Answer:
f'(x) = 6/x
Step-by-step explanation:
1. Use logarithm rules to move the power to the front so ln(x)^6 becomes 6 ln(x).
2. Differentiate ln(x) which is always 1/x
3. multiply 1/x by the 6
6/x
A film on TV starts at 8:30 pm. If the film takes 136 minutes, at
what time does it end?
Answer:
10:46
Step-by-step explanation:
8:30 + 136 min.
= 8:30 + 2:16
= 10:46
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees based on the region of the country the warehouse is located. She randomly selects 35 employees who work in warehouses on the East Coast (Group 1) and 35 employees who work in warehouses in the Midwest (Group 2) and records the number of parts shipped out from each for a week.
She finds that East Coast group ships an average of 1276 parts and knows the population standard deviation to be 347.
The Midwest group ships an average of 1439 parts and knows the population standard deviation to be 298.
Using a 0.01 level of significance, test if there is a difference in productivity level. What is the test statistic?
(Round to 4 decimal places)
z =
please use excel to solve
Answer:
The test statistic is z = -2.11.
Step-by-step explanation:
Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Group 1: Sample of 35, mean of 1276, standard deviation of 347.
This means that:
[tex]\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537[/tex]
Group 2: Sample of 35, mean of 1439, standard deviation of 298.
This means that:
[tex]\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712[/tex]
Test if there is a difference in productivity level.
At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = \mu_1 - \mu_2 = 1276 - 1439 = -163[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-163 - 0}{77.3144}[/tex]
[tex]z = -2.11[/tex]
The test statistic is z = -2.11.
The length of a rectangle is 3 yd longer than its width.
If the perimeter of the rectangle is 70 yd, find its length and width.
Answer:
Length= 19
Width=16
Step-by-step explanation:
(16x2)+(19x2)=70
38+32=70
Initially Sam receives $40 and every year she receives a deposit that increases the amount by $20 from
the previous year. Find the total amount deposited by her 18th birthday.
Answer:
1080
Step-by-step explanation:
13. Describe the type of solution for the
linear system of equations given below.
(x+4y=7
8y = 14 - 2x
Answer: infinite solutions
Step-by-step explanation:
I'm a bit confused about this, can anyone help? Giving 69 points to whoever answers by 12:30 PM (PST)!!
Find the area of the polygon:
Answer: i can give you tips of how to find the area of a polygon.
OK SO To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides.
Step-by-step explanation:
And you have to add all the sides of the lengths of the sum of the polygon
Select the expressions that are equivalent to 9p + 8p.
A. 17p
B. 2p + 16p
C. p • 17
D. 3p + 13p
A. 17p
Step-by-step explanation:
hope this helps ya :)
Plz help me well mark brainliest if you are correct!!
Answer:
don't know sorry
Step-by-step explanation:
Cher works in retail sales. Her salary is $400 plus 15% commission on weekly
sales.
Find her sales for the week if her wages for the week is $940.
Answer:
Sales of the week = 3600
Step-by-step explanation:
Given - Cher works in retail sales. Her salary is $400 plus 15% commission on weekly sales.
To find - Find her sales for the week if her wages for the week is $940.
Solution -
Let us assume that,
Her sales of the week = x
Now,
Given that, Her salary is $400 plus 15% commission on weekly sales.
So,
Equation of salary becomes
Salary = 400 + [tex]\frac{15}{100}x[/tex]
i.e.
Salary = 400 + 0.15x .......(1)
Now,
Given that,
her wages for the week is $940.
i.e. Salary = $940
Put in equation (1), we get
940 = 400 + 0.15x
⇒0.15x = 940 - 400
⇒0.15x = 540
⇒x = 3600
∴ we get
Sales of the week = x = 3600
It takes 2 minutes to fill a tank with 16 gallons of gasoline.
Answer:
and the question is...
Step-by-step explanation:
Find the slope, x-intercept, and y-intercept of the lines with the given equations.
y=2x+4
Answer:
here you go! y = 2 x + 4. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side. 2x+4=y. 2 x + 4 = y. Subtract 4 from both sides. Subtract 4 from both sides. 2x=y-4. 2 x = y − 4
Answer:
2, 4, -2
Step-by-step explanation:
The slope is directly in the equation, the variable m in the slope-intercept form of y = mx + b. This means that the slope is 2.
The y-intercept is the variable b in standard form, so 4 in this case.
