The probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
What is probability ?
Probability is a metric used to determine how likely an event or result is to occur. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.
A group of potential possibilities is referred to as an event in probability theory. By dividing the number of positive possibilities by the total number of possible outcomes, the probability of an event happening is determined.
The fish in the hatchery tank are distributed in length according to a normal distribution, with a mean length of 9.7 inches and a standard deviation of 1.2 inches.
With a mean that is equal to the population mean and a standard deviation that is equal to the population standard deviation divided by the square root of the sample size, the distribution of the sample means will also follow a normal distribution.
The formula to calculate the z-score for the sample mean is:
z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] )
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we want to find the probability that the sample mean is less than 10 inches. So we need to calculate the z-score for a sample mean of 10 inches:
z = (10 - 9.7) / (1.2 /[tex]\sqrt{40}[/tex]) = 1.21
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.21 is approximately 0.8869. This means that there is an 88.69% chance of getting a sample mean less than 10 inches.
Therefore, the probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
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(1,-3),(4,-5),(2,2),(1,9) function or not function
Answer: Function
Step-by-step explanation:
Give the domain of
s(x)=6/25-x^2
Answer: The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).
In this case, the function s(x) = 6/25 - x^2 has no restrictions on the input values for x, so the domain of the function is all real numbers.
Therefore, the domain of the function s(x) = 6/25 - x^2 is:
(-∞, ∞)
This means that the function can be evaluated for any real value of x.
Step-by-step explanation:
-2√x+5 +1
End behavior
Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.
For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:
lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞
As x approaches negative infinity, the square root of x approaches 0, so the function approaches:
lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7
Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.
Step-by-step explanation:
With a combined volume of a 4-foot cube and a 6-foot cube equal to the volume of a 10-foot cube? Use a diagram to justify your answer.
The combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.
What is the volume of the cube?The volume of a cube is calculated by cubing the length of its side.
here,
Let's denote the length of the sides of the 4-foot and 6-foot cubes as "a" and "b", respectively. Then the length of the side of the 10-foot cube is "c", and we know that:
a³ + b³ = c³
We want to confirm if the combined volume of a 4-foot cube and a 6-foot cube is equal to the volume of a 10-foot cube. We can calculate the volumes of the cubes as follows:
Volume of 4-foot cube: a³ = 4³ = 64 cubic feet
Volume of 6-foot cube: b³ = 6³ = 216 cubic feet
Volume of 10-foot cube: c³ = 10³ = 1000 cubic feet
The sum of the volumes of the 4-foot and 6-foot cubes is:
64 + 216 = 280
Therefore, the combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.
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Every month, the bakery orders blueberries to use in their blueberry muffins. They had a stock of 1.38 kilograms of blueberries. Last month, they used 1.12 kilograms. This month, they need a total of 1.26 kilograms of blueberries.
How many kilograms of blueberries do they need to order?
0.12
0.26
1
1.26
Drag numbers to write an inequality to represent the following: 2.45 less than a number x is greater than or equal to 4.6.
A graph of the solution to this inequality 2.45 < x ≥ 4.6 is shown in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would translate the word problem into an algebraic equation as follows;
2.45 < x ≥ 4.6
By splitting, we have the following compound inequality:
x > 2.45
x ≥ 4.6
In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the graph contains a dashed line because of the greater than (>) symbol.
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Ionosphere (Aurora)
Mesosphere
90 km
Stratosphere
18 km
Troposphere
50 km
Earth
Ozone
Layer
Tropopause
TASK 1
How much more of the atmosphere is nitrogen than all other
gases combined? Explain how to find the answer.
TASK 2
in the Tronosphere was separated out from
Answer: TASK 1: The answer to how much more of the atmosphere is nitrogen than all other gases combined can be found by measuring the atmospheric composition. Nitrogen makes up the largest fraction of the Earth's atmosphere, at around 78%. Oxygen makes up around 21%, while all other gases make up the remaining 1%. So, nitrogen makes up around 77% more of the atmosphere than all other gases combined.
TASK 2: I'm sorry, but there seems to be a typo in your prompt. Can you please clarify what you meant by "in the Tronosphere was separated out from"?
Step-by-step explanation:
2. 34 is 34% of what number?
What is the value of 6[4-94]?
O -36
O-33
O-32
O-30
Answer:
-30
Step-by-step explanation:
Name two pairs of suplimentary angles. need ASAP PLSS IM BEGGING
angle BCE and angle CEF
b
angle BFE and ang BCE
c
angle CBF and angle CEF
d
angle CBF and angle BFE
In the given figure angle CBF and angle CEF are supplementary angles. So Option C is correct.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Given that,
A figure which contains one trapezium BCEF
And in this portion angle CBF and angle BCE are opposite angles
and opposite angles are supplementary angles,
Hence, the pairs of angles are ∠CBF & ∠CEF
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If f(x) = x sinx/1+cos x find f'(π/2).
