Answer:
One possible answer is:
f(x) = (2/x) + 3 and g(x) = x².
Step-by-step explanation:
Explanation:
We are to write this equation as y = f(g(x)). This means we want it to be a composite of functions; in f(x), we take the value of g(x) and use in place of x.
If we let g(x) = x², this means everywhere we see an x in f(x), we will replace it with x². To make our equation y = 2/x² + 3, working backward we would substitute x for x²; this would give us f(x) = 2/x + 3.
Please answer this correctly without making mistakes
Step-by-step explanation:
Option A and B are the correct answer because it equal to 688.5 and 688.05
Answer:
it is 1377/2 and 688 1/17 thats the answer
Step-by-step explanation:
Suppose that the neighboring cities of Tweed and Ledee are long-term rivals. Neal, who was born and raised in Tweed, is confident that Tweed residents are more concerned about the environment than the residents of Ledee. He knows that the average electricity consumption of Tweed households last February was 854.11 kWh and decides to test if Ledee residents used more electricity that month, on average. He collects data from 65 Ledee households and calculates the average electricity consumption to be 879.28 kWh with a standard deviation of 133.29 kWh. There are no outliers in his sample data. Neal does not know the population standard deviation nor the population distribution. He uses a one-sample t-test with a significance level of α = 0.05 to test the null hypothesis, H0:µ=854.11, against the alternative hypothesis, H1:μ>854.11 , where μ is the average electricity consumption of Ledee households last February. Neal calculates a t‑statistic of 1.522 and a P-value of 0.066.
Based on these results, complete the following sentences to state the decision and conclusion of the test.
Neal's decision is to__________ the __________ (p 0.066). There is_________ evidence to _________ the claim that the average electricity consumption of ____________ is _________ , ________
Complete Question
The option to the blank space are shown on the first uploaded image
Answer:
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 854.11[/tex]
The sample size is [tex]n = 65[/tex]
The sample mean is [tex]\= x = 879.28 \ kWh[/tex]
The standard deviation is [tex]\sigma = 133.29 \ kWh[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o: \mu = 854.11[/tex]
The alternative hypothesis is [tex]H_a : \mu > 854.11[/tex]
The t-statistics is [tex]t = 1.522[/tex]
The p-value is [tex]p-value = 0.066[/tex]
Now from the given data we can see that
[tex]p-value < \alpha[/tex]
Generally when this is the case , we fail to reject the null hypothesis
So
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
How many odd numbers with 4 different digits, can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8? (No repetition is allowed)
A. 71
B. 200
C. 210
D. 840
E.1680
Answer:
840 ( D )
Step-by-step explanation:
GIVEN DIGITS : 1,2,3,4,5,6,7,8
Number of odd numbers = 4
Number of even numbers = 4
therefore the number of odd numbers with 4 different digits can be formed by the same way the number of even numbers ( without repetition )
Hence the number of ways odd numbers with 4 different digits = Total number of ways of forming 4 digit numbers / 2
8*7*6*5 = 1680 / 2 = 840 ways
The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point
of the preimage. Point D′ of the image coincides with point
of the preimage.
Answer:
Point C: G
Point D: F
Step-by-step explanation:
A hexagon has 6 sides.
360/6=60
Every 60°, it moves one section.
240/60=4.
So it moves 4 sections.
C would move 4 sections BACK (B, A, F, G)
D would also move 4 sections back (C, B, A, F)
Answer:
Point C is: E
point D is : F
Step-by-step explanation:
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
Complete Question
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
a.
The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen’s d.
b.
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
c.
The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen’s d.
d.
The larger sample is less likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
Answer:
The Cohen's d value is [tex]d = 0.895[/tex]
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample mean of each population is [tex]M = 84[/tex]
The variance of each population is [tex]s^2 = 20[/tex]
The first sample size is [tex]n_1 = 10[/tex]
The second sample size is [tex]n_2 = 20[/tex]
The null hypothesis is [tex]H_o : \mu = 80[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]s = \sqrt{20 }[/tex]
=> [tex]s = 4.47[/tex]
The first test statistics is evaluated as
[tex]t_1 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_1} } }[/tex]
=> [tex]t_1 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{10} } }[/tex]
=> [tex]t_1 = 2.8298[/tex]
The second test statistics is evaluated as
[tex]t_2 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_2} } }[/tex]
=> [tex]t_2 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{20} } }[/tex]
=> [tex]t_2 = 4.0[/tex]
The sample with the larger test statistics (sample size) will more likely reject the null hypothesis
Generally the Cohen's d value is mathematically evaluated as
[tex]d = \frac{M - \mu }{s }[/tex]
=> [tex]d = \frac{ 84 - 80 }{4.47 }[/tex]
=> [tex]d = 0.895[/tex]
Given that the the sample mean and sample size are the same for both sample the Cohen's d value will be the same
You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage
Answer:
the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.
