Answer:
The fact that shows that p+q+r=1 is at most 2/3 is well explained from what we have below.
Step-by-step explanation:
Given that:
The maximum of function P = 2pq+2pr+2rq is at most 2/3.
where ;
p+q+r=1
From p+q+r=1
Let make r the subject ; then r = 1 - p - q
If we replace the value for r into the given function; we have:
P = 2pq+2pr+2rq
P = 2pq+2p(1 - p - q)+2(1 - p - q)q
P = 2pq + 2p - 2p² - 2pq + 2q -2pq -2q²
P = 2p - 2p² + 2q -2pq -2q²
By applying the standard method for determining critical points we obtain:
[tex]P_p[/tex] = -4p - 2q + 2 = 0
[tex]P_q[/tex] = -4q - 2p + 2 = 0
Divide all through by 2
[tex]P_p[/tex] = -2p - q + 1 = 0
[tex]P_q[/tex] = -2q - p + 1 = 0
[tex]P_p[/tex] = -2p - q = - 1
[tex]P_q[/tex] = -2q - p = - 1
Multiplying both sides by - ; we have:
[tex]P_p[/tex] = 2p + q = 1 ----- (1)
[tex]P_q[/tex] = 2q + p = 1 ------(2)
From equation (1) ; let make q the subject ; then
2p + q = 1
q = 1 - 2p
Now; let us replace the value of q = 1-2p into equation (2) , we have:
2q + p = 1
2(1-2p)+ p = 1
2 - 4p+p = 1
2 - 3p = 1
3p = 2-1
p = 1/3
Replacing the value of p = 1/3 into equation (1) ; we have :
2p + q = 1
2(1/3) + q = 1
2/3 + q = 1
q = 1 -2/3
q = 1/3
Taking the second derivative D; we have
[tex]D = P_{pp}P_{qq}-p^2_{pq}[/tex]
D = -4 × -4 - (2²)
D = 16 - 4
D = 12
This implies that the given function has a minimum or maximum at its critical point for which 12 > 0
Therefore , the value for function p = q = r since p, q, and r are the proportions of A, B, and O in the population.
Hence r = 1/3
P=2pq+2pr+2rq
P = 2(1/3)(1/3) + 2(1/3)(1/3) + 2(1/3)(1/3)
P = 6/9
P = 2/3
The lengths of nails produced in a factory are normally distributed with a mean of 3.34 centimeters and a standard deviation of 0.07 centimeters. Find the two lengths that separate the top 3% and the bottom 3%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
3.47 and 3.21
Step-by-step explanation:
Let us assume the nails length be X
[tex]X \sim N(3.34,0.07^2)[/tex]
Value let separated the top 3% is T and for bottom it would be B
[tex]P(X < T)= 0.97[/tex]
Now converting, we get
[tex]P(Z < \frac{T-3.34}{0.07})= 0.97[/tex]
Based on the normal standard tables, we get
[tex]P(Z < 1.881)= 0.97[/tex]
Now compare these two above equations
[tex]\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47[/tex]
So for top 3% it is 3.47
Now for bottom we applied the same method as shown above
[tex]P(Z < \frac{B-3.34}{0.07})= 0.03[/tex]
Based on the normal standard tables, we get
[tex]P(Z < -1.881)= 0.03[/tex]
Now compare these two above equations
[tex]\frac{B-3.34}{0.07} = -1.881[/tex]
[tex]= -1.881 \times 0.07 + 3.34 \\\\ = 3.21[/tex]
hence, for bottom it would be 3.21
i need help asap first answer gets brainly
Hey there! I'm happy to help!
The domain is any possible number you can input into the function to get a real output. The domain of h just means the domain of this entire function, which is called h.
Let's look at the answer options.
OPTION A
All real values of x such that x≠0.
The only way to make it so that we do not have a real output is if we get a negative square root. You cannot multiply any number by itself to get a negative number unless you use imaginary numbers, but using imaginary numbers makes our output not real.
Anyways, plugging in 0 would give us √-10, which is not a real number. That part is correct, but this option says ALL REAL NUMBERS except for 0. The problem is is that we can take any number less than ten and plug it in and we would get a negative square root, a fake number. So, this option is incorrect.
OPTION B
All real values of x such that x≥10.
Let's say we use 10 for our x and plug it in. This gives us √0, which is 0, a real output. Anything bigger than this 10 will give us a real output as well, so this option is correct.
We don't even need to check the other options because we have already found the correct answer. C,D, and E are all incorrect though because they include values less ten, which would give us a negative square root, a fake number.
