what is the base 8 representation of 1100111 base 2

Answer: a.     c(n) = 15 + 0.75(n - 10)

b.   15 + 0.75(n - 10) = 2.50(n - 10)=

Simplifying and solving for n, we get:

n = 50

c.  n > 50

Step-by-step explanation:

a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:

c(n) = 15 + 0.75(n - 10)

The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

The cost c of the bank account in terms of the number of checks written n can be expressed as:

c(n) = 2.50(n - 10)

The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:

15 + 0.75(n - 10) = 2.50(n - 10)

Simplifying and solving for n, we get:

n = 50

So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.

c. The solution to the inequality is:

n > 50

This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.

Before we begin we must know:

An equation is an algebraic equality in which letters (unknowns) with unknown value appear. The degree of an equation is given by the largest exponent of the unknown. To solve an equation is to determine the value or values of the unknowns that transform the equation into an identity.

Solving the equation, we will first add what is in the first, I mean:

Now we must convert to a fraction, first we will put the greater number on top and the smaller number below.

Now the last thing we should do is divide both numbers by nine (9), and we will have the following:

∴ The result of our equation is y = 9

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As a result, the point on the number line that represents 10 miles would be much more to the right and outside the bounds of the image.

The line number 10.12, for instance, refers to page 10, line 12. The part of the line number to the left of the period is referred to as the "page" or "part," and the part to the right is referred to as the "line."

A number line is a representation of numbers along a straight line. It acts as a template for grouping and contrasting numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

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Question:

The distance from Cory's home to the library is mile. Which point is at on the number line?

A. Point A

B. Point B

C. Point C

D. Point D

Therefore, 65% of all nurses have a starting salary of more than $71,725.31.

Random variable: X, the starting salary of a randomly selected nurse.

b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)

Using the Z-score formula:

z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≥ 1.03) ≈ 0.1492

Therefore, P (X ≥ 78371.8) ≈ 0.1492.

c) P (X ≤ 91407.1)

Using the Z-score formula:

z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probability in the standard normal table or using a calculator, we get:

P(Z ≤ 2.30) ≈ 0.9893

Therefore, P (X ≤ 91407.1) ≈ 0.9893.

d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)

Using the Z-score formula:

z1 = (78371.8 - 67694) / 10333 ≈ 1.03

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probabilities in the standard normal table or using a calculator, we get:

P(Z < 1.03) ≈ 0.8498

P(Z < 2.30) ≈ 0.9893

Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.

e) P (X ≤ 41861.5)

Using the Z-score formula:

z = (41861.5 - 67694) / 10333 ≈ -2.50

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≤ -2.50) ≈ 0.0062

Therefore, P (X ≤ 41861.5) ≈ 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.

g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.

Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.

Using the Z-score formula:

z = (X - μ) / σ

Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:

0.3853 = (X - 67694) / 10333

Solving for X, we get:

X = 10333(0.3853) + 67694 ≈ 71725.31

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The list of intervals on which the function is constant is:

A(-4,-3) and B(3,6).

A constant function is a function that returns the same value regardless of the input. In other words, for every value of x, the output of the function is the same constant value. For example, the function f(x) = 2 is a constant function because no matter what value of x is plugged into the function, the output will always be 2. Constant functions are often represented by horizontal lines on a graph.

A list of intervals in a graph typically indicates the range of values or intervals on a given axis. For example, on the x-axis of a graph, a list of intervals might represent the range of values from a lower bound to an upper bound, with each interval indicating a range of values that falls between two specific points on the axis. On the y-axis, the intervals might represent the range of possible values for the dependent variable or data being plotted. In general, the intervals on a graph provide a visual representation of the range of values being considered or plotted.

The given function in the graph on intervals A(-4,-3) and B(3.6) is a horizontal line which means there is no change in output. So the function is constant.

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the solution to the equation  is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation

what is distributive property ?

The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,

In the given question,

To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.