Step-by-step explanation:
From the given information:
Sample size n = 200
The standard deviation for a sampling distribution for two brands are equally likely because the individual has no ability to discriminate between the two soft drinks.
∴
The population proportion [tex]p_o[/tex] = 1/2 = 0.5
NOW;
[tex]\sigma _p = \sqrt{\dfrac{p_o(1-p_o)}{n}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.5(1-0.5)}{200}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.5(0.5)}{200}}[/tex]
[tex]\sigma _p = \sqrt{\dfrac{0.25}{200}}[/tex]
[tex]\sigma _p = \sqrt{0.00125}[/tex]
[tex]\sigma _p = 0.035355[/tex]
However, in order to determine the symmetrical limits of the population percentage given that the z probability is 90%.
we use the Excel function as computed as follows in order to determine the z probability = NORMSINV (0.9)
z value = 1.281552
Now the symmetrical limits of the population percentage can be determined as: ( 1.28, -1.28)
[tex]1.28 = \dfrac{X - 0.5}{0.035355}[/tex]
1.28 × 0.035355 = X - 0.5
0.0452544= X - 0.5
0.0452544 + 0.5 = X
0.5452544 = X
X [tex]\approx[/tex] 0.545
X = 54.5%
[tex]-1.28 = \dfrac{X - 0.5}{0.035355}[/tex]
- 1.28 × 0.035355 = X - 0.5
- 0.0452544= X - 0.5
- 0.0452544 + 0.5 = X
0.4547456 = X
X [tex]\approx[/tex] 0.455
X = 45.5%
Therefore , we can conclude that the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.
x
Find the value
of x. Show
3
10
your work.
Step-by-step explanation:
Hello, there!!!
Let ABC be a Right angled triangle,
where, AB = 3
BC= 10
and AC= x
now,
As the triangle is a Right angled triangle, taking angle C asrefrence angle. we get,
h= AC = x
p= AB = 3
b= BC= 10
now, by Pythagoras relation we get,
[tex]h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
[tex]or ,\: h = \sqrt{ {3}^{2} + {10}^{2} } [/tex]
by simplifying it we get,
h = 10.44030
Therefore, the answer is x= 10.
Hope it helps...
Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron. What is the standardized score for a binding site position of 2.03 microns? (Enter your answer rounded to one decimal place.)
Answer:
The values is
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2.45[/tex]
The standard deviation is [tex]\sigma = 0.35 \ mi[/tex]
The random value is [tex]x = 2.03[/tex]
The standardized score for a binding site position of 2.03 microns is mathematically represented as
[tex]z-score = \frac{x - \mu}{ \sigma }[/tex]
=> [tex]z-score = \frac{2.03 - 2.45}{ 0.35}[/tex]
=> [tex]z-score = -1.2[/tex]
Find the product . Write your answer in exponential form 8^-2•8^-9
Answer:
8^-11
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
Then we have ...
(8^(-2))·(8^(-9)) = 8^(-2-9) = 8^-11
Help Quick Please. Will give brainliest.
Answer:
72[tex]\sqrt{3}[/tex] units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = ST = a = 12 and h = RS
To calculate RS use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )
RS = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²
URGENT, PLEASE HELP! (4/5) -50 POINTS- ! please no wrong answers for the points.! A) y = -3x + 2 B) y = -x + 2 C) y = 3x + 2 D) y = x + 1
Answer:
D y= x+1
Step-by-step explanation:
The line has a positive slope since it goes up from left to right
We can eliminate A and B
3 is a fairly steep slope for line C
Lets check with point x=7
y = 3*7 +2 = 21+2 = 23
Way too steep
Lets check 2
y = 3*2+2 = 6+2 = 8
Still above the points
Checking D
y = x+1
x=7
y = 7+1 =8 A little high
x=2
y = 2+1 =3 A little low but much better than C
Answer:
[tex]\huge \boxed{y=x+1}[/tex]
Step-by-step explanation:
Using a graph,
we can see the line y=x+1 is best fit for the data.
