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
The speed of the light is approximately 3x10^14 centimeters per second.how much will it take light to Tavel 9x10^14 centimeters
Answer:
3 seconds
Step-by-step explanation:
First, let's calculate the approximate speed of light.
3 · 10^14 = 3 · 100,000,000,000,000
= 300,000,000,000,000
Approximately, light travels 300,000,000,000,000 centimeters per second.
Now, let's simplify 9x10^14.
9 · 10^14 = 9 · 100,000,000,000,000
= 900,000,000,000,000
To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.
900,000,000,000,000/300,000,000,000,000 = 3
Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.
It will take 3 seconds to cover the distance of 9×10¹⁴ cm.
What is scientific notation?We use the scientific notation of numbers to write very large numbers in compact form.
In the scientific form, we write a number in the form of base×10ⁿ.
Where 0 ≤ base < 10 and n can be any rational number.
Given the speed of light s approximately 3×10¹⁴ cm/sec.
∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.
We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.
learn more about scientific notation here :
https://brainly.com/question/18073768
#SPJ2
The following list shows the colours of a random selection of sweets.
red green red blue pink red
yellow pink blue yellow red yellow
Select the type of the data.CHOOSE ONE PLEASE HELP
Discrete
Continuous
Categorical
Quantitative
Answer:
Categorical or Continuous.
Step-by-step explanation:
Because the red appears in each colours (continuous)
Which graph best represents the equation –x + 2y = 4?
Answer:
C
Step-by-step explanation:
Convert the equation into slope intercept form : y=mx+b
2y=x+4
y=1/2x + 2
The m is the slope and the b is the y intercept
In this equation, the slope is 1/2 and the y intercept is 2
The only graph with y intercept 2 is C
Show why (2×3×7)^4 = 2^4 × 3^4 × 7^4 show work
[tex] {a}^{m} \times {b}^{m} = ( {ab)}^{m} [/tex]
(2×3×7)⁴=(2×3)⁴×7⁴(2×3×7)⁴=(2×3×7)⁴RHS=LHSplease mark this answer as brainlist
Find the equation of the midline of the function y = 2 sin(1∕4x) – 3.
A) y = –3
B) y = 3
C) y = 2
D) y = 1∕4
Explanation:
The general sine equation is
y = A*sin(B(x-C)) + D
where the D variable directly determines the midline. In this case, D = -3, so that corresponds to a midline of y = -3
The sine curve oscillates going up and down, passing through this middle horizontal line infinitely many times. See the graph below.
Answer:
A) y = –3
Step-by-step explanation:I took the test
Can someone help
Me please?
9514 1404 393
Answer:
minimum: 2 at x=0maximum: 10 at x=10Step-by-step explanation:
When looking for extremes, one must consider both the turning points and the ends of the interval. Here, there is a relative minimum at x=7, and a relative maximum at x=3. However, the values at the ends of the interval are more extreme than these.
The absolute minimum on the interval is 2 at x=0.
The absolute maximum on the interval is 10 at x=10.
-36 = 6(2-8n) please
Answer:
n=1
Step-by-step explanation:
-36 = 6(2-8n)
-36=12-48n
-36-12=-48n
-48=-48n
n=1
The population of a city increased from 23,400 to 27,800 between 2008 and 2012. Find the change of population per year if we assume the change was constant from 2008 to 2012.
Find the amount of the increase:
27800 - 23400 = 4,400
Find number of years: 2012 - 2008 = 4 years
Divide amount of change by number of years:
4,400 / 4 = 1,100 people per year.
A 10-sided die is rolled. Find the probability of rolling an even number. The set of equally likely outcomes is shown below. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The probability of rolling an even number on a 10-sided die is:
Answer:
1/2
Step-by-step explanation:
There are ten sides on this die. As stated in your question, there are five even numbers and five odd numbers. If we take the amount of even numbers over the total, you get 5/10, which simplifies to 1/2.
The probability of rolling an even number on a 10 - sided die is 1/2 or 0.5
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
The value of probability lies between 0 and 1
Given data ,
Let the data set be S = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
So , the number of elements in the data set = 10 elements
Now , in order to get an even number when dolling the dice ,
The set of possible outcomes P = { 2 , 4 , 6 , 8 , 10 }
The number of elements in the data set P of outcomes = 5 elements
So , the probability of getting an even number from the data set when rolling a 10 sided dice is P ( x ) =
number of elements in the data set P of outcomes / number of elements in the data set
The probability of getting an even number from the data set when rolling a 10 sided dice is P ( x ) = 5 / 10
The probability P ( x ) = 1/2
= 0.5
Hence , The probability of rolling an even number on a 10 - sided die is 1/2 or 0.5
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ2
Which of the following choices is equivalent to the equation below?
5(2x−1) = 5(5x−14)
A 2x − 1 = 5x − 14
B 5(2x − 1) = 5x − 14
C 2x − 1 = 5
D None of these choices are correct.
Answer:
2x-1 = 5x-14
Step-by-step explanation:
5(2x−1) = 5(5x−14)
Divide each side by 5
5/5(2x−1) = 5/5(5x−14)
2x-1 = 5x-14
Answer:
A.
Step-by-step explanation:
5(2x−1) = 5(5x−14)
10x - 5 = 25x - 70
65 = 15x
x = 13/3.
Take Option A.
2x - 1 = 5x - 14
3x = 13
x = 13/3 so its this one.
B: 10x - 5 = 5x - 14
5x = -9
x = -9/5 so NOT B.
C. simplifies to x = 3. so NOT C.
In a survey of 938 U.S. adults, 235 say the phrase "you know" is the most annoying conversational phrase. Let p be the proportion of the population who respond yes. Use the given information to Construct a 90% confidence interval for p.
Answer:
CI 90% = ( 0.227 ; 0.273)
Step-by-step explanation:
Information from the survey:
sample size n = 938
number of people with yes answer x = 235
proportion of people p = 235/938
p = 0.25 then q = 1 - 0.25 q = 0.75
Confidence Interval 90 % .
CI 90% = ( p ± SE )
CI 90% = ( p ± z(c)*√(p*q)/n)
CI 90 % then significance level is α = 10 % α/2 = 5%
α/2 = 0.05 we find in z-table z (c) = 1.64
√(p*q)/n = √0.25*0.75/938
√(p*q)/n = √0.000199
√(p*q)/n = 0.014
CI 90% = ( p ± z(c)*√(p*q)/n)
CI 90% = ( 0.25 ± 1.64*0.014)
CI 90% = ( 0.25 ± 0.023 )
CI 90% = ( 0.227 ; 0.273)
modeled by a cylinder with diameter 15 feet
the question is in the photo. it is asking for 2 answers
9514 1404 393
Answer:
2nd force: 99.91 lbresultant: 213.97 lbStep-by-step explanation:
In the parallelogram shown, angle B is the supplement of angle DAB:
∠B = 180° -77°37' = 102°23'
Angle ACB is the difference of angles 77°37' and 27°8', so is 50°29'.
Now, we know the angles and one side of triangle ABC. We can use the law of sines to solve for the other two sides.
BC/sin(A) = AB/sin(C)
AD = BC = AB·sin(A)/sin(C) = (169 lb)sin(27°8')/sin(50°29') ≈ 99.91 lb
AC = AB·sin(B)/sin(C) = (169 lb)sin(102°23')/sin(50°29') ≈ 213.97 lb
The hiking trail 2600 miles long and passes through fourteen states. Because it is their first time hiking the trail, Janet and kellen plan to start hiking in Georgia and hike 416 miles. What percent of the trail will they hike?
Answer:
They will hike 16% of the trail in Georgia.
Step-by-step explanation:
We have that:
The hiking trail is of 2600 miles.
416 of those miles are in Georgia?
What percent of the trail will they hike?
Georgia distance multiplied by 100% and divided by the total distance. So
416*100%/2600 = 16%
They will hike 16% of the trail in Georgia.
- Mean test score was 200 with a standard deviation of 40- Mean number of years of service was 20 years with a standard deviation of 2 years.In comparing the relative dispersion of the two distributions, what are the coefficients of variation
Answer:
The correct answer is "Test 20%, Service 10%".
Step-by-step explanation:
As we know,
The coefficient of variation (CV) is:
⇒ [tex]CV=\frac{Standard \ deviation}{Mean}\times 100[/tex]
Now,
CV of test will be:
= [tex]\frac{40}{200}\times 100[/tex]
= [tex]20[/tex] (%)
CV of service will be:
= [tex]\frac{2}{20}\times 100[/tex]
= [tex]10[/tex] (%)
What number increased by 30% is 34.5
Answer:
44.85
Step-by-step explanation:
There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85
What is the formula for the volume of a pyramid?
V = πr2h
V = 3/4πr2h
V = 1/3πr2h
V = 1/3Bh
How do you write it in digits
27 million, 200
Answer:
27,000,200
Step-by-step explanation:
Going by basic math you know a million has six 0's.
So; one million is represented as 1,000,000.
Hence twenty-seven million as 27,000,000.
Using you tens, hundreds and thousands you'll know 200 will fall into the last area.
HELP ME PLEASE I NEED HELP
Answer:
1. 3-5
2. 5-3
3. 3-5
4. 5-3
Step-by-step explanation:
This is simple! Just get rid of the parenthesis for each of the expressions shown.
3 + (-5)
the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes
3 - 5
Now do the same for the rest!
For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]
Hope this helps !!
-Ketifa
3. An elevator is moving upward with a speed of 14.3 m/s . Two seconds later, the elevator is still moving upward, but its speed bas been reduced to 3.7 m/s . What is the average acceleration of the clevator during the 2.0 interval?
By definition of average acceleration,
a (average) = (3.7 m/s - 14.3 m/s) / (2.0 s) = -5.3 m/s²
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
Test scores: n = 92, = 90.6, σ = 8.9; 99% confidence
Options:
A.) 88.2 < μ < 93.0
B.) 88.4 < μ < 92.8
C.) 89.1 < μ < 92.1
D.) 88.8 < μ < 92.4
Answer: Choice A.) 88.2 < μ < 93.0
=============================================================
Explanation:
We have this given info:
n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence levelBecause n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).
At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.
The lower bound of the confidence interval (L) is roughly
L = xbar - z*sigma/sqrt(n)
L = 90.6 - 2.576*8.9/sqrt(92)
L = 88.209757568781
L = 88.2
The upper bound (U) of this confidence interval is roughly
U = xbar + z*sigma/sqrt(n)
U = 90.6 + 2.576*8.9/sqrt(92)
U = 92.990242431219
U = 93.0
Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)
When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.
We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0
Which points are also part of this set of equivalent ratios? Select all that apply.
a. (3, 2)
b. (4, 2)
c. (4, 8)
d. (8, 4)
e. (12, 6)
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Answered by GAUTHMATH
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Step-by-step explanation:
the person above me is correct
2(3+ ‐ 4)(7‐3)÷(2‐ ‐2)
Simplify: −4(b+6)−2b(1−4b
Step-by-step explanation:
-4b-24-2b+8b2
8b2-6b-24=0
One angle of an isosceles triangle is 16 what are the other 2 angles
Answer:
other two angle will be
82
as 82+82+16 = 180'
can someone help me pls
Answer:
D NO IS THE WRITE ANSWER .
Answer:
D)
Step-by-step explanation:
A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands. Using the data from the two brands, what would be the standard error of the estimated difference, Dp = A – B, if it were believed that the two population proportions were, in fact, equal (i.e., )?
Answer:
The standard error of the estimated difference is of 0.0313.
Step-by-step explanation:
To solve this question, 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.
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]
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.
Brand A:
33 out of 197, so:
[tex]p_A = \frac{33}{197} = 0.1675[/tex]
[tex]s_A = \sqrt{\frac{0.1675*0.8325}{197}} = 0.0266[/tex]
Brand B:
25 out of 290, so:
[tex]p_B = \frac{25}{290} = 0.0862[/tex]
[tex]s_B = \sqrt{\frac{0.0862*0.9138}{290}} = 0.0165[/tex]
What would be the standard error of the estimated difference?
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.0266^2+0.0165^2} = 0.0313[/tex]
The standard error of the estimated difference is of 0.0313.
What is the image of (-4, -12) after a dilation by a scale factor of centered at the 1/4 origin?
9514 1404 393
Answer:
(-1, -3)
Step-by-step explanation:
Each coordinate is multiplied by the dilation factor when dilation is centered at the origin.
(1/4)(-4, -12) = (-1, -3) . . . . the image of the given point
The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?
Answer:57*91547
Step-by-step explanation:
