Given,
Two concentric circles with AB tangent to smaller circle at point R.
Now,
Draw OA, OB ⇒ Auxiliary lines.
OR ⊥ AB ⇒ Radius ⊥ to tangent .
OR = OR ⇒ Reflexive .
OA = OB ⇒ Radii of same circles are congruent .
ΔAOR ≅ ΔBOR ⇒ Hypotenuse leg .
AR = RB ⇒ Congruent Parts of Congruent Triangle are Equal .
Hence proved.
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A pebble falls of a cliff at a height of 256 ft. If the equation for the height as a function is h(t)=-16^2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the pebble to hit the ground?
Answer:
After 4secs
Step-by-step explanation:
Given the function of the height expressed as;
h(t)=-16^2 + initial height
If initial height = 256, then;
h(t) = -16t^2 + 256t
The pebble will hot the ground at when h(t) = 0
Substitute
0 = -16t^2 + 256t
16t^2 = 256
t^2 = 256/16
t^2 = 16
t = 4
Hence the pebble will hit the ground after 4secs
A math teacher researches the relationship between 7th and 8th grade involvement in speech and debate and drama club
Based on the information, we can infer that the percentage of eighth grade students who belong to the drama club is 52.5%.
How to find the percentage of students who belong to the drama club?To calculate the percentage of eighth grade students who belong to the drama club, we must take into account how many students there are in total in this grade. So we must add:
21 + 19 = 40So, we know that we have 40 students in the eighth grade. Now to know the percentage to which the 21 students that belong to the drama are equivalent, we must carry out the following rule of 3:
40 = 100%21 = %?21 + 100 / 40 = 52.5%Note: This question is incomplete. Here is the complete information:
Attached image:
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Suppose the SAT math score of a University of Georgia student can be approximated by a normal distribution with mean 400 and variance 225. Find the probability that the UGA Einstein will score at least a 415.
The probability that the UGA Einstein will score at least a 415 on the SAT math is approximately 0.1587, or 15.87%.
To find the probability that the UGA student will score at least a 415 on the SAT math, we need to calculate the area under the normal distribution curve.
First, we need to standardize the score using the z-score formula:
z = (x - μ) / σ
where x is the desired score, μ is the mean, and σ is the standard deviation.
In this case, x = 415, μ = 400, and σ (standard deviation) is the square root of the variance, which is √225 = 15.
Calculating the z-score:
z = (415 - 400) / 15
z ≈ 1
Next, we can use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1. The table or calculator will provide the area under the curve to the left of the z-score.
The probability that the UGA student will score at least a 415 is equivalent to finding the area to the right of the z-score (or 1 minus the area to the left).
P(Z ≥ 1) ≈ 1 - P(Z < 1)
Looking up the corresponding value in the standard normal distribution table or using a calculator, we find that P(Z < 1) is approximately 0.8413.
Therefore, P(Z ≥ 1) ≈ 1 - 0.8413 = 0.1587.
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jose bought 9 movie tickets for a total of $54. Adult tickets cost $8 each and child tickets
cost $3.50 each. How many adult tickets did he buy?
well i cant tell because you did not tell me how many kid tickets he bought
What is the result when the number 10 is increased by 20%?
Answer:
1.20 percent
Step-by-step explanation:
I NEED HELP FOR THIS PLEASE sushensnsjskdnsndjdndndn
Answer:
Step-by-step explanation:
y=-1/4x-13/4
now put any value for x, then u get a y value. Then find the points on the graph.
please help meee i need all the answers
The answers to all parts are shown below.
1. The number of ways are
= 11!/ (11-1)!
= 11! /10!
= 11
2. The favorable outcomes of the event
Triangle= 1
star = 4
Not square= 9
Not circle= 8
3. C( 12, 1)= 12!/ 1! 11!
= 12 ways
4. Choose a cat = C(18, 12)= 18! / 12! 6!
= 18564
5. Choose a dog
= C(18, 6)
= 18!/ 6! 12!
= 18564
6. Bus arrive on time= 1-2/7 = 5/7
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Hi i need help with this problem, its due Monday
A rectangle has an area of 21x + 81 square units. If the width is 3 units, what is the length of the rectangle?
A. 18x + 78 units
B. 7x + 27 units
C. 7x + 81 units
D. 21x + 27 units
The answer is B. 7x + 27 units.
