The probability that a randomly selected student majors in business or economics is 44.8%.
Describe the union set in probability?A set that contains every element in at least one of two sets is called a union of two sets. The union is denoted by the symbols A∪B or “A or B” A fresh batch that includes every element from both sets is created when two sets intersect. The intersection is denoted by the symbols A∩B or “A and B”.Let 'B' be the students of business.
P(B) = 35.1%
Let 'E' be the students of business.
P(E) = 12.3%
Thus,
P(E ∩ B) = 2.6%
P(E ∪ B) = probability for student majors in business or economics.
P(E ∪ B) = P(B) + P(E) - P(E ∩ B)
Put the values-
P(E ∪ B) = 35.1% + 12.3% - 2.6%
P(E ∪ B) = 44.8%
Thus, the probability that a randomly selected student majors in business or economics is 44.8%.
To know more about the union set in probability, here
https://brainly.com/question/16629677
#SPJ4
you have 600 ft of fencing material to construct a rectangular pen for cattle. what are the dimensions (in feet) of the pen that maximize the area (enter number only)?
The dimension of pen that maximize the area is 150 ft by 150 ft.
What is the dimension of a area?
In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
Given the perimeter of the rectangular is 600 ft.
Assume that the length of the rectangular be l and the breadth be b.
The perimeter of the rectangular is 2(l+b).
According the question:
2(l+b) = 600
Divide both sides by 2:
(l+b) = 300
l = 300 - b
The area of rectangular is A = lb
Substitute the value of l in the above equation:
A = (300 - b) b
A = 300b - b^2
The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).
Compare Ax^2+BX+C with 300b - b^2:
A = -1 and B = 300.
Putting A = -1 and B = 300 in b= - B/(2A).
b= - 300/(2×(-1))
b = 150.
Putting b =150 in l = 300 - b
l = 300 - 150
l = 150
The dimension is 150 ft × 150 ft.
To learn more about maximize area, you can visit:
https://brainly.com/question/17096963?
#SPJ4
According to a report for veterinarians in the united states, 36. 5 percent of households in the united states own dogs and 30. 4 percent of households in the united states own cats. If one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?.
Find quotation 1 3/4 divided by 3
Please help I think it’s 7/12
The quotation for division of 7/4 that is 1 3/4 divided by 3 will be 7/12 by the rule of division that is a/b÷c/d=a/b*d/c.
What is division?A number is divided in division, which is a straightforward operation. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. A division is the division of a given sum into equal parts. For instance, we could split a group of 20 people into four groups of 5, five groups of 4, and so on. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. To determine how many equal groups are created or how many people are in each group, division is the primary objective.
Here,
1 3/4=7/4
7/4÷3/1,
a/b÷c/d=a/b*d/c
7/4*1/3=7/12
According to the division rule a/b÷c/d=a/b*d/c, the quotation for 7/4, which is 1 3/4 divided by 3, will be 7/12.
To know more about division,
https://brainly.com/question/21416852?referrer=searchResults
#SPJ13
HELP ITS DUE IN A LITTLE BIT!!!
Answer:
Step-by-step explanation:
Yes it does
10 and 15
Answer:
A. the independent and dependent variables are the number of miles and total fee (y = 2.8 + 3.5x)
B. the domain is 0 <= x <= 20 and range is 2.8≤x≤20
Step-by-step explanation:
Heidi thinks the rule for the table below is y = x + 3.
Is she correct?
X
-2
-1
0
1
2
y
-7
-4
-1
2
5
What is an equation of the line that passes through the points (-4, 5)(−4,5) and (-4, -2)(−4,−2)?
Answer:
∅
Step-by-step explanation:
set up your equation which will be [tex]\frac{-2-5}{-4+4}[/tex] which is undefined because denominator cannot be 0
Factor the expression using the GCF.
The expression $32z-48$ factored using the GCF is
The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The expression is given below.
⇒ 32z - 48
The expression can be rewritten as,
⇒ 32z - 48
⇒ 16 · 2z - 16 · 3
⇒ 16 (2z - 3)
The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.
More about the greatest common factor link is given below.
https://brainly.com/question/11221202
#SPJ1
The green point is marked on the coordinate plane. What ordered pair represents the green point?
Answer:
pretty sure its (-6, -4)
Step-by-step explanation:
in the ||| quadrant so I know they are both negative.
The point is 6 units to the left and 4 units down.
Hope this helps! Good luck!
The points P, Q, R and S all lie on the same line segment, in that order, such that the ratio of PQ:QR:RSPQ:QR:RS is equal to 1:3:1.1:3:1. If PS=35,PS=35, find PR.PR.
The distance of PR is 21
Given,
The points P, Q, R and S all lie on the same line segment.
The ratios;
PQ:QR:RS = 1:3:1.
Distance of PS = 35
We have to find the distance of PR.
