The distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).
How is the sample explained?Calculating the sample mean is as simple as adding up the number of items in a sample set and then dividing that sum by the number of items in the sample set.
Here, the distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).
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There are 9.5 ounces of juice in a container. An additional 1.75 ounces of juice are poured into the container each second. How many ounces of juice are in the container after 6 seconds? Enter your answer in the box
By concept of capacity and the assumption of constant flow rate, the amount of ounces of juice in the container after 6 seconds is 20 ounces.
How to determine the final capacity of a container
Given that the additional juice is added to the container at constant rate. Hence, the final capacity (C'), in ounces is equal to the sum of the initial capacity (C), in ounces, and the product of the flow rate (q), in ounces per second, and time (t), in seconds.
C' = C + q · t (1)
If we know that C = 9.5 oz, q = 1.75 oz/s and t = 6 s, then the final capacity of the container is:
C' = 9.5 oz + (1.75 oz/s) · (6 s)
C' = 20 oz
By concept of capacity and the assumption of constant flow rate, the amount of ounces of juice in the container after 6 seconds is 20 ounces.
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If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?
A. Triangle ABC is scalene because all side lengths of the triangle are different.
B. Triangle ABC is isosceles because two sides of the triangle are equal in length.
C. Triangle ABC is equilateral because all sides of the triangle are equal in length.
D. Triangle ABC is acute because all angles of the triangle are acute angles.
Answer: A
Step-by-step explanation:
Using the distance formula,
[tex]AB=\sqrt{(5-1)^{2}+(-4-2)^{2}}=\sqrt{16+36}=2\sqrt{13}\\BC=\sqrt{(-3-5)^{2}+(-4-2)^{2}}=\sqrt{64+36}=10\\AC=\sqrt{(-3-1)^{2}+(2-2)^{2}}=4[/tex]
From this, we can conclude that ABC is scalene.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The length of different sides are:
[tex]AB = \sqrt{(5-1)^2+(-4-2)^2} = \sqrt{16+36} = \sqrt{52}\rm\ units[/tex]
[tex]BC = \sqrt{(-3-5)^2+(2+4)^2} = \sqrt{64+36} = 10\rm\ units[/tex]
[tex]AC = \sqrt{(2-2)^2+(-3-1)^2} = \sqrt{16} = 4\rm\ units[/tex]
Since the length of all the sides of the triangle is not equal it is a scalene triangle.
Hence, the correct option is A.
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Which step is the same when constructing an inscribed square and an inscribed regular hexagon?
O Construct a circle first
O Construct a line first
O Set the compass to the radus
Set the compass to greater than half the diameter
Question 4 Multiple Choice Worth 1 points)
(01.03 MC)
After the construction of a circle, we have to "Set the compass to the radius of the circle" so, option C is correct.
What is a regular hexagon?A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles. The sum of the measure of angles of a regular hexagon is 120 degrees.
Steps to create an inscribed hexagon:
1: The structure needs to adjust the box thickness towards that radius.
2: Afterward moves around the outside of the circular path to just produce the 6 vertices of that similar hexagon.
"Set the compass to the radius of the circle" so, option C is correct.
Thus the above answer is correct.
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Answer:
Construct a circle first
Step-by-step explanation:
If you're going to inscribe any figure in a circle, the first construction you need to do is construct the circle.
__
Additional comment
The attached shows our construction of an inscribed square and an inscribed regular hexagon. Here are the steps we used. You will notice the first step is construct a circle. (It could be, construct line AB, then construct circle A with radius AB.)
We have used line AB in the construction of the hexagon, but the hexagon could have been constructed without it. That is why "construct a circle first" is likely a better choice for a common first step.
square
construct circle A and locate a point B on itconstruct line AB, and locate point C at the other intersection of AB and circle Aset the compass to greater than half the diameterusing B as a center, draw arc RSusing C as a center, draw arc RS using the same compass setting. Label the intersection points R and S.draw line RS. Label the points of intersection with the circle as T and U.draw inscribed square CTBUregular hexagon
construct circle A and locate a point B on itconstruct line AB, and locate point C at the other intersection of AB and circle Awithout changing the compass, using B as a center, draw arc KL. Label intersection points K and L.using C as a center, draw arc JM. Label intersection points J and M.draw inscribed hexagon CJKBLM__
Arguably, the first step to constructing a circle is set the compass to the radius. We chose to ignore this because one of the ways to construct an inscribed hexagon is to mark off successive arcs around a circle that have a radius equal to the radius of the circle. We did not use that method. (The use of diameter BC made drawing 5 arcs around the circle unnecessary. We drew 2 instead.)