I hope that this helps! Have a wonderful day!
The surface area of a sphere is 3000 m square units. What is the volume of the sphere to the nearest hunderedth?
Answer:
The answer is
15448m³Step-by-step explanation:
To find the volume of the sphere we must first find the radius
Surface area of a sphere = 4πr²
where r is the radius
From the question surface area = 3000m²
3000 = 4πr²
Divide both sides by 4π
750/π = r²
Find the square root of both sides
r = 15.45 cm
Volume of a sphere is 4/3πr³
So we have
4/3π(15.45)³
= 15448.06
= 15448m³ to the nearest hundredth
Hope this helps you
graph the line that represents the equation y=-2/3 x+1 helppp :(
Step-by-step explanation:
Hi there!!
Here, your equation is y= -2/3 x +1
so, let's find coordinate.
To find coordinate you must put the value of x.
so, when you keep value of x you will get,
x 0 3 6
y 1 -1 -3
Therefore, the coordinates are (0,1), (3,-1), (6,-3).
let me make you clear on using the value of x.
we generally put the value of variable (which is in right side) from a smaller digit like 0,1,2... or you may use 0,-1,-2... but they must be in eqaul interval such like i used the values in equal interval of 3 in above question.
I hope you got it...
if not you can ask me help..
now plot those points on graph, alright.
best of luck...
find the value of x in the figure below. (picture included)
Answer:
Option D. 6√5.
Step-by-step explanation:
Please see attached photo for details.
The value of x can be obtained by using pythagoras theory as illustrated below:
In triangle ΔABC:
x² = z² + 12².... (1)
In triangle ΔABD:
15² = x² + y²...... (2)
In triangle ΔACD:
y² = z² + 3²....(3)
Substitute the value of y² in equation 3 into equation 2. We have:
15² = x² + y²
15² = x² + z² + 3²... (4)
From equation:
x² = z² + 12²
Make z² the subject
z² = x² – 12²
Substitute the value of z² into equation 4. We have:
15² = x² + z² + 3²
15² = x² + x² – 12² + 3²
15² = 2x² – 12² + 3²
225 = 2x² – 144 + 9
Collect like terms
225 + 144 – 9 = 2x²
360 = 2x²
Divide both side by 2
360/2 = x²
180 = x²
Take the square root of both side
x = √180
Expressing in surd form, we have:
x = √(36 x 5)
x = √36 x √5
x = 6√5
linear equations: w-3=15
Answer:
w = 18
Step-by-step explanation:
w-3=15
Add 3 to each side
w-3+3=15+3
w = 18
Answer:
w = 18.
Step-by-step explanation:
w - 3 = 15
w = 15 + 3
w = 18
Check your work!
18 - 3 = 15.
Hope this helps!
Candice is analyzing the length of time of each song in her playlist. Complete the sentences with the correct terms. Candice wants one number to summarize all of the values in the data set, so she should find a measure of center . She can calculate the or the of the data set.
Answer:
Candice wants one number to summarize all of the values in the data set, so she should find a measure of center. She can calculate the mean or the median of the data set.
Step-by-step explanation:
Measures of Central tendency is a distinct value that describe a data set by recognizing the central location within that data set. The measures of central tendency are every so often are known as measures of central location. They are also known as summary statistics.
The three measures of central tendency are:
Mean
Median
Mode
The mean is the average value of the data set.
The median is the middle value of the data, when arranged in ascending or descending order.
The mode of the data set is the value with the highest frequency.
The data collected by Candice is continuous and is measured on an interval scale.
The interval level of measurement classifies and arranges the data set. It also defines a specific difference between each interval of scale.
The measure of central tendency for an interval level of measurement are mean and median.
Thus, the complete sentence is:
"Candice wants one number to summarize all of the values in the data set, so she should find a measure of center. She can calculate the mean or the median of the data set."
A company offering online speed reading courses claims that students who take their courses show a 5 times (500%) increase in the number of words they can read in a minute without losing comprehension. A random sample of 100 students yielded an average increase of 415% with a standard deviation of 220%. Calculate a 95% confidence interval for the average increase in number of words students can read in a minute without losing comprehension. Choose the closest answer.
Answer:
C.I = (371.88 , 458.12)
Step-by-step explanation:
Given that:
sample size n = 100
sample mean [tex]\overline x =[/tex] 415
standard deviation = 220
The objective is to calculate the 95% confidence interval for the average increase in number of words students who can read in a minute without losing comprehension.
