Answer: Part a) [tex]P(a)=\frac{1}{\binom{r+w}{r}}[/tex]
part b)[tex]P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}[/tex]
Step-by-step explanation:
The probability is calculated as follows:
We have proability of any event E = [tex]P(E)=\frac{Favourablecases}{TotalCases}[/tex]
For part a)
Probability that a red ball is drawn in first attempt = [tex]P(E_{1})=\frac{r}{r+w}[/tex]
Probability that a red ball is drawn in second attempt=[tex]P(E_{2})=\frac{r-1}{r+w-1}[/tex]
Probability that a red ball is drawn in third attempt = [tex]P(E_{3})=\frac{r-2}{r+w-1}[/tex]
Generalising this result
Probability that a red ball is drawn in [tex}i^{th}[/tex] attempt = [tex]P(E_{i})=\frac{r-i}{r+w-i}[/tex]
Thus the probability that events [tex]E_{1},E_{2}....E_{i}[/tex] occur in succession is
[tex]P(E)=P(E_{1})\times P(E_{2})\times P(E_{3})\times ...[/tex]
Thus [tex]P(E)[/tex]=[tex]\frac{r}{r+w}\times \frac{r-1}{r+w-1}\times \frac{r-2}{r+w-2}\times ...\times \frac{1}{w}\\\\P(E)=\frac{r!}{(r+w)!}\times (w-1)![/tex]
Thus our probability becomes
[tex]P(E)=\frac{1}{\binom{r+w}{r}}[/tex]
Part b)
The event " r red balls are drawn before 2 whites are drawn" can happen in 2 ways
1) 'r' red balls are drawn before 2 white balls are drawn with probability same as calculated for part a.
2) exactly 1 white ball is drawn in between 'r' draws then a red ball again at [tex](r+1)^{th}[/tex] draw
We have to calculate probability of part 2 as we have already calculated probability of part 1.
For part 2 we have to figure out how many ways are there to draw a white ball among (r) red balls which is obtained by permutations of 1 white ball among (r) red balls which equals [tex]\binom{r}{r-1}[/tex]
Thus the probability becomes [tex]P(E_i)=\frac{\binom{r}{r-1}}{\binom{r+w}{r}}=\frac{r}{\binom{r+w}{r}}[/tex]
Thus required probability of case b becomes [tex]P(E)+ P(E_{i})[/tex]
= [tex]P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}\\\\[/tex]
The probability that all r red balls will be obtained before any white balls are obtained is 1. Before two white balls are obtained, all red balls must be drawn, so the probability is 1/w. This is based on the assumption that the draws are random.
Explanation:The subject of this question is probability theory, which falls under the broad subject of Mathematics. The first part of the question asks for the probability that all r red balls will be obtained before a white ball is obtained. The second part asks for the probability that all r red balls will be obtained before two white balls are obtained.
For part (a), the probability that all r red balls will be obtained before any white balls are obtained is 1 because the balls are drawn without replacement and we are considering r draws. Therefore, every draw will be a red ball before a white ball.
For part (b), as for drawing one white ball after obtaining all r red balls, the first white ball can be the (r+1)th draw. But before drawing the second white ball, all the red balls have to be obtained. Because the balls are drawn without replacement, the probability that all r red balls will be obtained before two white balls are obtained is 1/w, where w is the total white balls.
The main assumption here is that the draws are random. So the probability of drawing a red or white ball does not change after each draw. This question is at a High School level because it involves basic probability theory and combinatorial principles.
Learn more about Probability Theory here:https://brainly.com/question/31469353
#SPJ3
Write a two-column proof.
Given: Quadrilateral GKJH is a parallelogram
Prove: Triangle GLH is congruent to Triangle JLK
Answer:
GLH is congruent to JLK as the quadrilateral is a parallelogram,
KJ = GH OR HJ = GK
GL = LJ OR. HL = LK
triangle JKG = GHJ
triangle HGK = KJH
Answer:
A parallelogram has two pairs of opposite parallel congruent sides.
Given :
Quadrilateral GKJH is a parallelogram,
To prove :
Δ GLH ≅ Δ JLK
Proof :
Statement Reason
1. GH ║ KJ Definition of parallelogram
2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ Alternate interior angle theorem
3. GH ≅ KJ Definition of parallelogram
4. Δ GLH ≅ Δ JLK ASA postulate of congruence
Hence, proved...
