Using the normal distribution and the central limit theorem, the probability the sample mean is more than 10 words is of 0.0210.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 8.6, \sigma = 4.3, n = 39, s = \frac{4.3}{\sqrt{39}} = 0.6885[/tex]
The probability that the sample mean is more than 10 words is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{10 - 8.6}{0.6885}[/tex]
Z = 2.03.
Z = 2.03 has a p-value of 0.979.
1 - 0.979 = 0.021.
The probability the sample mean is more than 10 words is of 0.0210.
More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24663213
#SPJ1
8. Higher Order Thinking There are points on a grid at (0, 0) and (3, 0).
a. What is a possible coordinate of the third vertex if the triangle has
a perimeter of 11 units? Explain.
b. Is there another point that could be the third vertex? Explain.
par poib
signe
Higher Order Thinking There are points on a grid at (0, 0) and (3, 0).
a. What is a possible coordinate of the third vertex if the triangle has
a perimeter of 11 units? Explain.
b. Is there another point that could be the third vertex? Explain.
par poib
signe
We have a part-whole ratio of 2 : 10. How can we represent this ratio as a percent?
Answer:
20%
Step-by-step explanation:
2:10 = 2/10 = 20/100 = 20%
Julianna has thirty two pieces of candy in a candy jar. Julianna only has two kinds of candy.
jolly rangers and twix. For every four twix bars, she has two pieces of jolly rangers. How many
pieces of each candy are in the candy jar?
The number of jolly rangers candy she has is 22. The number of twix bars she has is 11.
What are the linear equations that represent this question?
j + t = 33 equation 1
4t = 2j
j = 2t equation 2
Where:
j = number of jolly rangers
t = j = number of twix
How many twix candies does Julianna have?
Substitute for j in equation 1 using equation 2
2t + t = 33
3t = 33
t = 11
How many jolly candies does Julianna have?Subsitute for t in equation 2
j = 11 x 2 = 33
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
#SPJ1
What is the area of a triangle whose vertices are J(-2, 1), K(0, 3), and L(4,4)?
Answer: 3
Step-by-step explanation:
help pls
14 numbers are written in a row so that the sum of any three consecutive numbers is
19, and the sum of all the numbers is 77. Find the 9th number.
The series of numbers that meets the requirements is 5+6+8+9+4+6+7+3+9+2+8+9+1.
How to check that the series meets the requirements?To verify that the series meets the requirements, we must establish what the requirements are:
Every 3 consecutive numbers must add up to 19.In total there must be 14 numbers.The total sum of all the numbers must be 77.To verify that every 3 consecutive numbers add up to 19, we separate them into 4 groups of 3 and one number is left over.
5 + 6 + 8 = 199 + 4 + 6 = 197 + 3 + 9 = 192 + 8 + 9 = 19In total there must be 14 numbers and they must add up to 77.
5+6+8+9+4+6+7+3+9+2+8+9+1 = 77
Learn more about numbers in: https://brainly.com/question/17429689
#SPJ1
0.596 as a fraction and 0.596 as a percentage.
596/1000 and 59.6%
Step-by-step explanation:
because when we make 596/1000 is 0.596
8. (06.04 MC)
Find the total surface area of a cylinder with a height of 8 cm and radius of 4 cm. Leave your answer in terms of r. (1 point)
O 80 cm²
96 cm²
128 cm²
192 cm²
The total surface area of the cylinder in terms of π is 96π cm². The correct option is the second option 96π cm²
Calculating Total surface area of a CylinderFrom the question, we are to determine the total surface area of the cylinder
The total surface area of a cylinder can be calculated by using the formula,
T.S.A = 2πr² + 2πrh = 2πr(r +h)
Where r is the radius
and h is the height
From the given information,
h = 8 cm
r = 4 cm
Putting the parameters into the formula, we get
T.S.A = 2π×4(4 +8)
T.S.A = 8π(12)
T.S.A = 96π cm²
Hence, the total surface area of the cylinder in terms of π is 96π cm². The correct option is the second option 96π cm²
Learn more on Calculating Total surface area of a Cylinder here: https://brainly.com/question/15389804
#SPJ1
Work out the surface area of this cylinder
Answer:
in terms of pi: 24pi cm squared
substituting pi for 3.14: 75.36 cm squared
Step-by-step explanation:
8pi + 16pi = 24pi
I need help PLEASE HELPP
Answer:
1 and 5 are corresponding angle
8 and 4 are corresponding angle
4 and 6 are alternate interior angle
2 and 8 are alternate exterior angle
7 and 3 are corresponding angle
2 and 6 are corresponding angle
3 and 5 are alternate interior angle
1 and 7 are alternate exterior angle
Using the identity sin? O + cos? O = 1, find the value of tan O, to the nearest
hundredth, if sin 0 = 0.27 and 0 < 0 < 7
Answer:
3.7
Step-by-step explanation:
Given
sin²θ + cos²θ = 1sinθ = 0.27Solving for cosθ
cos²θ = 1 - sin²θcos²θ = 1 - (0.27)²cos²θ = 0.0729Finding tanθ
tanθ = sinθ / cosθtanθ = 0.27 / 0.0729tanθ = 3.7Verifying it lies in the range
θ = tan⁻¹ (3.7)θ = 74.88° Range is : 0 < θ < π/2 [or 0 < θ < 90°]It lies in the range [Verified]Help me please help me
Answer:
j=-56
Step-by-step explanation:
Hi!
j-38 = -95
Because -95 is negative, j has to be less than one. If a negative is subtracted off of a negative, the number becomes smaller -95+39= j.