Area is length multiplied by width, so to find the length, simply divide the expression 21x + 81 by the width --> 3.
21x becomes 7x, and 81 becomes 27.
candace askes 100 studes what flouvor crisp they like
Answer:
This is a survey
Step-by-step explanation:
???????????????????????????????????
It’s due today pls help me
Answer:
the probability of getting a six = 5/8
the probability of not getting a six or p(6')
= 1- 5/8
=3/8
A cone of radiu 3cm i made from a ector. If the area of the ector i 66cm2 find the volume of the cone
Using the formula of surface area to calculate the height and using the formula for volume , The answer is 24.98 \(cm^{3}\) .
What is a cone?A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.
What is the formula to calculate the surface area and volume of cone?The required formula are :
\(SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})\) (Surface Area)
\(V = \pi r^{2} \frac {h}{3}\) (Volume)
radius = 3 cm
Area= 66 \(cm^{2}\)
\(SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})\)
h = 2.65 cm
\(V = \pi r^{2} \frac {h}{3} = \pi * 3^{2} * \frac {2.65}{3}\)
=24.98 \(cm^{3}\)
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The Lees, a family of Hmong refugees living in California in the 1980s, went through an ordeal with U.S. medical personnel when their daughter Lia started suffering from an illness they called quag dab peg and American doctors called
The Lees, Hmong refugees in 1980s California, faced challenges with U.S. doctors when their daughter had "quag dab peg" (Hmong term) later diagnosed as epilepsy.
The Lees, a Hmong refugee family in 1980s California, faced difficulties with U.S. medical professionals when their daughter Lia developed a condition known as "quag dab peg" in their language. The American doctors diagnosed Lia's illness as epilepsy. This cultural and linguistic barrier led to misunderstandings and challenges in providing appropriate medical care.
The Lees' experience made clear the value of cultural sensitivity in healthcare practices and the importance of effective cross-cultural communication between healthcare professionals and patients from various backgrounds in order to ensure accurate diagnosis and appropriate treatment for diverse communities.
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pls help me. Will mark brainliest if right
Answer:
1st one
Step-by-step explanation:
use the linear approximation to estimate δδf for ()=112 2f(x)=112 x2 when =2a=2 and δ=−12.
The estimated δf for f(x) = 112 * x^2 when a = 2 and δx = -1/2 is approximately -224.
To estimate δf using linear approximation, we will use the formula: δf ≈ f'(a) * δx
Here, f(x) = 112 * x^2, a = 2, and δx = -1/2. First, we need to find the derivative of f(x) with respect to x: f'(x) = d(112 * x^2) / dx = 224 * x
Now, we will find the derivative at the point a: f'(a) = f'(2) = 224 * 2 = 448
Finally, we'll use the linear approximation formula to estimate δf: δf ≈ f'(a) * δx = 448 * (-1/2) = -224
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Find the radius of the sphere with the given volume. (15 points)
volume= 32/3 times pie yd cubed
show your work please
Answer:
r=1.37
Step-by-step explanation:
so first we have to change 32/2 to a decimal
to do that you have to divide 32÷3=10.66...7
the formula to find the radius when given the volume is r=(\(\frac {v}{4*pi}\))^1/3
r=(\(\frac {10.6666666667}{4*pi}\))^1/3
r= 1.37
then to check your work-
v=4/3π1.37^3
v=10.77
technically 10.77 and 10.6666666667 aren't equal but that's as close as it'll get
good luck :)
i hope this helps
have a nice day !!
wich is bigger 51.243 or 5.1243
Answer:
The number 51.243 is bigger than 5.1243.
Step-by-step explanation:
To compare two decimal numbers, we start by looking at the digits to the left of the decimal point. In this case, both numbers have the same digit in the tens place, which is 5. So we need to look at the next digit to the right of the decimal point.In 51.243, the digit to the right of the decimal point is 2, which is larger than the digit to the right of the decimal point in 5.1243, which is 1. Therefore, we can conclude that 51.243 is bigger than 5.1243.
Answer:
51.243
Step-by-step explanation:
because 51 is greater than 5.1
Dos libros han costado $13. 000 y el doble del precio del más barato vale $200 más de lo que cuesta el otro. ¿Cuál es la diferencia entre los precios de ambos libros?
The difference between the prices of both books is: $4,266.67.
