Answer:
Step-by-step explanation:
Consider the augments matrix (the right most column is the extra vector).
[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]
By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix
[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]
Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.
In 2014, 2.756 billion dollars of e-cigarettes were sold worldwide. Fill in the table with the 2014 sales amount written in millions of dollars.
Answer:
$2756 million
Step-by-step explanation:
2.756×10⁹ = 2756×10⁶
Sales in 2014 were $2756 million.
_____
Comment on the question
In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.
Classify the following triangle .check all that apply
Answer:
acute and scalene
Step-by-step explanation:
Answer:no entiendo esta en ingles
Step-by-step explanation:
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: Sample Service Life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 What is the mean of the sampling distribution of sample means when the service life is in control
Answer:
[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
For the given scenario, it is known from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.
On three recent production batches, he tested service life on random samples of four headlamps.
We are asked to find the mean of the sampling distribution of sample means when the service life is in control.
Since we know that the population is normally distributed and a random sample is taken from the population then the mean of the sampling distribution of sample means would be equal to the population mean that is 500 hours.
[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]
Whereas the standard deviation of the sampling distribution of sample means would be
[tex]\text {standard deviation} = s = \frac{\sigma}{\sqrt{n} } \\\\[/tex]
Where n is the sample size and σ is the population standard deviation.
[tex]\text {standard deviation} = s = \frac{20}{\sqrt{4} } \\\\ \text {standard deviation} = s = \frac{20}{2 } \\\\ \text {standard deviation} = s = 10 \: hours \\\\[/tex]
Find the x- and y-intercepts of the equation 7x + 14y = 28.
Answer: The x-intercept is 4 and the y-intercept is 2.
Step-by-step explanation:
The x is intercept is when y is 0 and the y intercept is when x is 0.So using this information you can put in 0 for x and another 0 for y and solve for the x and y intercepts.
7(0) + 14y = 28
0 + 14y = 28
14y = 28
y = 2
7x + 14(0) = 28
7x + 0 = 28
7x = 28
x = 4
The [tex]x[/tex]-intercept of the given equation is [tex]4[/tex] and the [tex]y[/tex]-intercept is [tex]2[/tex].
Given:
The equation is:
[tex]7x+14y=28[/tex]
To find:
The [tex]x[/tex]-intercept and [tex]y[/tex]-intercept of the given equation.
Explanation:
We have,
[tex]7x+14y=28[/tex] ...(i)
Substitute [tex]x=0[/tex] in (i) to find the [tex]y[/tex]-intercept.
[tex]7(0)+14y=28[/tex]
[tex]14y=28[/tex]
[tex]\dfrac{14y}{14}=\dfrac{28}{14}[/tex]
[tex]y=2[/tex]
Substitute [tex]y=0[/tex] in (i) to find the [tex]x[/tex]-intercept.
[tex]7x+14(0)=28[/tex]
[tex]7x=28[/tex]
[tex]\dfrac{7x}{7}=\dfrac{28}{7}[/tex]
[tex]x=4[/tex]
Therefore, the [tex]x[/tex]-intercept of the given equation is [tex]4[/tex] and the [tex]y[/tex]-intercept is [tex]2[/tex].
Learn more:
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Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.
Market
Weekly Gross Revenue
($100s)
Television Advertising
($100s)
Newspaper Advertising
($100s)
Mobile
101.3
5
1.5
Shreveport
51.9
3
3
Jackson
74.8
4
1.5
Birmingham
126.2
4.3
4.3
Little Rock
137.8
3.6
4
Biloxi
101.4
3.5
2.3
New Orleans
237.8
5
8.4
Baton Rouge
219.6
6.9
5.8
(a) Use the data to develop an estimated regression with the amount of television advertising as the independent variable.
Let x represent the amount of television advertising.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x
Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(b) How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?
If required, round your answer to two decimal places.
%
(c) Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.
Let x1 represent the amount of television advertising.
Let x2 represent the amount of newspaper advertising.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x1 + x2
Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(d) How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?
If required, round your answer to two decimal places.
%
(e) Given the results in part (a) and part (c), what should your next step be? Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(f) What are the managerial implications of these results?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
A sample of 500 nursing applications included 60
from men. Find the 90% confielence interval
for the
true proportion of men who applied to the nursing
program.
Answer:
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 500
sample proportion
[tex]p = \frac{x}{n} = \frac{60}{500} = 0.12[/tex]
Level of significance ∝= 0.90 or 0.10
90% confidence interval for the true proportion of men who applied to the nursing program.
[tex](p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })[/tex]
On calculation , we get
( 0.12 - 0.02326 , 0.12 + 0.02326)
(0.09674 ,0.14326)
Final answer:-
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
A tree casts an 8-foot shadow on the ground. The length from the tip of the shadow to the top of the tree is 17 feet. What is the height of the tree?
