Answer:
x=9
Step-by-step explanation:
3x subtracted by 2y
is 1 then 1 multiplied by 2 is 2 then 7 + 2 is 9
PEMDAS
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order DE y'' − y = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y(−1) = 9, y'(−1) = −9
Answer:
[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]
Step-by-step explanation:
This problem is very simple, since they give the solution for the differential equation from the start. So basically, you need to evaluate the initial conditions into the solution, and the derivative of the solution in order to find the value of the constants [tex]c_1[/tex] and [tex]c_2[/tex].
So, first of all, let's find the derivative of [tex]y(x)[/tex]:
[tex]y'(x)=c_1 e^{x} -c_2e^{-x}[/tex]
Now, let's evaluate the first initial condition:
[tex]y(-1)=c_1e^{-1} +c_2e^{-(-1)} =9\\\\c_1e^{-1} +c_2e^{1}=9\hspace{10}(1)[/tex]
Now, the second initial condition:
[tex]y'(-1)=c_1 e^{-1} -c_2e^{-(-1)}=-9\\\\c_1 e^{-1} -c_2e^{1}=-9\hspace{10}(2)[/tex]
Combining (1) and (2) we have a 2x2 System of Equations. Let's use elimination method in order to solve it:
[tex](1)+(2):\\\\c_1e^{-1} +c_2e^{1} +c_1e^{-1} -c_2e^{1}=9-9\\\\2c_1e^{-1} =0\\\\Hence\\\\c_1=0[/tex]
Replacing [tex]c_1[/tex] into (1)
[tex](0)e^{-1} +c_2e^{1}=9\\\\c_2e^{1}=9\\\\Hence\\\\c_2=\frac{9}{e^{1} } =3.310914971[/tex]
Therefore the solution of the second-order IVP is:
[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]
According to a recent study, some experts believe that 15% of all freshwater fish in a particular country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 150 fish we consider randomly sampled from the population of edible freshwater fish. Use the Central Limit Theorem (and the Empirical Rule) to find the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15. You can use the Central Limit Theorem because the fish were randomly sampled; the population is more than 10 times 150; and n times p is 22.5, and n times (1 minus p) is 127.5, and both are more than 10.
Answer:
The approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=0.15[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
As the sample size is large, i.e. n = 150 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
Compute the mean and standard deviation as follows:
[tex]\mu_{\hat p}=0.15\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.15(1-0.15)}{150}}=0.0292[/tex]
So, [tex]\hat p\sim N(0.15, 0.0292^{2})[/tex]
In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the Normal distribution lie within one, two and three standard deviations of the mean, respectively.
Then,
P (µ-σ < X < µ+σ) ≈ 0.68
P (µ-2σ <X < µ+2σ) ≈ 0.95
P (µ-3σ <X < µ+3σ) ≈ 0.997
Then the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.
That is:
[tex]P(\mu_{\hat p}-2\sigma_{\hat p}<\hat p<\mu_{\hat p}+2\sigma_{\hat p})=0.95\\\\P(0.15-2\cdot0.0292<\hat p<0.15+2\cdot0.0292)=0.95\\\\P(0.092<\hat p<0.208)=0.95[/tex]
A restaurant has a main location and a traveling food truck. The first matrix A shows the number of managers and associates employed. The second matrix B shows the average annual cost of salary and benefits (in thousands of dollars). Complete parts (a) through (c) below.
Managers Associates
Restaurant 5 25 = A
Food Truck 1 4
Salary Benefits
Managers 41 6 = B
Associates 20 2
a. Find the matrix product AB .
b. Explain what AB represents.
c. According to matrix AB , what is the total cost of salaries for all employees (managers and associates) at the restaurant? What is the total cost of benefits for all employees at the food truck?
Answer:
A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]
Step-by-step explanation:
Given A= [tex]\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right][/tex] = B
Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.
so A*B= [tex]\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right][/tex]
Now multiply and add the separate elements of the matrix A*B=
[tex]\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right][/tex]
A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]
b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.
c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785
Total cost of benefits for all employees at the food truck= 121 + 14= 135
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.36, the analogous probability for the second signal is 0.51, and the probability that he must stop at least one of the two signals is 0.67.What is theprobability that he must stop.
a) At both signals?
b) At the first signal but not at the second one?
c) At exactly on signal?
