Using the normal distribution and the central limit theorem, it is found that:
P(x < 0.29) = 0.2981.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
31% of the candies are orange, hence p = 0.31.We randomly sample 100 candies, hence n = 100.Then, the mean and the standard error are given by:
[tex]\mu = p = 0.31[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.31(0.69)}{100}} = 0.04625[/tex]
The probability our sample is 29% orange candies or less is the p-value of Z when X = 0.29, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.29 - 0.31}{0.04625}[/tex]
[tex]Z = -0.43[/tex]
[tex]Z = -0.43[/tex] has a p-value of 0.2981.
Hence:
P(x < 0.29) = 0.2981.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Find a polynomial that represents the surface area of a sphere with a radius of (3x – 5) cm.
The surface area of a sphere is 4π^2. Leave your answer in terms of it.
Answer:
π(36x^2 - 120x + 100)
Step-by-step explanation:
4π(3x - 5)^2 = 4π[(3x)^2 - 2*3x*5 + 5^2] = 4π(9x^2 - 30x + 25)
= π(36x^2 - 120x + 100)
PLEASE HELP!!! If the height of the lighthouse is 53 meters and the angle of elevation is 47°, which of the following may be used to find the distance, z, between the boat and the base of the lighthouse?
Answer:
tan(47)=53/z
Step-by-step explanation:
Using trig ratio tan(x)=O/A
there x is the angle of elevation, O is the side opposite the angle (the lighthouse) and A is the side adjacent the angle (distance between boat and bottom of lighthouse)
Therefore, tan(47)=53/z
[tex]\\ \tt\hookrightarrow tan47=\dfrac{H}{B}[/tex]
[tex]\\ \tt\hookrightarrow tan47=\dfrac{53}{B}[/tex]
[tex]\\ \tt\hookrightarrow B=\dfrac{53}{tan47}[/tex]
71.5*(-9.2)
A. –657.8
B. –65.78
C. 65.78
D. 657.8
Answer:
(A)
Step-by-step explanation:
you can multiply normally like 71.5 × -9.2 =-657.8
Pls solve this I can do it after school I can do it after school , I’m going to cry again
Answer:
s = 71
j = 23
71 = 3j+2
71 - 2 = 3j
39 = 3j
j = 23
Answer:
j=23
s=71
Step-by-step explanation:
Here we have two parallel lines lines( UB and DK).
And we have another line, called a transversal that intersects( crosses) both parallel line. Doing so creates the following angles,
Vertical Angles, Angles are equal in measure Alternate Exterior Angles, Angles are equalAlternate Interior Angles. Angles are equalConsective Angles. Angles are equalLinear Pair Angles. Angles add up to 180So now we look at the graph
First, we know that 3j+2 and s are vertical angles since they are across of each other. So they are equal to each other so let look at another angle first.
3j+s and 71 are Alternate Interior Angles since they lie inside the transversal and are across from each other.
Since they are Alternate Interior Angles, they are equal.
So we set them equal to each other.
[tex]3j + 2 = 71[/tex]
Subtract 2 from both sides
[tex]3j = 69[/tex]
Divide both sides by 3
[tex]j = 23[/tex]
The value of j is 23.
Know to find S, we know s is equal to 3j+2, which when we plug in 23 for j, we get 71.
So s=71
Please Help! ASAP. Will give Brainliest
Answer:
3 Not too sure though
Step-by-step explanation:
don't input my answer, i'm not too sure!
2) It takes me 25 minutes to drive to school in the morning and 20 minutes to drive home after
school if those times stay the same every day, how much time do I spend driving to and from school
in a week?
Answer:
225 minutes if school is 5 days a week.
Step-by-step explanation:
20+25=45. 45x5=225
What is the lcm of 12 and 18
Answer:
36
Step-by-step explanation:
Hi there!
We want to find the least common multiple (LCM) of 12 and 18
One easy way to do that is to split up the numbers into one of their factor pairs, find the factor pairs between the numbers we just split apart, and then keep on going, until we only get prime numbers (numbers that only have 1 and itself as multiples)
Let's start with 12.
There are multiple ways to multiply to get to 12, but we can use 3 and 4 for example
12= 3*4
4 is 2 * 2
Substituting 2*2 for 4, 12 is equal to 2*2*3
Now for 18.
18 can also be split up multiple ways; one way would be 9 and 2
18 = 2*9
9 is 3*3
Substitute 3*3 for 9.
18=2*3*3
Now look at 2*2*3; 2 shows up twice in that string of numbers
In 2*3*3, 3 shows up twice in that string of numbers
We multiply the numbers based off of the highest number of times that they occur
In other words, we will multiply 2 * 2 and 3 * 3 together
2 * 2 * 3 * 3 = 4 * 9 = 36
The LCM of 12 and 18 is 36
Hope this helps!
See more on finding the LCM here:
https://brainly.com/question/20380514
Solve the equation: 30 = 5 + 0.5d
Answer:
d = 50
Step-by-step explanation:
30 = 5 + 0.5d ( subtract 5 from both sides )
25 = 0.5d ( divide both sides by 0. 5 )
50 = d
can you simplify 4(-5+100)
Find the volume of this cylinder if it has a diameter of 4mm and a height of
14mm.
Answer:
V≈1.76×10-7m³
Step-by-step explanation:
What fraction of an hour is four minutes
Answer
1hr/15 mins=60 mins/15 mins=4 minutes.
Step-by-step explanation:
( SHOW UR WORK) Find the value of 8.41 + 42.320
Answer:
See below.
Step-by-step explanation:
42.32
+8.41
50.73
-hope it helps
Answer:
50.73
Step-by-step explanation:
8.41
42.32
+_________
50.73
Hope this helps! Have a great day!!
Is (6,3) a solution to the equation "a"? Yes or No.
Yes
No
Answer:
Yes
Step-by-step explanation:
Which polynomials are prime? Check all of the boxes that apply.
x2 + 9
x2 – 9
x2 + 3x + 9
–2x2 + 8
Answer:
Answer:
The prime polynomials are
x² + 9
x² + 3x + 9
Step-by-step explanation:
can you tell me the answer please
Answer:
11
Step-by-step explanation:
140-129=11
Answer:
140 - 129
Step-by-step explanation:
If Alyanna has more cookies than Alyssa, and we want to find how much more, we need to subtract Alyssa's amount from Alyanna's amount
Therefore, Alyanna has 11 more cookies than Alyssa.
Can someone please help me with all of these. And thank you.
Answer/Step-by-step explanation:
1. x = -3.6
Add 1 on both sides.
18x = 23x + 18
Subtract 23x on both sides.
Combine like terms.
Divide the answer.
-5x = 18
x = -3.6
2. x = 11/3 (2.66666...)
Add 5 on both sides.
6x = 3x + 11
Subtract 3x on both sides.
Combine like terms.
Divide the answer.
3x = 11
x = 11/3
3. x = 23
Subtract 12 on both sides.
5x = 6x - 23
Subtract 6x on both sides.
Combine like terms.
Divide the answer.
-x = -23
x=23
(that's all.)
Jimmy's height is 156 cm, Kessie's height is 168 cm, while Lya's height is 132 cm. Define:
Answer:
132<156<168 or 12×1, 12×2 ...
Step-by-step explanation:
Jimmy's 24cm taller than Lya, and Kessie's 12cm taller than Jimmy
A lookout tower above a canyon is 4 meters above ground level. The depth of the canyon is 16 meters below ground level. If 0 represents ground level, which number sentence correctly compares their distances above and below ground level?
A) 4<-16
B)4>-16
C)-4<16
D)-4>16
Answer:
B
Step-by-step explanation:
4 meters above. So 4 will not be negative, this eliminates C and D.
16 is definitely negative. So that eliminates C and D again.
< the number on the left of this is smaller than the right
> the number of the right of this is bigger than the left
4 is larger than -16
4>-16
B
(3x-1)•(5x-3)
find area and perimeter in feet
Answer:
21 is the answers to your question
Can someone help me with this please!
Answer:
Step-by-step explanation:
17. Alexis has a painting presently valued at $2000. An art dealer told her the painting would
appreciate at a rate of 8% each year. In how many years will the painting be worth $5000?
Round your answer to the nearest tenth.
Show work please
Answer:
18.8 years
Step-by-step explanation:
8% of $2000 = $160
To be worth $5000, the painting need to rise by $3000
And every year it rise by $160, so it will need 3000 : 160 = 18.75 (round to 18.8) years.
Help pleaseeee helpp!!
Answer:
D
Step-by-step explanation:
i did the math
NEED HELP!! Urgently!
What is the ratio in decimal form of 75 people in a 10ft X 10ft square?
Answer:
(100 ft^2) / (75 people) is a ratio: 1.3333... ft^2/person
Step-by-step explanation:
There are 75 people in a 100 square foot area. The amount of space (floor space) is (100 ft^2) / (75 people) = 1 1/3 square feet.
(100 ft^2) / (75 people) is a ratio: 1.3333... ft^2/person
Find the missing lengths:
LN=
MN=
Answer:
LN=4.33
MN=5
Step-by-step explanation:
sine 60
A box is 20 inches long and 21 inches high. What is the diagonal length of the box?
Answer:
29 inches
Step-by-step explanation:
Answer:
Use Pythagoras' Theorem:
c²=a²+b²
c²=20²+21²
c²=841
c=√841
c=29 inches
Step-by-step explanation:
amelia mom baked 48 cookies after amelia and her friends walk in the kitchen there are 18 cookies left
PLEASE HELP HURRY WILL MARK THE BRAINLIEST ONLY ANSWER IF U KNOW 25 POINTS!!!what is the value expression 2⁴ plus 3²
Answer:
25
Step-by-step explanation:
2x2x2x2=16
3x3=9
16 + 9= 25
Write an equation for the line parallel to the given line that contains C.
c(3,8); y= 5/8x + 8
Answer:
x= - 64/5
Step-by-step explanation:
1- Substitute y = 0
2- Multiply both sides
3- Move the variable to the left
4- Divide both sides
Simplify (3x2 − 2) (2x2 − 6x 3). 5x2 − 6x 1 5x2 − 6x − 1 x2 − 6x 1 5x2 − 8x 3.
Answer:
-566
Alternative form:
-5.66 x [tex]10^{2}[/tex]