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
f'(π/2) = π/2 + 1.Kindly refer the attachment.Step-by-step explanation:
Hope it helps you~Students are reading a book that has 280 pages. Nora already read 30% of the book. She is choosing between two options to finish reading the book.
Option 1: read 25% of the remaining pages each night
Option 2: read 28 pages each night
Which option should Nora use to finish the book in the least amount of time?
Explain your reasoning.
Answer:
Step-by-step explanation:
To determine which option is faster, we need to determine the total number of nights required for each option.
First, let's find the number of pages Nora still needs to read by subtracting the number of pages she's already read from the total number of pages: 280 pages * 30% = 84 pages
So, Nora still needs to read 280 pages - 84 pages = 196 pages.
For Option 1, Nora would read 25% of the remaining pages each night, so the number of pages she reads each night would be: 196 pages * 25% = 49 pages
The total number of nights required would be 196 pages / 49 pages/night = 4 nights.
For Option 2, Nora would read 28 pages each night, so the total number of nights required would be 196 pages / 28 pages/night = 7 nights.
Since 4 nights is less than 7 nights, Nora should choose Option 1 to finish reading the book in the least amount of time.
Find the slope of the line on the graph. Reduce all fractional answers to lowest terms.
-4
-1
-2
The slope of the line on the graph will be a negative one. Then the correct option is A.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,
m = (- 2 - 2) / (2 + 2)
m = - 4 / 4
m = - 1
The slope of the line on the graph will be a negative one. Then the correct option is A.
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The complete question is attached below.
Find the common ratio of the geometric sequence
-8,40,-200...
Answer:
Multiplied by -5
Step-by-step explanation:
-8 X -5 = 40
40 X -5 = -200
I can’t figure out this other one, can I get some help?
place g(x) as the value x, into p(x)
to gain p(g(x)) = (1 / SqrRt(x) )² - 4
simplify = ( 1 / x ) - 4
find domain
x =/= 0 (undefined) & (1/4)
just need a answers thank u mwa
Answer:
The answer is 112ft
Step-by-step explanation:
32+16+8+8+16+8+8+16 = 112ft
Answer:
112ft
Step-by-step explanation:
The length of the little rectangle jutting out is the only unmarked length, so once we find that we can just add up all the sides to find the perimeter.
We see the overall length of the shape is 24ft and the length of the top of the shape, minus the unmarked length, is 16ft. This means the unmarked length is 24ft-16ft=8ft
Now add up each side to get to the perimeter:
32ft + 16ft + 16ft + 8ft +8ft +8ft +8ft +16ft = 112ft
The base of a triangle is 2inches more than 2 times the height. If the area of the triangle is 12 square inches, find the base and height.
Answer:
Base: 8. Height: 3.
Step-by-step explanation:
Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.
select the equivalent expression.
Answer:
Step-by-step explanation: Option A is correct.
4. The first term in the sequence is 5 and the fifth term is 17. What is the common difference?
(1) 2.4
(2) 12
(3) 3
(4) 4
Answer:
(3) 3
Step-by-step explanation:
Arithmetic Sequence:An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.
So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.
An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)
So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]
Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]
25. KAYAKING It takes 3 hours to paddle a kayak
12 miles downstream and 4 hours for the
return trip upstream. Find the rate of the
kayak in still water.
Let k = the rate of the kayak in still water and
c = the rate of the current. (Lesson 6-4)
R t d rt=d
Upstream. k+c 3 12 3(k + c) = 12
Downstream k-c 4 12 4(k - c) = 12
Answer:
Step-by-step explanation:
For part a:
Mean: Use the AVERAGE function to find the mean of the "Number" column.
Median: Use the MEDIAN function to find the median of the "Number" column.
Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.
Maximum: Use the MAX function to find the maximum value in the "Number" column.
Minimum: Use the MIN function to find the minimum value in the "Number" column.
For part b:
Mean: Use the AVERAGE function to find the mean of the "Percent" column.
Median: Use the MEDIAN function to find the median of the "Percent" column.
Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.
Maximum: Use the MAX function to find the maximum value in the "Percent" column.
Minimum: Use the MIN function to find the minimum value in the "Percent" column.
For part c:
The statistics on children whose parents do not have secure employment provide important insights into the state of the economy. In this case, the mean and median of the number of children in each state seem to be around 450,000. The mode cannot be determined since there are no repeated values in the "Number" column. The maximum number of children is 678,000 in Ohio, while the minimum number is 141,000 in Iowa.
Comparing the states, Indiana has a slightly higher mean and median percent of children whose parents do not have secure employment at 27%, compared to the other surrounding states which range from 20% to 31%. However, there is no clear state with the best or worst data as the range of the percent values is not too wide.
