Answer:
y=-3x-2
Step-by-step explanation:
There is enough information to make a point-slope form equation that which we can convert into slope-intercept form.
Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]
We are given the slope of -3 and the point of (1,-5).
[tex]y-y_1=m(x-x_1)\rightarrow y+5=-3(x-1)[/tex]
Convert into Slope-Intercept Form:
[tex]y+5=-3(x-1)\\y+5-5=-3(x-1)-5\\\boxed{y=-3x-2}[/tex]
Evie has two sets of blocks of identical size and shape with the colors given. Evie will randomly select on block from each set. What is the probability she will select an orange block and a red block?
set A has 4 orange blocks and 3 yellow blocks.
set B has 5 blue blocks and 2 red blocks.
3/7
2/7
8/49
6/49
Answer:
[tex]\frac{8}{49}[/tex]
Step-by-step explanation:
Orange: [tex]\frac{4}{7}[/tex]
Red: [tex]\frac{2}{7}[/tex]
[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]
express the measure in standard notation 5 gal 6qt 48 oz
Answer: 880 oz
Step-by-step explanation:
We want to write it in the same units, let's use oz as our common unit.
1 gal = 128 oz
then 5 gal = 5*128 oz = 640 oz
1 qt = 32 oz
then 6 qt = 6*32 oz = 192 oz
Then we have:
640 oz + 192 oz + 48 oz = 880 oz
The value of standard notation is,
⇒ 880 oz
We have to given that,
Measures are,
⇒ 5 gal 6qt 48 oz
We have to change it into standard notation as,
We want to write it in the same units, let's use oz as our common unit.
1 gal = 128 oz
then 5 gal = 5 x 128 oz = 640 oz
1 qt = 32 oz
then 6 qt = 6 x 32 oz = 192 oz
Then we have:
⇒ 5 gal 6qt 48 oz
⇒ 640 oz + 192 oz + 48 oz
⇒ 880 oz
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Q 2.20: In a survey, there are two categories of respondents, employed and unemployed people, and two options, A and B. The proportion of those who have chosen option B is greater than 0.5 among the total number of the respondents, but is lower than 0.5 among the unemployed respondents. We know that 314 employed and 512 unemployed people chose option A and 356 employed chose option B. How many unemployed people chose option B
Answer:
The answer is 508
Step-by-step explanation:
Solution
First of all, the proportion of B is exceeds 0.5 in total.
Now,
To find the total of A it we have A =314 +512 = 826
The number of employed that choose B = 356
For us to have the proportion of B to be higher than the 0.5, the unemployed B from what is shown here should exceed the difference between total A and B employed
what this suggest is that the employed B is greater than 826-356 = 470
So,
The respondent that are unemployed that choose B must be greater than 470
Thus,
We recall that the B proportion among the unemployed respondent is lesser than .50
Thus suggests that the respondent that are unemployed who choose be is lesser than 512
The conditions becomes
470 lesser than the number of unemployed respondents who selected B lesser than 512
Hence the needed number of the number of unemployed respondents who chose B should be between 470 and 512
So, possible answer here is 508.
An online shopping website collected data regarding its operations and obtained the following linear regression model for the estimated revenue in millions, Y-hat, based on the click-through rate in thousands, x. Y-hat = 1.2+0.2x
What is the best interpretation of the value of the estimated slope of 0.2?
Answer:
There is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks
Step-by-step explanation:
The slope (0.2) is the rate of change in Y-hat for each unit change in x.
In this specific case, since Y-hat is the revenue, in millions, and x is the number of clicks, in thousands, the best interpretation is that there is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
Answer:
-3 =n
Step-by-step explanation:
11(n – 1) + 35 = 3n
Distribute
11n -11 +35 = 3n
Combine like terms
11n +24 = 3n
Subtract 11n from each side
11n +24 -11n = 3n -11n
24 = -8n
Divide each side by -8
24/-8 = -8n/-8
-3 =n
Answer: n=-3
Step-by-step explanation:
11n-11+35=3n
24=-8n
n=-3
The sum of an infinite geometric sequence is seven times the value of its first term.
a) Find the common ratio of the sequence.
b) Find the least number of terms of the sequence that must be added in order for the sum to exceed half the value of
the infinite sum.
