A square is inscribed in a circle. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
Answers
d also is the hypotenuse of the square
Through the pythagorean theorem, we know that
x^2 + x^2 = d^2
2x^2 = d^2
Because d = 2r, this means
2x^2 = d^2
2x^2 = (2r)^2
2x^2 = 4r^2
x^2 = 2r^2
The area of the square is x^2, which is the same as 2r^2 as shown above
The area of the circle is A = pi*r^2
Divide the area of the square over the area of the circle to get
(x^2)/(pi*r^2) = (2r^2)/(pi*r^2) = 2/pi
The exact answer, in terms of pi, is the fraction 2/pi
If you want an approximate answer, then use a calculator to get roughly 0.6366 which is about 63.66%
The probability of the point will be in the shaded region is 0.64 or 64%.
A square is inscribed in circle. Probability of point to be pick from the square to be find out.
Venn diagram are the Figures of probabilities to understand better.
Here, diameter of circle = d and radius r =d/2, edge of the square = a
By Pythagorean theorem,
a²+a²=d²
2a²= (2r)²
a²=2r²
Area of the square =2r²
Area of the circle = πr²
Now probability = Area of the square/Area of the circle
= 2r²/πr²
= 2/π
= 0.64
Thus, The probability of the point will be in the shaded region is 0.64 or 64%.
Learn more about Venn diagram here:
https://brainly.com/question/1605100
#SPJ2
Related Questions
Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Answers
3F<300 divide both sides by 3
F<100
Frank has less than 100 books.
Simplify 3 - (2 - 8).
Answers
3 - ( -6 ) =
3 + 6 =
9
44^4 = 22^4 * ? find the missing factor in exponential form. How would you solve this?
Answers
Answer:
Step-by-step explanation:
The number of bagels sold daily for two bakeries is shown in the table. Bakery A Bakery B 53 34 52 40 50 36 48 38 53 41 47 44 55 40 51 39 Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below.
Answers
bakery A
mean (A) = [53 + 34 + 52 + 40 + 50 + 36 + 48 + 38]/8 = 43.88
Bakery B
mean (B) = [53 + 41 + 47 + 44 + 55 + 40 + 51 + 39]/8 = 46.25
Even if bakery A and B has the 38 and 39 as the lowest data respectively, they are still near the average data.
Considering the information about the asymmetry in Bakery B's distribution, the median would be a more appropriate measure of central tendency for both Bakery A and B. It would provide a better representation of the "typical" number of cupcakes sold in each bakery, even if there might be outliers in the data.
Understanding Mean and Median:
Mean: The mean, also known as the average, is calculated by adding all the values in a dataset and dividing by the number of values. It's a good measure of central tendency when the data is symmetrical and free from outliers.Median: The median is the 'middle' value when the data is ordered from least to greatest. It's less sensitive to extreme values (outliers) compared to the mean.Why Median is More Appropriate (Considering the Information):
The information mentions that the distribution for Bakery B is not symmetric. This suggests that the data points in Bakery B might be skewed towards one side, with a few possibly higher or lower values compared to the majority.
Reasoning:
Option A (Mean): The mean is easily influenced by outliers. If Bakery B has outliers, the mean might not accurately represent the "typical" number of cupcakes sold for Bakery B.Option B (Mean for Perfect Symmetry): This option specifies the mean if the distributions are perfectly symmetrical. Since we know Bakery B's distribution isn't symmetrical, the mean wouldn't be the best choice.Option C (Median for Bakery B Asymmetry): This correctly identifies that the median is a better choice for Bakery B due to the asymmetry in its data.Option D (Median for Outliers): While outliers can be present in both Bakery A and B, the key factor is the asymmetry in Bakery B's distribution. The median is generally more resistant to the influence of outliers, making it a better choice in this case, even if outliers exist in both datasets.complete question:
The number of bagels sold daily for two bakeries is shown in the following table: Uchange Bakery A Bakery B 53 34 52 40 50 36 48 38 53 41 47 44 55 40 51 39 Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below. (3 points)
a. Mean, because there are no outliers to affect the data
b. Mean, because the distribution is perfectly symmetric for both bakeries
c. Median, because the distribution for Bakery B is not symmetric
d. Median, because there are outliers that affect both data sets
If f(x) = 5x – 6, what is the equation for f–1(x)?
