Answer: [tex]\sqrt[3]{a}[/tex]
Step-by-step explanation:
Just as the square root is [tex]\sqrt[2]{a}[/tex], the cube root is [tex]\sqrt[3]{a}[/tex]
Hope it helps <3
Answer:
[tex]\sqrt[3]{a}[/tex]
Step-by-step explanation:
a cube root of a number x is a number a such that a³ = x.
7.1 A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings.
Answer:
1.875
Step-by-step explanation:
To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.
In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:
[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]
[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]
[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]
Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:
[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]
[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]
[tex]E_2 = 1 + \frac{7}{8}[/tex]
[tex]E_2 = \frac{15}{8} = 1.875[/tex]
The point (3, 6) is on the graph of y= 5f(2(x+3))-4 . Find the original point on the graph of y=f(x).
Answer:
(12, 2) is the original point on the graph of [tex]y=f(x)[/tex].
Step-by-step explanation:
Given:
[tex]y= 5f(2(x+3))-4[/tex] has a point (3, 6) on its graph.
To find:
Original point on graph [tex]y=f(x)[/tex] = ?.
Solution:
We are given that The point (3, 6) is on the graph of [tex]y= 5f(2(x+3))-4[/tex]
If we put x = 3 and y = 6 in [tex]y= 5f(2(x+3))-4[/tex], it will satisfy the equation.
Let us the put the values and observe:
[tex]6= 5f(2(3+3))-4\\\Rightarrow 6= 5f(2(6))-4\\\Rightarrow 6= 5f(12)-4\\\Rightarrow 6+4=5f(12)\\\Rightarrow 5f(12)= 6+4\\\Rightarrow 5f(12)= 10\\\Rightarrow f(12)= \dfrac{10}{5}\\\Rightarrow f(12)= 2\\OR\\\Rightarrow 2=f(12)[/tex]
Now, let us compare the above with the following:
[tex]y=f(x)[/tex]
we get y = 2 and x = 12
So, the original point on graph of [tex]y=f(x)[/tex] is (12, 2).
Solve the system by graphing (Simplify your answer completely.)
Will someone please help me with this and give an explanation on how you got it? I don’t understand.
{x+y=8
{x-y=4
Answer:
(6,2)
Step-by-step explanation:
1) convert both equations to slope intercept form:
y=-x+8
and
y=x-4
now graph both equations separately by intercepts:
x int: 0=-x+8
-8=-x
8=x
y int: y=0+8
y=8
so the two coordinate points for first equation are (0,8) and (8,0)
lets move on two second equation: y=x-4
x int: 0=x-4
4=x
y int y=0-4
y=-4
so the 2 coordinate points are (4,0) and (0,4)
lets graph these two equations and see where they intersect:
(see graph below), the intersection is at (6,2) so (6,2) is our answer
hope this helps
What is the value of 45-0.023
The value is 44.977
Feel pleasure to help u
Answer:
44.977
Step-by-step explanation:
What is the x-intercept of the graph?
Answer: (6,0)
Step-by-step explanation: To find the x-intercept, we plug a 0 in for y.
So we have 2x - 3(0) = 12.
Simplifying from here, we have 2x = 12.
Now divide both sides by 2 and we get x = 6.
So our x-intercept is 6.
This means that our line crosses the x-axis 6
units to the right of the origin or at the point (6,0).
Answer:
(6,0)
Step-by-step explanation:
The x intercept is where the graph crosses the x axis
QUESTION 2
Find Percent Increase:
The original price for a product is $53.93 and the sale's tax rate is 29%. Find the amount of tax and the total selling price. Round to the nearest cent.
A $15.64 and $69.57
B. $38.29 and 592.22
C. $15.64 and $38.29
D. $16.78 and $70.21
QUESTION 3
Find Future Value Using Simple Interest Formula:
Chad got a student loan for $10,000 at 8% annual simple interest. How much does he owe after two years?
A $12,800
B. $10,800
C. $11,600
D. $11,664
Answer:
QUESTION 2 -> Correct option: A.
QUESTION 3 -> Correct option: C.
Step-by-step explanation:
QUESTION 2
To find the amount of tax we just need to multiply the tax rate by the original price of the product:
[tex]Tax = 29\% * 53.93[/tex]
[tex]Tax = 0.29 * 53.93[/tex]
[tex]Tax =\$15.64[/tex]
Then, to find the total selling price, we need to sum the original price to the tax value:
[tex]Total = tax + price[/tex]
[tex]Total = 15.64 + 53.93[/tex]
[tex]Total = \$69.57[/tex]
Correct option: A.
