The total number of marbles are 30.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, to start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
Here, m/3 =10
m=30
Therefore, the total number of marbles are 30.
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A newspaper article headline reads "One in Five Believe the Path to Riches is the Lottery". A survey was done to test the claim that 20% of adult Americans believe that the lottery is the path to riches. The hypothesis test of H0: p=.2 versus Ha: p>.2 resulted in 0.79 for a right-tailed test. Calculate the p-value and write the correct conclusion in context.
The p-value for right tailed test based on the information will be 0.2147.
What is the p-value?The p-value, under the assumption that the null hypothesis is true, is the likelihood of obtaining results from a statistical hypothesis test that are at least as extreme as the observed results. The p-value provides the smallest level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by stronger evidence when the p-value is lower.
In this case, the survey was done to test the claim that 20% of adult Americans believe that the lottery is the path to riches. The hypothesis test of H0: p=.2 versus Ha: p>.2 resulted in 0.79 for a right-tailed test
The Z statistic given to be =0.79 for a right tailed test. Here, by looking aththe distribution table, the p value for Z=0.79 for one tail test is 0.2147.
So, we do not reject null hypothesis and then conclude that data does not provide sufficient evidence that the proportion of Americans who believe path to riches is the lottery is greater than 0.2
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Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes
Point
Slopes
(1, 1)
(a) 3 (b) -3 (c) -5/2 (d) Undefined
The sketch for slope is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Point Slopes
(1, 1) (a) 3
_ (b) -3
_ (c) -5/2
_ (d) Undefined
a) Now, using slope intercept form
y - 1= 3 (x-1)
y- 1= 3x- 3
y= 3x - 2
(b) Equation of a line has a slope -3 is given by
y - 1= (-3) (x-1)
y-1 = 3- 3x
y = -3x + 4
(c) Equation of a line has a slope -5/2 is given by
y - 1= (-5/2) (x-1)
y-1 = -5/2x + 5/2
y= -5/2x + 7/2
(d) The line parallel to y axis and passes through given point : x=1
"undefined" means the line is vertical.
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The quadrilateral DEFG,show. On the coordinate plane below is dilated from the origin by a space factor r= 2/3. Identify the coordinates of the dilated figure D^1 E^1 F^1 G^1 and the draw and label on the coordinate plane
Resizing or changing an object is the process of dilation. Through the use of the specified scale factor, it is a transformation that reduces or enlarges the objects.
What is Dilation Geometry?The pre-image refers to the original figure and the new figure that results from dilation is known as the image. Two forms of dilation exist:An object's size expands when it undergoes expansion.When an object gets smaller, the process is called contraction.The following illustration, which depicts a square dilating, should be noted. However, the square's shape doesn't change; rather, its size is raised.In mathematics, dilation is the process of modifying an object's or shape's size without altering its shape. The form could be a point, a section of a line, a polygon, etc. It should be noted that while the shape can be altered in size, the proportions of its various dimensions and angles never change.The angles are the same when PQR is increased to P'Q'R. After dilatation, the vertices of the PQR have new coordinates.P(1,3) → P' (3,9) (3,9)
Q(3,1) → Q' (9,3) (9,3)
R(1,1) → R' (3,3) (3,3).
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factor: x^2 -x -2
plssss
Answer:
(x+1)(x-2)
Step-by-step explanation:
[tex](x+1)(x-2)=x^{2} -x-2[/tex]
Hope this helps
Mick's zoo offers a promotional deal: get a free $3 cotton candy and a free
$2 soda with the purchase of five $12 admission tickets. A group of 20
students will each purchase a ticket. If half of them want cotton candy and
1/4 of them want soda, how many dollars would they save by using the
promotional deal?
(I typed it wrong last time) ✋
Answer: $34.25
Step-by-step explanation:
what is 36 percent of 128
Answer:
Step-by-step explanation:
36 percent can be written as 36/100. So now the question is 36/100 x 28.
Its easier if you simplify 100 and 28 by a common factor, which im going to use 4 for. So instead you get 36/25 x 7.
36x7=252
252/25=10.08
Answer:
46.08
Step-by-step explanation:
Remember that a percent is always a fraction out of 100, in this case 36/100, so it can also be written as a decimal number, in this case 0.36. Now all you need to do is multiply 128*0.36
GEOMETRY HELPPPP PLS
The new equation is y=-1/2x+5. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
What is mathematical equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2. The smallest equivalent fraction of the number is considered to be its simplest form. What to do to discover the simplest form? Investigate the numerator and denominator for shared factors. To see if a fractional number is a prime number, check it.Our first line in this equation is y=2x-1. By applying the equation y=mx+b, where "m" stands for the slope, we can see that our "m" in this instance is 2. then negate 2. It turns into -2.
Change the denominator and numerator after that. Since -2 is actually -2/1, let's change it to -1/2. The perpendicular line's slope is that.
We must now make it pass through (-2,6). We just have a line like this to work with at the moment: y=-1/2x
Plugging in the x-coordinate of our target location, -2, yields y=-1/2(-2), or 1. But hold on, because the y-coordinate we were given is 6, shouldn't y be equal to 6 as well? Yes! The only thing left to do is to add 5 to get from 1 to 6!
The complete question is,
Write an equation for a line perpendicular to y = 2 x − 1 and passing through the point (-2,6)
Write an equation for a line perpendicular to y=2x−1 and passing through the point (-2,6)
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Nicole cycled 9 laps on a bicycle path around the lake. If each lap was 9540ft long, what was the total distance she cycled? Write your answers in miles.
Answer:
162 miles.
Step-by-step explanation:
To find the total distance Nicole cycled, we can multiply the number of laps by the length of each lap.
The total distance Nicole cycled is:
9 laps * 9540 ft/lap = 858,600 ft
To convert this distance to miles, we can use the conversion factor that there are 5280 feet in a mile.
858,600 ft / 5280 ft/mile = 162 miles
So the total distance Nicole cycled is 162 miles.
toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat?
Answer:
A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.
making it a 33% chance of one of the toddler triplets to end up with their own coat.
100% divided by 3 = 0.33
A Pupil got to school by 7:30 am and left by 2:20pm. How many minutes did he spend in the school? Leave your answer in minutes.
Answer: Timespan is 410 minute(s).
Step-by-step explanation:
Understanding the meanings of words and phrases helps translate into algebraic expressions.
Example: 6 multiplied by the absolute value of 7 less than the cube of a number
6 · |n³ – 7|
? Question
What algebraic expression belongs with each verbal description?
the square root of the ____
of the ____ of a ____ and 11 → √x2² - 11 the ____ of __ times a number and -11 → -2x/11
the __ of the ____ ___ of two times a number and 11 → √2x + 11
Answer:
the square root of difference of the square of a number and 11the quotient of two times a number and -11the sum of the square root of two times a number and 11Step-by-step explanation:
Solve for n. 7n - 2 = 5n + 6
Answer:
n = 4
Step-by-step explanation:
Pre-SolvingWe are given the equation 7n - 2 = 5n + 6, ans we want to solve it for n.
To do this, we need to isolate n one one side.
SolvingLet's start by adding 2 to both sides.
7n - 2 = 5n + 6
+2 +2
_______________
7n = 5n + 8
Now, subtract 5n from both sides.
7n = 5n + 8
-5n -5n
_______________
2n = 8
Divide both sides by 8 to get the value of n.
2n = 8
÷2 ÷2
________
n = 4
Sea level is defined as having an elevation of 0. A dolphin is 7 meters below sea level.
How should the value 2(-7) be interpreted in this context?
A. a location that is twice as far below sea level as the dolphin
B. a location that is twice as far above sea level as the dolphin
C. a location that is 2 meters closer to sea level than the dolphin
D. a location that is 2 meters farther from sea level than the dolphin
Help…
The value 2(-7) is interpreted that a location that is twice as far below sea level as the dolphin. Option A is the correct option.
What is the meaning of interpretation?
Elucidate, explain, explicate, and expound are some synonyms for interpret. While all of these words mean "to make something clear or understandable," interpretation adds to explain why dealing with something requires imagination, sympathy, or special knowledge.
Given that sea level is defined as having an elevation of 0. A dolphin is 7 meters below sea level.
If the level is below sea level, then it can represent by a negative number.
The statement "A dolphin is 7 meters below sea level." can be written as:
A dolphin is -7 meters far from sea level.
Thus 2(-7) represents a location that is 7 meters below the dolphin's position.
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If 7 more than twice a number is 5 less than three times the same number, what is the number?
Answer:
12
SolutionLet X be the unknown number we are supposed to find.
Given information from the question, we can form up an equation:
2X + 7 = 3X - 5
3X - 2X = 7 + 5
X = 12
Therefore the unknown number is 12
In triangle ABC, M is the midpoint of AB and N divides CB such as NB:NC = 1:5. Find the area of triangle MNB, MNC and ABC
The area of triangle MNB, MNC and ABC 6 in.², 60 in.², and 30 in.² respectively
How to find the area of the triangle?The ratio of the base of the triangles ΔMNB and ΔCBM, that shares a common vertex, is the ratio of their areas.