Answers
Answer:
5x-2+^3 hole
Step-by-step explanation:
The inverse of f(X) = (x +6 ) /5
What is inverse function?The inverse of a function f is denoted by f^-1 and it exists only when f is both one-one and onto function. Note that f^-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x.
(f o f^-1) (x) = (f^-1 o f) (x) = x
Steps To Find An Inverse FunctionThe following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps.
For the given function f(x) = ax + b, replace f(x) = y, to obtain y = ax + b.Interchange the x with y and the y with x in the function y = ax + b to obtain x = ay + b.Here solve the expression x = ay + b for y. And we obtain y = (x - b/aFinally replace y = f^-1(x), and we have f^-1(x) = (x - b)/a.Given:
f(x) = 5x – 6
let y= f(x) = 5x – 6
Now, Interchange the x with y and the y with x.
x= 5y -6
x+6 = 5y
y = (x +6 ) /5
So, f^-1(x) = (x +6 ) /5
Learn more about inverse of function here:
https://brainly.com/question/2541698
#SPJ5
the sum of two numbers is 8 and their difference is 2. find the numbers
Answers
Average maintenance costs are $1.50 per machine-hour at an activity level of 8,000 machine-hours and $1.20 per machine-hour at an activity level of 13,000 machine-hours. assuming that this activity is within the relevant range, total expected maintenance cost for a budgeted activity level of 10,000 machine-hours would be closest to:
Answers
C = a + bx
where
x = machine hours
a, b are constants.
When x=8,000 hours, C=$1.50, therefore
a + 8000b = 1.5 (1)
When x=13,000 hours, C=$1.20, therefore
a + 13000b = 1.2 (2)
Subtract (2) from (1).
a + 8000b - (a + 13000b) = 1.5 - 1.2
-5000b = 0.3
b = -6 x 10⁻⁵
From (1), obtain
a = 1.5 - 8000*(-6 x 10⁻⁵) = 1.98
Therefore
C = 1.98 - 6x10⁻⁵ x
When machine hours is x=10,000, obtain
C = 1.98 - 6x10⁻⁵ * 10000
= 1.38
Answer: $1.38
In the x -y plane, the line 3x + 2y =72 intersects the x -axis at x=b,for some number b. What is the value of b?
Answers
Since it is specifically stated that the line intersects the x-axis, then this means that y = 0. Therefore substituting y = 0 into the given equation will us the value of x.
Substituting y = 0:
3 x + 2 * 0 = 72
3 x = 72
x = 24
Therefore this means that the line intersect the x-axis at point (24, 0).
What are the zeros of f(x)=4x^3-13x^2-37x+10
Answers
The product of (n^2-6n+3)and -4 is
Answers
-4n^2+24n-12
An open rectangular box has volume 32 cm3. find the lengths of the edges giving the minimum surface area
Answers
An open rectangular box with a volume of 32 cm³ would have its minimum surface area when it takes the form of a cube. In this case, each side of the box would be approximately 3.174 cm.
Explanation:To minimize the surface area of an open rectangular box given a constant volume, the box should take the shape of a cube. This is because a cube is the three-dimensional shape that has the minimum surface area for a given volume. The volume V of the box is given as 32 cm³. Since for a cube, the volume V = a³ where a is the side length of the cube, we need to find the value of a such that the volume is equal to 32cm³.
To do this, we use the cube root function as follows: a = ∛V = ∛32 = 3.174 cm.
So, for a rectangular box with a volume of 32 cm³, the lengths of the edges that would give the minimum surface area would all be approximately 3.174 cm.