At 95% confidence interval; level of significance ∝ = 1 - 0.95
level of significance ∝ = 0.05
[tex]z_{\alpha/2} = 0.05/2[/tex]
[tex]z_{\alpha/2} = 0.025[/tex]
The critical value at [tex]z_{\alpha/2} = 0.025[/tex] is 1.96
C.I = [tex]\overline x \pm M.O,E[/tex]
C.I = [tex]\overline x \pm z_{\alpha/2} \dfrac{\sigma }{\sqrt{n}}[/tex]
C.I = [tex]415\pm 1.96 \dfrac{220 }{\sqrt{100}}[/tex]
C.I = [tex]415\pm 1.96 *\dfrac{220 }{10}[/tex]
C.I = [tex]415\pm 1.96 *22[/tex]
C.I = [tex]415\pm 43.12[/tex]
C.I = (371.88 , 458.12)
rational equations representing work and rate
Answer:
3.6hours
Step-by-step explanation:
kevin-6hrs
so he gets 1/6 called in 1 minute
Anne-9 hrs
so she gets 1/9 called in 1 minute
together
1/6+1/9=5/18 called in one minute
so what about all which are 18/18
you get 3.6 hrs I guess
What is the domain of the function f(x) 2/5 startroot x = ? all real numbers all real numbers less than 0 all real number less than or equal to 0 all real numbers greater than or equal to 0
Answer:
[tex]\boxed{\sf all \ real \ numbers \ greater \ than \ or \ equal \ to \ 0}[/tex]
Step-by-step explanation:
The domain of a function is all possible values for x.
[tex]\sf f(x)=\frac{2}{5} \sqrt{x}[/tex]
There are restrictions on x.
The square root of a number can be undefined if that number is less than 0.
The value of x is all real numbers greater than or equal to 0.
The domain of the function f(x) = (2/5)√x will be all real numbers greater than or equal to zero. Then the correct option is C.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = (2/5)√x
The value under the square root should not be negative. Then the equation is given below.
x ≥ 0
Then the domain of the function f(x) = (2/5)√x will be all real numbers greater than or equal to zero.
Then the correct option is C.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
The distance from Parrot Point Airport to the Ivy Cliffs is 291 miles at and angle of 9.1 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 3 hours by flying straight there. At what speed* and heading should you fly?
Answer:
The flight speed should be 84.79 miles per hour at angle of 22.92° Northeast
Step-by-step explanation:
The given information are;
The distance from Parrot Point Airport to Ivy Cliffs = 291 miles
The direction from Parrot Point Airport to Ivy Cliffs = 9.1° Northeast
The speed of the wind = 25 miles per hour
The direction of the wind = Southeast
The time for the journey = 3 hours
The component of the wind velocity are;
For Southeast direction which is an inclination of 45°
Speed of the wind = -25 × sin(45) + 25 × cos(45)
Without the wind, the velocity of flight will be V = Displacement/time, which gives;
V = 291/3 = 97 miles/hour = 97 mph
Let the required velocity of flying = X, we have;
X×sin(θ) + X×cos (θ) -25× sin(45) + 25 × cos(45) = 97×sin(9.1) + 97×cos(9.1)
X×sin(θ) -25× sin(45) = 97×sin(9.1)
X×sin(θ) = 97×sin(9.1 )+25× sin(45 ) = 33.02
X×sin(θ) = 33.02
X×cos (θ) + 25 × cos(45) = 97×cos(9.1)
X×cos (θ) = 97×cos(9.1)- 25 × cos(45) = 78.1
X×cos (θ) = 78.1
∴X×sin(θ)/(X×cos (θ)) = tan(θ) = 33.02/78.1 = 0.423
tan⁻¹(0.423) = 22.918≈ 22.92°
X×sin(θ) = 33.02
X = 33.02/(sin(θ)) = 33.02/(sin(22.92°)) = 84.79 miles per hour
Therefore, the flight speed should be 84.79 miles per hour at angle of 22.92° Northeast.
Which of the following is a trinomial?
A. 13x^3
B. 12x2 + 2x+10
c.9/5x2
D. 3x - 15
Answer:
B is a trinomial.
Step-by-step explanation: A trinomial is a math equation with 3 terms connected by plus or minus notations. In these 4 answer choices, choice B is the only one with 3 terms.
Answer
13x^3 i think its the right answer but am not sure :(
the scale on the map of a park is 5 in. : 3 mi.
Answer:
If the scale on a map is 5in : 3 miles, it means every 3 inches is 5 miles. 6 inches is 10 miles and so on.
Jamie and Imani each play softball. Imani has won 5 fewer games than Jamie. Is it possible for Jamie to have won 11 games if the sum of the games Imani and Jamie have won together is 30?
