Simplify the f(x) and g(x) to get it

The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.

In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;

y = 3.01x + 89.63

Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;

y = 3.01x + 89.63

y = 3.01(24.5) + 89.63

y = 163.375 ≈ 163.38 centimeters.

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Answer:

m = -3

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is  y = -3x + 2

m = -3

So, the slope of the line is -3

Answer:

The slope is -3

Step-by-step explanation:

You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and       the y-intercept.

y=mx+b, Where m is the slope and b is the y-intercept.

Hello!

V

= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)

= 1,620cm³ + 630cm³

= 2,250cm³

Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.

To calculate the population size after 4 hours, we can use the formula for exponential growth:

Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]

Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:

Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]

Calculating the exponent first:

[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879

Now, we can substitute this value back into the formula:

Population size = 3.3 million * 1.7879

Calculating the population size:

Population size = 5.892 million

Therefore, the population size after 4 hours is approximately 5.892 million cells.

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Answer:

The number is 16

Step-by-step explanation:

This follows a multiplication rule,

4 times 1 = 4

4 times 2 = 8

4 times 3 = 12

4 times 4 = 16

So, the number is 16

The given statement "An event with probability 3/4 is more likely to happen than an event with probability 4/5" is true.

The reason why we say an event with a higher probability is more likely to happen is because probability is the measure of how often an event will occur during a large number of trials.

Therefore, when we compare the probabilities of two events, we can expect that the one with the higher probability will occur more often and therefore is more likely to happen.For instance, in the context of a coin flip, the probability of getting heads is 1/2 while the probability of getting tails is also 1/2.

Therefore, both events are equally likely to happen. On the other hand, if we were to compare the probability of rolling a six-sided die and getting a 1, which has a probability of 1/6, with the probability of rolling the die and getting a number less than or equal to 4, which has a probability of 4/6 or 2/3, we can say that the latter is more likely to happen since it has a higher probability.

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Answer: it contains 12 containers

Step-by-step explanation: i dont know  what the answer is but i know what i can help you with all you have to do is round the answer.

Combining the results of a given triangle, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.

To find the value of 'x' in a triangle with side lengths 'x', 37, and 15, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, we have:

x + 37 > 15 (Sum of x and 37 is greater than 15)

x + 15 > 37 (Sum of x and 15 is greater than 37)

37 + 15 > x (Sum of 37 and 15 is greater than x)

From the first inequality, we can subtract 37 from both sides:

x > 15 - 37

x > -22

From the second inequality, we can subtract 15 from both sides:

x > 37 - 15

x > 22

From the third inequality, we can subtract 15 from both sides:

52 > x

Combining the results, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.

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Answer:

To calculate the selling price of each amplifier, we need to consider the cost, import duty, sales tax, and the desired profit margin.

Cost of each amplifier: sh. 3,750

Import duty of 125% on the cost:

Import duty = 125% of sh. 3,750

= 125/100 * sh. 3,750

= sh. (125/100 * 3,750)

= sh. 4,687.50

Cost of each amplifier including import duty:

Total cost = Cost + Import duty

= sh. 3,750 + sh. 4,687.50

= sh. 8,437.50

Sales tax of 20% on the total cost:

Sales tax = 20% of Total cost= 20/100 * sh. 8,437.50

= sh. (20/100 * 8,437.50)

= sh. 1,687.50

Total cost including sales tax:

Total cost = Total cost + Sales tax

= sh. 8,437.50 + sh. 1,687.50

= sh. 10,125

Desired profit margin of 10% on the total cost:

Profit = 10% of Total cost

= 10/100 * sh. 10,125

= sh. (10/100 * 10,125)

= sh. 1,012.50

Selling price of each amplifier:

Selling price = Total cost + Profit

= sh. 10,125 + sh. 1,012.50

= sh. 11,137.50

The length of this line segment is: B. 2√13 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(4 + 2)² + (1 + 3)²]

Distance = √[(6)² + (4)²]

Distance = √[36 + 16]

Distance = √52

Distance = 2√13 units.

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The correct answer choice is: A. The system has exactly one solution. The solution is (13, 5).

The correct answer choice is: A. all three countries had the same population of 5 thousand in the year 2013.

Based on the information provided above, the population (y) in the year (x) of the counties listed are approximated by the following system of equations:

-x + 20y = 87

-x + 10y = 37

y = 5

where:

By solving the system of equations simultaneously, we have the following solution:

-x + 20(5) = 87

x = 100 - 87

x = 13

-x + 10(5) = 37

x = 50 - 37

x = 13

Therefore, the system of equations has only one solution (13, 5).

For the year when the population are all the same for three countries, we have:

x = 2010 + (13 - 10)

x = 2013

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Answer:

P(Colin) = 20/38

P(Paul) = 18/38

Step-by-step explanation:

Colin won 20 times out of 38, so the probability that he wins would be 20/38 (or 10/19 simplified).

