Complete question is;
The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?
Answer:
dC/dt = 49.45
Step-by-step explanation:
Since C(x) = ⅔x² + 6x + 45
And x(t) = 0.3t² + 0.04t
This means that;
C(x) = C(x(t))
The rate at what cost is changing with respect to time is given as;
dC/dt
Thus, from chain rule;
dC/dt = (dC/dx) × (dx/dt)
dC/dx = (4/3)x + 6
dx/dt = 0.6t + 0.04
Now, when t = 5, then;
x(5) = 0.3(5)² + 0.04(5)
x = 7.7
Thus;
dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267
At 5 hours,
dx/dt = 0.6(5) + 0.04 = 3.04
Thus;
dC/dt = 16.267 × 3.04
dC/dt = 49.45
use de moivre's theorem to write
[2(cos 12 degrees + i sin 12 degrees)]^5
in standard form
DeMoivre's theorem says
(2 (cos(12°) + i sin(12°)))⁵ = 2⁵ (cos(5×12°) + i sin(5×12°))
… = 32 (cos(60°) + i sin(60°))
… = 32 (1/2 + √3/2 i )
… = 16 + 16√3 i
write your answer in simplest radical form
Answer:
[tex]9\sqrt{3}[/tex]
Step-by-step explanation:
This is a 30-60-90 triangle.
It's good to remember this. The side length opposite to the 60 degree angle is always the base multiplied by [tex]\sqrt{3}[/tex]
Answer:
9√3.
Step-by-step explanation:
tan 60 = √3
So w/9 =√3
w = 9√3
Emma went out shopping with her father and bought a dress that cost $40.00. In class, she
learned to find the sales tax by multiplying by .08 (the sales tax in her state is 8%). Emma
found the tax, and then added the tax to the original amount. Emma's mother suggested that
she should just multiply the cost of the dress by 1.08 and that this method would give her the
final answer with the tax included. Emma was confused. Who is right? Work it out both ways
and explain your thinking.
Answer:
Both ways are correct
If you multiply the cost by 8% and add, you will still get 108% as your total.
Answer:
Both ways are correct
Step-by-step explanation:
Father's way is ( 40 × 0.08 ) + 40 = $43.2
Mothers way is 40 × 1.08 = $43.2
Simplify the following expression.
(1565)
———-
(562)3
The correlation coefficient, r, between the prices of smartphones, x, and the number of sales of phones, y, equals −0.63.
Select the statement which best describes the relationship between the price and sales.
The value of r indicates that the number of sales decreases as the price decreases.
The value of r indicates that the number of sales decreases as the price stays the same.
The value of r indicates that the number of sales decreases as the price increases.
The value of r indicates that the number of sales is not related to the price.
I think its (C): The value of r indicates that the number of sales decreases as the price increases.
Answer:
(C) The value of r indicates that the number of sales decreases as the price increases.
ED2021.
The best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.
What is a Negative Correlation Coefficient?A negative correlation coefficient has a negative sign, and implies a negative relationship between two variables.
This means that, as one variable decreases, the other variable increases.
Thus, a correlation coefficient of -0.63 shows a negative relationship between prices of smartphones and the number of sales.
Therefore, the best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.
Learn more about correlation coefficient on:
https://brainly.com/question/4219149
Mr. Allway’s math class surveyed all the seventh-grade students to find out their favorite sport. The following circle graph shows a breakdown of the survey findings.
Find the number of degrees represented by Basketball.
108°
101°
11°
140°
Answer:
101 is the answer of the question
Answer:
101 degrees
Step-by-step explanation:
First you add all the percentages
39 + 28 + 30 + 3 = 100%
To find the number of degrees of basketball you multiply 28% by 360 because it’s a circle.
28/100 * 360 = 10,080/100 = 100.8 ~ 101
PLEASE HELPPPPPP!!!!! THIS IS DUE ASAP PLEASEEE
Answer:
1
Step-by-step explanation:
list the numbers that are odd or greater than 2
1,2,3,4,5,6
aka every single outcome
therefore the answer is just 1
Answer:
5/6
Step-by-step explanation:
The possible outcomes are 1,2,3,4,5,6
Odd numbers are 1,3,5
Greater than 2 are 3,4,5,6
Good solutions are 1,3,4,5,6 = 5 outcomes
P( odd or greater than 2) = good solutions / total
= 5/6
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
Answer:
The first three terms in the geometric sequence are 18, 24, 32.
Step-by-step explanation:
A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]
Given
[tex]x = 1, y = 7, z = 15[/tex]
We know
[tex]\alpha _1 = 1+t[/tex]
[tex]\alpha _2 = 7+t[/tex]
[tex]\alpha _3 = 15+t[/tex]
Recall that a geometric sequence is in the form
[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]
Therefore, once [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,
[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]
To find the ratio, for
[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]
we know
[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]
Therefore,
[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]
[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]
The ratio is therefore
[tex]r=\dfrac{4}{3}[/tex]
Therefore, the first three terms in the geometric sequence are 18, 24, 32.
The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume the variable is normally distributed.
Answer:
The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.
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.
The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.
This means that [tex]\mu = 2000, \sigma = 100[/tex]
A sample of 20 cables is selected and tested.
This means that [tex]n = 20, s = \frac{100}{\sqrt{20}} = 22.361[/tex]
Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.
This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.645 = \frac{X - 2000}{22.361}[/tex]
[tex]X - 2000 = -1.645*22.361[/tex]
[tex]X = 1963.2[/tex]
The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.
Help me with this math problem !!!
Answer:
multiply the numerator together and denominator together
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Use a 0.05 significance level to test the claim that the volumes of Bubbly Beverage filled by the old machine vary more than the volumes of juice filled by the new machine.
Answer:
We Reject the Null, H0 and conclude that the volume of juice filled by old machine varies more than volume filled by new machine
Step-by-step explanation:
Given the data:
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
Sample size, n = 10
Using calculator :
s1² = 0.37889.
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Sample size, n = 9
s2² = 0.006111
Hypothesis :
H0 : s1² = s2²
H1 : s1² > s2²
New machine :
s2² = 0.006111 ; n = 9
Using the Ftest :
Ftest statistic = larger sample variance / smaller sample variance
Ftest statistic = 0.37889 / 0.006111
Ftest statistic = 62.0
Decision region :
Reject H0 ; If Test statistic > Critical value
The FCritical value at 0.05
DFnumerator = 10 - 1 = 9
DFdenominator = 9 - 1 = 8
Fcritical(0.05, 9, 8) = 3.388
Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine
Convert 37.5% to a fraction. (Reduce your answer to lowest terms.)
Answer:
3/8
Step-by-step explanation:
The value of 37.5% reduced to the lowest terms is 15/40.
What is a fraction?A fraction is written in the form p/q, where q ≠ 0. Fractions are of two types they are proper fractions and improper fractions. Fractions can also be converted into percentages by multiplying them by 100.
We know e can convert percentages into decimals and fractions by dividing the percentage value by hundred.
Given we have to convert 37.5% as a fraction which is,
= 37.5/100.
= 375/1000.
= 75/200.
= 15/40.
learn more about percentages here :
https://brainly.com/question/24159063
#SPJ2
Find the Sample size for 99% confidence level with a margin of error of 4% and p unknown.
Answer:
za/2: Divide the confidence level by two, and look that area up in the z-table: .95 / 2 = 0.475. ...
E (margin of error): Divide the given width by 2. 6% / 2. ...
: use the given percentage. 41% = 0.41. ...
: subtract. from 1.
Help me please, is it d?
Answer:
Yes D is the correct answer :)
Answer:
Yes, D
Step-by-step explanation:
Can someone help me? I don’t know how to solve the rest. I am struggling and I would be so happy if any of you helped me. Thank you for your help!
When x = 12, the value of the expression is ???
Choose the slope-intercept form of 3x + 2y = 5.
3.
у==x
5
2.
O
O y=-x+
5
0
5
v=-x+
O
yox
5
3
Answer:
y = -3x/2 + 5/2
Step-by-step explanation:
Well, basically what you do is modify it so that y is on one side.
3x+2y = 5
2y = 5-3x
y = (5-3x)/2
y = 5/2 -3x/2
So, the answer is the second option.
Answer:
B
Step-by-step explanation:
3x + 2y = 5
Our goal is this form:
y = mx + b
- move 3x to right anc change its sign
2y = -3x + 5
- divide each member by 2
y = -3/2 x + 5/2
The starting line up for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard. There are four forwards and six guards from which to choose the line up. If the starting players are chosen at random, what is the probability that the two brothers will end up in the starting line up
Answer:
0.25 = 25% probability that the two brothers will end up in the starting line up
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the players are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[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]
Desired outcomes:
Matthew plus another forward from a set of 3.
Tony plus another two guards from a set of 5.
So
[tex]D = C_{3,1}C_{5,2} = \frac{3!}{1!2!} \times \frac{5!}{2!3!} = 3*10 = 30[/tex]
Total outcomes:
Two forwards from a set of 4.
Three guards from a set of 6.
So
[tex]T = C_{4,2}C_{6,3} = \frac{4!}{2!2!} \times \frac{6!}{3!3!} = 6*20 = 120[/tex]
What is the probability that the two brothers will end up in the starting line up?
[tex]p = \frac{D}{T} = \frac{30}{120} = 0.25[/tex]
0.25 = 25% probability that the two brothers will end up in the starting line up
what is the value of f'(6) if the formula is f(x)=-8x-3
Explanation:
Applying the derivative to f gets us
f(x) = -8x - 3
f ' (x) = -8
The fact that f(x) being linear directly means that the derivative is simply the slope value. No matter what we replace x with, the result is always -8.
Answer:
f'(6) = -8
Step-by-step explanation:
f(x)=-8x-3
First find the derivative of the function
f'(x) = -8
This is a constant so when x=6 it will be -8
f'(6) = -8
PLS HELP !! Is the following a fair sampling of the contents of the jar? Why?
Pour a 2” layer of lentils into a jar. Then pour a 2” layer of kidney beans into the jar. Then pour a 2” layer of pinto beans into the jar. Stir the contents of the jar well. Then pull out a handful of beans.
write
the following numbers using Roman numerals 20
Step-by-step explanation:
xx is the Roman number of 20
The SAT and ACT college entrance exams are taken by thousands of students each year. The scores on the exam for any one year produce a histogram that looks very much like a normal curve. Thus, we can say that the scores are approximately normally distributed. In recent years, the SAT mathematics scores have averaged around 480 with standard deviation of 100. The ACT mathematics scores have averaged around 18 with a standard deviation of 6.
a. An engineering school sets 550 as the minimum SAT math score for new students. What percent of students would score less than 550 in a typical year?
b. What would the engineering school set as comparable standard on the ACT math test?
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
Answer:
a) 75.8% of students would score less than 550 in a typical year.
b) The comparable standard would be a minimum ACT score of 22.2.
c) 0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
Step-by-step explanation:
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.
Question a:
SAT, so mean of 480 and standard deviation of 100, that is, [tex]\mu = 480, \sigma = 100[/tex]
The proportion is the p-value of Z when X = 550. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{550 - 480}{100}[/tex]
[tex]Z = 0.7[/tex]
[tex]Z = 0.7[/tex] has a p-value of 0.758.
0.758*100% = 75.8%
75.8% of students would score less than 550 in a typical year.
b. What would the engineering school set as comparable standard on the ACT math test?
ACT, with a mean of 18 and a standard deviation of 6, so [tex]\mu = 18, \sigma = 6[/tex]
The comparable score is X when Z = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.7 = \frac{X - 18}{6}[/tex]
[tex]X - 18 = 0.7*6[/tex]
[tex]X = 22.2[/tex]
The comparable standard would be a minimum ACT score of 22.2.
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
This is 1 subtracted by the p-value of Z when X = 700, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 480}{100}[/tex]
[tex]Z = 2.2[/tex]
[tex]Z = 2.2[/tex] has a p-value of 0.9861.
1 - 0.9861 = 0.0139
0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
create a graph of 4.95 + 3.99
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
Graph 5 and it’s opposite on the number line
Answer:
See pic below.
Step-by-step explanation:
The opposite of 5 is -5.
If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as
V=5000 (1-1/50*t)^2 0⤠t ⤠50.
1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
a. 5 min
b. 10 min
c. 20 min
d. 50 min
2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?
Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation
answer:
1) a) -180 gallons/minute ,
b) -160 gallons/minute
c) -120 gallons/minute
d) 0
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins
Step-by-step explanation:
Volume of tank = 5000 gallons
Time to drain = 50 minutes
Volume of water remaining after t minutes by Torricelli's law
V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )
1) Determine the rate at which water is draining from the tank
First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank
V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]
a) After t = 5minutes
V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]
= -180 gallons/minute
b) After t = 10 minutes
V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]
= - 160 gallons/minute
c) After t = 20 minutes
V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]
= -120 gallons/minute
d) After t = 50 minutes
V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]
= 0 gallons/minute
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins because no water flows out after 50 minutes
When a teacher in a private school points out to her high school principal that since there are empty seats in all classrooms, the cost of additional students is really zero, she is using the
Answer:
The answer is "Principal of marginal analysis".
Step-by-step explanation:
To determine unless the benefits of even an aggressive resource would outweigh its costs, and therefore increase utility, individuals and businesses can use a valuation model to compare the risks versus the benefits of more activities, like whether to create or consuming more. It's the amount during which net value is greater than or equal to marginal cost that's the optimal quantity in this situation. The amount where the marginal social cost curve and consumer surplus line connect.
10-[5-{6+2 (7-7-4)}]
Answer:
might be wrong too
Step-by-step explanation:
hope u like it
10-[5-{6+2(7-7-4)}]=10-[5-{6+2×(-4)}]=10-[5-2]=10-3=7
Which is an example of using an open-ended question to uncover a problem? O a) "Do you have a problem you'd like addressed today?" b) "Is there a problem? C) "What seems to be the problem?" O d) "Can I help you?"
Answer:
(D)
Step-by-step explanation:
i think dat is an open ended question
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
Answer:
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Solve the equation by factoring: 5x^2 - x = 0
Answer:
Step-by-step explanation:
x = 0, 1/5
