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The weight of an organ in adult males has a bell shaped distribution with a mean of 320 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following. A.) About 68% of organs will be between what weights? B.) what percentage of organs weighs between 280 grams and 360 grams? C.) what percentage of organs weighs less than 280 grams or more than 360 grams? D.) what percentage of organs weighs between 300 grams and 360 grams?
Answer:
A.) About 68% of organs will be between what weights?
Therefore, 68% of the organs will weigh between 300 and 340 grams.
B.) what percentage of organs weighs between 280 grams and 360 grams?
95%
C.) what percentage of organs weighs less than 280 grams or more than 360 grams?
5%
D.) what percentage of organs weighs between 300 grams and 360 grams?
81.5%
Step-by-step explanation:
Empirical formula states that:
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Where:
μ = Population mean
σ = Population standard deviation
From the above question, we have the following information
Mean weight = 320 grams
Standard deviation = 20 grams
a) About 68% of organs weight between:
To solve for this, we would use the empirical rule:
68% of the data values lie within 1 standard deviation of the mean
Hence, 68% of the data values lie in the range:
Mean - 1 standard deviation to Mean + 1 Standard Deviation.
Mean - 1 Standard Deviation
μ - σ
= 320grams - 20grams = 300 grams
Mean + 1 Standard Deviation
μ + σ
= 320grams + 20grams = 340 grams
Therefore, 68% of the organs will weigh between 300 and 340 grams.
B.) what percentage of organs weighs between 280 grams and 360 grams?
Mean weight = 320 grams
Standard deviation = 20 grams
Hence,
x - mean = 280 grams - 320 grams = -40 grams
x - mean = 360 grams - 320 grams = 40 grams
Note that both differences = 2 × standard deviation
Hence, from the empirical formula above,
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies
Therefore, 95% of the organs fall between 280 grams and 320 grams
C.) what percentage of organs weighs less than 280 grams or more than 360 grams?
Mean weight = 320 grams
Standard deviation = 20 grams
Hence,
x - mean = 280 grams - 320 grams = -40 grams
x - mean = 360 grams - 320 grams = 40 grams
So, from the empirical formula above,
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies
Therefore, 95% of the organs fall between 280 grams and 320 grams
It is important to note that finding the percentage of data that weighs less than or more than the given range of values, the formula is given as:
Percentage of Value outside( less than or more than) the range = 100% - Percentage of values within the range
100% - 95%
= 5%
Therefore, the percentage of organs weighs less than 280 grams or more than 360 grams is 5%
D.) what percentage of organs weighs between 300 grams and 360 grams?
Mean weight = 320 grams
Standard deviation = 20 grams
Hence,
x - mean = 300 grams - 320 grams = -20 grams
20 grams = 1 × standard deviation
For 300 grams, the empirical formula that states that:
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ applies.
It is important to note that the percentage of values below the mean and above the mean must be the same.
But since this is a bell shaped distribution, the percentage of data between 300 and 320 grams = 68%/2
= 34%
x - mean = 360 grams - 320 grams = 40 grams
40 = 2 × standard deviation
For 360 grams , the empirical formula that states that,
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies
It is important to note that the percentage of values below the mean and above the mean must be the same.
Since this is a bell shaped distribution, the percentage between 320 and 360grams = 95%/2
= 47.5%
Therefore, the percentage of organs that weighs between 300 grams - 360 grams = 34% + 47.5%
= 81.5%
AB = 2x + 3, BC = 3x + 7, AC = 60. what does x represent
Answer:
AC=AB+BC
60=2x+3+3x+7
60=2x+3x+3+7
60=5x+10
60-10=5x
50=5x
x=10
Rewrite the expression in the form x
Answer:
See below (I hope this helps!)
Step-by-step explanation:
When dividing exponential terms of the same base, we can simply subtract the exponents, therefore:
[tex]\frac{x^{6} }{x^{8} } = x^{(6-8)} = x^{-2}[/tex]
Use the order of operations to solve the problem. 7 x 8 + 4 +1
Answer:
7x8 is 56 plus four plus one equals 61
Step-by-step explanation:
FIRST TO ANSWER GETS BRAINLIEST
Step-by-step explanation:
3x - y = 74
4y = x
Replace x in the first expression by 4y
3x - y = 74 ➡ 3(4y) - y = 74
12y - y = 74
11y = 74
y = 74/11 we can use this to find x
4y = x
4 × 74/11 = x
296/11 = x
AB formed by (-8, -1) and (-4, 2)
CD formed by (0, -3) and (12, 6)
The lines AB and CD are parallel lines.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The slope of line AB is m=2+1/-4+8
m=3/4
The slope of line CD is m=9/12=3/4
Both the lines AB and CD having the same slopes.
