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.
What is expression?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.
To learn more about expression
https://brainly.com/question/30350742
#SPJ1
I need help with this
Answer:
1500
Step-by-step explanation:
Number of boxes = 12
Number of pencils in each box = 125
Total number of pencils
= 12 × 125
= 1500 pencils
Which function represents the inverse of function f?
= 3x + 5
O A. T (2)
O B.
O c.
O D.
=-3x - 5
x+ //
– ž
g(x) =
p(x) =
8(x) = 3z +5
x
The inverse function of f(x) = 3x + 5 is given as follows:
C. p(x) = 1/3x - 5/3.
How to obtain the inverse function?The function in the context of this problem is defined as follows:
f(x) = 3x + 5.
To obtain the inverse function, first we must exchange the variables x and y, hence:
y = 3x + 5
x = 3y + 5.
Now we must isolate the variable y, hence:
3y = x - 5
y = (x - 5)/3.
p(x) = 1/3x - 5/3.
More can be learned about inverse functions at https://brainly.com/question/3831584
#SPJ1
3. Choose the best answer.
The ABC Ad Agency has two automotive tire chains as clients. This could lead to a(n)
A)conflict of interest
B)defect
C)stereotype
D)overworked staff
The correct option - A) conflict of interest is caused due to ABC Ad Agency has two automotive tire chains as clients.
Explain about the conflict of interest:A conflict of interest arises when a person's personal interests, such as those related to their family, friends, finances, or social standing, potentially impair their judgement, choices, or actions at work. Conflicts of interest are taken seriously enough by government organisations that they are governed.
Conflicts of interest happen most frequently when requirements and interests collide. Because of the nature of connections against policies of organisations or regulations of the federal and state levels, various forms of conflicts of interest may arise. Humans are prone to prejudice (having an unfair preference) due to trivial considerations like friendship, food, or flattery. They can also be persuaded to make a choice by the prospect of gaining money, status, or power.For the given data- The ABC Ad Agency has two automotive tire chains as clients.
This, could lead to a(n) conflict of interest.
Know more about the conflict of interest
https://brainly.com/question/12703600
#SPJ1
A skydiver jumps out of a plane from a certain height. The graph below shows their height h in meters after t seconds. How long is the skydiver in the air? Height (in meters) 3000 2500 2000 h 1500 1000 500 0 (0, 2592.1) 2 4 6 8 10 12 14 16 Time (in seconds) 18 20 (23, 0) t 22 24
The skydiver is in the air for 23 seconds.
What is graph?A diagram or pictorial representation that organises the depiction of facts or values is known as a graph.
The relationships between two or more items are frequently represented by the points on a graph.
The skydiver is in the air as long as their height is greater than zero. From the graph, we can see that the skydiver reaches a height of zero at t = 23 seconds. Therefore, the skydiver is in the air for:
t = 23 seconds - 0 seconds = 23 seconds
Learn more about graph on:
https://brainly.com/question/11234618
#SPJ9
Suppose 16 cars start at a car race. In how many ways can the top 3 cars finish the race
there are 3,360 ways in which the top 3 cars can finish the race.
How to Determine the number of ways?
To determine the number of ways in which the top 3 cars can finish the race, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, the order of the cars finishing the race matters.
The number of ways to determine the first place finisher is 16, as any of the 16 cars can finish in first place. Once the first place finisher has been determined, there are only 15 cars remaining, and any one of them can finish in second place. Therefore, there are 15 possible ways to determine the second place finisher.
Similarly, once the first and second place finishers have been determined, there are 14 cars remaining, and any one of them can finish in third place. Therefore, there are 14 possible ways to determine the third place finisher.
To find the total number of ways in which the top 3 cars can finish the race, we can multiply the number of possibilities for each place together:
16 x 15 x 14 = 3,360
Therefore, there are 3,360 ways in which the top 3 cars can finish the race.
It is important to note that this calculation assumes that each car is unique and that there are no ties for any of the top 3 positions. If there were ties, the calculation would become more complicated and would involve combinations as well as permutations.
To know more about permutations visit :-
https://brainly.com/question/1216161
#SPJ1
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The shaded area covers around 0.8664 square feet of space.
What is the typical normal distribution where the standard deviation is 0 and the mean 1?The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.
Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.
Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:
0.9332 - 0.0668 = 0.8664
To know more about area visit:-
https://brainly.com/question/27683633
#SPJ1
Samuel went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.
the system of equations is: [tex]300x + 450y = 6000[/tex]
[tex]y = x + 5[/tex]
What best define about variables?Let's define the variables:
Let "x" be the number of cans of soup purchased by Samuel.
Let "y" be the number of frozen dinners purchased by Samuel.
