Answer:
Step-by-step explanation:
Hello!
There are two values of n in the text, I'll use the one that appears in all the questions.
The variable of interest is
X: pollutants found in waterways near large cities. (ppm)
This variable has a normal distribution with parameters μ= 9ppm and σ= 1.5ppm
1) X~N(μ;σ²)
X~N(9;2.25)
2) The distribution of the sample mean is X~N(μ;σ²/n)
σ²/n= 2.25/37= 0.06
X~N(9;0.06)
3) P(X>9.6)
To calculate this probability you have to use the standard normal distribution. Using the population parameters, you can calculate the corresponding Z value:
Z= (X-μ)/σ= (9.6-9)/1.5= 0.4
P(Z>0.4)= 1-P(Z≤0.4)= 1 - 0.65542= 0.34458
The probability of selecting a city at random and finding 9.6ppm pollutants.
4) In this item, instead of calculating the probability of one value of the variable you have to calculate the probability of the sample average taking a determined value. Because of this, you have to work using the distribution of the sample mean, instead of the distribution of the variable.
P(X[bar]>9.6)
Z= (X[bar]-μ)/(σ/√n)= (9.6-9)/√0.06= 2.45
P(Z>2.45)= 1 - P(Z≤2.45)= 1 - 0.99286= 0.00714
5) The assumption of a normal distribution is not necessary for item 4. Since the sample size is large enough (greater than 30) you can apply the central limit theorem and approximate the distribution of the sample mean to normal, regarding the distribution of the original variable.
6)
In this case, you have to work starting with the standard normal distribution and then "translate" the Z values into values of the average amount of pollutants.
The first quartile divides the bottom 25% of the distribution from the top 75%, symbolically:
P(Z≤z₁)= 0.25
z₁= -0.674
z₁= (X[bar]-μ)/(σ/√n)
z₁*(√n/σ)=X[bar]-μ
X[bar]=z₁*(√n/σ)+μ
X[bar]=(-0.674)*(√37/1.5)+9= 6.27ppm
The third quartile divides the bottom 75% of the distribution from the top 25%, symbolically:
P(Z≤z₂)= 0.75
z₂= 0.674
z₂= (X[bar]-μ)/(σ/√n)
z₂*(√n/σ)=X[bar]-μ
X[bar]=z₂*(√n/σ)+μ
X[bar]=(0.674)*(√37/1.5)+9= 11.7.3ppm
IQR= Q₃-Q₁= 11.73-6.27= 5.46ppm
I hope this helps!
The following crosstabulation summarizes the data for two categorical variables, x and y. The variable x can take on values low, medium, or high and the variable y can take on values yes or no.
Y
X Yes No Total
Low 20 10 30
Medium 15 35 50
High 20 5 25
Total 55 50 105
1. Compute the row percentage
2. Construct a sketch percentage of frequency bar chat with x on horozontal axis.
Answer:
Step-by-step explanation:
From the given data:
The row percentage can be determined by: taking each box in each row and by dividing it with its total on that line, after that we will multiply it by 100 to get the result of it's equivalent percentage.
Table reconstruct the table from the question ; we have:
y
x Yes No Total
Low 20 10 30
Medium 15 35 50
High 20 5 25
Total 55 50 105
For Low; the total on the row is 30 ;
so for Yes: we have 20/30 × 100 = 66.7
for No ; we have 10/30 × 100 = 33.3
For Medium ; the total on the row is 50 ;
so for Yes: we have 15/50 × 100 = 30
for No ; we have 35/50 × 100 = 70
For High ; the total on the row is 25;
so for Yes: we have 20/25 × 100 = 80
for No ; we have 5/25 × 100 = 20
y
x Yes No Total
Low 66.7 33.3 100
Medium 30 70 100
High 80 20 100
b. The construction of a sketch percentage of the frequency bar chat with x on horizontal axis is shown in the attached file below.
One day Pat Unger worked for a total of 8
hours. She worked 3 hours more in the after-
noon than she worked in the morning. How
long did she work in the afternoon?