Answer:
Height of tree = 15 ft
Step-by-step explanation:
Given:
Length of shadow (Base) = 8 ft
Length from the tip to top of the tree (Hypotenues) = 17 ft
Find:
Height of tree = ?
Computation:
Using Pythagoras theorem:
[tex]Height\ of\ tree = \sqrt{Hypotenues^2 - base^2} \\\\Height\ of\ tree = \sqrt{17^2 - 8^2} \\\\Height\ of\ tree = \sqrt{289-64}\\\\Height\ of\ tree = \sqrt{225}\\\\ Height\ of\ tree =15[/tex]
Height of tree = 15 ft
Answer:
The answer is 15 feet from the ground to the top of the tree.
Step-by-step explanation:
The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2500. A random sample of 36 intermediate level executives is selected. What is the probability that the mean annual salary of the sample is between $71000 and $73500?
Answer:
11.51% probability that the mean annual salary of the sample is between $71000 and $73500
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 normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 74000, \sigma = 2500, n = 36, s = \frac{2500}{\sqrt{36}} = 416.67[/tex]
What is the probability that the mean annual salary of the sample is between $71000 and $73500?
This is the pvalue of Z when X = 73500 subtracted by the pvalue of Z when X = 71000. So
X = 73500
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{73500 - 74000}{416.67}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151
X = 71000
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{71000 - 74000}{416.67}[/tex]
[tex]Z = -7.2[/tex]
[tex]Z = -7.2[/tex] has a pvalue of 0.
0.1151 - 0 = 0.1151
11.51% probability that the mean annual salary of the sample is between $71000 and $73500
Please help. I’ll mark you as brainliest if correct!
Answer:
[tex]\sqrt{-6} \sqrt{-384}=\sqrt{(-6)(-384)}=\sqrt{2304}=48\\ a=48\\b=0[/tex]
or
[tex]a=-48\\b=0[/tex]
both solutions are correct because root square has two solutions, one positive and one negative.
Answer:
a= -48
b=0
Step-by-step explanation:
[tex]\sqrt[]{-6} = i\sqrt{6}[/tex]
[tex]\sqrt{-384} =i\sqrt{384}[/tex]
[tex](i\sqrt{6} )(i\sqrt{384} )[/tex]
[tex]i^{2} \sqrt{2304}[/tex]
(-1)(48) = -48
a + bi
a= -48
b= 0
The probability of drawing a pearl bead out of a bag of mixed beads is 2/3. What is the probability of drawing a bead which is not a pearl?
Answer:
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
Step-by-step explanation:
For each bead that you draw, there are only two possible outcomes. Either it is a pearl bead, or it is not. The sum of these probabilities = 100% = 1.
So
2/3 probability of drawing a pearl bead.
p probability of drawing a non pearl bead.
What is the probability of drawing a bead which is not a pearl?
[tex]p + \frac{2}{3} = 1[/tex]
[tex]p = 1 - \frac{2}{3}[/tex]
[tex]p = \frac{3*1 - 2}{3}[/tex]
[tex]p = \frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
22,056 people went to the baseball game on Sunday. Half as many people came on money. How many people were at the baseball game on Sunday and Monday altogether?
Answer:33084
Step-by-step explanation:
22056 divided by 2 = Monday
Monday= 11028
11028+22056=33084
Answer:
33084 People were at the baseball game on Sunday and ~Money~ Monday all together.
Step-by-step explanation:
Sunday - 22056
Monday - "Half as many" 22056 Divided by 2
= 11028
Altogether - Sunday + Monday = 33084
As a shortcut on your calculator, you could do:
22056 + (22056 divided by 2)
= 33084
What is the difference? Negative 6 minus (11)
Answer:
-17
Step-by-step explanation:
-6-11=-17
Answer:
the answer is -17
Step-by-step explanation:
Please help . I’ll mark you as brainliest if correct! Only the one marked with an X is wrong . I don’t get it
Answer:
(x+7)² = 9
Step-by-step explanation:
x² + 14x + 40 = 0
(x² + 14x) + 40 = 0
(x² +14x +49) + 40 - 49 = 0
(x+7)² - 9 = 0
(x+7)² = 9
Hope this helps!
Answer:
(x+7)² = 9
Step-by-step explanation:
What letter completes the puzzle? The answer is probably easy for you guys but I don't understand how the letters go along with the puzzle. Thank you!
Answer:
the answer is E the number at the top tells you which position it falls under in the alphabet
A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?
Answer:
[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]
[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
What single decimal multiplier would you use to increase by 7% followed by a 4% decrease?
Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93
Step-by-step explanation:
A newspaper posted this question on its web "How often do you seek medical information online?" Of 1072 Internet users who chose to respond, 38% of them responded with "frequently." What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? What is wrong with this type of sampling method? What term is used to describe this type of survey? Select all that apply.
What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond?
a. The respondents are a census.
b. The respondents are a population.
c. The respondents are a voluntary response sample.
d. The respondents are a self-selected sample.
What is wrong with this type of sampling method?
a. The survey question is "loaded," or intentionally worded to elicit a desired response.
b. It is too expensive.
c. Many people may choose not to respond to the survey.
d. Responses may not reflect the opinions of the general population.
e. It is too time consuming
Answer:
1. Option c
2. Option d
Step-by-step explanation:
This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.
This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.
Part A: The respondents are a voluntary response sample (Option C)
Part B: Responses may not reflect the opinions of the general population (Option D)
The total number of internet users = 1072
Percentage of the total number of people that chose to respond = 38%
Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.
Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.
In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples
The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population
Learn more on sampling methods here: https://brainly.com/question/16587013
A rectangle has an area of 96 cm2 The length of the rectangle is 4 cm longer than the width. Work out the length and width of the rectangle.
Match each linear equation with the name of its form.
y=-x+8
slope-intercept form
2x - 5y = 9
standard form
y + 6 = -3(x - 1)
point-slope form
Answer:
y + 6 = -3(x - 1) - Point Slope
y=-x+8 - Slope Intercept
2x - 5y = 9 - Standard
Step-by-step explanation:
Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]
y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.
Slope-intercept form is: [tex]y=mx+b[/tex]
y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.
This only leaves 2x - 5y = 9, which is in standard form.
All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
All the expressions are,
1) y = -x + 8
2) 2x - 5y = 9
3) y + 6 = -3(x - 1)
Now, All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
Learn more about the mathematical expression visit:
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#SPJ2
Really in need of help :( please !
Answer:
A
Step-by-step explanation:
(2,1) - only one in the table. Remember (x,y)
A public relations firm found that only 27% of voters in a certain state are satisfied with their U.S. senators. How large a sample of voters should be drawn so that the sample proportion of voters who are satisfied with their senators is approximately normally distributed?a) 38b) 14c) 10d) 48
Answer:
a) 38
Step-by-step explanation:
The normal distribution can be applied if:
[tex]np \geq 5[/tex] and [tex]n(1-p) \geq 5[/tex]
In this question:
[tex]p = 0.27[/tex]
Then
a) 38
n = 38.
Then
38*0.27 = 10.26
38*0.73 = 27.74
Satisfies. But is this the smallest sample of the options which satisfies.
b) 14
n = 14
Then
14*0.23 = 3.22
14*0.77 = 10.78
Does not satisfy
c) 10
Smaller than 14, which also does not satisfy, so 10 does not satisfy.
d) 48
Greater than 38, which already satisfies. So the answer is a)
The method of Problem 20 can be extended to second order equations with variable coefficients. If y1 is a known nonvanishing solution of y′′ + p(t)y′ + q(t)y = 0, show that a second solution y2 satisfies (y2 /y1 )′ = W (y1 , y2 )/y21 , where W (y1 , y2 ) is the Wronskian of y1 and y2 . Then use Abel’s formula [Eq. (23) of Section 3.2] to determine y2 .
Answer:24y
Step-by-step explanation:
The total energy need during pregnancy is normally distributed, with a mean of 2600 kcal/day and a standard deviation of 50 kcal/day. Include your Normal curve for all parts! a) [4 pts] If one pregnancy is randomly selected, find the probability that the total energy need is more than 2650 kcal/day. b) [4 pts] The middle 30% of total energy need during pregnancy are between what values? c) [4 pts] What is the probability that a random sample of 20 pregnant women has a mean energy need of more than 2625 kcal/day?
Answer:
a) 0.3085
b) 2574
c) 0.0125
Step-by-step explanation:
mean (μ) = 2600 kcal/day and a standard deviation (σ) = 50 kcal/day
a) The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{x-\mu}{\sigma}=\frac{2650-2600}{50}=1[/tex]
From the normal distribution table, P(x > 2650) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587
b) A probability of 30% corresponds with a z score of -0.52
[tex]z=\frac{x-\mu}{\sigma}\\-0.52=\frac{x-2600}{50} \\x-2600=-26\\x=2600-26\\x=2574[/tex]
c) For a sampling distribution of sample mean, the standard deviation is [tex]\frac{\sigma}{\sqrt{n} }[/tex]
The z score is given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]
n = 20
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} }}=\frac{2625-2600}{\frac{50}{\sqrt{20} }}=2.24[/tex]
From the normal distribution table, P(x > 2625) = P(z > 2.24) = 1 - P(z < 2.24) = 1 - 0.9875 = 0.0125
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
670
Step-by-step explanation:
2003-814=1189
1189-519=670
Answer: The third number is 670.