Answer:
a) P(X∩Y) = 0.2
b) [tex]P_1[/tex] = 0.16
c) P = 0.47
Step-by-step explanation:
Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.
So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67
Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.36 + 0.51 - 0.67
P(X∩Y) = 0.2
On the other hand, the probability [tex]P_1[/tex] that he must stop at the first signal but not at the second one can be calculated as:
[tex]P_1[/tex] = P(X) - P(X∩Y)
[tex]P_1[/tex] = 0.36 - 0.2 = 0.16
At the same way, the probability [tex]P_2[/tex] that he must stop at the second signal but not at the first one can be calculated as:
[tex]P_2[/tex] = P(Y) - P(X∩Y)
[tex]P_2[/tex] = 0.51 - 0.2 = 0.31
So, the probability that he must stop at exactly one signal is:
[tex]P = P_1+P_2\\P=0.16+0.31\\P=0.47[/tex]
Question 3 of 10
2 Points
If h(x) =(fºg)(x) and h(x) = 3(x + 2), find one possibility for f (x) and g(x).
Answer:
[tex]\boxed{\sf \ \ \ \text{one possibility is } f(x)=3x \ and \ g(x)=x+2 \ \ \ }[/tex]
Step-by-step explanation:
hello
h(x)=f(g(x))=3(x+2)
if we have f(x)=3x and g(x)=x+2 then
f(g(x))=f(x+2)=3(x+2)
hope this helps
Show all work to solve 3x^2 – 5x – 2 = 0.
Answer:
Step-by-step explanation:
3x2−5x−2=0
For this equation: a=3, b=-5, c=-2
3x2+−5x+−2=0
Step 1: Use quadratic formula with a=3, b=-5, c=-2.
x= (−b±√b2−4ac )2a
x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)
x= (5±√49 )/6
x=2 or x= −1 /3
Answer:
x=2 or x= −1/ 3
The solutions to the equation are x = -1/3 and x = 2.
Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:
First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Next, we set each factor equal to 0 and solve for x.
(3x + 1)(x - 2) = 0
3x + 1 = 0
3x = -1
x = -1/3
x - 2 = 0
x = 2
Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.
Here is the explanation for each of the steps:
Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.
Learn more about equation here: brainly.com/question/29657983
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Find the percent of increase. Original Price: $200 Retail Price: $250
Answer:
The percent of increase is 25%
Step-by-step explanation:
Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%
Use the function below to find f(4).
f(x)=1/3x4^x
A. 8/3
B.256/3
C.64/3
D.16/3
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Simply replace X with 4
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Denise is planning to put a deck in her back yard. The deck will be a 10-by-7-foot rectangle with a semicircle of diameter 4 feet, as shown below. Find the area of the deck (in square feet).(round your answer to two decimal places)
Answer:
[tex]approx. = 85.28 {ft}^{2} [/tex]
Step-by-step explanation:
You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.
(l×w)+(πr^2)/2
(10×7)+((π2^2)/2
79+2π
[tex]approx. = 85.28 {ft}^{2} [/tex]
pls pls help me help me help me
Answer:
2
Step-by-step explanation:
Answer:
I hope it will help you....
PLEASE HELP SOLVE THIS!!!!!
Answer:
20) -43
21) 25
22)-9
Step-by-step explanation:
20) -6 (-6 + 49)/6 = -43
21) 10 - (-10 - (-1 + 6)) = 25
22) 1 - 10/2 - 5 = -9
Step-by-step explanation:
22Let's calculate the expression khowing that m= 1 and n = 5
m-[tex]\frac{m+m}{2}[/tex] -nm- [tex]\frac{2m}{2}[/tex]-n m-m-n0-n0-5-520Let's calculate the expression khowing that n= -7 and p= - 6
[tex]\frac{p(p+n^{2}) }{6}[/tex] [tex]\frac{-6(-6+(-7)^{2}) }{6}[/tex][tex]\frac{-6(-6+49)}{2}[/tex] [tex]\frac{-6*43}{6}[/tex] -1*43-4321Let's calculate the expression khowing that n = -6 and m = -1 and p = -10
mp-(p-(m-n))mp-(p-m+n)mp-p+m-n(-1)*(-10)-(-10)+(-1)-(-6)10+10-1+620-1+619+62511- In
how many ways 3 mathematics books, 4 history books ,3
chemisidy books and a biology books can be arranged
on an Shelf so thet all books of the same subjects are
together!