Paul won 18 times out of 38, so the probability that he wins would be 18/38 (or 9/19 simplified).

Answer:

a) Probability of Colin winning = 10/19

b) Probability of Paul winning = 9/19

Step-by-step explanation:

Total number of matches = 38

Colin won 20,

Paul won the rest so, 38 - 20 = 18

Paul won 18 matches,

From this data, we calculate the probabilities of Colin or Paul winning,

a) Estimate the probability that Colin wins.

Colin won 20 out of 38 matches, so his probability of winning is,

20/38 = 10/19

Probability of Colin winning = 10/19

b) Estimate the probability that Paul wins

Paul won 18 out of 38 matches, so his probability of winning is,

18/38 = 9/19

Probability of Paul winning = 9/19

Answer: Nope

Step-by-step explanation:

No, receiving a 20% discount followed by an additional 30% discount does not result in a total discount of 50%.

To understand why, let's consider an example with an item priced at $100.

If there is a 20% discount applied initially, the price of the item would be reduced by 20%, which is $100 * 0.20 = $20. So the new price after the first discount would be $100 - $20 = $80.

Now, if there is an additional 30% discount applied to the $80 price, the discount would be calculated based on the new price. The 30% discount would be $80 * 0.30 = $24. So the final price after both discounts would be $80 - $24 = $56.

Comparing the final price of $56 to the original price of $100, we can see that the total discount is $100 - $56 = $44.

Therefore, the total discount received is $44 out of the original price of $100, which is a discount of 44%, not 50%.

Hence, receiving a 20% discount followed by an additional 30% discount does not result in a total discount of 50%.

The formula to find the value of a combination is

[tex]C(n, r) = n! / (r!(n-r)!),[/tex]

where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1

In the  combination,

n = 10 and r = 0,

so the formula becomes:

C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1

This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.

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In a right triangle, the length of side "a" is 12.

The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, can be used to find the length of side "a" in a right triangle with sides of 13 and 5 units.

Let's assign "a" as the unknown side. According to the Pythagorean theorem, we have the equation: [tex]a^{2}[/tex] = [tex]13^{2}[/tex] - [tex]5^{2}[/tex].

Simplifying the equation, we get [tex]a^{2}[/tex] = 169 - 25, which becomes [tex]a^{2}[/tex] = 144.

To solve for "a," we take the square root of both sides: a = √144.

The square root of 144 is 12. Therefore, side "a" has a length of 12 units.

In summary, using the Pythagorean theorem, we determined that side "a" in the right triangle with side lengths 13 and 5 units has a length of 12 units.

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The correct answer choice is: A. The system has exactly one solution. The solution is (11, 7).

The correct answer choice is: A. all three countries had the same population of 7 thousand in the year 2011.

Based on the information provided above, the population (y) in the year (x) of the countries listed are approximated by the following system of equations:

-x + 20y = 129

-x + 10y = 59

y = 7

where:

By solving the system of equations simultaneously, we have the following solution:

-x + 20(7) = 129

x = 140 - 129

x = 11

-x + 10(7) = 59

x = 70 - 59

x = 11

Therefore, the system of equations has only one solution (11, 7).

For the year when the population are all the same for three countries, we have:

x = 2010 + (11 - 10)

x = 2011

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Answer:

$248.00

Step-by-step explanation:

Hours worked on Friday:  6 hr and 30 min = 6.5 hr

Money earned on Friday:  $15.5/hr x 6.5 hr = $100.75

Hours worked on Saturday:  6.5 hr - 1.167 hr = 5.33   *10 min = 10/60 = 0.1667 hr

Money earned on Saturday:  $15.50 x 5.33 hr = $82.67

Hours worked on Monday:  4.167 hr

Money earned on Monday:  $15.50/hr x 4.167 hr = $64.58

Total money made:  100.75 + 82.67 + 64.58 = $248.00

Answer:

Step-by-step explanation:

To determine which option will yield the most money after three years, let's calculate the final amount for each option.

Option #1 - CD for 3 years:

Principal (initial investment) = $1000

Interest rate = 3% per year (compounded monthly)

No additional money can be added

To calculate the final amount, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Final amount

P = Principal (initial investment)

r = Interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

For Option #1:

P = $1000

r = 3% = 0.03 (as a decimal)

n = 12 (compounded monthly)

t = 3 years

A = $1000 * (1 + 0.03/12)^(12*3)

Calculating the final amount for Option #1, we get:

A = $1000 * (1 + 0.0025)^(36)

A ≈ $1000 * (1.0025)^(36)

A ≈ $1000 * 1.0916768

A ≈ $1091.68

Option #2 - CD for 1 year:

Principal (initial investment) = $1000

Interest rate = 2% per year (compounded quarterly)

Money can be added at the end of each year

To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.

