Given the following expression:
[tex]\text{ 9 x 3 = 27}[/tex]Making a comparison statement out of this will be: 27 is 3 times more than 9.
The sample space S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]
Given A = [E1, E3, E6, E9], define Ȃ
Given A = [E1, E3, E7, E9] and B = [E2. E3, E, E9]
a) What is A intersection B?
b) What is the union of A & B?
c) Is the union of A & B collectively exhaustive?
A is defined as a subset of the sample space, that is, the universal set
a. A∩B = { E3, E9}
b. A∪B = {E, E1, E2, E3,E7, E9}
c. Yes, the union of A and B is collectively exhaustible
What are sets?Sets are defined as in mathematical and logical collection of elements or objects, numbers or functions.
The members of a set are listed in enclosed braces.
The elements and objects of a set are well-defined and fixed.
Given the sets as;
S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]
A = [E1, E3, E6, E9]
A is defined as a subset of the sample space, S
a. It is important to note that the intersection of two sets involves the elements or objects that are common between them.
Given that;
A = [E1, E3, E7, E9]
B = [E2. E3, E, E9]
A∩B = { E3, E9}
b. Note that the union of sets involves the collection of the elements of both sets without repetition.
A∪B = {E, E1, E2, E3,E7, E9}
c. The union of the sets A and B are together exhaustive as it contains all the elements in both sets.
Hence, A is defined as a subset of the universal set.
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Matt and Wei are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Matt sold 18 small boxes of fruit and 25 large boxes of fruit for a total of $529.50. Wei sold 18 small boxes of fruit and 10 large boxes of fruit for a total of $282.00. Find the cost of one small box of fruit and the cost of one large box of fruit.
Answer:
The small box price is 6.5 and The large box price is 16.5
Step-by-step explanation:
I did the question with a simultaneous equation
let's say the price of the small box = x and the price of the large box = y
Then, I just subtract downward;
18x+25y=529.50
- 18x+10y=282.00
_____________
0+15y=247.50
15y=247.50
— ————
15 15
I just canceled 15 by 15:
Then, y=247.50÷15=16.5
so I just find the value of Y which is 16.5, then I insert it into the second equation:
18x+10y=282
18x+10(16.5)=282
18x+165=282
18x=282-165
18x=117
— —
18 18
Cancel 18 by 18
finally x=6.5
Insert x and y into both equations, it works
2(x+4)-3(2x-5)=-3
What is the answer
Answer: x= 13/2 or 6 1/2
Step-by-step explanation:
2(x+4)-3(2x-5)=-3
Simplify the equation,
2x+8-6x+15 = -3
-4x+23= -3
-4x = -26
Cancel the minus sign, now we get
2x = 13
i.e., x= 13/2
Given the system of equation 3x - 2y-9=0 X + 8y-3 = 0 Is (3, 0) a solution to the given system?
Yes (3,0) is the solution of the given equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given Data
Equation
3x - 2y-9=0
X + 8y-3 = 0
Solution(3, 0)
Finding the values of x,
x + 8y - 3=0
x = 3 + 8y...(1)
Substituting x in the equation
3x - 2y = 9
3(3+ 8y) -2y = 9
9 + 24y - 2y = 9
22y = 0
y = 0
Substituting the value in (1)
x = 3 + 8(0)
x = 3
Yes (3,0) is the solution of the given equation.
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A company uses two factories to manufacture three different sizes of boats. Each boat takes a different amount of time to perform each task. For example, the small boat requires 1 hour of cutting, 0.5 hours of assembly, and 0.2 hours of packaging. The medium boat requires 1.6 hours of cutting, 1 hour of assembly, and 0.2 hours of packaging. Finally, the large boat requires 2.5 hours of cutting, 2 hours of assembly, and 1.4 hours of packaging time. The factory pays each department at each factory differently, according to this pay scale: Factory A pays out $15 per hour for cutting, $12 for packaging, and $11 for assembly. Factory B pays out $13 for cutting, $11 for assembly, and $10 for packaging. How much will each factory have to pay in wages to construct each type of boat?