Step-by-step explanation:
The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.
814 + 519 + x = 2003 where x is the third number
1333 + x = 2003
-1333 -1333
x = 670 So the third number is 670
Check:
814 + 670 + 519 = 2003
2003 = 2003 so yes again 670 is the third number.
Given the following diagram, are and opposite rays? yes no
Answer:
Where is the diagram?
Step-by-step explanation:
Answer:
OC and OE are apposite rays so the Answer is yes
A glucose solution is administered intravenously into the bloodstream at a constant rate r. As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at that time. Thus a model for the concentration C = C(t) of the glucose solution in the bloodstream is dC/dt = r - kC where k is a positive constant. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
Answer:
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
[tex]C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex] we can conclude that the function is an increasing function.
Step-by-step explanation:
Given that:
[tex]\dfrac{dC}{dt}= r-kC[/tex]
[tex]\dfrac{dC}{r-kC}= dt[/tex]
By taking integration on both sides ;
[tex]\int\limits\dfrac{dC}{r-kC}= \int\limits \ dt[/tex]
[tex]- \dfrac{1}{k}In (r-kC)= t +D[/tex]
[tex]In(r-kC) = -kt - kD \\ \\ r- kC = e^{-kt - kD} \\ \\ r- kC = e^{-kt} e^{ - kD} \\ \\r- kC = Ae^{-kt} \\ \\ kC = r - Ae^{-kt} \\ \\ C = \dfrac{r}{k} - \dfrac{A}{k}e ^{-kt} \\ \\[/tex]
[tex]C(t) =\frac{ r}{k} - \frac{A}{k}e^{ -kt}[/tex]
where;
A is an integration constant
In order to determine A, we have C(0) = C0
[tex]C(0) =\frac{ r}{k} - \frac{A}{k}e^{0}[/tex]
[tex]C_0 =\frac{r}{k}- \frac{A}{k}[/tex]
[tex]C_{0} =\frac{ r-A}{k}[/tex]
[tex]kC_{0} =r-A[/tex]
[tex]A =r-kC_{0}[/tex]
Thus:
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
b ) Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
[tex]C_{0} < \lim_{t \to \infty }C(t)[/tex]
[tex]C_0 < \dfrac{r}{k}[/tex]
[tex]kC_0 <r[/tex]
The equation for C(t) can therefore be re-written as :
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
[tex]C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]
Thus; we can conclude that the above function is an increasing function.
Solve the equation and state a reason for each step.
23+11a-2c=12-2c
Simplifying
23 + 11a + -2c = 12 + -2c
Add '2c' to each side of the equation.
23 + 11a + -2c + 2c = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a + 0 = 12 + -2c + 2c
23 + 11a = 12 + -2c + 2c
Combine like terms: -2c + 2c = 0
23 + 11a = 12 + 0
23 + 11a = 12
Solving
23 + 11a = 12
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-23' to each side of the equation.
23 + -23 + 11a = 12 + -23
Combine like terms: 23 + -23 = 0
0 + 11a = 12 + -23
11a = 12 + -23
Combine like terms: 12 + -23 = -11
11a = -11
Divide each side by '11'.
a = -1
Simplifying
a = -1
Indicate in standard form equation of the line passing through the given 
Answer:
x - 3y= -14
Step-by-step explanation:
Slope is rise over run
m = (6-5)/(4-1) = 1/3
we write in slope-intercept form:
y = 1/3x + b
solve for b by plugging in either point
i'm going to plug in H
5 = 1/3 + b
b = 14/3
we get our equation
y = 1/3x + 14/3
now re-write it in standard form
-1/3x + y = 14/3
make it pretty
x - 3y = -14
Is f(x) continuous at x equals 4? Why or why not? A. No, f(x) is not continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. Yes, f(x) is continuous at x equals 4 because f (4 )exists. C. No, f(x) is not continuous at x equals 4 because f (4 )is undefined. D. Yes, f(x) is continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )equals f (4 ).
Corrected Question
Is the function given by:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
continuous at x=4? Why or why not? Choose the correct answer below.
Answer:
(D) Yes, f(x) is continuous at x = 4 because [tex]Lim_{x \to 4}f(x)=f(4)[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
A function to be continuous at some value c in its domain if the following condition holds:
f(c) exists and is defined.[tex]Lim_{x \to c}$ f(x)[/tex] exists. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]At x=4
[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]Therefore: [tex]Lim_{x \to 4}f(x)=f(4)=2[/tex]
By the above, the function satisfies the condition for continuity.
The correct option is D.