A line segment is a piece of a straight line that has all of the points on the line contained within and is bounded by two distinct endpoints. A line segment's length is determined by the Euclidean distance that separates its two ends.
Here,
PQ : QR : RS = 1 : 3 : 1.
Now let PQ = x, QR = 3x and RS = x.
Therefore,
PQ + PR + RS = PS.
x + 3x + x = 35
5x = 35
x = 7
Therefore,
PR = 3x
PR = 3 × 7
PR = 21
The distance of PR is 21
Learn more about line segment here;
https://brainly.com/question/28793582
#SPJ1
in a particular game, a fair die is tossed. if the number of spots showing is either four or five, you score 1 point. if the number of spots showing is six, you score 4 points. and if the number of spots showing is one, two, or three, you score 0. you are going to play the game twice. what is the probability that you score 4 points both times?
1/36 is the probability that you score 4 points both times.It is the likelihood of scoring four points twice.
1/6 * 1/6 =1/36
The probability of an event occurring is measured by its probability. It determines the probability of an event. The probability calculation is P(E) = Number of Favourable Outcomes/Total Outcomes.A game is a formalized form of play that is frequently done for amusement or fun but can also serve as a teaching game tool.
learn more about probabilty from here:
https://brainly.com/question/14210034
#SPJ4
Need some help on this question:
The rule to get from one term to the next in a sequence is
Un+1 = 2Un
If U1=4, work out the values of U2, U3 and U4.
Will mark as Brainliest if correct answer is given. Thanks.
Answer:
8, 16, 32
Step-by-step explanation:
using the recursive formula [tex]U_{n+1}[/tex] = 2[tex]U_{n}[/tex] and U₁ = 4 , then
U₂ = 2 U₁ = 2 × 4 = 8
U₃ = 2 U₂ = 2 × 8 = 16
U₄ = 2 U₃ = 2 × 16 = 32
PLEASE HELP ASAP WILL MARK BRAINLIST
Answer:
what is your problem
9500000000000000 in standard form
What is the equation of the line that passes through the points (-4, -6) and (2, 8)
The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.
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.
A linear equation or function is given as ;
y = mx + c
Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).
The slope of the line passing through (-4, -6) and (2, 8) will be,
m = (8 + 6)/(2 + 4)
m = 14/6
So, y = (14/6)x + c
Substitute, (2, 8)
8 = (14/6)2 + c
c = 8 - 14/3 = 10/3
Therefore, y = (14/6)x + 10/3
Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".
For more about the equation,
brainly.com/question/10413253
#SPJ1
At barlow school ,4/9 of the 873 students are boys at willow school, 2/3 of the 630 are girls which school has the greater number of boys and by how many
Answer:
Barlow School has 178 more boys
Step-by-step explanation:
At Barlow School, 4/9 of 873 students are boys. At Willow School, 2/3 of 630 students are girls. You want to know which school has more boys, and by how many.
Barlow SchoolThe number of boys is ...
4/9 × 873 = 388
Willow SchoolThe 1/3 of students that are not girls are presumed to be boys. That number is ...
1/3 × 630 = 210
DifferenceThe difference in the number of boys is ...
388 -210 = 178
Barlow School has 178 more boys.
50 points
Please help
Graph -8+x=4y-16
Equation of the line - 8 + x = 4y - 16
In order to graph the line, find its x- and y- intercepts, then connect the two pointsx- intercept, at y = 0:
- 8 + x = 0 - 16x = - 16 + 8x = - 8y- intercept, at x = 0:
- 8 = 4y - 164y = 16 - 84y = 8y = 2The points are (0, 2) and (- 8, 0), plot them and connect to get the graph.
The graph that connects points (-8,0) and (02) is shown below
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
-8+x=4y-16
x- intercept, at y = 0:
- 8 + x = 4(0) - 16
x = - 16 + 8
x = - 8
y- intercept, at x = 0:
- 8 + 0 = 4y - 16
4y = 16 - 8
4y = 8
y = 2
The points are (-8,0) and (02)
So, the graph that connects points (-8,0) and (02) is shown below
To know more about Equation on:
https://brainly.com/question/187506
#SPJ1
an equilateral triangle and a regular hexagon have perimeters of the same length. if the area of the triangle is 2 square units, what is the area of the hexagon?
The area of hexagon is found to be 18 square units by using the giving conditions.
What is the equation for calculating a hexagon's perimeter?P = 6a, where an is the length of one of its sides, is the formula for a regular hexagon's perimeter. Here, the hexagon's interior angles are all 120 degrees.
How do you calculate a hexagon's area?The formula for calculating the area of a hexagon is derived from the formula for calculating the area of an equilateral triangle since a regular hexagon is made up of six equilateral triangles. The formula for calculating a hexagon's area is 6([tex]\sqrt{3}[/tex]/4)a² where a is the regular hexagon's side length.Given: The perimeters of an equilateral triangle and a regular hexagon are equal.
