Hello, please consider the following.
We know that
[tex]a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}[/tex]
And we can write that.
[tex](p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})[/tex]
It means that, by replacing p by [tex]p^{1/3}[/tex]
[tex](p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\<=>\boxed{ a^3+3a=p-\dfrac{1}{p} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the solution to the system of equations? -2x-3y+z=-6, z=6, 3x-y+z=13
Answer:
B is the correct answer.
Step-by-step explanation:
-2x+3y+z=-6
z=6
-2x+3y+6=-6
-2x+3y=-12
-2(3)+3(2)
-6+6=0 A is incorrect
-2(3)+3(-2)=-12
-6-6=-12
B is the correct answer.
I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.
You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (Enter your answer as a fraction.) (b) What is the probability of getting a sum of 10? (Enter your answer as a fraction.) (c) What is the probability of getting a sum of 6 or 10? (Enter your answer as a fraction.) Are these outcomes mutually exclusive? Yes No
Answer:
5/36 ; 1/12 ; 2/9 ; yes
Step-by-step explanation:
Given the following :
Roll of two fair dice : green and red
Probability = (number of required outcomes / number of total possible outcomes)
(a) What is the probability of getting a sum of 6?
Number of required outcomes = 5
P(sum of 6) = 5/36
b.) What is the probability of getting a sum of 10?
Number of required outcomes = 3
P(sum of 10) = 3 / 36 = 1/12
c.) What is the probability of getting a sum of 6 or 10?
P(getting a sum of 6) + P(getting a sum of 10)
(5/36) + (1/12) = (5 + 3) / 36
= 8/36 = 2/9
The events are mutually exclusive because each event cannot occur at the same time.
URGENT, PLEASE HELP! (1/5) -50 POINTS- !please no wrong answers for the points.! A) [tex]y = 6x - \frac{11}{8}[/tex] B) [tex]y = -6x - 2[/tex] C) [tex]y = \frac{3}{2} x - \frac{1}{8}[/tex] D) [tex]y = -3x + 9[/tex]
Answer:
C y = 3/2x - 1/8
Step-by-step explanation:
We know that the line has a positive slope, because it goes up from the lower left to upper right
We can eliminate B and D
For y = 6x - 11/8
A slope of 6 is very steep
Putting in 6
y = 6*6 -approximately 1 = 35 so the value at 3 would be 35
This is too big
Checking C
y = 3/2(6) - 0 = 9 or 9 This would be about right
HELP PRECALC NEED IN PROOF FORM
Hello, please consider the following.
We know the following, right ?
[tex](\forall a, b \in \mathbb{R}) \left( sin(a+b)=sin(a)sin(b)+cos(a)cos(b) \right)[/tex]
So, here, it gives.
[tex]Asin(\omega t+\phi)=Asin(\phi){\sf \bf sin(\omega t)}+Acos(\phi){\sf \bf cos(\omega t)}\\\\=c_2{\sf \bf sin(\omega t)}+c_1{\sf \bf cos(\omega t)}\\\\\text{ *** where }c_2=Asin(\phi) \text{ and } c_1=Acos(\phi) \text{ ***}[/tex]
Do not hesitate if you need further explanation.
A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. The table shows the results. A person is randomly selected from those tested. What is the probability that the person is from Texas, given that the person prefers Brand B? PLEASE HELP! I'll name you Brainliest if you're answer is the best!
Answer:
A
Step-by-step explanation:
It would be A because there are 45 people in Texas that prefer brand B. There are 105 people in total that prefer brand B. 45/105 is .42857... so rounded it would be .43, therefore A. I hope this helps.
Answer:
A
Step-by-step explanation:
Three students were given the expression shown and were asked to take a common factor out of two of the terms. Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent.
Answer:
Step-by-step explanation:
Given: 4 - 9x +21
Factorizing this expression, we have;
4 -3(3x - 7)
i. Chang's expression: 4 - 3(3x + 7)
This is not an equivalent expression, because by expansion of the bracket, the expression gives: 4 -9x -21
ii. Benjamin's expression: 4 + 3(3x + 7)
This is not an equivalent expression, because by expansion of the bracket, the expression gives: 4 +9x +21
iii. Habib's expression: 4 + 12x
This is not an equivalent expression, because the expression is not related to the given question
Comparing the three student's answers with the appropriate expression, none of the student's is an equivalent expression.
This expression that is equivalent to the given question is;
4 -3(3x - 7) = 4 -9x + 21
Answer:
1,2,4
Step-by-step explanation:
The relative frequency approach to probability uses long term relative frequencies, often based on past data.
a. True
b. False
Answer:
True
Step-by-step explanation:
Relative frequency is the ratio of the occurrence of a singular event and the total number of outcomes. This is a tool that is often used after you collect data. You can compare a single part of the data to the total amount of data collected.
For example, if a particular machine produces 50,000 widgets one at a time, and 5,000 of those widgets are faulty, the probability of that machine producing a faulty widget is approximately 5,000 out of 50,000, or 0.10.
How do you find volume for prisms?
Answer:
V =140 units^3
Step-by-step explanation:
The volume of the prism is V = Bh
Where B is the area of the base and h is the height
B is the area of the triangle
B = 1/2 (5 * 7) = 35/2
V = 35/2 * 8
V =140 units^3
Fuller bought 4 cantaloupes at the grocery store. Each cantaloupe weighed between 4.5 and 6.3 pounds. Fuller estimates a reasonable weight of all the cantaloupes to be 21.2 pounds.
Answer:
Step-by-step explanation:
3w + 2c = 32
4w + 3c = 44
Multiply the 1st equation by 4 and 2nd equation by 3, we get:
12w + 8 c = 128
12w + 9 c = 132
Subtracting the top equation from the bottom equation, we get: c = 4
Substituting c = 4 in any one of the above equations and solving, we get: w = 8
Therefore, weight of 2w + 1c = 2(8) + 4 = 20 pounds (Answer)
Find the rectangular coordinates of the point with the given polar coordinates.
Answer:
[tex]( - \sqrt{3} \: an d \: 1)[/tex]
Use a double angle identity to rewrite the formula r(Θ)=[tex]1/16v^2sin(theta)cos(theta)[/tex]
Answer:
1/32v²sin2θ
Step-by-step explanation:
Given the expression r(theta) = 1/16v²sinθcosθ
According to double angle of trigonometry identity;
Sin2θ = sin(θ+θ)
Sin2θ = sinθcosθ + cosθsinθ
Sin2θ = 2sinθcosθ
sinθcosθ = sin2θ/2 ... **
Substituting equation ** into the question
1/16v²sinθcosθ = 1/16v²(sin2θ/2)
1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)
1/16v²sinθcosθ = 1/32v²sin2θ
Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ
Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your work and include units. If he had a jet pack, would you use distance or displacement? Why?
Answer:
First, when he walks, we can see in the image that between the school and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.
Then he needs to walk 2km.
Now if he has a jet-pack, he can ignore the buildings and just take the shorter path, here we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.
One of the catheti is the vertical distance (two blocks of 0.5km, so this catheti has a length of 2*0.5km = 1km), and the other one is the horizontal distance, also 1km.
The actual distance of this path is given by the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse, then:
H^2 = 1km^2 + 1km^2
H = (√2)km = 1.41km.
Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, in this case the distance and the displacement would be the same.
This is because the definitions of distance and displacement are:
Distance: "how much ground an object has covered"
Displacement: "Difference between the final position and the initial position"
When he walks, the distance is 2km and the displacement is 1.41km , but when he uses the jet pack, the distance is equal to the displacement, both are 1.41km.
Answer and Step-by-step explanation:
The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km. The result of this is a total of 4¨*0.5 km = 2 km. The second thing is that he must walk 2 kilometers. On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings. This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home. As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km. The result is that these catheti have a length of 2*0.5 km = 1 km. The other is the distance of the horizontal line, which is 1 km. The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2. Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2. As well, H = (√2)km = 1.41 km. Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow. For this specific situation, the displacement, and the distance would be the exact same. The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered. Also, when he walks, the distance is 2 km and the displacement is 1.41 km. Also, when he utilizes the jet pack, the distance is equal to the displacement. Both of these are 1.41 km.
A speedboat moves at a rate of 25 km/hr in still water. How long will it take
someone to ride the boat 87 km downstream if the river's current moves at a rate of
4 km/hr?
Answer:
3 hours
Step-by-step explanation:
Downstream, the speeds add up:
25 + 4 = 29 km/hIt will take:
87/29= 3 hrsTo ride 87 km.
Which is the best definition of mathematical proof? a/A sequence of statements that demonstrates the truth of an assertion. b/Statements that show the assertion is false using a counterexample. c/A paragraph that always has three parts and shows that an assertion is true. d/Statements in any order that show that an assertion is true.
Answer:
A. A sequence of statements that demonstrates the truth of an assertion.
Step-by-step explanation:
Mathematical proofs are a series of statements in order that help prove that something is true.
Proofs do not prove that something is false, they are not always 3 parts, and they are not in any order, because they have to be in an organized sequence.
So, A is correct.
Answer:
A sequence of statements that demonstrates the truth of an assertion.
Step-by-step explanation:
Travis has a budget of $300 that he can spend on perennial flowers and at least 6 annual flowers. Perennial flowers are 18 dollars per plant and annual flowers are 15 dollars per plant. Let x be the amount spent on perennial flowers, and let y be the amount spent on annual flowers. What system of inequalities describes this situation?
Answer:
18x + 15y ≤ 300x ≥ 0; y ≥ 6Step-by-step explanation:
Variables are defined in the problem statement.
18x +15y ≤ 300 . . . . total budget
y ≥ 6 . . . . . . . . . . . . minimum number of annuals
x ≥ 0 . . . . . number of perennials cannot be negative
This system of inequalities describes the situation.
Which equation represents this statement: A number minus 6 is 168? 6 − n = 168 n ÷ 6 = 168 n − 6 = 168 6n = 168
Answer:n-6=168
Step-by-step explanation:
The statement starts with the variable first.
Answer:
n - 6 = 168.
Step-by-step explanation:
Let's say that the value of the number is n.
n minus 6 is 168, so n - 6 = 168.
n - 6 = 168
n = 174.
Hope this helps!
3 1/2 ft into inches
Answer:
42 inches
Step-by-step explanation:
1 ft = 12 inch
Answer:
42 inches.
Step-by-step explanation:
Unit of measurement:
1 foot = 12 inches.
3 ft x 12 inches = 36 inches.
1/2 foot x 12 inches = 12/2 = 6 inches.
36 inches + 6 inches = 42 inches
42 inches is your answer.
~
What is the value of n
Answer:
9 + 18 = 27
27 + n + 1
= n = 27 - 1 = 26.
n = 26
9 + 18 + 26 + n + 7 =
53 + n + 7
53 + 7 + n
60 + n = 360
n = 360 - 60 = 300
so, n 300
so = 9, 18, 300, 26
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?
Answer:
The answer and explanation are below
Step-by-step explanation:
i followed the data that was given in the question.
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
a.) please refer to the attachment for the scatter diagram. Y was plotted against X.
b. The equation is given as:
Y = b₁ + b₀X
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²
b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)
= 1375-1309.5/275-225
= 65.5/50
= 1.31
b₀ = 87.3/5 - 1.31(15/5)
= 87.3/5 - 1.31x3
= 13.53
the regression line is
Y = 13.53 + 1.31X
please refer to the attachment for the diagram for the regression line.
c. we are required to find r.
r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
inserting these values:
r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29
= 65.5/106.69
= 0.6139
Coefficient of determination = r²
r = 0.6139
r² = 0.3769 = 37.69%
Therefore 37.69% variation in y is explained by variation in x and the least square model.
Question 2: Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
Answer:
?
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
Let "x" be the number of nickels, of dimes, and of quarters.
The value of the nickels is 5x cents.
The value of the dimes is 10x cents
The value of the quarters is 25x cents.
Equation:
Value of nickels + Value of dimes + Value of quarters =1320 cents
5x + 10x + 25x = 1320
Sove for "x". Then you will know the number of each coin.
can anyone show me this in verbal form?
Answer:
2 * (x + 2) = 50
Step-by-step explanation:
Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.
Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46
Answer:
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Step-by-step explanation:
We formulate our null and alternative hypotheses as
H0 u≤ 6 ug Ha : u > 6 ug
The significance level ∝ = 0.05
The test statistic used is
t = X` - u / s/ √n
which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.
The critical region t > t (0.05,11) = 1.796
We compute the t value from the data
Xi Xi²
8.92 79.5664
6.99 48.8601
5.54 30.6916
5.73 32.8329
6.38 40.7044
5.51 30.3601
6.45 41.6025
7.50 56.25
8.48 71.9104
5.56 30.9136
6.90 47.61
6.46 41.7316
80.42 553.0336
Now x` = ∑x/ n = 80.42/12 = 6.70
S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)
= 1/11 (553.034-538.948) = 1.2805
s= 1.1316
Putting the values in the test statistics
t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12
= 2.1698
The critical region t > t (0.05,11) = 1.796
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
What is the domain of h?
Answer:
{-2, -1, 1, 5, 6}
Step-by-step explanation:
The domain includes the five x-values (inputs): {-2, -1, 1, 5, 6}
Answer:
The x-values -2, -1,1,5 and 6
Step-by-step explanation:
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 13)2 + 6
Answer:
Step-by-step explanation:
if we shift 13 units right and 6 units down we get the reqd. graph.
Answer:
see explanation
Step-by-step explanation:
Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)
• If k > 0 then shift left by k units
• If k < 0 then shift right by k units
Thus y = (x - 13)² represents a shift to the right of 13 units
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Thus
y = (x - 13)² + 6 is the graph of y = x² translated 13 units right and 6 units up
This table shows a linear relationship.
The slope of the line is ?
Answer:
2
Step-by-step explanation:
2,8 to 4,12 has a rise of 4 and a run of 2.
4/2 = 2
The slope is 2.
Remember rise/run!
Answer:
2
Step-by-step explanation:
We take take two points and use the slope formula
m = (y2-y1)/(x2-x1)
m = (12-8)/(4-2)
= 4/2
= 2
Which relation is a function?
The number two is a function
First rule of function: for each element of A there is one and only one element of B
For example, in the first one -5 is "collegated" to -2 and 3. So this isn't a function.
Naturally, every element of B can have more element of A
Theresa bought 2 pineapples for $6. She be wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part A
Using the diagram, find the constant of proportionality in terms of dollars per pineapple.
Answer:
$3 per pineapple
Step-by-step explanation:
Hey there!
If 2 pineapples are $6,
6 / 2 = 3
So 1 pineapple is $3.
Hope this helps :)
Answer:
3 dollars for 1 pineapple
Step-by-step explanation:
well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.
A lime passes through the point (5,7) has a slope of 3. Which of the following gives the equation of the line
Answer:
Hey There!! The answer to this is (6, 10) There are no answer choices, so I will just list a few. But first, we need to create the equation.
Plugging in (5,7) into the equation y=mx+b, we can solve for b since all of the other variables are known, with m=3 as the slope.
So, 7=3*5+b
7=15+b
b = -8
y=3x-8 is your equation.
So, you can plug in any value of x you get a certain value of y.
(1,-5), (2,-2), (3,1), (4,4), (5,7), (6,10), (7,13) Thus, for The correct option (6, 10). Hope It Helped!~ ♡
ItsNobody~ ☆
Answer:
y=3x-8
Step-by-step explanation:
We can start by writing the equation of the line in point-slope form.
Point-slope form is y-y1=m(x-x1)
This is where:
y1= y-coordinate of a given point on the line
m= slope of the line
x1= x-coordinate of a given point on the line
The given point in this example is (5,7)
A point is (x-coordinate, y-coordinate)
Therefore,
y1=7
m=3
x1=5
Plug that into the form.
y-7=3(x-5)
We can now simplify that to slope-intercept form,since that is most standard.
y-7=3(x-5)
Start by distributing the right side.
y-7=3x-15
Add 7 to both sides.
y=3x-8
find the value of x? please help
Answer:
49
Step-by-step explanation:
With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!
Maxwell Communications paid a dividend of $1.20 last year. Over the next 12 months, the dividend is expected to grow at 13 percent, which is the constant growth rate for the firm (g). The new dividend after 12 months will represent D1. The required rate of return (Ke) is 17 percent. Compute the price of the stock (P0). (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Answer:
The price of the stock is [tex]P_o = \$ 33.9[/tex]
Step-by-step explanation:
From the question we are told that
The dividend is [tex]k = \$ 1.20[/tex]
The expected growth rate is [tex]r = 13\% = 0.13[/tex]
The required rate of return is [tex]K_e = 17 \% = 0.17[/tex]
The new dividend after 12 months is mathematically represented as
[tex]D_1 = k * (1 + r)[/tex]
substituting values
[tex]D_1 = 1.20 * (1 + 0.13)[/tex]
[tex]D_1 = \$ 1.356[/tex]
The price of the stock the price of stock is mathematically represented as
[tex]P_o = \frac{D_1}{ K_e - r }[/tex]
substituting values
[tex]P_o = \frac{ 1.356}{ 0.17 - 0.13 }[/tex]
[tex]P_o = \$ 33.9[/tex]