Here are the steps:

Distribute the 3 on the left-hand side of the equation:

3(x+6) = 3x + 18

Combine the two x terms on the right-hand side of the equation:

3x + 18 = 2x + 8

Subtract 2x from both sides of the equation:

3x - 2x + 18 = 2x - 2x + 8

Simplifying this expression gives:

x + 18 = 8

Finally, subtract 18 from both sides of the equation:

x + 18 - 18 = 8 - 18

Simplifying this expression gives:

x = -10

Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.

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According to the factor form of the quadratic equation 4 · x² - 484, x = - 11 and x = 11 are the lesser x and the greater x of the expression.

Herein we find a quadratic equation of the form a² · x² - b², whose factor form is introduced below by means of algebra properties:

a² · x² - b² = a² · (x² - b² / a²) = a² · (x - b / a) · (x + b / a)

Where - b /a is the lesser x and + b / a is the greater x.

If we know that a² = 4 and b² = 484, then the roots of the quadratic equation are:

4 · x² - 484 = 4 · (x - 11) · (x + 11)

The lesser x and the greater x are - 11 and 11, respectively.

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a. The probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. The probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

Explain probability

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. Probability is a fundamental concept in mathematics and is used in many fields, including statistics, science, and finance.

According to the given information

a. The total number of brownies sold for a random sample of 56 days, Y, is a normal random variable with mean µ_Y = 56µ_X = 5638 = 2128 and standard deviation σ_Y = √(56)*σ_X = √(56)*6 = 25.21.

We want to find P(Y < 2070). Standardizing Y, we get:

Z = (Y - µ_Y) / σ_Y = (2070 - 2128) / 25.21 = -2.31

Using a standard normal distribution table or calculator, we can find that P(Z < -2.31) is approximately 0.0107. Therefore, the probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. 2X₁ + X₂ + 3X₃ + X₄ is also a normal random variable with mean 2µ₁ + µ₂ + 3µ₃ + µ₄ = 2(3.6) + 0.9 + 3(1.8) + 7.4 = 18.5 and variance 4o² + o² + 9o² + o² = 14o².

We want to find P(2X₁ + X₂ + 3X₃ + X₄ ≤ 17.6). Standardizing the variable, we get:

Z = (17.6 - 18.5) / √(14o²) = -0.5735 / √(o²)

To find P(Z ≤ -0.5735 / √(o²)), we need to know the value of o². If o² = 1, then P(Z ≤ -0.5735) = 0.2831. If o² is a different value, we would need to adjust accordingly.

Therefore, the probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

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Answer:

78.5 cm²

Step-by-step explanation:

Diameter = 10 cm

Formula

Radius ( r ) = Diameter/2

r = 10/2

r = 5 cm

Formula

Area of circle = πr²

Note

The value of π is 3.14 ( approximately )

Area of circle

= 3.14 × 5²

= 3.14 × 5 × 5

= 3.14 × 25

= 78.5 cm²

Hence,

The area of circle is 78.5 cm².

The exact value of the expressions 6os(a + 6), 6in(a + b) and tan(a + beta) under the given conditions is 6*cos(A/6), -6*sin(b) and tan(a) + 12/13 respectively.

Expression is a way for an individual to convey their thoughts, feelings, beliefs, and ideas. It can be done through different forms such as verbal communication, art, dance, music, writing, and body language. Expression allows people to express themselves in a way that can be understood by others. It can help to create a connection between people by allowing them to connect with one another on a deeper level.