We need to find the area of the hexagon.
Let,
x = side of trainagle
a = side of hexagon
3x = 6a
x = 2a
Area of equilateral triangle = ([tex]\sqrt{3}[/tex]/4)x² = 12 square units
Area of hexagon is given as follows:
= 6([tex]\sqrt{3}[/tex]/4)a²
= (6[tex]\sqrt{3}[/tex]/4)(x²/4)
= 12(6)/4
= 18 square units
Therefore, the area of hexagon is found to be 18 square units by using the giving conditions.
Learn more about perimeter of hexagon here:
https://brainly.com/question/28821374
#SPJ4
Cual es la respuesta de:
6(-?)+1=-47
The value of missing number is 8.
What are Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
6(-?)+1=-47
let the unknown value be x.
6(-x ) + 1= -47
Now, Subtract 1 from both side
-6x + 1 - 1= -47 - 1
-6x = -48
x= -48/(-6)
x = 8
Hence, -6(8) + 1 = -47.
Learn more about Integers here:
https://brainly.com/question/15276410
#SPJ1
The kinetic energy of an object is directly proportional to the square of its
velocity.
An airplane with velocity 220 m/s has a kinetic energy of 10,890 megajoules.
What is the kinetic energy of the same airplane when its velocity is 300 m/s?
By using the concept of kinetic energy, it is obtained that
Kinetic energy of the airplane when its velocity is 300 m/s is 20250 megajoule
What is Kinetic energy?
Kinetic energy is the energy possessed by the body by virtue of its motion
If m is the mass of the body and v is the velocity of the body, then kinetic energy is given by the formula
Kinetic energy = [tex]\frac{1}{2} \times m \times v^2[/tex]
Let the mass of the airplane be m kg
Velocity = 220 m/s
Kinetic energy = [tex]\frac{1}{2} \times m \times (220)^2[/tex]
By the problem,
[tex]\frac{1}{2} \times m \times (220)^2 = 10890\times 10^6[/tex]
[tex]m = \frac{10890\times 10^6\times 2}{220\times 220}[/tex]
m = [tex]0.45 \times 10^6[/tex] kg
Now,
Velocity = 300 m/s
Kinetic energy = [tex]\frac{1}{2} \times 0.45 \times 10^6 \times 300 \times 300[/tex]
= [tex]20250 \times 10^6[/tex] J
= 20250 mega joules
To learn more about Kinetic energy, refer to the link-
https://brainly.com/question/25959744
#SPJ13
A 20-sided regular polygon has an angle measure represented as 3gº.
Determine the value of g.
O g = 180
O g=1
O g = 60
O g = 54
The value of g in the 20 sided regular polygon is 54.
How to find the angles of a regular polygon?If all the polygon sides and interior angles are equal, then they are known as regular polygons.
The polygon given is a 20 sided regular polygon and the measure of each angle is 3g degrees.
Therefore, let's find g.
The sum of interior angles of a 20 sided polygon is as follows:
180(n - 2) = 180(20 - 2) = 180(18) = 3240
Therefore,
each angle = 3240 / 20 = 162
Hence,
162 = 3g
g = 162 / 3
Therefore,
g = 54
learn more on regular polygon here: brainly.com/question/16992545
#SPJ1
What is the product?
3 6 1
24 0
0 6 2
x 2 0 1
Answer:
Step-by-step explanation:
Nick starts with 20
20
milligrams of a radioactive substance. The amount of the substance decreases by 12
1
2
each week for a number of weeks,
w
. He writes the expression 20(12)
20
(
1
2
)
w
to find the amount of radioactive substance remaining after
w
weeks.
Autumn starts with 1
1
milligram of a radioactive substance. The amount of the substance decreases by 50%
50
%
each week for a number of weeks,
w
. She writes the expression (1−0.5)
(
1
-
0
.
5
)
w
to find the amount of radioactive substance remaining after
w
weeks.
Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
Each part of Nick's and Autumn's expressions mean can be explained as follows;
Nick;
the amount of substance he begins with = 20the amount of substance left after each week = 1/2Autumn:
The one outside of parentheses = the initial amount of the substance.The one inside of parentheses = 100% of the original amount of the substance.0.5 represents the 50% of the substance that is lost each time periodHow to explain each variable in an expression?ler
Number of weeks = wNick expression:
[tex] {20( \frac{1}{2} })^{w} [/tex]
Where,
the amount of substance he begins with = 20
the amount of substance left after each week = 1/2
If w = 2
[tex] {20( \frac{1}{2} })^{w} [/tex]
[tex]{20( \frac{1}{2} })^{2} [/tex]
= 20(0.25)
= 5 milligrams
Autumn's expression:
[tex] {(1 - 0.5)}^{w} [/tex]
The one outside of parentheses = the initial amount of the substance.