Answer:
5.5 hours
Step-by-step explanation:
Let the no. of hours worked in morning by Pat = x hours
given that "She worked 3 hours more in the after-
noon than she worked in the morning"
No. of hours worked in Afternoon by Pat = x + 3 hours
Total hours worked in the day = x + x+3 = 2x +3 hours (1)
It is given that Pat worked for 8 hours that day (2)
thus, using 1 and 2 we have
2x +3 = 8
=>2x = 8 - 3 = 5
=> x = 5/2 = 2.5
no. of hours worked in morning by Pat = x hours = 2.5 hours
No. of hours worked in Afternoon by Pat = x + 3 hours = 2.5 + 3 hours
No. of hours worked in Afternoon by Pat = 5.5 hours --- Answer.
The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is nonnegative and less than the speed of light, c which is constant. Use lower case letters here. E = mc^2 (1/Squareroot1 - v^2/c^2 - 1)
(a) Find E/m = c^2Squareroot1 - v^2/c^2 - c^2/1 - v^2/c^2 what is the sign of this partial? Positive negative
(b) Find E/v =?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\frac{\delta E}{\delta m}= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
b
[tex]\frac{\delta E}{\delta V} = \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Step-by-step explanation:
From the question we are given
[tex]E = mc^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } }- 1 ][/tex]
So we are asked to find [tex]\frac{\delta E}{\delta m}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta m} = \frac{\delta }{\delta m} [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 )][/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2 } } } -1 ] \frac{\delta m}{\delta m}[/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
Also we are asked to find [tex]\frac{\delta E}{\delta V}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta V} = \frac{\delta }{\delta v } [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } - 1 )][/tex]
[tex]\frac{\delta E}{\delta V} = mc^2 [\frac{\delta }{\delta v} (\frac{c}{\sqrt{c^2 -v^2} } - 1 )][/tex]
[tex]= mc^2 [c* [\frac{\delta }{\delta v} (c^2 - v^2 )^{-\frac{1}{2} }] - 0][/tex]
[tex]= mc^3 [- \frac{1}{2} (c^2 - v^2 )^{-\frac{3}{2} } * (-2v)][/tex]
[tex]= \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Select the correct answer
Why are online payment services necessary?
OA
Individuals who sell items online cannot afford to deal with credit card companies.
B.
It is too risky to use credit cards online, and online payment services have better security
C. Government regulations require all online transactions be made using online payment services.
D.
Online payment services are the only payment method that individuals who sell items online trust.
Reset
Nalut
Answer:
B
Step-by-step explanation:it is really too risky to use credit card online because for someone who doesnt now if the busines is really considered as a trustful source or just a scam.
Answer:
Its A.) Individuals who sell items online cannot afford to deal with credit card companies.
Step-by-step explanation:
On plato
Find the area of the triangle
Answer:
54
Step-by-step explanation:
A = (9*12)/2
A = 9*6
A = 54
Answer:54
Step-by-step explanation:
multiply 9 and 12 then divide by 2 because a triangle is half of a square
Which of the following is a subset of every set? * 1)Universal Set 2)Null Set 3)Both of these 4)None of these
Answer:
[tex]1[/tex]
Step-by-step explanation:
Universal set contains all elements and of which all other sets are subsets.
Which is the same as asking:
To what power must 5 be raised to get 3,125?
Answer: 5^5
Step-by-step explanation:
Since 5x5x5x5x5 = 3,125
Simplify (1+√3) (2-√3).
Answer:
[tex] \sqrt{3} - 1[/tex]
Step-by-step explanation:
[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]
The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7
Answer:
-2 is an output of the function.
Step-by-step explanation:
The given table is as follows:
[tex]\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right][/tex]
Here, the values written on the left side of table i.e. values of [tex]x[/tex] are known as the domain values or input values to a function.
The values written on the right side of table i.e. values of [tex]f(x)[/tex] are known as the range values or output values of the function [tex]f(x)[/tex].