Learn more about Minimum Surface Area here:https://brainly.com/question/32318252
#SPJ11
An open rectangular box with a volume of 32 cm³ would have its minimum surface area when it takes the form of a cube.
In this case, each side of the box would be approximately 3.174 cm.
To minimize the surface area of an open rectangular box given a constant volume, the box should take the shape of a cube.
This is because a cube is the 3-dimensional shape that has the minimum surface area for a given volume.
The volume V of the box is given as 32 cm³.
Since for a cube, the volume V = a³ where a is the side length of the cube, we need to find the value of a such that the volume is equal to 32cm³.
To do this, we use the cube root function as follows:
a = ∛V
= ∛32
= 3.174 cm.
So, for a rectangular box with a volume of 32 cm³, the lengths of the edges that would give the minimum surface area would all be approximately 3.174 cm.
A 5-foot ladder is leaning against a 4-foot wall. How far must the bottom of the ladder be from the base of the wall so that the top of the ladder rests on the top of the wall?
Answers
C would be the hypotenuse, which in this case is the five ft ladder.
The other known length of the leg is 4 ft.
5^2-4^2=25-16=9
9 must equal a^2 and a must equal 3
The correct answer is 3 ft
so for now the length is the unknown. therefore,
length = sqrt (5^2 - 4^2)
length = sqrt 9
length = 3 foot
3ft is the answer
What is the answer to this problme
Answers
x=-2
-2-4=-6
the answer is -6
can someone please explain proportions?
Answers
A statement or assertion that exppresses a judment or opinion
if f(x)=x-3/x, g(x)=x+3, and h(x)=2x+1, what is (g*h*f)(x).
A. 3x-6/x
B. 6x-6/x
C. 2x+4/2x+7
D. 4x-3/x
Answers
Answer:
Option B - 6x-6/x
Step-by-step explanation:
Given : If [tex]f(x)=\frac{x-3}{x}, g(x)=x+3,h(x)=2x+1[/tex].
To find : What is the value of [tex](g(h(f)))(x)[/tex]
Solution :
[tex](g(h(f)))(x)=g(h(f(x)))[/tex]
i.e, substitute the value of f(x) in h(x) and then put that h(x) in g(x).
[tex]g(h(f(x)))=g(h(\frac{x-3}{x}))[/tex]
[tex]g(h(f(x)))=g(2(\frac{x-3}{x})+1)[/tex]
[tex]g(h(f(x)))=(2(\frac{x-3}{x})+1)+3[/tex]
Solving the RHS,
[tex]=(2(\frac{x-3}{x})+1)+3[/tex]
[tex]=(\frac{2x-6}{x})+1)+3[/tex]
[tex]=(\frac{2x-6+x}{x})+3[/tex]
[tex]=\frac{3x-6}{x}+3[/tex]
[tex]=\frac{3x-6+3x}{x}[/tex]
[tex]=\frac{6x-6}{x}[/tex]
Therefore, The value of [tex](g(h(f)))(x)=\frac{6x-6}{x}[/tex]
Hence, Option B is correct.
A telephone survey uses a random digit dialing machine to call subjects. the random digit dialing machine is expected to reach a live person 15% of the time. in eight attempts, what is the probability of achieving exactly two successful calls?
Answers
We have
[tex]n=8[/tex]
[tex]r=2[/tex]
[tex]P(Success)=0.15[/tex]
[tex]P(Failure)=0.85[/tex]
Substitute these values into the formula, we have
P( 2 success in 8 trials) = ⁸C₂ × (0.15)² × (0.85)⁶
P( 2 success in 8 trials) = 0.2376.... ≈ 0.24 = 24%
The probability of achieving exactly two successful calls in eight attempts in a telephone survey using a random digit dialing machine is approximately 0.324 or 32.4%.
Explanation:To calculate the probability of achieving exactly two successful calls in eight attempts in a telephone survey using a random digit dialing machine, we can use the binomial distribution formula. The formula is:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
Where:
P(x) is the probability of getting exactly x successful callsn is the total number of attemptsx is the number of successful callsp is the probability of reaching a live personPlugging in the values from the question, we have:
P(2) = (8C2) * (0.15^2) * ((1-0.15)^(8-2)) = 28 * 0.0225 * 0.411771 = 0.3239965
Therefore, the probability of achieving exactly two successful calls in eight attempts is approximately 0.324 or 32.4%.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ2
A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the equation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?
Answers
well, we can get that off either equation, if we just know A coordinates, so let's see what "x" is at those A and B points.
[tex]\bf \begin{cases} y=-0.3x^2+3x\\ ----------\\ -2x+5.5y=19.5\\\\ y=\cfrac{19.5+2x}{5.5} \end{cases}\implies -0.3x^2+3x=\cfrac{19.5+2x}{5.5} \\\\\\ -1.65x^2+16.5x=19.5+2x\implies 0=1.65x^2-14.5x+19.5 \\\\\\ \textit{using the quadratic formula}\quad x=\cfrac{14.5\pm\sqrt{210.25-4(1.65)(19.5)}}{2(1.65)} \\\\\\ x\approx \begin{cases} 7.13\\ 1.66 \end{cases}\textit{ so those are A and B, who is who?, dunno, let's check}[/tex]
[tex]\bf y=-0.3x^2+3x\qquad x=7.13\qquad y=-0.3(7.13)^2+3(7.13) \\\\\\ y\approx 6.14\\\\ -------------------------------\\\\ y=-0.3x^2+3x\qquad x=1.66\qquad y=-0.3(1.66)^2+3(1.66) \\\\\\ y\approx 4.15[/tex]
so, as you can see, clearly 6.14 is higher, and thus is B.
thus A is 4.15, so the y-coordinate for point A is 4.15, and that's the distance from the beam hitting the fountain at A, to the ground.
an architect designs a rectangular flower garden such that the width is exactly two thirds of the length if 320 ft of the antique picket fencing are to be used to enclose the garden find the dimensions of the garden
Answers
what's the width? well, w = (2/3)l.
The dimensions of the garden where 320 ft of the antique picket fencing are to be used to enclose the garden are 96 feet and 64 feet.
Given that:
A garden is in rectangular shape.
The length of the antique picket fencing used to enclose the garden is 320 feet.
The perimeter defines the enclosing length.
So, the perimeter is 320 feet.
Let P = 320.
Let l represent the length and w represents the width of the garden.
The width is exactly two-thirds of the length.
So, [tex]w=\frac{2}{3} l[/tex].
The perimeter of the garden is:
P = 2(l + w)
= 2 (l + [tex]\frac{2}{3} l[/tex])
= [tex]\frac{10}{3} l[/tex]
So, substitute P = 320.
[tex]\frac{10}{3} l=320[/tex]
Simplifying,
l = 96 feet
So, w = 64 feet
Hence, the dimensions are 96 feet and 64 feet.
Learn more about Perimeter here :
https://brainly.com/question/7486523
#SPJ6
Choose the polynomial that is written in standard form. 2x3y2 + 4x4y + 8x7 −3x4y2 + 4x4y5 + 10x2 6xy2 + 4x3y8 + 9x2 −2x5y3 + 4x2y2 + x2
Answers
If a term has x in it, it should be considered before y.
Then sort by powers. For example, x^3 should go before x^2.
Finally sort by coefficient if the variables and their powers are the same.
A is incorrect because 8x^7 should go before all else.
B is incorrect because 4x^4 should go before -3x^4.
C is incorrect because the order should be 4x^3, then 9x^2, then 6x
D is correct.
a cell phone company offers two different monthly plans.plan a charges $41 for unlimited cell phone minutes plus $0.10 per text message.Plan b charges $31 for unlimited cell phone minutes plus $0.15 per text message.How many text messages must a customer send in order for the cost of plan a to be equal to cost of plan b?