M is the midpoint of side AB in ΔABC
NB:CB = 1:5
Area of ΔCAM = 30 in.²
The area of ΔMNB and ΔABC
Area = 1/2 * base * height
Height of ΔCAM = Height of ΔCBM = Altitude of point C above line AB
MA = MB by definition of midpoint
MA is the base of ΔCAM, and MB is the base of ΔCBM
Therefore; Area of ΔCAM = 1/2 AM * Height of ΔCAM
= 1/2 * AM* height of ΔCAM
Which gives;
Area of ΔCAM = Area of ΔCBM = 30 in.²
Area of ΔABC = Area of ΔCAM + Area of ΔCBM = 30 + 30 = 60
Area of ΔABC = 60 in.²
Taking CB as the base of ΔCBM, we have;
Height of ΔMNB = Height of ΔCBM from line CB
Base length of ΔCBM = 5 × Base length of ΔMNB
Therefore; Area of ΔMNB = 30/5 = 6 in²
Area of ΔCBM = 30 in.² = 5 × The area of ΔMNB
Conclusively, the Area of ΔMNB = 6 in.²
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Correct question:
In a triangle ABC, M is the mid point of the side AB and N is the mid point of the side AC. Find the lenght of the segment MN if AB =18, BC = 10 and AC = 20
pleasr help me out with this
Answer:
3π - π√2/2 or 7.2 cm-------------------------
According to the given we can state:
AD = BC = AB = 2AO = 2,EO is the perpendicular bisector of AB,Arc AC and arc BD are of equal length.Find arc AB, it is a semicircle of 1 cm radius:
arc(AB) = 1/2 × 2πr = πr = π cmΔAEO and ΔBEO are both isosceles, hence ∠A and ∠B are both 45°.
Find arcs ABD and BAC:
arc(ABD) + arc(BAC) = 2 × 45/360 × 2πr = 1/2 × πr = π cm∠AEB is a right angle since ∠AEO and ∠BEO are both 45°.
Hence ∠CED is also right angle as vertical angle with ∠AEB.
Find the length of EC and ED.
We know AD = BC = 2 cm and ΔAEO is 45° right triangle.
It gives us:
AE = √2Then:
ED = AD - AE = 2 - √2Find arc ECD:
arc(ECD) = 1/4 × 2πr = 1/2 × π(2 - √2) = π - π√2/2 cmThe perimeter is the sum of all the arc measures:
P = π + π + π - π√2/2 = 3π - π√2/2 or 7.2 cm (rounded)Answer:
[tex]\textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}=7.20333649...\; \sf cm[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
To convert degrees to radians, multiply the angle in degrees by π/180°.
Arc AB
As arc AB has center O, the radius of arc AB is OA = 1 cm.
As AB is a straight line, ∠AOB is 180° = π.
Therefore, the length of arc AB is:
[tex]\implies AB=r \:\theta=1 \cdot \pi = \pi[/tex]
Arc AC
Triangle BOE is a right triangle with base of 1 cm and height of 1 cm.
Therefore, ∠OBE is 45° = π/4
If arc AC has center B, then the radius is AB = 2 cm.
Therefore, the length of arc AC is:
[tex]\implies AC=r \:\theta=2 \cdot \dfrac{\pi}{4} = \dfrac{\pi}{2}[/tex]
Arc BD
Arc BD is the same as arc AC.
[tex]\implies BC= \dfrac{\pi}{2}[/tex]
Arc CD
As triangle BOE is a right triangle with base of 1 cm and height of 1 cm, the length of its hypotenuse BE is:
[tex]\implies BE=\sqrt{1^2+1^2}=\sqrt{2}[/tex]
As arc AC has center B and radius of AB = 2 cm, then BC is also its radius and therefore BC = 2 cm
Therefore:
[tex]\implies CE=BC-BE[/tex]
[tex]\implies CE=2-\sqrt{2}[/tex]
The arc CD has center E so its radius is CE = 2-√2.
As ∠BEO and ∠AEO are both 45° then ∠AEB is 90°.
According to the vertical angle theorem, ∠CED is also 90° = π/2.
Therefore, the length of arc CD is:
[tex]\implies CD=r \:\theta=(2-\sqrt{2}) \cdot \dfrac{\pi}{2} = \dfrac{(2-\sqrt{2})\pi}{2}[/tex]
Perimeter of the egg
The perimeter of the egg is the sum of the found arcs:
[tex]\implies \textsf{Perimeter}=AB+AC+BD+CD[/tex]
[tex]\implies \textsf{Perimeter}=\pi+\dfrac{\pi}{2}+\dfrac{\pi}{2}+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{2 \pi}{2}-\dfrac{\sqrt{2}\:\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\sqrt{2}\:\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}[/tex]
[tex]\implies \textsf{Perimeter}=7.20333649...\; \sf cm[/tex]
The area of the regular octagon is 10.15 cm².