Using proportions, the costs for the boats are given as follows:
Factory A:
Small: $22.9.Medium: $37.4.Large: $76.3.Factory B:
Small: $20.5.Medium: $33.8.Large: $68.5.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using the standard operations such as addition, subtraction, multiplication and division with the unit rates to find the equivalent amounts.
Considering the costs per hour and the number of hours needed, the cost of a small boat at Factory A is given by:
15 x 1 + 11 x 0.5 + 12 x 0.2 = $22.9.
For example, 15 x 1 is because it requires one hour of cutting, and each hour of cutting pays of $15.
The cost of a medium boat at Factory A is given by:
15 x 1.6 + 11 x 1 + 12 x 0.2 = $37.4.
The cost of a large boat at Factory A is given by:
15 x 2.5 + 11 x 2 + 12 x 1.4 = $76.3.
The cost of a small boat at Factory B is given by:
13 x 1 + 11 x 0.5 + 10 x 0.2 = $20.5.
The cost of a medium boat at Factory B is given by:
13 x 1.6 + 11 x 1 + 10 x 0.2 = $33.8.
The cost of a large boat at Factory B is given by:
13 x 2.5 + 11 x 2 + 10 x 1.4 = $68.5.
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4. (01.02 LC) Brandi earned $78 in interest after one and one half years on an account that paid 7.5% simple interest annually. Use the formula I = Prt to find Brandi's principal balance. Round to the nearest hundredth. (1 point) $69.33 $87.75 $693.33 $768.00
The principal amount is $693.33.
What is Simple Interest?Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount.
The formula is
Simple Interest = P x R x T/100
Given:
Interest = 78
Rate= 7.5%
Time= 1 and half year = 1.5 year
Now, Simple Interest= P x R x T / 100
78 = P x 7.5 x 1.5 / 100
7800= P x 11.25
P = 7800/11.25
P = 693.33
Hence, the principal amount is $693.33.
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Mr. House wrote 8 tenths minus 5 hundredths on the board. Maggie said the answer is 3 hundredths
because 8 minus 5 is 3. 5 Is she correct? Explain.
A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $35 and then an additional 6 cents per minute of use.
For what amounts of monthly phone use will Plan A cost less than Plan B?
Use m for the number of minutes of phone use, and solve your inequality for m
Answer: Less than 470 minutes
Step-by-step explanation:
This equation represents this problem.
0.04x + 44.4 = 0.06x + 35
Solve,
0.02x = 9.4
1 / .02 = 50
x = 470
At 470 minutes they're equal and we are looking for when Plan A is cheaper then Plan B, so x < 470
Use m instead of x in this problem, sorry didn't read the last line.
Assuming the population has an approximate normal distribution,
if a sample size n = 12 has a sample mean
= 36 with a sample standard deviations = 9, find the margin of error at a 98% confidence level. Round
the answer to two decimal places.
E = 38.33 the margin of error at a 98% confidence level by standard deviation mean.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to a measurement of the data's divergence from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average error of each statistic from the mean.Given that,
bar x = 36
s = 9
n = 12
Degrees of freedom = df = n - 1 =12 - 1 = 11
At 98% confidence level the t is ,
∝ = 1 - 98% = 1 - 0.98 ⇒ 0.02
∝/2 = 0.02/2 = 0.01
t∝/2 df = t0.01 ,11 = 1.231
Margin of error = E = t∝/2, df * ( s/n/sqrtn)
E = 1.231 * ( 9 /0.01/sqrt12)
E = 38.33
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What is Prime factorization ?
the prime factors of a positive integer are the prime numbers that divide that integer exactly.
Emily works at a factory that makes computer parts. The machine that produces internal hard drives results in a certain number of defects during the day. The table below represents the probability density function for the random variable X, the number of defects per day. Find the standard deviation of X. Round the final answer to two decimal places.
The standard deviation of the discrete distribution of the number of defects in a day is of 0.75 defects.
What are the mean and the standard deviation of a discrete distribution?The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The standard deviation of a discrete distribution is given by the square root of the sum of the difference squared between each outcome and the mean, multiplied by it's respective probability.From the distribution at the end of the answer, the mean is:
E(X) = 0.1667 x 4 + 0.3333 x 5 + 0.5 x 6 = 5.3333.
