The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 ounces and a standard deviation of 6 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
a) 95% of the widget weights lie between _______ and ________.
b) What percentage of the widget weights lie between 37 and 67 ounces?c) What percentage of the widget weights lie above 49 ?
Answers
Answer:
a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:
[tex] \mu -2\sigma = 55 -2*6 =43[/tex]
[tex] \mu +2\sigma = 55 +2*6 =67[/tex]
95% of the widget weights lie between 43 and 67
b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:
[tex] 100 -0.15-2.5 = 97.85[/tex]
c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%
Step-by-step explanation:
For this case our random variable of interest for the weights is bell shaped and we know the following parameters.
[tex]\mu = 55, \sigma =6[/tex]
We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.
Part a
For this case and using the empirical rule we can find the limits in order to have 9% of the values:
[tex] \mu -2\sigma = 55 -2*6 =43[/tex]
[tex] \mu +2\sigma = 55 +2*6 =67[/tex]
95% of the widget weights lie between 43 and 67
Part b
For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:
[tex] 100 -0.15-2.5 = 97.85[/tex]
Part c
We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%
Related Questions
what is the arc measure of minor arc DE in degrees?
help lol
Answers
Answer:
DE= 39°
Step-by-step explanation:
(4w+ 4 )+(4w+8)= 180
Solve for w
8w + 12 = 180
8w = 180-12
8w = 168
W= 21°
(4w+ 4)+(2w+11)+DE = 180
But w= 21°
((4*21 )+4)+((2*21)+11)+DE = 180
88 + 53 + DE = 180
DE = 180-88-53
DE= 39°
Zara travelled in a train moving at an average speed of 120km/h and covered a distance of 40km towards East. i. Calculate the time taken by the train to cover this distance.
Answers
Answer:
20 minutes
Step-by-step explanation:
Distance= 40 km
Speed= 120 km/h
Time= distance/speed= 40/120= 1/3 hour= 20 min
Answer:
Time = 0.33 hrs
Step-by-step explanation:
Given:
Speed = 120 km/hr
Distance = 40 km
Required :
Time = ?
Formula:
Speed = Distance/Time
Solution:
Time = Distance / Speed
Time = 40/120
Time = 0.33 hrs
what is the equation of the graph that represents the parent function f(x) = x4 stretched vertically by a factor of 2, and then shifted down 3 spaces
Answers
Answer:
f(x) = 2x^4 - 3
Step-by-step explanation:
First multiplying by 2 giving f(x) = 2x^4 stretches it vertically by factor 2.
Then subtract 3 to move it down 3 units:
f(x) = 2x^4 - 3.
Answer:
g(x)=2x^4-3
Step-by-step explanation:
The graph of f(x) is reflected across the x-axis. Write a function g(x) to describe the new graph. g(x)=
Answers
Answer: g(x) = -f(x)
Step-by-step explanation:
When we have a point (x, y) and we reflect it over the x-axis, the end result of the reflection is the point (x, -y)
In this case we have a function reflected, and we know that we can write a function as (x, f(x))
So when we reflect it, the result will be (x, g(x)) = (x, -f(x))
So we have g(x) = -f(x)
The sum of three consecutive even integers is 186. Find the Integers.
Answers
Answer:
60, 62, 64
Step-by-step explanation:
Let x, (x + 2) & (x+ 4) be three consecutive even integers.
[tex] \therefore \: x + (x + 2) + (x + 4) = 186 \\ \therefore \:3x + 6 = 186 \\ \therefore \:3x = 186 - 6 \\ \therefore \:3x = 180 \\ \therefore \:x = \frac{180}{3} \\ \therefore \:x = 60 \\ \implies \\ x + 2 = 60 + 2 = 62 \\ x + 4 = 60 + 4 = 64[/tex]
Hence, the three consecutive even integers are 60, 62 and 64.
Find the future value of 575 at 5.5% compounded quarterly for 5 years. Round to the nearest cent
Answers
Answer:
Future value = $755.61 ( to the nearest cent)
Step-by-step explanation:
The formula for calculating the future value of an invested amount compounded periodically for a number of years is given as:
[tex]FV = PV (1+\frac{r}{n} )^{n*t}[/tex]
where:
FV = future value = ???
