It is known that that the median divides the range into half.
And the first and third quartiles are the landmark for 25% and 75% of the data values.
Therefore, a dot plot is divided into 4 parts, each of ehich represents 25% of the population.
In the given dot plot diagram, it is observed that the mean of the construction worker's salary, coincide with the upper quartile of the salary., at $45,000
It means that 50% population of construction workers is getting at most $45,000 while 75% population of teachers is getting at most $45,000.
So if a construction worker is making the median salary i.e. $45,000, so he/she will be making more than 75% of the teachers.
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
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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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.
(-35) x 6 =? i need help!
Answer: -210 is your answer
Step-by-step explanation:
I took the test and worked it out
Answer: -210
Step-by-step explanation: remembered answering this question once and -210 was the right answer
There is a 0.99967 probability that a randomly selected 30-year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of $900,000. How much should the company charge for this policy if it wants an expected return of $400 from all similar policies?
Using probability we can calculate that the company must charge $697 for an expected return of 400 .
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
The probability that a 30 year old female lives throughout the year
= 0.99967
Death benefit = $900,000
Expected amount the company would pay = probability that a person dies × insurance amount.
Expected amount = (1 - 0.99967) × 900000 = $297
Now Company wants a profit of $400
Cost charged by company =$( 297 + 400 ) = $ 697
Therefore using probability we can calculate that the company must charge $697 for an expected return of $400 .
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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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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:
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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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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HELPPPP PLEASEEE!!!
(MATH AND CHEMISTRY RELATED)
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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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
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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9 ft19 ftPlease refer to the rounding rules in the instructions.Circumference of the base = 59.5feetArea of the base = 254.3square feetSlant height = 19feetHeight = 16.7feetLateral area =536.9square feetSurface area = 791.2square feetVolume =cubic feetBlank 1: 59.5Blank 2: 254.3Blank 3: 19Blank 4: 16.7Blank 5: 536.9Blank 6: 791.2Blank 7:
The volume of a right cone is one-third of the product of the area of the base B and the
[tex]V=\frac{1}{3}Bh[/tex]Since the area of the base and the height is already given, substitute the values in to the equation and then simplify.
[tex]\begin{gathered} V=\frac{1}{3}(254.3)(16.7) \\ =\frac{1}{3}(4246.81) \\ \approx1415.603 \end{gathered}[/tex]We may also find the exact value by substituting the given values into the equation below.
[tex]V=\frac{\pi r^2h}{3}[/tex]where V is the volume, r is the radius, and h is the height.
To obtain the exact value of the height, we use the Pythagorean theorem.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]where a and b are the legs of the formed right triangle while c is its hypothenuse.
From the figure, the slant height is the hypothenuse while the radius, 9 ft, serve as one of the legs. Thus, the other leg, which is the height of the cone can be solved as follows.
[tex]\begin{gathered} a=\sqrt[]{19^2-9^2} \\ =\sqrt[]{361-81} \\ =\sqrt[]{280} \end{gathered}[/tex]Therefore, the height of the cone is as stated above.
Substitute the obtained height and the radius into the second formula that was stated.
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{\pi(9^2)(\sqrt[]{280})}{3} \end{gathered}[/tex]Simplify the right side of the equation. Evaluate the exponential expression.
[tex]V=\frac{\pi(81)(\sqrt[]{280})}{3}[/tex]Multiply the numerator and then divide it by 3.
[tex]\begin{gathered} V=\frac{\pi(81)(\sqrt[]{280})}{3} \\ \approx\frac{(3.1416)(81)(16.7332)}{3} \\ \approx\frac{4258.0907}{3} \\ \approx1419.36 \end{gathered}[/tex]Note that the value that we obtain at first, 1415,603, is slightly different from the one that we obtained, which is 1419.36, since there are values that we already rounded off before substituting the values in the equation.
Therefore, to be more exact, it is best to indicate that the volume of the given cone is approximately 1419.36 ft³.
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
A math class consists of 21 female students and 16 male students. Two students are selected at random to participate in a probability experiment. Compute the following probabilities. Write your answers in decimal form. Round to the nearest thousandth as needed.a. A male is selected, then a female. b. A female is selected, then a male. c. Two males are selected. d. Two females are selected. e. No males are selected.
To solve this problem, we will use the conditional probability definition: Given events A,B such that P(B)>0 we have that
[tex]P(A|B)=\frac{P(\text{A}\cap B)}{P(B)}[/tex]Where P(A|B) means the probability of A given B occurred. This also leads to the following
[tex]P(A|B)\cdot P(B)=P(A\cap B)[/tex]Now, let us define two events. Let M1 be the event that we select a male first and let F2 be the event that we select a female second. We want to calculate the following probabilty
[tex]P(M_1\cap F_2)_{}[/tex]Using the definition of conditional probability, this is the same as
[tex]P(M_1\cap F_2)=P(F_2|M_1)\cdot P(M_1)[/tex]Now, we will calculate P(M1). At the beginning, when we have not picked anyone yet, we have 37 people (21 Female and 16 Male). So the probability of picking a male first is simply
[tex]P(M_1)=\frac{16}{37}[/tex]Now, we will calculate the second probability. Since we already picked one male, we have now 36 people (21 female and 15 male). Then the probability of picking a female is
[tex]P(F_2|M_1)=\frac{21}{36}[/tex]So,
[tex]P(M_1\cap F_2)=\frac{16}{37}\cdot\frac{21}{36}=\frac{28}{111}=0.252[/tex]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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1. A survey of 36 students was conducted to find out how many students enjoy playing volleyball, and 17 said they did. If 648 students were surveyed, how many would say they enjoy playing volleyball?
The total number of students calculated with the method called simplification and who are playing volleyball is 206.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:
survey of students: 36
play volleyball: 17
As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?
Therefore, the required simplified expression can be written as:
Required expression: 648÷36= 18
Now, playing volleyball =18×17=206 students play volleyball
Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.
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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
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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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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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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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
(X^3- 5x+ 3) ÷ (x- 2)
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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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
please help me out with this
Answer:
c
Step-by-step explanation:
What is Prime factorization ?
the prime factors of a positive integer are the prime numbers that divide that integer exactly.
--- 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.
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