Answer:
No.
Step-by-step explanation:
They are giving us the information that Imani has 5 fewer wins than Jamie and they combine for 30 wins total. The question is asking us is it possible for Jamie to have one 11 games. To find how many games Imani won, we have to subtract 5 from Jamie's wins. 11-5 = 6. To then see if the wins add up to 30, we have to add Jamie's and Imani's wisn together, 11 + 5 ≠ 30, so therefore it is not possible for Jamie to have won 11 games.
Given trapezoid PQRS, find the length of midsegment TU.
Answer:
Option (4)
Step-by-step explanation:
In the given picture,
Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.
Segment TU joins the midpoints of the sides PS and RQ.
Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."
Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]
7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]
7x - 26 = 6x + 10
7x - 6x = 26 + 10
x = 36
m(TU) = 7x - 26
= 7(36) - 26
= 252 - 26
= 226
Therefore, Option (4) will be the answer.
The angle of elevation from a sailboat in a lake to the top of a vertical cliff is 60∘60∘. The sailboat is 210 feet from the foot of the cliff. How high is the cliff?
Answer:
363.741 feet
Step-by-step explanation:
Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;
Tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
Tan [tex]60^{0}[/tex] = [tex]\frac{x}{210}[/tex]
cross multiply to have;
x = 210 × Tan [tex]60^{0}[/tex]
= 210 × 1.7321
= 363.741
The cliff is 363.741 feet high.
help me please explain is not needed but would be appreciated
Answer:
B = 18°Step-by-step explanation:
To find angle B we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the side adjacent to angle B
So we have
tan B = AC / BC
tan B = 6/9
tan B = 1/3
B = tan-¹ 1/3
B = 18.43°
B = 18° to the nearest hundredth
Hope this helps you
What value is the independent variable and the dependent variable represents to ?
Answer:
Step-by-step explanation:
Independent Variable
The independent variable is the condition that you change in an experiment. It is the variable you control. It is called independent because its value does not depend on and is not affected by the state of any other variable in the experiment. Sometimes you may hear this variable called the "controlled variable" because it is the one that is changed. Do not confuse it with a "control variable," which is a variable that is purposely held constant so that it can't affect the outcome of the experiment.
Dependent Variable
The dependent variable is the condition that you measure in an experiment. You are assessing how it responds to a change in the independent variable, so you can think of it as depending on the independent variable. Sometimes the dependent variable is called the "responding variable."
HELP PLEASE! Find the standard deviation for Data set 1 and 2. round to the nearest hundred. DATA SET ONE: 8.2, 11.6 8.7, 10.6, 9.4, 10.1, 9.3 DATA SET TWO: 9.3, 10.2, 8.1, 12.3, 8.7, 9.9, 10.1
Answer:
0.92 and 1.25 respectively
Step-by-step explanation:
0.92 and 1.25 respectively
first the mean of each value which is 9.7 and 9.8 respectively
standard deviation = square root of the mean deviation of each value
then deduct the mean from each element
and square each value and add them together. not you should square each deviation value before you add them
at last divide the result by the number of frequency and find it's square root
Answer:
0.92 and 1.25
Step-by-step explanation:
My other answer was deleted, I'm not sure why.
Find the arc length of AB!!! (NEED ASAP)
9.77 in
Step-by-step explanation:
arc length is 80/360 × 2 × pi × radius
2/9 × 2 × 22/7 × 7
88/9
9.77in
Answer:
arc length = 9,76(8) inches
Step-by-step explanation:
Find the arc lengthFormula
2π·r(x°/360°)
= 2·3,14·7in·80°/360°
= 3516,8in/360
= 9,76(8) inches
calculate the area and leave your answer in term of pie
Answer: [tex]2.25\sqrt{3}[/tex]
Not sure what you mean by terms of pi, unless you want us to find the area of the sector, not the triangle.
Step-by-step explanation:
Assuming you mean the area of the triangle...
First draw an altitude from the 120 degree angle to the opposite base. You will find that the altitude will also be a median. This forms 2 30-60-90 right triangles. Thus, the height of the altitude is 1.5 and the base of the triangle is 1.5*root3. Thus, the base of the triangle is [tex]3\sqrt{3}[/tex] and the height is 1.5. Thus, the area of the triangle is [tex]2.25\sqrt{3}[/tex]
PLEASE ANSWER I WILL GIVE BRAINLIEST AND THANKS DESCRIBE FULLY THE SINGLE TRANSFORMATION THAT MAPS A ONTO C
Step-by-step explanation:
Shape A is flipped horizontally onto the x-axis
The new shape is mirroring Shape A
Find the surface area of the regular pyramid shown to the nearest whole number
Answer:
740 m^2
Step-by-step explanation:
Round Ed to the nearthest tenth and answer now question
Answer:
[tex] y = 9.1 [/tex]
Step-by-step explanation:
y can be found using the Law of sines as explained below:
m < Y = 106°
m < X = 58°
WY = x = 8
WX = y = ?