PV = present value = $575
r = interest rate in decimal = 5.5% = 0.055
n = number of compounding periods per year = quarterly = 4
t = time of investment = 5 years
∴ [tex]FV = 575 (1+\frac{0.055}{4} )^{4*5}[/tex]
[tex]FV = 575 (1+0.01375)^{20}\\FV = 575 (1.01375 )^{20}\\FV = 575 * 1.3141\\FV = 755.607[/tex]
∴ Future value = $755.61 ( to the nearest cent)
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answers
Answer:
4
4
Step-by-step explanation:
x litres of 15% solution + y litres of 19% solution= 8 gallons of 17% solution
disinfectant content of the final solution= 8*0.17= 1.36 gallons
0.15x+0.19y=1.36
x+y= 8 ⇒ x=8-y
0.15*(8-y)+0,19y= 1.361.2-0.15y+0.19y=1.360.04y=0.16y= 0.16/0.04y=4 gallonsx= 8-4= 4 gallonsThomas is in charge of selling roses for the Graduation dance. The roses sell for $3.50 each. He estimates that the expenses of the roses will be $30. Thomas wants to write an equation for the profit.
Answers
Answer:
P= $3.5x -$30
Step-by-step explanation:
Let the number of roses Thomas bought and sold be x.
Hence the total selling price would be;
$3.5 × x= $3.5x
The profit = selling price-expenses
P= $3.5x -$30
1 Point
In mathematics, when we talk about a(n) we are talking about some of
the people, places, or things under consideration.
Answers
Answer:
Population
Step-by-step explanation:
In mathematics, when we talk about the people, places, or things under consideration, we are referring to the population. The Population is the entire sum of objects in a study. When a researcher wants to study factors that concern a particular set of people, places, or things, the group under study is the population. For example, the researcher might want to do a study on the amount of food consumed by Brazilian students in the year 2019. The Brazilian students represent the population, because they are the group of people being studied.
The population under study might sometimes be difficult to study as a whole. For example, the study of the entire Brazilian students might be cumbersome. In such cases, a sample can be drawn from the population and studied, or the population narrowed down a little more, so that it can be easily studied.
What is the volume of the cylinder below?
O A. 70K units
O B. 2257, units
O C. 1757 units
O D. 357 units
Answers
Answer:
V = V = 175 pi units^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V =pi ( 5)^2 ( 7)
V = 175 pi units^3
PLEASE HELP ME
Angles PTQ and STR are vertical angles and congruent.
Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn to connect points P and Q and points S and R to create secants. Angles P T Q and R T S are congruent.
Which arcs are congruent?
Arc S P and Arc S R
Arc P Q and Arc S R
Arc P Q and Arc Q R
Arc S P and Arc P R
Answers
Answer:
PQ AND SR on ED
Step-by-step explanation:
Based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.
What is vertical angle theorem?The vertical angles theorem is a theorem that states that when two lines intersect and form vertically opposite angles, each pair of vertical angles has the same angle measures. A pair of vertically opposite angles are always equal to each other.
For the given situation,
Angles PTQ and STR are vertical angles and congruent.
Line segments T P, T Q, T R, and T S are radii.
So, T P = T Q = T R = T S.
The two sides T P = T Q and T R = T S and [tex]\angle PTQ = \angle RTS[/tex],
then by SAS similarity theorem two triangles,
Δ PTQ ≅ Δ STR.
When two triangles are congruent, then the corresponding arc are also congruent.
The congruent central angles intercept congruent arcs PQ and SR.
Hence we can conclude that based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.
Learn more about vertical angle theorem here
https://brainly.com/question/17702030
#SPJ2
Is 1.06 greater than 0.6
Answers
Answer:
it is
Step-by-step explanation:
What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?
Answers
Answer:69
Step-by-step explanation:
Because i am smart.
Item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm
Answers
Answer:
Step-by-step explanation:
item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm
You did not state the diameter or radius of the window
so, i will use 90cm as the diameter of the window
First, I'd calculate the half circumference of the window.
The formula for circumference is [tex]c = 2\pi r[/tex],
Half of it would just be [tex]c/2 = r\pi[/tex]
Since our diameter is 90 cm, our radius is 45 cm.
Circumference =
[tex]=45\pi \\= 141.37 cm[/tex]
circumference is also the same with perimeter
so, the answer is 141.37cmto nearest tenth = 141.4cmAnswer:
141.4cm
Step-by-step explanation:
=>
please give barinlist
Which of the following source documents is used to summarize all of the costs incurred for a specific job?
Answers
Answer:
job cost sheet.
