The solution to the equation x3 = 125 is: 5 -5 ±5
Answer:
x=5
Step-by-step explanation:
x^3 = 125
Take the cubed root of each side
x^3 ^ (1/3) = 125 ^ (1/3)
x = 5
Solve the following inequality.
- 202-16
Which graph shows the correct solution?
Need help with this math
Answer:
first option : sqrt(26) + 6 units
Step-by-step explanation:
distance office to supermarket OS
OS² = (-7 - -2)² + (-5 - -6)² = (-7+2)² + (-5+6)² = (-5)² + 1² =
= 25 + 1 = 26
OS = sqrt(26)
distance supermarket to home SH
SH² = (-2 - 4)² + (-6 - -6)² = (-6)² + 0² = 36
SH = 6
so in total she travels sqrt(26) + 6 units
Suppose 35.45% of small businesses experience cash flow problems in their first 5 years. A consultant takes a random sample of 530 businesses that have been opened for 5 years or less. What is the probability that between 34.2% and 39.03% of the businesses have experienced cash flow problems?
1) 0.6838
2) 20.3738
3) 0.3162
4) - 11.6695
5) 1.2313
Answer:
1) 0.6838
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
35.45% of small businesses experience cash flow problems in their first 5 years.
This means that [tex]p = 0.3545[/tex]
Sample of 530 businesses
This means that [tex]n = 530[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.3545[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.3545(1-0.3545)}{530}} = 0.0208[/tex]
What is the probability that between 34.2% and 39.03% of the businesses have experienced cash flow problems?
This is the p-value of Z when X = 0.3903 subtracted by the p-value of Z when X = 0.342.
X = 0.3903
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.3903 - 0.3545}{0.0208}[/tex]
[tex]Z = 1.72[/tex]
[tex]Z = 1.72[/tex] has a p-value of 0.9573
X = 0.342
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.342 - 0.3545}{0.0208}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a p-value of 0.27425
0.9573 - 0.2743 = 0.683
With a little bit of rounding, 0.6838, so option 1) is the answer.
Sarah invests £2000 for 2 years in a saving account. She earns 3% per annum in compound interest.
How much did Sarah have in her saving account after 2 years?
£
Use the formula:
A=P(1+r100)n
Where;
A = the amount of money accumulated after n years, including interest
P = the principal sum (the initial amount borrowed or invested)
r = the rate of interest (percentage)
n = the number of years the amount is borrowed or invested
Answer:
£2120.27
Step-by-step explanation:
A = P (1 + r100)
A = 2000 (1+ 0.03/365)^365(2)
A = 2000 ( 1.00008)^730
A = 2000 (1.060)
A = £2120.27
find the first three common multiplies
6 and 8
Answer:
24,48,72
Step-by-step explanation:
multiples of 6- 6,12,18,24,30,36,42,48,54,60,66,72
multiples of 8- 8,16,24,32,40,48,56,64,74,80
What is the product of x(x + 1)?
1. 2x + x
2. x2+ 2x
3. 212 + x
4. x2 + x
Answer:
4. x²+x
Step-by-step explanation:
the product of x(x + 1) = (x)(x) + (x)(1)
= x²+x
Given: f(x) = x- 7 and h(x) = 2x + 3
Write the rule for f(h(xc)).
Answer:
[tex]f(h(xc)) = 2xc-4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 7[/tex]
[tex]h(x) = 2x + 3[/tex]
Required
[tex]f(h(xc))[/tex]
First, calculate h(xc)
If [tex]h(x) = 2x + 3[/tex]
Then
[tex]h(xc) = 2xc + 3[/tex]
Solving further:
[tex]f(x) = x - 7[/tex]
Substitute h(xc) for x
[tex]f(h(xc)) = h(xc) - 7[/tex]
Substitute [tex]h(xc) = 2xc + 3[/tex]
[tex]f(h(xc)) = 2xc + 3 - 7[/tex]
[tex]f(h(xc)) = 2xc-4[/tex]
The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the lower class limits.
Answer:
79.5, 110.5, 141.5, 172.5, 203.5, 234.5
Step-by-step explanation:
Given
The attached distribution
Required
The lower class limits
To do this, we simply subtract 0.5 from the lower interval
From the attached distribution, the lower intervals are:
80.0, 111.0, 142.0, 173,0 .......
So, the lower class limits are:
[tex]80.0-0.5 = 79.5[/tex]
[tex]111.0-0.5 = 110.5[/tex]
[tex]142.0-0.5 = 141.5[/tex]
[tex]173.0-0.5 = 172.5[/tex]
[tex]204.0-0.5 = 203.5[/tex]
[tex]235.0-0.5 = 234.5[/tex]
What is the solution to this system of equations?
Answer:
（2,1）
Step-by-step explanation:
the graph intersects at 2 and 1
To determine the organic material in a dried lake bed, the percent carbon by mass is measured at two different locations. To compare the means of the two different locations, it must first be determined whether the standard deviations of the two locations are different. For each location, calculate the standard deviation and report it with two significant figures.
Answer:
[tex]\sigma_1 = 0.08[/tex] --- Location 1
[tex]\sigma_2 = 0.34[/tex] --- Location 2
Step-by-step explanation:
Given
See attachment for the given data
Required
The standard deviation of each location
For location 1
First, calculate the mean
[tex]\bar x_1 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]
[tex]\bar x_1 =\frac{151.60}{5}[/tex]
[tex]\bar x_1 =30.32[/tex]
The standard deviation is calculated as:
[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]
[tex]\sigma_1 = \sqrt{0.007}[/tex]
[tex]\sigma_1 = 0.08[/tex]
For location 2
First, calculate the mean
[tex]\bar x_2 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]
[tex]\bar x_2 =\frac{152.2}{5}[/tex]
[tex]\bar x_2 =30.44[/tex]
The standard deviation is calculated as:
[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]
[tex]\sigma_2 = \sqrt{0.118}[/tex]
[tex]\sigma_2 = 0.34[/tex]
f it take 20 minutes to boil 6 crates of eggs, how much time will it take to boil 18 crates of eggs
a hour,.....................
y is inversely proportional to x when y=9, x=24
Answer:
216
Step-by-step explanation:
y=k÷x
k=xy
k=9×24
k=216
For any real number √a²
a
- |al
lal.
-a
Answer:
|a|
Step-by-step explanation:
For any positive or negative a, when you square it, the answer is positive.
The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.
Answer: |a|
A sample of 100 is drawn from a population with a proportion equal to 0.50. Determine the probability of observing between 43 and 64 successes.
Answer:
The probability of observing between 43 and 64 successes=0.93132
Step-by-step explanation:
We are given that
n=100
p=0.50
We have to find the probability of observing between 43 and 64 successes.
Let X be the random variable which represent the success of population.
It follows binomial distribution .
Therefore,
Mean,[tex]\mu=np=100\times 0.50=50[/tex]
Standard deviation , [tex]\sigma=\sqrt{np(1-p)}[/tex]
[tex]\sigma=\sqrt{100\times 0.50(1-0.50)][/tex]
[tex]\sigma=5[/tex]
Now,
[tex]P(43\leq x\leq 64)=P(42.5\leq x\leq 64.5)[/tex]
[tex]P(42.5\leq x\leq 64.5)=P(\frac{42.5-50}{5}\leq Z\leq \frac{64.5-50}{5})[/tex]
[tex]=P(-1.5\leq Z\leq 2.9)[/tex]
[tex]P(42.5\leq x\leq 64.5)=P(Z\leq 2.9)-P(Z\leq- 1.5)[/tex]
[tex]P(42.5\leq x\leq 64.5)=0.99813-0.06681[/tex]
[tex]P(43\leq x\leq 64)=0.93132[/tex]
Hence, the probability of observing between 43 and 64 successes=0.93132
3.
If 9x = 27, what is the value of x?
What is 2225 rounded to the nearest thousand? Hurry please
Answer:
2000
Step-by-step explanation:
2225 to the nearest 100 is 2300 but 3
<5 so it is 2000
HW HELP PLZZZZ ASAPPPP
Answer:
[tex]\frac{3v}{a^{2}} = h[/tex]
Step-by-step explanation:
[tex]v = \frac{1}{3} a^{2} h[/tex]
[tex]3v = a^{2} h[/tex]
[tex]\frac{3v}{a^{2}} = h[/tex]
Questions 23 and 29: Use the following information to answer each question. A recent book noted that only 20% of all investment managers outperform the Dow Jones Industrial Average over a five-year period. A random sample of 200 investment managers that had graduated from one of the top ten business programs in the country were followed over a five-year period. Fifty of these outperformed the Dow Jones Industrial Average. Let p be the true proportion of investment managers who graduated from one of the top ten business programs who outperformed the Dow Jones over a five-year period.
23. Based on the results of the sample, a 95% confidence interval for p is:
a. (1.95, 3.15)
b. (0.0195, 0 .0315)
c. (0.190, 0.310)
d. (0.028, 0.031)
e. (0.195, 0.315)
f. We can assert that p = 0.20 with 100% confidence, because only 20% of investment managers outperform the standard indexes.
24. Suppose you had been in charge of designing the study. What sample size would be needed to construct a margin of error of 2% with 95% confidence? Use the prior estimate of pâ=0.2 for this estimate.
a. n=2401
b. n=1537
c. n=16
d. n=1801
e. n>30
Suppose you wish to see if there is evidence that graduates of one of the top ten business programs performs better than other investment managers. Conduct a hypothesis test. Use a level of significance of α=0.05
25. Which of the following pairs of hypotheses is the most appropriate for addressing this question?
a. H0: p=0.2
Ha: p<0.2
b. H0: p=0.2
Ha: pâ 0.2
c. H0: p=0.2
Ha: p>0.2
d. H0: p<0.2
Ha: p=0.2
e. H0: pâ 0.2
Ha: p=0.2
f. H0: p>0.2
Ha: p=0.2
26. How many measurements must you have in order to assure that p^ is normally distributed?
a. nâ¥30
b. nâ¥5
c. npâ¥10 and n(1âp)â¥10
d. npâ¥5 and n(1âp)â¥5
27. The value of your test statistic is:
a. 1.768
b. 0.039
c. 1.923
d. 0.077
28. The P-value of your test is:
a. 1.768
b. 0.039
c. 1.923
d. 0.077
29. Is there sufficient evidence to conclude that graduates from the top ten business programs perform better than other investment managers?
a. Yes. I rejected H0
b. Yes. I failed to reject H0
c. Yes. I accepted Ha
d. No. I rejected H0
e. No. I failed to reject H0
f. No. I failed to accept Ha
Answer:
https://www.chegg.com/homework-help/questions-and-answers/questions-23-29-use-following-information-answer-question-recent-book-noted-20-investment--q13619465
Step-by-step explanation:
this might help you
If the sum of a number and one is triple, the result is five less than twice the number
Answer:
Step-by-step explanation:
3(x + 1 ) =2x - 5 This is the way the equation reads. Remove the brackets.
3x + 3 = 2x - 5 Subtract 2x from both sides
-2x -2x
x + 3 = - 5 Subtract 3 from both sides.
-3 -3
x = - 8
Graph Ex+ 3y = 24
a.
b.
c.
d.
Answer:
(b)
Step-by-step explanation:
Given
[tex]8x + 3y = 24[/tex]
Required
The graph
First, make y the subject
[tex]3y = 24 - 8x[/tex]
Divide through by 3
[tex]y = 8 - \frac{8}{3}x[/tex]
Let x = 3
[tex]y = 8 - \frac{8}{3}*3 = 8 - 8 = 0[/tex]
Let x = 6
[tex]y = 8 - \frac{8}{3}*6 = 8 - 16 = -8[/tex]
So, we plot the graph through
[tex](3,0)[/tex] and [tex](6,-8)[/tex]
See attachment for graph
Four times a number is 88 less than 6 times the number. Find the number.
Answer:
44
Step-by-step explanation:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
The number is 44.
To find the number.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).
Given that:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
Learn more about arithmetic here:
https://brainly.com/question/24163536
#SPJ2
g Vectors ???? and ???? are sides of an equilateral triangle whose sides have length 4. Compute ????⋅????. (Give your solution as a number to one decimal place.
Answer:
[tex]v \cdot w = 8.0[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]|v| = |w| = 4[/tex] --- the side lengths
Required
[tex]v \cdot w[/tex]
[tex]v \cdot w = |v| \cdot |w| \cdot (cos\theta)[/tex]
From the question, we understand that v and w are sides of an equilateral triangle.
This means that:
[tex]\theta = 60^o[/tex] --- angles in an equilateral triangle
So:
[tex]v \cdot w = |v| \cdot |w| \cdot (\cos 60)[/tex]
So, we have:
[tex]v \cdot w = 4 * 4 * 0.5[/tex]
[tex]v \cdot w = 8.0[/tex]
A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given below. At the 1% level of significance, test the claim that the sensory measurements are lower after hypnotism (scores are in cm. on a pain scale). Assume sensory measurements are normally distributed. Note: You do not need to type these values into Minitab Express; the data file has been created for you.Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6 After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0
Answer:
sensory measurement are lower after hypnotism
Step-by-step explanation:
Given the data :
Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6
After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0
The difference ;
After - Before, d = 0.2, - 4.1, - 1.6, - 1.8, - 3.2, - 2, - 2.9, - 9.6
Hypothesis :
H0 : μd = 0
H0 : μ < 0
The test statistic ;
T = μd / sd/√n
Where, xd = mean of difference
sd = standard deviation of difference
n = sample size
Mean of difference, μd = Σx/n = - 3.13
Standard deviation of difference, sd = 2.91
T = - 3.13 / 2.91/√8
T = - 3.13 / 1.0288403
T = - 3.042
α = 0.01
The Pvalue using a Pvalue calculator ;
Degree of freedom, df = n - 1 ; 8-1 = 7
Pvalue(-3.042, 7) = 0.00939
Pvalue < α ; we reject the null and conclude that sensory measurement are lower after hypnotism
If the range of the coordinate transformation (, ) = (−2,−3 +1) is (4, −2), (2, −5), (−6, 4), what is the domain?
A. (-2, 1), (-1, 2), (3, -1)
B. (-8, 7), (-4, 16), (19, -11)
C. (-8, 1), (-4, 2), (19, -1)
D. (-2, 7), (-1, 16), (3, -11)
Consider the below figure attached with this question.
Given:
The transformation is:
[tex]f(x,y)=(-2x,-3y+1)[/tex]
The range is (4,-2), (2, −5), (−6, 4).
To find:
The domain of the transformation.
Solution:
We have,
[tex]f(x,y)=(-2x,-3y+1)[/tex]
For the point (4,-2),
[tex](-2x,-3y+1)=(4,-2)[/tex]
On comparing both sides, we get
[tex]-2x=4[/tex]
[tex]x=\dfrac{4}{-2}[/tex]
[tex]x=-2[/tex]
And,
[tex]-3y+1=-2[/tex]
[tex]-3y=-2-1[/tex]
[tex]-3y=-3[/tex]
[tex]y=\dfrac{-3}{-3}[/tex]
[tex]y=1[/tex]
So, the domain of (4,-2) is (-2,1).
Similarly,
For the point (2,-5),
[tex](-2x,-3y+1)=(2,-5)[/tex]
On comparing both sides, we get [tex]x=-1,y=2[/tex]. So, the domain of (2,-5) is (-1,2).
For the point (-6,4),
[tex](-2x,-3y+1)=(-6,4)[/tex]
On comparing both sides, we get [tex]x=3,y=-1[/tex]. So, the domain of (-6,4) is (3,-1).
So, the domain of the given transformation is (-2, 1), (-1, 2), (3, -1).
Therefore, the correct option is A.
Eight more than one-half of a number is twenty-two. Find the number.
Answer:
Below.
Step-by-step explanation:
22-8 = 14x2 = 28.
What are the intercepts of the graphed function?
3
-2
Х
O x-intercept = (-1,0)
y-intercept = (-3,0)
O x-intercept = (0, -1)
y-intercept = (0, -3)
O x-intercept = (0, -1)
y-intercept = (-3,0)
x-intercept = (-1,0)
y-intercept = (0, -3)
6
Step-by-step explanation:
x intercept=(-1,0) because the graph is passing this point on the x axis
y intercept=(0,-3)
Answer:
4th option
Step-by-step explanation:
The x- intercept is where the graph crosses the x- axis.
This is at (- 1, 0 )
The y- intercept is where the graph crosses the y- axis.
This is at (0, - 3 )
Parallel Lines never intersect because...
Answer:
Parallel lines are lines that never intersect because they have the same slope (m). So, this means that they only possible difference in there equations is the y-intercept (b). ... The slope in each equation is one-half, but each equation has a different y-intercept.
The radius of a circle is 6 kilometers. What is the length of a 60° arc.
Answer:
6.284
Step-by-step explanation:
* means multiply
formula is arc length = radius * theta
theta is fancy way of saying
make degrees into radians
you have to make 60 degrees into radians
you do that by
60 * Pi/180 = Pi/3
then you multiply that with the radius
6 * Pi/3 = 2 * Pi = 6.284
write the following statement in symbolic mongo are delicious but expensive .
Step-by-step explanation:
let a=mangoes are delicious
b=mangoes are expensive
the symbolic form is a^b