Thus,
[tex] \frac{x}{sin(X)} = \frac{y}{sin(Y)} [/tex]
[tex] \frac{8}{sin(58)} = \frac{y}{sin(106)} [/tex]
[tex] \frac{8}{0.848} = \frac{y}{0.961} [/tex]
Multiply both sides by 0.961 to solve for y
[tex] \frac{8}{0.848}*0.961 = \frac{y}{0.961}*0.961 [/tex]
[tex] \frac{8*0.961}{0.848} = y [/tex]
[tex] \frac{8*0.961}{0.848}*0.961 = y [/tex]
[tex] 9.07 = y [/tex]
[tex] y = 9.1 [/tex] (to the nearest tenth)
A certain family can afford a monthly mortgage payment of $1,340.00. With an APR of 5.25% per annum, what is the maximum mortgage amount they can afford if they prefer a 20-year amortization period?
Answer:
$198,859.03
Step-by-step explanation:
The amortization formula is good for this. Fill in the given numbers and solve for the unknown.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where A is the monthly payment, P is the principal amount of the loan, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
1340.00 = P(0.0525/12)/(1 -(1 +0.0525/12)^(-12·20)) ≈ 0.00673844·P
P ≈ 1340/0.00673844 ≈ $198,859.03
The family can afford a loan for $198,859.
John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to model this situation, and find the cost of one large drink
Answer:
cost of one drink: $1.70
Step-by-step explanation:
P = price of pizza
L = Price of each large drink
Gift certificate discount =$ 7
Net paid= $12.10
P +3L -7 = 12.10
14 +3L -7 =12.10
7+3L =12.10
3L = 12.10 -7 = 5.10
L = $1.70 for each large drink
hopefully this helped :3
Answer: The equation to model this situation is 3d + $14.00 – $7.00 = $12.10 and the cost of one large drink is $1.7 .
Step-by-step explanation:
As given
John and 2 friends are going out for pizza for lunch.
They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10.
let us assume that the numbers of large drinks are represented by d .
Than the equation becomes
Total money spend = Number of drinks × d + Pizza cost - Gift certificate amount .
Putting all the values in the above
12.10 = 3d + 14.00 - 7.00
Simplify the aboves
12.10 = 3d + 14 - 7
12.10 = 3d + 7
12.10 - 7 = 3d
5.1 = 3d
d = $ 1.7
Therefore the equation to model this situation is 3d + $14.00 – $7.00 = $12.10 and the cost of one large drink is $1.7 .
The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter. The cost of every mirror is proportional to the cube of the mirror's radius. What is the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors? Express your answer as a common fraction
Answer: 1:5
Step-by-step explanation:
Given: The cost of every mirror is proportional to the cube of the mirror's radius.
i.e. [tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}[/tex]
Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.
Then,
[tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}[/tex]
The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:
[tex]\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}[/tex]
Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .
HELP PLEASE!! I don't get it!!!!!!
Answer:
294.5 m²
Step-by-step explanation:
portion of circle is 360 - 130 = 230
πr²*x/360 = π(11.1)²*230/360 = 247.3
then add the non-right triangle area, 1/2ab sinC
1/2(11.1)(11.1) sin 130 = 47.2
247.3 + 47.2 = 294.5 m²
Veronica wants to check her work after evaluating Negative 108 divided by (negative 6). What steps can she follow to verify her answer?
Answer:
The answer to your question is 18
Step-by-step explanation:
Process
1.- Write the fraction given
[tex]\frac{-108}{-6}[/tex]
2.- Divide the numbers as usual
18
6 108
48
0
3.- Divide the signs
negative / negative = positive
4.- Write the answer
[tex]\frac{-108}{-6}= 18[/tex]
5.- Check the result
Multiply 18 by -6 and the result must be -108
-6 x 18 = 108
We know a negative times a negative is equal to a positive.
- 108 / - 6 is the same as 108 / 6 because the larger number is on top.
Therefore she can drop the negative signs and solve 108/6 to verify her answer.
There are x boys and y girls at the camp. How many children are at the camp altogether?
Answer:
x+y
Step-by-step explanation:
#boys+#girls=#children