6os(a + 6) = 6*sin(a + 6) = 6*sin(a)cos(6) + 6*cos(a)sin(6)
Since a lies in quadrant 1, sin(a) = 1 and cos(a) = 0. Therefore,
6os(a + 6) = 6*sin(a)cos(6) + 6*cos(a)sin(6) = 6*1*cos(6) + 6*0*sin(6) = 6*cos(6) = 6*cos(A/6)
6in(a + b) = 6*cos(a + b) = 6*cos(a)cos(b) - 6*sin(a)sin(b)
Since a lies in quadrant 1, sin(a) = 1 and cos(a) = 0. Therefore,
6in(a + b) = 6*cos(a)cos(b) - 6*sin(a)sin(b) = 6*0*cos(b) - 6*1*sin(b) = -6*sin(b)
tan(a + beta) = tan(a) + tan(beta)
Since sin(0) = 12/13, tan(beta) = 12/13. Therefore,
tan(a + beta) = tan(a) + tan(beta) = tan(a) + 12/13
The exact value of the expressions 6os(a + 6), 6in(a + b) and tan(a + beta) under the given conditions is 6*cos(A/6), -6*sin(b) and tan(a) + 12/13 respectively.

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The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.

Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.

We are to find the coordinates of the vertices of the image.

We know that

if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :

(a, b)   ⇒    (-a, -b).

So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes

A(-3, 0)   ⇒  (3, 0)

B(-2, 3)   ⇒   (2, -3)

C(-1, 1)    ⇒   (1, -1).

Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).

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The next entry on the long division would be 0.054, and 0.0054

Long division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:

Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.

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(a) (i) The probability that 10 or more are extroverts is 0.965. (ii) the probability that 5 or more are extroverts 0.999. (iii) the probability that all are extroverts is 0.035. (b) (i) 0.03125 (ii) 0.5 (iii) 0.031.

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has a constant probability of success. The distribution is named after the 17th-century mathematician James Bernoulli, who introduced it in his Ars Conjectandi.

The binomial distribution is commonly used in statistical inference, hypothesis testing, and decision making in various fields such as economics, finance, psychology, and biology. It is used to model the probability of events such as the number of heads in a series of coin tosses, the number of defective items in a batch of products, or the number of individuals in a population who have a certain characteristic.

(a) Let X be the number of extroverts in a group of 15 marketing personnel. X follows a binomial distribution with parameters n = 15 and p = 0.8.

(i) The probability that 10 or more are extroverts is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - P(X ≤ 9)

Using a binomial distribution table or a calculator with a binomial probability function, we can find:

P(X < 10) = 0.0352

Therefore,

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.0352 = 0.9648

So the probability that 10 or more marketing personnel are extroverts is approximately 0.965.

(ii) The probability that 5 or more are extroverts is:

P(X ≥ 5) = 1 - P(X < 5) = 1 - P(X ≤ 4)

Using a binomial distribution table or a calculator with a binomial probability function, we can find:

P(X < 5) = 0.0008

Therefore,

P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.0008 = 0.9992

So the probability that 5 or more marketing personnel are extroverts is approximately 0.999.

(iii) The probability that all 15 marketing personnel are extroverts is:

P(X = 15) = (15 choose 15) * 0.8^15 * 0.2^0 = 0.0352

So the probability that all 15 marketing personnel are extroverts is approximately 0.035.

(b) Let Y be the number of introverts in a group of 5 computer programmers. Y follows a binomial distribution with parameters n = 5 and p = 0.5.

(i) The probability that none are introverts is:

P(Y = 0) = 0.5⁵ = 0.03125

So the probability that none of the 5 computer programmers are introverts is approximately 0.031.

(ii) The probability that 3 or more are introverts is:

P(Y ≥ 3) = P(Y = 3) + P(Y = 4) + P(Y = 5)

Using a binomial distribution table or a calculator with a binomial probability function, we can find:

P(Y = 3) = 0.3125

P(Y = 4) = 0.15625

P(Y = 5) = 0.03125

Therefore,

P(Y ≥ 3) = 0.3125 + 0.15625 + 0.03125 = 0.5

So the probability that 3 or more of the 5 computer programmers are introverts is 0.5.

(iii) The probability that all 5 computer programmers are introverts is:

P(Y = 5) = 0.5⁵ = 0.03125

So the probability that all 5 computer programmers are introverts is approximately 0.031.

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Answer:

1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:

h(t) = -16t^2 + 72t + 4

To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:

t = -b/2a = -72/(2(-16)) = 2.25 seconds

To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):

h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet

The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.

2. Using the same kinematic equation as before, we have:

h(t) = -16t^2 + 80t + 3

To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:

t = -b/2a = -80/(2(-16)) = 2.5 seconds

To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):

h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet

The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.

Step-by-step explanation:

Answer:

6.5875 × 10^2

Step-by-step explanation:

Standard form format is: a×10^b

A number is written in standard form when it is represented as a decimal number times a power of 10.

As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 10^8.

Example: Convert 459,608 to Standard Form

Move the decimal 5 places to the left to get 4.59608

a = 4.59608

We moved the decimal to the left so b is positive

b = 5

The number 459,608 converted to standard form is 4.59608 x 10^5

hope this helps <3

Answer:

y = 0.028t + 230,000 Step-by-step explanation: We know t = number of years since the start of the study y = be the city's population Each year the population

Step-by-step explanation:

After 6 fluid ounces , Naya uses 4 glasses as a result.

A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce .  A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce

In Naya's pitcher, there are three glasses of salted lassi.

She fills each glass with six fluid ounces of lassi.

By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.

8 fluid ounces make constitute a cup.

Consequently, 3 cups equal 24 fluid ounces (3 x 8).

24 divided by 6 results in:

4 glasses are equal to 24/6.

Naya uses four glasses as a result.

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Answer:

29i

Step-by-step explanation:

While multiplying complex numbers we should remember that i^2=−1.

As p=2 and q=5i,

(2−5i)(p+q)i

= (2−5i)(2+5i)i

= (2×2+2×5i−5i×2−5i×5i)×i

= (4+10i−10i−25×i2)×i

= (4+10i−10i−25×(−1))×i

= (4+25)×i

=29i

Answer:

the mass of the solid glass cylinder is approximately 350.67 grams.

Step-by-step explanation:

The diameter of the cylinder is 3 centimeters, which means that its radius is 1.5 centimeters (half the diameter). The area of the base of the cylinder is the area of a circle, calculated as pi (π) multiplied by the radius squared:

Base area = π x radius^2

Base area = π x (1.5 cm)^2

Base area = 7.07 cm^2 (approximately)

The volume of the cylinder is calculated by multiplying the area of the base by the height:

Cylinder Volume = Base Area x Height

Cylinder volume = 7.07 cm^2 x 31 cm

Cylinder volume = 219.17 cm^3 (approximately)

Now that we know the volume of the cylinder, we can calculate its mass using the density of the glass:

Mass = Density x Volume

Mass = 1.6 g/cm^3 x 219.17 cm^3

Mass = 350.67 grams (approximately)

Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.

In the given question,

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.

Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.

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Answer: Amaterasu

Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.

The product of the binomial (d-1)(d+2)(d-3) is d³-2d²-5d+6.

A binomial is an expression with two terms. For example 3x+4 is an example of binomial and also 3x²+3x is also an example of binomial.

To find the product of (d-1)(d+2)(d-3) , we multiply the three binomial together to give us a polynomial expression.

(d-1)(d+2) = d(d+2) -1( d+2)

= d²+2d-d-2

= d²+d-2

now solving (d²+d-2)(d-3)

= d( d²+d-2) -3(d²+d-2)

= d³+d²-2d-3d²-3d+6

collect like terms

= d³+d²-3d²-2d-3d+6

= d³-2d²-5d+6

therefore the product of (d-1)(d+2)(d-3) is d³-2d²-5d+6

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Answer:          To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).

In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.

Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:

I = $325 ∙ 0.08 ∙ 15 = $390

Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.

To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.

The total amount of money that Charlie will have after the 15 years is:

Total amount = Initial investment + Interest earned

Total amount = $325 + $390

Total amount = $715

Therefore, Charlie will have $715 after 15 years.

Step-by-step explanation:

The probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.

What is fraction?

A fraction is a method of representing a part of a whole or a ratio of two numbers. It is a number that is written in the form of one integer (the numerator) over another integer (the denominator), separated by a line or slash.

