A dish containing bacteria has a diameter of 0.0001 kilometer. The diameter of a bacterium is 10^-16 How many times larger is the diameter of the dish than the diameter of the bacterium

Answer:

1. Mode = 7

2. Range = 8

Step-by-step explanation:

The following set of data were obtained from the question:

4, 6, 5, 9, 3, 2, 7, 7, 1, 8

Mode =?

Range =?

1. Determination of the mode of the data.

Mode is simply defined as the mark (score) with the highest frequency. Thus we can obtain the mode as follow:

Scores >>>>>>> Frequency

4 >>>>>>>>>>>> 1

6 >>>>>>>>>>>> 1

5 >>>>>>>>>>>> 1

9 >>>>>>>>>>>> 1

3 >>>>>>>>>>>> 1

2 >>>>>>>>>>>> 1

7 >>>>>>>>>>>> 2

1 >>>>>>>>>>>> 1

8 >>>>>>>>>>>> 1

From the above illustration, we can see that the mark 7 has the highest frequency. Therefore, 7 is the mode of the data .

2. Determination of the range of the data.

Range of a given data is simply obtained by calculating the difference between the highest and the lowest score. The range can be obtained as follow:

Highest score = 9

Lowest score = 1

Range = Highest – Lowest

Range = 9 – 1

Range = 8

Answer:

7/8

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Because its the square root of 12

Answer:656.7577

Step-by-step explanation:

If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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Answer:

fg(x) = 3x² + 1

Step-by-step explanation:

fg(x)

f(3x² - 1)

(3x² - 1) + 2

3x² + 1

The value of the required function is \((3x^{3} + 6x^{2} - x - 2)\).

A function represents the relation between two sets. The first one is called domain and the second one is called range.

Two given functions are:

\(f(x) = x + 2 \\g(x) = 3x^{2} - 1\)

Therefore the required function,

\((fg)(x)= f(x)g(x) \\= (3x^{2} - 1)(x + 2)\\= 3x^{3} - x + 6x^{2} - 2\\ = 3x^{3} + 6x^{2} - x - 2\)

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Drag the following expressions accordingly to complete the proof:

1/sinx· cos x)/ (sinx/cosx  + cosx/sinx) = cos²x

(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x

(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x

(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x

(cos x/sinx) · (sinx·cosx) = cos²x

Given: (csc x cos x)/ (tan x + cot x) = cos²x

We want to prove the trigonometric identity.

We have:

(csc x· cos x)/ (tan x + cot x) = cos²x

Recall the following trig. expressions and substitute for them:

csc x = 1/sinx

tan x = sinx/cosx

cot x = cosx/sinx

(1/sinx· cos x)/ (sinx/cosx  + cosx/sinx) = cos²x

(cos x/sinx)/ ([sin²x/[sinx·cosx] + cos²x/[sinx·cosx]) = cos²x

(cos x/sinx)/ ([sin²x+cos²x] / sinx·cosx) = cos²x

Recall sin²x+cos²x = 1. Subsitiute for it to get:

(cos x/sinx)/ ( 1 / sinx·cosx) = cos²x

(cos x/sinx) · (sinx·cosx) = cos²x

cosx  · cos x = cos²x

cos²x = cos²x

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Answer:

a) The area of the right of z=0 is P(z >0) =0.5.

b) The area of the left of z=0 is P(z < 0) =0.5.

c) The area of the left of z=-1.35 is P(z <- 1.35) =0.0885.

d) The area of the left of z=-0.48 is P(z <-0.48) =0.3156.

Step-by-step explanation:

Here are the graphs respectively.

An expression which the model represent include the following: A. \(\frac{7}{8} \div \frac{1}{8}\).

In Mathematics and Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

By critically observing the model shown in the image attached below, we can reasonably infer and logically deduce that each interval represents the numerical value, 1/8.

Since the arrow increased from 0 to 7/8, it implies that an expression which the model represent can be written as follows;

\(\frac{7}{8} \div \frac{1}{8}\)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

y=2x-5/2

Step-by-step explanation:

Answer:

its 2.5cm i guess so.. check my answer given here

The answers are: \(F^{-1}\)(3) = -2

                            \((F^{-1} )^{1}\)(3) = -6

A function is an expression, equation or rule that defines a relationship between two or more variable.

Analysis:

Inverse of the function, f(x) = x-1/x+1

Let y = x-1/x+1

y(x+1) = x - 1

yx + y = x - 1

y +1 = x - yx

y+1 = x(1-y)

x = y+1/1-y

Inverse \(f^{-1}\) = x+1/1-x

at x = 3

\(f^{-1}\)(3) = 3+1/1-3 = 4/-2 = -2

To find the derivative of x+1/1-x

u = x+1, du/dx = 1, v = 1-x, dv/dx = -1

derivative d\(f^{-1}\)(x)/dx = 1-x(1) -(x+1)(-1)/\((1-x)^{2}\) = -2x/\((1-x)^{2}\)

at x = 3

-2(3) / (1-3)2 = -6/4 = -3/2

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The total surface area of the pyramid is 220 cm squared

The total surface area of the pyramid is the sum of the area of the four triangles and the area of the square. That is:

total surface area of the pyramid = 4*(area of triangle) + area of square

total surface area of the pyramid = 4*(30) + 10²

total surface area of the pyramid = 120 + 100

total surface area of the pyramid = 220 cm²

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Here we have a problem of rates of work, where we want to find the rate at which two people would work together, so we can find the time it takes to complete a given job when these two work together..

We will find that they need to work for 6/5 hours to do the laundry together.

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

We know that:

Then we can define:

Where the rates are computed as the quotient between 1 (1 total laundry completed) and the amount of time it takes to do it.

