Answer:
The confidence interval is [tex]25.16 < \mu < 26.85[/tex]
Step-by-step explanation:
From the question we are given a data set
25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.
The mean of the this sample data is
[tex]\= x = \frac{\sum x_i}{n}[/tex]
where is the sample size with values n = 10
[tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]
[tex]\= x = 26[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]
substituting values
[tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]
[tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]
[tex]\sigma = 1.625[/tex]
The confidence level is given as 90% hence the level of significance is calculated as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha =10[/tex]%
[tex]\alpha = 0.10[/tex]
Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining the critical values of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because we are considering two tails of the area under the normal curve
The margin of error is evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]
[tex]MOE = 0.845[/tex]
The 90%, two sided confidence interval is mathematically evaluated as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
[tex]26 - 0.845 < \mu < 26 + 0.845[/tex]
[tex]25.16 < \mu < 26.85[/tex]
Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours
3 is what percentage of 12?
Answer:
25%
Step-by-step explanation:
First you have the fraction of 3/12 and need to turn it into a decimal. So to do that you divide 3 by 12 = 0.25. So your percent is 25%
Suppose that the relation T is defined as follows. =T, , p9, , 0m, , 9p, 66 Give the domain and range of T. Write your answers using set notation.
domain=
range =
Answer:
Step-by-step explanation:
Set notation { } is used in this case, to represent the domain and the range.
The values that go into T are the domain while the values that come out of T are the range.
The domain comprises all x (independent) values while the range comprises all y (dependent) values.
This should be applied in the clear definition of the relation T.
The sides of a number cube have the numbers 9, 3, 5, 3, 7, and 9. If the cube is thrown once, what is the probability of rolling a number less than 10?
Fraction:
Decimal:
Percentage:
Likelihood of the event happening:
What is x when: 2/x = 5/9
Answer: 3.6
Step-by-step explanation:
2/x=5/9
Multiply(x)
2=5/9x
Divide by 5/9
x=3.6
Hope it helps <3
What is the measure of <A in the triangle below?
Answer:
62
Step-by-step explanation:
180-116 makes us find out that angle C is 64, thus to find out the inner angles you gotta do 64+ (2x+4)+(3x-13)=180
You follow this operation, find out x and perform 3(25)-13, which ends up giving you 62
Answer:
62°
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is not sharing a common side
2x + 4 + 3x - 13 = 116° add like terms
5x - 9 = 116°
5x = 125° divide both sides by 5
x = 25 and angle A is 3x - 13 so 3×25 - 13 = 62°
Which of the following is the slope-intercept form of 6x + 2y = 28
a) y= 3x-4
b) y= 3x +4
c) y= -3x+4
d) y= -3x-4
Simplify the expression.(4+2i)-(1-i)
ANSWER :
6i - (1-i)
Step - by - step explanation:
( 4 + 2i ) - ( 1 - i )
( 4 + 2 × i) - ( 1 - i )
( 6× i ) - ( 1 - i )
= 6i- (1-i)
Hope this helps and pls mark as brainliest :)
Classify the polynomial 2x^3+6x^2-4 by the number of terms. binomial. trinomial. cubic. quadratic.
Answer:
monomial
Step-by-step explanation:
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answer:
b = sqrt(57)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
8^2 + b^2 = 11^2
64+ b^2 = 121
Subtract 64
b^2 = 121-64
b^2 =57
Take the square root of each side
b = sqrt(57)
Write an algebraic expression that represents The quotient of a number squared and eight
Answer:
[tex]\boxed{\frac{x^2 }{8} }[/tex]
Step-by-step explanation:
The quotient is the result from division.
Let x be that number.
Division between x² and 8.
[tex]\frac{x^2 }{8}[/tex]
The algebraic expression representing the quotient of a number squared and eight is x²/8.
What is an algebraic expression?An algebraic expression is a combination of terms formed using mathematical operators (+, -, *, /). The terms are made by the combination of variables and constants.
How to solve the given question?In the question, we are asked to write an algebraic expression that represents the quotient of a number squared and eight.
We know that an algebraic expression constitutes both variables and constants.
We assume the number in the expression to be x.
The number squared is then represented by x².
The quotient of the number squared and eight can be represented as x²/8.
Therefore, the algebraic expression representing the quotient of a number squared and eight is x²/8.
Learn more about the algebraic expressions at
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The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2. What is the lateral area of the smaller cylinder? 17.1π mm2 33.6π mm2 60π mm2 84π mm2
Answer:
84π mm^2
Step-by-step explanation:
formula for circumference is 2πr where r is the radius of circle
Given,The circumference of the base of a cylinder is 24π mm
Thus,
2πr= 24π mm
=> r = 24π mm/2π = 12 mm
________________________________________
A similar cylinder has a base with circumference of 60π mm.
radius for this cylinder will be
2πr= 60π mm
r = 60π mm/2π = 30mm
______________________________________________
Given
The lateral area of the larger cylinder is 210π mm2
lateral area of cylinder is given by 2πrl
where l is the length of cylinder
thus,
r for larger cylinder = 30mm
2π*30*l = 210π mm^2
=> l = 210π mm^2/2π*30 = 3.5 mm
___________________________________________
the lateral area of the smaller cylinder
r = 12 mm
l = 3.5 mm as both larger and smaller cylinder are same
2πrl = 2π*12*3.5 mm^2 = 84π mm^2 answer
Answer:
33.6pi mm2 is the correct answer
edge 2021
Step-by-step explanation:
The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.
What is the lateral area of the smaller cylinder?
17.1π mm2
33.6π mm2
60π mm2
84π mm2
What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3 . A.x - 3y - 7 = 0 B.x - 3y + 7 = 0 C.3x - y - 7 = 0
Answer:
The answer is option A
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
Equation of the line using point (1 , - 2) and slope 1/3 is
y + 2 = 1/3( x - 1)
Multiply through by 3
That's
3y + 6 = x - 1
Simplify
x - 3y - 1 - 6 = 0
We have the final answer as
x - 3y - 7 = 0Hope this helps you
Plz help asap!!!!!!!!!!!!!
Answer:
6.64 ft²
Step-by-step explanation:
Given the above triangle with 2 sides of lengths 3.2 ft and 4.7 ft respectively, and angle 62° in between, the following formula can be used to calculate the area: ½*a*b*sin(θ).
Thus, a and b are the 2 given sides and θ is the included angle in between both sides.
Therefore,
Area = ½*3.2*4.7*sin(62)
Area = ½*15.04*0.88295
Area = ½*13.279568
Area = 6.639784
Area = 6.64 ft² (to the nearest hundredth)
what is the value of A when we rewrite 4^31x as A^x
Answer:
.
Step-by-step explanation:
The value of A is A = 4³¹
What are Exponents?Exponents are the base raised by power, it is written in the superscript of a number.
The expression is
[tex]\rm 4^{31x}\\[/tex]
To write in form Aˣ
A will be obtained by comparing the expressions
Aˣ = [tex]\rm 4^{31x}\\[/tex]
A = 4³¹
Therefore, the value of A is A = 4³¹.
To know more about Exponents
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in how many ways cvan 5 people be chosen and arranged in a straight line, if there are 6 people to choose from'
Answer:
720 different waysStep-by-step explanation:
Permutation has to do with arrangement. If r objevt selected from n pool of objects are to be arranged in a straight line, this can be done in nPr number of ways.
nPr = n!/(n-r)!
If 5 people are to be chosen and arranged in a straight line, if there are 6 people to choose from, this can be done in 6P5 numbe of ways.
6P5 = 6!/(6-5)!
6P5 = 6!/1!
6P5 = 6*5*4*3*2*1
6P5 = 720 different ways
I have 25% off coupon that I would like to apply to this purchase.” Since the sticker price is $93.78,the actual cost to you will be what after discount applied”.
Answer:
$70.33
Step-by-step explanation:
sticker price = $93.78
discount coupon in percentage = 25%
Thus, discount will be 25% of sticker price
discount amount = 25% of $93.78 = 25/100 * $93.78 = $23.45
Thus, amount paid = sticker price - discount amount = $93.78-$23.45
amount paid = $70.33
actual cost to you will be what after discount applied is $70.33
Which line has a slope of -? 2 x – y = 0 - x + 2 y = 0 x - 2 y = 0 x + 2 y = 0 NEXT
Answer:
Easiest way to do this is to get the X's on one side of the equals sign and the Y's on the other. Then, you can choose the one with the negative sign in it.
When you do that,
First one is 2x=0+y, or y = 2x
Second one is 2y=0+x, or 2y = x (weird right)
Third one is x=0+2y, or 2y = x (again, weird right)
Final one is 2y=0-x, or 2y = -x
The final one is the answer. Cheers, but don't forget to remember this for next time bro.
g The average salary in this city is $45,600. Is the average different for single people? 53 randomly selected single people who were surveyed had an average salary of $46,356 and a standard deviation of $15,930. What can be concluded at the α α = 0.05 level of significance?
Answer:
Step-by-step explanation:
The average salary in this city is $45,600.
Using the formula
z score = x - u /(sd/√n)
Where x is 46,356, u is 45,600 sd is 15,930 and n is 53.
z = 46,356 - 45600 / (15930/√53)
z = 756/(15930/7.2801)
z = 756/(2188.1568)
z = 0.3455
To draw a conclusion, we have to determine the p value, at 0.05 level of significance for a two tailed test, the p value is 0.7297. The p value is higher than the significance level, thus we will fail to reject the null and can conclude that there is not enough statistical evidence to prove that the average is any different for single people.
Which value of x would make NO IKI
?
K
(x + 2) in
o 1
N
(x - 3) in
06
o 8
x-4) in 0
x in
o 10
Save and Exit
Next
Submit
Answer:
[tex]\boxed{x = 8}[/tex]
Step-by-step explanation:
For NO ║ KJ, The two triangles must be similar and their sides must be proportional.
So, the proportion of their sides is:
=> [tex]\frac{x-4}{x} = \frac{x-3}{x+2}[/tex]
Cross Multiplying
[tex]\sf x (x-3)= (x-4)(x+2)\\Multiplying\\x^2-3x = x^2+2x-4x-8\\x^2-3x = x^2-2x-8\\Subtracting\ x^2\ to \ both \ sides\\ -3x = -2x -8\\Adding \ 2x\ to\ both\ sides\\-3x+2x = -8\\-x = -8\\[/tex]
x = 8
So, For x = 8, NO will be parallel to KJ.
Help thank you!!!!!!!
[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]
Answer: D. 160
If (5^4)m=5^12 What is the value of M
Answer:
Step-by-step explanation:
Easy way to solve
5^4 = 625.
5^12=244140625.
Thus, 625m=244140625.
Divide both sides by 625/
m=390625, or 5^8.
Better way to solve
When dividing by exponents [tex]x^{4}/x^{2} =x^{4-2}=x^2[/tex]
Thus, simply do 12-4=8 to know that m=5^8.
Hope it helps <3
Answer:
5⁸Step-by-step explanation:
(5⁴)m = 5¹²
Divide both sides by 5⁴
((5⁴)m)/5⁴ = 5¹²/5⁴
m = 5⁸
The diagram shows the floor plan for Harry's new tree house. The entry terrace on the tree house is shaped like an isosceles trapezoid.
Answer:
what do you need help with its not really clear
Answer
1. 48 2. 308
Step-by-step explanation:
Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help
Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
6th grade math, help me pleasee:)
Answer:
8 pounds
Step-by-step explanation:
2 x 3 = 6 tb of chili powder in pot 2
find pounds per tablespoon: 48 / 6 = 8 pounds
Answer:
1/2 pound per tablespoon
Step-by-step explanation:
Jaden sure does like his chili!
