frac{-2}{3}\) = (n⁻¹)^\(^\frac{-2}{3}\)

         = \(n^{-1*\frac{-2}{3}\)

         = \(n^\frac{2}{3}\)

         = \(n^{2*\frac{1}{3}\)

         = \((n^{2})^\frac{1}{3}\)

By the definition of radicals, \(\sqrt[n]{x}\) = \((x)^\frac{1}{n}\), where x is positive integer.

So, \((n^{2})^\frac{1}{3}\) = \(\sqrt[3]{n^2}\)

Hence the equivalent expression is \(\sqrt[3]{n^2}\).

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Answer:

a4 = 5/9

Step-by-step explanation:

a1 = 15 , r = 1/3

, a4 =?

Explanation:

To find a4 we use formula

an = a1 · r

n−1

In this example we have a1 = 15 , r = 1/3

, n = 4. After substituting these values to above

formula, we obtain:

an = a1 · r

n−1

a4 = 15 ·

1

3

4−1

a4 = 15 ·

1

27

a4 =

5

9

Answer:

\(q^{-30}\)

Step-by-step explanation:

\((p^{2}q^{5})^{-4}\cdot(p^{-4}q^{5})^{-2}\\=p^{-8}q^{-20}\cdot p^{8}q^{-10}\\=p^{-8+8}\cdot q^{-20+-10}\\=q^{-30}\\\)

Answer:

40 乘以 2，答案是 80，所以我猜是 209/5。

我不太确定，但是...

希望有帮助

! :)

Answer:

The answer is 209/5=41.8

Step-by-step explanation:

40 2/5= 40.4

436/11=39.63...

209/5=41.8

201/5=40.2

40 1/4=40.25

Answer:

Answe 6 yeah i know 6

because you due

Answer:

1

Step-by-step explanation:

move like terms to each side

-f+4f+3f=8-2

simplify

6f=6

divide by 6 each side

f=1

Answer: I think the answer is Infinity.

Step-by-step explanation:

Answer:

n

Step-by-step explanation:

Answer:

List B

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, you must find the actual decrease in temperature.

Decrease = Yesterday's temperature - Today's temperature

Decrease = 80 - 75

Decrease = 5 degrees

Now, find the percentage decrease.

% Decrease = Actual decrease / Yesterday's temperature x 100

% Decrease = 5/80 x 100

% Decrease = 0.0625 x 100

% Decrease = 6.25 %

So, the percent decrease in high temperature from yesterday to today is 6.25%