QUESTION 3
To find the final value after 2 years, we can use the formula:
[tex]P = Po * (1 + r*t)[/tex]
Where P is the final value, Po is the inicial value, r is the interest and t is the amount of time. Then, we have that:
[tex]P = 10000 * (1 + 0.08 * 2)[/tex]
[tex]P = \$11600[/tex]
Correct option: C.
g On a certain daily flight, Air Northeast has a policy of booking as many as 22 people on an airplane that can seat only 19. Past studies have revealed that only 89% of the booked passengers actually arrive for the flight. If the airline books 22 people on a flight, find the probability that there will not be enough seats available for all booked passengers. Show sufficient work to justify answer
Answer:
55.82% probability that there will not be enough seats available for all booked passengers.
Step-by-step explanation:
For each booked passenger, there are only two possible outcomes. Either they arrive for the flight, or they do not arrive. The probability of a booked passenger arriving is independent of other booked passengers. So we used the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The airline books 22 people on a flight
This means that [tex]n = 22[/tex]
Past studies have revealed that only 89% of the booked passengers actually arrive for the flight.
This means that [tex]p = 0.89[/tex]
Find the probability that there will not be enough seats available for all booked passengers.
The airplane seats 19, so this is the probability of more than 19 passengers arriving.
[tex]P(X > 19) = P(X = 20) + P(X = 21) + P(X = 22)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 20) = C_{22,20}.(0.89)^{20}.(0.11)^{2} = 0.2718[/tex]
[tex]P(X = 21) = C_{22,21}.(0.89)^{21}.(0.11)^{1} = 0.2094[/tex]
[tex]P(X = 22) = C_{22,22}.(0.89)^{22}.(0.11)^{0} = 0.0770[/tex]
[tex]P(X > 19) = P(X = 20) + P(X = 21) + P(X = 22) = 0.2718 + 0.2094 + 0.0770 = 0.5582[/tex]
55.82% probability that there will not be enough seats available for all booked passengers.
How many solutions does the system have? { y = − 3 x + 9 3 y = − 9 x + 9 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=−3x+9 3y=−9x+9
Answer:
no solutions
Step-by-step explanation:
y = − 3 x + 9
3 y = − 9 x + 9
Multiply the first equation by -3
-3(y )=-3( − 3 x + 9)
-3y = 9x -27
3 y = − 9 x + 9
-------------------------
0 = 0 -18
0 = -18
This is never true so there are no solutions
Answer:
for kahn academy -- b -- ( no solutions)
Step-by-step explanation:
The assets of Big Baller Brand consists entirely of current assets and net plant equipment. The firm has total assets of $3.5 million and the net plant equipment equals $2.75 million. It has notes payable of $350,000, long term debt of $825,000 and total common equity of $2 million. The firm does have accounts payable and accruals on its balance sheet. The firm only finances with debt and common equity, so it has no preferred stock on its balance sheet. a. What is the company's total debt? b. What is the amount of the liabilities and equity that appear on the firm's balance sheet? c. What is the balance of current assets on the firm's balance sheet? d. What is the balance of the current liabilities on the firm's balance sheet? e. What is the firm's net working capital? f. What is the firm's operating working capital? g. What is the amount of accounts payable and accruals on its balance sheet?
Answer:
a. $825,000
b. $1,175,000
c. $750,000
d. $350,000
e. $3,150,000
f. $2,675,000
g. Accounts payable and accruals
Step-by-step explanation:
a. Total debt is long term debt $825,000
b. The amount of liability apearing on balance sheet is $1,175,000 ($825,000 + $350,000)
The amount of equity appearing in balance sheet is $2,000,000
c. Current Assets balance on the balance sheet is $750,000 ($3.5m - $2.75m)
the difference of total assets and net plant equipment.
d. Current liabilities to be reported on the balance sheet is $350,000 and the amount of accounts payable and other payable.
e. Net working capital is calculated by taking total assets and then deducting current liabilities from it. $3,150,000 ($3500,000 - $350,000)
f. Operating working capital is calculated by subtracting total liablities from total assets. $2,675,000 ($3,500,000 - $825,000)
g. The amount of accounts payable and accruals is not provided in the question the amount will be reported in the balance sheet.
what is the difference of rational expressions below 6x/x-3 - 5/x
Answer:
[tex]$ \frac{6x^2-5x+15 }{x^2-3x} $[/tex]
Step-by-step explanation:
[tex]$\frac{6x}{x-3} -\frac{5}{x} $[/tex]
[tex]$\frac{6x(x)}{x(x-3)} -\frac{5(x-3)}{x(x-3)} $[/tex]
[tex]$\frac{6x^2}{x^2-3x} -\frac{5x-15}{x^2-3x} $[/tex]
[tex]$ \frac{6x^2-5x+15 }{x^2-3x} $[/tex]
2. A line passes through the point (0,4).
The gradient of this line is 2.