In parallel lines the slope will be same.
Hence, the lines AB and CD are parallel lines.
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In order to get a grade of a 2 on your objective summary, what must you include
?
How many solutions does the equation 4x + 2(x − 5) = 3(2x − 4) have? Group of answer choices infinitely many solutions no solution at least two solutions exactly one solution
Answer:
absolutley no solutions
Step-by-step explanation:
Jin’s soccer team has 4 coaches and 22 players, and his twin sister’s team has 2 coaches and 11 players. If the relationship between the number of players and coaches is proportional throughout the league, which ordered pair could represent the total number of coaches and players in the entire league?
Answer:
B
Step-by-step explanation:
Anthony and Andrew raised money for charity in the ratio 3:7. Anthony raised $177. How much did Andrew raise?
Answer:
I'm pretty sure it's 413
Step-by-step explanation:
so I divided 177 by 3 to get 59
then multiplyed 59 by 7 to get 413
can you please help me
Answer:
I dont understand what their asking but there are three problems I do know. 2x+5=19 is a equation A=2l+2w is an equation and 3w+4 is an expression.
Step-by-step explanation:
Anyone know it’s middle school work
Answer:
B
Step-by-step explanation:
Using the conversion
1 Kg = 1000 g , then
3745 ÷ 1000 = 3.745 Kg
kim and stacy like to make necklaces. kim has 25 and stacy has made t necklaces. they have made a total of 57 necklaces all together.
Answer:
32
Step-by-step explanation:
you subtract 25 by 57 to show how many necklaces stacy made which is t.
-2 + 2 =
Need help with this asap❗️
Answer:
0
Step-by-step explanation:
Answer:
Zero
Step-by-step explanation:
In integers what is -11 -6
Answer:
-17
Step-by-step explanation:
Lindsay is playing a video game. She begins with an initial score of
500 points but loses 280 point throughout the game. She represents
her score using the expression shown.
500 - 280
Which of the following expressions also represents Lindsay's video
game score?
O A. 280 - 500
O B. 280 + 500
O C. 500 - (-280)
O D. 500 + (-280)
The expressions also represent Lindsay's video game score is 500 + (-280). The correct option is D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Lindsay is playing a video game. She begins with an initial score of 500 points but loses 280 points throughout the game.
The expression will be written as below:-
E = 500 + (-280)
Therefore, the expressions also represent Lindsay's video game score is 500 + (-280). The correct option is D.
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russell bought a CD player that costs $120 before it went on sale for 15% discount. If he paid 5% sales tax on the sale price, how much did russell pay for the cd player?
Answer:
$107.10
Step-by-step explanation:
The original price of the CD player is $120 and we need to take 15% off.
We can find how much we need to subtract by multiplying 120 by .15, which equals 18. Then we can subtract that from 120, to get a sales price of $102.
A shortcut is subtracting 15 from 100 to get 85, and then doing 120*.85 = 102.
From the sales price of 102, there's a 5% tax to add on. 102 * .05 = 5.1
102+5.1 = 107.1
Answer:
$107.10
Step-by-step explanation:
First, find the discount.
Multiply the discount rate, 15% by the price of the CD player, $120
discount rate * price
15% * $120
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100= 0.15 or 15.0 --> 1.5 --> 0.15
0.15 * $120
$18
Since it is a discount, subtract $18 from the regular price of $120.
$120-$18
$102
Next, find the tax.
Multiply the tax rate, 5% by the price of the discounted CD player, $102
tax rate * discounted price
5% * $102
Convert 5% to a decimal. Divide 5by 100 or move the decimal place two spots to the left.
5/100= 0.05 or 5.0 --> 0.5 --> 0.05
0.05* $102
$5.10
Since it is tax, add $5.10 to the discounted price of $102.
$102 + $5.10
$107.10
Russell will pay $107.10 for the CD Player after a discount and tax.
Simplify the expression 2k+10k-(2k+3)+13
Use inverse operations to find the inverse of y = 27x?
The inverse of y = 27x3 is y =
Answer:
y = (∛x)/3
Step-by-step explanation:
To undo the multiplication by 27, you multiply by its inverse:
(1/27)y = (1/27)(27x^3)
y/27 = x^3 . . . . . . . . . . . simplify
To undo the cube, you take the cube root:
(∛y)/(∛27) = ∛(x^3)
(∛y)/3 = x
Apparently, you want the inverse function, so you swap the variables:
y = (∛x)/3
_____
You can swap the variables at the beginning or end. It doesn't matter. If you do it at the beginning, you have ...
x = 27y^3
and you're solving for y. You use the same inverse operations that we used above.
