Answer:48
Step-by-step explanation:
Given
Amar wants 12 tablespoons of sugar in water.
Amar has teaspoon whose four times is equivalent to 1 tablespoon
i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]
therefore
[tex]12 tablespoon is 4\times 12[/tex]
[tex]\Rightarrow 4\times 12[/tex]
[tex]\Rightarrow 48\ \text{teaspoons}[/tex]
So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade
Answer:6328565394729
Step-by-step explanation:213
sorry
A construction company has to complete a project no later than 4 months from now or there will be significant cost overruns. The manager of the construction company believes that there are four possible values for the random variable X, the number of months from now it will take to complete this project: 2, 2.5, 3, and 3.5. It is currently believed that the probabilities of these four possibilities are .4, .3, .2, and .1, respectively. What is the expected completion time (in months) of this project from now?
Answer:
The expected completion time of this project from now is 2.5 months.
Step-by-step explanation:
To find the expected completion time for the project, we multiply each projection by it's probability.
We have that:
0.4 = 40% probability it takes 2 months to complete the project.
0.3 = 30% probability that it takes 2.5 months to complete the project.
0.2 = 20% probability it takes 3 months to complete the project.
0.1 = 10% probability it takes 3.5 months to complete the project.
What is the expected completion time (in months) of this project from now?
E = 0.4*2 + 0.3*2.5 + 0.2*3 + 0.1*3.5 = 2.5
The expected completion time of this project from now is 2.5 months.
The accompanying data are the times to failure (in millions per cycle) of high-speed turbine engine bearings made out of two different compounds. These were taken from "Analysis of Single Classification Experiments Based on Censored Samples from the Two-parameter Weibull Distribution" by J.I. McCool (The Journal of Statistical Planning and Inference, 1979) Compound 1 3.03 5.53 5.60 9.30 9.92 12.51 12.95 15.21 16.04 16.84 Compound 2 3.19 4.26 4.47 4.53 4.67 4.69 5.78 6.79 9.37 12.75 (a) Find the 0.84 quantile of the Compound 1 failure times (b) Give the coordinates of the two lower-left points that would appear on a normal plot of the compound 1 data (c) Make back-to-back stem-and-leaf plots for comparing the life length properties of bearings made from Compounds 1 and 2 (d) Make (to scale) side-by-side boxplots for comparing the life lengths for the two compounds. Mark numbers on the plots indicating the locations of their main features (e) Compute the sample means and standard deviations of the two sets of lifetimes (f) Describe what your answers to parts (c), (d), and (e) above indicate about the life lengths of these turbine bearings.
Find the given attachments
Which flight has the fastest average speed
Answer:
Fastest wind speed ever recorded
That is, however, a patch on the top speed ever reached by an aircraft, a record held by the Lockheed Blackbird, which tickled 2,193mph in 1976
Step-by-step explanation:
The data from the data sample o 10 paired observations are shown:
Pair Population 1 Population 2
1 19 24
2 25 27
3 31 36
4 52 53
5 49 55
6 34 34
7 59 66
8 47 51
9 17 20
10 51 55
1. If you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses?
2. Assuming that the within-pair differences are approximately normally distributed, conduct
the test using α = 0.1. What is your decision.
3. Find a 90% confidence interval for µd.
Answer:
Step-by-step explanation:
Corresponding means for population 1 and population 2 form matched pairs.
The data for the test are the differences between the mean for population 1 and mean for population 2.
μd = the mean for population 1 minus the mean for population 2.
