Answers
Step One
Find AB, BC, AC
Before beginning this problem, I'm going to arbitrarily name
c = AB
a = BC
b = AC It just makes the calculations easier.
AB = radius of the large circle - radius of the medium circle = 20.62 - 8.04 = 12.58
BC = Radii of the two smaller circles added together = 8.04 + 7.35 = 15.39
AC = Radius of the large circle - Radius of the small circle = 20.62 - 7.35 = 13.27
So
a = 15.39
b = 13.27
c = 12.58
Step Two
Find Angle A or <BAC
a^2 = b^2 + c^2 - 2*b*c * Cos(A)
15.39^2 = 12.58^2 + 13.27^2 - 2 * 12.58 * 13.27 * Cos(A)
236.852 = 158.26 + 176.1 - 333.87 * Cos(A)
236.852 = 334.4 - 333.87*Cos(A)
-97.55 = - 333.87 * Cos(A)
-97.55 / -333.87 = Cos(A)
0.2922 = cos(A)
A = cos-1(0.2922)
A = 73.01 degrees
Step Three
Just to see if you understand what was done, I'll give you the givens for finding c, and the answer and you can work through the calculations to see if your answer agrees with mine. If it doesn't PM me.
c = 12.58
b = 13.27
a = 15.39
12.58^2 = 13.27^2 + 15.39^2 - 2*13.27*15.39*Cos(C)
C = 51.42
Step Four
Find <B
Every triangle has 180 degrees so
B = 180 - <A - C
B = 180 - 51.42 - 74.01
B = <54.57.
I have found a moderator who opened the question up so that I can show you why the Cos law is the only way to do this. If the circles are very disproportionate as in this diagram, then no simple assumption can be made. The cos law is all that will work. I would have posted this earlier, but I didn't think anyone would find another method. It's ingenious but not possible for the situation below.
Related Questions
A florist earns a profit of $2.00 on each bunch of carnations, $3.00 on each bunch of lilies and $1.00 on a bunch of roses. On a particular day, she sold 46 bunches of flowers and made a profit of $82.00. She sold twice as many bunches of roses as bunches of lilies.
Answers
jk its b. love yah
will give brainiest if correct
A. 69.1
B. 20.9
C. 22.4
D. 67.6
Answers
sin A/ a = sinB/ b
where A = C or 90 degrees; a = 21
B = ? , b = 8
solving for b;
sin(90) / 21 = sin(B) / 8 ; B = 22.39 degrees
Total angle of triangle = 180
180 - 90 - 22.39 = x
x = 67.607 degrees
simplify 15r+7r+9r-7s
Answers
12r + 2r
14r
_____________________
12r + 2r = simplified
answer is 14r
______________________
Hope this helps,
QueenBeauty666
You choose a marble at random from a bag containing 8 brown marbles 6 yellow marbles and one purple marble. You replace the marble and then choose again.find p (both yellow)
Answers
Pick 2: 6 yellow out of 15 total marbles = 6/15 = 2/5
Pick 1 AND Pick 2
2/5 x 2/5 = 4/25
The product of some negative number and 10 less than three times that number is 25. find the number.
Answers
n=2+1/3√111 or n=2+-1/3√111
A coin is unbalanced such that it comes up tails 55% of the time.
a.what is the probability that you don't flip a head until the fourth flip?
b.what is the probability that you don't flip a tail until the fourth flip?
c.how many tosses would it take, on average, to flip a head?
d.how many tosses would it take, on average, to flip a tail?
Answers
b. P[HHHT] = .45^4*.55 = .0226
c. 1/.45 = 2.222
d. 1/.55 = 1.818
Megan consumed 3.5 gallons of water in one day. How many milliliters are equal to 3.5 gallons, if 1 liter equals 1,000 milliliters and 1 gallon = 3.785 liters?
Answers
There are 3,785 milliliters in one gallon.
Then, multiply that by 3.5 3,785 x 3.5 = 13,247.5
There are 13,247.5 ml in 3.5 gallons
Answer:
There are 13,247.5 ml in 3.5 gallon
Daniel is setting up rows for a concert. He decides to put 9 chairs in each row. There are 45 chairs. Let x represent the number of rows of chairs. Which equation can be used to find the number of rows of chairs Daniel needs to set up?
Answers
*divide 45 by 9 which is 5
x=5
hope this helps!
Consider the function f(x)=(x-9)/(x^3-81x)
Find the vertical asymptote(s) of f(x)
Answers
Answer:
Its A
x=0, -9
Step-by-step explanation:
just got it correct
The function f(x)=(x-9)/(x^3-81x) has three vertical asymptotes at x = 0, x = 9, and x = -9.