Answer: 20,736
Step-by-step explanation:
Math and History and Chemistry and Biology and Subjects
3! x 4! x 3! x 1! x 4! = 20,736
Hurry!! Determine the intervals for which the function shown below is decreasing.
Answer:
everywhere except between 2 and 5
(between -inf and 2 and between 5 and inf)
Step-by-step explanation:
In triangle ABC, the right angle is at vertex C, a = 714 cm and the measure of angle A is 78° . To the nearest cm, what is the length of side c?
Answer:
c = 730cm
Step-by-step explanation:
The first thing we would do is to draw the diagram using th given information.
Find attached the diagram.
a = 714 cm
the measure of angle A = 78°
To determine c, we would apply sine rule. This is because we know the opposite and we are to determine the hypotenuse
sin78 = opposite/hypotenuse
sin 78 = 714/c
c = 714/sin 78 = 714/0.9781
c= 729.99
c≅ 730 cm ( nearest cm)
I NEED HELP PLEASE, THANKS! :)
A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. (Show work)
Answer: 136
Step-by-step explanation:
An= A1+(n-1)d
A1=16, d=8, and n=16
A16= 16 +(16-1)(8)
A16= 16(15)(8)
A16= 16+120
A16=136
Hey there! :)
Answer:
f(16) = 136 seats.
Step-by-step explanation:
This situation can be expressed as an explicit function where 'n' is the row number.
The question also states that the number of seats increases by 8. Use this in the equation:
f(n) = 16 + 8(n-1)
Solve for the number of seats in the 16th row by plugging in 16 for n:
f(16) = 16 + 8(16-1)
f(16) = 16 + 8(15)
f(16) = 16 + 120
f(16) = 136 seats.
How many meters are in 18,200 milliliter
Answer:
18.2 :)
Have a great day!!!
I NEED HELP FAST, THANKS! :)
Answer:
33 units²
Step-by-step explanation:
A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...
A = (1/2)(8 + 8.5)(4) = 33
__
If you do the integration, it gets a bit messy.
[tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]
The appropriate answer choice is 33 square units.
Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB
Answer:
Step-by-step explanation:
Given:
AB║DC and BC║AE
To prove:
[tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]
Statements Reasons
1). ∠ABE ≅ ∠CDB 1). Alternate interior angles
2). ∠AEB ≅ ∠CBD 2). Alternate interior angles
3). ΔCBD ~ ΔAEB 3). AA property of similarity
4). [tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex] 4). Property of similarity [Corresponding sides of two similar triangles are proportional]
Which of the following points is NOT a solution of the inequality y ≥ Ixl + 3?
A. (-3, 0)
B. (-3, 6)
C. (0, 4)
Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!
Which sentence in this excerpt from Common Sense by Thomas Paine supports the claim that the American colonies could thrive independently from Britain? I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain that the same connection is necessary towards her future happiness, and will always have the same effect. Nothing can be more fallacious than this kind of argument. We may as well assert that because a child has thrived upon milk that it is never to have meat, or that the first twenty years of our lives is to become a precedent for the next twenty. But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her. The commerce, by which she hath enriched herself, are the necessaries of life, and will always have a market while eating is the custom of Europe.
Answer:
A
Step-by-step explanation:
Answer:
"But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her."
Step-by-step explanation:
Checked 2021
HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..
Approximately, what was the rate of change for the number of the websites for this time period??
=============================================================
How I got that answer:
We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.
Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.
----------
You could use the slope formula to get the job done. This is because the slope represents the rise over run
slope = rise/run
The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...
In a more written out way, the steps would be
slope = rise/run
slope = (y2-y1)/(x2-x1)
slope = (793 - 54)/(2004 - 1995)
slope = 739/9
slope = 82.111....
