Answer:
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 344 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 344, \sigma = 10[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{10}{\sqrt{10}}[/tex]
What is the probability that their mean weight will be between 334 grams and 354 grams?
This is the p-value of Z when X = 354 subtracted by the p-value of Z when X = 334.
X = 354
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{354 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = 3.16[/tex]
[tex]Z = 3.16[/tex] has a p-value of 0.9992.
X = 334
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{334 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = -3.16[/tex]
[tex]Z = -3.16[/tex] has a p-value of 0.0008.
0.9992 - 0.0008 = 0.9984
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
The square pyramid shown below has a base with sides of 10 units. The slant height of the pyramid is 8 units. What is the vertical height, h?
Round your answer to the nearest tenth.
Answer:
h = 6.2 units
Step-by-step explanation:
Given triangle ABC is a right triangle with the measures of the two sides,
BC = [tex]\frac{10}{2}[/tex] = 5 units
AC = 8 units
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
8² = AB² + 5²
AB² = 64 - 25
AB = √39
AB = 6.24 units
AB ≈ 6.2 units
what's the radius of 16x^2+16y^2=1 With a center of (0,0) ?
Answer:
The center is (0,0) and the radius is 1/4
Step-by-step explanation:
The formula for a circle is
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
16x^2+16y^2=1
Divide by 16
x^2+y^2=1/16
x^2 + y^2 = (1/4) ^2
(x-0)^2 + (y-0)^2 = (1/4) ^2
The center is (0,0) and the radius is 1/4
What is 23– 48? Need awnser now
HELP PLEASE ASAP!!! So for this problem I got the scientific notation however I can not seem to figure out the standard notation. Can someone please help me out here please?
Answer:
0.000000073
Step-by-step explanation:
Given number is,
7.3E - 8
In scientific notation number will be,
7.3 × 10⁻⁸
In standard form the number will be,
0.000000073
60 units needed, 14 units per case. What is the number of cases and the number of additional units?
Answer:
5 cases
10 additional units
Step-by-step explanation:
Given that :
Total number of units needed = 60 units
Total number of units per case = 14
Hence, the total number of cases required will be :
Number of units needed / number of units per case
Number of cases required = 60 / 14 = 4.285 (this means that 5 cases are required as 4 cases won't be up to 60 units)
With 5 cases, we have exceeded the required units needed :
Additional units will be : (14 * 5) - 60
Additional units = 70 - 60 = 10 units
PLEASE HELPPP THIS IS DUE ASAPPPP!!!!!!!!!!!!!! WILL GIVE BRAINLIEST
Answer:
I think the answer is 5/6
Step-by-step explanation:
There are three even numbers and two uneven numbers less than four. Therefore, on a standard die, the.probability of Rollin a number that is even or less than for is 5/6.
Jeff has 20 coins. 2/5 of them are quarters. How many quarters does he have? How many coins are not quarters?
A class contains 18 girls and 14 boys. For all parts of this question, each boy and girl are distinguishable from one another. Answer the following questions:a)In how many ways can a committee of one boy and one girl be chosen
Answer:
The total number of ways is 252.
Step-by-step explanation:
Number of girls = 18
number of boys = 14
Commitee of one girl and a boy
(18 C 1)(14 C 1)
= 252
What is the difference of the two polynomials? (NineX squared plus 8X) minus (twoX squared plus 3X)
Answer:
[tex]7x {}^{2} + 5x[/tex]
Step-by-step explanation:
[tex]9x {}^{2} + 8x - (2x {}^{2} + 3x) \\ \\ = 9x {}^{2} + 8x - 2x {}^{2} - 3x (remove \: brackets) \\\ \\ = 7x {}^{2} - 5x [/tex]
Help
The table shows the results of a survey of students in two math classes.
Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Be sure to show and explain your work.
Did You Watch More Than One Hour of TV Last Night?
Answer:
0.6
Step-by-step explanation:
In this question, the | symbol means "given", so we can phrase the question as "Find the probability that a student watches more than one hour of TV given that they are in the 6th period class"
Next, because there is a 100% chance that the student is in the 6th period class, we can disregard the results of the 3rd period class.
Given that the student is in the 6th period class, there are 15 total students (as 9+6=15 = the sum of the yes and no answers for 6th period) and 9 students that said yes. Therefore, there is a 9/15 = 3/5 = 0.6 probability that a student watches more than 1 hour of TV given that they are in the 6th period class
In a poll, adults in a region were asked about their online vs. in-store clothes shopping. One finding was that % of respondents never clothes-shop online. Find and interpret a % confidence interval for the proportion of all adults in the region who never clothes-shop online.
The question is incomplete. The complete question is :
In a poll, 1100 adults in a region were asked about their online vs. in-store clothes shopping. One finding was that 43% of respondents never clothes-shop online. Find and interpret a 95% confidence interval for the proportion of all adults in the region who never clothes-shop online.
Solution :
95% confidence interval for p is :
[tex]$\hat p - Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}} < p < \hat p + Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$[/tex]
[tex]$0.43 - 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}} < p < 0.43 + 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}}$[/tex]
0.401 < p < 0.459
Therefore, 95% confidence interval is from 0.401 to 0.459
A human resources office is working to implement an increase in starting salaries for new
administrative secretaries and faculty at a community college. An administrative secretary
starts at $28,000 and new faculty receive $40,000. The college would like to determine the
percentage increase to allocate to each group, given that the college will be hiring 8
secretaries and 7 faculty in the upcoming academic year. The college has at most $5,000 to
put towards raises. What should the percentage increase be for each group?
Answer:
Step-by-step explanation :
Let % increase in administrative secretary be = x
Let % increase in new faculty receive be = y
Administrative secretary salary = 28,000
New faculty receive Salary = 40,000
(8)*(x/100)* (28000) + (7)*(y/100)*(40000) = 5,000
2240x +2800 y = 5,000
224x +280 y = 500
56x +70y = 125
Therefore, x and y should be chosen such that it satisfy the above equation.
Please help 20 points an will give Brainiest to who ever is right
Answer:
horizontal expansion factor of 2
2^x =2(2)=4
2^4=2×2×2×2= 16
If the total income generated from Gasoline for AER was $408 millions, how much would be the cost for a barrel of gasoline
Each side of a square is increasing at a rate of 8 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 49 cm2
Answer:
Step-by-step explanation:
This is nice and simple. I'm going to walk through it like I do when teaching this concept to my class for the first time. This is a good problem for that.
We are given a square and we are looking for the rate at which the area is increasing when a certain set of specifics are given. That means that the main equation for this problem is the area of a square, which is:
[tex]A=s^2[/tex] where s is a side.
Since we are looking for the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], we need to take the derivative of area formula implicitly:
[tex]\frac{dA}{dt}=2s\frac{ds}{dt}[/tex] that means that if [tex]\frac{dA}{dt}[/tex] is our unknown, we need values for everything else. We are given that the initial area for the square is 49. That will help us determine what the "s" in our derivative is. We plug in 49 for A and solve:
[tex]49=s^2[/tex] so
s = 7
We are also given at the start that the sides of this square are increasing at a rate of 8cm/s. That is [tex]\frac{ds}{dt}[/tex]. Filling it all in:
[tex]\frac{dA}{dt}=2(7)(8)[/tex] and
[tex]\frac{dA}{dt}=112\frac{cm^2}{s}[/tex]
The surface area of a square of side L is given by
[tex]A = L^2[/tex]
The rate of change of the area per unit time is
[tex]\dfrac{dA}{dt} = 2L\dfrac{dL}{dt}[/tex]
We can express the length L on the right hand side in terms of the area A [tex](L = \sqrt{A})[/tex]:
[tex]\dfrac{dA}{dt} = 2\sqrt{A}\dfrac{dL}{dt}[/tex]
[tex]\:\:\:\:\:\:\:=2(\sqrt{49\:\text{cm}^2})(8\:\text{cm/s})[/tex]
[tex]\:\:\:\:\:\:\:=112\:\text{cm}^2\text{/s}[/tex]
F(4) =
If g(x) = 2, x=
An
Step-by-step explon:
Given the function R(x)=x+3/x−5, find the values of x that make the function greater than or equal to zero. Write the solution in interval notation.
