find the critical numbers of the function.
f(x)=x^2(x-3)^2

Answers

Answer 1
To find the critical numbers of the function f(x) = x^2(x-3)^2, we need to find the values of x where the derivative of f(x) is zero or undefined.

First, we find the derivative of f(x) using the product rule:

f'(x) = 2x(x-3)^2 + x^2(2(x-3))

Simplifying, we get:

f'(x) = 2x(x-3)(2x-6+x) = 2x(x-3)(3x-6)

Setting f'(x) = 0, we get:

2x(x-3)(3x-6) = 0

This equation is zero when x = 0, x = 3, and x = 2.

Now we need to check if these values make the derivative undefined. None of these values make the derivative undefined.

Therefore, the critical numbers of the function f(x) = x^2(x-3)^2 are x = 0, x = 3, and x = 2.

Related Questions

Let p(x) = a1x^2 + b1x +c1 and q(x) = a2x^2 + b2x + c2 be polynomials in P2. Define an inner product in P2 as follows {p,q} = 5a1a2 + 4b1b2 + 3c1c2.
Given p(x) =5x^2 + (-1)x + (-3) and q(x) = 2x^2 + (4)x +(-3). Evaluate the following expressions
1. p(x) - q(x) = 3x^2 - 5x
2. {p - q, p-q} = 145
3. llp-qll = sqrt({p-q,p-q}) = sqrt(145)

For part 1, I know the answer and how to get it.
For part 2, I know the answer but I'm not sure how to get to it

Answers

Answer:

Step-by-step explanation:

To evaluate the expression {p - q, p - q}, which represents the inner product of the polynomial (p - q) with itself, you can follow these steps:

Given p(x) = 5x^2 - x - 3 and q(x) = 2x^2 + 4x - 3.

Subtract q(x) from p(x) to get (p - q):

(p - q)(x) = (5x^2 - x - 3) - (2x^2 + 4x - 3)

= 5x^2 - x - 3 - 2x^2 - 4x + 3

= (5x^2 - 2x^2) + (-x - 4x) + (-3 + 3)

= 3x^2 - 5x

Now, calculate the inner product of (p - q) with itself using the given inner product formula:

{p - q, p - q} = 5(a1)(a2) + 4(b1)(b2) + 3(c1)(c2)

= 5(3)(3) + 4(-5)(-5) + 3(0)(0)

= 45 + 100 + 0

= 145

Therefore, the value of {p - q, p - q} is 145.

The better definition of Intersection is:
OA system that has at least one solution.
O Where lines cross over each other. The lines have a common point.
OA value we can put in place of a variable (such as x) that makes the equation true.
OA system that has no solutions.

Answers

Answer:

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

Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4

Answers

Answer:

[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

[tex]\cos(105\°)[/tex]

Using the angle sum identity for cosine.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]

Now applying the identity.

[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]

Now utilizing the unit circle.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]

[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]

Now simplifying...

[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]

Which linear function has the greatest y-intercept?
y = 6 x + 1
On a coordinate plane, a line goes through points (0, 2) and (5, 0).
On a coordinate plane, a line goes through points (1, 2) and (0, negative 3).
y = 3 x + 4

Answers

The linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].

In a linear equation, the y-intercept is where the line crosses the y-axis.

It is represented by the constant term in the equation.

So, to determine which linear function has the greatest y-intercept, we need to look at the constant term of each equation.

Let's consider each equation: [tex]y = 6x + 1[/tex]

The constant term in this equation is 1.

So, the y-intercept is 1.

On a coordinate plane, a line goes through points (0, 2) and (5, 0).

To find the equation of this line, we can use the point-slope form:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is a point on the line.

Using the points (0, 2) and (5, 0), we get:

[tex]m = \frac{(0 - 2)}{(5 - 0)} =-\frac{2}{5}[/tex]

So, the equation of the line is:

[tex]y - 2 = (\frac{-2}{5} )(x - 0)[/tex]

[tex]y = (\frac{-2}{5} )x + 2[/tex]

The constant term in this equation is 2.

So, the y-intercept is 2.

On a coordinate plane, a line goes through points (1, 2) and (0, -3).

To find the equation of this line, we can use the point-slope form:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is a point on the line.

Using the points (1, 2) and (0, -3), we get:

[tex]m = \frac{ (-3 - 2) }{(0 - 1)} = -5[/tex]

So, the equation of the line is:

[tex]y - 2 = (-5)(x - 1)y = -5x + 7[/tex]

The constant term in this equation is 7.

So, the y-intercept is 7.

[tex]y = 3x + 4[/tex]

The constant term in this equation is 4.

So, the y-intercept is 4.