The expression $16x^2-106x-105$ can be written as $(8x + a)(2x + b),$ where $a$ and $b$ are integers. What is $a + 2b$?
Answer:
-23
Step-by-step explanation:
16x² - 106x - 105
factoring X
14 x -120 = -1680
14 - 120 = -106
16x² + 14x - 120x - 105
(16x² + 14x) -(120x - 105)
factor out 2 and -15 to get the same expression (8x + 7)
2x(8x + 7) - 15(8x + 7)
(8x + 7)(2x - 15)
a = 7
b = -15
a + 2b
7 + (-15 x 2)
7 + (-30)
= -23
What is the value of this expression when x = -6 and y = — 1/2? 4(x^2+3) -2y A. -131 B. -35 C. 57 1/2 D. 157
Answer:
D
Step-by-step explanation:
[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]
The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
4(x² + 3) - 2y
Substitute x = -6 and y = -1/2 to find the value of expression,
= 4 ((-6)² + 3) - 2(-1/2)
= 4 (36 + 3) + 1
= 4 x 39 + 1
= 156 + 1
= 157
The required value of the expression is 157.
To know more about Algebraic expression on:
https://brainly.com/question/19245500
#SPJ2
What is the probability of the spinner landing on an odd number? A spinner is split into 4 equal parts labeled 1, 2, 3, and 4. One-fourth One-third One-half Three-fourths
Answer:
One half, or 1/2.
There are an equal amount of odd numbers as there are even numbers on the spinner.
Answer:
C. 1/2
One-half
Which is the graph of g(x) = (0.5)x + 3 – 4?
Answer:
Graph (A)
Step-by-step explanation:
Given question is incomplete; find the question in the attachment.
Given function is g(x) = [tex](0.5)^{x+3}-4[/tex]
Parent function of the given function is,
f(x) = [tex](0.5)^{x}[/tex]
When the function 'f' is shifted by 3 units left over the x-axis, translated function will be,
h(x) = f(x+3) = [tex](0.5)^{x+3}[/tex]
When h(x) is shifted 4 units down, translated function will be,
g(x) = h(x) - 4
g(x) = [tex](0.5)^{x+3}-4[/tex]
g(x) has a y-intercept as (-4).
From the given graphs, Graph A shows the y-intercept as (-4).
Therefore, Graph A will be the answer.
Answer:
The Answer A is correct
Step-by-step explanation:
I took the edg2020 test
) A jar contains 4 white balls and 6 black balls. A ball is chosen at random, and its color noted. The ball is then replaced, along with 3 more balls of the same color. Then, another ball is drawn at random from the jar. (a) Find the chance that the second ball drawn is white. (b) Given that the second ball drawn is white, what is the probability that the first ball drawn is black
Answer:
The answer is "[tex]\bold{\frac{2}{5}\ \ and \ \ \frac{6}{13}}[/tex]".
Step-by-step explanation:
You have 4/10 opportunities to choose a white ball, and there'll be 7 white balls and 6 black balls out of 13, and so the second time they choose a white one is 7/13, as well as the second time they choose a black, 6/13. people will also have a 4/10 chance.
There are 6/10 chances which users pick its black ball and 4 white balls would still be picked, but 9 black balls and out 13 balls and thus, its second and third time you select the white one is 4/13 but you are likely to pick a black for the second time is 9/13.
Taking the diagram of the next tree. The very first draw is marked with a and the second draw is marked with b.