Find the critical value z Subscript alpha divided by 2 that corresponds to the given confidence level. 80%
Answer:
[tex] Conf= 0.80[/tex]
With the confidence level we can find the significance level:
[tex]\alpha =1-0.8=0.2[/tex]
And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.28[/tex]
Step-by-step explanation:
For this problem we have the confidence level given
[tex] Conf= 0.80[/tex]
With the confidence level we can find the significance level:
[tex]\alpha =1-0.8=0.2[/tex]
And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.28[/tex]
Simplify: |4-5| / 9 × 3³ - 2/5 a.61/10 b.13/5 c.11/10 d.-2/15
━━━━━━━☆☆━━━━━━━
▹ Answer
Answer = b. 13/5
▹ Step-by-Step Explanation
|4 - 5| ÷ 9 × 3³ - 2/5
|-1| ÷ 9 × 3³ - 2/5
1 ÷ 9 × 3³ - 2/5
1/9 × 3³ - 2/5
1/3² × 3³ - 2/5
3 - 2/5
Answer = 13/5
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
[tex] \boxed{\sf b. \ \frac{13}{5}} [/tex]
Step-by-step explanation:
[tex] \sf Simplify \: the \: following: \\ \sf \implies \frac{ |4 - 5| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf 4 - 5 = - 1 : \\ \sf \implies \frac{ | - 1| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf Since \: - 1 \: is \: a \: negative \: constant, \: |-1| = 1: \\ \sf \implies \frac{1}{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf {3}^{3} = 3 \times {3}^{2} : \\ \sf \implies \frac{ \boxed{ \sf 3 \times {3}^{2}} }{9} - \frac{2}{5} \\ \\ \sf {3}^{2} = 9 : \\ \sf \implies \frac{3 \times 9}{9} - \frac{2}{5} \\ \\ \sf \frac{9}{9} = 1 : \\ \sf \implies 3 - \frac{2}{5} [/tex]
[tex] \sf Put \: 3 - \frac{2}{5} \: over \: the \: common \: denominator \: 5 : \\ \sf \implies 3 \times \frac{5}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{3 \times 5}{5} - \frac{2}{5} \\ \\ \sf 3 \times 5 = 15 : \\ \sf \implies \frac{ \boxed{ \sf 15}}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{15 - 2}{5} \\ \\ \sf 15 - 2 = 13 : \\ \sf \implies \frac{13}{5} [/tex]
. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7
Answer:
The 68% confidence interval is (6.3, 6.7).
The 95% confidence interval is (6.1, 6.9).
The 99.7% confidence interval is (5.9, 7.1).
Step-by-step explanation:
The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error)is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]
As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.
(a)
Compute the 68% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]
The 68% confidence interval is (6.3, 6.7).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]
(b)
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]
The 95% confidence interval is (6.1, 6.9).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]
(c)
Compute the 99.7% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]
The 99.7% confidence interval is (5.9, 7.1).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]
Does the following systems produce an infinite number of solutions 2y + x = 4 ; 2y = -x +4
Answer:
Yes.
Step-by-step explanation:
In the future, simply plug both equations into Desmos.
Which equation can be used to find the area of the rectangle? A. A=9+4 B. A=1/2 (9)(4) C. A=9+9+4+4 D. A=(9)(4)
Answer:
D. A=(9)(4)
Step-by-step explanation:
area= length x width = 9x4
by how much is 25% of #25 greater than 15% of #15
Answer:
4
Step-by-step explanation:
25% of 25
0.25 × 25 = 6.25
15% of 15
0.15 × 15 = 2.25
Find the difference.
6.25 - 2.25
= 4
How do you write 0.0683 in scientific notation? ____× 10^____
Answer:
It's written as
[tex]6.83 \times {10}^{ - 2} [/tex]
Hope this helps you
Answer:
6.83 × 10 -2
hopefully this helped :3
if it takes four men to dig a land in 6 days.how many days will it take 6 men to build that same land.
Answer:
4 daysSolution,
____________________________
Men ------------------------------ Days
4 ------------------------> 66 ------------------------> X (suppose)_____________________________
In case of indirect proportion,
4/6= 6/X
or, 6*X= 6*4 ( cross multiplication)
or, 6x= 24
or, 6x/6= 24/6 ( dividing both sides by 6)
x= 4 days
Hope this helps...
Good luck on your assignment..
Answer:
[tex]\boxed{4 days}[/tex]
Step-by-step explanation:
M1 = 4
D1 = 6
M2 = 6
D2 = x (we've to find this)
Since, it is an inverse proportion (more man takes less days for the work to complete and vice versa), so we'll write it in the form of
M1 : M2 = D2 : D1
4 : 6 = x : 6
Product of Means = Product of Extremes
=> 6x = 4*6
=> 6x = 24
Dividing both sides by 6
=> x = 4 days