-95+39=-56
Answer:
j = -56
Step-by-step explanation:
j - 39 = -95
Add 39 to both sides:
j - 39 = -95
+ 39 + 39
j = -56
Final answer: j = -56
Hope this helps!
When Lillian goes bowling, her scores are normally distributed with a mean of 130
and a standard deviation of 11. Using the empirical rule, what percentage of the
games that Lillian bowls does she score between 119 and 141?
Using the Empirical Rule, it is found that she scores between 119 and 141 on 68% of the games that she bowls.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering that the mean is of 130 and the standard deviation is of 11, the interval between 119 and 141 is within one standard deviation of the mean, hence she scores between 119 and 141 on 68% of the games that she bowls.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
What is the solution of rootindex 3 startroot x 8 endroot = negative 4?
The solution to the equation [tex]\sqrt[3]{x + 8} = -4[/tex] is x = 72
How to determine the solution?The equation is given as:
[tex]\sqrt[3]{x + 8} = -4[/tex]
Take the cube of both sides
x + 8 = -64
Subtract 8 from both sides
x = 72
Hence, the solution to the equation [tex]\sqrt[3]{x + 8} = -4[/tex] is x = 72
Read more about equation solutions at:
https://brainly.com/question/2972832
#SPJ4
There were 16 teams that competed in men's ice hockey at the Salt Lake City Olympics of 2002.
Find the number of permutations for the gold, silver, and bronze metals at the awards ceremony.
Answer:
3360.
Step-by-step explanation:
That would be the number of permutations of 3 from 16.
= 16P3
= 16!/(16-3)!
= 16*15*14
= 3360
Answer:
3 360 permutations
Step-by-step explanation:
the number of permutations :
16P3 = 16 × 15 × 14 = 3 360
Below is the work a student completed with an error. Identify the step where the error first occured an
Step 1: (7 - 10) – 2(6y - 5) + 17
Step 2: (3) - 12y – 5 + 17
Step 3:3 - 12y + 12
Step 4: - 12y + 15
А
Step 2
B
Step 3
C
Step 4
D
Answer should be 12y - 9
E
Answer should be 12y + 9
C2022 Illuminate Education, Inc.
TM
Answer:
Step 2
Step-by-step explanation:
Solving
(7 - 10) - 2(6y - 5) + 17 [Step 1]3 - 12y + 10 + 18 [Step 2]3 - 12y + 28 [Step 3]-12y + 31 [Step 4]The error has occurred in Step 2.
The distribution of -2 to 6y and -5 gives -12y and 10 respectively.
Instead, the distribution has not happened between -2 and -5.
what is the surface area
3. In which quadrant do lines land m Intersect?
m
A. Quadrant !
B. Quadrant II
C. Quadrant III
D. Quadrant IV
Answer:
Quadrant 3 so the answer should be c
please help me with this
A B and F seem like questions that make sense :)
Answer:
Abc
Step-by-step explanation:
they make the most reasonable answers
What is the greatest common factor of
21xy^3 6x^4y^2
A. 42x^4 y^3
B. 42x^5 y^5
C. 3x^4 y^3
D. 3xy^2
What is 3,740,231,580 rounded to the nearest million
Step-by-step explanation:
3,740,231,580
we normally start rounding from the end so the last number should be checked. If it's not more than 5, then make it a zero and move on to the next. if it's more than five, make the number zero and add 1 to the the next number. So this is how it will look.
3,740,231,580
3,740,231,580
3,740,231,590
3,740,231,600
3,740,232,000
3,740,230,000
3,740,200,000
3,740,000,000
And I think that's it
Can someone explain the right answer? The question and answer is below.
Answer:
x -3y +4Pythagorean theoremStep-by-step explanation:
You want to find the horizontal and vertical distances between two points, and you want to know how to use those to find the distance between those points.
__
horizontal distanceThe x-coordinate of a point is its horizontal distance from the y-axis. The horizontal distance between two points will be the difference of their x-coordinates.
If the points are (3, -4) and (x, y), the x-coordinates are 3 and x. The difference between those coordinates can be written as x-3. (Usually, we subtract the first point from the second one.)
The horizontal distance from (3, -4) to (x, y) is (x -3).
__
vertical distanceIn like fashion, the y-coordinate of a point is its vertical distance from the x-axis. The vertical distance between two points will be the difference of their y-coordinates.
For the points (3, -4) and (x, y), the y-coordinates are -4 and y. The difference between those coordinates is y -(-4) = y +4.
The vertical distance from (3, -4) to (x, y) is (y +4).