[tex]\to P(a) = \frac{4}{10}\ \ \ \ \ \ \ \ \ P(b) = \frac{6}{10}\\\\\to P(\frac{a2}{a1}) = \frac{7}{13} \ \ \ \ \ \ \ \ \ \ P(\frac{a}{b}) = \frac{4}{13}\\\\\to P(\frac{b2}{a1}) = \frac{6}{13} \ \ \ \ \ \ \ \ \ \ P(\frac{b2}{b1}) = \frac{9}{13}[/tex]
Calculating the second drawn ball is white:
[tex]\to P(b2)=P(a)P(\frac{a2}{b1})+P(b)P(\frac{a}{b})\\[/tex]
[tex]=\frac{4}{10}\frac{7}{13}+\frac{6}{10}\frac{4}{13}\\\\=\frac{28}{130}+\frac{24}{130}\\\\=\frac{28+24}{130}\\\\=\frac{52}{130}\\\\=\frac{2}{5}\\\\[/tex]
In point b:
[tex]\to P(\frac{b}{a1})= \frac{P(B)P(\frac{a}{b})}{P(a)P(\frac{a2}{b1})+P(b)P(\frac{a}{b})\\}[/tex]
[tex]=\frac{\frac{6}{10} \frac{4}{13}}{\frac{52}{130}}\\\\=\frac{\frac{24}{130}}{\frac{52}{130}}\\\\=\frac{24}{130} \times \frac{130}{52}\\\\=\frac{24}{52}\\\\=\frac{6}{13}\\[/tex]
Could someone help me pls! And could you explain if possible? Thanks you
Answer:
3%
Step-by-step explanation:
1. Set up the equation
6(0.18) + 12x = 18(0.08)
2. Simplify
1.08 + 12x = 1.44
3. Solve
12x = 0.36
x = 0.03
0.03 = 3%
Jonah read 5 1/2 chapters in his book in 90 minutes how long did it take him to read one chapter
Answer:
around 16 minutes. you partition an hour and a half (all out) by what number of sections he read (5.5
Step-by-step explanation:
HELPP PLEASEE ��2222 is the diameter of a circle. The coordinates are �(−2, −3) and �(−12, −5). At what coordinate is the center of the circle located? A. (5, 1) B. (−5, −1) C. (−4, −7) D. (−7, −4)
Answer:
(-7, -4) which is your answer D in the list of options
Step-by-step explanation:
The center of the circle should be located half way in between the given points on the plane.
Then the center ahs to be located half way for the x coordinates of both points:
half way between -12 and -2 (notice that there is a difference of 10 units between them), therefore half way would be at 5 units to the right from the furthest point, that is -12 + 5 = -7
Similarly, for the y coordinate, we see that the difference is between -5 and -3 (a difference of two units) therefore the center point will be located half way (that is one unit) up from the lowest y coordinate: -5 + 1 = -4
Then the center of the circle is located at (-7, -4)
A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.
2(2^3+7)^3+2(7^2+5)2
Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36. Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0 Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Ordered pair negative square root 65 comma 0 and ordered pair square root 65 comma 0 Center: (0, 0); Vertices: (0, -3), (0, -3); Foci: Ordered pair 0 comma negative square root 5 and ordered pair 0 comma square root 5 Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Ordered pair 0 comma negative square root 65 and ordered pair 0 comma square root 65
Answer:
Option A.
Step-by-step explanation:
The given equation of ellipse is
[tex]4x^2+9y^2=36[/tex]
Divide both sides by 36.
[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]
[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]
[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex] ...(1)
The standard form of an ellipse is
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] ...(2)
where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.
On comparing (1) and (2), we get
[tex]h=0,k=0,a=3,b=2[/tex]
Now,
Center [tex]=(h,k)=(0,0)[/tex]
Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]
We know that
[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]
Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]
Therefore, the correct option is A.
Given f(x) = –2x+5 find f'(x).
a f'(x)=- 5x+1.5
b.
x 5
2 2
f'(x) =
C. f'(x) = 2x-5
d.
x 5
2 2
f'(x) -- +
R
Please select the best answer from the choices provided
B.
ОООО
D
Answer: D
Step-by-step explanation:
To find the inverse function, you switch y with x and x with y. Then you solve for y.
y=-2x+5 [replace y with x and x with y]
x=-2y+5 [subtract both sides by 5]
x-5=-2y [divide both sides by -2]
(x-5)/-2=y
Now that we have our inverse function, we can rewrite it so that it matches the answer choice. D matches our answer choice the best.
Molly’s house is located at point X. Molly wants Sophia and Cole to meet at her house because she thinks it is the same distance from Sophia’s house and Cole’s house. Which could prove that Molly’s house is the samedistance from Sophia’s and Cole’s houses?
