Answers
Answer:
[tex]A_{\Delta ABP}=\sin \theta[/tex]
Step-by-step explanation:
Let the center of the circle be O.
Recall that the area of a triangle can be given by:
[tex]\displaystyle A=\frac{1}{2} ab\sin C[/tex]
Where C is the angle between the two sides.
ΔABP is equal to the sum of ΔAPO and ΔBOP.
Let a = OP and b = OB. Since this is the unit circle and PO and BO are radii, they both equal one. C will be θ. Hence, the area of ΔBOP is:
[tex]\displaystyle A_{\Delta BOP}=\frac{1}{2}(1)(1)\sin \theta=\frac{1}{2}\sin\theta[/tex]
For ΔAPO, we can use the two sides OP and OA. Again, they are the radii of the unit circle, so they equal one. The angle in this case will be π - θ radians. Hence:
[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}(1)(1)\sin\left(\pi -\theta\right)=\frac{1}{2}\sin\left(\pi -\theta\right)[/tex]
However, note that sin(π - θ) = sin(θ). Hence:
[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}\sin\left(\theta\right)[/tex]
Hence, the area of ΔABP is:
[tex]\displaystyle A_{\Delta ABP}=\frac{1}{2}\sin \theta+\frac{1}{2}\sin\theta =\sin \theta[/tex]
Related Questions
help! can a big strong màn help me
Answers
Step-by-step explanation:
hear is your answer 9 is correct answer
The manager of a new supermarket wished to estimate the likely expenditure of his customers. A sample of till slips from a similar supermarket describing the weekly amount spent by 500 randomly selected customers was collected and analysed. This expenditure was found to be approximately normally distributed with a mean of $50 and a standard deviation of $15.
Find the probability that any shopper selected at random spends more than $80 per week?
Find the percentage of shoppers who are expected to spend between $30 and 80 per week?
Answers
Answer:
0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.
88.54% of shoppers are expected to spend between $30 and 80 per week.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of $50 and a standard deviation of $15.
This means that [tex]\mu = 50, \sigma = 15[/tex]
Find the probability that any shopper selected at random spends more than $80 per week?
This is 1 subtracted by the p-value of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 50}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.
Find the percentage of shoppers who are expected to spend between $30 and 80 per week?
The proportion is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 30.
X = 80
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 50}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 30
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 50}{15}[/tex]
[tex]Z = -1.33[/tex]
[tex]Z = -1.33[/tex] has a p-value of 0.0918
0.9772 - 0.0918 = 0.8854
0.8854*100% = 88.54%
88.54% of shoppers are expected to spend between $30 and 80 per week.
Assume that y varies inversely with the
square of x, then solve.
When x is 5, y is 4/5. Find y when x is 8.
Answers
Answer:
y = 5/16
Step-by-step explanation:
[tex]y\ \alpha\ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\y = \frac{4}{5}, x = 5.\\\\\frac{4}{5} = k \times \frac{1}{5^2}\\\\\frac{4}{5} \times 5^2 = k\\\\20 = k\\\\Now \ find\ y, \ when \ x = 8\\\\y = k \times \frac{1}{x^2} = 20 \times \frac{1}{8^2} = 20 \times \frac{1}{64} = \frac{5}{16}[/tex]
HELP PLEASE
Question: 1. Line segment AB has endpoints A(8, 3) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2. 2. Line segment AB has endpoints A(6, 4) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.
Answers
Answer:
a) (6,4)
b) (5, 4.5)
Step-by-step explanation:
much like when you find them midpoint where you average the x-coordinates and the y-coordinates to find the midpoint coordinates, you'll do the same thing here.
to set context, a midpoint would break the segment into a ratio of 1:1.
so in the first part, a ratio of 1:2 means you are breaking the segment into 3-parts. So you'll do this for the coordinates:
[tex]x = \frac{8 + 2}{3} \: and \: y = \frac{3 + 6}{3} [/tex]
for the second part as the ratio is 1:3, you are breaking the segment into 4 parts.
[tex]x = \frac{6 + 2}{4} \: and \: y = \frac{4 + 6}{4} [/tex]
What is the solution to the equation: 3 + 5 = 14 Show work.