Let us consider the pairs of values:
(-6,8) then left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=-6[/tex], the output value [tex]f(x) =8[/tex].
The same thing applies for all the pairs of values.
similarly for the pair (3,-2):
Left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=3[/tex], the output value [tex]f(x) =-2[/tex].
So, the answer is:
-2 is an output of the function.
Answer:
-2
Step-by-step explanation:
how do you add 9 1/6 + 2 1/12
Answer:
11 1/4
Step-by-step explanation:
first make the fractions equal. So 9 1/6 would be 9 2/12 so that we canadd them together.
9 2/12 + 2 1/12 = 11 3/12
but u can simplify the answer so itll be 11 1/4
[tex]answer = 11 \ \frac{3}{12} \\ solution \\ 9 \ \frac{1}{6} + 2 \ \frac{1}{12} \\ = \frac{55}{6} + \frac{25}{12} \\ = \frac{55 \times 2 + 25}{12} \\ = \frac{110 + 25}{12} \\ = \frac{135}{12} \\ = 11 \ \ \frac{3}{12} \\ hope \: it \: helps[/tex]
The weekly salaries of sociologists in the United States are normally distributed and have a known population standard deviation of 425 dollars and an unknown population mean. A random sample of 22 sociologists is taken and gives a sample mean of 1520 dollars.
Find the margin of error for the confidence interval for the population mean with a 98% confidence level.
z0.10 z0.05 z0.025 z0.01 z0.005
1.282 1.645 1.960 2.326 2.576
You may use a calculator or the common z values above. Round the final answer to two decimal places.
Answer:
[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:
[tex]z_{\alpha/2}= 2.326[/tex]
And replacing we got:
[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\sigma = 425[/tex] represent the population deviation
[tex] n =22[/tex] the sample size
[tex]\bar X =1520[/tex] represent the sample mean
We want to find the margin of error for the confidence interval for the population mean and we know that is given by:
[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:
[tex]z_{\alpha/2}= 2.326[/tex]
And replacing we got:
[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]
What is the approximate value of sin B?
B
>
17.46
7
A
16
Answer:
Option (B)
Step-by-step explanation:
From the figure attached,
AB = 7 units
BC = 17.46 units
AC = 16 units
Now we apply the sine rule in the given triangle ABC,
SinB = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{16}{17.46}[/tex]
= 0.916
≈ 0.92
Therefore, Option (B) will be the answer.
Answer:
DIFFERENT PICS
Step-by-step explanation:
I had one and the awnser was 0.40, and C had a arch whereas B did not.
The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.
Part A
Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.
Express your answer using two significant figures.
Part B
The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
Express your answer using two significant figures.
Part D
Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?
Express your answer using two significant figures.
Answer:
A. 1.8 ×[tex]10^{30}[/tex] Kg
B i. 3.0 × [tex]10^{17}[/tex] seconds
ii. 9.6 × [tex]10^{9}[/tex] years
C. After 9.2 × [tex]10^{9}[/tex] (9.2 billion) years
Step-by-step explanation:
Given that the mass of the Sun = 2× [tex]10^{30}[/tex] Kg.
Mass of hydrogen when Sun was formed = 76% of 2× [tex]10^{30}[/tex] Kg
= [tex]\frac{76}{100}[/tex] ×2× [tex]10^{30}[/tex] Kg
= 1.52 × [tex]10^{30}[/tex] Kg
Mass of hydrogen available for fusion = 12% of 1.52 × [tex]10^{30}[/tex] Kg
= [tex]\frac{12}{100}[/tex] × 1.52 × [tex]10^{30}[/tex] Kg
= 1.824 ×[tex]10^{30}[/tex] Kg
A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 ×[tex]10^{30}[/tex] Kg.