Answer:
a). r = [tex]\frac{6}{7}[/tex]
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,
[tex]S_{\inf}=\frac{a}{1-r}[/tex]
Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.
[tex]7a=\frac{a}{1-r}[/tex]
[tex]7=\frac{1}{1-r}[/tex]
7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r = [tex]\frac{6}{7}[/tex]
b). Since sum of n terms of the geometric sequence is given by,
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]
If the sum of n terms of this sequence is more than half the value of the infinite sum.
[tex]\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}[/tex] > [tex]\frac{7a}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{1}{2}[/tex]
[tex]-(\frac{6}{7})^{n}> -\frac{1}{2}[/tex]
[tex](\frac{6}{7})^{n}< \frac{1}{2}[/tex]
[tex](0.85714)^{n}< (0.5)[/tex]
n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n > [tex]\frac{0.30102}{0.06695}[/tex]
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.
Which equation can be used to solve for b?
B
5 cm
С
10 cm
b
30
A
O tan(30)=5/b
O tan(30)=b/5
O tan(30)=10/b
O tan(30)=b/10
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: oppo. = 5 \\ let \: adj. = b \\ let \: θ = 30[/tex]
[tex] \tan(30) = \frac{5}{b} [/tex]
The correct answer is option (A) tan(30)=5/b
Tangent functionThe tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.How to solve this problem?The steps are as follow:
The right angle triangle is given whose sides are as follow:AB = 10 cm
BC = 5 cm
AC = b cm
To find the tan(30) we will use following formula:tan(x) = opposite side / adjacent side
tan(30) = BC / AC
tan(30) = 5 / b
So, the correct answer is option (A) tan(30)=5/b
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Find the quotient
-99 over -11
Answer:
the quotient is 9 because a negative divided by a negative is a positive
Analyze the diagram below and answer the question that follows.
Answer:
B. Complements of congruent angles are congruent.
Step-by-step explanation:
Angles <DCF and <FEG have angles measures that are complementary to to angles E and C.
Duke takes a car in for basic service. The service agent says a few extra repairs are needed, so Duke adds the cost of those repairs mentally, rounding to the nearest 10. What is Duke's total estimate for the repairs? The costs are as follows: Wheel alignment: $82 Transmission fluid flush: $157 Cabin air filter: $58 Note: 4 or less rounds down, 5 or more rounds up. For example, 14 becomes 10, while 15 becomes 20.
Answer:
The total repair cost was around $300 .
Step-by-step explanation:
I wasn't sure when you were saying to round, so here are two options.
(For rounding at the end) :
82+157+58 = 297
Rounds to 300.
(For rounding as he's adding everything up) :
80+160+60= 300.
So either way it's 300!
Hope this helped!
5. The value of 25sqare -24sqare
Answer:
49
Step-by-step explanation:
25²-24²
625-576
=49
use calculator lah dehh
A digital scale measures weight to the nearest 0.2 pound. Which measurements shows an appropriate level for the scale ?
Answer: Answer choices 1, 3, 4
Step-by-step explanation:
As long as it ends in .0, .2, .4, .6, or .8 it's fine. Therefore the first and last 2 work, since 0.2 can end in either of those 5 values.
Hope that helped,
-sirswagger21
What’s the correct answer for this? Select two answers that, when combined, show that circles are similar
Answer:
A and F
Step-by-step explanation:
First we'll dilate it by a scale factor of 2. After that, we'll translate in 6 units left and 6 units up to map circle J onto circle K
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answer:
y = (-3/4)x + 7/4
Step-by-step explanation:
Step 1: Define general form of equation of line
An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept
Step 2: Set up the system to solve for parameters of equation of line
(solve for M and b)
That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).
Substitute these values of x and y into the original equation in step 1:
-2 = 5M + b
4 = -3M + b
Step 3: Solve the system of equations in step 2 for M and b
Subtract 1st equation from 2nd equation:
6 = -8M
=> M = -6/8 = -3/4
Substitute M back into 1st equation:
=> -2 = 5*(-3/4) + b
=> b = -2 + 15/4
=> b = 7/4
=> The equation of the line that passes through (5, -2) and (-3, 4):
y = (-3/4)x + 7/4
Hope this helps!