__
total distanceAs the attachment shows, the horizontal and vertical distances between the two points can be considered to be the legs of a right triangle. The "total" distance between the points is the straight-line distance. It is the hypotenuse of that triangle.
The Pythagorean theorem gives the relation between the sides and hypotenuse of a right triangle. In this context, the Pythagorean theorem can be used to create an equation showing the relationship between the legs of the triangle and the distance from (x, y) to the center. (That distance is the radius.)
In particular, the equation created is ...
(x -3)² +(y +4)² = 7²
_____
Additional comment
For right triangle legs 'a' and 'b', and hypotenuse 'c', the Pythagorean theorem tells you ...
a² +b² = c²
The sum of the squares of the sides is equal to the square of the hypotenuse.
!!100!! POINTS PLEASE HELP
Answer:
[tex]\sf x = 6\dfrac{2}{3} \ \ or \ \ 6.67 \ (rounded \ to \ nearest \ hundreth)[/tex]
Build a proportional equation:
[tex]\rightarrow \sf \dfrac{AB}{AD} = \dfrac{BC}{DE}[/tex]
[tex]\rightarrow \sf \dfrac{10}{x+10} = \dfrac{6}{10}[/tex]
[tex]\rightarrow \sf 10(10) = 6(x+10)[/tex]
[tex]\rightarrow \sf 100 = 6x+60[/tex]
[tex]\rightarrow \sf 40= 6x[/tex]
[tex]\rightarrow \sf x = 40/6[/tex]
[tex]\rightarrow \sf x = \dfrac{20}{3}[/tex]
[tex]\rightarrow \sf x = 6\dfrac{2}{3}[/tex]
Answer:
Step-by-step explanation:
1. Create a porportianal equation. ab/ad=bc/de
2. plug in the variables for each line segment. 10/x+10=6/10
3. multiply each side by x + 10. (6x+60)/10=10
4. Multiply each side by 10. 6x+60=100
5. simplify. 6x=40 3x=20
6. divide each side by 3. x=20/3
(Sorry about my last answer)
what is the measure of the angle in degrees
Answer:
35°
Step-by-step explanation:
7π=210°
so I assume you just divide 210° by 6 and that comes out to 35°
I HOPE this helps!
Which equation matches the graph?
y=-2x
Step-by-step explanation:
it can't be y=2x and y=-½ because it passes by the opposite side of the given graph
Rewrite each fraction with a denominator of 24. 2/3 and 5/8
Answer:
2/3 of 24 is 16/24
5/8 of 24 is 15/24
Step-by-step explanation:
if you multiply across 2/3 by 8/8 it equal to 16/24
if you multiply across 5/8 by 3/3 it equal to 15/24
Answer:
16/24 and 15/24
Step-by-step explanation:
To get the denominator in 2/3 to be 24 we multiply by 8 since 3 * 8 = 24, since we multiplied the denominator by 8 we must multiply the numerator by 8 as well to keep things equal, therefore 2 * 8 = 16, and we arrive at 16/24.
Likewise for 5/8, to get the denominator 8 to be 24, we multiply by 3, multiplying the numerator by 3 to keep things equal will result in 15/24.
Connor is 6 feet tall and casts a shadow that is 2.5 feet long. He stands next to a tree that is 25 feet tall. How long is the shadow the tree casts? Round your numerical answer to the nearest whole number.
Answer:
10
Step-by-step explanation:
[tex]\frac{6}{2.5} =\frac{25}{x} \\6x=2.5*25\\6x=62.5\\x=10.417=10[/tex]
The Tree casts a height of 10.41 feet tall.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Connor is 6 feet tall and casts a shadow that is 2.5 feet long.
He stands next to a tree that is 25 feet tall.
let the shadow of tree is x feet long.
Using proportion
6/ 2.5 = 25/x
6x = 62.5
x= 10.41 feet
Learn more about Proportion here:
https://brainly.com/question/26974513
#SPJ2
Simplify the following expression. (3m-4)²+8(3m-2)
A. 8m/4
B. 9m/4
C. 3m+24/4
D. 3m+28/4
Step-by-step explanation:
(3m-4)² + 8(3m-2) = (3m-4)(3m-4) + 24m - 16 =
= 9m² - 3m×4 - 4×3m + 16 + 24m - 16 =
= 9m² - 24m + 16 + 24m - 16 = 9m²
so, there is seemingly something missing in your original expression.
going from 9m², the most likely solution would be 9m/4 and therefore B.
but we cannot be sure, because again, I don't know what you left out in the beginning.
A small class has 10 students, 6 of whom are girls and 4 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the teacher will choose two girls? Write your answer as a fraction in simplest form.
Answer:
2
5
Step-by-step explanation:
fraction of girls in the class is 6
5
so........the total number of girls is 6 and only 2 are chosen,meaning you have to subtract 2 from 6 which is 4 and then 4
10(total number of students) is
2
5 when simplified
PLS ANSWER FOR MEEEE FAST TYYYYSMM
The following sphere has. A diameter of 18 cm.
Answer:
I think your answer is A, correct me if I'm wrong
7!
——————-
————-
please help!!
——————
math geniuses where r uuuu
————
help!
Answer:
It is the fourth option, D.