Population 1 population 2 diff
19 24 - 5
25 27 - 2
31 36 - 5
52 53 - 1
49 55 - 6
34 34 0
59 66 - 7
47 51 - 4
17 20 - 3
51 55 - 4
Sample mean, xd
= (- 5 - 2 - 5 - 1 - 6 + 0 - 7 - 4 - 3 - 4)/10 = - 3.7
xd = - 3.7
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (- 5 + 3.7)^2 + (- - 2 + 3.7)^2 + (- 5 + 3.7)^2+ (- 1 + 3.7)^2 + (- 6 + 3.7)^2 + (0 + 3.7)^2 + (- 7 + 3.7)^2 + (- 4 + 3.7)^2 + (- 3 + 3.7)^2 + (- 4 + 3.7)^2 = 73.7
Standard - eviation = √(73.7/10
sd = 2.71
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.7 - 0)/(2.71/√10)
t = - 4.32
We would determine the probability value by using the t test calculator.
p = 0.00097
Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
3) for population 1,
Mean = (19 + 25 + 31 + 52 + 55 + 34 + 59 + 47 + 17 + 51)/10 = 38.4
Summation(x - mean)² = (19 - 38.4)^2 + (25 - 38.4)^2 + (31 - 38.4)^2+ (52 - 38.4)^2 + (49 - 38.4)^2 + (34 - 38.4)^2 + (59 - 38.4)^2 + (47 - 38.4)^2 + (17 - 38.4)^2 + (51 - 38.4)^2 = 2042.4
Standard deviation, s1 = √2042.4/10 = 14.3
for population 2,
Mean = (24 + 27 + 36 + 53 + 55 + 34 + 66 + 51 + 20 + 55)/10 = 42.1
Summation(x - mean)² = (24 - 42.1)^2 + (27 - 42.1)^2 + (36 - 42.1)^2 + (53 - 42.1)^2 + (55 - 42.1)^2 + (34 - 42.1)^2 + (66 - 42.1)^2 + (51 - 42.1)^2 + (20 - 42.1)^2 + (55 - 42.1)^2 = 2248.9
Standard deviation, s2 = √2248.9/10 = 15
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18
z = 1.734
x1 - x2 = 38.4 - 42.1 = - 3.7
√(s1²/n1 + s2²/n2) = √(14.3²/10 + 15²/10)
= 6.55
Margin of error = 1.734 × 6.55 = 11.4
The 90% confidence interval is
- 3.7 ± 11.4
Using the following data on the Observations 10, 13, 4, and 20 confirm that the complete linkage distance between the cluster containing 《10, 13) and the cluster containing (4, 20) s 2.577 units as displayed in the dendrogram
Observation
13 20 0.032 0.195 -0510 0.466 0.741 0.8750.207 0.474 0.700 0.748 -0.004 -0.490 -0.892 0.735 0.219 0.655 -0.1731.013 0.943 0.083 -0.693 -0.489-0.702 -0.458 1.620 2.275 1328 1.733 -0.863 1.035 0.724 0.721 10 Income/Debt Return Cost Load Peak Sales TotalFuelCosts
If required, round your answers to three decimal places.Do not round intermediate calculations
1. Distance from Observation 10 and Observation 4:
2. Distance from Observation 10 and Observation 20:
3. Distance from Observation 13 and Observation 4:
4. Distance from Observation 13 and Observation 20:
Answer:
Step-by-step explanation:
The distance between:
10 and 4: 1.492
10 and 20: 2.055
13 and 4: 2.577
13 and 20: 2.226
The R code:
#Convert your datafile into csv and make sure your row names are 10,13,4 and 20
data=read.csv(file.choose())
data
row.names(data)=c(10,13,4,20)
data
d=dist(data,method="euclidean")
d
fit=hclust(d,method="complete")
plot(fit)
groups=cutree(fit,k=2)
rect.hclust(fit,k=2,border="red")
how to find a local minimum of a function?
Answer:
Find the places where the derivative is zero and the second derivative is positive.
Step-by-step explanation:
By definition, a function has a minimum where the first derivative is zero and the second derivative is positive.
That will be a "local" minimum if there are other points on the function graph that have values less than that. It will be a "global" minimum if there are no other function values less than that. A global minimum is also a local minimum.