Or, you could argue that construct a line first is needed before you set the compass to the radius. If this is the first step, then the next steps would be to mark the center of the circle on the line, and mark another point at a distance of the radius from that center point.
What you consider to be the first step depends on the level of detail you want to attend to.
Simplify 5 + 20 - 4².
O 21
09
O 17
O 441
Answer:9
Step-by-step explanation:addition and subtraction done in order of appearance. 5+20-16
5 + 20 - 4²
Add 5 and 20 to get 25.
25 - 4²
Calculate 4 to the power of 2.
To calculate a power, multiply the base as indicated by its exponent.
4 is the basis2 is the exponentSo 4 is multiplied 2 times, so
4 x 4 = 1625 - 16
Subtract 16 from 25 to get 9.
9 ===> Answer[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
²-6x +10 is to be written in the form (x-p)² +g. Find the values of p and q.
Answer:
[tex]p = 3\\\\q= 1[/tex]
Step-by-step explanation:
[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]
Which best explains how to graph this location on the coordinate plane ? -
Write an explicit formula that represents the sequence defined by the following recursive formula
which fraction would you find marked on a ruler?
1/8 inch
1/5 inch
1/10 inch
1/9 inch
Answer:
1/8 is marked on a ruler
Step-by-step explanation:
4(x-5)-(6x + 1)= 2x -19
Answer:
Step-by-step explanation:
Comment
I take it you want the value for x.
Solution
4(x-5)-(6x + 1)= 2x -19 Remove the Brackets.
4x - 20 - 6x - 1 = 2x - 19 Combine like terms
-2x - 21 = 2x - 19 Add 2x to both sides
-2x-21+2x = 2x + 2x - 19 Combine
-21 = 4x - 19 Add 19 to both sides
-21+19 = 4x -19 + 19 Combine like terms
-2 = 4x Divide by 4
-2/4 = x
x = - 1/2
Answer: x = - 1/2
or x = -0.5
What happens when the function f(x)=cos(x) is transformed by the rule g(x)=f(1/2x)?
A: f(x) is stretched away from the y-axis by a factor of 2.
B: f(x) is compressed toward the y-axis by a factor of 1/2.
C: f(x) is compressed toward the x-axis by a factor of 1/2.
Answer:
A: f(x) is stretched away from the y-axis by a factor of 2
Step-by-step explanation:
Parent function:
[tex]f(x)=\cos(x)[/tex]
Given transformation:
[tex]g(x)=f\left(\dfrac{1}{2}x\right)=\cos \left(\dfrac{1}{2}x\right)[/tex]
Translation:
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis by a factor of} \: \dfrac{1}{a}[/tex]
Therefore, f(x) is stretched parallel to the x-axis (horizontally) by a factor of 2:
[tex]a=\dfrac{1}{2} \implies \dfrac{1}{a}=\dfrac{1}{\frac{1}{2}}=2[/tex]
graph the function y=[x-3] on the set of axis below
Answer:
Step-by-step explanation:
To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point.
The array shown has two numbers filled in: 2 and 7. What does the 2 mean in the
array? What does the 7 mean in the array?
An array data structure is a data structure that consists of a collection of items. In the array, 7 means that the sum of the number cube 1 and number cube 2 is equal to 7(3+4).
What is an array?An array data structure, often known as a simple array, is a data structure that consists of a collection of items, each of which is identifiable by at least one array index or key. A mathematical method is used to determine the location of each element from its index tuple in an array.
In the array, 2 means that the sum of the number cube 1 and number cube 2 is equal to 2(1+1).In the array, 7 means that the sum of the number cube 1 and number cube 2 is equal to 7(3+4).Hence, In the array, 7 means that the sum of the number cube 1 and number cube 2 is equal to 7(3+4).
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23.4571 to the nearest 10
23.4571 to the nearest 10
asnwer: 23.5
Can someone help me with this pls.
Answer:
a. 1/20, 1 out of twenty, or 5%
b. three out of ten, 3/10, 30%
c. 3/20 = 3/20 yes.
Step-by-step explanation:
a. It is a fraction. out of the 20 divisions there is only one 20. so there is 1 out of twenty which as a fraction is 1/20. this is equal to 1 divided by 20 wich eqauls 0.05. You move the decimal to the right twice to get 5%.
b. 6 out of twenty, 6/20. They are both even so it can be simplified.
6 ÷ 2 = 3
20 ÷ 2 = 10
It becomes 3/10, 0.3 or 30%
c. I decided that 3, 17, 2, 15, 10, and 9 are the lower right region.
the odds are 6/20 wich we know is 3/10
I only see 20 hits, but out of the 20, 6 are in the lower right region.
the odds from this is 6/20 which we know is 3/10.