In terms of comparison, the number of children may provide a more comprehensive understanding of the extent of the problem, as it gives a clearer picture of the actual number of children affected. However, the percentage provides a more relative comparison between the states, allowing for easier comparison and a clearer understanding of the proportion of children affected in each state.
(b) At the beginning of the term, Caroline bought p notebooks and Bert bought 5 notebooks less than Caroline. During the term, Caroline gave 2 of her notebooks to her sister. Caroline then had twice as many notebooks as Bert. By writing a suitable equation, calculate the number of notebooks Caroline now has.
The number of Caroline's textbook is 8
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
Represent the Notebook bought by Bert as q
q = p-5
p-2= 2q
p = 2q +2
substitute 2q +2
q = 2q+2-5
2q-q = 3
q = 3
substitute 3 for q
3 = p-5
p = 5+3
p= 8
Therefore Caroline's number of notebook is 8
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Solve for x using the quadratic formula:
1.2x2-x-1=0
2. x2 - 10x - 11 - 0
Determine the discriminant and explain what the result means
3. 4x2 - 5x + 10 = 0
4. x2 + 18x +81 = 0
5. 4x2 - 4x - 24 = 0
The solutions of the quadratic equation are;
1) x = 1 or -1/2
2) x = 11 or -1
What is the quadratic formula?We know that the quadratic formula is one of the ways that we can use to solve for the variables that we have in a quadratic equation. We can be able to obtain x by using the formula;
x = -b ±√b^2 - 4ac/2a
To use the discriminant;
√b^2 - 4ac
√(-5)^2 - (4 * 4 * 10)
√-135
The roots are imaginary
√18^2 - 4(1 * 81)
= 0
The roots are equal
√(-4)^2 - (4 * 4 * -24)
=20
The equation roots are real and different
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HELP! I need help on this one
Answer:B costs less than A
Step-by-step explanation:
i am not quite sure but i think,
A)8----2,89
1------x
x=0.38
B)12----4,19
1---------y
y=0.35
How many quarts are in8.25 gallons?
Answer:
8.25 gallan=33 quart
Step-by-step explanation:
Please help!!!!! Due tomorrow need to understand how to properly do this question :(
Answer:
f(x)=3x^2+2
Step-by-step explanation:
use pm
What is the value of r^2 for the following data yo three decimal places ?
The correlation coefficient of the data-set in this problem is given as follows:
C. r² = 0.931.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The points from the table in this problem are given as follows:
(3,2), (4,4), (5,5), (7,6), (10,20).
Inserting these points into a calculator, the correlation coefficient is obtained as follows:
r² = 0.931.
Meaning that the correct option is given by option C.
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How to find the vertex of the function y = 2x^2 + 4
The vertex of the given function is (0,4)
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
identify the coefficients a and b of the quadratic function
y =ax² +bx+c-------(1)
a=2, b=0
x-coordinate of the vertex is x= -b/2a = -(0)/(2(2)) = 0
Substitute x=0 into given equation to get y-coordinate of the vertex
y= 2(0)² + 4 = 0+4 = 4
Vertex= (x,y) = (0,4)
The vertex of the given function is (0,4)
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In-State tuition at UNCW is currently
$6,691. NC is raising tuition 1% each year for the next 4 years. What will be the new tuition 4 years from now?
The new tuition 4 years from now is $6962.68.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$6691, rate of interest=1% and time period=4 years.
Now, A=6691(1+1/100)⁴
=6691(1+0.01)⁴
=6691(1.01)⁴
= 6691×1.04060401
= $6962.68
Therefore, the new tuition 4 years from now is $6962.68.
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What is r in the following equation? 5(-4) - r +1 = -37 PLEASE HELPP ILL GIVE EXTRA CREDIT
Answer:
Step-by-step explanation:
5 times -4 is -20, so the equation becomes -20 - r + 1 = -37
-20 plus 1 equals -19, so the equation is now -19 - r = -37
Then you add 19 to both sides to isolate r
-r = -18
To get a positive r, divide or multiply both sides by -1, and you get r = 18
[tex]5(-4)-r+1=-37[/tex]
Simplify:
[tex]-20-r+1=-37[/tex]
Combine Like Terms:
[tex](-r)+(-20+1)=-37[/tex]
[tex]-r-19=-37[/tex]
Add 19 to both sides:
[tex]-r-19+19=-37+19[/tex]
[tex]-r=-18[/tex]
Divide both sides by -1:(To remove the negative from the variable r)
[tex]\dfrac{-r}{-1}=\dfrac{-18}{-1}[/tex]
[tex]\boxed{r=18}[/tex]
Carl deposits a check for $34.50 in his checking account and then writes a check for $82.89 what is the change in carls account balance?
Answer:
-$48.39
Step-by-step explanation:
