The mean is 2 Pounds and the standard deviation is 0.3340 for the population of products produced with this process
Sampling distributions are sets of data that can depict probability for all feasible samples taken from a population. Every one of these distributions is measured for a specific measure. The sampling distribution of means, for instance, calculates the average value for all feasible samples of a certain size.
Given that:
30 samples are used (n).
X stands for the sample mean weights.
Over 2.1 pounds make up 5% of the x values, while under 1.9 pounds makeup 5%.
Let the mean and standard deviation of the goods produced by this process be the population measurements.
According to the central limit theorem, if the sample size is greater than 30, any population distribution would result in a normal sampling distribution of means.
Let x represent the weights' sample mean.
x ∼ N(μX, σX2)
∼ N(μ, σ / √n)
∼N(μ, σ / √30)
5% of the x values are over 2.1 pounds and 5% are under 1.9 pounds, according to the statistics provided.
Therefore, P(x > 2.1) = 0.05
P [x − μ / (σ / √30) > 2.1 − μ / (σ / √30)] = 0.05
P [Z > 2.1 − μ / (σ / √30) = 0.05 --- (1)
P(x < 1.9) = 0.05
P [x − μ / (σ / √30) > 1.9 − μ / (σ / √30)] = 0.05
P [Z < 1.9 − μ / (σ / √30) = 0.05 --- (2)
The Z-scores that fulfill equations (1) and (2) using the common normal table are:
P(Z < −1.64) = 0.05
P(Z > 1.64) = 0.05 (An assortment of standard normative services)
Equations (1) and (2) are used to compare the values:
2.1 − μ / (σ / √30) = 1.64 ⇒ μ = 2.1 − 0.2994σ -- (3)
1.9 − μ / (σ / √30) = -1.64 ⇒ μ = 1.9 + 0.2994σ -- (4)
Adding the equations (3) and (4) :
σ = 2 − 1.9 / (0.2994) = 0.3340
In light of this, the population's mean weight is 2 pounds, and its standard deviation is 0.3340 pounds.
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HELL WILL GIVE BRAINLY
Question
Given: 3x−22=5
Prove: x = 4
Select from the drop-down menus to correctly complete the proof.
Argent please!!
Objects weigh 3 times as much on Earth as they do on Mercury. Write an expression to represent the weight of an object on Earth.
An expression to represent the weight of an object on Earth is y = 3x.
What is an algebraic expression?Variables and constants are used to create algebraic expressions using a variety of techniques.It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc.Let the weight of an object on Mercury be x and the weight of an object on Earth be y.
As given objects weigh 3 times as much on Earth as they do on Mercury.
Expression to represent the weight of an object on Earth is,
y = 3x
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Evaluate. [4.2−3(2.1)] + 1 (-0.2)² What is the value of the expression? Enter your answer as a decimal in the box.
On evaluating the value of the expression [4.2−3(2.1)] + 1 (-0.2)² is -2.06 .
In the question ,
the expression is given as
[4.2−3(2.1)] + 1 (-0.2)²
the value of (-0.2)²= (-0.2)*(-0.2)
= 0.04
Substituting the value of (-0.2)² in expression , we get
=[4.2−3(2.1)] + 1*0.04
=[4.2−3(2.1)] + 0.04
Solving the terms inside [ ] , we have
multiplying 3 with 2.1 we get
3*2.1= 6.3
Substituting it in the expression above we get
= [4.2−6.3] + 0.04
Simplifying further , we get
= -2.1 + 0.04
= -2.06
Therefore , on evaluating the value of the expression [4.2−3(2.1)] + 1 (-0.2)² is -2.06 .
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Answer:
Step-by-step explanation:
The answer is -2.06.
hope you get a good grade!!!
sssssssssssolve for f
f/3-1=1
For equation f/3-1=1 the value of f is 6
In this question, we have been given an equation f/3-1=1
We need to solve given equation for f.
⇒ f / 3 - 1 = 1 ................(Given equation)
⇒ f/3 = 1 + 1 .................(add 1 to each side)
⇒ f/3 = 2
⇒ f = 2 × 3 ....................(Multiply each side by 3)
⇒ f = 6
Therefore, For equation f/3-1=1 the value of f is 6
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use the quadratic formula to find the solutions to the equation 3x^2-10+5=0
2. Tell whether the lines through the given points are parallel, perpendicular,
or neither.
a. Line 1: (2, -3), (-4, -6)
Line 2: (-3, 2), (2, -8)
b. Line 1: (-4,-5), (4, 1)
Line 2: (6, 10), (-3,-2)
c. Line 1: (0, -4), (-2,-8)
Line 2: (-1, 5), (1,9)
Answer:
A is Perpendicular
B is Neither
C is Parallel
12 is the geometric mean of 16 and what number?
Answer:
Step-by-step explanation:
12/x = x/16
x^2 = 192
x = ± √192 = ± 8√3
EASY TRIG MATHEMATICS QUESTION! PLEASE HELP ME SOLVE! THANK YOU!
LOOK AT IMAGE FOR DETAILS !
Answer: YES
Step-by-step explanation:
use order of operations to simply the expression.
Answer:
[tex] - 9 - |9 - 3 - 5 | \\ - 9 - |1| \\ - 9 - 1 \\ - 10[/tex]
Answer: The correct answer is: " - 10 ".
___________________
However, this answer, " -10 ", does not correspond to any of the answer choices given.
___________________
Step-by-step explanation:
Given: -9 −︱9 + (-3) + (-5)︱ ;
We are to simplify this expression by using the 'order of operations'—as follows:
__________________
BE MD AS ; or: PE MD AS
⇒ ⇒ ⇒ ⇒
__________________
which is a mnemonic device to remember the "order of operations":
Be Excused, My Dear Aunt Sally (Susan).
or: Please Excuse My Dear Aunt Sally (Susan).
Note: the "B" stands for "Brackets" ,
and the "P" stands for "Parentheses."
Note that "parentheses" can function as "brackets."
The "E" stands for "Exponents".
→ The "Brackets/Parentheses" —if they occur; take priority.
Then: MD for "Multiplication and Division" are the next priority;
⇒
________
→ and that neither takes priority over the other. Take note of the " ⇒ " symbol" below the "MD". This means that we perform "multiplication and division"—as they occur, from the far left of ["beginning of"] the expression to the end of the expression.
Then: We do the same with "Addition and Subtraction"—from the beginning to the end of the expression, in that order [that is, from "left to right"—as/if they occur]—hence the "⇒" notation.
_____________________
So again, our given expression is:
" -9 −︱9 + (-3) + (-5)︱ " ;
So; we have an "absolute value" (the positive integer of what is enclosed within the "vertical lines" that indicate "absolute value"—or, if the value of what is enclosed within the "vertical lines" is "0" [zero], then the absolute value would be "0" [zero]; since the absolute value of 0 is 0.
____________
So, let's start simplifying by using the 'order of operations.'
Do we have brackets or parentheses? No; except for the absolute value lines — which do take priority. The parentheses within those lines do not count for our purposes—but if they did, then we would use the order of operations within the "absolute value" bars!
So as a matter of 'semantics', we could say: 'Yes"; that the absolute value bars function as "brackets."
Do we have any "exponent(s)"? No.
Is there any multiplication/division? No.
Do we have any addition or subtraction? Yes; only one:
→ " - 9 −︱9 + (-3) + (-5)︱.
→ {not including the addition and subtraction within the absolute value bars.}.
____________
Let's start by simplifying the expression within the absolute value bars:
︱9 + (-3) + (-5)︱;
Note: The only operations are additional and subtraction; so we just calculate from left to right; as these operations occur:
" 9 + (-3) " = 9 − 3 " ; Note: Adding a "negative value" is the same as subtracting a "possible value" ;
to get: " 6 " ;
Then: the next step is:
" 6 + (-5) " = 6 − 5 " ; Note:
Adding a "negative value" is the same as subtracting a "positive value" ;
to get: " 1 ".