B. Given that the Sun fuses 6 × [tex]10^{11}[/tex] Kg of hydrogen each second.
i. The Sun's initial hydrogen would last;
[tex]\frac{1.8*10^{30} }{6*10^{11} }[/tex]
= 3.04 × [tex]10^{17}[/tex] seconds
The Sun's hydrogen would last 3.0 × [tex]10^{17}[/tex] seconds
ii. Since there are 31536000 seconds in a year, then;
The Sun's initial hydrogen would last;
[tex]\frac{3.04*10^{17} }{31536000}[/tex]
= 9.640 × [tex]10^{9}[/tex] years
The Sun's hydrogen would last 9.6 × [tex]10^{9}[/tex] years.
C. Given that our solar system is now about 4.6 × [tex]10^{9}[/tex] years, then;
[tex]\frac{9.6*10^{9} }{4.6*10^{9} }[/tex]
= 2.09
So that; 2 × 4.6 × [tex]10^{9}[/tex] = 9.2 × [tex]10^{9}[/tex] years
Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × [tex]10^{9}[/tex] years.
Part(A): The total mass of hydrogen available 9.6 billion years.
Part(B): The total time is 5.10 billion years.
Part(D): The hydrogen will last [tex]5.04\times 10^9 \ years[/tex]
Mass of the sun:Our sun is the largest object in our solar system. The mass of the sun is approximately [tex]1.988\times 1030[/tex] kilograms
Part(A):
Given that,
The total mass of the Sun =[tex]2\times10^{30} kg[/tex]
Mass of hydrogen in Sun = [tex]2\times10^{30} \times0.76\ kg[/tex]
The mass of hydrogen ever available for fusion is,
[tex]2\times10^{30} \times 0.76 \times 0.12 kg = 1.824\times 10^{29}[/tex]
Mass of hydrogen fuses each second = 600 billion kg/second.
Time hydrogen will last in seconds=[tex]1.824\times 10^{29}seconds.[/tex]
[tex]= 0.00304\times 10^{29 }= 3.04\times 10^{17}.[/tex]
Time hydrogen will last in seconds =[tex]1 year = 31,536,000 seconds.[/tex]
[tex]31,536,000 x = 3.04\times 10^{17} = 9.6 \ billion \ years.[/tex]
(B) Present age of sun = [tex]9.6-4.5 \ billion \ years[/tex]
The time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.
(D) The solar system is 4.6 billion years old that is [tex]4.6\times 10^9\ years[/tex]
And in part (B) we have calculated that hydrogen will last [tex]9.64\times 10^9[/tex] then,
[tex]9.64\times 10^9-4.6\times 10^9=5.04\times 10^9[/tex]
Learn more about the topic mass of the sun:
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Express loga 6 + loga 70 as a single logarithm
Answer:
logₐ(420)
Step-by-step explanation:
Answer:
The answer is
[tex] log_{a}(420) [/tex]
Step-by-step explanation:
You have to use Logarithm Law,
[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]
* Take note, number b and c can only be multiplied when they have the same base, a
So for this question :
[tex] log_{a}(6) + log_{a}(70) [/tex]
[tex] = log_{a}(6 \times 70) [/tex]
[tex] = log_{a}(420) [/tex]
A start-up news company is looking to expand their audience and is interested in studying the how many adults regularly use social media as a source of news. According to the Pew Research Center, 62% of adults get their news from social media, but researchers want to determine of this proportion is actually greater than 62% in region they plan on advertising on.
They take a random sample of 200 adults in the region they are interested in advertising in and what they use to typically get their news. A total of 137 adults reported regularly getting their news from social media.
The point estimate for this problem is: (report your answer to 3 decimal places)
Checking Conditions: We are told that the sample was randomly selected. Are the other conditions met to perform a hypothesis test for p?
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
C) Yes, the population standard deviation is known.
D) No, the population mean is unknown.
Answer:
Step-by-step explanation:
The point estimate is the sample proportion.