Answers
41+0.10x = 31+0.15x
10 +0.10x=0.15x
10=0.05x
x=10/.05
x= 200 text messages
check 200*0.10 = 20 +41 =61
200*0.15 = 30+31 = 61
they equal each other so number of texts is 200
G for exercises 13 and 14, assume the sample populations do not have equal standard deviations and use the .05 significance level: (a) determine the number of degrees of freedom, (b) state the decision rule, (c) compute the value of the test statistic, and (d) state your decision about the null hypothesis.
Answers
EASY 5 POINTS!!! You have a new pool and want to know its volume. The pool is 5 feet deep and has a radius of 7 feet. About how much water can the pool hold? Use 3.14 for pi.
Answers
Answer:
The volume of water that can be hold by the pool is approximately 770 cubic feet.
Step-by-step explanation:
To calculate it we have to use the volume formula for a cylinder. This is:
[tex]Volume=pi*r^{2}*h\\pi=3.14\\r=radius\\h=deep[/tex]
Solving the equation with the given values:
[tex]Volume=3.14*7^{2} *5\\Volume=769.3 cubic feet \\Aprox.Volume= 770 cubic feet[/tex]
The volume of water that can be hold by the pool is approximately 770 cubic feet.
Lori rented a car for one day. The daily rental rate was $12.50 plus 25 cents per mile. The total cost of her rental was $46. How many miles did she drive that day?
Answers
33.5=.25x
x=134
Final answer: 134 miles
2/3 (5 x 4) ÷ 3 + 6/7 I divided 3/2 is 1.5*(20)=30/3=10+1.16=11.16 is that correct not so good in math
Answers
2/3 (5 × 4) ÷ 3 + 6/7 = 334/63
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem.
Let's write down the problem that is wanted to be solved:
[tex]\frac{2}{3} ( 5 \times 4 ) \div 3 + \frac{6}{7}[/tex]
[tex]\frac{2}{3} ( 20 ) \div 3 + \frac{6}{7}[/tex] → Parentheses First
[tex]\frac{40}{3} \div 3 + \frac{6}{7}[/tex] → Multiplication
[tex]\frac{40}{9} + \frac{6}{7}[/tex] → Division
[tex]\frac{280}{63} + \frac{54}{63}[/tex] → Match the denominator of the fraction
[tex]\frac{334}{63}[/tex] → Final Answer
From the results above, it can be concluded that the results of this operation 2/3 (5 × 4) ÷ 3 + 6/7 is 334/63
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Order of Operations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS
Is this less than
Greater than
Or equal too?
Answers
Root 5.76= 2.4
-2.4=-2.4
The volume of 10,000 drops of a liquid is 1 fluid ounce.
What is the volume of 10
drops?
Answers
Given line L = ax + by + c = 0, b(its suppose to be the equal sign with the slash going thru it) 0
What is the slope of this function?
-a/b
a/b
b/a
Answers
by = - ax - c
y = -a/b (x) - c/b
so slope = -a/b
answer
-a/b
A 20-year, $148,000 mortgage is taken out with a 4.9% APR. If payments are scheduled monthly and there are no additional costs, determine the balance on the account after the first month's payment has been made.
Answers
[tex]\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right][/tex]
[tex]\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to & \begin{array}{llll} 148,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\to &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &20 \end{cases} \\\\\\ pymt=148000\left[ \cfrac{\frac{0.049}{12}}{1-\left( 1+ \frac{0.049}{12}\right)^{-12\cdot 20}} \right][/tex]
A map has a scale of 1 in. 4 mi. You measure 3 inches between your house and the movie theatre. How many miles is it from your house to the Movie Theatre
Answers
1in:4m
3in:xm
3/1 = 3
4 x 3 = 12
1in:4m
3in:12m
The answer is 12
Hope this helps! :)
Answer: x = 12
Step-by-step explanation:
1/3 = 4/x
1x = 12
X = 12
Write a function rule for the table. (2, $16.00), (4, $32.00), (6, $48.00), (8, $64.00)