According to the given information, each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup, so we can write the following equations:
The total sodium from cans of soup: 300x mg
The total sodium from frozen dinners: 450y mg
The total sodium from both cans of soup and frozen dinners: [tex]6000 mg[/tex]
So the first equation is:
[tex]300x + 450y = 6000[/tex] (since the total sodium from cans of soup and frozen dinners is 6000 mg)
Since Samuel purchased 5 more frozen dinners than cans of soup, we can write the second equation:
[tex]y = x + 5[/tex] (since y is 5 more than x)
Therefore, the system of equations is:
[tex]300x + 450y = 6000[/tex]
[tex]y = x + 5[/tex]
Learn more about variables here:
https://brainly.com/question/17344045
#SPJ1
The length of a side of an equilateral triangle is 14 centimeters.
What is the length of the altitude of the triangle?
2√ 7cm
3√ 7 cm
7√ 2 cm
7√ 3 cm
Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]
Step-by-step explanation:
Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.
Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:
[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]
Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]
{[2+(11+9)]-2)+12 if you get this you get a five star rated
Answer: 32
Step-by-step explanation:
We will use the Order of Operations. First, we will do parentheses (), then brackets [], then lastly the braces {}, then lastly add 12.
Given:
{[2+(11+9)]-2)+12
Add 11 to 9:
{[2+20]-2)+12
Add 2 to 20:
{22-2)+12
Subtract 2 from 20:
20 + 12
Add 20 and 12:
32
x f(x) f ′(x) g(x) g′(x)
2 5 1 2 1
4 −2 −6 5 4
5 1 2 4 5
6 5 1 2 −2
The functions f and g have continuous derivatives. The table gives values of f, f ′, g, and g′ at selected values of x.
Part A: Find h′(2) if h(x) = g(f(x)). (5 points)
Part B: Find m′(2) if m(x) = f(x2). (5 points)
Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 4. (10 points)
Part D: Let j of x is equal to g of x divided by f of x. Find j′(2). (10 points)
Answer:
A. h'(2) = 5
B. m'(2) = -24
C. y = 8x - 31
D. j'(2) = 3/25 = 0.12
Step-by-step explanation:
When differentiating composite functions, use the chain rule.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]
Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.
Part AUsing the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).
To find h'(2), substitute x = 2 into the differentiated equation:
[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]
Therefore, h'(2) = 5.
Part BUsing the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.
To find m'(2), substitute x = 2 into the differentiated equation:
[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]
Therefore, m'(2) = -24.
Part CTo find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).
If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).
Therefore, the slope of the tangent line is:
[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]
Now calculate k(x) when x = 4:
[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]
To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]
Therefore, an equation for the line tangent to the graph of k at x = 4 is:
y = 8x - 31Part DTo find the derivative of j(x) use the quotient rule.
[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]
To calculate j'(2), substitute x = 2 into the equation:
[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]
Therefore, j'(2) = 3/25 = 0.12.
Solve. Complete the table for the consecuIf the sum of a number and eight is tripled, the result is four less than twice the number. Find the number.
tive integers.
We can condense and find n's solution: 3n + 24 = 2n - 4
Since n = -14, the unknowable number is also -14.
What is an algebraic expression?A mathematical expression called an algebraic expression includes variables, integers, and mathematical operations including addition, subtraction, multiplication, and division. Algebraic expressions can be straightforward, like "2x," or they can be more complicated, like
[tex]3x^2+4y-5[/tex].
Variables are used to represent unknown quantities and have a range of possible values. In problems requiring unknown values or to represent connections between quantities, algebraic expressions are widely used.
A mathematical expression that includes variables, constants, and operations involving algebra (addition, subtraction, etc.) is known as an algebraic expression. Terms comprise expressions.
To know more about variables, visit:
brainly.com/question/17344045
#SPJ1
What is the value of x in this equation?
2x + 6
5
= −1(x - 11)
Answer:
To solve the equation 2x + 6/5 = -1(x - 11), we can use the distributive property of multiplication over addition/subtraction to simplify the right-hand side of the equation:
2x + 6/5 = -x + 11
Next, we can rearrange the terms so that all the x terms are on one side of he equation and all the constant terms are on the other side:
2x + x = 11 - 6/5
Combining like terms and simplifying the right-hand side, we get:
3x = 49/5
Dividing both sides by 3, we get:
x = 49/15
Therefore, the value of x in the equation 2x + 6/5 = -1(x - 11) is 49/15.
How can I solve this math problem within 5 minutes
The equation a² + b² = c² represents the Pythagorean theorem.
What is the Pythagorean theorem?This is a theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.
To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:
If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):
Plug in the known values for a and b into the equation and solve for c.
Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.
Find out more on the Pythagorean theorem at https://brainly.com/question/27997683
#SPJ1
Which of the following is an even function?
f(x) = (x - 1)^2
f(x) = 8x
f(x) = x^2-x
f(x) = 7
Answer: An even function is a function that satisfies the condition:
f(-x) = f(x)
Let's check which of the given functions satisfies this condition:
f(x) = (x - 1)^2
f(-x) = (-x - 1)^2 = x^2 + 2x + 1
f(x) = (x - 1)^2
The two expressions are not equal, so f(x) is not an even function.
f(x) = 8x
f(-x) = -8x = -f(x)
f(x) = 8x
The two expressions are equal with opposite signs, so f(x) is an odd function.
f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
f(x) = x^2 - x
The two expressions are not equal, so f(x) is not an even function.
f(x) = 7
f(-x) = 7 = f(x)
f(x) = 7
The two expressions are equal, so f(x) is an even function.
Therefore, the only even function among the given functions is:
f(x) = 7.
Step-by-step explanation:
In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%
thought i would leave this but ⇒ty to whoever answers this, have an amazing day <3
The percentage of females with brown eyes as follows is 25%.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".
According to question:Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:
Population Males Females
Total 60 40
Brown eyes 18 ?
From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.
We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.
Finally, we can calculate the percentage of females with brown eyes as follows:
% of females with brown eyes = (10 / 40) x 100% = 25%
Therefore, the answer is (C) 25%.
To know more about percentage visit:
https://brainly.com/question/29116686
#SPJ1
A 9th grade teacher at a local high school wants to know which subject the 9th grade students in the high school like best which group of people should make up a sample that will best answer her question a, other 9th grade teachers in her school
B, parents of 9th graders in her school
C, 9th graders in her school
D,9th graders in her homeroom
The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.
What are subjects?Subjects are the different sets of information which is studied.
9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.
The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.
Thus, the correct option is C, 9th graders in her school.
Learn more about subjects, here:
https://brainly.com/question/23548366
#SPJ1
112+18x14 divided by 14-19 i need help
the answer to the equation 112+18*14/14-19 is 111.
How to solve the question?
To solve this equation, we need to follow the order of operations (also known as PEMDAS), which is as follows: parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).
So let's break down the equation step by step:
18*14 = 252 (multiplication)
252/14 = 18 (division)
112+18 = 130 (addition)
130-19 = 111 (subtraction)
Therefore, the answer to the equation 112+18*14/14-19 is 111.
It's important to note that if we had performed the operations in a different order, we would have gotten a different answer. That's why following the order of operations is crucial in solving mathematical equations.
In general, it's important to have a good understanding of basic arithmetic and algebraic concepts to solve equations like this one. This includes knowing the order of operations, how to perform operations with fractions and decimals, and how to use variables and solve for unknowns. Practicing these skills regularly can help improve your problem-solving abilities in math and other subjects.
To know more about addition visit :-
https://brainly.com/question/25421984
#SPJ1
The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 84 square inches. Solve for the dimensions (length and width) of the poster.
Step-by-step explanation:
w = width
2w + 2 = Length
Area = W x L = 84 = w (2w+2)
84 = 2w^2 + 2w
0 = 2w^2 + 2w - 84 Use Quadratic Formula
a = 2 b=2 c = -84
to find
W = 6 then L = 14 inches
Graph X-3<8 and 6x<72
Answer:
x < 11 & x < 12
Step-by-step explanation:
x - 3 < 8 and 6x < 72
x < 11 & x < 12
Find the area of the triangle. Round to 2 decimal places.
Answer:
20 ..............................
Question 6(Multiple Choice Worth 5 points) (Statistical Measurements LC) Which of the following is a statistical question that can result in numerical data? What is the name of your favorite pizza store? How many hours this week did you spend on homework? O How many times did you go swimming this year? How many pink erasers do the students in your class have?
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
Identifying the statistical question that can result in numerical data?The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.
"What is the name of your favorite pizza store?" is a question that asks for a categorical response, "How many times did you go swimming this year?" is a question that asks for a countable response, And "How many pink erasers do the students in your class have?" is a question that asks for a discrete numerical response.Read more about statistical question at
https://brainly.com/question/22334957
#SPJ1
50 Points! Multiple choice algebra question. Transform both sides of each equation to determine which is a polynomial identity. Photo attached. Thank you!
The only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).
How to express the valueIt should be noted that to determine which equation is a polynomial identity, we need to simplify both sides of each equation and see if they are equal for all values of c and d.
(A) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ - d³ + 3cd(c + d)
The left-hand side can be expanded using the binomial formula. The right-hand side is a polynomial of degree 3, so we can see that equation (A) is a polynomial identity.
(B) (c+d) = c + d³ + 3cd(c + d)
= d³ + c³ + 3cd(c + d) + c + d - c³
= d³ + c³ + 3cd(c + d) + c + d
The right-hand side can be simplified, but it is not equal to the left-hand side for all values of c and d. Therefore, equation (B) is not a polynomial identity.