Considering the sample,
Sample proportion, p = x/n
Where
x = number of success = 137
n = number of samples = 200
p = 137/200 = 0.685
From the information given,
Population proportion = 62% = 62/100 = 0.62
The correct options are
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
if jm = 5x - 8 and lm = 2x - 6, which expression represents jl
Answer:
7x -14 = jl
Step-by-step explanation:
Assuming a straight line
jm+ ml = jl
5x-8 + 2x-6 = jl
Combine like terms
7x -14 = jl
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
Answer:
The expected value of each warranty sold is $23.8.
Step-by-step explanation:
0.8% probability of the product failling.
If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.
100 - 0.8 = 99.2% probability of the product not failling.
If the product does not fail, the company gains $27.
What is the company's expected value of each warranty sold?
We multiply each outcome by its probability.
0.008*(-373) + 0.992*27 = 23.8
The expected value of each warranty sold is $23.8.
Ben bought 4 volleyballs and 5 footballs for $352.65 altogether. If Ben’s brother bought 2 volleyballs and 4 footballs for $249.12 altogether, what was the price of each football?
Answer:
$48.53
Step-by-step explanation:
The purchases can be written in equation form as ...
4v +5f = 352.65
2v +4f = 249.12
Doubling the second equation and subtracting the first gives ...
2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)
3f = 145.59 . . . . simplify
f = 48.53 . . . . . . divide by 3
The price of each football was $48.53.
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of balloon = 4/3πr³
= 4/3(3.14)(0.5)³
= 0.52 cubic feet
Now
A helium tank contains 50 cubic feet of helium So,
Spherical balloons = 50/0.52
= 95.4
≈ 100
If y = x² + 2x,
find the value of y when x = 5
_____________________________
Hey!!
Solution,
X=5
Now,
y=x^2+2x
=(5)^2+2*5
=25+10
= 35
So the value of y is 35
hope it helps
Good luck on your assignment
___________________________
For the given equation y = x² + 2x, the value of y when x = 5 is, 35
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation, y = x² + 2x
The value of y when x is equal to 5 = ?
after putting value of x in a equation
⇒ y = 5² + 2 × 5
⇒ y = 25 + 10
⇒ y = 35
Hence, the value of y is 35
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Jodie Meeks's Free Throws During the 2015-16 NBA season, Jodie Meeks of the Detroit Pistons had a free throw shooting percentage of 0.906 . Assume that the probability Jodie Meeks makes any given free throw is fixed at 0.906 , and that free throws are independent.If Jodie Meeks shoots 6 free throws in a game, what is the probability that he makes at least 5 of them?
Answer:
0.8973
Step-by-step explanation:
Relevant data provided in the question as per the question below:
Free throw shooting percentage = 0.906
Free throws = 6
At least = 5
Based on the above information, the probability is
Let us assume the X signifies the number of free throws
So, Then X ≈ Bin (n = 6, p = 0.906)
[tex]P = (X = x) = $\sum\limits_{x}^6 (0.906)^x (1 - 0.906)^{6-x}, x = 0,1,2,3,.., 6[/tex]
Now
The Required probability = P(X ≥ 5) = P(X = 5) + P(X = 6)
[tex]= $\sum\limits_{5}^6 (0.906)^5 (1 - 0.906)^{6-5} + $\sum\limits_{6}^6 (0.906)^6 (1 - 0.906)^{6-6}[/tex]
= 0.8973
ABDC is a rhombus with side length 10cm
angle ADC=40degrees
DAC is a sector of a circle with center D
BAC is a sector of a circle with center B
CALCULATE THE SHADED AREA (in cm2)
A survey was sent out to compare the proportion of adults who use their car horns when driving for two age populations (1=younger adults, defined as between 20 and 39 years old and 2 =older adults, defined as over 60 years old). The following data was obtained from those who responded.
Calculate the 90% confidence interval using the standard normal distribution. Note that 1 =0.52. P2= 0.35, and s.e.(P1-P2) =0.0338. Round to the fourth decimal point. Please enter you answer in the following format: (lower value, upper value)
Use the horn Use the horn
Group Yes No Total
1= younger adults 261 240 501
2= older adults 123 229 352
Answer:
The 90% confidence interval for the difference between proportions is (0.115, 0.228).