Explanation:To find the vertical asymptote(s) of the function f(x) = (x-9)/(x^3-81x), we need to determine the values of x for which the denominator equals zero. Setting the denominator equal to zero and solving for x, we get:
x^3 - 81x = 0x(x^2 - 81) = 0x(x - 9)(x + 9) = 0Therefore, the function has three vertical asymptotes at x = 0, x = 9, and x = -9.
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Frazier has $1,200 in savings. He works because he is saving money for college, and he earns $9 an hour. If Frazier saves 25 percent of his net pay, after 20 percent is taken out for tax, identify the expression which represents Frazier's savings.
A) 1.8x + 1,200
B) 3.6x + 1,200
C) 7.2x + 1,200
D) 9x + 1,200
Answers
the correct answer is A..!! I think...:(
Answer: The correct option is (A) [tex]1.8x+1200.[/tex]
Step-by-step explanation: Given that Frazier is saving money for college and has $1200 in savings. He earns $9 per hour. He saves 25% of his net pay after 20% taken out for tax.
We are to identify the expression that represents Frazier's savings.
Let, x represents the number of hours for which Frazier works.
So, the net pay of Frazier = $ 9x.
Since 20% of the net pay is taken out for tax, so total pay of Frazier after taking out tax is given by
[tex]I_t=9x-20\%\times 9x=9x-\dfrac{20}{100}\times 9x=9x-\dfrac{9x}{5}=\dfrac{36x}{5}.[/tex]
Now, Frazier's savings from his net pay is given by
[tex]I_s=25\%\times \dfrac{36x}{5}=\dfrac{25}{100}\times \dfrac{36x}{5}=\dfrac{9x}{5}=1.8x.[/tex]
Since Frazier has $1200 already in savings, so the equation representing Frazier's savings will be
[tex]1.8x+1200.[/tex]
Thus, the required equation is [tex]1.8x+1200.[/tex]
Option (A) is CORRECT.
Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of them said they play football. Twenty of them said they do not play baseball or football.
Enter your answers in the boxes to complete the two-way table based on the given data.
Answers
We start out placing 31 in the Total column beside the Don't Play Baseball row. We then place 16 in the Total row under the Play Football column. 20 goes in the Don't Play Baseball row under the Don't Play Football column.
Since there are 31 people that do not play baseball, and 20 of them don't play football, this leaves us with 31-20=11 that do not play baseball and play football.
There are 58 people total, so this goes in the Total row under the Total column.
There are 58 people, and 31 of them do not play baseball; this leaves us 58-31=27 total that play baseball.
16 total people play football, and 11 of them don't play baseball. This leaves us 16-11=5 people that play football and play baseball.
There are 58 people, and 16 of them play football; this leaves us 58-16=42 total that don't play football.
42 people don't play football, and 20 of them don't play baseball; this leaves us 42-20=22 people that don't play football and play baseball.
5 people play baseball and play football, and 22 people play baseball and don't play football; this gives us 5+22=27 people total that play baseball.
can someone please explan how I got this wrong?
Solve for x in the triangle
using laws of cosine
Answers
Martha states that –6 is a rational number. Which is a correct explanation for this statement?
The number –6 is the opposite of 6.
The number –6 is a negative integer.
The number –6 can be written as -6/1
The number –6 is less than 0.
Answers
Martha's statement saying - 6 is a rational number is correct as - 6 can be written as - 6/1.
What are rational numbers?Rational numbers consist of fractions and integers.
Any rational number can be written in the form of p/q, where q ≠ 0.
Any integer can be written in the form of a rational number p/q, where q ≠ 0 and q = 1.
Given, Martha states that - 6 is a rational number.
First, it is a negative integer but it can be written in the form - 6/1 as - 6/1 is equal to 6.
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Martha is correct in stating that -6 is a rational number because it can be written as -6/1.
Explanation:Martha is correct in stating that -6 is a rational number because it can be written as -6/1. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. In this case, -6 can be written as the fraction -6/1.
If you answer 110 questions and get a 94% how many did you get wrong
Answers
Set up a ratio.
x= number correct out of 110
x/110= 94/100
cross multiply
(x * 100)= (110 * 94)
100x= 10,340
divide both sides by 100
x= 103.4
STEP 2:
subtract number correct in step 1 from total number of questions
=110 - 103.4
=6.6 questions wrong
ANSWER: There were exactly 6.6 questions wrong on the test. Since you cannot have a partial question (unless otherwise stated), but only whole questions, round up to 7 whole questions wrong.
Hope this helps! :)
A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?