Hence the standard deviation is of:
S(X) = sqrt(0.1667 x (4-5.3333)² + 0.3333 x (5 - 5.3333)² + 0.5 x (6 - 5.3333)²) = 0.75 defects.
What is the missing information?The distribution is missing, and is given as follows:
P(X = 4) = 0.1667.P(X = 5) = 0.3333.P(X = 6) = 0.5.More can be learned about the standard deviation of a discrete distribution at https://brainly.com/question/19054123
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Riders for the Kiddie Koaster at the State Fair must be no more than 48 inches tall. Which inequality best expresses the height of the riders?
Answer:Note that at least means greater than or equal to (≥) . It was stated that you must be at least 48 inches tall to ride the roller coaster. Hence, the inequality is h≥48 h ≥ 48
Step-by-step explanation: poopity poop UWU UWU UWU oodfijdisfioahgioahiodfhipodioajhierfia MUSIC MUSIC MUSIC MUSIC MUSIC MUSIC HACKER HACKER HAKER HACKER HACKER OMG UWU UWU UWU YOUR 13 LOL YOUR FATHERLESS GT DELETED TRASH KID
There are 9 candidates for three positions at a restaraunt. One position is for a cook. The second position is for a food server. The third position is for a cashier. If all 9 candidates are equally qualified for the three positions, in how many different ways can the three positions be filled?
The number of different ways that the three positions can be filled is 504 ways.
How to calculate the value?From the information, there are 9 candidates for three positions at a restaraunt. Based on the data, one position is for a cook, the second position is for a food server and the third position is for a cashier.
Therefore, the number of ways will be:
= 9P3
= 9! / (9 - 3)!
= 9! / 6!
= 9 × 8 × 7
= 504
The number of ways is 504 ways.
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(X^3- 5x+ 3) ÷ (x- 2)
Zach and Ginny are building model cars. Ginny's car is 2 more than 3 times the length of Zach's car. The sum of the lengths of both cars is 30 inches. Write an equation to determine the lengths of Zach's and Ginny's cars.
3x + 2 = 30
x + 2 + 3x = 30
2x + 3 = 30
x + 2x + 3 = 30
HELPPPP PLEASEEE!!!
(MATH AND CHEMISTRY RELATED)
You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (b) What is the probability of getting a sum of 4? (c) What is the probability of getting a sum of 6 or 4? Are these outcomes mutually exclusive?
Based on the number of dice rolled, the probability of getting the sum of 6, and 4 and 6 or 4 can be found to be:
Probability of getting sum of 6 = 5 / 36Probability of getting sum of 4 = 1 / 12Probability of getting sum of 6 or 4 = 2 / 9How to find the probability?Probability of getting sum of 6:
(1 and 5) (2 and 4) (3 and 3) (4 and 2) ( 5 and 1)
= 5 / (6 x 6)
= 5 / 36
The number of sums of 4 are:
= (1 and 3), (2 and 2), (3 and 1)
= 3 / (6 x 6)
= 1 / 12
The probability of getting sums of 6 and 4 are:
= (5 + 3) / (6 x 6)
= 8 / 36
= 2 / 9
These events are mutually exclusive because they cannot roll a sum of 6 or 4.
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--- nerweter de 2 mm. em. 4 em 12 manam 2) Find the perimeter. Use 3.14 for it when needed. 20 m semicircle -2n trola To 31.1 10 m 2 2 P. = 314 = 77.4 D 31.141/2 + 2+2 P - Find area of figure. Round to the nearest hundredth if neces 41 in. 136 in. 45.5 in. 1 area of figure. Round to the nearest hundredth if ne 17 m 9 m n
The perimeter of the semicircle with different r values is:
(When r = 2) = 10.28 mm(When r = 4) = 20.56 mm(When r = 12) = 61.68 mmWhat is a semicircle?A circle is divided into exactly two parts in geometry to create a semicircle, a plane figure. Therefore, using the area and perimeter of a circle, we can calculate the area and perimeter of a semicircle. A semicircle is a one-dimensional locus of points in mathematics (and more specifically geometry) that makes up one-half of a circle. A semicircle's full arc (equivalent to π radians or a half-turn) is always 180° in length. It only has one symmetry line (reflection symmetry).So, the formula for the perimeter of the semicircle:
πr + 2rNow, insert values as follows:
(A) (When r = 2)
πr + 2r3.14 × 2 + 2 × 26.28 + 410.28 mm(B) (When r = 4)
πr + 2r3.14 × 4 + 2 × 412.56 + 820.56 mm(C) (When r = 12)
πr + 2r3.14 × 12 + 2 × 1237.68 + 2461.68 mmTherefore, the perimeter of the semicircle with different r values is:
(When r = 2) = 10.28 mm(When r = 4) = 20.56 mm(When r = 12) = 61.68 mmKnow more about semicircles here:
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The correct question is given below:
2 mm. em. 4 em 12 Manam. Find the perimeter of the semicircle. Use 3.14 for it when needed.