__
On a graph, a local minimum is the bottom of the "U" where the graph changes from negative slope to positive slope.
help me about this integral
The gradient theorem applies here, because we can find a scalar function f for which ∇ f (or the gradient of f ) is equal to the underlying vector field:
[tex]\nabla f(x,y,z)=\langle2xy,x^2-z^2,-2yz\rangle[/tex]
We have
[tex]\dfrac{\partial f}{\partial x}=2xy\implies f(x,y,z)=x^2y+g(y,z)[/tex]
[tex]\dfrac{\partial f}{\partial y}=x^2-z^2=x^2+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=-z^2\implies g(y,z)=-yz^2+h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=-2yz=-2yz+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]
where C is an arbitrary constant.
So we found
[tex]f(x,y,z)=x^2y-yz^2+C[/tex]
and by the gradient theorem,
[tex]\displaystyle\int_{(0,0,0)}^{(1,2,3)}\nabla f\cdot\langle\mathrm dx,\mathrm dy,\mathrm dz\rangle=f(1,2,3)-f(0,0,0)=\boxed{-16}[/tex]
123 grams is rounded to nearest whole. Write down the minimum possible mass it could have been.
Answer:
The nearest whole is 122.99 repeated
Step-by-step explanation:
I need help solving this
Answer:
The answer is the first one on the bottom left.
Step-by-step explanation:
Which formula can be used to describe the sequence? - 2/3, -4, -24, -144
Answer:
They are all multiplied by 6
Answer:
Geometric sequence.
Step-by-step explanation:
Here are the terms :
-2/3, -4, -24, -144
Now the first term T1 = -2/3
The second Term T2 = -4
But T2/T1 = -4÷ -2/3 = -4 x -3/2 = 6
Similarly Term 3, T3 = -24
T3/T2 = -24/-4= 6
Hence the expression is a geometric sequence.
a×r^(n-1); a is the first term
r is the common ratio 6
n is the number of terms.
From which point of view is the story told?
Answer:
there are 5 types of point of views
please brainliest me
Step-by-step explanation:
1rst person: Writing in first person means writing from the author's point of view or perspective. This point of view is used for autobiographical writing as well as narrative.
2 person: The second-person point of view belongs to the person (or people) being addressed. This is the “you” perspective. Once again, the biggest indicator of the second person is the use of second-person pronouns: you, your, yours, yourself, yourselves.
3 person: In the third-person point of view, a narrator tells the reader the story, referring to the characters by name or by the third-person pronouns he, she, or they.
4 person: The term fourth person is also sometimes used for the category of indefinite or generic referents, which work like one in English phrases such as "one should be prepared" or people in people say that..., when the grammar treats them differently from ordinary third-person forms."
5 person:From a fifth person perspective, one starts to “feel” the system in a different way, recognizing that one's own perspective on and in the Anthropocene is merely a perspective, which itself is a perspective, which in turn is a perspective.
please help i dont know how to answer this
Answer:
The answer is s / s + 3
Step-by-step explanation:
I applied the fraction rule a/b divided by c/d = a/b times c/d
Please mark BRAINLIEST!
Sander bought 5 bags of nuts. Each bag costs $5.69.
How much did Sander spend for the nuts?
Enter your answer in the box.
Answer:
28.45.
Step-by-step explanation:
5 x 5.69
a football team had 50 players at the start of the season, but then some players left the team. After that, the team had 42 players
Answer:
50 = p + 42
Step-by-step explanation:
The unknown part of this equation is the variable p, the number of people that left. So you want to add p to 42 and that will give you the total number of football players, which is 50. In order to get p, you need to get it by itself and make it equal something. Subtract 42 from both sides and you are stuck with 50-42 = p
p = 8
Answer:
50-p=42
Step-by-step explanation:
x/2 = -5 solve for x
Answer:
[tex]x=-10[/tex]
Step-by-step explanation:
[tex]\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10[/tex]
A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:
Car Radial-Tires Belted-Tires
1 4.2 4.1
2 4.7 4.9
3 6.6 6.2
4 7.0 6.9
5 6.7 6.8
6 4.5 4.4
7 5.7 5.7
8 6.0 5.8
9 7.4 6.9
10 4.9 4.7
11 6.1 6.0
12 5.2 4.9
A two-sample t-test was used to compare the mean kilometers per liter for the two types of tires using a .05 level of significance. The resulting p-value was .0152.