Therefore, we can see that the linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].

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My dance lesson starts at 11:40 am. It always 1 your and 10 minutes what time does it end?

Answers

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?

Mia makes $15.50 per hour. For the Memorial holiday she worked 6 hours and 30 minutes on Friday. On Saturday, she worked for 1 hour and 10 minutes less than she did on Friday and on Monday she worked 4 hours and 10 minutes. How much money did Mia make for the Memorial holiday?

Answers

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

nt- Maths ACSF Level 3
Your mum has saved $12,000 and has agreed to give you a share.
Would you rather have
1/5 or 1/10

Answers

It depends on how much you want to receive. If you choose to receive 1/5, you will get a larger share of the $12,000, but if you choose to receive 1/10, you will get a smaller share.

To calculate the amount you would receive with each option, you can use the following formulas:

1/5 share = (1/5) x $12,000 = $2,400
1/10 share = (1/10) x $12,000 = $1,200

So, if you choose to receive 1/5, you will receive $2,400, and if you choose to receive 1/10, you will receive $1,200.

What is the five-number summary for the data set? 73, 62, 90, 28, 45, 90

Answers

Answer:

it's easy

Step-by-step explanation:

first take a deep breath and then search it

Find the value of the combination. 10C0 0 1 10

Answers

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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Determine the limit in the following equation.

Answers

The limit of the expression lim (x² - √x⁴ + 3x²) as x approaches any value is indeterminate (∞ - ∞), except when x approaches zero, where the limit is 0.

How did we get the value?

To find the limit of the expression lim (x² - √x⁴ + 3x²) as x approaches a certain value, we can simplify the expression and evaluate the limit.

First, let's simplify the expression:

lim (x² - √x⁴ + 3x²)

= lim (4x² - x² - √x⁴)

= lim (3x² - √x⁴)

Now, let's consider the behavior of the expression as x approaches a value.

As x approaches any finite value, the term 3x² will approach a finite value.

For the term √x⁴, as x approaches a finite value, the square root of x⁴ will approach the absolute value of x².

Therefore, the limit becomes:

lim (3x² - √x⁴) = lim (3x² - |x²|)

Next, let's consider the different cases as x approaches positive infinity, negative infinity, and zero.

1. As x approaches positive infinity, the term 3x² will tend to positive infinity, and |x²| will also tend to positive infinity. Thus, the expression becomes:

lim (3x² - |x²|) = lim (∞ - ∞)

In this case, the limit is indeterminate (∞ - ∞).

2. As x approaches negative infinity, the term 3x² will tend to positive infinity, and |x²| will also tend to positive infinity. Thus, the expression becomes:

lim (3x² - |x²|) = lim (∞ - ∞)

Again, in this case, the limit is indeterminate (∞ - ∞).

3. As x approaches zero, the term 3x² will tend to zero, and |x²| will also tend to zero. Thus, the expression becomes:

lim (3x² - |x²|) = lim (0 - 0) = 0

Therefore, the limit of the expression lim (x² - √x⁴ + 3x²) as x approaches any value is indeterminate (∞ - ∞), except when x approaches zero, where the limit is 0.

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omari's monthly taxable income is ksh 24200. calculate the tax charged on omari's monthly earning​

Answers

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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What is the coefficient in the expression
6-4x-8+2

Answers

Answer:

-4 is the coefficient or -4x whatever the answers are

Step-by-step explanation:


the coefficient in mathematics is basically whatever the number is infront of a variable in an expression, equation, etc.

The coefficient in the expression 6-4x-8+2 is -4. The coefficient is the number that is multiplied by the variable, and in this case, the variable is x. The coefficient of x is the number that appears in front of x, which is -4.

Devaughn's age is three times Sydney's age. The sum of their ages is 80 . What is Sydney's age?

Answers

Here we go ~

[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]

Sum up ;

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]

So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years

Answer:

Sydney= 20, Devaughn= 60

Step-by-step explanation:

Let Sydney's age be 'x'

Devaughn's age = 3 times x = 3x

We Know That

The sum of their ages is 80.

So,

3x + x = 80

4x = 80

If we shift the 4 to the 80 side

x = 80/4

x = 20

So, Sydney's age is 20

Therefore, Devaughn's age =

3x = 3 times x

= 3 times 20

= 60

Given that p(x)=2(5−x)2+1 , what is the value of p(-4)? Responses

Answers

Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

HELPPPPPP ME PLEASEEEEE!!