Let's call the price of the cheapest book "x". According to the statement, the other book costs twice the price of the cheapest one, that is, "2x". Furthermore, we are told that this second book is worth $200 more than the other.
Therefore, we can establish the following equation:
x + 2x + $200 = $13,000
Add like terms:
3x + $200 = $13,000
We subtract $200 from both sides of the equation:
3x = $12,800
We divide both sides by 3 to solve for "x":
x = $4,266.67
The price of the most expensive book is 2 times the price of the cheapest, that is, 2 * $4,266.67 = $8,533.33.
The difference between the prices of both books is:
$8,533.33 - $4,266.67 = $4,266.67.
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a firefighter is placing a 15-foot ladder against a house. he places the ladder 10 feet away from the house. how high up the house will he be able to reach? round to the nearest foot
A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the wioth; Matenal for the base costs 515 per stcuare ineter. Material for the sides costs $9 per square meter. Let w dencte the width of tho base. Find a function in the varlable w giving the cost C (in dollars) of constructing the box: C(w)= ___Find the derivitive of cin c′(w)= Find the cost (in doliars) of materials for the least expensive such containes. (Round your answer to the nearest cent.)
The cost of materials for the least expensive such container is obtained by substituting the value of w in the expression for C(w).C(0.465) = 1030(0.465)² + 360/0.465 + 180(0.465) ≈ $433.84
Let the width of the base be denoted by w. Therefore, the length of the base will be twice the width, so it is 2w. Thus, the height of the box will be V/lw × wh = 10/w × wh, so it is 10/w². Then, the surface area of the bottom of the container is 2w × w = 2w² square meters. Therefore, the cost of the material for the base will be 515 × 2w² = 1030w² dollars. The surface area of the sides is 2 × (2w × 10/w²) + 2 × (w × 10/w) = 40/w + 20w.
Therefore, the cost of the material for the sides is 9 × (40/w + 20w) = 360/w + 180w dollars. The function C(w) giving the cost (in dollars) of constructing the box is given as follows:C(w) = 1030w² + 360/w + 180w
To find the derivative of C with respect to w, we differentiate the expression for C with respect to w. We have;
C'(w) = d/dw[1030w² + 360/w + 180w]
= 2060w - 360/w² - 180
Since C'(w) is a continuous function,
we need to find the value of w that makes C'(w) = 0 and then determine if it's a minimum or maximum value. C'(w) = 0 implies that 2060w - 360/w² - 180 = 0 or 2060w³ - 360 - 180w³ = 0.This reduces to 1880w³ - 360 = 0 or 1880w³ = 360 or w³ = 360/1880.
Therefore, w ≈ 0.465m. We need to determine if this is the minimum value or not. To do this,
we find the second derivative of C with respect to w as follows:
C''(w) = d/dw[2060w - 360/w² - 180]
= 2060w² + 720/w³Since C''(w) > 0 for all w, it follows that the value of w = 0.465m is the minimum value. The cost of materials for the least expensive such container is obtained by substituting the value of w in the expression for C(w).C(0.465) = 1030(0.465)² + 360/0.465 + 180(0.465) ≈ $433.84
Therefore, the cost of materials for the least expensive such container is approximately $433.84.
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Solve the following system of equations by graphing each line.
x+y=4
3x+4y=10
*mark the solution with a point
Answer:
y = -2
x = 6
Step-by-step explanation:
hope it help
plz follow me
1. (a) Let R be a relation on a set X. Define what it means for R to be reflexive, sym-
metric, anti-symmetric, and transitive.
Now let X be the set of 6-bit strings. Define a relation R on X by sRt if and only if s and t
have the same number of zeroes. (So for instance 011100 R 010101, but 0111006R 010010.)
(b) Show that R is an equivalence relation.
(c) How many elements are there in the equivalence class of 001100? Explain.
Define another relation S on X by sSt if and only if the first or third digit (or both) of
s and t are the same. (So for instance 011100 S010101 since the first digit is the same,
but 0111006S110010 since the first and third digits are both different.)