State the null and alternate hypotheses, state whether the null hypothesis should be rejected or not rejected and your reason for that conclusion, state the meaning of that conclusion specifically in terms of the problem being studied.
Answer:
Step-by-step explanation:
Corresponding gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used form matched pairs.
The data for the test are the differences between the gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used.
μd = the gasoline consumption when radial tires is used minus the gasoline consumption when regular belted tires is used.
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The resulting p-value was .0152.
Since alpha, 0.05 > than the p value, 0.0152, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the gasoline consumption when regular belted tires is used is higher than the gasoline consumption when radial tires is used.
Graph: y = 3/4 x + 5
Answer: The graph is
The graph is plotted and attached.
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is y = 3/4 x + 5
The slope of the line is (3/4)
and the y intercept is 5.
The graph is plotted and attached with the answer.
To know more about Function
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Use any method to multiply (-14ab)(a + 3b - 4c).
Answer:
-14a^2b-42ab^2+56abc
Step-by-step explanation:
You can use the FOIL method
multiply the first numbers
then inner
then outer
then last
3. Find the mean and range of the following data.
14, 14, 15, 15, 16, 15, 15, 16
A 15; 15
B 12; 15
C 12; 2
D 15; 2
Answer:
D: 15 and 2
Step-by-step explanation:
Mean
To find the mean, or average, add up all the values in the data set,then divide by the number of values in the data set.
1. Add up all the values
Values: 14, 14, 15, 15, 16, 15, 15, 16
Add them :14+14+15+ 15+16+15+15+16=120
120
2. Divide by the number of values
Count how many numbers are in the data set. In this case there are 8. Divide 120 by 8.
120/8=15
The mean is 15
Range
To find the range, subtract the smallest number in the set from the biggest number in the set.
14, 14, 15, 15, 16, 15, 15, 16
Biggest number: 16
Smallest number: 14
biggest-smallest
16-14=2
The range is 2
Therefore, the answer is D: 15 and 2
observation means number.
mean= sum of all observation ÷ number of observation
= 14+ 14+ 15+ 15+ 16+ 15+ 16
7
= 105
7
= 15
range= the highest observation - lowest observation
= highest number- 16
lowest number- 14
= 16-14
= 2
therefore the answer is
OPTION- D 15;2
HELP ME QUICK!! The best answer I will mark brainlest!
Answer: 1. (4, 8); 2. (3, 4)
Step-by-step explanation: I tried to get this to you fast but I can give you an explaination if you would like one :)
Three dogs eat 30 pounds of food in 10 days. If each dog eats the same amount, how much food does 1 dog eat in 1 day? 1 pound 3 pounds 9 pounds 10 pounds
Answer:
Unable to read entire question, but see explanation for answer
Step-by-step explanation:
First, you need to find the unit rate per dog. If it takes 3 dogs 10 days to finish 30 pounds of food, then it takes 1 dog 1 day to finish 1 pound of food. I cannot read the entirety of the question because of the cropping, but you can find how much food a single dog eats in that amount of days by just multiplying by the number of days (say, 1 pound in 1 day, or 3 pounds in 3 days). Hope this helps!
Answer:
1
Step-by-step explanation:
took test
What is the square root of x if x = 25?
Answer:
5 is your answer
Step-by-step explanation:
The [tex]\sqrt{25}[/tex] will equal to 5, because [tex]5^2[/tex] = 25
Answer:
5
Step-by-step explanation:
5 x 5 =25, so it is the square root of 25
A = (5,2), B = (2,4), C = (6,7) and D = (9,5) What is the length of the shorter diagonal of parallelogram ABCD?
Answer:
[tex] AC = \sqrt(26) \approx 5.1 [/tex]
Step-by-step explanation:
The diagonals are AC and BD.
Now we find the lengths of the diagonals using the distance formula.
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
AC:
[tex] AC = \sqrt{(6 - 5)^2 + (7 - 2)^2} [/tex]
[tex] AC = \sqrt{(1)^2 + (5)^2} [/tex]
[tex] AC = \sqrt{1 + 25} [/tex]
[tex] AC = \sqrt{26} [/tex]
BD:
[tex] BD = \sqrt{(9 - 2)^2 + (5 - 4)^2} [/tex]
[tex] BD = \sqrt{(7)^2 + (1)^2} [/tex]
[tex] BD = \sqrt{49 + 1} [/tex]
[tex] BD = \sqrt{50} [/tex]
Since sqrt(26) < sqrt(50), then the shorter diagonal is AC.
Answer: AC = sqrt(26) or approximately 5.1
Answer:
A = (5.2)
Step-by-step explanation:
c2= (6-5)^2 + (7-2)^2
To find AC we calculate within parenthesis (6-5) : 1
c2= 1 + (7-2)^2
calculate within parenthesis (7-2) : 5
c2 = 1^2 + 5^2
then calculate exponents 1^2:1
c^2 = 1+5^2
add and subtract left to right
c^2 = 1+25
c^2 =26
Sr of 26 = 5.09901951359
Which means the closest answer is A = 5.2
To find BD we calculate within parenthesis (9-2):7
c2= (9-2)^2 + (5 - 4)^2
calculate within parenthesis (5-4) : 1
c2 = (7)^2 + (1)^2
calculate exponents 1 ^2 : 1
c2 = 49 +1
add and subtract left to right
c2 = 50
Sr of 50 = 7.07106781187
Using propositional logic to prove that each argument is valid.If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Kraso was not in town. If a crime was committed, then Mr. Krasov was in town. Therefore Jose did not take the jewerly. Use letters J, L, C, T.So for this question, I am very confused and would appreciate any help offerd.
Answer:
Step-by-step explanation:
We will first translate the situation to propositional logic. First, some notation is needed: [tex]\lor[/tex] is the or logical operation and [tex]\implies[/tex] is the symbol for logical implication. Define the following events:
J: Jose took the jewelry. L: Mrs Krasov lied, C: a crime was committed. T: Mr Krasov was in town.
We will symbol the propositions in logical symbols. Recall that [tex]\neg[/tex] means negation
If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed: [tex]J\lor L \implies C[/tex]
Mr. Krasov was not in town: [tex]\neg T[/tex]
If a crime was committed, then Mr. Krasov was in town: [tex]C\implies T[/tex]
We want to check if the conclusion Jose did not take the jewerly: [tex]\neg J[/tex] can be deduced from the premises.
First, recall the following:
- if [tex] a\implies b[/tex] and a is true, then b is true.
- [tex] a\implies b[/tex] is logically equivalent to [tex]\neg b \implies a[/tex]
Coming back to the problem, we have the following premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg(J\lor L)[/tex]
where the equivalence for the logical implication was applied. REcall that the negation of an or statement is g iven by
[tex] \neg( a \lor b ) = \neg a \land \neg b [/tex] where [tex] \land[/tex] is the and logical operator.
USing this, we get the premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg J\land \neg L[/tex]
Since [tex]\neg T[/tex], by having [tex]\neg T \implies \neg C[/tex], then it must be true that [tex]\neg C[/tex]. Since [tex]\neg C \implies \neg J\land \neg L[/tex], then it must be true that [tex] \neg J\land \neg L[/tex]. This final conclusion implies that it is true that [tex]\neg J[/tex] which is the statement that Jose did not take the jewelry.
Help me, please ?? :)
Answer:
a) 11
b) 16
c) between 5 and 6
d) 16
Step-by-step explanation:
[tex]\text{a. }\quad\sqrt{121}=\sqrt{11^2}=\boxed{11}\\\\\text{b. }\quad 8\sqrt{4}=8\sqrt{2^2}=8\cdot 2=\boxed{16}\\\\\text{c. }\quad\sqrt{35}\ \dots\ \sqrt{25}<\sqrt{35}<\sqrt{36}\\\\\text{ }\qquad\sqrt{5^2}<\sqrt{35}<\sqrt{6^2}\\\\\text{ }\qquad \boxed{5<\sqrt{35}<6}\\\\\text{d. }\quad\dfrac{.8}{.05}=\dfrac{0.80\cdot 20}{.05\cdot 20}=\dfrac{16}{1}=\boxed{16}[/tex]
Moise Moliere
Mrs. Johnson has 159 chickens that she puts in shelters at night to keep safe. She places 12 chickens in a shelter
and continues putting this number of chickens in each shelter until she comes to the last one. How many chickens
will Mrs. Johnson put in the last shelter?