Write down the equation of this line
Answer:
[tex]\boxed{y = 2x+4}[/tex]
Step-by-step explanation:
Gradient = m = 2
Y-intercept = b = 4 (Because here x = 0 as in the point (0,4))
So, the equation becomes
=> [tex]y = mx+b[/tex]
=> [tex]y = 2x+4[/tex]
Precalc experts! I need your help!
Answer:
[tex]f(x)\to 1[/tex]
Step-by-step explanation:
The function approaches its horizontal asymptote in both directions as the magnitude of x gets large. The limit is y = 1.
Which statement describes the system of equations?
X+ 2y = 2
x-2y=-2
It has infinitely many solutions.
It has no solution.
It has one solution (0, 1).
It has one solution (4, -1).
Answer:
It has one solution (0, 1).
Step-by-step explanation:
Easiest and fastest way to solve the systems of equation is to graph them on a graphing calc and analyzing where the 2 graphs intersect (if they are not parallel).
Would you need to use the chain rule to find the derivative of this function?
Answer:
TRUE. We need to use the chain rule to find the derivative of the given function.
Step-by-step explanation:
Chain rule to find the derivative,
We have to find the derivative of F(x)
If F(x) = f[g(x)]
Then F'(x) = f'[g(x)].g'(x)
Given function is,
y = [tex]\sqrt{2x+3}[/tex]
Here g(x) = (2x + 3)
and f[g(x)] = [tex]\sqrt{2x+3}[/tex]
[tex]\frac{dy}{dx}=\frac{d}{dx}(\sqrt{2x+3}).\frac{d}{dx} (2x+3)[/tex]
y' = [tex]\frac{1}{2}(2x+3)^{(1-\frac{1}{2})}.(2)[/tex]
= [tex](2x+3)^{-\frac{1}{2}}[/tex]
y' = [tex]\frac{1}{\sqrt{2x+3}}[/tex]
Therefore, it's true that we need to use the chain rule to find the derivative of the given function.
US consumers are increasingly using debit cards as a substitute for cash and checks. From a sample of 100 consumers, the average amount annually spent on debit cards is $7,790. Assume that this average was based on a sample of 100 consumers and that the population standard deviation is $500.
A. At 99% confidence, what is the margin of error?
B. Construct the 99% confidence interval for the population mean amount spent annually on a debit card.
Answer:
A. Margin of error = 128.79
B. The 99% confidence interval for the population mean is (7661.21, 7918.79).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is know and is σ=500.
The sample mean is M=7790.
The sample size is N=100.
As σ is known, the standard error of the mean (σM) is calculated as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{500}{\sqrt{100}}=\dfrac{500}{10}=50[/tex]
The z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_M=2.576 \cdot 50=128.79[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 7790-128.79=7661.21\\\\UL=M+t \cdot s_M = 7790+128.79=7918.79[/tex]
The 99% confidence interval for the population mean is (7661.21, 7918.79).
Determine f-1(0). Hurry.
Answer:
since f(0) is -4 , f^-1(0) will be the multiplicative inverse of f(0)
hence, the answer is 1/-4
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Inverse of a function.
so hére after solving here we get as,
==> f^-1(0) = 1
The amount of time spent updating websites for small businesses averages 50 minutes per week with a standard deviation of 10 minutes per week. if we consider the distribution of times as mound-shaped and symmetric, use the standard deviation to explain where we would expect "most" of the times will fall each week?
a) Way too long
b) Between 30 and 70 minutes
c) Between 40 and 60 minutes
d) Between 20 and 80 minutes
Answer:
I think the answer is C - Between 40 and 60 minutes
Step-by-step explanation:
Since each week the amount of time spend updating websites takes 50 minutes per week with an addition of 10 minutes it would be 1 hour per week (60 minutes)
A- y=-2x-4
B- y=2x+4
C- y=-2x+4
D- y= 2x-4
Answer:
A. y=-2x-4
Step-by-step explanation:
The slope is negative when the line is going down from up.
Options B and D are wrong.
The y-intercept is (0, -4) as shown in the graph.
Option C is wrong.
y = mx + b
y = -2x - 4
A submarine is searching for underwater features with help from an underwater robotic vehicle. At one time the submarine is 55m below the surface, and the underwater robotic vehicle is 227m below the surface. What is the distance between the underwater robotic vehicle and the submarine?
Answer:
172m
Step-by-step explanation:
From the question above we are told:
The distance of the submarine below the surface = 55m
The distance of the underwater robotic vehicle below the surface = 227m
The distance between the underwater robotic vehicle and the submarine is calculated as:
The distance of the underwater robotic vehicle below the surface - The distance of the submarine below the surface
= 227m - 55m
= 172m
Therefore, the distance between the underwater robotic vehicle and the submarine is 172m
johnathan needs 70 liters of a 50% alcohol solution. he has a 30% solution and an 80% solution available. How many liters of the 30% solution and hjow many liter of the 80% solution should he mix to make the 50% solution?
Answer:
28 l of 80%
42 l of 30%
Step-by-step explanation:
Target is 70 l of 50% solution
It will contain 70*0.5= 35 l of alcohol
x l of 80% solution and y l of 30% solution mixed to get the target solution
x+y=70 is the equation for total volume, and
0.8x+0.3y= 35 is the equation for the alcohol content. Solving this:
y= 70-x0.8x+0.3*(70-x) = 350.8x+21- 0.3x= 350.5x= 35-210.5 x= 14x= 14/0.5x=28 l of 80% solutionthen
y= 70-x= 70 -28 l= 42 l of 30% solutionWhen five times a number is decreased by 8, the result is 7. What is the number?
The number is
Answer:
3
Step-by-step explanation:
5x - 8 = 7
5x = 7+8
5x = 15
x = 15 ÷ 5
x = 3
Prove the identity cos x/1 - sin x = sec x + tan x
Answer:
Proved
Step-by-step explanation:
Given
Prove that
[tex]\frac{cos x}{1 - sin x} = sec x + tan x[/tex]
[tex]\frac{cos x}{1 - sin x}[/tex]
Multiply the numerator and denominator by 1 + sinx
[tex]\frac{cos x}{1 - sin x} * \frac{1 + sin x}{1 + sin x}[/tex]
Combine both fractions to form 1
[tex]\frac{cos x (1 + sin x)}{(1 - sin x)(1 + sin x)}[/tex]
Expand the denominator using difference of two squares;
[tex]i.e.\ (a - b)(a + b) = a^2 - b^2[/tex]
The expression becomes
[tex]\frac{cos x (1 + sin x)}{(1^2 - sin^2 x)}[/tex]
[tex]\frac{cos x (1 + sin x)}{(1 - sin^2 x)}[/tex]
From trigonometry; [tex]1 - sin^2x = cos^2x[/tex]
The expression becomes
[tex]\frac{cos x (1 + sin x)}{(cos^2 x)}[/tex]
Divide the numerator and the denominator by cos x
[tex]\frac{(1 + sin x)}{(cos x)}[/tex]
Split fraction
[tex]\frac{1}{cos x} + \frac{sin x}{cos x}[/tex]
From trigonometry; [tex]\frac{1}{cos x} = sec x \ and\ \frac{sin\ x}{cos\ x} = tan\ x[/tex]
So;
[tex]\frac{1}{cos x} + \frac{sin x}{cos x}[/tex] = [tex]sec x + tan x[/tex]
4 builders are building some new classrooms at Trinity. It takes them 5 months to build the classrooms. How long will it take 10 builders?
Answer:
it takes
[tex]\boxed {\red {2 \: \: months}}[/tex]
for 10 builders
Step-by-step explanation:
[tex]4 \: \: \: builders = 5 \: month \\ 10 \: builders = x[/tex]
Let us solve
[tex]4 = 5 \\ 10 = x[/tex]
so
[tex]4 = x \\ 10 = 5[/tex]
use cross multiplication
[tex]5 \times 4 = 10 \times x \\ 20 = 10x \\ \frac{20}{10} = \frac{10x}{10} \\ \green {x = 2}[/tex]
Answer:
[tex]\boxed{2months}[/tex]
Step-by-step explanation:
B1 = 4
M1 = 5
B2 = 10
M2 = x (we have to find this)
Since it is an inverse proportion (more builders will take less time and vive versa), we'll write it in the order of
=> B1 : B2 = M2 : M1
=> 4:10 = x : 5
Product of Means = Product of Extremes
=> 10*x = 4*5
=> 10x = 20
Dividing both sides by 10
=> x = 2 months
So, it will take 2 months to build classrooms by 10 builders.
Pls help asap <3 This is very confusing to me
Answer:Yes, alternate interior angles converse
What are the divisors of 60?
Answer:
Step-by-step explanation:
The divisors of a number are the numbers that divide it exactly.
60/2
2/30
3/3
5/5
one
divisors = 1,2,3,, 4,5,6,10,12,15,20,30,60.
answer:
1, 2, 3, 6, 10, 30, 60
Step-by-step explanation:
i am pretty sure!
A research group wants to know if the online platform to play Settlers of Catan is being accessed more after the stay at home order than before it. The mean for number of games started per minute before the stay at home order was 1000. The researchers hypothesize that after the stay at home order, the online platform was accessed more so than before the stay at home order. They set alpha = .05 The mean for number of games started per minute after the stay at home order, was 1378 with a standard deviation of 489. The sample size was 108,000.
a. Given this conclusion, what can you say about the p value of this test statistic?
b. Please calculate the effect size. Is it small, medium, or large?
Answer:
a) The P-value is 0.
At a significance level of 0.05, there is enough evidence to support the claim that the online platform was accessed significantly more so than before the stay at home order.
b) Effect size d = 0.77
Medium.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the online platform was accessed significantly more so than before the stay at home order.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1000\\\\H_a:\mu> 1000[/tex]
The significance level is 0.05.
The sample has a size n=108000.
The sample mean is M=1378.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=489.
The estimated standard error of the mean is computed using the formula:
s_M=\dfrac{s}{\sqrt{n}}=\dfrac{489}{\sqrt{108000}}=1.488
Then, we can calculate the t-statistic as:
t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1378-1000}{1.488}=\dfrac{378}{1.488}=254.036
The degrees of freedom for this sample size are:
[tex]df=n-1=108000-1=107999[/tex]
This test is a right-tailed test, with 107999 degrees of freedom and t=254.036, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>254.036)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the online platform was accessed significantly more so than before the stay at home order.
The effect size can be estimated with the Cohen's d.
This can be calculated as:
[tex]d=\dfrac{M-\mu}{\sigma}=\dfrac{1378-1000}{489}=\dfrac{378}{489}=0.77[/tex]
The values of Cohen's d between 0.2 and 0.8 are considered "Medium", so in this case, the effect size d=0.77 is medium.
A bag contains 75 marbles:35 are blue and 25 of these blue marbles are swirled. The rest of them are red, and 30 of the red ones are swirled. The marbles that are not swirled are clear. What is the probability of drawing? (a) A blue marble (b) A blue swirled marble (c) A red clear marble.
Answer:
a) 35/75
b)25/75
c)10/75
Step-by-step explanation:
solve the right triangle abc for the missing side and angles to the nearest tenth given sides a=13.2 and b=17.7
Step-by-step explanation:
Assuming c is the hypotenuse:
c = √(a² + b²)
c = 22.1
tan A = a/b
A = 36.7°
tan B = b/a
B = 53.3°
Solve the following system of equations. Express your answer as an ordered
pair in the format (a,b), with no spaces between the numbers or symbols.
2x+7y=-7
-4x-3y=-19
Answer:
(7, -3)
Step-by-step explanation:
Isolate x for 2x +7y = -7:
x = (-7 - 7y)/2
Substitute:
-4((-7 - 7y) / 2) - 3y = -19
Solve for y:
-2(-7y - 7) - 3y =
14y + 14 - 3y =
11y + 14 = -19
11y = -33
y = -3
Substitute -3:
x = (-7 - 7(-3))/2
= 14/2
x = 7
Answer:
(7,-3)
Step-by-step explanation:
. Please answer this correctly
Answer:
In both cases, the spider has already crawled up 3 feet. In order for the answer to be 0 the spider must crawl down 3 feet because 3 - 3 = 0, therefore the answer is the first story.
Answer:
Question 1
Step-by-step explanation:
1) The spider is 3 feet above the patio : +3
Now, due to strong wind, it crawls down 3 feet: -3
+ 3 - 3 = 0