(d) Is S an equivalence relation? Justify your answer
(a) Reflexive: R is reflexive if every element in X is related to itself. Symmetric: R is symmetric if for every pair (s, t) in R, (t, s) is also in R. Anti-symmetric: R is anti-symmetric if whenever (s, t) and (t, s) are both in R, s (b) R is an equivalence relation because it satisfies the properties of reflexivity, symmetry, and transitivity. (c) These elements are the 6-bit strings that have the same number of zeroes as 001100. (d) S is not an equivalence relation because it does not satisfy the transitivity property.
(a) Reflexive: In the relation R on X, for every 6-bit string s, s has the same number of zeroes as itself, so R is reflexive.
Symmetric: If sRt, it means s and t have the same number of zeroes. This implies that t and s also have the same number of zeroes, so R is symmetric.
Anti-symmetric: If sRt and tRs, it means s and t have the same number of zeroes, and t and s have the same number of zeroes. This implies that s and t are the same element, satisfying the anti-symmetric property.
Transitive: If sRt and tRu, it means s and t have the same number of zeroes, and t and u have the same number of zeroes. This implies that s and u also have the same number of zeroes, satisfying the transitive property.
(b) To show that R is an equivalence relation, we need to demonstrate that it satisfies reflexivity, symmetry, and transitivity. We have already established that R satisfies all three properties.
(c) The equivalence class of 001100 consists of all the 6-bit strings that have the same number of zeroes as 001100. To count the number of elements in this equivalence class, we need to consider all possible combinations of ones and zeroes in a 6-bit string while maintaining the same number of zeroes as 001100. The number of combinations can be calculated using combinatorial techniques, which results in 21 elements in the equivalence class of 001100.
(d) The relation S is not an equivalence relation because it fails to satisfy the transitivity property. There exist cases where if the first or third digit (or both) of s and t are the same, and the first or third digit (or both) of t and u are the same, it does not guarantee that the first or third digit (or both) of s and u are the same. This violates the transitivity condition, indicating that S is not an equivalence relation
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What two numbers add to get -8 and multiply to get 12
Answer:
-2 and - 6
Heres the answer to the question
could you guys help me?
Answer:
15.6 feet
Step-by-step explanation:
I have no time to explain
Use Evcel fo find the probabinty that in 112 trials with probabinty
0.42
of success that there are 30 or fewer suce ses. Round to 6 decimaiplaces Type your answer hern
Answer:
0.5
Step-by-step explanation:
0.5=0.42 then the answer is 0.5
Does anyone know what happened to the tutor option?
Answer:
no i didnt even know there was a tutor option
Step-by-step explanation:
When an object is projected into the air, it follows the path of a parabola. The equation always has the
same form, but the numbers change based on the data for the projectile:
If a cannonball is launched from a height of 29.4 m above the ground with an initial velocity of 24.5 m/s,
then the equation that models its path would be h(t) =
-4.9+7 + 24.5t + 29.4. This graph shows its
path: What is the height of the cannonball before it is launched,
at t=0? Remember to include units
Answer:
29.4 m
Step-by-step explanation:
From the graph
You can clearly infer from the graph that the initial height of the cannon ball, before it is launched is 29.4 mJust find t = 0, and see where the line of the graph intersects the y-axis, which represents height of the cannon ball w.r.t time.From the equation
An even simpler method is substitute t = 0 into the equation for the motion of the cannon ballh(0) = -4.9(0)² + 24.5(0) + 29.4h(0) = 29.4 mI need help with solving these math problems please!!!
Answer:
In the triangle below the red side is a leg and should be labeled a . The pink side is a leg and should be labeled b. and the light blue side is the hypotenuse and should be labeled c.
In right triangles the angles are labeled with upper case letters and the sides are labeled with lower case letters.
Step-by-step explanation:
Carly went to walk her dog at 11:45 a.m. and got back home at 12:30 p.m. How long
was her walk
Answer:
45 minutes
Step-by-step explanation:
Solve the write an equation of the line that passes through a pair of points a. y=x+3 b. y=x-3 c. y=-x+2 d. y=-x-2
The equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, and can be represented using symbols and/or words. Equations are used to solve problems in mathematics, science, engineering, and other fields.
In the given question,
We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line passing through the points (0,-2) and (2,0):
slope = (change in y)/(change in x)
slope = (0 - (-2))/(2 - 0)
slope = 2/2
slope = 1
Now that we have the slope, we can use one of the given equations and substitute the coordinates of one of the points to find the y-intercept:
y = mx + b
-2 = 1(0) + b
b = -2
So the equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.
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