The two triangles are similar. What is the value of x?
Check the picture below.
Given the variables fullAdmissionPrice and discountAmount (already declared and assigned values), write an expression corresponding to the price of a discount admission. (The variable discountAmount holds the actual amount discounted, not a percentage.)
Answer: Price of a discount amision= Full Admission Price - discount Amount
Step-by-step explanation:
We have two variables "X" and "Y", where X= Full Admision Price and Y= Discount Price of Admision and we have to get the price of a discount admision or "Z" so the expresion will be Z= X-Y or Price of a discount admision = Full admision Price- discount Amount.
A jar contains 50 jelly beans: 5 lemon,10 watermelon, 15 blueberry, and 20 grape.Suppose that two jelly beans are randomly selected in succession without replacement.Find the probability of selecting two blueberry jelly beans.
[tex]|\Omega|=50\cdot49=2450\\|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{2450}=\dfrac{3}{35}\approx8.6\%[/tex]
The probability of randomly selecting two jelly beans in succession without replacement is;
0.0857
The jar contains 50 jellybeans.
Thus; N = 50
The individual berries include;
5 lemon
10 watermelon
15 blueberry
20 grape
Probability of first being a jelly bean = 15/50
Probability of second being jelly bean = 14/49
Thus,probability of selecting 2 jelly beans in succession without replacement is =
15/50 × 14/49 = 0.0857
Read more at; https://brainly.com/question/10271452
A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90degrees. see the illustration. (a) what depth will provide maximum cross-sectional area and hence allow the most water to flow? (b) what depths will allow at least 16 square inches of water to flow?
Answer:
a) max area for depth of 3 inchesb) ≥ 16 in² for 2 in ≤ depth ≤ 4 inStep-by-step explanation:
(a) For a depth of x, the two sides of the rain gutter are length x, and the bottom is length (12-2x). The cross sectional area is the product of these dimensions:
A = x(12 -2x)
This equation describes a parabola that opens downward. It has zeros at ...
x = 0
12 -2x = 0 . . . . x = 6
The maximum area is halfway between these zeros, at x=3.
The maximum area is obtained when the depth is 3 inches.
__
(b) For an area of at least 16 square inches, we want ...
x(12 -2x) ≥ 16
x(6 -x) ≥ 8 . . . . . divide by 2
0 ≥ x² -6x +8 . . . . subtract the left side
(x -4)(x -2) ≤ 0 . . . factor
The expression on the left will be negative for values of x between 2 and 4 (making only the x-4 factor be negative). Hence the the depths of interest are in that range.
At least 16 square inches of water will flow for depths between 2 and 4 inches, inclusive.
The maximum cross-sectional area of the gutter which allows the most water flow is achieved at a depth of 4 inches. For a flow rate of 16 square inches, we need to solve the equation for the cross-sectional area equal to 16 to find the corresponding depth.
Explanation:Your question pertains to maximizing the cross-sectional area of a rain gutter made from 12-inch wide aluminum sheets. This involves the use of calculus, specifically optimization, and basic geometry.
Let's denote 'x' as half the width of the base. When the sides are turned up 90 degrees, the sides will be of length 'x'. Since the gutter is 12 inches wide, the equation for the width is 2x+x=12. So, x=4.
To maximize the cross-sectional area, you need to set the derivative of the area function equals to zero.
For your second question, to find the depths that will allow at least 16 square inches of water to flow, equate the cross-sectional area equals to 16, and solve for 'x'.
In conclusion,
The depth that would allow maximum cross-sectional area and the most water flow is when x = 4 inches,. To allow 16 square inches of water to flow, solve for 'x' when the cross-sectional area equals to 16.
Learn more about Optimization here:https://brainly.com/question/37742146
#SPJ3
BRAINLIEST! what are the next 2 terms in the geometric sequence?
a1=2,r=-3
Answer:
The next two terms after a1 is
-6 and then 18
Step-by-step explanation:
Geometric sequence means your pattern for the terms is multiplication by the same number.
So a1 is the first term and r is your common ratio.