Answers
Answer:
You can't solve that I think
A third-grade class is using plaster of Paris to make impressions of their hands. Each student needs 12 ounces of plaster to make an impression. There are a total of 20 students in the class. How many pounds of plaster will the teacher need for the activity?
Answers
Answer:
15 pounds of plaster
Step-by-step explanation:
First, convert ounces to pounds.
In 1 pound, there are 16 ounces. Create a proportion to convert 12 ounces to pounds.
[tex]\frac{1}{16}[/tex] = [tex]\frac{x}{12}[/tex]
Cross multiply and solve for x:
16x = 12
x = 0.75
So, each student will need 0.75 pounds of plaster. Multiply this by 20 to find the total amount the teacher will need:
20(0.75)
= 15
So, the teacher will need 15 pounds of plaster
Answer:
15 pounds
Step-by-step explanation:
How do I find the length
Answers
a warehouse has a height of
Answers
L*W*H
Hope this helps :D
simplify when q = − 7 ; r = 2 ; s = q
8 -8r - 3s + 6q
Answers
Answer:
3q - 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
q = -7
r = 2
s = q
8 - 8r - 3s + 6q
Step 2: Simplify
Substitute in variables: 8 - 8(2) - 3q + 6qMultiply: 8 - 16 - 3q + 6qCombine like terms: 3q - 8The Pentagon's ABCDE & PQRST are similar find the length X of QR
Please help I will give 50 points and give branliest!!!!
Answers
Answer:
x = 3.2
Step-by-step explanation:
Since they are similar the ratio of the side lengths must be the same
Using the bottom side and the unknown side from the left figure and the right figure
5 4
----- = --------
4 x
Using cross products
5x = 4*4
5x = 16
Divide by 5
x = 16/5
x =3.2
Round .335 to
the nearest:
tenths
hundredths
Answers
Hundredths=0.34
Simplify the expression:
3(5+3k) whoever first gets brainliest
Answers
Answer:
Step-by-step explanation:
15+9k
Name the diameter for the circle Q. A. QH. B.EH. C.HC. D.QE
Answers
Answer:
B) EH
Step-by-step explanation:
Answer:
QH = radius
EH = Diameter
QE = radius
Step-by-step explanation:
NOTEThe diameter is the full length dividing the circle into two equal halfs
Where as the radius divides the diameter into two halfs
.
Evaluate the expression below:
7 + (8 • 2)
Answers
Answer:
The answer is 23
Step-by-step explanation:
8 · 2=16+7=23
Answer:
23
Step-by-step explanation:
1. Calculate the action in () 8*2 =16
2. Sum 7 + 16 = 23
Find out what t means please
Answers
Answer:
19330
Step-by-step explanation:
t-1096=18234
+1096 +1096
t = 19330
Hope that helps! Have a wonderful day :)
Please help and don’t give links
Answers
Answer:
B.d.c.b.a.c.b is. respectively answer
[tex] - 9 - ( - 4) = [/tex]
i don't know
Answers
[tex]\sf\purple{-5}[/tex] ✅
Step-by-step explanation:
[tex] - 9 - ( - 4) \\ = - 9 + 4 \\ = - 5[/tex]
Note:-
[tex]\sf\red{(-)\:x\:(-)\:=\:+}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Answer:
- 9 -( -4) = -5
Step-by-step explanation:
-9-(-4)
solve the one in the bracket first because there is a minus sign between 9 and the bracket so we cannot use the 9 to multiple the number four in the bracket.
-9+4
the sign has changed to positive because when negative numbers are multiplying each other to will turn in to become positive.
so -9+4= -5
solution.
-9-(-4)
-9+4
-9+4= -5
therefore the answer is -5.
Solve AABC. Round your answers to the nearest hundredth, if necessary
Answers
Answer:
[tex]C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83[/tex]
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be [tex]180-90-65=25^{\circ}[/tex].
In any triangle, the Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex].
Therefore, we have:
[tex]\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}[/tex]
[tex]\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}[/tex]
factored form for 12a-b
Answers
The factored form of the given expression 12a - b, is not possible.
To determine the factor form of 12a-b.
What is simplification?In mathematics, the process of operating and interpreting a function to make it simpler or more understandable is known as simplifying, and the process is known as simplification.
here,
Given expression = 12a -b
The factored form for the given expression, cannot be determined because the given expression is a simplified expression its factor cannot be possible.
Thus, It is not possible to factor the supplied expression 12a - b.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
please answer this question
Answers
Answer:
328
Step-by-step explanation:
To find the lenght of the far left side use SOH, CAH, TOA
we have the hypotonouse and need the opposite side so we'll use SOH
sin(38)=x/26
26sin(38)=16
Then use pathagoreyous theroem to solve for the last side
a²+16²=26²
a= 20.4882
Then the area is just length*width so
16*20.4882=327.9599 which rounds to 328
Answer:
Solution given:
we have
sin 38=opposite/hypotenuse
opposite=breadth [w=b]=sin38*26=16
by using Pythagoras law
l²+b²=26²
l²=26²-16²
l=√420
l=20.5
now
Area =l*w=20.5*16=328cm²
I’m confused:/ can somebody help me??
Answers
Answer:
I got ya :D
the answer is
[tex] \binom{ - 18 \: \: \: 10 }{5 \: \: \: - 3} [/tex]
explanation in the attachment
a portion of 7200 is invested at 5 1/2 percent interest, and the rest is invested at 5 percent interest. if the yearly income from the money is rs. 387 how much is invested at each rate ?
Answers
Answer:
A 5.5% = 5400 B 5% = 1800
Step-by-step explanation:
A + B = 7200
A * 0.055 + B * 0.05 = $387
A = 7200 - B
(7200 - B)*0.055 + B*0.05 = 387
396 - 0.055B + 0.05B = 387
396 - 0.005B = 387
0.005B = 9
B = 1800
A = 7200 - B = 7200 - 1800
A = 5400
Can someone please help me?!!!!
Answers
Answer:
The answer is:
0.18
0.92
0.15
1.80
help me I got 25 missing assignments
Answers
Answer:
think it's the last one
Step-by-step explanation:
sorry if i'm wrong
Here are two datasets: Dataset A: 64 65 66 68 70 71 72 Dataset B: 64 65 66 68 70 71 720 For dataset A, the mean and median are 68. Looking at dataset B, notice that all of the observations except the last one are close together. Which measure will be affected by this last observation in dataset B
Answers
Answer:
Mean will be affected.
Step-by-step explanation:
The mean value of the data set will be affected as it depends on the magnitude of data points and not its position. The median however will not change since it depends on the relative position of data points.
Let U = {1, 2, 3, 4, 5, 6, 7), A = {2, 4, 6, 7), and B = {1, 4, 7}. Find the set (A U B)'.
Answers
Step-by-step explanation:
(A U B) = {1,2, 4, 6, 7}
(A U B)'= U- (A U B) = { 3,5}<------- Answer
A person is in a plane 12.5 km above the ocean. How far from the plane can the person see out on the ocean? (The radius of Earth is 6378 km.)
The person can see approximately km.
(Type an integer or a decimal rounded to two dečimal places as needed.)
Answers
Answer:
Step-by-step explanation:
The line fron the airplane wich is tangent to earth surface is also perpendicular to the radius as you can see in the figure. So is valid to contruct the right-angled triangle as shown in the second figure.
[tex]r^2+(r+h)^2=x^2\\\\r=6378Km,~h=12.5Km\\\\x^2=81517374.25\\\\x=9028.7Km[/tex]
Which of the following is the definition for combination?
Answers
Answer:
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected. For example, suppose we have a set of three letters: A, B, and C. ... Each possible selection would be an example of a combination. The complete list of possible selections would be : AB, AC, and BC.
the distance from kevins home to his school is 2 kilometers. adrian lives 750 meters from the same school. how much closer does adrian live next to the school than kevin
Answers
2000m -750m=1250m thats the answer
how many years (to two decimal places) will it take an investment of $17,000 to grow to $41,000 if it is invested at 2.95% compounded continuously
Answers
Answer:
30 years
Step-by-step explanation:
Given data
P=$17,000
A= $41,000
R=2.95%
the expressio for the time is
t= ln(A/P)/r
t= ln(41,000 /17000)/0.0295
t= ln(2.41176)/0.0295
t= 0.8803/0.0295
t= 29.8
about 30 years