As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.
Step-by-step explanation:
We want to calculate the bounds of a 90% confidence interval.
For a 90% CI, the critical value for z is z=1.645.
The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.
[tex]p_1=X_1/n_1=261/501=0.5210[/tex]
The sample 2 (older adults), of size n2=352 has a proportion of p2=0.3494.
[tex]p_2=X_2/n_2=123/352=0.3494[/tex]
The difference between proportions is (p1-p2)=0.1715.
[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]
The 90% confidence interval for the difference between proportions is (0.115, 0.228).
Trapezoid ABCD is graphed in a coordinate plane,
What is the area of the trapezoid?
4
3
B
С
16 square units
O 24 square units
32 square units
48 square units
-5 4 3 2 -11
1 2 3 4 5 x
-5
Answer:
24 square units
Step-by-step explanation:
The formula for computing the area of a trapezoid is shown below:
As we know that
Area of a trapezium is
[tex]= \frac{1}{2} \times h(a+b)[/tex]
where
h = perpendicular height
The a and b = length of the parallel sides.
Now,
h = 2 - -2 = 4 units
a = 5 - -3 = 8 units
b = 3 - -1 = 4 units
Now placing these values to the above formula
So, the area of a trapezoid is
[tex]= \dfrac{1}{2} \times 4(8+4)[/tex]
[tex]= 2 \times 12[/tex]
= 24 square units.
Hence we applied the above formula so that the area of trapezoid could come
2- = - 6 – 4.0
Solve for x:
Simplify the expression and then evaluate it for the given value of the variable: (6−2x)+(15−3x) for x=−0.2
PLEASE HELP!!!!!!
Answer:
20
Step-by-step explanation:
The simplified expression is -5x+21
-5(0.2)+21=
-1+21= 20
Answer:
24
Step-by-step explanation:
f(x)= (6−2x)+(15−3x)
x=-0.2
f(-0.2)=(6−2(-0.2)+(15−3(-0.2))
f(-0.2)=(6+0.4)+(15+0.6)
f(-0.2)=6.4+15.6
f(-0.2)=22
Please answer this correctly
Answer:
24.99
Step-by-step explanation:
If the area of the quarter circle is 38.465, then the equation to find this would be
3.14*r^2 / 4 = 38.465. we solve for r, the radius, and get two solutions. 7 and -7. Obviously the length of the radius can't be -7, so we know the radius is 7.
Now we must solve for the perimeter. The perimeter is equal to 2r + (2*3.14*r)/4
Plugging 7 in as the radius, r, we get 24.99 as our final answer.
round 0.004198223 to 3 significant figures
I will give brainliest
Answer:
0.00420 is the answer
Step-by-step explanation:
The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.
The rounding number of 0.004198223 to 3 significant figures is 0.0042
Here,
The number is 0.004198223.
We have to find, 0.004198223 to 3 significant figures.
What is Rounding number?
Rounding means making a number simpler but keeping its value close to what it was.
Here,
The number is 0.004198223.
To find 3 significant figures,
We round a number to three significant figures in the same way that we would round to three decimal places.
Then, We count from the first non-zero digit for three digits. We then round the last digit.
Here, the digit is 9 then it will be round.
We get, the number is;
0.0042
We fill in any remaining places to the right of the decimal point with zeros.
So, The rounding number of 0.004198223 to 3 significant figures is 0.00420
Learn more about the rounding number visit:
https://brainly.com/question/4896544
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A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =
Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
Find the diameter and radius of a circle with a circumference of 65.98 Please help
Answer:
21 and 10.5 respectively
Step-by-step explanation:
Remember circumference of a circle is given as;
C= 2×π×r; r is raduis
r = C / 2×π
=65.98/(2×3.142)= 10.50
D= 2× r = 2× 10.50= 21.0( D represent diameter)
Note π = 3.142 a known constant