The common ratio is what you are multiplying by each time to figure out the next term.
So the geometric sequence goes like this:
a1 , a1*r , (a1*r)*r or a1*r^2 , a1*r^3 ,....
So anyways you have
first term a1=2
second term a2=2(-3)=-6
third term a3=-6(-3)=18
And so on...
It is a hot day at the beach. Ice water costs $1 per bottle and this is your only option. Your marginal benefit for water follows the equation MB = $10 - $x.x is represents the number of bottles of ice water you have had. So, for example, the marginal benefit of the first bottle is $10 - $1 = $9. The MB of the 2nd bottle is $8 .. and so on.Assuming you are an economically rational consumer how many bottles of water will you buy?
Answer:
9 bottles of water
Step-by-step explanation:
Marginal benefit is a microeconomic concept that explains how much the consumer adds satisfaction to each unit consumed of a given product. Usually, the marginal benefit is decreasing, which makes logical sense, the more a customer consumes a particular good, the smaller the benefit of the next unit.
At first, the first bottle of water has a high benefit as mentioned in the exercise: 9
In the second, you are a little less thirsty, so the benefit will be 10 - 1x2 = $8
In the ninth bottle, you will have very little thirst and the benefit will be 10 - 1x9 = $1
In the tenth bottle there is no benefit, the consumer is indifferent. As a rational consumer, you will buy until the bottle is still usable, even if minimal, for 9 bottles when your benefit is $1.
As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, you will buy a total of 10 bottles of water.
Explanation:As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, the price of water is $1 per bottle.
The marginal benefit equation is given as MB = $10 - $x, where x represents the number of bottles of water you have had. So, for each bottle of water you consume, the marginal benefit decreases by $1.
To determine the number of bottles of water you will buy, you need to compare the marginal benefit to the price of water:
MB = $10 - $1 = $9. Since $9 is greater than $1, you will buy the first bottle of water.MB = $8. Since $8 is greater than $1, you will buy the second bottle of water.MB = $7. Since $7 is greater than $1, you will buy the third bottle of water.Continuing this pattern, you will keep buying bottles of water as long as the marginal benefit is greater than or equal to $1.Therefore, you will buy a total of 10 bottles of water.
Use the Quadratic Formula to solve the equation 4x^2-7=4x.
Select one:
a. x=-1/2+sqrt2 or x=-1/2-sqrt2
b. x=7/8+sqrt113/8 or x=7/8-sqrt113/8
c. x=1/2+sqrt2 or x=1/2-sqrt2
d. x=2+4sqrt2 or x=2-4sqrt2
The quadratic equation 4x^2 - 4x - 7 = 0 is solved using the Quadratic Formula with coefficients a = 4, b = -4, c = -7. The correct solutions obtained are x = 1/2 + √2 and x = 1/2 - √2, corresponding to option (c).
Explanation:To solve the quadratic equation 4x^2 - 4x - 7 = 0 using the Quadratic Formula, we first identify the coefficients: a = 4, b = -4, and c = -7.
The Quadratic Formula is given by:
x = √((-b ± √(b^2 - 4ac)) / (2a)).
Substitute the identified coefficients into the formula:
x = √(((-(-4) ± √((-4)^2 - 4(4)(-7))) / (2(4))).
Simplify the expression:
x = √(((4 ± √(16 + 112)) / 8),
x = √(((4 ± √(128)) / 8),
x = √((4 ± 8√2) / 8).
Simplify further:
x = 1/2 ± √2.
Therefore, the correct answers are:
x = 1/2 + √2 and x = 1/2 - √2,
which corresponds to option (c).
2.42. Consider f (x) = x3????x and g(x) = x2????1 on x 2 [????1;1]. (a) Verify that f (x) is an odd function and g(x) is an even function, meaning f (????x) = ????f (x)) and g(????x) = g(x). (b) Directly compute that h f (x);g(x)i = 0.