Over the last three evenings, James received a total of 90 phone calls at the call center. The second evening, he received 2 times as many calls as the third evening. The first evening, he received 6 more calls than the third evening. How many phone calls did she receive each evening?
Answer:
first evening = 27 calls
second evening = 42 calls
third evening = 21 calls
Step-by-step explanation:
Total of 90 calls
f = first evening
s = second evening
t = third evening
Solve:
f=t+6
s = 2t
t=t
f+s+t=90
t+6 + 2t + t
(2t+t+t)+6 = 90
4t+6 = 90
4t=84
t=21
ANSWER:f=t+6=21+6
= 27
s = 2t
= 42
t = t
= 21
Last year, Singer A performed two more than five times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 74. How many concert shows did each perform?
Singer A had
Correct shows and Team B had
Correct
ANSWER. B = 18, A = B + 23 = 18+23 = 41.
Step-by-step explanation:
Recall that the sum of the measures of the angles of a triangle is 180°. In the triangle below, angle Chas the same measure as angle B, and angle measures 42° less than angle B.
Find the measure of each angle.
Answer:
180=x+42
collect like terms
x=180-42
x=138
Is a tutor availible
So if i have a bag of rice of 3.5 pounds, that means that it weighs:
[tex]3.5\text{ pounds = 56 ounces}[/tex]since
[tex]3.5\text{ x 16 = 56}[/tex]that means that you will have enough rice for the recipe
A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda races the bicycle for 35 m. How many times does the wheel turn as the bicycle travels this distance?
Use the value 3,14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer:
37.2 rotations
Step-by-step explanation:
35 / (3.14 x .3) = 37.15499
Rounded = 37.2 rotations
Shureka Washburn has scores of 86, 84, 83, and 49 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 76 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
The most appropriate choice for average will be given by-
Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.
What is average?
In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.
Average is calculated by sum of all observations divided by total number of observations.
Here,
Let the score of Shureka Washburn in her last test be x
Score of Shurek Washburn on first test = 86
Score of Shurek Washburn on second test = 84
Score of Shurek Washburn on third test = 83
Score of Shurek Washburn on fourth test = 49
Total sum of all her scores = 86 + 84 + 83 + 49 + x
= 302 + x
Average = [tex]\frac{302 + x }{5}[/tex]
By the problem,
[tex]\frac{302 + x}{5} \geq 76[/tex]
[tex]302 + x \geq 76[/tex] [tex]\times 5[/tex]
[tex]302 + x \geq 380[/tex]
[tex]x \geq 380 - 302[/tex]
[tex]x \geq 78[/tex]
Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.
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Triangle ABC has its vertices at the following coordinates:
A(5,-10) B(-8, 4) C(2, 0)
Give the coordinates of the image triangle A'B'C' after a 90 rotation counterclockwise about the origin.
]
A'(-10, 5) B'(4,-8) C'(0, 2)
A (10, 5) B (-4,-8) C (0, 2)
A'(10, 5) B'(-4,-8) C'(0, 2)
A'(5, 10) B'(-8,-4) C'(2, 0)
A (5, 10) B (-8,-4) C (2, 0)
The coordinates of the vertices of the image triangle A'B'C' after a rotation 90° counterclockwise about the origin are: A' (10, 5), B' (-4, -8), C'(0, 2)
What is a rotation?A rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).