:)
Answer:
Y= -4/3(x-7/2)
Step-by-step explanation:
So first calculate the difference between them,
changes by 8 x units, and -6 y units.
Then substitute them into y/x to find gradient
-6/8 = -4/3
so now we have a part of the equation:
Y= -4/3(x-a)
substitute Y= -2 and x=5 (from (5,-2))
-2= -4/3(5-a)
-2= -20/3+4a/3
Multiply by 3 on both sides
-6= -20+4a
add 20 on both sides
14=4a
a=7/2
use this as the value of a
Y= -4/3(x-7/2)
Which are steps that could be used to solve 0 = 9(x2 + 6x) – 18 by completing the square? Check all that apply. 18 + 81 = 9(x2 + 6x + 9) 18 + 9 = 9(x2 + 6x + 9) 18 + 36 = 9(x2 + 6x + 36) 11 = (x + 3)2 StartRoot 342 EndRoot = (x + 6)2 StartRoot 99 EndRoot = (x + 3)2
Answer:
18 + 81 = 9(x² + 6x + 9)
11 = (x + 3)²
When we are completing the square, we are going to move the value of c across the equals. We will do that by adding, and end up with
18=9(x²+6x)
We take the value of b (the coefficient of x), divide it by 2 and square it:
(6/2)²=3²=9
This is the value that completes the square. However, since the entire square is multiplied by 9, this value must be multiplied by 9 before we can add it across the equals:
18+9(9) = 9(x²+6x+9)
18+81=9(x²+6x+9)
99=9(x²+6x+9)
Dividing both sides by 9, we have:
11=x²+6x+9
11=(x+3)²
Answer:
18 + 81 = 9(x2 + 6x + 9) and 11 = (x + 3)2
Step-by-step explanation:
EDG
expand and simplify (x - 2)^2
these are the options
2 + 4 + 4 2 − 4 2 − 4 + 4 2 + 4
Answer:
[tex]x^2-4x+4[/tex]
Step-by-step explanation:
[tex](x - 2)^2[/tex]
[tex](x - 2)(x - 2)[/tex]
[tex]x(x-2)-2(x-2)[/tex]
[tex]x^2-2x-2x+4[/tex]
[tex]x^2-4x+4[/tex]
Answer:
[tex]{x}^{2} - 4x + 4 \\ [/tex]
Step-by-step explanation:
[tex] {(x - 2)}^{2} \\ (x - 2)(x - 2) \\ x(x - 2) - 2(x - 2) \\ {x}^{2} - 2x - 2x + 4 \\ {x}^{2} - 4x + 4[/tex]
hope this helps you
The probability that an event will happen is Upper P (Upper E )equalsStartFraction 13 Over 17 EndFraction . Find the probability that the event will not happen. The probability that the event will not happen is nothing.
Answer:
The probability that the event will not happen is [tex]\frac{4}{17}[/tex]
Step-by-step explanation:
The occurrence of an event can be divided into two parts, the event would occur or the event would not occur. But the probability of an event is 1.
From the given question;
The probability of the event = 1
The probability that the event will happen, P = [tex]\frac{13}{17}[/tex]
Thus,
The probability that the event will not happen = probability of the event - probability that the event will happen
= 1 - P
= 1 - [tex]\frac{13}{17}[/tex]
= [tex]\frac{17 - 13}{17}[/tex]
= [tex]\frac{4}{17}[/tex]
Thus, the probability that the event will not happen is [tex]\frac{4}{17}[/tex].
If 20 drops fall in 76 seconds, how long will 8 drops take?
Answer:
x =30.4 seconds
Step-by-step explanation:
We can use ratios to solve
20 drops 8 drops
--------------- = ----------------
76 seconds x seconds
Using cross products
20x = 8*76
20x =608
Divide each side by 20
20x/20 = 608/20
x =30.4 seconds
Answer:
30.4 secs = 30secs
Step-by-step explanation:
20 drops fall in 76s
Hence 1 drop is 76/20
Therefore 8 drops would be ;
76/20 × 8 = 30.4 secs
You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this. If you roll a 1, 2 or 3, you win $50. If you roll a 4 or 5, you lose $20. If you roll a 6, you lose $90.