Answer:
f(x) is an odd function and g(x) is an even function
Step-by-step explanation:
Even Function :
A function f(x) is said to be an even function if
f(-x) = f(x) for every value of x
Odd Function :
A Function is said to be an odd function if
f(-x)= -f(x)
Part a)
[tex]f(x)=x^3+x[/tex]
let us substitute x with -x
[tex]f(-x) = (-x)^3-x\\=-x \times -x \times -x\\=-x^3-x\\=-(x^3+x)\\=-f(x)[/tex]
Hence
f(-x)=-f(x)
There fore f(x) is an odd function
[tex]g(x)=x^2+1[/tex]
Substituting x with -x we get
[tex]g(-x)=(-x)^2+1\\=-x \times -x+1\\=x^2+1\\=g(x)[/tex]
Hence g(-x)=g(x)
Therefore g(x) is an even Function.
Part b)
hf(x)=hx^3
Please I need help with this ASAP
[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_4&18\\ s_5&18r\\ s_6&18rr\\ &18r^2 \end{array}\qquad \qquad \stackrel{s_6}{8}=18r^2\implies \cfrac{8}{18}=r^2\implies \cfrac{4}{9}=r^2 \\\\\\ \sqrt{\cfrac{4}{9}}=r\implies \cfrac{\sqrt{4}}{\sqrt{9}}=r\implies \boxed{\cfrac{2}{3}=r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=6\\ s_6=8\\ r=\frac{2}{3} \end{cases}\implies 8=s_1\left( \frac{2}{3} \right)^{6-1} \\\\\\ 8=s_1\left( \frac{2}{3} \right)^5\implies 8=s_1\cdot \cfrac{32}{243}\implies 8\cdot \cfrac{243}{32}=s_1\implies \boxed{\cfrac{243}{4}=s_1}[/tex]
In 1983, a winter hat cost $12.95. Today, a winter hat costs $24.50. If the CPI is 219, what is the percent relation of the actual price of a winter hat to the expected price?
Answer:
The actual price is 13.6 % lower than the expected price....
Step-by-step explanation:
Lets suppose the expected price = x
CPI = ( expected price ) : ( price in 1983 ) *100
219 = ( x : 12.95 ) *100
Divide both sides by 100.
x : 12.95 = 2.19
x =2.19*12.95
= $28.36 ( expected price )
p = ( 24.50*100 ) / 28.36
p= 2450/28.36
= 86.4 %
100 % - 86.4 % = 13.6 %
The actual price is 13.6 % lower than the expected price....
Answer:
c
Step-by-step explanation:
because i said so brudda
If the square root of 61 is the longest side length in the triangle and the shorter sides are x and x+1, find the value of x that makes the triangle above a right triangle. Write your answer in simplest radical form.
Answer:
x = 5
Step-by-step explanation:
You want to find x such that ...
x^2 +(x +1)^2 = 61
2x^2 +2x -60 = 0 . . . . . simplify, subtract 61
x^2 +x -30 = 0 . . . . . . . divide by 2
(x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.
The relevant solution is x = 5.
Suppose you are managing 14 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same qualifications/skills so that everyone has the same probability of getting choosen. In how many different ways can the teams be chosen so that the number of employees on each project are as follows: 8,3,3
Answer:
60060 different ways that teams can be chosen
Step-by-step explanation:
Given data
employees n = 14
team = 3
each project employees
n(1) = 8
n(2) = 3
n(3) = 3
to find out
how many different ways can the teams be chosen
solution
we know according to question all employees work on a team so
select ways are = n! / n(1) ! × n(2) ! × n(3) ....................1
here n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1
and n(1)! = 8! = 8 ×7 ×6 ×5 ×4 × 3× 2× 1
n(2)! = 3! = 3× 2× 1
n(3)! = 3! = 3× 2× 1
so now put all these in equation 1 and we get
select ways are = (14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) / (8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) × ( 3× 2× 1) × ( 3× 2× 1)
select ways are = (14 × 13 ×12 ×11 ×10 ×9 ) / ( 3× 2× 1) × ( 3× 2× 1)
select ways are = 2162160 / 36
select ways are = 60060
60060 different ways that teams can be chosen
Answer:
60060
Step-by-step explanation:
#copyright
The golf clubs have been sorted into woods and irons. The number of irons is four more than two times the number of woods. The equipment is 75% irons. How many woods are there?
4
5
6
7
Answer:4
Step-by-step explanation:16/4 = 4
if 75% of equipment is iron then do the math
So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16
The number of woods in the golf club is equal [tex]4[/tex].