Now, the absolute of " 1" is " 1".
→ or; write as: ︱1︱= 1 .
Now, we can rewrite the entire expression:
" - 9 − 1 " ; to calculate and simplify:
to get: " - 10 " .
__________________
Hope this answer is correct and helpful!
__________________
However, this answer, "-10", does not correspond to any of the given answer choices.
__________________
Best wishes!
__________________
100 identical muffins have a total mass of 5802 g.
What is the mass of each muffin?
Give your answer in grams (g).
The mass (in grams of each muffin out of the 100 muffins is 5802 g
How to find the mass in grams, of each muffingiven data
number of identical muffins = 100
Total mass of muffins = 5802 g
Deductions from the question
The statement means that the masses of each muffin is added to 5802 g. since the muffins are identical they have same masslet each muffin have a mass of x such that
100 * x = 5820
100x = 5802
x = 5802 / 100
x = 58.02
Therefore the mass of each muffin is 58.02 g. and this results to mass of 100 muffins being 5802 g
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Simplify the expression. Write the answer in scientific notation.
(9x10-3) (4x10-3)
Simplification the expression in scientific notation 3.6 x 10^(-5)
What is Simplification ?
To implify is to make something simple. In mathematics, simply or simplification means reducing the expression/fraction/problem in a simpler version. Calculations and problem-solving techniques simplify the issue.
We have to multiply the expression
(9x10^-3) (4x10^-3)
We can rewrite this multiplication as
(9 x 4) x (10^-3 x 10^-3)
Now, use the exponent rule,
a^n x a^m = a^(n+m)
(9 x 4) x (10^(-3-3))
(9 x 4) x (10^(-6))
36 x 10^(-6)
Finally, write in scientific notation
3.6 x 10^(-5)
Hence, the scientific notation of the expression is 3.6 x 10^(-5)
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Y is inversely proportional to x when Y =16 x=3 when Y =12 x =
Answer:
y=84x
Step-by-step explanation:
a genetic experiment with peas resulted in one sample of offspring that consisted of green peas and yellow peas. a. construct a % confidence interval to estimate of the percentage of yellow peas. b. based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow? question content area bottom part 1 a. construct a % confidence interval. express the percentages in decimal form. enter your response herep enter your response here (round to three decimal places as needed.) part 2 b. based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow? yes, the confidence interval does not include 0.25, so the true percentage could not equal 25% no, the confidence interval includes 0.25, so the true percentage could easily equal 25%
Null hypothesis : [tex]H_{0} : p=0.25[/tex]
Alternative hypothesis : [tex]H_{a};p\neq 0.25[/tex]
Given : A genetic experiment with peas resulted in one sample of offspring that consisted of 429 green peas and 159 yellow peas.
i.e. p=159/429=0.3706
For 95% level of confidence interval , significance level :
Critical value of z =[tex]Z_{a/2}[/tex]=1.96
Confidence interval for population proportion :
p±[tex]Z_{a/2}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
=0.37±(1.96)[tex]\sqrt{0.37(1-0.37)/429[/tex]
=0.37±0.045687
=0.37±0.05
(0.32, 0.12)
Since 0.25 is not contained in the confidence interval , it means is not reasonable that the true proportion is 0.25 (25%).
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You are making a colorful cake for a birthday party and need to use 2 drops of food coloring for every 5 ounces of icing. How many drops of food coloring do you need if you are using 40 ounces of icing?
Answer: 16 drops
Step-by-step explanation: For every 2 drops is 5 ounces. We can set up an equation such as: 2/5*8/8=16/40. If you divide 40/5 you get 8, and now multiply by 2, you get 16.
The Distributive Property Use the Distributive Property to rewrite each expression without parenthesis
1. 9(3x + 2) 2. -3(7 + 3p) 3. (2y + 7) 6
The distributive property should be used to rewrite each expression without parenthesis as follows:
9(3x + 2) = 27x + 18-3(7 + 3p) = -21 - 21p(2y + 7)6 = 12y + 42What is the distribution property?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
In conclusion, the distributive property of multiplication can be used to evaluate and rewrite a mathematical expression as shown above.
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Josephine was building a community playground. The playground had to be fenced. The perimeter of the fence is 54 feet, and the width of the playground is 12 feet. Use the perimeter formula to find the length of his rectangular yard in inches: P = 2L + 2W. (1 foot = 12 inches)
The length of rectangular yard given its perimeter and width is 300 inches
What is the length?A rectangle is a 2-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals of equal length that bisect each other .
The perimeter of a rectangle is the distance round the rectangle. It is the sum of the length of the four sides of the rectangle.
Perimeter of a rectangle = 2 x (length + width)
54 = 2(l + 12)
54 / 2 = l + 12
27 = l + 12
l = 27 - 12
l = 25 feet
Now, convert feet to inches
25 x 12 = 300 inches
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Please help me please please pleaE
You manage a clothing store and budget $6000 to restock 200 shirts.
You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for $36 each. If you want to have twice as many rugby shirts as polo shirts, how many of each type of shirt should you buy?
A fter solving system of equations, we can conclude that, you should buy 60 Polo Shirts, 20 T- Shirts, 120 Rugby Shirts.
Let, x be the number of T-shirts, y be the number of polo shirts and z be the number of rugby shirts
A clothing store and budget $6000 to restock 200 shirts.
So, we get an equation,
x + y + z = 200 ...................(1)
If you want to have twice as many rugby shirts as polo shirts.
So, we get an equation,
z = 2y ......................(2)
You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for $36 each.
So, we get an equation,
12x + 24y + 36z = 6000
We rewrite above expression as,
x + 2y + 3z = 500 ..............(3)
Now we substitute z = 2y, into equations (1) and (3)
x + y + 2y = 200
x + 3y = 200 ..................(4)
and equation (3) becomes,
x + 2y + 3(2y) = 500
x + 8y = 500 ...............(5)
After solving equations (4) and (5) we get,
y = 60 and x = 20
Now substitute above value of y in equation z = 2y
z = 2(60)
z = 120
Therefore, after solving system of equations, we can conclude that, you should buy 60 Polo Shirts, 20 T- Shirts, 120 Rugby Shirts.
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use multiplication to show how how many twenty fourths equal 3/6
Using multiplication the number of twenty fourths that equal 3/6 is one tenths
How to find the number of twenty fourths that equal 3/6
let the number of twenty fourths in 3/6 be x
twenty fourths is written mathematically as 20/4
using multiplication the number of twenty fourths in 3/6 is written as
20/4 * x = 3/6
solving the equation gives
20x/4 = 3/6
multiplying both sides by 4 gives
20x = 3/6 * 4
20x = 12/6
20x = 2
dividing both sides by 20 gives
x = 2/20
x = 1/10
Therefore, we can say that the number of twenty fourths in 3/6 is 1/10 or one tenths.
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Ximena and some friends are going to the movies. At the theater, they sell a bag of popcorn for $5 and a drink for $5.75. How much would it cost if they bought 8 bags of popcorn and 6 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks?
Answer: 74.5
6 drinks would cost 34.5 dollars
5.75 x 6 = 34.5
8 bags of popcorn would cost 40 dollars
5 x 8 = 40
Now add both numbers
40 + 34.5 = 74.5
74.5 is our answer
hope this helps :)
Answer:
Popcorn:40 Drinks:34.5
Step-by-step explanation:
All you gotta do is 5 times 8 for the popcorn and that would equal 40. For the drinks 5.75 times 6 abd you'll get 34.5 Sorry if I'm wrong
How do I solve this by factoring
Antidisestablishmentarianism
4-2(3-7)+16 divided 4
PLEASE HELPP
Answer:
7
Step-by-step explanation:
3-7=(-4), -2*(-4)=8, 4+8+16=28, 28/4=7
An accountant receives a yearly salary of $72,000. Find his monthly salary.