Answers
To evaluate for P(0.372<x<0.428) we shall proceed as follows:
z-score is given by:
z=(x-μ)/σ
thus when x=0.372:
z=(0.372-0.4)/0.028
z=-1
thus
P(x<0.372)=P(z<-1)=0.1587
when x=0.428
z=(0.428-0.4)/(0.028)=1
P(x<0.428)=P(z<1)=0.8413
thus
P(0.372<x<0.428) =P(z<1)-P(z<-1)=0.8413-0.1587=0.6826
To find the percentage of observations between two values in a normal distribution, we can convert the values to z-scores and use a z-table to find the corresponding areas. In this case, the percentage of observations between 0.372 and 0.428 is 68.26%.
Explanation:To find the percentage of observations that will lie between 0.372 and 0.428 in a normal distribution with a mean of 0.40 and standard deviation of 0.028, we need to find the area under the curve between these two values.
Using a standard normal distribution table or z-table, we can convert the values to z-scores by subtracting the mean and dividing by the standard deviation. The z-score for 0.372 is (0.372 - 0.40) / 0.028 = -1, and the z-score for 0.428 is (0.428 - 0.40) / 0.028 = 1.
By looking up the corresponding area for these z-scores in the z-table, we find that the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. To find the percentage between -1 and 1, we subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826 or 68.26%.
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How do you simplify # (x+3)/(x^2+7x+12)#?
Answers
hope it is helpful
WILL MAKE BRAINLIEST!!!!!!!The arc length of a sector is equal to twice the radius. Express the arc length s as a function of the area a of the sector.
s=
Answers
==>
Since r = s/2, it follows that , or , or
.
The arc length as a function of the area of the sector is l=2√A.
What is the area of a sector?Area of a sector = 1/2 * arc length(l) * radius(r)
[tex]A=[/tex] [tex]\frac{1}{2} l*r[/tex]......(1)
It is given that the arc length of a sector is equal to twice the radius.
This means [tex]l=2r\\[/tex]
So, [tex]r=\frac{l}{2}[/tex]
Putting the value of r in (1)
[tex]A = \frac{l^{2} }{4}[/tex]
[tex]l^{2} =4A[/tex]
[tex]l=2\sqrt{A} \\[/tex]
So, the required function is l=2√A
Hence, the arc length as a function of the area of the sector is l=2√A.
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Complete the equation of the line through (-6,5) and (-3,-3) Use exact numbers. y=
Answers
slope = (5+3)/(-6 + 3) = 8/-3 = -8/3
y = mx + b
b = y - mx
b = -3 - (-8/3)(-3)
b = -3 - 8
b = -11
equation
y = -8/3 x - 11
hope it helps
The equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(-6,5) and (-3,-3)
Then the equation of the line passing through the points (-6,5) and (-3,-3) will be
[tex]\rm (y + 3) = \left (\dfrac{-3-5}{-3+6} \right ) (x + 3)[/tex]
Simplify the equation, then the equation of the line will be
y + 3 = -(8/3)(x + 3)
y = -(8/3)x - 8 - 3
y = -(8/3)x - 11
Then the equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.
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Simplify the function f(x)= 1/2 (27) 2x/3. Then determine the key aspects of the function
Answers
[tex]f(x)= \frac{1}{2}(27)^{ \frac{2x}{3} } \\ \\ f(x)= \frac{1}{2}((27)^{ \frac{2}{3} })^{x} \\ \\ f(x)= \frac{1}{2}(9)^{x} [/tex]
From the above equation, we can answer all the 4 questions.
a) Initial value occurs when x = 0
So,
[tex]f(0)= \frac{1}{2}(9)^{0}= \frac{1}{2} [/tex]
So, the Initial value of the function is 1/2.
b) Simplified Base:
The base of an exponential function is the term which contains the exponent.
From the simplified equation, we can see that the base has been simplified and is equal to 9.
So, the simplified base is 9
c) Domain:
From the equation we can see that there is no such value which makes the function undefined. So all reall numbers are included in the Domain.
So, Domain is Set of All real numbers.
In Interval notation this can be expressed as: (-∞,∞)
d) Range:
Range is the set of all y values that a function can take. Since the graph is not shifted vertically up or down, the range will be the set of all real numbers greater than zero.
So, Range is equal to All real numbers greater than 0.
In Interval notation, this can be expressed as (0,∞)
Answer:
The last one is y>0
Selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red pens
Answers
please help asap 50 pts
Answers
The vertex is always the lowest or highest point:
When a parabola looks like a smiley face, it has a minimum (like this one).
When a parabola looks like a frowning face, it has a maximum.
The coordinate for the vertex is (-2, -3).
So, your answer is C.
Anyone know this? Will give brainiest
Answers
Hope this helps
What is the value of x?
28
47
56
33
Answers
______________________________________________________
→ " x = 47 " .
______________________________________________________
Explanation:
______________________________________________________
Note: The "vertex" is "floating around" inside the circle.
Answer:
47
Step-by-step explanation:
The Bright Star Video Club offers the two membership plans described below.
Plan A: $50 yearly membership fee and $2 for each video rental
Plan B: $10 yearly membership fee and $4 for each video rental
Greg is planning to enroll in one of these plans. For how many video rentals would the total cost of Plan A be equal to the total cost of Plan B?
A. 50
B. 20
C. 30
D. 40
Answers
Plan A: y = 2x + 50
Plan B: y = 4x + 10
2x + 50 = 4x + 10
Now solve the combined equation.
2x + 50 = 4x + 10
- 10 - 10
2x + 40 = 4x
-2x -2x
40 = 2x
x = 20
Plan A: y=2x+50
Plan B: y=4x+10
and see where they intersect, and that will give you the answer.
OR
You can substitute each answer for x, like this,
A. 50
Plan A:
y=2(50)+50
y=100+50
y=150
Plan B:
y=4x+10
y=4(50)+10
y=200+10
y=210
So, therefore, A.50 is not the answer.
B.20
Plan A:
y=2x+50
y=2(20)+50
y=40+50
y=90
Plan B:
y=4x+10
y=4(20)+10
y=80+10
y=90
So, B.20 is correct but always check the rest of the answers. Just in case
C.30
Plan A:
y=2x+50
y=2(30)+50
y=60+50
y=110
Plan B:
y=4x+10
y=4(30)+10
y=120+10
y=130
So, C.30 is incorrect.
D.40
Plan A:
y=2x+50
y=2(40)+50
y=80+50
y=130
Plan B:
y=4x+10
y=4(40)+10
y=160+10
y=170
So, in conclusion the correct answer is B.20.
A number cube numbered from 1 to 6 is rolled. what is the probability of the number cube showing a 5 or an even number?
Answers
An alloy of copper is 10% copper and weighs 25 pounds. A second alloy is 18% copper. How much (to the nearest lb.) of the second alloy must be added to the first alloy to get a 13% mixture.
Answers
Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?
Answers
The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)
Answers
y(t)=4t^2+1
Time (seconds):
Where is the ship after 10 seconds?
t=10→Position: Point: P=(x(t), y(t))=(x(10), y(10))=?
t=10→x(10)=3(10)→x(10)=30
t=10→y(10)=4(10)^2+1=4(100)+1=400+1→y(10)=401
Position: P=(x(10), y(10))=(30, 401)
Answer: Option C.) (30, 401)
a bag contains 7 red marbles 6 green marbles 5 yellow marbles and 2 orange. marbles are drawn twice with a replacement. what is p {yellow and green?
a coin is tossed and a number cube is rolled. what is p{h, then prime number?
letter tiles that spell the word happiness are replaced in a bag. a tile is drawn and then a second tile is drawn. find p then vowel p?
Answers
[tex]226[/tex]
Question 1:
We have been given that a bag contains 7 red marbles, 6 green marbles, 5 yellow marbles, and 2 orange. Further we are given that marbles are drawn twice with a replacement. We need to figure out the probability P(Yellow and Green).
Basically, we need to determine the probability that first marble drawn is yellow and second marble drawn is green.
Probability of first marble drawn being yellow is [tex]\frac{5}{20}=\frac{1}{4}[/tex] and probability of second marble drawn being green is [tex]\frac{6}{20}=\frac{3}{10}[/tex].
Therefore, the probability P(Yellow and Green) = [tex]\frac{1}{4}\cdot \frac{3}{10}=\frac{3}{40}[/tex].
Question 2:
We have been given that a coin is tossed and a number cube is rolled and we need to find the probability P(H, prime number).
Probability of getting head on the coin is [tex]\frac{1}{2}[/tex].
Probability of getting a prime number on the cube is [tex]\frac{3}{6}=\frac{1}{2}[/tex].
Therefore, probability P(H, prime number) = [tex]\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}[/tex]
A town has a population of 13000 and grows at 4.5% every year. What will be the population after 13 years, to the nearest whole number?
Answers
y=13,000(1.045)^t
t=13
You get 1.045 because you add 1+ the percentage in decimal form.
Answer:
population after 13 years is around 23,039
Step-by-step explanation:
A town has a population of 13000 and grows at 4.5% every year.
Population growth is given by [tex]y=a(1+r)^t[/tex]
y is the population after t years
'a' is the initial population= 13000
'r' is the rate of growth=4.5%= 0.045
t is the number of years=13
[tex]y=a(1+r)^t[/tex]
[tex]y=13000(1+0.045)^13[/tex]
y=23,038.54