Using the normal distribution and the central limit theorem, it is found that:
[tex]P(246 \leq \bar{x} \leq 260) = 0.5693[/tex]
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, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of [tex]\mu = 250[/tex].The standard deviation is of [tex]\sigma = 50[/tex].A sample of 36 is taken, hence [tex]n = 36, s = \frac{50}{\sqrt{36}} = 8.3333[/tex].The probability of a sample mean between 246 and 260 is the p-value of Z when X = 260 subtracted by the p-value of Z when X = 246, hence:
X = 260:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 250}{8.3333}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a p-value of 0.8849.
X = 246:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{246 - 250}{8.3333}[/tex]
[tex]Z = -0.48[/tex]
[tex]Z = -0.48[/tex] has a p-value of 0.3156.
0.8849 - 0.3156 = 0.5693, hence:
[tex]P(246 \leq \bar{x} \leq 260) = 0.5693[/tex]
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Do not understand it??
help please, i dont know how to do this
Answer:
they are not simular
Step-by-step explanation:
one has longer sides then the other and one has shorter sides
A person rolls a standard six-sided die 6 times. In how many ways can he get 3 fours, 2 ones, and I two?
Answer:
Good afternoon! no. of ways = 10! / [ 6! * 3! * 1!]
= 840
So the answer is 10.
_AnnieTheDreamGirl, 3/8/2022
A piece of art is in the shape of an equilateral triangle with sides of 15 in.
What is the area of the piece of art to the nearest tenth?
O 73.45 inches squared
84.5 inches squared
O 97.4 inches squared
169 inches squared
Answer:
97.4 inches squared
y = 5 and y = -1
Is it parallel,perpendicular or neither
Answer:
Parallel
Step-by-step explanation:
The graphs of these two equations will never intersect. Hope this helps.
Prism A is a dilation of Prism B. The height of Prism A is 612 ft, and the volume of Prism A is 8734 ft³. The height of Prism B is 314 ft.
What is the volume of Prism B?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
volume of prism B=4481.16993463 ft^3
Step-by-step explanation:
Prism B's height was multiplied by the scale factor to get prism A's height.
So x is the scale factor and 314x=612
x=1.949
volume of prism A is volume of prism B multiplied by x
8734=1.949(volume of prism B)
Volume of prism B=4481.16993463 ft^3
Answer:
10 31/32
Step-by-step explanation:
I took the k12 test
Factor the expression. 81x^2 - 121
[tex]81x^{2} -121=(9x-11)(9x+11)[/tex]
Hope that helped!
Factoring:
[tex]81x^2-121=(9x+11)(9x-11)[/tex]
Hope that helps!
The measure of the
central angle of a circle
is 74°. What is the
measure of the
intercepted arc?
Answer: 74 degrees
Step-by-step explanation:
The measure of a central angle is equal to the measure of the arc that it intercepts.
Find the factors pairs of 78
Answer:
Therefore, the pair factors are (1, 78), (2, 39), (3, 26), and (6, 13).
Give me brainliest answer
Answer:
1 x 78, 2 x 39, 3 x 26, 6 x 13
Step-by-step explanation:
Factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78.
Solve both Question related to Volume of Solids. 50 Points
Given for the cone:
base radius: 3aperpendicular height: 4agiven for the spheres:
radius: aFind volume of cone:
[tex]\sf \hookrightarrow \dfrac{1}{3} \pi r^2h[/tex]
[tex]\sf \hookrightarrow \dfrac{1}{3} \pi (3a)^2(4a)[/tex]
[tex]\sf \hookrightarrow 12\pi a^3[/tex]
Find volume of sphere:
[tex]\sf \hookrightarrow \dfrac{4}{3} \pi r^3[/tex]
[tex]\sf \hookrightarrow \dfrac{4}{3} \pi a^3[/tex]
Divide volume of cone by volume of sphere:
[tex]\sf \hookrightarrow \dfrac{12\pi a^3}{ \dfrac{4}{3} \pi a^3}[/tex]
[tex]\rightarrow 9[/tex]
Therefore proved 9 such spheres can be made using the metal cone.
We know that volume of cone is [tex]12\pi a^3[/tex]
[tex]\sf \rightarrow 12\pi a^3 = 12936[/tex]
[tex]\sf \rightarrow a^3 = \dfrac{12936}{12\pi}[/tex]
[tex]\sf \rightarrow a = \sqrt[3]{\dfrac{12936}{12\pi}}[/tex]
[tex]\sf \rightarrow a =7[/tex]
Therefore the radius of sphere is 7 cm
10. The number of people who have heard a rumor increases exponentially. If all who hear a rumor repeat it
to two people per day, and if 20 people start the rumor, the number N(t) of people who have heard the
rumor after t days is given by N(t) 20(2).
a. After what amount of time will 1000 people have heard the rumor?
=
1000 people will have heard the rumor
by 6 days.
1000 = 2012)
20
20
Soat
2t - 50
10g (50) = +
5.643856
b. What is the doubling time for the number of people who have heard the rumor?
+
Answer:
2000 is the answers.............
1/3 of 3 feet = how many inches
Answer:
12 Inches
Step-by-step explanation:
3 ÷ 3 = 1
1 feet is 12 inches
+
Question 9 (Multiple Choice Worth 5 points)
(05.02 MC)
The angles shown below are supplementary:
10x
70°
What is the value of x?
O 100
O 110
O 20°
021
Answer:
x=11
Step-by-step explanation:
supplementary angles add up to 180 degrees
10x + 70 =180
10x = 110
x=11
11x10 = 110
110+70 = 180
The line of best fit for a scatter plot is shown (6.04)
Answer:
y- 1/2x+8
Step-by-step explanation:
the slope is negative 1/2
A dilation produces a smaller figure. Which is a possible scale factor? –2 One-third 1 4
Answer:
1/3 (one-third)
Step-by-step explanation:
A scale factor that produces an image smaller than the original figure is less than 1. A scale factor that produces an image bigger than the original figure is more than 1.
Thus, the only option that's less than 1 is one-third.
yall I need help with Algebraic Experrion could yall like help me with a & b & c with the work it would really help me
Thank you! <3
Answer:
A) is 9b
B) is 2
C) is 3y+6
Step-by-step explanation:
A) (b)(2+7)
=(b)(2) + (b)(7)
= b2+b7
=b9
B) (2)(4-3)
= (2)(1)
= 2
C) 3(2+y) =(3)(2+y)
=(3)(2)+(3)(y)
=6+3y
=3y+6
A line passes through the point (-10,-7) and has a slope of
2 Write an equation in slope-intercept form for this line.
Answer: Below
Step-by-step explanation:
so using slope intercept form, we know that y = mx + b. We plug in our values. Since -10 is the x value and -7 is the y value, and 2 is the slope:
-7 = 2(-10) + b
Simplify.
-7 = -20 + b
13 = b
We plug b into the slope intercept form, this time without an x or y value to make it apply to all points on the line.
y = 2x + 13
That's our answer.
ayuda por favor
Resta: 4805 - 1568
Answer:
4805 - 1568 = 3237
Please mark as brainliest;)
Given: ABCD is a parallelogram GEC ∠GEC≅∠HFA and AE ≅ FC .
Prove: △GEC≅△HFA.
Answer:
Step-by-step explanation:
3) Congruent segments added to congruent segments form congruent segments
4) [tex]\overline{AD} \parallel \overline{BC}[/tex] (opposite sides of a parallelogram are parallel)
5) [tex]\angle FAH \cong \angle GCE[/tex] (if 2 parallel lines are cut by a transversal, the alternate interior angles are congruent)
6) [tex]\triangle GEC \cong \triangle HFA[/tex] (ASA)
Question 4 of 5
Find the height of a cone with a diameter of 12 m whose volume is 340 m2
Use 3.14 for tr and round your answer to the nearest meter.
12 m
A. 28 m
O B.2 m
O C. 12 m
O D. 9m
Answer:
h = 9 m
Step-by-step explanation:
[tex]V_{cone}=340\: m^3[/tex]
diameter (d) = 12 m
[tex]\implies radius\:(r)= \frac{12}{2}=6\:m[/tex]
[tex] \because \: V_{cone}= \frac{1}{3} \pi {r}^{2} h \\ \\ \implies \: h = \frac{3V_{cone}}{\pi {r}^{2} } \\ \\ \implies \: h = \frac{3(340)}{3.14 {(6)}^{2} } \\ \\ \implies \: h = \frac{1020}{113.04} \\ \\ \implies \: h = 9.02335456 \\ \\ \implies \: h \approx 9 \: m[/tex]
Helppp!
a. box 1: always, sometimes , never / box 2: remain ,do not remain
b. box 1: always, sometimes , never/ box 2: always, sometimes , never
c. box 1 : always, sometimes , never/ box 2: remain, not remain/ box 3: remain, not remain
d. box 1 : awlays, sometimes, never/ box 2 : an equal distance, different distance/ box 3 : some, all, no
e. box 1 : awlays, sometimes, never/ box 2 : would, would not / box 3 : all, no.
Answer:
They are all correct i think
Step-by-step explanation:
1. Assume that segments that appear to be tangent are tangent.
Find ML to the nearest tenth.
2. Assume that segments that appear to be tangent are tangent.
Find WY.
1. Applying the pythagroean theorem, ML = 6.4.
2. Applying the two tangents theorem, WY = 37.
What is the Two Tangents Theorem?The two tangents theorem states that two tangents drawn from a circle to meet at a point outside the circle are congruent.
Thus:
1. ΔJKL is a right triangle, find JL using the Pythagorean theorem:
JL = √(16² - 9.6²)
JL = 12.8
Therefore:
ML = 1/2(JL)
ML = 1/2(12.8) (radius of circle)
ML = 6.4.
2. Based on the two tangents theorem, we have:
43 - 2x = 12x + 1
-2x - 12x = -43 + 1
-14x = -42
x = 3
WY = 43 - 2x
Plug in the value of x
WY = 43 - 2(3)
WY = 37
Learn more about the two tangents theorem on:
https://brainly.com/question/9892082
8 ounces ____ 1/4 pound
Which one is bigger,equal or less
Answer: GREATER
Step-by-step explanation:
1/4 of a pound is 0.125 divided by 4 please correct if wrong 8 ounces to a pound would be 0.5/0.50
Logan has a budget of $400 to have family pictures taken. There is a sitting fee of $38. Prints cost $25 per page. How many pages of prints can Logan order?
Answer:
14
Step-by-step explanation:
You take the 400 and you minus 38 you get 362 then u divide that by 25 you get 14.48. I personally would just go with 14
f(x) = 6x + 4. Find the inverse of f(x).
A. f^-1(x) = 6x - 4
B. f^-1(x) = x-6/4
C. f^-1(x) = 4 - 6x
D. f^-1(x) = x-4/6
D. f-1(x) = x-4/6
Step-by-step explanation:
y = 6x + 4
-4
y-4 = 6x
÷6
y-4/6 = x
(Swap y and x around to find the inverse)
Inverse will be:
x - 4/6 = y
So, f-1(x) = x-4/6
Hope this helps!
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!
Answer:
option c
Step-by-step explanation:
Quadratic function in vertex form:
y = a(x - h)² + k
Where (h, k) is the vertex
vertex(5 , 12)
y = a(x - 5)² + 12
This passes through (8, 9)
9 = a(8 - 5)² + 12
9 = a(3)² + 12
9 = 9a + 12
9 - 12 = 9a
9a = -3
a = -3/9
a = -1/2
[tex]Answer:\ y = \dfrac{-1}{3}(x - 5)^{2}+12[/tex]
If 60% of a number is 90, what is the number
Answer:
60% in a fraction is: 60/100
60/100 of a variable, x, is equal to 90.
So we format it this way and solve for x;
60/100 * x = 90
60/100x = 90
0.6x = 90
/0.6 /0.6
x = 150, is the number.
PLEASE HELP HURRY! I HAVE AN F IN MATH!!!
A prism is completely filled with 64 cubes that have edge lengths of 12 in.
What is the volume of the prism?
Enter your answer in the box.
__ in³
Answer:
Step-by-step explanation:
Volume of cube = edge³
= 12*12*12
= 1728 in³
Volume of prism = volume of 64 cubes
= 64 * volume of a cube
= 64 * 1728
= 110592 in³
evaluate the expression 6n^2-15 when n=5
Hey there!
6n^2 - 15
= 6(5)^2 - 15
= 6(5^2) - 15
= 6(5 * 5) - 15
= 6(25) - 15
= 150 - 15
= 135
Therefore, your answer is: 135
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what is the sum of -4y+3 and 11y-5, i will give brainliest
Answer:
so the answer is 7y - 2 (i think)
Step-by-step explanation:
you just have to minus 11y and 4y then add 3 - 5
please mark me brainliest
Answer:
7y - 2
Step-by-step explanation:
solving variable and constant terms separately,
variable term:
-4y + 11y = 7y
constant term :
-5 + 3 = -2
together:
7y - 2