Answer:
Cole's House
Step-by-step explanation:
Cole house is closer because molly and Sophia can go there together because there both girls
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:
21, 14, 13, 24, 17, 22, 25, 12
Required:
a. Calculate the sample mean and the sample standard deviation.
b. Construct the 90% confidence interval for the population mean.
c. Construct the 95% confidence interval for the population mean
Answer:
a
[tex]\= x = 18.5[/tex] , [tex]\sigma = 5.15[/tex]
b
[tex]15.505 < \mu < 21.495[/tex]
c
[tex]14.93 < \mu < 22.069[/tex]
Step-by-step explanation:
From the question we are are told that
The sample data is 21, 14, 13, 24, 17, 22, 25, 12
The sample size is n = 8
Generally the ample mean is evaluated as
[tex]\= x = \frac{\sum x }{n}[/tex]
[tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]
[tex]\= x = 18.5[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]
[tex]\sigma = 5.15[/tex]
considering part b
Given that the confidence level is 90% then the significance level is evaluated as
[tex]\alpha = 100-90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 2.995[/tex]
The 90% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]
[tex]15.505 < \mu < 21.495[/tex]
considering part c
Given that the confidence level is 95% then the significance level is evaluated as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 3.569[/tex]
The 95% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]
[tex]14.93 < \mu < 22.069[/tex]
The U.S. National Whitewater Center in Charlotte uses a pump station to provide the flow of water necessary to operate the rapids. The pump station contains 7 pumps, each with a capacity to deliver 80,000 gallons per minute (gpm). The water channels and ponds in the facility contain 13 million gallons of water. If the pump station is operating 5 pumps simultaneously, assuming ideal conditions how long will it take to completely pump the volume of the system through the pump station
Answer:
t = 32,5 minutes
Step-by-step explanation:
Volume to fill = 13000000 Gal
5 pumps delivering 80000 gal/min
5 * 80000 = 400000 gal/min
If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then
t = 13000000/ 400000
t = 32,5 minutes
Evaluate 2/3 + 1/3 + 1/6 + … THIS IS CONTINUOUS. It is NOT as simple as 2/3 + 1/3 + 1/6.
[tex]a=\dfrac{2}{3}\\r=\dfrac{1}{2}[/tex]
The sum exists if [tex]|r|<1[/tex]
[tex]\left|\dfrac{1}{2}\right|<1[/tex] therefore the sum exists
[tex]\displaystyle\\\sum_{k=0}^{\infty}ar^k=\dfrac{a}{1-r}[/tex]
[tex]\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\ldots=\dfrac{\dfrac{2}{3}}{1-\dfrac{1}{2}}=\dfrac{\dfrac{2}{3}}{\dfrac{1}{2}}=\dfrac{2}{3}\cdot 2=\dfrac{4}{3}[/tex]
which operation should you perform first when evaluating the expression 3²+ 2
Answer:
You should calculate 3² first.
Step-by-step explanation:
In PEMDAS, E (which stands for exponents) comes before A (which stands for addition) so therefore you should calculate 3² first.
Explanation:
The acronym PEMDAS helps determine the order of operations
P = parenthesis
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
With the expression [tex]3^2+2[/tex] we have two operations going on here: exponents and addition.
Since exponents comes before addition (E comes before A in PEMDAS), this means we evaluate [tex]3^2[/tex] first, then add later.
I
Ifm DGF = 72, what equation can you use to find mZEGF?
Answer:
see explanation
Step-by-step explanation:
∠ DGE + ∠ EGF = ∠ DGF , that is
∠ EGF = ∠ DGF - ∠ DGE
∠ EGF = 72° - ∠ DGE
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.966 grams and a standard deviation of 0.315 grams. Find the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less.
Answer:
The probability is [tex]P(X \le 0.305 ) = 0.01795[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.966 \ grams[/tex]
The standard deviation is [tex]\sigma = 0.315 \ grams[/tex]
Given that the amounts of nicotine in a certain brand of cigarette are normally distributed
Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )[/tex]
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )[/tex]
From the z-table(reference calculator dot net ) value of [tex]P(Z >-2.0984 ) =0.98205[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205[/tex]
=> [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795[/tex]
=> [tex]P(X \le 0.305 ) = 0.01795[/tex]