By applying a rotation of 90° counterclockwise to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:
(x, y) → (-y, x)
Point A = (5, -10) → Point A' = (-(-10), 5) = (10, 5)
Point B = (-8, 4) → Point B' = (-4, -8)
Point C = (2, 0) → Point C' = (0, 2)
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7.
Write and solve the system of equations needed to model this situation: You have thirty coins
a total value of $3.40, which are made up of nickels, dimes, and quarters. There are twice as many
nickels than quarters. How many of each type of coin do you have?
The system of equations for the given conditions in question includes equation: 3.40 = 0.05x + 0.1y + 0.25z, and 2x = z. and we have 2 nickels, 23 dimes, and 4 quarters.
What is system of equations?
A system of equations is a collection of some equations with one or more numbers of variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.
Let the quantities of nickels, dimes, and quarters are x, y, and z respectively.
We know that, 1 nickel = $0.05, 1 dime = $0.1, and 1 quarter = $0.25
So, the values of nickels, dimes, and quarters would be value of one times total quantity.
Nickels = 0.05x, dimes = 0.1y, and quarters = 0.25z
As given in the question, the total value is 3.40
So, we get equation:
3.40 = 0.05x + 0.1y + 0.25z
Also it is given that there are twice as many nickels than quarters.
2x = z
Combining above two equations
3.40 = 0.05x + 0.1y + 0.25(2x)
3.40 = 0.05x + 0.1y + 0.5x
3.40 = 0.55x + 0.1y
Lets put 2 in place of x, we get y
(3.40 - 1.1)0.1 = y
y = 23.
Now, putting values of x, y in equation to get value of z
3.40 = 0.05(2) + 0.1(23) + 0.25z
3.40 = 0.1 + 2.3 + 0.25z
(3.40 - 2.4)/0.25 = z
z = 4
Therefore, we have 2 nickels, 23 dimes, and 4 quarters.
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Enter a range of values for x.85°5x - 1025Sk[ ? ]
°
the two triangles have a bisetor that makes the adjacent side equal, so based on this 25 = 5x- 10
25+ 10 = 5x
meaning your x = 7
but on the equation 5x-10 =0
we get that x = 10/5
x >2
so the range would be 2
Solve the inequality.
C - 12 > -1
Answer:
c>11
Step-by-step explanation:
you +12 on both sides then u now have 11 rather than -1 which leaves u with c>11
The lengths of the side of a triangle are 6, 8, 10. Can the triangle be a right triangle?
Yes, the triangle is a right-angle triangle.
Right angle triangle is a triangle in which one of the angles as 90 degree.
For the triangle to be right angle triangle
perpendicular² + base² = hypotenuse²
The three sides of a triangle are 6, 8 and 10
So,
6² + 8² = 10²
36 + 64 = 100
100 = 100
Therefore the triangle is a right-angle triangle.
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Graph the function. Label the vertex and axis of symmetry. Hint: Recall when in Standard form use x value=-b/2a. ( SHOW WORK)
The features of the graphs are
Graph 1: Vertex = (4, 3); Axis of symmetry: x = 4Graph 2: Vertex = (-0.4, -1.8); Axis of symmetry: x = -0.4How to graph the functions?Function 1
The equation of the function is given as
f(x) = 3(x - 4)^2 + 3
A quadratic equation can be represented as
f(x) = a(x - h)^2 + k
Where, the vertex is
Vertex = (h, k)
And the axis of symmetry is
x = h
By comparing the equations, we have
Vertex = (4, 3)
Axis of symmetry: x = 4
See attachment 1 for the graph of the function
Function 2
The equation of the function is given as
f(x) = 5x^2 + 4x - 1
Differentiate the function
f'(x) = 10x + 4
Set to 0
10x + 4 = 0
This gives
x = -0.4
Substitute x = -0.4 in f(x) = 5x^2 + 4x - 1
f(-0.4) = 5(-0.4)^2 + 4(-0.4) - 1
Evaluate
f(-0.4) = -1.8
This means that
Vertex = (-0.4, -1.8)
Axis of symmetry: x = -0.4
See attachment 2 for the graph of the function
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