Step-by-step explanation:
When planning or working on a specific project/job all the actual costs that are incurred for that job are written down in the job cost sheet. This report is an entire compilation that should be created by the accounting department and then distributed to all the members of the management department who then analyze it and determine whether the job was correctly bided. This sheet gets updated as the job is undergoing and fully completed when the job is closed.
Confidence Interval Concept Check 3 1 point possible (graded) In a new experiment consisting of 150 couples, 75 couples are observed to turn their heads to the left and the remaining 75 couples turned their heads to the right when kissing. Let p denote the (unknown) parameter which specifies the probability that a couple turns their head to the right.
Which of the following statements are correct regarding this experiment? You are given that exactly one but not both of choices 3 and 4 is correct. Also, assume that the given confidence intervals are an instance of a random interval computed upon observing the given data.
10,05] is a 50% asymptotic confidence interval for p. [0.5, 1] is a 50% asymptotic confidence interval for p. 10.466, 0.533 is a 50% asymptotic confidence interval for p. 10.48, 0.52 is a 50% asymptotic confidence interval for p. O
Answers
Answer:
Step-by-step explanation:
There are four options given above.
P specifies the probability that a couple turns their head to the right when kissing. P is 0.5 because the probability of turning right when kissing is 75÷150 = 1/2 = 0.5
Assuming that the given confidence intervals are an instance of a random interval computed upon observing the given data,
The correct statements are statements 1 and 4
Find the sum of the geometric series 1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}
Answers
Answer:
S20 ≈ 4.942
Step-by-step explanation:
Sum of a geometric series is expressed as Sn = a(1-rⁿ)/1-r if r<1
a is the first term
r is the common ratio
n is the number of terms
Given the geometric series
1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}
Given a = 1,
r = 0.8/1 = 0.8²/0.8 = 0.8
n = 20 (The total number of terms in the series is 20)
Substituting this values in the formula above.
S20 = 1(1-0.8^20)/1-0.8
S20 = 1-0.01153/0.2
S20 = 0.9885/0.2
S20 ≈ 4.942
The length of human pregnancies from conception to birth is normally distributed with mean 266 days and standard deviation 16 days. What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?
Please put the answer in the standard deviation percentages!
Answers
Answer:
68% of the lengths of pregnancies fall between 250 days and 282 days.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 266
Standard deviation = 16.
What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?
250 = 266 - 16
So 250 is one standard deviation below the mean.
282 = 266 + 16
So 282 is one standard deviation above the mean.
By the Empirical Rule, 68% of the lengths of pregnancies fall between 250 days and 282 days.
Answer:
[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]
So then we will have approximatetly 68.26% of the values between 250 and 282 days
Step-by-step explanation:
Let X the random variable that represent the The length of human pregnancies from conception to birth, and for this case we know the distribution for X is given by:
[tex]X \sim N(266,16)[/tex]
Where [tex]\mu=266[/tex] and [tex]\sigma=16[/tex]
We are interested on this probability
[tex]P(250<X<282)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]
So then we will have approximatetly 68.26% of the values between 250 and 282 days
A triangle undergoes a sequence of transformations. First the triangle is dilated by a scale factor of 1/3 about the orgin. The the triangle is reflected over the x axis. Finally, the triangle is translated left 3 units and up 2 units. How does the image triangle compare to the preimage triangle
Answers
Answer:
Since there was a dilation, the two triangles will be similar. The scale factor is less than one and is a reduction, therefore, the image will be smaller than the pre-image.
Area of composite shapes
Find the area of the shape shown below.
Answers
Answer:
32 units
Step-by-step explanation:
The large triangle on top has an area of 20, cause 4*10 = 40
40/2 = 20.
the square on the bottom has an area of 4, well, cause 2*2 = 4.
The smaller triangle on the left has an area of 2, cause 2*2=4
4/2=2
The triangle on the right, has an area of 6, because 6*2=12
12/2=6
20+4+2+6 = 32
Answer:
32 Units =)
Step-by-step explanation:
divide a number line from 0 to 1 into 8 equal lengths. What should he label the first tick mark to the right of 0?