Using Accuracy and Precision
-vani is building a rectangular play area. The length of
me play area is 75 meters. The width of the play area is
- 3 meters. If she wants to cover the area in foam, how
much foam does she need to buy?
Due to the accuracy of the tape measure Avani used
the amount of foam needed to cover the play area is
38.9 square meters
Answer:
a little bit confusing
hat is the value of x in the equation 4 x plus 8 y equals 40, when y equals 0.8? 4.6 8.4 10 12
Step-by-step explanation:
4x + 8y = 40
4x + (8×0.8) = 40
4x + 6.4 = 40
4x = 33.6
4x÷4 = 33.6 ÷ 4
x = 8.4
Answer:
8.4
Step-by-step explanation:
:D
I'm on a 10 minute time limit. Please Answer!!!!! Show Work.
Answer:
623.64
Step-by-step explanation:
Really?!? Just use a calculator. I think thats right haven't done this in a while
Which of the following units is incommensurable with miles? Select the two correct answers. (1 point)
acres
inches
meters
yards
grams
Answer:
grams
Step-by-step explanation:
Miles measures distance
Looking through the given options; acres, inches, metres and yards are also units of length.
So, we can conclude that they are commensurable with miles.
However, grams measures weights.
Hence,
From the list of given options; grams is incommensurable with miles because they measure different entities.
Answer:
acres and grams
Step-by-step explanation:
Miles is a measure of distance. Acres is a measure of area, and grams is a measure of mass. Knowing this you should know that these two are the answer. Your welcome!
In a family of 4 children under 10 years old, the sum of the square of the ages of the 3 youngest is equal to the square of the age of the oldest. How old are these children
Answer: 2, 3, 6 and 7.
Step-by-step explanation:
We have four natural numbers A, B, C and D.
such that all of these numbers are smaller than 10, and:
A < B < C < D.
A, B and C are the ages of the smaller ones, and D is the age of the larger kid.
Now we have the relation
A^2 + B^2 + C^2 = D^2
We can write this as:
D = √(A^2 + B^2 + C^2)
And remember that D must be smaller than 10, then now we can play with the numbers A, B and C in order to find D.
Suppose for example:
A = 1, B = 2, C = 3
D = √( 1^2 + 2^2 + 3^2) = √(1 + 4 + 9) = √14
This is not a whole number.
Then we have that A^2 + B^2 + C^2 must be a perfect square.
The perfect squares we can aim for are:
4*4 = 16
5*5 = 25
6*6 = 36
7*7 = 49
8*8 = 64
9*9 = 81
now, looking at that comes to my mind to try to reach the 49.
because we can take the 36, add 4 to that (4 = 2*2) and then add 9 (9 = 3*3)
A^2 + B^2 + C^2 = 49
where we can use:
A = 2. B = 3 and C = 6
2^2 + 3^2 + 6^2 = 4 + 9 + 36 = 49
Then we have:
D = √(2^2 + 3^2 + 6^2 ) = √49 = 7
Then the ages of the children (for smallest to largest) are:
2, 3, 6 and 7.
In a drama classroom, 75% of the students are chosen to perform a play. Of those choosen, 15% have singing roles. What is the probability that a student chosen for the play has a singing role?
Answer:
1/5 or 0.2
Step-by-step explanation:
probability=No of students with singing roles/No of people in the play15/75=1/5 or 0.26x + 2y = 18 -4x - 2y = -6
Answer:
x=6, y = -9
Step-by-step explanation:
6x + 2y = 18
-4x - 2y = -6
Add the two equations together to eliminate y
6x + 2y = 18
-4x - 2y = -6
------------------------
2x +0y = 12
Divide by 2
2x/2 = 12/2
x = 6
Then find y
6x+2y = 18
6*6 +2y = 18
36+2y = 18
Subtract 36 from each side
36+2y-36 = 18-6
2y = -18
Divide by 2
2y/2 = -18/2
y = -9
The diagonal of a square is 10m long. What is the length of the side of the square?(Give your answer to the nearest cm)
h -7/J = k solve for J
Answer:
see I need help for chemistry pls anyone here helps me I must submit before 10:30
i need to know the answer as soon as possible.
Answer:
Opinion B
Step-by-step explanation:
hope that will help you
Nick's class did an experiment. They put the same amount of water into four paper cups. To start the temperature was the each cup They put the cups in four different places They left them for thirty minutes, Next they used a thermometer to find the temperature of each cup of water. Predict which location should have the highest temperate
Answer: in a sunny spot of the classroom and im guessing 95?
Step-by-step explanation:
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