What is number?" Number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the number of irons
[tex]'y'[/tex] represents the number of woods
As per given condition we have,
[tex]x= 2y +4[/tex] [tex](1)[/tex]
[tex]x = 75\%(x+ y)\\\\\implies x = \frac{75}{100}(x + y)\\ \\\implies x = \frac{3}{4} (x+y)\\\\\implies 4x= 3x + 3y\\\\\implies x = 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]
Substitute the value of [tex](2)[/tex] in [tex](1)[/tex] to get the number of woods,
[tex]3y = 2y +4\\\\\implies y =4[/tex]
Therefore,
[tex]x= 3\times 4\\\\\implies x=12[/tex]
Hence, the number of woods in the golf club is equal [tex]4[/tex].
Learn more about number here
brainly.com/question/3589540
#SPJ2
I need help with this problem please.
Answer:
b.
Step-by-step explanation:
First off, let's name these endpoints. We will call them J(3, -2) and K(8, 0). The point we are looking for that divides this into a 3:1 ratio let's call L. We are looking for point L that divides segment JK into a 3:1 ratio.
A 3:1 ratio means that we need to divide JK into 3 + 1 equal parts, or 4. Point L divides JK into a 3:1 ratio. We need to find the constant of proportionality, k, that can be used in the formula to find the coordinates of L. k is found by putting the numerator of the 3/1 ratio over the sum of the numerator and denominator. Therefore, our k value is 3/4.
Now we need to find the slope of the given segment.
[tex]m=\frac{0-(-2)}{8-3}=\frac{2}{5}[/tex]
The coordinates of L can be found in this formula:
[tex]L(x, y)=(x_{1}+k(run),x_{2}+k(rise))[/tex]
Filling in:
[tex]L(x,y)=(3+\frac{3}{4}(5),-2+\frac{3}4}(2))[/tex]
Simplifying we have:
[tex]L(x,y)=(3+\frac{15}{4},-2+\frac{6}{4})[/tex]
Simplifying further:
[tex]L(x,y)=(\frac{12}{4}+\frac{15}{4},\frac{-8}{4} +\frac{6}{4})[/tex]
And we have the coordinates of L to be
[tex]L(x,y)=(\frac{27}{4},-\frac{1}{2})[/tex]
27/4 does divide to 6.75
Which products result in a difference of squares? Check all that apply.(x – y)(y – x)(6 – y)(6 – y)(3 + xz)(–3 + xz)(y2 – xy)(y2 + xy)(25x – 7y)(–7y + 25x)(64y2 + x2)(–x2 + 64y2)
1. (3 + xz)(–3 + xz)
2. (y² – xy)(y² + xy)
3. (64y2 + x2)(–x2 + 64y2)
Explanation
The difference of 2 squares is in the form (a+b)(a-c).
(3 + xz)(–3 + xz) = (3 + xz)(xz -3)
= (xz + 3)(xz - 3)
= x²y²-3xy+3xy-9
=x²y² - 3²
(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²
= y⁴ - x²y²
(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)
= 4096y⁴-64y²x²+64y²x²-x⁴
= 4096y⁴ - x⁴
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at most 51 households have a gas stove.
Answer:
the area left to 51 on normal distribution curve
Step-by-step explanation:
we have to find the probability that at most 51 it means the probability of less than 51 . The probability of at most 51 or less than 51 on the normal distribution curve will be the area lest side of 51 for example if we have to find the are of at least 51 then the area on the normal distribution curve will be right of 51
so the answer will be the area left side of 51
When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. To find the probability that at most 51 households have a gas stove, we convert the binomial random variable to a standard normal random variable and find the area to the left of 51 on the normal curve, which is extremely close to 0.
Explanation:When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. In this case, we want to find the probability that at most 51 households have a gas stove. To do this, we need to find the area to the left of 51 on the normal curve.
To find this probability, we use the standard normal distribution table or a calculator. We convert the binomial random variable to a standard normal random variable using the formula z = (x - np) / √(npq), where x is the number of households, n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, np = 500 * 0.2 = 100 and npq = 500 * 0.2 * 0.8 = 80. So, z = (51 - 100) / √80 ≈ -6.325.
Looking up this value in the standard normal distribution table, we find that the area to the left of -6.325 is extremely close to 0. Therefore, the probability that at most 51 households have a gas stove is approximately 0.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
The stopping distance for a boat in calm water is modelled by the function d(v) = 0.004v2 + 0.2v + 6, where d(v) is in metres and v is in kilometres per hour.
a. What is the stopping distance if the speed is 10km/h?
b. What is the initial speed of the boat if it takes 11.6m to stop?
Please help :(
Answer:
a. 8.4 km b. 20 km/hr or 20,000 m/hr
Step-by-step explanation:
This is your polynomial:
[tex]d(v)=.004v^2+.2v+6[/tex]
The important thing to realize is that d(v) is the distance it takes for the boat to stop. That will come later, in part b. Besides that, we also need to remember that v is velocity, which is speed, in km/hr.
For part a. we are looking for d(v), the stopping distance, when v = 10. That means that we will sub in a 10 for each v in the function and solve for d(v):
[tex]d(10)=.004(10)^2+.2(10)+6[/tex] so
d(10) = 8.4 km
Now comes the part I was referring to above. Part b is asking us the speed of the boat if it takes 11.6 meters to stop. If d(v) is the stopping distance, we sub 11.6 in for d(v) in the function:
[tex]11.6=.004v^2+.2v+6[/tex]
The only way w can solve this for velocity is to get everything on one side of the equals sign, set the polynomial equal to 0, then plug the values into the quadratic formula.
[tex]0=.004v^2+.2v-5.6[/tex]
Plugging that into the quadratic formula gives you 2 values of velocity:
v = 20 km/hr and -70 km/hr
We all know that neither time nor distance in math will EVER be negative so we can discount the negative number. However, I believe that you asked for the distance in meters, so 20 km/hr is the same as 20,000 m/hr.
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
[tex]m(RS)=17[/tex] inches (answer rounded to nearest tenths)
Step-by-step explanation:
Central angle there is 150 degrees.
The radius is 6.48 inches.
The formula for finding the arc length, RS, is
[tex]m(RS)=\theta \cdot r[/tex]
where [tex]r[/tex] is the radius and [tex]\theta[/tex] ( in radians ) is the central angle.
I had to convert 150 degrees to radians which is [tex]\frac{150\pi}{180}[/tex] since [tex]\pi \text{rad}=180^o[/tex].
[tex]m(RS)=\frac{150\pi}{180} \cdot 6.48[/tex]
[tex]m(RS)=16.96[/tex] inches
Answer: [tex]17\ in[/tex]
Step-by-step explanation:
You need to use the following formula for calculate the Arc Lenght:
[tex]Arc\ Length=2(3.14)(r)(\frac{C}{360})[/tex]
Where "r" is the radius and "C" is the central angle of the arc in degrees.
You can identify in the figure that:
[tex]r=6.48\ in\\C=150\°[/tex]
Then, you can substitute values into the formula:
[tex]Arc\ Length=Arc\ RS=2(3.14)(6.48\ in)(\frac{150\°}{360})\\\\Arc\ RS=16.95\ in[/tex]
Rounded to the nearest tenth, you get:
[tex]Arc\ RS=17\ in[/tex]
In triangle ABC, a = 4, b = 7, and c = 10. Find A.
18°
34°
56°
162°
Answer:
18°
Step-by-step explanation:
The law of cosines tells you ...
a² = b² + c² -2bc·cos(A)
Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.
cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140
A = arccos(133/140) ≈ 18.2° ≈ 18°
Calculate the average rate of change for the graphed sequence from n=2 to n=6.
Answer:
-3
Step-by-step explanation:
The average rate of change is the y-difference divided by the x-difference:
(2 -14)/(6 -2) = -12/4 = -3
The average rate of change for the sequence is -3.
Answer:
-3
Step-by-step explanation:
The formula m = 12,000 + 12,000rt 12t gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years. What would Keri's monthly loan payment be if she got a 4% loan for 5 years? $ ___per month
Answer:
$240
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
[tex]m=\dfrac{12,000+12,000rt}{12t}=\dfrac{12,000+12,000\cdot 0.04\cdot 5}{12\cdot 5}\\\\m=\dfrac{14,400}{60}=240[/tex]
Keri's monthly loan payment is $240 per month.