If they work together, the rate just adds up, so we will have:

rate = (M + R) = 1/3h + 1/2h

Now we need to write that as a single fraction, so we get:

rate =  1/3h + 1/2h = 2/6h + 3/6h = 5/6h

Now we can write an equation of the form:

rate*time = 1

Where the 1 again, means "one complete laundry done".

Then we have:

(5/6h)*T = 1

T = (6/5)h

This means that they need to work for (6/5) hours to do the laundry together.

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Answer:

Vertical

Step-by-step explanation:

Answer:

∠1 and ∠3 = vertical

Step-by-step explanation:

vertically opposite angles are equal

Answer:

8=8 so it is true

Step-by-step explanation:

Answer:

3rd  option

Step-by-step explanation:

\(\frac{5}{7}\) y = 6

multiply both sides by \(\frac{7}{5}\) , the reciprocal of \(\frac{5}{7}\) )

\(\frac{7}{5}\) ( \(\frac{5}{7}\) y ) = \(\frac{7}{5}\) (6) , that is

y = \(\frac{42}{5}\)

Answer:

D

Step-by-step explanation:

The equation is: (2x + 8) / 4 - 3 = x - 7

The solution is x = 12

Let x be the number you thought of at the beginning. Following the steps:

Multiply by 2: 2x

Add 8: 2x + 8

Divide by 4: (2x + 8) / 4

Subtract 3: (2x + 8) / 4 - 3

The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7

The equation is: (2x + 8) / 4 - 3 = x - 7

2. (2x + 8) / 4 - 3 = x - 7

(1/2)x + 2 - 3 = x - 7

(1/2)x - 1 = x - 7

Now add 1 to both sides:

(1/2)x = x - 6

Subtract (1/2)x from both sides:

-1/2x = -6

Now multiply both sides by -2:

x = 12

3. Properties used to solve the puzzle

Addition Property of Equality

Multiplication Property of Equality

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Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer: 2(3x+1)

Step-by-step explanation:

2(3x+1) ==> 2(3x)+2(1)

6x+2

Answer:

2(3x + 1)

Hope that helps! :)

Step-by-step explanation:

Answer:

The probability is    \(P( \= X > 268 ) =0.35376\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 266\)

    The standard deviation is  \(\sigma = 16\)

Generally the standard error of mean is mathematically represented as

        \(\sigma_{\= x} = \frac{\sigma}{\sqrt{n} }\)

=>     \(\sigma_{\= x} = \frac{16}{\sqrt{9} }\)

=>     \(\sigma_{\= x} = 5.33\)

Generally the probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is mathematically represented as

        \(P( \= X > 268 ) = P (\frac{ \= x - \mu }{ \sigma_{\= x}} > \frac{268 - 266}{5.33 } )\)

\(\frac{\= X -\mu}{\sigma_{\= x} }  =  Z (The  \ standardized \  value\  of  \ \=  X )\)  

          \(P( \= X > 268 ) = P (Z > 0.3752 )\)

From the z table  the area under the normal curve to the right  corresponding to  0.3752  is

P (Z  >  0.3752)   =    0.35376

So  

       \(P( \= X > 268 ) =0.35376\)

Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

Answer:

On a number line, 1/6 would land in the exact middle between 0 and 2/6

Step-by-step explanation:

Not too sure what your question meant, but I hope my answer helped!

If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)

Answer:

x = 3°

Step-by-step explanation:

Given the equilateral triangle with the following angles:

m∠1 = (21x - 3)°

m∠2 = (17x + 9)°

m∠3 = (15x + 15)°

In order to solve for the value of x, we must apply the Triangle Sum Theorem, which states that the sum of the measures of all interior angles of a triangle is 180°.

Thus, we can set up the following equation to solve for x:

m∠1 + m∠2 + m∠3 = 180°

(21x - 3)° + (17x + 9)° + (15x + 15)° = 180°

21x°  - 3°  + 17x°  + 9° + 15x° + 15° = 180°

Combine like terms and constants:

21x°  - 3°  + 17x°  + 9° + 15x° + 15° = 180°

53x° + 21° = 180°

Subtract 21° from both sides:

53x° + 21° - 21° = 180° - 21°

53x° = 159°

Divide both sides by 53 to solve for x:

\(\displaystyle\mathsf{\frac{53x^\circ}{53^\circ}\:=\:\frac{159^\circ}{53^\circ}}\)

x = 3°

Therefore, the value of x = 3°.

In order to verify whether we have the correct value of x, we must substitute its value into the given angles:

m∠1 = (21x - 3)° = 21(3)° - 3° = 60°

m∠2 = (17x + 9)° = 17(3)° + 9° = 60°

m∠3 = (15x + 15)° = 15(3)° + 15° = 60°

m∠1 + m∠2 + m∠3 = 180°

60° +  60° +  60° =  180°

180° = 180° (True statement).

The values in the missing places are 26, 52, 14, 40 and 50

A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.

Given is a frequency table with some missing places,

For every missing places, we just need to add or subtract from the total.

Types of food                                             Age

                                            child          adult (18+)              Total

Fruit                                       26                  26                        52

Vegetable                              14                  24                        38

Total                                       40                  50                       90

First missing place = 50-24 = 26

Second missing place = 26+26 = 52

Third missing place = 38-24 = 14

Fourth missing place = 26+14 = 40

Fifth missing place = 90-40 = 50

Hence, The values in the missing places are 26, 52, 14, 40 and 50

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97.75 - 85 = 12.75

This means the amount of tax was $12.75.

If we divide the amount of tax by the original price of the shirt, it gives us the percent of the tax:

      12.75 ÷ 85 = 0.15 = 15%

Sales tax is 15%.

The key in the calculation is to divide by the original price of the shirt.