We can see that the odds are equal.
HELP ILL GIVE BRAINLIEST!
Solve 2u² = 90, where u is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
u=
Answer:
I think maybe u=6.71 but I'm not sure. wait for another answer
The enrollment at a local university increased from 14,000 students to 20,000 students over a six-year period. What was the approximate average percent increase per year in student enrollment at the university?
A. 5%
B. 30%
C. 7%
D. 43%
The approximate average percent increase per year in student enrollment at the university is = 5%. That is option A.
Calculation of average percent increaseInitial number of student = 14,000 students
Total number of students over 6 years = 20,000 students
The total additional students for 6 years,
= 20,000- 14,000
= 6,000 students.
Therefore every year additional 1000 students where admitted into the local university.
The average percent increase per year in student enrollment at the university,
= 1000/20000 × 100
= 100000/20000
=5%
Therefore, the approximate average percent increase per year in student enrollment at the university is = 5%.
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A farmer has 13 cows.a bolt of lightening kill all but 5 of them.how many cows survived?
Answer:
8 cows survived
Step-by-step explanation:
13-x=5
-x=5-13
-x=-8
x=8
give brainliest please!
hope this helps :)
Answer:
all of them
Step-by-step explanation:
a litghing bolt isnt strong inof to kill a cow
find the equation of the function that is graphed.
The equivalent equation of the function that is graphed is g(x) = (x-1)² + 1
Graph of a quadratic functionThe quadratic function is a function that has a leading degree of 2. The parent graph of the given function is f(x) = x²
The vertex of the parabola of the parent function is at the origin. The given curve shows a translation of the function by 1 unit to the right and 1 unit up to have the function g(x) = (x-1)² + 1
Therefore the equivalent equation of the function that is graphed is g(x) = (x-1)² + 1
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Based on the measures
provided in the diagram,
determine the measure of
the angle 0
(You may assume that point A is the
center of the circle and that DC is a
diameter.)
O 40°
O 50⁰
O 45⁰
1000
A circle is a curve sketched out by a point moving in a plane. The measure of the ∠ACB or θ is 50°.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In order to solve the problem, we need to draw a line segment AB. Since A is the center of the circle AC and AC both will be the radius of the triangle ΔABC. Since two sides of the triangle are equal, the measure of ∠ABC and ∠ACB will be equal therefore, we can write,
∠ACB + ∠ABC + ∠BAC = 180°
2∠ACB + 80° = 180°
∠ACB = 50°
Hence, the measure of the ∠ACB or θ is 50°.
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Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.
Answer: AAS
Step-by-step explanation:
We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.
What is the slope of a line perpendicular to the line whose equation is 2x+3y=21. Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
therefore then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
Answer:
2x+3y=21.
the answer is [tex]\frac{3}{2}[/tex]
simplify the answer I think. x = 2 + y = 3 = 21
x = 2
x + 1 = 3
y = 3
y - 1
2 + 1 = 3
3 - 1 = 2
The answer will only be [tex]\frac{3}{2}[/tex] no y = [tex]\frac{3}{2}[/tex] just [tex]\frac{3}{2}[/tex]
Don't forget to look at the picture
0.00002165 in scientific notation.
Answer:
2.165 × 10⁻⁵
Step-by-step explanation:
Move the decimal -5 places to the right. For every scientific notation, 10 is the default number you are multiplying the decimal by. The exponent is the number of places you moved the decimal point. The exponent is positive when moving left, negative when moving right.
Hope it helps!
Which polynomial is prime?
x2 + 7
x2 – 25
3x2 – 27
2x2 – 8
x² + 7 can not be factorized with rational numbers.
What is prime polynomial?A prime polynomial defined as a polynomial has only two factors 1 and itself. It is a polynomial with integer coefficients that cannot be factored into polynomials of lower degrees.
x² + 7 can not be factorized with rational numbers.
Therefore, it is a prime polynomial.
x² - 25 can be factored into (x+5)(x-5).
Therefore, it is not a prime polynomial.
3x² – 27 can be factored into 3(x+3)(x-3).
Therefore, it is not a prime polynomial.
2x² – 8 can be factored into 2(x+2)(x-2).
Therefore, it is not a prime polynomial.
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exponential decay functions
Exponential decay function is a form of an exponential function
What are exponential decay function?These are exponential functions that reduce in value as the input value increases.
This in other words, means that the rate of an exponential decay function is less than 1.
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where b is the rate.
When b < 1, the function is an exponential decay function
For instance:
[tex]y = 3(0.9)^x[/tex] is an exponential decay function
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Solve: −8(−3m−5)+2=5(−m−3)−1.