EV= $
Step-by-step explanation:
Take the $50 and quit.
(Each game as outlined by drwls has an expected value of $1.50.
You are playing it 5 times, so the expected return is $7.50.
Your choice was to either accept $50 or play the game)
If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and the sum of the ages of all 3 is 147 years, what is the age difference between oldest the youngest?
Answer:
48
Step-by-step explanation:
Esinam shere a common ratio hence,
the lcm of 3 and 5 is 15
Kissi:Esinam= 9:15 and Esinam:Lariba=15:25
Combining; 9:15:25
Let x be the ages such that,
Kissi=9x and Esinam=15x and Lariba=25x
9x+15x+25x=147
49x=147
x=3
Youngest; Kissi=9x=9(3)=27
Oldest; Lariba=25x=25(3)=75
Difference 75-27=48
help me please!!!! Dan's car depreciates at a rate of 8% per year. By what percentage has Dan's car depreciated after 3 years? Give your answer to the nearest percent.
Answer:
22%
Step-by-step explanation:
Car's price is reduced by 8% or 0.92 times a year
after 3 years it will make:
0.92³= 0.778688≈ 0.78 timesor
0.78 = 1- 0.22price decrease = 22%Answer:
Hello!
Here is your answer:
22%
I hope I was able to help you. If not, please let me know!
Step-by-step explanation:
Adam earns $45,000 in his first year as an accountant and earns a 3% increase in each
successive year.
(a) Write a geometric series formula,
n S
, for Adam’s total earnings over
n
years.
(b) Use this formula to find Adam’s total earnings for her first 12 years of his job, to the nearest
cent.
Answer:
$638641.33
Step-by-step explanation:
Adam earns $45,000 in his first year.
His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.
This is a geometric sequence where the:
First Term, a= $45,000Common ratio, r =103%=1.03(a)
Sum of geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]
Substituting the given values, Adam's total earnings over n years
[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]
(b)When n=12 years
[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]
if you’re good with probability in math 30 please help and answer the question below!!
A six-sided number cube has faces with the numbers 1 through 6 marked on it. What is the probability that a number less than 3 will occur on one toss of the number cube?
a) 1/6
b) 1/2
c) 1/3
d) 2/3
Answer: b) 1/3
Step-by-step explanation:
The numbers LESS THAN 3: 1, 2
[tex]\dfrac{\text{Quantity of numbers less than 3}}{Total\ number}\quad =\dfrac{2}{6}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/10
There are 42 red marbles in the bag and each is equally likely to be chosen.
How many marbles in total must there be?
Answer:
There are 60 marbles in the bag
Step-by-step explanation:
The total number of marbles times the probability of red marbles = number of red marbles
total * 7/10 = 42
Multiply each side by 10/7
total * 7/10 * 10/7 = 42*10/7
total
60
There are 60 marbles in the bag
A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds x=20.6 months and s=8 months. Test the claim that u=18.7 months at the 0.05 significance level.
Answer:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
Step-by-step explanation:
Information given
[tex]\bar X=20.6[/tex] represent the sample mean
[tex]s=8[/tex] represent the sample standard deviation
[tex]n=11[/tex] sample size
[tex]\mu_o =18.7[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypotesis to test
We want to verify if the true mean is equal to 18.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu =18.7[/tex]
Alternative hypothesis:[tex]\mu \neq 18.7[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
How would you use a completely randomized experiment in each of the following settings?
Is a placebo being used or not? Be specific and give details.
a. A charitable nonprofit organization wants to test two methods of fund-raising. From a list of 1000 past donors, half will be sent literature about the successful activities of the charity and asked to make another donation. The other 500 donors will be contacted by phone and asked to make another donation. The percentage of people from each group who make a new donation will be compared.
b. A tooth-whitening gel is to be tested for effectiveness. A group of 85 adults have volunteered to participate in the study. Of these. 43 are to be given a gel that contains the tooth-whitening chemicals. The remaining 42 are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals. A standard method will be used to evaluate the whiteness of teeth for all participants. Then the results for the two groups will be compared. How could this experiment he designed to be double-blind?
c. Consider the experiment described in part (a). Describe how you would use a randomized block experiment with blocks based on age. Use three blocks: donors younger than 30 years old. donors 30 to 59 years old. donors 60 and older.