Answer: 300 per month
Step-by-step explanation:
As part of video game, the point (4,6) is rotated counterclockwise about the origin through an angle of 15 degrees. Find the new coordinates of this point
Answer:
(2.31079, 6.83083)
Step-by-step explanation:
The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...
(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))
Here, that means the new coordinates are ...
(4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)
To rotate the point (4,6) counterclockwise about the origin by 15 degrees, we can use the rotation formulas. The new coordinates are approximately (2.833, 6.669).
Explanation:To rotate a point counterclockwise about the origin, we can use the rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
Using the given point (4,6) and an angle of 15 degrees, we can substitute the values into the formulas to find the new coordinates:
x' = 4 * cos(15) - 6 * sin(15) = 4 * 0.9659258263 - 6 * 0.2588190451 ≈ 2.833166271
y' = 4 * sin(15) + 6 * cos(15) = 4 * 0.2588190451 + 6 * 0.9659258263 ≈ 6.669442572
Therefore, the new coordinates of the point after rotation are approximately (2.833, 6.669).
Learn more about Rotation here:https://brainly.com/question/34828607
#SPJ11
Which linear function represents the line given by the point-slope equation y + 7 = –(x + 6)? f(x) = –x – 11 f(x) = –x – 1 f(x) = –x + 3 f(x) = –x + 13
Hey There!
We'd distribute the negative sign first:
[tex]y + 7 = -x - 6[/tex]
Now, we'd have to isolate the variable y by subtracting seven in both sides:
[tex]y = -x - 13[/tex]
Replace y with f(x):
[tex]f(x) = -x - 13[/tex]
Our answer would be [tex]f(x) = -x - 13[/tex]
Answer:
f(x)-x-13
Step-by-step explanation:
write an expression in for the area of the shaded region
Please help me WILL GIVE BRAINLIEST :)
Answer:
15/2 x^2y - 5xy
Step-by-step explanation:
First find the area of the rectangle
A = l*w
= 5xy * 2x
10x^2y
The find the area of the triangle
A = 1/2 bh
= 1/2 (5xy) (x+2)
= 1/2((5x^2y + 10xy)
= 5/2 x^2y +5xy
The shaded region is the area of the rectangle minus the area of the triangle
10x^2y - (5/2 x^2y +5xy)
Distribute the minus sign
10x^2y -5/2 x^2y -5xy
Combining like terms by getting a common denominator
20/2x^2y -5/2 x^2y -5xy
15/2 x^2y - 5xy
PLS HELP FIRST CORRECT ANSWER GETS BRAINLIEST !! A pile of tailings from a gold dredge is in the shape of a cone. The diameter of the base is 34 feet and the height is 16 feet. Approximately, how many cubic feet of gravel is in the pile? Use π = 3.14.
A. 14,527 ft³
B. 285 ft³
C. 4,840 ft³
D. 6,032 ft³
Answer:
C: [tex]V=4840 (2 s.f.)[/tex]
Step-by-step explanation:
The formula for the volume of a cone is:
[tex]V= \frac{1}{3} \pi r^2h[/tex]
Therefore,
[tex]V=\frac{1}{3}\times 3.14\times(\frac{34}{2})^2\times 16\\\\V=4840 (2 s.f.)[/tex]
The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
Volume can be defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A pile of tailings from a gold dredge is in the shape of a cone.
The diameter of the base is 34 feet and the height is 16 feet.
As we know,
The volume of the cone is given by:
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
r = 34/2 = 17 ft
h = 16 feet
Plug the above values in the formula:
[tex]\rm V=\pi (17)^2\dfrac{16}{3}[/tex]
After solving:
V = 1541.33π cubic feet
Take π = 3.14
V = 1541.33(3.14) cubic feet
V = 4839.78 ≈ 4840 cubic ft
Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.
Learn more about the cone here:
brainly.com/question/16394302
#SPJ5
The resting heart rate of US females 20 years old or older is normally distributed with a mean of 75 bpm (beats per minute). Suppose the standard deviation was 15 bpm. If one randomly selected female's resting heart rate falls in the bottom 33% of all women, at most what could her rate have been?
A. 70.05
B. 68.4
C. 79.95
D. 84.439
E. .6
F. 65.561
Answer:
69 bpm
Step-by-step explanation:
Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve. Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.
Next we use the formula for z score to determine the x value representing this woman's heart rate:
x - mean x - 75 bpm
z = ----------------- = -0.43073 = --------------------
std. dev. 15
Thus, x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm
Solve the inequality. 2(4+2x)≥5x+5
x≤−2
x≥−2
x≤3
x≥3
The solution of the inequality is:
[tex]x\leq 3[/tex]
Step-by-step explanation:We are given a inequality in terms of variable x as:
[tex]2(4+2x)\geq 5x+5[/tex]
Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.
We may simplify this inequality as follows:
On using the distributive property of multiplication in the left hand side of the inequality we have:
[tex]2\times 4+2\times 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3[/tex]
The solution is: [tex]x\leq 3[/tex]
Answer:
Option C.
Step-by-step explanation:
The given inequality is given as
2(4 + 2x) ≥ 5x + 5
8 + 4x ≥ 5x + 5 [Simplify the parenthesis by distributive law]
Subtract 5 from each side of the inequality
(8 + 4x) - 5 ≥ (5x + 5) - 5
3 + 4x ≥ 5x
subtract 4x from each side of the inequality
(4x + 3) - 4x ≥ 5x - 4x
3 ≥ x
Or x ≤ 3
Option C. x ≤ 3 is the correct option.
HELP ME WITH THIS MATH QUESTION
For this case we have that by definition, the arc length of a circle is given by:
[tex]AL = \frac {x * 2 \pi * r} {360}[/tex]
Where:
x: Represents the angle between JM. According to the figure we have that x = 90 degrees.
[tex]r = \frac {16.4} {2} = 8.2[/tex]
So:
[tex]AL = \frac {90 * 2 \pi * 8.2} {360}\\AL = \frac {90 * 2 * 3.14 * 8.2} {360}\\AL = 12.874[/tex]
Rounding:
[tex]AL = 12.9[/tex] miles
Answer:
12.9 miles
Answer: 12.9
Step-by-step explanation:
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 4x + 3 intersect are the solutions of the equation 2−x = 4x + 3. (4 points)
Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3. (4 points)
Part C: How can you solve the equation 2−x = 4x + 3 graphically? (2 points)
Answer:
Step-by-step explanation:
Part A:
The solution of a system is not just the x coordinates; it is the whole coordinate pair that is the solution, where both x and y are the same. Normally, when you have a system and are solving them simultaneously, you are looking for the point at which they are equal. This is a very useful concept in business and finance, both in the home for personal information, and in the office setting where companies are. Where the 2 equations intersect is a point where they are equal.
Part B:
The graphs do not intersect right at a perfect integer of x. Therefore, we will solve these equations simultaneously to solve first for x, then we will plug in x to solve for y. Since we have the equations set to equal each other, we can solve for x by getting everything on one side of the equation and then setting it equal to 0.
2 - x = 4x + 3 so
5x + 1 = 0. Solving for x,
5x = -1 so
[tex]x=-\frac{1}{5}[/tex]
The y coordinate can be found by subbing in this value of x into either equation. If y = 2 - x, and x = -1/5, then
y = 2 -(-1/5) and y = 2 + 1/5 and y = 10/5 + 1/5 gives us that y = 11/5
Thus, the coordinate pair that is the solution to that system is
[tex](-\frac{1}{5},\frac{11}{5})[/tex]
Part C:
You would solve the system graphically by graphing both lines on the same window. However, since their intersection is not an integer pair, but are fractions, you would not be able to tell EXACTLY where they intersect. From the graphing window, you would hit your 2nd button then "trace" which is in the row at the very top of the buttons below the window. Then hit 5: intersect. You'll be back to your graph of the lines, and there will be a cursor blinking along the line you graphed under Y1. Move the cursor til it is right over the intersection of the lines and hit "enter". Then you'll be back to the graphs with a blinking cursor over the line you entered in Y2. Move that cursor along the line til it is dead-center over the other point on the first line and hit "enter" again. At the bottom, you will see the x and y coordinates that are the intersection of this system.