Answers

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

GEOMETRY 100 POINTS

TY​

Answers

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

An import company brought into the country some amplifiers that cost sh. 3,750-each. The government imposed an import duty of 125% and a sales tax of 20 %. If the company decided to make a 10% profit on the sales, calculate the selling price of each amplifier. ​

Answers

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

need help please see attacged

Answers

The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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There are 12 containers containing various amounts of water, as shown below. ←+ 0 H ½ X X X X X X 1 X 1½ X X X 2 Cups If all of the water were dumped into one container, how many cups would be in the container?​

Answers

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.

An event with probability 3/4 is more likely to happen than an event with probability 4/5

True or False why?

Answers

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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A store has a sale with 20% off every item. When you enter the store, you receive a coupon that states that you receive an additional 30% off. Is this equal to a 50% discount? Explain your answer

Answers

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%.

Ms. Florinda is a kindergarten teacher. She buys 100 pencils and wants to give 2 pencils to each of her students. She has 2 classes, a class with 22 students and a class with 19 students.

Part A
Write an expression for how many pencils she has left after giving them out to her students.

A.
100

2
×
(
22

19
)
B.
100

2
×
22

19
C.
100

2
×
22

2
×
19
D.
100

22

19
Part B
Does she have enough pencils to give each of her students 2?

Yes or no

, she has
15,18,37,59

More or fewer
than she needs.

Answers

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.

Which expression is equivalent to 10f - 5f + 8 +6g +4?

Answers

The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.

To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:

10f - 5f + 8 + 6g + 4

Combining the terms with 'f', we have:

(10f - 5f) + 8 + 6g + 4

This simplifies to:

5f + 8 + 6g + 4

Next, we can combine the constant terms:

8 + 4 = 12

Thus, the simplified expression is:

5f + 12 + 6g

This expression is equivalent to 10f - 5f + 8 + 6g + 4.

In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.

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Find Tan A 6-11, please?

Answers

Answer:

5) tan A = 0.42

6) Acute angle is less than 90°

7) Right angle is exactly 90°

8) Obtuse angle is greater than 90° but less than 180°

9) Straight angle is exactly 180°

10) Complementary angles add up to 90°

11) Supplementary angles add up to 180°

Step-by-step explanation:

tan A = opposite / adjacent

= 5/12

= 0.42

Colin and Paul have played 38 tennis matches.
Colin has won 20 times.
Paul won the rest.
a) Estimate the probability that Colin wins.
b) Estimate the probability that Paul wins.

Answers

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

GEOMETRY 50POINTS
FIND x​

Answers

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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Instructions: Complete the following proof by dragging and dropping the correct reason into the space provided.
Given: ∠NYR and ∠RYA form a linear pair, ∠AXY and ∠AXZ form a linear pair, ∠RYA≅∠AXY
If you are using a screen-reader, please consult your instructor for assistance.

Prove: ∠NYR≅∠AXY
Step Reason
∠NYR and ∠RYA form a linear pair
∠AXY and ∠AXZ form a linear pair Given
∠NYR and ∠RYA are supplementary
m∠NYR+m∠RYA=180
∠AXY and ∠AXZ are supplementary If two angles form a linear pair, then they are supplementary angles
Definition of Supplementary Angles
m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality
∠RYA≅∠AXY
m∠NYR+m∠RYA=m∠AXY+m∠RYA Substitution Property of Equality
m∠NYR=m∠AXY

Answers

Answer:

Step Reason

∠NYR and ∠RYA form a linear pair

∠AXY and ∠AXZ form a linear pair Given

∠RYA≅∠AXY Given

∠NYR and ∠RYA are supplementary Definition of Linear Pair

If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair

∠NYR and ∠AXY are supplementary Transitive Property of Equality

m∠NYR+m∠RYA=180

m∠AXY+m∠AXZ=180 Definition of Supplementary Angles

m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality

m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality

m∠RYA=m∠AXZ Subtraction Property of Equality

∠NYR and ∠AXY are supplementary Definition of Supplementary Angles

m∠NYR+m∠AXY=180

m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality

m∠RYA=m∠AXY Subtraction Property of Equality

∠NYR≅∠AXY Definition of Congruent Angles.

in this chart, × is the length of a persons forearm in centimeters and y is the persons height in centimeters. the question is if someones forearm (x) is 24.5 cm, how tall would they be? how do i find this? and how would i make a linear regression graph? thanks

Answers

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

How to construct and plot the data in a scatter plot?

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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A population of a particular yeast cell develops with a constant relative growth rate of 0.4465 per hour. The initial population consists of 3.3 million cells. Find the population size (in millions of cells) after 4 hours. (Round your answer to one decimal place.)

Answers

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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An author is writing and illustrating a new book. The gale diagram represent the ratio of area. In cm2 with text to area with illustrations .based on the ratio there 500cm2 of illustrations

Answers

Pulse oximeter radius
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