First Year:

P = $1000

r = 2% = 0.02 (as a decimal)

n = 4 (compounded quarterly)

t = 1 year

A = $1000 * (1 + 0.02/4)^(4*1)

A ≈ $1000 * (1.005)^(4)

A ≈ $1000 * 1.0202

A ≈ $1020.20

At the end of the first year, the total amount is $1020.20.

Second Year:

Now we add an additional $60 to the previous amount:

P = $1020.20 + $60 = $1080.20

r = 2% = 0.02 (as a decimal)

n = 4 (compounded quarterly)

t = 1 year

A = $1080.20 * (1 + 0.02/4)^(4*1)

A ≈ $1080.20 * (1.005)^(4)

A ≈ $1080.20 * 1.0202

A ≈ $1101.59

At the end of the second year, the total amount is $1101.59.

Third Year:

Again, we add $60 to the previous amount:

P = $1101.59 + $60 = $1161.59

r = 2% = 0.02 (as a decimal)

n = 4 (compounded quarterly)

t = 1 year

A = $1161.59 * (1 + 0.02/4)^(4*1)

A ≈ $1161.59 * (1.005)^(4)

A ≈ $1161.59 * 1.0202

A ≈ $1185.39

At the end of the third year, the total amount is $1185.39.

Comparing the final amounts:

Option #1: $1091.68

Option #2: $1185.39

Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.

Answer:

Step-by-step explanation:

This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?

Answer:

So we have $11.64 in American dollars and £5 in British pound coin

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let x be the number of American dollars and y be the number of British pound coins. Then we have:

x + y/1.65 = 20.25 (since each British pound coin is worth 1.65 American dollars)

x = 17 - y (since there are 17 items altogether)

Substituting the second equation into the first, we get:

(17 - y) + y/1.65 = 20.25

Multiplying both sides by 1.65, we get:

28.05 - y + y = 33.4125

y = 33.4125 - 28.05

y = 5.3625

Therefore, we have 5 British pound coins and:

x = 17 - y = 17 - 5.3625 = 11.6375

Answer:

Where lines cross over each other. The lines have a common point.

The figure that shows a reflectional symmetry would be figure C. That is option A.

The reflectional symmetry of shapes is defined as the type of symmetry where one-half of the object reflects the other half of the object.

This is also called a mirror symmetry. This is because the image seen in one side of the mirror is exactly the same as the one seen on the other side of the mirror.

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Answer:

A.

Step-by-step explanation:

In this case, we have to use tan ([tex]\frac{opposite}{adjacent}[/tex] because we are asked for the opposite side (x) given the adjacent side (20 m).

So tan(75)=[tex]\frac{x}{20}[/tex]

Solve for x

x = 20 * tan(75)

x = 74.641...

x = 74.64 m

Answer:

The height is 74.64 meters

Step-by-step explanation:

We have a ΔABC with ∠B = 75°, hypotenuse = AB

[tex]cos\; 75\textdegree = \frac{\sqrt{3} -1}{2\sqrt{2} }\\\\\frac{1}{cos\; 75\textdegree} = \frac{2\sqrt{2} }{\sqrt{3} -1}[/tex]

cos B = adjacent/hyppotenuse

⇒ hypotenuse (AB) = adjacent/cosB = 20/cosB

[tex]= 20 \frac{2\sqrt{2} }{\sqrt{3} -1}\\\\= \frac{40\sqrt{2} }{\sqrt{3} -1}\\\\= 77.27[/tex]

⇒ AB = 77.27

By pythagoras theorem,

AB² = AC² + BC²

⇒ AC² = AB² - BC²

= 77.27² - 20²

AC² = 5570.65

⇒ AC = √5570.65

AC = 74.64

Answer:

Step-by-step explanation:

The quadratic formula is y=ax^2+bx+c

If we move everything to the left side of the equation,

-6x^2=-9x+7 becomes

-6x^2+9x-7=0

a=-6, b=9, c=-7, so the third answer choice

The equation to determine the initial amount of money Cecilia had is x = 0.

Let's denote the initial amount of money Cecilia had as "x" dollars.

According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.

Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.

Since she had $8 left, we can set up the equation:

((x - (1/4)x) - ((1/2)x - 8)) = 8

To simplify the equation, we can first combine like terms:

(x - (1/4)x - (1/2)x + 8) = 8

Now, let's solve the equation step by step:

(x - (1/4)x - (1/2)x + 8) = 8

Multiplying the fractions by their common denominator, which is 4, we get:

(4x - x - 2x + 32) = 32

Simplifying further:

(x + 32) = 32

Subtracting 32 from both sides:

x = 0

Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.

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Answer:

Part A:

The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:

A. 100 - 2 × (22 - 19)

Part B:

To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.

If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.

Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.

Yes, she has enough pencils to give each of her students 2.

She has 18 more than she needs.