To find the x-intercept, set y equal to zero.
0 = 2x + 4
2x = -4
x = -2
Find the midpoint of the segment with the following endpoints
(-8, 9) and (0, 1)
Answer:
(-4,5)
x-midpoint -4
y-midpoint 5
Step-by-step explanation:
M=x1+x2/2 ,y1+y2/2
M=-8+0/2 , 9+1/2
M=-8/2,10/2
M=-4,5
x-midpoint -4
y-midpoint 5
Russell surveyed 16 students at his school and found that 4 of them planned to take orchestra as their next elective. If Russell surveys 12 more students, how many of them are probably planning on taking orchestra as an elective, based on past data?
Answer:3
Step-by-step explanation:
The probability that the number of students who take orchestra as an elective is 1/4 and the number of students who joined extra is 4
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the number of students who take orchestra as an elective be represented as P
Now , the equation will be
The total number of students = 16 students
The number of students who opted for orchestra as elective = 4 students
So , the probability that the number of students who take orchestra as an elective P = number of students who opted for orchestra as elective / total number of students
Substituting the values in the equation , we get
The probability that the number of students who take orchestra as an elective P = 4/16
The probability that the number of students who take orchestra as an elective P = 1/4 = 25 %
Now , when the number of students = 16 + 12 = 28 students
The probability that the number of students who take orchestra as an elective P₁ = ( x + 4 ) / 28
Substituting the values in the equation , we get
1/4 = ( x + 4 ) / 28
Multiply by 28 on both sides of the equation , we get
x + 4 = 7
Subtracting 4 on both sides of the equation , we get
x = 3 students
So , the number of students who will take orchestra from the group of 12 students is 3 students
Hence , the probability is 1/4
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Question 6
2 pts
Charlotte invested $100 per year into a business for 3 years. The total value of her
investment after 3 years is represented by the algebraic expression below, where x is the
growth in value each year.
100 (x3 + x2 + x)
What is the total value of her investment when x = 2?
O $6400
O $1200
O $600
O $1400
evan is sending a package of some of his produce to his friend in California. The package measures 12 by 9 by 6 inches. He wraps it in brown paper, addresses it, and takes it to the post office to mail. How much brown paper will he need to wrap the box ____in2
Answer:
[tex]468in^{2}[/tex]
Step-by-step explanation:
L=12
W=9
H=6
2lw+2lh+2wh=468
Many think ts, "oh LWH" well actually lwh is volume
The brown paper required to wrap the package is 468 square inches.
What is a cuboid?A cuboid is a three-dimensional shape in which all sides are rectangles. A cuboid has 6 faces, 8 vertices, and 12 edges. All the angles formed at the vertices of a cuboid are right angles. The opposite edges are parallel to each other.
For the given situation,
The diagram shows the package that is cuboid in shape.
The dimensions of cuboid are
The length of the cuboid = 12 in
The wide of the cuboid = 9 in
The height of the cuboid = 6 in
The package is wrapped using the brown paper. The brown paper needed can be calculated by using the surface area formula,
[tex]A=2(lw+hl+hw)[/tex]
⇒ [tex]A=2[(12)(9)+(6)(12)+(6)(9)][/tex]
⇒ [tex]A=2[108+72+54][/tex]
⇒ [tex]A=2[234][/tex]
⇒ [tex]A=468[/tex]
Hence we can conclude that the brown paper required to wrap the package is 468 square inches.
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Find the zeros of the function y=x(x+2)(x-4)
Answer:
first x= -2
second x= 2
third x= 4
A sample of 300 subscribers to a particular magazine is selected from a population frame of 9,000 subscribers. If, upon examining the data, it is determined that no subscriber had been selected in the sample more than once:________.
A. the sample could not have been random
B. the sample may have been selected without replacement or with replacement
C. the sample had to have been selected without replacement
D. the sample had to have been selected with replacement
Answer:
C
Step-by-step explanation:
It is determined that no subscriber had been selected in the sample more than once the sample had to have been selected without replacement.
What is the sample?A sample is a subset of data drawn from a larger population by a researcher using a predetermined selection process. These components are referred to as sample points, sampling units, or observations.
If it is determined that no subscriber had been selected in the sample more than once, this means that each subscriber was only included once in the sample. This can only occur if the sample was selected without replacement, meaning that each subscriber was selected once and only once from the population frame.
Therefore, the correct answer is C. the sample had to have been selected without replacement.
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pls help finding this out
What is the value of x in the solution to this system of equations?
5x+2y=67x=3y−7
Answer:
x=4/29, y=77/29
Step-by-step explanation:
Write the algebraic expression: 4p times the sum of 7 and 5p
Answer:
4p(7 + 5p)
Step-by-step explanation:
4p times the sum of 7 and 5p
4p(7 + 5p)
lemme explain, im a middle schooler and my school just jumped into this with no explanation.
Answer:
the first question is c
Step-by-step explanation:
2 x pi x the radius
2 x 3.14 x 8
Which statement is true for the values of Pand Q on this number line? + Q + -2 1 -4 -3 0 1 A 응 4 B. PxQ5 C P+Q> -4 D P - Qo
Indiana now has 8 different area codes. How many different phone numbers are available within Indiana if the numbers can repeat? Remember that phone numbers have an area code followed by 7 digits.
Answer:
Well, this could turn out to be a simple permutation problem: you have ten number choices (0-9) for each digit of a phone number and repetitions are allowed. Technically, there could be as many as \begin{align*}10^{10} = 10,000,000,000\end{align*}, or 10 billion possible phone numbers.
Step-by-step explanation:
:D
How is everbody doing today?
Answer:
:)))))))))))))))))) boring
Answer:
Doing alright.
Thanks for asking.
Step-by-step explanation:
Select the converse, inverse, and contrapositive of this theorem. If two lines intersect, then the vertical angles formed are equal.
1) If the vertical angles are not equal, then lines do not intersect.
2) If the two lines do not intersect, then the vertical angles are not equal.
3) If the vertical angles are equal, then the two lines intersect.
options: (use one for each statement)
Converse
Inverse
Contrapostive
sentence:-
If two lines intersect, then the vertical angles formed are equal.
p[tex]\bold{\dashrightarrow}[/tex]q1) If the vertical angles are not equal, then lines do not intersect.
it is CONTRAPOSITIVE~q[tex]\bold{\dashrightarrow}[/tex]~p2) If the two lines do not intersect, then the vertical angles are not equal.
it is INVERSE~p[tex]\bold{\dashrightarrow}[/tex]~q3) If the vertical angles are equal, then the two lines intersect.
it is CONVERSEq[tex]\bold{\dashrightarrow}[/tex]p[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
◇[tex] sentence:-[/tex]
If two lines intersect, then the vertical angles formed are equal.
1) If the vertical angles are not equal, then lines do not intersect.
◇[tex]\sf{it is CONTRAPOSITIVE}[/tex]
2) If the two lines do not intersect, then the vertical angles are not equal.
◇[tex]\sf{it is INVERSE}[/tex]
3) If the vertical angles are equal, then the two lines intersect.
◇[tex]\sf{it is CONVERSE}[/tex]
Two angles are complementary. One has a measure of 25 degrees. What is the measure of the other angle
90 degrees
65 degrees
25 degrees
155 degrees
9514 1404 393
Answer:
(b) 65 degrees
Step-by-step explanation:
When angles are complementary, their total is 90°. The measure of the other angle is ...
90° -25° = 65° . . . . . the measure of the other angle
Accounting
A company borrowed $68000 on September 1st, 2020. Principle and interest at 12% will be paid on August 31, No accrual was made for interest in 2020. What is the adjustment for interest.
Answer: $2,720
Step-by-step explanation:
Assuming the payment will be done in 2021 on August 31, that means that the loan period is a year.
In this case, the interest should be apportioned per month. There are four months in 2020 that the loan was active for so these months should have an adjustment for interest:
Total interest = 12% * 68,000
= $8,160
Monthly rate is:
= 8,160 / 12 months
= $680
There are 4 months in 2020 so the interest for 2020 is:
= 680 * 4
= $2,720
A box, containing 25 bolts and 25 washers, has a mass of 475 g. Another box, containing 17 bolts and 34 washers, has a mass of 442 g. Determine the mass of one bolt and the mass of one washer
Answer:
bolts=12g and washers=7 g
Step-by-step explanation:
honestly, i tried to solve this by hand and made an error somewhere, but i set up two equations, then tried to use elimintation to solve for one variable. but in the end i went to my trusty calculator and created a matrix, then used the rref math to solve. sorry i couldnt be of more help
The National Collegiate Athletic Association (NCAA) requires colleges to report the graduation rates of their athletes. At one large university, 91% of all students who started their studies in 2000-2010 graduated within 6 years. A sports reporter contacted 152 athletes randomly sampled from that same university and time period and found that 132 of them had graduated within 6 years.
(a) (5 points) Perform the appropriate hypothesis test to determine whether this is significant evidence that the percentage of athletes who graduate is less than for the student population at large, using the significance level a = 0.05. Remember for state the null and alternative hypotheses, the decision rule, and your conclusion.
(b) (3 points) Calculate the P-value for this test. Explain how this P-value can be use to test the hypotheses in part (a).
Answer:
a)
The null hypothesis is [tex]H_0: p = 0.91[/tex].
The alternate hypothesis is [tex]H_1: p < 0.91[/tex].
The decision rule is: accept the null hypothesis for [tex]z > -1.645[/tex], reject the null hypothesis for [tex]z < -1.645[/tex].
Since [tex]z = -1.79 < -1.645[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
b)
The p-value for this test is 0.0367. Since this p-value is less than the significance level of [tex]\alpha = 0.05[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
Step-by-step explanation:
Question a:
Perform the appropriate hypothesis test to determine whether this is significant evidence that the percentage of athletes who graduate is less than for the student population at large:
At the null hypothesis, we test if the proportion is the same as the student population, of 91%. Thus:
[tex]H_0: p = 0.91[/tex]
At the alternate hypothesis, we test that the proportion for athletes is less than 91%, that is:
[tex]H_1: p < 0.91[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Test if the proportion is less at the 0.05 level:
The critical value is z with a p-value of 0.05, that is, z = -1.645. Thus, the decision rule is: accept the null hypothesis for [tex]z > -1.645[/tex], reject the null hypothesis for [tex]z < -1.645[/tex].
0.91 is tested at the null hypothesis:
This means that [tex]\mu = 0.91, \sigma = \sqrt{0.91*0.09}[/tex]
A sports reporter contacted 152 athletes randomly sampled from that same university and time period and found that 132 of them had graduated within 6 years.
This means that [tex]n = 152, X = \frac{132}{152} = 0.8684[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.8684 - 0.91}{\frac{\sqrt{0.91*0.09}}{\sqrt{152}}}[/tex]
[tex]z = -1.79[/tex]
Since [tex]z = -1.79 < -1.645[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
(b) (3 points) Calculate the P-value for this test. Explain how this P-value can be use to test the hypotheses in part (a).
The p-value of the test is the probability of finding a sample proportion of 0.8684 or below. This is the p-value of z = -1.79.
Looking a the z-table, z = -1.79 has a p-value of 0.0367.
The p-value for this test is 0.0367. Since this p-value is less than the significance level of [tex]\alpha = 0.05[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
In a recent international sport competition, the top three countries—Country A, Country B, and Country C—won a total of 124 medals. Country B won 13 more medals than Country C. Country A won 34 more medals than the total amount won by the other two. How many medals did each of the top three countries win?
Answer:
Country A won 79 medals, country B won 29 medals and country C won 16 medals.
Step-by-step explanation:
This question is solved by a system of equations.
I am going to say that:
Country A won x medals.
Country B won y medals.
Country C won z medals.
Total of 124 medals:
This means that [tex]x + y + z = 124[/tex].
Country B won 13 more medals than Country C.
This means that [tex]y = z + 13[/tex]
Country A won 34 more medals than the total amount won by the other two.
This means that:
[tex]x - (y + z) = 34[/tex]
From the first equation, we have that:
[tex]y + z = 124 - x[/tex]
So
[tex]x - (y + z) = 34[/tex]
[tex]x - (124 - x) = 34[/tex]
[tex]2x - 124 = 34[/tex]
[tex]2x = 158[/tex]
[tex]x = \frac{158}{2}[/tex]
[tex]x = 79[/tex]
Finding z:
Since [tex]x = 79, y = z + 13[/tex]
[tex]x + y + z = 124[/tex]
[tex]79 + z + 13 + z = 124[/tex]
[tex]2z + 92 = 124[/tex]
[tex]2z = 32[/tex]
[tex]z = \frac{32}{2} = 16[/tex]
Finding y:
[tex]y = z + 13 = 16 + 13 = 29[/tex]
Country A won 79 medals, country B won 29 medals and country C won 16 medals.