Answer:
Step-by-step explanation:
[tex]R(x)=\frac{x+3}{x-5} \geq 0\\R(x)=0,gives~x+3=0,x=-3\\R(x)>0 ,if~both~numerator ~and~denominator~are~of~same~sign.\\let~x+3>0,x>-3\\and~x-5>0,x>5\\combining \\x>5\\\\again~let~x+3<0,x<-3\\x-5<0,x<5\\combining\\x<-3\\Hence~R(x)\geq 0\\if ~x \in ~[- \infty,-3]U(5,\infty)[/tex]
Solve the following equation by first writing the equation in the form a x squared = c:
3 a squared minus 21 = 27
A. a = 4
B. a = plus-or-minus 4
C. a = plus-or-minus 16
D. a = 16
9514 1404 393
Answer:
B. a = plus-or-minus 4
Step-by-step explanation:
3a² -21 = 27 . . . . . . . given
3a² = 48 . . . . . . . . . . add 21 to both sides (desired form)
a² = 16 . . . . . . . . . . . divide both sides by 3
a = ±4 . . . . . . . take the square root
14. In a statistics class with 15 males and 13 females, five students are selected to put problems on the board. What is the probability that:
a. 3 females and 2 males are selected? b.all five students selected are males? c. all five students selected are females? d.at least one male is selected?
Answer:
a) 0.3056 = 30.56% probability that 3 females and 2 males are selected.
b) 0.0306 = 3.06% probability that all five students selected are males.
c) 0.0131 = 1.31% probability that all five students selected are females.
d) 0.9869 = 98.69% probability that at least one male is selected.
Step-by-step explanation:
The students are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
15 + 13 = 28 students, which means that [tex]N = 28[/tex]
5 are selected, which means that [tex]n = 5[/tex]
13 females, which means that [tex]k = 13[/tex]
a. 3 females and 2 males are selected?
3 females, so this is P(X = 3).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,28,5,13) = \frac{C_{13,3}*C_{15,2}}{C_{28,5}} = 0.3056[/tex]
0.3056 = 30.56% probability that 3 females and 2 males are selected.
b.all five students selected are males?
0 females, so this is P(X = 0).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,28,5,13) = \frac{C_{13,0}*C_{15,5}}{C_{28,5}} = 0.0306[/tex]
0.0306 = 3.06% probability that all five students selected are males.
c. all five students selected are females?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,28,5,13) = \frac{C_{13,5}*C_{15,0}}{C_{28,5}} = 0.0131[/tex]
0.0131 = 1.31% probability that all five students selected are females.
d.at least one male is selected?
Less than five females, so:
[tex]P(X < 5) = 1 - P(X = 5) = 1 - 0.0131 = 0.9869[/tex]
0.9869 = 98.69% probability that at least one male is selected.
Test for symmetry and then graph the polar equation.
r=3−5sinθ
Answer:
Symmetric with respect to the x-axis
Symmetric with respect to the y-axis
Symmetric with respect to the origin
Help with solving this Functions problem
Answer:
See answers below
Step-by-step explanation:
Given the following functions:
r(x) = x - 6
s(x) = 2x²
r(s(x)) = r(2x²)
Replacing x with 2x² in r(x) will give;
r(2x²) = 2x² - 6
r(s(x)) = 2x² - 6
(r-s)(x) = r(x) - s(x)
(r-s)(x) = x - 6 - 2x²
Rearrange
(r-s)(x) = - 2x²+x-6
(r+s)(x) = r(x) + s(x)
(r-s)(x) = x - 6 + 2x²
Rearrange
(r-s)(x) = 2x²+x-6
Let $f$ be a linear function for which $f(6)-f(2)=12$. What is $f(12)-f(2)?$ Please explain how you found your answer. Thank you!
========================================================
Explanation:
Since f(x) is linear, this means f(x) = mx+b
m = slopeb = y interceptLet's plug in x = 6
[tex]f(x) = mx+b\\f(6) = m*6+b\\f(6) = 6m+b[/tex]
Repeat for x = 2
[tex]f(x) = mx+b\\f(2) = m*2+b\\f(2) = 2m+b[/tex]
Now subtract the two function outputs
[tex]f(6)-f(2) = (6m+b)-(2m+b)\\f(6)-f(2) = 6m+b-2m-b\\f(6)-f(2) = 4m\\[/tex]
The b terms cancel out which is very handy.
Set this equal to 12, since f(6)-f(2) = 12, and solve for m
[tex]f(6)-f(2) = 12\\4m = 12\\m = 12/4\\m = 3\\[/tex]
So the slope of f(x) is m = 3
-------------------------------------------------------------------------
Next, plug in x = 12
[tex]f(x) = mx+b\\f(12) = m*12+b\\f(12) = 12m+b[/tex]
We can then say:
[tex]f(12)-f(2) = (12m+b)-(2m+b)\\f(12)-f(2) = 12m+b-2m-b\\f(12)-f(2) = 10m\\[/tex]
Lastly, we plug in m = 3
[tex]f(12)-f(2) = 10m\\f(12)-f(2) = 10*3\\f(12)-f(2) = 30\\[/tex]
A paper factory makes cardboard sheets like the one shown below. If the area of each sheet is given by the expression 6x ^ 2 + 7x + 2, what are the dimensions of each sheet of cardboard?
Answer:
(3x+2) by (2x+1)
Step-by-step explanation:
A cardboard is a rectangle, and has two dimensions. Given a quadratic equation, you should find a way to split it in two.
The easiest way to do so is through factoring. (There are many ways to do this, take a look at the plethora of sources offered on the internet.)
When the expression 6x^2 + 7x + 2 is factored, it is (3x+2)(2x+1). Hence, these are your dimensions.
5(6t-3)=5t+35
find the value of t
Answer:
t = 2
Step-by-step explanation:
5(6t-3)=5t+35
Step 1 distribute the 5 by multiplying 5 to what is inside of the parenthesis
5(6t) - 5(3) = 5t + 35
Outcome: 30t - 15 = 5t + 35
Step 2 add 15 to both sides
30t - 15 + 15 = 5t + 35 + 15
Outcome: 30t = 5t + 50
Step 3 subtract 5t from both sides
30t - 5t = 5t - 5t + 50
Outcome: 25t = 50
Step 4 divide both sides by 25
25t/25 = 50 we're left with t = 2
for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?
Answer:
21
Step-by-step explanation:
5/3=35/x
3 x 35=105
5 x x= 5x
105=5x
105/5=5x/5
21=x
The number of people who bought the more expensive ticket is 21.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
For every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If every 35 people bought a $9.75 ticket,Let the number of people be X so we can form the following expression given below:-
5/3=35/x
3 x 35=105
5 x x= 5x
105=5x
105/5=5x/5
21=x
Therefore the number of people who bought the more expensive ticket is 21.
To know more about Expression follow
https://brainly.com/question/723406
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Which sequence or sequences are correct and why?
Answer:
didn't get the question did u forget to put the sequence ???????
pls write the question fully so that I can help you
find all complex numbers z such that z^2=2i
please answer in a+bi
thank you
2 Answers:
z = 1 + i and z = -1 - i
========================================================
Explanation:
We want z to be a complex number in the form z = a+bi, where a,b are real numbers and [tex]i = \sqrt{-1}[/tex] is imaginary.
Let's plug that into the equation your teacher gave you
[tex]z^2 = 2i\\\\(a+bi)^2 = 2i\\\\(a+bi)(a+bi) = 2i\\\\a(a+bi)+bi(a+bi) = 2i\\\\a^2+abi+abi+b^2*i^2 = 2i\\\\a^2+2abi+b^2*(-1) = 2i\\\\a^2+2abi-b^2 = 2i\\\\(a^2-b^2)+2abi = 0+2i\\\\[/tex]
You could use the FOIL rule to take a shortcut. I'm deciding to be a bit more wordy to show a further breakdown how everything is multiplying out.