Compare 3.5 • 10^4 to standard form
Answer:
35,000
Step-by-step explanation:
^4 means 4 zeros
10^4 = 10,000
3.5 times 10,000 =
35,000
The line plot shows the number of letters in the last name of 12 children.
Answer:
The mode is 9 letters: True
The median is 7.5 letters: True
The mean is 7 letters: False
The graph is skewed right with an outlier of 2: False
Step-by-step explanation:
1) The mode is 9 letters. (True)
The mode is the value that shows up the most. 9 letters shows up the most as the length of a child's last name.
2) The median is 7.5 letters. (True)
The median is one of the middle points of a data set. This can be found by writing out all of the results from least to greatest, and crossing out each number starting from the ends.
2, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9
Once you meet in the middle, you should be left with 7 and 8. In this case, we find the mean of the two numbers, which is 7.5. (In cases where the data set has an odd amount - if there were 13 children instead of 12), you'd just use the middle piece of data.
3) The mean is 7 letters. (False)
The mean is also a middle point of a data set. However, this one is different. The mean can be found by adding up all of the numbers in the data set ([tex]2+6+6+7+7+7+8+8+9+9+9+9[/tex]) and then dividing that number by the amount of numbers are in the data set. Setting this up as an expression would look like: [tex]\frac{2+6+6+7+7+7+8+8+9+9+9+9}{12}[/tex]. By plugging this into a calculator you'd get 7.25 instead of just 7.
4) The graph is skewed right with an outlier of 2.
Although the outlier of 2 part of the statement is correct, the graph is not skewed right; it is skewed left.
Deb started doing yard work at 9:52 A.M. After working for 1 hour and 48 minutes, she stopped to have lunch. It took her 36 minutes to eat lunch.
The time Deb finished eating lunch is 12:16 P.M. The correct option is the first option 12:16 P.M.
Calculating timeFrom the question, we are to determine when Deb finished eating lunch
From the given information,
Deb started doing yard work at 9:52 A.M and she stopped to have lunch after working for 1 hour and 48 minutes.
After working for 1 hour and 48 minutes, the time will be
9:52 A.M + 1 hour 48 minutes = 11:40 A.M
This means she stopped to have lunch at 11:40 A.M.
Then,
It took her 36 minutes to eat lunch
The time Deb finished eating lunch will be
11:40 A.M + 36 minutes = 12:16 P.M.
Hence, the time Deb finished eating lunch is 12:16 P.M. The correct option is the first option 12:16 P.M.
Here is the complete question:
Deb started doing yard work at 9:52 A.M. After working for 1 hour and 48 minutes, she stopped to have lunch. It took her 36 minutes to eat lunch.
When did Deb finish eating lunch?
12:16 P.M.
12:32 P.M.
1:16 P.M.
1:32 P.M.
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Pretest: Unit 2
Question 34 of 45
If WXWZ, which of the following statements CANNOT be true?
Answer:
B.
Step-by-step explanation:
The statement that cannot be true is "length RW is a mid segment of the triangle". option D.
What is mid segment of a triangle?The mid segment of a triangle is a line segment that connects the midpoints of two sides of a triangle. More specifically, if a triangle has sides of lengths a, b, and c, then the mid segment connects the midpoints of the two sides of length a and is parallel to the side of length c. The length of the mid segment is half the length of the third side (c/2).
here, we have,
In other words, if a triangle has sides AB, BC, and AC, then the mid segment connects the midpoint of AB (denoted as M) to the midpoint of BC (denoted as N) and is parallel to AC.
The length of the mid segment MN is equal to half the length of AC
(MN = 1/2 * AC).
we have,
For the given diagram, the midpoint is S, so the length RW cannot be the length of the mid segment.
Hence, The statement that cannot be true is "length RW is a mid segment of the triangle". option D.
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8. Jia's Fashions recently paid a $2 annual dividend. The company is projecting that its dividends will grow by 20 percent next year, 12 percent annually for the two years after that, and then at 6 percent annually thereafter. Based on this information, how much should Jia's Fashions common stock sell for today if her required return is 10.5%?
Answer:
the stock will sell for $59.16
Step-by-step explanation:
P0 = 2 * (1+0.2) / (1+0.105) + 2 * (1+0.2) * (1+0.12) / (1+0.105)^2 +
2*(1+0.2)*(1+0.12)^2 / (1+0.105)^3 +
[(2 * (1+0.2) * (1+0.12)^2 * (1+0.06) / (0.105-0.06)) / (1+0.105)^3 ]
P0 = $59.16