Using the normal distribution and the central limit theorem, it is found that the probability that the mean plant height is less than 9.5 cm is of 0.9388.
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 and the standard deviation are given, respectively, by [tex]\mu = 9.31, \sigma = 0.55[/tex].
For samples of n = 20, the standard error is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.55}{\sqrt{20}}[/tex]
s = 0.123.
The probability that the mean plant height is less than 9.5 cm is the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9.5 - 9.31}{0.123}[/tex]
Z = 1.54.
Z = 1.54 has a p-value of 0.9388.
Hence the probability that the mean plant height is less than 9.5 cm is of 0.9388.
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93. In 1939 a hamburger sold for 5¢, but a worker would only earn 30¢/h.
If in a later year, a hamburger sells for 85¢, how much would the
worker earn if earnings went up at the same rate?
Answer:
$5.10/h
Step-by-step explanation:
85/5 = 17
it increased 17 times, so did the worker
.30x17= $5.10
_ __
0.47 and 0.47 as simplified fractions
Answer:
Here is your answer
Step-by-step explanation:
What is 0.47 as a fraction? 0.47 as a fraction in simplest form is written as 47/100.
A fraction represents a part of a whole, written in the form of p/q where p and q are integers.
Here we will show you how to convert 0.47 decimal number to fraction form and as a mixed number with steps.
0.47 as a simplified fraction
47/100
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Answer:
47/100
Step-by-step explanation:
0.47 as a fraction in simplest form is written as 47/100.
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HELP PLEASE!!!! Posting a lot of these for a lot of points!
Answer:
Step-by-step explanation:
Area of figure I = length *width
= 4 * 5
= 20 m²
Figure II is a trapzium.
a and b are the parallel sides. a = 21 m
b = 20 - 5 = 15 m
h = 3 + 4 = 7 m
[tex]\text{area of figure 2 = $\dfrac{(a + b)*h}{2}$}[/tex]
[tex]=\dfrac{(21+15)*7}{2}\\\\\\=\dfrac{36*7}{2}\\\\\\= 18*7\\\\= 126 \ m^{2}[/tex]
Area of the figure = 20 + 126
= 146 m²
Answer:
146 m²
Step-by-step explanation:
Formulae
Area of a rectangle = width x length
Area of a triangle = 1/2 x base x height
Divide the figure into 2 rectangles and a triangle (see attachment).
Area of Rectangle 1 = 4 x 5 = 20 m²
Area of Rectangle 2 = (3 + 4) x (20 - 5) = 105 m²
Area of triangle 3 = 1/2 x (21 + 5 - 20) x (3 + 4) = 21 m²
Total area = 20 + 105 + 21 = 146 m²
How do you recognize a geometric sequence? Can you find terms within a geometric sequence using a formula?
Answer:
See step by step explanation
Step-by-step explanation:
To reconize a geometric sequence, the factor at which one number is greater than the previous number should always be the same
For example,
2,4,8,16,32,64,128,256,512,1024 is a geometric sequence since the next number is always greater than the previous number by a factor of 2
to find the n-th term in a sequence, we can use a formula.
Going back to the example, let's label each number with a term
to find the nth term of this specific sequence, we need to find two things
the first number of the sequence, and the factor at which this sequence increases at
the first number is 2, so n1 = 2
each term increases by a factor of 2 (2*2=4, 4*2=8, 8*2=16, 16*2=32, 32*2=64), so the factor is 2
the equation is:
(the initial term)*(the factor)^(the term number - 1)
so,
[tex]2*2^{n-1}[/tex] is our equation
We can check our equation by plugging in a number
looking back at our list, we see that the 7th term is 128
plug in 7 into out equation
[tex]2*2^{7-1}=2*2^6=2^1*2^6=2^7=128[/tex], so our equation works
Here's a practice problem
for the sequence 3,9,27,81,243,729, what is the factor which the sequence increases at? what's the initial number? what's the equation for this sequence?
a harder practice problem:
for the sequence 2,6,18,54,162,486, what is the factor at which the sequence increases at? what's the intitial number? what's the equation for this sequence? what's the 8th term of this sequence if it were to be continued?
Yes we can
the formula given to find the terms is
a_n=ar^n-1Where
a_n is n the terma is first termr is common ration is an positive integerHELP RN IM FAILING PLEASE
Answer:
Top left.
Step-by-step explanation:
Answer: 3x + y = 3
Step-by-step explanation: For a line to be parallel it must have the same slope but a different y intercept. y = mx + b, where M is the slope, and B is the y intercept.
We can solve for y, using 3x + y = 3. Subtracting both sides from 3x, we get y = -3x + 3, which is a different y intercept but the same slope.
A line passes through the point (4,1) and has a slope of 5/4
Write an equation in slope-intercept form for this line.
Please help
Use the two-way frequency table to calculate the probability that the person is a democrat, given the fact that the person supports the issue,
P(democrat supports the issue)
Answer:
23/58
Step-by-step explanation:
number of people that support the issue. (58)
start with that first because it is given
now find the number of democrats that are in that column which is 23
At how many hours will blake earn the same amount in both jobs?
Answer: 6.15 you already solved it congrats
Step-by-step explanation:
you already equal both amount equations to each other therefore you are solving for the hours he gets equal pay
The outer angle at the top C of the ABC is 112 °. If the bisector of the side AB intersects the side AC at point Q and the segment BQ is perpendicular to AC, find the magnitude of ABC
Step-by-step explanation:
The outer angle at the top C of the ABC is 112 °. If the bisector of the side AB intersects the side AC at point Q and the segment BQ is perpendicular to AC, find the magnitude of ABC
 Find the length of the third side. If necessary, write in simplest radical form.
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In circle K with \text{m} \angle JKL= 82^{\circ}m∠JKL=82 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{JL}. JL⌢ .
Answer:
M< JKL = 82°Solution: UP
The angle measure of the minor arc JL equals 82°.
What is Arc of a Circle?An arc of a circle is defined as the part of the boundary of a circle. The straight line drawn joining the two end points of the arc is called chord of the circle.
If we mark any two points on the circle, by joining those points along the circle, we get two arcs. The smaller arc is called the minor arc and the longer arc is called the major arc. If the length of the arc exactly equals the half length of the circle, then the arc is called semicircular arc.
An arc can be measured in two ways : By finding the measure of the angle of arc and finding the length of the arc.
Here we are asked to find the measure of the minor arc which is the measure of the angle of the arc JL.
Measure of the angle of the arc equals the angle formed at the center of the circle by joining the end points of the arc to the center of the circle.
We have ∠JKL = 82°
∴ measure of arc JL = 82°
Hence, the measure of the minor arc JL equals 82°.
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Jack hit a baseball on 13 out of 30 tries during practice. what is the experimental probability that he will hit the ball on his next trial write your answer as a fraction as a decimal and as a percent
Answer:
Fraction: 13/30
Decimal: 0.43
Percentage: 43%
pls help me to answer this
Answer:
hi! this is (insert your name) what does this sybol/mathematical term mean?
√
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
Greetings Mrs.(name here)!
I got my recent test back and I was wondering why this question was incorrect.
For #4, I was sure that you had to find the square root and then multiply by pi, but apparently that's not what some people did and they got it correct.
How do I properly do this question?
-*name here*
please help. 50 points on the line
Answer:some where from 65-75 feet
Step-by-step explanation:
find the LCM of denominator 3/8 and 3/4
Answer:
Step-by-step explanation:
Actually, it is 8.
3/8: nothing need be done.
3/4: Multiply top and bottom of the fraction by 2.
3*2 / 4*2 = 6/8
So the lowest common multiple is 8.
The factions become 3/8 and 6/8
Find the m < VXW down below
Answer:
Step-by-step explanation:
Select all that apply.
Which pairs of angles are supplementary?