Notice that the real part a^2-b^2 must be 0 so that it matches the real part on the right hand side.
a^2-b^2 = 0
(a-b)(a+b) = 0 .... difference of squares rule
a-b = 0 or a+b = 0
a = b or a = -b
So whatever solution z = a+bi is, it must have either a = b or a = -b.
--------------------------------
If a = b, then the 2abi portion on the left side turns into 2a^2*i
Set this equal to 2i on the right hand side and isolate 'a'
[tex]2a^2*i = 2i\\\\2a^2 = 2\\\\a^2 = 1\\\\a = 1 \text{ or } a = -1\\\\[/tex]
So a = 1 leads to b = 1
Or a = -1 leads to b = -1
Two complex solutions so far are: z = 1 + i and z = -1 - i based on those two cases above.
--------------------------------
Now consider the case that a = -b
We'll effectively have the same steps as the previous section, but the equation to solve now is [tex]-2a^2*i = 2i\\\\[/tex]
The only difference is that negative is out front. You should find that it leads to a^2 = -1, but this has no solutions because we stated earlier that a,b were real numbers.
So if a = -b, then it concludes with a,b being nonreal numbers. Ultimately we rule out the case that a = -b is possible.
Put another way, note how -2a^2 is always negative which clashes with the idea that the right hand side is positive (ignore the 'i' portions). This contradiction means that no real values of 'a' will make the equation [tex]-2a^2*i = 2i\\\\[/tex] to be true.
--------------------------------
To wrap things up, we only have two solutions and they are
z = 1 + i and z = -1 - i
You can use a tool like WolframAlpha to confirm this.
In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.16 pounds. Determine the 90% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal.
Answer:
The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.9432.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.9432\frac{0.16}{\sqrt{7}} = 0.12[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.12 = 2.68 pounds.
The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.12 = 2.92 pounds.
The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.
Use the figure to find u.
Answer:
u = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj side / hypotenuse
cos 45 = sqrt(2) / u
u cos 45 = sqrt(2)
u = sqrt(2) / cos 45
u = sqrt(2) / 1/ sqrt(2)
u = sqrt(2) * sqrt(2)
u =2
u=2
Answer:
Solution given:
Relationship between base and hypotenuse is given by cos angle.Cos 45°=base/hypotenuse
[tex]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}[/tex]
doing crisscrossed multiplication
[tex]\sqrt{2}*\sqrt{2}=1*u[/tex]
u=2
Given: Line AC is parallel to DF, Line BE is perpendicular to DF, and angle AEB is congruent to angle CEB, prove angle BAE is congruent to angle BCE. Will give Brainliest if explained thoroughly.
9514 1404 393
Explanation:
There are several ways you can go at this. Here are a couple. All proofs will start with the given relations being repeated as part of the proof. Here are the next steps.
Angle Sum∠AED ≅ ∠BAE . . . . alternate interior angles are congruent
∠AED +∠AEB = 90° . . . . angle sum theorem
∠BAE +∠AEB = 90° . . . . substitution property of equality
∠CEF ≅ ∠BCE . . . . alternate interior angles are congruent
∠CEF +∠CEB = 90° . . . . angle sum theorem
∠BCE +∠CEB = 90° . . . . substitution property of equality
∠BAE +∠AEB = ∠BCE +∠CEB . . . . substitution property of equality
∠BAE +∠AEB = ∠BCE +∠AEB . . . . substitution property of equality
∠BAE = ∠BCE . . . . addition property of equality
Congruent Triangles∠ABE = ∠CBE = 90° . . . . BE ⊥ AC
BE ≅ BE . . . . reflexive property of congruence
ΔBEA ≅ ΔBEC . . . . ASA congruence theorem
∠BAE ≅ ∠BCE . . . . CPCTC
