A minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.
What is the standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
The given data is:
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
Now find the mean of the given data would be
Mean = sum of all points/n
= 491/10
= 49.1
Standard deviation(s) = [tex]\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
Standard deviation(s) = 29.31988
Considering one standard deviation from the mean, the lower and upper limits are given by the following
[49.1-29.31988, 49.1+29.31988}
=[19.78012, 78.41988]
We can see that only 6 {27,32,45,57,61,73} out of the 10 points, which is 60%, confine to the interval of one standard deviation from the mean.
Hence, a minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.
To learn more about standard deviation, visit:
https://brainly.com/question/475676
#SPJ1
a pizza has a diameter of 20 inches.one slice of the pizza is perfectly cut from the centre at a 360° angle.what is the area of sector of the pizza
Answer: The diameter of a pizza is 20 inches.
what is 122222×2222221÷12
Answer:
The result of the calculation is approximately 22535940185.17
Step-by-step explanation:
To solve this problem, we can use the order of operations. First, we perform the multiplication:
122222 * 2222221 = 2704312822242
Then, we perform the division:
2704312822242 / 12 = 22535940185.17
4) Which ordered pair is a solution to the linear
inequality below?
y ≥ -2x + 7
A. (-1, 5)
B. (3, 2)
C. (2, -8)
D. (-4, 0)
Answer: B
Step-by-step explanation:
Answer:
B. (3, 2)
Step-by-step explanation:
When looking for a solution to an inequality you have to look for a point that is located in the shaded part of the inequality when graphed. B.) (3,2) is the only point that is located in the shaded part meaning that, that is a solution to the inequality
Statement 5.109. Letf:X→Ybe a function. Then the functionfis a bijection iff the relation{(y,x)∈Y×X∣(x,y)∈f}is a function.
Let f:X→Ybe a function. Then the function f is a bijection if the relation {(y ,x)∈Y×X∣ (x ,y)∈f} is a function.
Assume that X→Y is a bijective function.
i.e. f:X→Y is one-one and onto function.
so different elements in X have different images in Y
and b ∈ Y there exists a ∈ X such that f(a)=b.
R= {(y ,x)∈Y×X∣(x ,y)∈f} is a relation
we wish to prove R is a function.
R is a relation from Y to X
let Y∈Y by assumption f is bijection function from X to Y
for all y ∈ Y there exists X∈ X such that f(x)=y.
so for every element in Y there is mapping element in X.
if (x ,y) ∈ f then (y ,x) ∈ R
therefore R is a function.
let X1, X2, ∈ X then there exists some y1, y2,∈ y such that
take f ( x1 )= y1 and f( x2)=y2
by assumption R is a function from Y to X that is inverse of f is existing means f is bijection.
for bijective functions only inverse exists.
If f:X→Y is a function. Then the function f is a bijection if the relation
{(y ,x)∈Y×X∣(x, y)∈f} is a function.
To learn About bijection:
https://brainly.com/question/14871175
#spj4
Ver en español
The volume of this cylinder is 1,570 cubic inches. What is the radius?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Therefore ,the radius of the given cylinder is 10 inches
What is volume ?A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.
Here,
The volume of the cylinder is 1570 cubic inches
Volume of the cylinder = 1570 cubic inches
Volume of cylinder = π[tex]r^{2}[/tex]h
Where r is the radius of cylinder
h is the height of cylinder
So,
Volume of the cylinder = 1570 cubic inches
=> 1570 = π[tex]r^{2}[/tex]h
=> 1570 = 3.14*[tex]r^{2}[/tex]*5
=> 1570/3.14 = [tex]r^{2}[/tex]*5
=> 500=[tex]r^{2}[/tex] *5
=> 500/5 =[tex]r^{2}[/tex]
=>100 =[tex]r^{2}[/tex]
=>r=10 inches
Therefore the radius of the given cylinder is 10 inches.