1 and 6
5 and 7
5 and 8
2 and 3
Answer:
1 and 6
5 and 7
Step-by-step explanation:
Supplementary angles are 180 degrees and so is a linear pair
1 and 6 add up to 180 degrees meaning they are supplementary. Angle 1 and angle 2 are a linear pair so 180-120=60 which is the degree of angle 1, angle 2 corresponds to angle 6, so angle 1 + angle 6 would equal 180 degrees. (120+60)
5 and 7 are a linear pair which automatically makes them supplementary
The others are vertical angles which don't add up to 180. (120+120=240)(60+60=120)
can a parking lot be built at angle K. why or why not
Solve the triangle. Round to the nearest tenth.
In AABC, c = 9, b = 25, mZA = 113°
Answer:
28.5
Step-by-step explanation:
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Please
Solve for x. Leave your answer in the simplest form.
Image down below!
Please help! Brainlist and points
(I named the empty line y)
y²= 9²+5²
= 81+25
=106
y= V106
y≈10.30
x²= 4²+y²
= 4²+ (V106)²
= 16+106
=122
x≈11.05
Please answer everything that at asks in the image above. this is very important and I need help.
Answer:
Step-by-step explanation:
I really need help! Pls! I'd appreciate it! :) Here's the question...
A block of metal has a mass of 1000g and dimensions of 7.5 cm by 6 cm by 10 cm. Use this information to find the density of the metal block.
When given the set of variables, solve for X
Answer: B
Step-by-step explanation:
SOMEONE PLEASE HELP ME WITH THIS!!
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Answer:
5.946
Step-by-step explanation:
The pythogorean theorem states that a^2+b^2=c^2.
We are given the hypotenuse, c, and a side length.
3.5^2+b^2=6.9^2
12.25+b^2=47.61
b^2=35.36
b=5.9464...., rounded to 5.946
18, 6, 2, ...
Find the 7th term.
Answer:
2/81
Step-by-step explanation:
Firstly find out the common ratio.
And then the general term.
And at last you can find any term(7th term in this case).
The 7th term of the sequence will be 13122.
What is a geometric sequence? What is a expression? What is a mathematical equation?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. The nth term of the sequence will be a[n] = arⁿ ⁻ ¹.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.We have the following sequence -
18, 6, 2 ...
The nth term of the geometric sequence will be a[n] = arⁿ ⁻ ¹.
a[7] = 18 x 3⁶
a[7] = 18 x 9 x 9 x 9
a[7] = 13122
Therefore, the 7th term of the sequence will be 13122.
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If f ( 1 ) = 2 f(1)=2 and f ( n ) = f ( n − 1 ) 2 − 5 f(n)=f(n−1) 2 −5 then find the value of f ( 4 ) f(4).
[tex]f(1) = 2\\f(2)=f(2-1)^2-5=(f(1))^2-5 = 2^2-5 = -1\\f(3) = f(3-1)^2 - 5=f(2)^2-5=(-1)^2-5=-4\\f(4) = f(4-1)^2-5 = f(3)^2-5 = (-4)^2-5 = 11[/tex]
so f(4) = 11
Hope that helps!
Answer:
f(4) = 11
Step-by-step explanation:
Given :
base function ⇒ f(n) = f(n - 1)² - 5f(1) = 2Solving :
f(2) = f(1)² - 5f(2) = 2² - 5 = 4 - 5 = -1f(3) = f(2)² - 5f(3) = (-1)² - 5 = 1 - 5 = -4
f(4) = f(3)² - 5f(4) = (-4)² - 5f(4) = 16 - 5 = 11
In a game, the suit and number of a card must be guessed while it is facedown. If the odds of guessing the suit correctly are 13/52 and the odds of guessing the number are 4/52, then what are the odds of guessing both the number and suit correctly?
Answer:
1/52.
Step-by-step explanation:
The suit AND the number must be correct.
When you see AND in a probability question think 'multiply'.
That would be 13/52 * 4/52
= 52/(52)^2
= 1/52.
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Answer:
14.3 Cm
Step-by-step explanation:
Step 1: A^2+B^2=C^2
Step 2: 3^2+14^2=C^2
Step 3: 9+196=C^2
Step 4: 205=C^2
Step 5: 14.3=C
b = 21 feet h = 16 feet Find the area of the triangle. 168 sq. feet 85 sq. feet 100 sq. feet 108 sq. feet
Answer:
168 sq
Np also you could've just searched it up