1.45 cm
What is the measure of the apothem, rounded to the
nearest hundredth of a centimeter
The measure of the apothem is 1.75cm.
What is a regular octagon?
Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.
Here, we have
Given: The area of the regular octagon is 10.15 cm².
We have to find the measure of the apothem.
The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.
Area (triangle AOB) = 10.15/8 = 1.27cm².
Area(triangle AOB) is also 1/2*MO*AB
1.27 = 1/2*MO*1.45
MO = 1.75cm
Hence, the measure of the apothem is 1.75cm.
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Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown. –15 –5 –3 3 5
Answer: To solve the inequality x^2 - 8x + 15 < 0, we first want to find the critical points, which are the points where the quadratic function changes direction (from increasing to decreasing or vice versa). To find the critical points, we need to set the quadratic equal to zero and solve for x. In this case, we have:
x^2 - 8x + 15 = 0
To solve this equation we should factor it or use the quadratic formula.
(x - 5)(x - 3) = 0
x = 5, x = 3
This means that the critical points for the inequality are x = 5 and x = 3. To find the solution set of the inequality, we test the signs of the function at the critical points and in the intervals between them.
The solution of the inequality is x < 3 or x > 5.
Step-by-step explanation:
Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?
Answer:
Step-by-step explanation:
Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?
"The pie he will give to his parents"
More pumpkin flavor less cinnamon flavor
Solve for x. -2x + 1 = 3x + 16
Answer:
x=-3
Step-by-step explanation:
I showed my work in the picture
Answer:
[tex]\boxed{\sf x=-3}[/tex]
Step-by-step explanation:
[tex]\sf -2x+1=3x+16[/tex]
Subtract 3x from both sides:-
[tex]\sf -2x+1-3x=3x+16-3x[/tex]
[tex]\sf -5x+1=16[/tex]
Subtract 1 from both sides:-
[tex]\sf -5x+1-1=16-1[/tex]
[tex]\sf -5x=15[/tex]
Divide both sides by -5:-
[tex]\sf \cfrac{-5x}{-5}=\cfrac{15}{-5}[/tex]
[tex]\sf x=-3[/tex]
Therefore, x = -3!
______________________
Hope this helps!
Have a great day!
The sides of MNPQ are represented by the expressions below. Find the perimeter of MNPQ.
MW=-2+37
QP= y+14
NP= x-5
MN=4y+5
perimeter: ? units
Answer:
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all its sides. To find the perimeter of MNPQ, we need to add up the lengths of MN, NP, PQ and PM.
Given that:
MW=-2+37 = 35
QP= y+14
NP= x-5
MN=4y+5
The perimeter can be calculated by adding up the above expressions:
Perimeter = MN + NP + QP + MW
= (4y + 5) + (x - 5) + (y + 14) + 35
= 4y + x + y + 54
= (4y + y) + (x + 54)
= 5y + x + 54
So the perimeter of MNPQ is 5y + x + 54 units.
Pls help solve asap!!!!! I don’t understand
-2а + 3 ≥ 6а - 1 > 3а - 10
Answer:
00088n886668hb76u8y687440
I need some help answering this question right here
The given expression can be as 2 + i as a complex number standard form.
Complex numbers:The combination of a number and an imaginary number is a complex number. Complex numbers are symbolized by the symbol z and have the form a + ib. a and b are said to be real numbers.
The imaginary portion of the complex number can be represented by the letter i called the iota.
Here i² = -1
Here we have
[tex]\frac{4 +\sqrt{16 - 4(5)}}{2}[/tex]
The above expression can be simplified as follows
=> [tex]\frac{4 +\sqrt{16 - 20}}{2}[/tex]
=> [tex]\frac{4 +\sqrt{- 4}}{2}[/tex]
As we know, [tex]i^{2} = -1[/tex]
=> [tex]\frac{4 +\sqrt{i^{2} (2)^{2} }}{2}[/tex]
=> [tex]\frac{4+2i}{2}[/tex]
=> [tex]\frac{2(2+i)}{2}[/tex]
= 2 + i
Therefore,
The given expression can be as 2 + i as a complex number standard form.
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A landscaping business is purchasing plants from a nursery to finish a project. It will
cost $14 each to buy each tree and $7 each to buy each bush. The landscaper wishes to
keep the spending to no more than $870. Let t be the number of trees and b be the
number of bushes.