To know more about Volume , visit
https://brainly.com/question/23477586
#SPJ1
For each system of equations, which operation will eliminate one of the variable? 2x+7y=32 and 2x+y=8
By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given system of equations,
2x + 7y = 32 and 2x + y = 8
Subtract both equations from each other,
(2x + 7y) - (2x + y) = 32 - 8
2x + 7y - 2x - y = 24
2x - 2x + 7y - y = 24
6y = 24
y = 4
Hence "By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations".
For more about the equation,
brainly.com/question/10413253
#SPJ1
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 396 people entered the park, and the admission fees collected totaled 1,094.00 dollars. How many children and how many adults were admitted?
Therefore by solving the equations we get to know that 196 children and 200 adults were present on that day.
What is equation?
equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.
Let's initially configure our system by giving the letters x and y meanings. Assume x is the number of kids and y is the number of adults.
Children are priced at $1.50, while adults are priced at $4.00. We multiply the total number of children, x, by 1.5 to get how much each child will cost. 1.5x is used to indicate this. We will use 4y for adults, whose entry fee is $4. On the specified day, $1094 in total revenue was earned. This sum requires the addition of 1.5x and 4y.
1.5x + 4y = 1094 works for the money equation involved.
Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.
x + y = 396
System of equations:
1.5x + 4y = 1094
x + y = 396
Thus,
x + y = 396
y = 396- x
Substitute y = 396 - x into the first equation.
1.5x + 4 (396 - x) = 1094
1.5x + 1584 - 4x = 1094
1584 - 2.5x = 1094
-2.5x = -490
x = 196
Substitute x =196 back into y = 396 - x
y = 396 - 196 = 200
Therefore by solving the equations we get to know that 196 children and 200 adults were present on that day.
To know more about equation , visit
https://brainly.com/question/12788590
#SPJ1
Combine the radicals
The combination of radical 5√27 - 17√3 is -2 √3, so option D is correct.
What are radicals?The opposite of an exponent, denoted by the symbol "√" and also known as the root, is a radical. The number before the symbol or radical is regarded as an index number or degree.
Given:
5√27 - 17√3
Simplify the value under roots,
5√(3 × 3 × 3) - 17√3
5 × 3 √3 - 17√3
√3 (15 - 17)
-2 √3
Therefore, the combination of radical 5√27 - 17√3 is -2 √3.
To know more about Radicals:
https://brainly.com/question/8020018
#SPJ1
The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 86 inches. Find the length and width of the rectangle.
The rectangle has the consecutive integers of 21 inches and 22 inches for its width and length respectively.
What are consecutive integersConsecutive integers are numbers that follow in a particular order, usually just one after the for example, 1, 2, 3,... and so on.
Let the width of the rectangle be represented by x so that the length will be x + 1 as they consecutive integers
The perimeter of the rectangle will have the equation;
x + x + x + 1 + x + 1 = 86 inches
4x + 2 = 86 inches {collect like terms}
4x = (86 - 2) inches {subtract 2 from both sides of the equation}
4x = 84 inches
x = (84/4) inches {divide through by the coefficient of x}
x = 21 inches
Therefore, the rectangle has width of 21 inches and length of 21 + 1 = 22inches.
Learn more about rectangle here:https://brainly.com/question/19819849
#SPJ1
10. A bag contains marbles: 5 purple, 6 blue, 8 yellow, 1 green. You will draw a
marble, keep it, and then draw another. What is the probability that you will
draw a purple and a green? SHOW YOUR WORK. Make sure to simplify your
answer if using a fraction. If using a percent, round to the nearest hundredth
after you change it to a percent.
Answer:
1st darw
[tex] p(purple)= \frac{5}{20} \\ = \frac{1}{4} [/tex]
[tex]p(green) = \frac{1}{20} [/tex]
2nd draw
[tex]p(purple) = \frac{4}{18} \\ = \frac{2}{9} [/tex]
[tex]p(green) = 0[/tex]
what is the value of p?
The value of p, using the exterior angle property is 53°.
What is the exterior angle property of a triangle?