Answers
Answer:
1/8
Step-by-step explanation:
since it is divided to 8 equal parts then the first tick is 1/8
PLEASE ANSWER ASAP (exponential and logarithms)
Answers
Answer:
1.4650 (the first option in the list of possible answers)
Step-by-step explanation:
Start by isolating the exponential expression on one side of the equal sign, thus subtracting 2 from both sides:
[tex]2+3^x=7\\3^x=7-2\\3^x=5[/tex]
Now, in order to solve for "x", we need to lower the exponent, and for that purpose we use logarithm base "3":
[tex]3^x=5\\x=log_3(5)[/tex]
In order to find this logarithm, we use the change of base formula:
[tex]log_3(5)=\frac{log(5)}{log(3)} =1.46497...[/tex]
which rounded to four decimals gives: 1.4650
greatest common factor of (12x^3-9x^2)+(8x-6)
Answers
Answer:
[tex](4x-3)(3x^2)+2)[/tex]
Step-by-step explanation:
Answer:
The greatest common factor for the first parenthesis is 3 and the greatest common factor for the second parenthesis is 2
Step-by-step explanation:
Hope this helps plz mark brainliest!
Solve the equation: 7(8 - 5z) + 17 = 3
Answers
Answer:
z=2
Step-by-step explanation:
56-35z+17=3
73-35z=3
-35z=-70
z=2
I don’t understand? Please help!
Answers
Jar A contains four liters of a solution that is 45% acid. Jar B contains five liters of a solution that is 48% acid. Jar C contains one liter of a solution that is k % acid. From jar C, 2/3 liters of the solution is added to jar A, and the remainder of the solution in jar C is added to jar B. At the end both jar A and jar B contain solutions that are 50% acid. Find k.
Answers
Answer:
k= 80%
Step-by-step explanation:
Jar A contains 4*0.45 L acid, and 4 L of a solution of acid.
Jar B contains 5*0.48 L acid., and 5 L of a solution of acid.
Jar C contains 1*k/100 = k/100 acid, and 1 L of a solution.
50% = 0.5
For jar A.
(2/3)*k/100 L acid is added to jar A.
Now jar A contains 4*0.45 L + (2/3)*k/100 L acid, and it has (4+2/3)L of a solution.
L solute/L solution = 0.5
[4*0.45 L + (2/3)*k/100 L]/(4+2/3)L = 0.5
[1.8 + (2k/300)]/[(12+2)/3] = 0.5
[1.8 + (2k/300)]/[14/3] = 0.5
[1.8 + (2k/300)]= 0.5*(14/3)
(2k/300) = 0.5*(14/3) - 1.8
2k = (0.5*(14/3) - 1.8)*300
k = (0.5*(14/3) - 1.8)*300/2 =80
k= 80%
We also can find k using jar B.
(1/3)k/100 L acid is added to jar B.
Now jar B contains 5*0.48 L+ (1/3)k/100 L acid, and it has (5+1/3) L of a solution.
L solute/L solution = 0.5
[5*0.48 L+ (1/3)k/100 L ]/(5+1/3)L= 0.5
[5*0.48 + (1/3)k/100 ]/(5+1/3)= 0.5
This equation also gives k=80%
Check.
We can check at least for jar A.
Jar A has 4L solution and 4*0.45=1.8 L acid.
2/3 L of the solution from jar C was added, and now we have 4 2/3 L of solution.
(2/3)* 80%= (2/3)*0.8 acid was added from jar C.
Now we have [1.8 +(2/3)*0.8] L acid in jar A.
L solute/L solution = [1.8 +(2/3)*0.8] L /(4 2/3) L = 0.5 or 50% as it is given that jar A has 50% at the end.
What is the dominan of the function f(x)= -6x+7
Answers
Answer:
(-∞,∞)
Step-by-step explanation:
It's just a line
Answer:
INFINITIE, INFINITIE
Step-by-step explanation:
What’s the correct answer for this question?
Answers
Answer:
C.
Step-by-step explanation:
60° in Radians = 1.047
Using Formula
s=rθ
s= 7(1.047)
s ≈ 7.36
Sue invests £9000 in an account for one year.
At the end of the year, interest is added to the account.
Sue pays tax on this interest at a rate of 20%.
She pays £30.24 tax.
Work out the percentage interest rate for the account.
Answers
Answer:
The interest rate = 1.68%
Step-by-step explanation:
Sue invests £9000 in an account for one year.
She pays £30.24 at a rate of 20%
So 20% of the interest =£ 30.24
Let the interest be x
X0.2= 30.24
X=£ 151.2
The total interest was£ 151.2
The rate R at which generated this interest
R = (100*151.2)/(1*9000)
R= 15120/9000
R= 1.68%
The interest rate = 1.68%
correct answer gets brainliest Please explain as well 3x+5y=21 4x-2y = -24
Answers
Answer:
x=-3 y=6
Step-by-step explanation:
it was a easyone ,don't forget to mark me as a brainlinest .☺️