Select the inequality that describes the situation.
14t+7b> 870
O 14t+ 76 2 870
O 14t+7b < 870
O 14t+7b ≤ 870
I think it is the third answer.
Because your problem says 'no more than' so it can't be the fourth one,because it has '≤' which means that the number is lower or equal.
So it is the third one.
Hope I helped you!
A human resource manager is researching the entry-level salary for a technician position. He determines that other companies in the area are paying $15.50, $16.85, $14.25 and $15.95 per hour. What is the average pay for an entry-level technician position?
The average pay for an entry-level technician position is $15.6375.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean
The formula for the mean of a given set of data is as follows:
Average = Sum of Observations/Total number of observations
Σx = 15.50 + 16.85 + 14.25 + 15.95 = 62.55
Here n = 4
⇒ Average = Σx/n
⇒ Average = 62.55/4
Apply the division operation, and we get
⇒ Average = 15.6375
Thus, the average pay is $15.6375.
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A student says the expression 4+3(2x+2) is equivalent to the expression 6x+10 . As your answer, explain/show why the student is correct. Name each property that you use as you simplify the longer expression.
if im not wrong
4+3(2x+2) multiply since its in parenthesis first
property of mulitplication i think
4+6x+6
property of addition
6x+10
(this should be right)
how do find the factors of a fraction Example 3 1/2 (unit rate, proportionality)
The factors of a fraction 3 1/2 is 3/2.
What are the factors?Generally, A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another number to generate n. Another name for this concept is a factor of n. One may also state that n is a multiple of m in this particular scenario.
Since 3/2 is a fraction, it does not have any factors since factors are integers that may evenly divide a number. Since 3/2 is a fraction, it does not have any factors. Only integers are capable of having factors; fractions are unable to do so.
To find the factors of a fraction, you can factor the numerator and denominator separately.
In the case of 3 1/2, the numerator 3 is a prime number and cannot be factored further.
However, the denominator 2 can be factored as 2 x 1.
Therefore, the factors of 3 1/2 are: (3 x 1) / (2 x 1),
which can be simplified to 3/2.
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A function f(x)=^3√x is transformed into the function g (x) = 2^3√x-4+5. Name and explain in
complete sentences the transformations that occurred to the parent cube root function.
The required transformations are
f(x) is shifted 5 units to the right andf(x) is shifted 5 units upWhat is function?A function is a mathematical equation which shows the relationship between two variables.
What is transformation?Transformation is the performing of the mathematical operations of dilation, translation, relection and rotation on a function.
How to describe the transformation?Given the function [tex]f(x) = 2^{3\sqrt{x} }[/tex] which is transformed into the function [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex], we describe the transformations as follows.
First Since we have x - 4, [tex]f(x) = 2^{3\sqrt{x} }[/tex] is shifted four units to the right. So, we have , [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex].
Also, since 5 is added to [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex]. [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex]. is shifted 5 units up to get [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex],
So, the required transformations are
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1. The sum of two three-digit numbers is a four-digit number.
Answer:
Step-by-step explanation:
What are the possible combinations of three-digit numbers that could add up to a four-digit number?
There are many possible combinations of three-digit numbers that can add up to a four-digit number. Here are some examples:
1. 100 + 900 = 1000
2. 200 + 800 = 1000
3. 300 + 700 = 1000
4. 400 + 600 = 1000
5. 500 + 500 = 1000
6. 600 + 400 = 1000
7. 700 + 300 = 1000
8. 800 + 200 = 1000
9. 900 + 100 = 1000
10. 111 + 889 = 1000
11. 222 + 778 = 1000
12. 333 + 667 = 1000
13. 444 + 556 = 1000
14. 555 + 445 = 1000
15. 666 + 334 = 1000
16. 777 + 223 = 1000
17. 888 + 112 = 1000
18. 999 + 001 = 1000
19. 123 + 877 = 1000
20. 234 + 766 = 1000
Suppose Kristen is researching failures in the restaurants business
The standard deviation of the number of restaurants that failed within a year is 3.46.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Given that the probability that an independent restaurant will fail in the first year is 48%. Therefore, the probability can be written as,
p = 48% = 0.48
q = 1-p = 1-0.48 = 0.52
Also, Kristen obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. Therefore, the sample size is 53.
n = 53
Now, the standard deviation can be calculated as,
Standard deviation, σ = √(npq)
= √(53 × 0.48 × 0.52)
= √11.9808
= 3.46
Hence, the standard deviation is 3.46.
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