3
4
13
11
6
7
8 9 10
14
Back
2 3 4 5
9:3
INTL
Answer: she putz 9 in the last shelter
Step-by-step explanation:
What is the value of (Negative one-half)–4?
A) -16
B) Negative StartFraction 1 Over 16 EndFraction
C) StartFraction 1 Over 16 EndFraction
D) 16
Answer:
It would be 16!!!
The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (-1/2)⁻⁴
Simplify the equation, then we have
⇒ (-1/2)⁻⁴
⇒ (-2)⁴
⇒ -2⁴
⇒ 16
The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.
More about the value of the expression link is given below.
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A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 86% reliable. In other words, if an individual lies, there is a 0.86 probability that the test will detect a lie. Let there also be a 0.070 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.
a. What is the probability of Type I error? (Round your answer to 3 decimal places.)
Probability
b. What is the probability of Type II error? (Round your answer to 2 decimal places.)
Probability
Answer:
Step-by-step explanation:
a) The probability of a Type I error in a lie detection test would be the probability that the lie detection machine incorrectly detected lie for the truth tellers. This is already given in the problem as 0.07.
Therefore,
[tex]P(Type-I) = 0.07[/tex]
Therefore 0.07 is the required probability here.
b) The probability of a Type II error in a lie detection test would be the probability that the lie detection machine incorrectly detected truth for the the people who are actually liars. This is thus 1 - reliability.
[tex]P(Type-II) = 1 - Reliability = 1- 0.86 = 0.14[/tex]
Therefore 0.14 is the required probability here.
Answer:
a) 0.070
b) 0.14
Step-by-step explanation:
Given that the tests are 86% reliable, i.e a probability of 0.86 a lie would be detected.
Probability of error = 0.070
a) For type I error, we have:
The probability of a type I error in this lie detector is the probability that the test erroneously detects a lie even when the individual is actually telling the truth, i.e
P(type I error) = P(rejecting true null)
= 0.070
b) The probability of a Type II error this lie detectot is the probability that the test erroneously detected truth insteax of lie.
i.e = 1 - reliability
P (Type II error) = P(Failing to reject false Null)
= P(Not detecting a lie)
= 1-0.86
= 0.14
A glucose solution is administered intravenously into the bloodstream at a constant rate r. As the gulcose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at the time. Thus a model for the concentration C=C(t) of the glucose solution in the bloodstream is
dC/dt=r-kC
Where r an dk are positive constants.
1. Suppose that the concentration at time t=0 is C0. Determine the concentration at any time t by solving the differential equation.
2. Assuming that C0
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] ,thus, the function is said to be an increasing function.
Step-by-step explanation:
Given that:
[tex]\dfrac{dC}{dt}= r-kC[/tex]
[tex]\dfrac{dC}{r-kC}= dt[/tex]
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]
here;
A is an integration constant
In order to determine A, we have [tex]C(0) = C0[/tex]
[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]
2. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
[tex]C_{0} < \lim_{t \to \infty }C(t) \\ \\C_0 < \dfrac{r}{k} \\ \\kC_0 <r[/tex]
The equation for C(t) can be rewritten as :
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]
Thus; the function is said to be an increasing function.
Express this number in scientific notation. 5.3×104+4.7×104
Answer:
for [tex]5.3 * 10^4 + 4.7 * 10^4[/tex] the answer would be [tex]1 * 10^5[/tex]
Step-by-step explanation:
After adding like terms we would get [tex]10^4 *10[/tex]
Then we use the exponent rule and get [tex]10^1^+^4[/tex]
Which after adding would result in [tex]10^5[/tex]