(C) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ + d³ + 3cd(c + d) + cd(c - d)
The right-hand side is not equal to the left-hand side for all values of c and d, so equation (C) is not a polynomial identity.
(D) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ - d³ + 3cd(c - d) + c³ + d³
= 2c³ + 3cd(c - d)
The right-hand side is not equal to the left-hand side for all values of c and d, so equation (D) is not a polynomial identity.
Therefore, the only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).
Learn more about polynomial on
https://brainly.com/question/2833285
#SPJ1
Find the number that makes the ratio equivalent to 36:84?
Answer: 3:7
Step-by-step explanation: since the simplest form of the fraction 36/84 is 3/7 that means 36:84 in simplest form is 3:7.
The states C and D spend a total of $56.8 million for tourism. The state C spends $1.8 million more than the state D. Find the amount that each state spends on tourism.
D spends $___ million on tourism , and state C spends $___million on tourism.
Let's denote the amount that state D spends on tourism as "x" million dollars. According to the given information, state C spends $1.8 million more than state D, so state C would spend "x + 1.8" million dollars on tourism.
The total amount spent by state C and state D combined is $56.8 million. So we can write the equation:
x + (x + 1.8) = 56.8
Now, we can solve this equation to find the values of x and x + 1.8, which represent the amount spent by state D and state C, respectively.
x + x + 1.8 = 56.8
2x + 1.8 = 56.8
2x = 56.8 - 1.8
2x = 55
x = 55 / 2
x = 27.5
So, state D spends $27.5 million on tourism, and state C spends $27.5 + $1.8 = $29.3 million on tourism.
I need help with this problem it's is
8x+5+3x+8=90
Answer:
x = 7
Step-by-step explanation:
8x + 5 + 3x + 8 = 90
11x + 5 + 8 = 90
11x + 13 = 90
11x = 77
x = 7
Let's Check
8(7) + 5 + 3(7) + 8 = 90
56 + 5 + 21 + 8 = 90
61 + 21 + 8 = 90
82 + 8 = 90
90 = 90
So, x = 7 is the correct answer!
Answer:
7
Step-by-step explanation:
First, collect common factors. This means put the x's together and the regular numbers together.
8x+3x=11x
5+8=13
11x+13=90
Subtract 13 from both sides
11x+13=90
-13 -13
11x=77
Divide 77 by 11
x=7
Hope this helps! :)
A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin in terms of pie?
Answer:
[tex]81\pi[/tex] [tex]mm^2[/tex]
Step-by-step explanation:
Let's recall the formula for the area of a circle:
[tex]A = \pi r^2[/tex]
We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:
[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]
Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:
[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]
So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].
To find the area of the coin/a circle use this equation:
(a = area, r = radius, d = diameter)
[tex]\text{a = r}^2[/tex]
So we need to do for the radius.
[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]
[tex]\text{r} = \dfrac{18}{2}[/tex]
[tex]\text{r} = 9[/tex]
Then solve
[tex]\text{a = 9}^2[/tex]
[tex]\boxed{\bold{a = 81}}[/tex]
A bag of M&M's has 6 red, 3 green, 8 blue, and 5 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? 2) a blue or green? 3) an orange?
The probability of randomly picking a yellow M&M is 5/22.
There are no orange M&M's in the bag, so the probability of randomly picking an orange M&M is 0.
What is the probability of randomly picking 1) a yellow? 2) a blue or green? 3) an orange?There are 22 M&M's in the bag in total. We can use this information to answer the following:
The probability of randomly picking a yellow M&M is 5/22.
The of randomly picking a blue or green M&M is the sum of the probabilities of picking a blue M&M and a green M&M, since these events are mutually exclusive(i.e., they cannot occur at the same time). The probability of picking a blue M&M is 8/22, and the probability of picking a green M&M is 3/22. Therefore, the probability of picking a blue or green M&M is (8/22) + (3/22) = 11/22.
There are no orange M&M's in the bag, so the probability of randomly picking an orange M&M is 0.
to know more about probability
brainly.com/question/30034780
#SPJ1
James is going to put a fence around his circular garden. The garden has a circumference of 40.82 m. What is the diameter of the garden? Use 3.14 for pie
Answer:
13m
Step-by-step explanation:
Circumference = 2×3.14.R = 40.82 => R = 40.82÷(2×3.14) = 6.5m
d = 2R = 2×6.5 = 13m
In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 106 million? Round your answer to the nearest year.
Answer:
2004
Step-by-step explanation:
Evelyn sells 4 bags of popcorn. Her teammate Sidney sells 5 bags of popcorn. How much money do they raise in all?