Answer:
6000
Step-by-step explanation:
6000
divide by 12
72000 ÷ 12 = 6000
part 2
often to get the yearly salary if you have an hour salary
quickest math to get that is to multiply by 20
so if someone makes 20 an hour its probably
40000 per year
Answer:
$6,000
Step-by-step explanation:
Because his yearly salary is $72,000 (72k).
You need to divide $72,000 by 12, because there is 12 months in a year.
Hope this helps! If you need further explanation, I’ll be happy to help!
<3
please help! math question for college algebra mth 107!
Answer:
Local Minimum: (-2.5, -2), (0, -2)
Local Maximum: (1, 2)
16 There are some children in a classroom.
The ratio of boys to girls is 3:1
(a) Work out the fraction of the children that are boys.
Ratio of number of boys to total number of children is 3:4 and number of girls is 8
What is ratio?The comparison of two values using the same unit is called a ratio. Divide the first amount by the second to get it. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0.
Let the number of boys be 3x and girls be x.(As they are in ratio of 3:1)
a) Total number of children = 3x + x = 4x
Ratio of number of boys to total number of children = [tex]\frac{3x}{4x}[/tex]
= 3:4
b) As, number of boys are 24
3x = 24
x = 8
, number of girls = x = 8
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evaluate this expression
5 - | c+ 1 |
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:4\pm c [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given expression is :
[tex]\qquad \tt \rightarrow \: 5 - |c + 1|[/tex]
[tex]\qquad \tt \rightarrow \: 5 - 1 - |c|[/tex]
[ as 1 is a positive number, it can come out of modulus function as it is ]
[tex]\qquad \tt \rightarrow \:4- |c| [/tex]
Now, there are two cases possible.
Case 1 :
[tex]\qquad \tt \rightarrow \: 4- c[/tex]
[ if c is a positive number, it will come out of modulus as it is ]
Case 2 :
[tex]\qquad \tt \rightarrow \: 4 - (-c)[/tex]
[tex]\qquad \tt \rightarrow \: 4 + c[/tex]
[ if b is a negative number, it will come out of modulus with a negative sign, to make the overall term out of modulus positive ]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The perimeter of a rectangle can be written as P = 2(L+W). If the length of a rectangle is 4, find the width in terms of P. Show the work that leads to your answer.
Answer:
P = 2(4+w)
P = 8+2w
P-8 = 2w
[tex] \frac{p - 8}{2w} = \frac{2w}{2} [/tex]
[tex] \frac{p - 8}{2} = w [/tex]
Find an equation for the line below
y=−0.2x+2.2 is the equation of line from the given graph .
How to find the equation of line ?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, you must first determine the slope and y-intercept. The slope is the ratio of the change in y to the change in x.
Calculation(-4 , 3 ) and ( 6 ,1 )
these are two points we will use to find the equation of the line
Slope is -0.2
Intercept is 2.2
y=−0.2x+2.2 is the equation of line
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I don't understand this question
can u please help!
i will give u 11 points <3
Answer:
year 7 have 135 students
year 9 have 45 students
Step-by-step explanation:
200=total students
360=value of the whole chart
1/2×360
=180
year 8 have 180students
360-180=180
the students remain are 180
1/4×180
=45
year 9 have 45 students
180-45
=135
year7 have 135 students
For the graph of a function f(x, y) with coordinates (7,-4), (3, 5), and (-6, -2), what are the new coordinates given the
function translation f(x, y)-(-x, -y).
1 (-7,4), (3,-5), (6,2)
2 (7,4), (-3,-5), (6,2)
3 (7,-4), (-3,-5), (-6,-2)
4 (-7,4), (-3,-5), (6,2)
For the graph of the function, the new coordinates after the function translation is (D) (-7,4), (-3,-5), and (6,2).
What is a graph of a function?To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location. The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f(x).So, given function is f(x, y) with coordinates: (7,-4), (3, 5), and (-6, -2)
After function translation: f(x, y)-(-x, -y)f(x, y) ⇒ (-7,4), (-3,-5), (6,2)Therefore, for the graph of the function, the new coordinates after the function translation are (D) (-7,4), (-3,-5), and (6,2).
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