The probability of selecting the 3 oldest people in a group of 10 people depends on the assumption that all 10 people are distinct individuals and that the selection process is truly random.

The total number of ways to select 3 people from a group of 10 people is given by the combination formula:

C(10, 3) = 10! / (3! * 7!) = 120

This means that there are 120 possible ways to select a group of 3 people from a group of 10 people.

Since we are interested in selecting the 3 oldest people, we assume that the 3 oldest people are identified and we only need to select them from the group of 10 people. There is only 1 way to select the 3 oldest people out of the group of 10 people.

Therefore, the probability of selecting the 3 oldest people in a group of 10 people is:

P = Number of ways to select the 3 oldest people / Total number of ways to select 3 people from a group of 10 people

P = 1 / 120

P = 0.0083

So, the probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.

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Answer:

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

Step-by-step explanation:

To find the rate of growth of the yeast population, we can use the exponential growth formula:

P(t) = P₀ * e^(kt)

where P(t) is the population size at time t, P₀ is the initial population size, k is the growth rate constant, and t is the time elapsed.

In this case, the initial population size P₀ is 5, the final population size P(5) is 160, and the time elapsed t is 5 hours. We want to find the growth rate constant k.

Plugging in the values, we get:

160 = 5 * e^(5k)

Divide by 5:

32 = e^(5k)

Now, take the natural logarithm (ln) of both sides to isolate k:

ln(32) = ln(e^(5k))

Using the property that ln(a^b) = b * ln(a):

ln(32) = 5k * ln(e)

Since ln(e) = 1:

ln(32) = 5k

Now, divide by 5:

k = (ln(32)) / 5 ≈ 0.4641 (rounded to four decimal places)

So, the growth rate constant k is approximately 0.4641 per hour.

To express the rate of growth as a percentage, multiply the growth rate constant by 100:

0.4641 * 100 ≈ 46.41%

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

The rate of growth of the yeast cells is 31 cells per hour.

The rate of growth of the yeast cells can be calculated by finding the average rate of change in the population over the given time period.

In this case, the population increased from 5 to 160 in 5 hours, so the average rate of growth can be calculated as (160 - 5) / 5 = 31. The rate of growth of the yeast cells is 31 cells per hour.

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

There are 13,800 different recital programs possible.

What is permutation?

In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.

The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:

25 x 24 x 23 = 13,800

There are 13,800 different recital programs possible.

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Therefore, the surface area of the prism is approximately 557.2 square feet when rounded to the nearest tenth.

The surface area of a prism is the total area of all its faces, including the bases. The formula for finding the surface area of a prism depends on the shape of its base. For a right prism, the surface area can be found by adding the area of the two bases to the lateral area, which is the sum of the areas of all the rectangular faces of the prism.

Here,

To find the surface area of the prism, we need to find the area of each of the six rectangular faces that make up the prism, and then add them together. The two triangular faces are congruent, so we can find the area of one and double it to get the total area of the two.

The area of a triangle is given by:

Area = (1/2) x base x height

For the given triangles, the base is 9 ft and the height is 8 ft (for one triangle) and 10 ft (for the other triangle), so the areas are:

Area1 = (1/2) x 9 ft x 8 ft

= 36 ft²

Area2 = (1/2) x 9 ft x 10 ft

= 45 ft²

The total area of the two triangles is:

TotalArea = 2 x (Area1 + Area2)

= 2 x (36 ft² + 45 ft²)

= 162 ft²

Now, we need to find the area of the four rectangular faces. Each face is a rectangle with a length of 13 ft and a height of 7.6 ft, so the area of each face is:

AreaRect = length x height

= 13 ft x 7.6 ft

= 98.8 ft²

The total area of the four rectangular faces is:

TotalRectArea = 4 x AreaRect

= 4 x 98.8 ft²

= 395.2 ft²

To find the total surface area of the prism, we add the area of the two triangles to the area of the four rectangular faces:

TotalSA = TotalRectArea + TotalArea

= 395.2 ft² + 162 ft²

= 557.2 ft²

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