In the first and second pot, he uses 3 pounds worth of ground beef, which means, 12 ounces of something is a pound. And because Jaden had used 3 times the amount of chili powder in the second pot, he used 6 tablespoons worth of powder. 3 pounds divided by 6 equals 1/2.
greater than (−3) but less than or equal to 3
Answer:
-2,-1,0,1,2,3
You just have to choose the numbers in between -3 to 3
Hope it helped ;)
Alex started a new social media account,which he used to post pictures of cute animals. On the first day he only had 8 followers.a However his account became popular very quickly and the numbers of the followers tripled everyday. Identify how many followers he had in the 5th day.
Answer:
648 followers
Step-by-step explanation:
Let first day=a1
Tripled followers everyday
Second day=a2=a1×3
Third day=a3=a2*3
Fourth day=a4=a3*3
Fifth day=a5=a4*3
a=8 followers
a2=a1×3
=3*8
=24 followers
a3=a2*3
=24*3
=72 followers
a4=a3*3
=72*3
=216 followers
a5=a4*3
=216*3
=648 followers
On the fifth day, Alex will have a total of 648 followers on his new social media account.
Answer:
624
Step-by-step explanation:
648 i used a calculator
"A motorist wants to determine her gas mileage. At 23,352 miles (on the odometer) the tank is filled. At 23,695 miles the tank is filled again with 14 gal- lons. How many miles per gallon did the car average between the two fillings?"
Answer:
24.5 mpg
Step-by-step explanation:
(23,695 - 23,252) / 14 = 24.5mpg
Answer:
The car averaged a total of 24.5 miles per gallon between the two fillings
Step-by-step explanation:
Firstly, we calculate the difference between the mileages.
This will give us the total distance traveled.
That would be 23,695 - 23,352 = 343 miles
The tank capacity obviously is 14 gallons
So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon
Heights of women (in inches) are approximately N(64.5,2.5) distributed. Compute the probability that the average height of 25 randomly selected women will be bigger than 66 inches.
Answer:
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
Step-by-step explanation:
From the summary of the given statistical dataset
The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:
[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5
[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]
[tex]\sigma_{\overline x }[/tex] = 0.5
Thus X [tex]\sim[/tex] N (64.5,0.5)
Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:
[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]
[tex]P(\overline X > 66) = P ( Z>3 })[/tex]
[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]
[tex]P(\overline X > 66) = 1- 0.9987[/tex]
[tex]P(\overline X > 66) =0.0013[/tex]
the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013
HELP ASAP PLEASEEEEE C is the center of the circle. Find the length of DGE A. s= 161 over 18 pie B. s= 343 over 35 pie C. s= 343 over 18 pie D. s= 343 over 9 pie
Answer:
C. [tex] \frac{343}{18} pie [/tex]
Step-by-step explanation:
Given a circle of:
Radius (r) = 14
Measure of minor arc = 115°
We are required to find the length of DGE = length of major arc.
Length of arc is given as 2πr(θ/360)
Measure of the major arc DGE (θ) = 360 - 115 = 245°
Length of major arc DGE = [tex] 2*pie*14*\frac{245}{360} [/tex]
[tex] = 28*pie*\frac{49}{72} [/tex]
[tex] = \frac{28*49}{72} pie [/tex]
[tex] = \frac{7*49}{18} pie [/tex]
[tex] = \frac{343}{18} pie [/tex]
Length of arc DGE =
[tex] \frac{343}{18} pie [/tex]
*4.
What is the value of (-ab)(a) when a = -2 and b = 3?
(A)
-12
(B) -6
(C)
(D) 12
Answer:
(D) 12
Step-by-step explanation:
Plug in the given values into the expression. a = -2 b = -3
(-ab)(a)
[-(-2)(-3)](-2)
(-6)(-2)
12