The exterior angle property of a triangle states that the sum of the measures of the two non-adjacent angles of a triangle is equal to the measure of the exterior angle of the triangle. This means that if a triangle has three interior angles, the measure of any non-adjacent angle of the triangle must be equal to the measure of the exterior angle of the triangle. This property is useful in solving for unknown angles when the measures of two angles are known. For example, if two angles of a triangle measure 30° and 45°, then the measure of the third angle must be 105°, which is the same measure of the exterior angle.
The Exterior angle is = Sum of the Interior opposite angles.
By using the exterior angle property, we can get the following:
p+p-13°=p+40°
=>p=40°+13°
=>p=53°
The value of p is 53°
To learn more about the exterior angle property of the triangle, visit the link below:
https://brainly.com/question/14256482
#SPJ1
What is Q(1.5) if ()=cos() f(x)=cos(x) and Q(x) is centered atπ/2? Round your answer to 4 decimals, for example, 0.1234.
Step-by-step explanation:
This is a Taylor series because our center is non-zero.
The goal of Taylor series is to approximate non polynomial functions using Calculus.
So let's be intuitive.
In order to be accurate, we need to match the center value at some center a.
We know that cos(pi/2)=0, so our first constant should be 0.
[tex]q(x) = 0[/tex]
Next, we must be spot on with the linear approximation
at x=pi/2
we know that
[tex] \frac{d}{dx} \cos(x) = - \sin(x) = - \sin( \frac{\pi}{2} ) = - 1[/tex]
We also want to divide this by 1! , which is just one so our constant there is
-1, since we want to use this as an linear approximation and we want to be general, and we have a center to stay in respect to,
our next term is
[tex] 0 - 1(x - \frac{\pi}{2} ) {}^{1} [/tex]
Next, up, we must be similar in concavity.
So we take the second derivative of cosine which is just
[tex] - \cos(x) = - \cos( \frac{\pi}{2} ) = 0[/tex]
Since our constant is 0, we can skip this, even if we divide by 2!
Our fourth term is the third derivative of cosine
which is
[tex] \sin(x) = \sin( \frac{\pi}{2} ) = 1[/tex]
We then divide that by 3!, which becomes
[tex] \frac{1}{6} [/tex]
since we want to use this as an cubic approximation and we want to be general, and we have a center to stay in respect to,
our next term is
[tex] - (x - \frac{\pi}{2} ) {}^{} + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} [/tex]
Let do one more term,
we know the 5th term is the fourth derivative of cosine evaluated at x=pi/2, which is just 0 so we can skip it.
The 6th term is the fifth derivative of cosine evaluated at x=pi/2, which is -1, then we divide by 5!, so we get
[tex]q(x) = - (x - \frac{\pi}{2} ) + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} - \frac{1}{120} ( x - \frac{\pi}{2} ) {}^{5} [/tex]
Using the approximations, plug in 1.5 for x and we get approximately
0.0707
Sum and Product of Rational and Irrational Numbers
Step-by-step explanation:
4_/12=4_/3*4=4*2_/3=8_/3
5_/3+8_/3=13_/3
The result is irrational number because it cannot be written as the ratio of two integers. and its decimal extention is neither terminating nor repeting.
(4, -22) and (9,-57)
A copy machine makes 44 copies per minute. How long does it take to make 165 copies?
John started his collection with 35 baseball cards and collects 4 new cards every week. Frank started the same collection with 50 baseball cards and collects 2 new cards every week. How long will it take John to collect more cards than Frank.
Answer: 8 weeks
Step-by-step explanation: It would take John 8 weeks to collect more basketball cards than Frank with 67 cards for John and 66 for Frank.
(TONS OF POINTS AND BRAINLYEST)
Please answer the question that is stated in the image below. Thank you. It really means a lot to me.
Answer:
Below
Step-by-step explanation:
a) they won 120 games out of 369 played = 40/23=.325
b) they lost 248 out of 369 played = 248/369 = .672
c) Home games are 185 out of 369 = .501
d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389
For what value of X is the parallelogram a rhombus?
Answer:
x = 8
Step-by-step explanation:
a rhombus has all equal sides so this means that you must set them equal to each other
8x - 5 = 5x + 19
now subtract 5x to both sides
3x = 24
x = 8
that is your answer
What is the probability that out of 125 babies born, at least 50 will be girls? Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent.
When boys and girls are equally likely, the likelihood that at least 50 of 125 infants born will be females is 0.40.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
total number of sample=125
number of girls=50
Probability that out of 125 babies born, at least 50 will be girls,
=50/125
=0.40
The probability that out of 125 babies born, at least 50 will be girls is 0.40 when boys and girls are equally probable.
To know more about probability,
https://brainly.com/question/11234923
#SPJ1
In how many ways can a committee of five Democrats and four
Republicans be formed from a group of twelve Democrats and twelve
Republicans?
Answer:
392040 ways------------------------------
Find the combination of 4 of 12 and 5 of 12:
C(12, 4) × C(12, 5) = 12!/(4!8!) × 12!/(5!7!) = 495 × 792 = 392040Question
What is the net signed area between f(x) = 2x-6 and the x-axis over the interval [-8,5]? Do not include any units in
your answer
Provide your answer below:
The net signed area of f(x) = 2x - 6 on the interval [-8, 5] is - 21 units.
What is the net signed area?The definite integral can be used to calculate the net signed area, which is the area above the x-axis less the area below the x-axis.
Given, f(x) = 2x - 6 and the x-axis over the interval [-8 , 5].
∴ The net signed area is,[tex]\[ \int_{-8}^{5} 2x -6 \,dx \][/tex].
[tex]= \[ \int_{-8}^{5} 2x \,dx \ - \ \int_{-8}^{5} 6 \,dx \][/tex].
= (5)² - (-8)² - {(5×6) - (-8×6)}.
= 25 - 64 - 30 + 48.
= - 21 units.
learn more about net signed area here :
https://brainly.com/question/22867526
#SPJ1
A can of campbell's chicken Noodles Soup has a diameter of 30 millimeters and a height of 5 inches Find the volume of the can in cubic millimeters
The volume of the can of campbell's chicken Noodles Soup in cubic millimeters is 89,725.5 cubic millimeters
What is the volume of the can?Volume of a cylinder = πr²h
Convert inch to millimeters:
1 inch = 25.4 millimeters5 inch = 127 millimetersHeight of the cylinder = 5 inches = 127 millimeters
Radius = diameter / 2
= 30 millimeters / 2
= 15 millimeters
Volume of a cylinder = πr²h
= 3.14 × 15² × 127
= 3.14 × 225 × 127
= 89,725.5 cubic millimeters
Consequently, the can of campbell's chicken Noodles Soup has a volume of 89,725.5 cubic millimeters
Read more on volume of a cylinder:
https://brainly.com/question/9554871
#SPJ1
The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 6 mg. Round your answers to 5 decimal places as needed. What was the initial mass (in mg) of the sample? What is the mass 7 weeks after the start?
Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.
What is the half-life of a substance?
Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time.
The half-life of a substance is the time it takes for half of the initial mass of the substance to decay.
Since the half-life of Palladium-100 is 4 days, after 4 days, the mass of the sample will be reduced to half of its initial value. After 8 days, it will be reduced to a quarter of its initial value, and after 12 days it will be reduced to an eighth of its initial value.
We are given that after 12 days, the mass of the sample is 6 mg. This means that the initial mass of the sample was 8 * 6 mg = 48 mg.
After 7 weeks (7 * 7 = 49 days), the mass of the sample will be reduced by a factor of
= [tex]8^{(49/4) }[/tex]
= [tex]8^{12.5}[/tex] =
approximately [tex]2.6 * 10^6[/tex]. The mass of the sample after 7 weeks will be approximately [tex]\frac{6 mg }{2.6 * 10^6}[/tex] = approximately [tex]2.3 * 10^{-6}[/tex] mg.
Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.
To learn more about half-life, visit:
https://brainly.com/question/10671600
#SPJ1
|v-8| +13=29
help me solve for v
Hello,
I hope you and your family are doing well!
To solve for V, we can start by subtracting 13 from both sides of the equation:
|v-8| = 16
Since the absolute value of a number is always nonnegative, we know that the value inside the absolute value must be either positive or zero. This means that we have two possible cases to consider:
Case 1: v-8 > 0
In this case, we can drop the absolute value symbols and solve the equation:
v-8 = 16
v = 24
Case 2: v-8 = 0
In this case, we can drop the absolute value symbols and solve the equation:
v-8 = 0
v = 8
So the possible values of V are 8 and 24.
-----
Please click the heart, 5 stars and brainliest if you find this helpful. It does encourage me to help more students.
Happy Holidays!
Step-by-step explanation:
|v-8| + 13 = 29
subtract 13 from both sides
|v-8| = 16
form two equations:
v-8 = 16 -(v-8) = 16
v-8 = 16
add 8 to both sides
v = 24
-(v-8) = 16
-v+8 = 16
subtract 8 from both sides
-v = 8
divide both sides by a -1
v = -8
check work:
|v-8| + 13 = 29
|24-8| + 13 = 29
|16| + 13 = 29
29 = 29
|v-8| + 13 = 29
|-8-8| + 13 = 29
|-16| + 13 = 29
|-29| = 29
29 = 29
What is the domain of the graph? *
{-5,-4,-3,-1,0,2,4}
All real numbers
{-5,-4,-3,-1}
{-4,0,2,4}
The domain of the graph is {-5,-4,-3,-1}.
How can I determine a graph's domain?
Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.To know more about domain check the below link:
https://brainly.com/question/26098895
#SPJ4
Which expression is equivalent to (3+4i)(2−3i)
The expression that is equivalent to the given value would be = 18-i . That is option C.
What is an equivalent expression?An equivalent expression is defined as the type of expression that is similar to a given value when simplified.
The given expression = ( 3 + 4i) ( 2 - 3i)
Expand the given expression by removing the brackets as follows:
= =2(3+4i)−3i(3+4i)
=(6+8i)−(9i−12)
= (6+12)+i(8−9)
=18−i.
Learn more about multiplication equation here:
https://brainly.com/question/28552292
#SPJ1
Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
The missing terms are 34t and 0.
Solving Linear Equations:Finding the solution to linear equations in one, two, three, or more variables is referred to as solving a linear equation. In simple words, finding the values that satisfy a Linear equation.
Here we have
Equation 3(18t +1) = 20t +3
Let's solve the given expression to get the missing step
=> 3(18t +1) = 20t +3
Multiply (18t + 1) by 3
=> 54t + 3 = 20t + 3
Subtract 3 from both sides
=> 54t + 3 - 3 = 20t + 3 - 3
=> 54t = 20t
Subtract 20t from both sides
=> 54t - 20t = 20t - 20t
=> 34t = 0
Divide by 34 into both sides
=> 34t/34 = 0/34
=> t = 0
Therefore,
The missing terms are 34t and 0.
Learn more bout Linear Equations at
brainly.com/question/11897796
#SPJ4
Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use 3.14 when necessary.
Answer:
Volume of a cuboid = length x width x height
8 x 8 x 32 = 2048
Volume of a cylinder = πr^2h
r = diameter/2 = 8/2 = 4
π(4)^2(32) = π(16)(32) = 1607.68
Volume of the shaded solid:
2048 - 1607.68 = 440.32
The correct answer would be C) 440.32 m^3
The amount of money he earns is directly proportional to the number of hours he w The graph shows the amount of money, w dollars, he earns in t hours.
Find the constant of proportionality.
Answer: dollars per hour.
How much money does Jonathan earn after working 3 hours?
Answer:
55 I think if I'm wrong sorry
GIVING BRAINLIEST NOW!!!
Click on the measure of the angle.
A. 34
B. 144
C. 36
D. 146
Answer:
A Hooe that helps. Brainliest