Answer:
Step-by-step explanation:
a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.
b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.
c. Using three blocks: the completely randomized design experiment would be:
Donors younger than 30 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 30 to 59 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 60 and older:
Sent literature: Yes No
Contact by phone: Yes No
(Yes means yes to another donation and No means no to another donation)
Answer:
Step-by-step explanation:
a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.
b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.
c. Using three blocks: the completely randomized design experiment would be:
Donors younger than 30 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 30 to 59 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 60 and older:
Sent literature: Yes No
Contact by phone: Yes No
(Yes means yes to another donation and No means no to another donation)
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained. 0.10 0.13 0.16 0.15 0.14 0.08 0.15 (a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars. (b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a),
The question is incomplete. Here is the complete qeustion.
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15
(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.
(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?
Answer: (a) 0.089 ≤ μ ≤ 0.171
(b) No
Step-by-step explanation:
(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample
X = [tex]\frac{0.1+0.13+0.16+0.15+0.14+0.08+0.15}{7}[/tex]
X = 0.13
s = [tex]\sqrt{\frac{(0.1-0.13)^{2} + (0.13 - 0.13)^{2} + ... + (0.15 - 0.13)^{2}}{7-1} }[/tex]
s = 0.029
The degrees of freedom is
N - 1 = 7 - 1 = 6
And since the confidence is of 99%:
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The t-test statistics for [tex]t_{6,0.005}[/tex] is 3.707
(Value found in the t-distribution table)
Now, calculate Error:
E = [tex]t_{6,0.005}[/tex] . [tex]\frac{s}{\sqrt{N} }[/tex]
E = 3.707. [tex]\frac{0.029}{\sqrt{7} }[/tex]
E = 0.041
The interval will be:
0.13 - 0.041 ≤ μ ≤ 0.13+0.041
0.089 ≤ μ ≤ 0.171
(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.
Suppose you are planning an experiment and a sample has yet been selected. For this experiment you plan on taking a SRS of 50 mice with pancreatic cancer measuring a particular hormone level. What would be the impact on a 95% confidence interval calculated from the experiment on these mice if instead of a SRS of 50 mice, a SRS of 200 mice were taken?
Answer:
The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)
- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.
- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value
Critical value for 95% = 1.96
The critical value for both samples are the same then.
- Standard Error of the mean = σₓ = (σ/√n)
where σ = population standard deviation
n = sample size
For the two distributions
Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)
(Sample mean)₅₀ = (Sample mean)₂₀₀
(Critical value)₅₀ = (Critical value)₂₀₀
(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ
(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ
0.1414σ = 2 × 0.0707σ
(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀
(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀
Hence,
(Margin of Error)₅₀ > (Margin of Error)₂₀₀
(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀
Confidence Interval = (Sample mean) ± (Margin of error)
Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.
Hope this Helps!!!
An architect creates a scale model. The volume of the scale model is 0.1 cubic meters. The volume of the real-world
building is 100,000 cubic meters. What is the ratio of corresponding sides from model to real world?
Answer:
1:0.4641
Step-by-step explanation:
We are told that the scale of the model with respect to the real world is 0.1 cubic meter. This means that for every 1 cubic meter in the real world the model represents 0.1.
They tell us that the real world volume is 100,000, that if we assume a cube, we have to:
V = l ^ 3
l = 100000 ^ (1/3)
l = 46.41
46.41 meters would be each side, now the volume of the model would be:
100,000 * 0.1 = 10,000
Which means that its sides would be:
V = l ^ 3
l = 100000 ^ (1/3)
l = 21.54
We calculate the scale of the sides:
21.54 / 46.41 = 0.4641
Which means that for every 1 meter in the real world the model represents 0.4641 meters.
Choose the equation of the graph shown below:
y = |x - 1| - 3
y = |x + 1| - 3
y = |x - 1| + 3
Answer:
y=[x+1]-3 because it's at the end of the line