The one inside of parentheses = 100% of the original amount of the substance.
0.5 represents the 50% of the substance that is lost each time period
If w = 2[tex] {(1 - 0.5)}^{w} [/tex]
[tex] {(1 - 0.5)}^{2} [/tex]
= (0.5)²
= 0.25 milligrams
Complete question:
Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligrams of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1-0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
Read more on equation:
https://brainly.com/question/11250752
#SPJ1
Determine the value of the expression −2(42−7)+(−5) .
The value of the expression −2(42−7)+(−5) is -75.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, we want to calculate the value of the expression:
−2(42−7)+(−5)
= -2(35) + (-5)
= -70 - 5
= -75
The value is -75.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
At 61°F, a certain insect chirps at a rate of 99 times per minute, and at 64°F, they chirp 117 times per minute. Write an equation in slope-intercept form that represents the situation.
An equation in slope-intercept form that represents the situation is C(x) = -267 + 6x.
What is the equation in slope intercept form?A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that can slope either upward or downward.
The general form of a linear equation is
y = mx + b
Where:
b = intercept y = dependent variable x = independent variable m = slopeSlope = change in the chirps / change in the temperature
Slope = (117 - 99) / (64 - 61)
Slope = 18 / 3
Slope = 6
99 = a + 6x
99 = a + 6(61)
99 = a + 366
a = 99 - 366
a = -267
C(x) = -267 + 6x
To learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
In the figure alongside, AB⊥BC and a-b =10° then find the value of a and b
Step-by-step explanation:
a-b=10--(1)
Same side interiors(vertical) have sum 180°
a+b=180--(2)
From both equations
2a=190
a=95
And
a-b=10
b=95-10
b=85
In AWXY, WY is extended through point Y to point Z, m/Y W X = (3x + 17)°, m/XYZ = (10z - 5)°, andm/W XY = (3x + 2)°. Find m/W XY.
Using the exterior angle theorem, the measure of angle WXY is calculated as: 20°.
How to Apply the Exterior Angles Theorem?Given the triangle in the image below has the following:
The measure of exterior angle XYZ = (10x - 5)°The measure of remote angle WXY = (3x + 2)°The measure of remote angle YWX = (3x + 17)°According to the exterior angles theorem, the sum of the two remote angles would be equal to the measure of the exterior angles, therefore:
10x - 5 = 3x + 2 + 3x + 17
Combine like terms
10x - 5 = 6x + 19
10x - 6x = 5 + 19
4x = 24
4x/4 = 24/4
x = 6
m∠WXY = 3x + 2 = 3(6) + 2
m∠WXY = 18 + 2
m∠WXY = 20°
Learn more about the exterior angle theorem on:
https://brainly.com/question/24756010
#SPJ1
What is the slope of the line that passes through the points (7,-5) and (16,7) in simplest form ?
Answer:
4/3
Step-by-step explanation:
look for gradientgradient=
[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]
change in y7--5=12
change in x16-7=9
gradient12÷9=4/3
the gradient is the same as slope
thus the answer is 4/3
What is the equation of the line that passes through the point (1, -3) and has a
slope of -3?
The equation of the line is, y = -3x.
What is point slope form of the line?
A line's point slope form equation is y - y1 = m(x – x1). Consequently,
y - 0 = m(x - 0), or y = mx, is the equation of a line passing through the origin with a slope of m.
Let the line passes through the point (1, -3) and having slope of -3.
Consider, the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug, [tex](x_1, y_1) = (1, -3), m = -3[/tex]
So, the above equation becomes
[tex]y-(-3)=-3(x-1)\\y+3=-3x+3\\y=-3x+3-3\\y=-3x[/tex]
Hence, the equation of line that passes through the point (1, -3) and having slope -3 is y = -3x.
To know more about the point slope form of the line, click on the link
https://brainly.com/question/6497976
#SPJ1
what is the probability that at most eight of ten independently selected specimens have a hardness of less than 73.84?
The probability that at most eight of ten independently selected specimens have a hardness less than 73.84 is 0.2639.
Probability:
The chance that a particular event (or set of events) will occur is expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.
Here we have to find the probability:
The probability that each specimen has a hardness less than 73.84 is:
p =Ф( Z< 973.84 - 70)/ 3)
= Ф(Z<1.28 ) = 0.899
P(X<=8) = 1 - P(X=9) - P (X=10)
= 0.2639
So out of 10 specimens, the probability that 8 or fewer have a hardness less than 73.84 is 0.2639
To know more about the probability refer to the link given below:
https://brainly.com/question/13604758
#SPJ4
helppp PLSSSSSSSSSSSSS I NEEED HELPPPPPPPPPPPPPPPPP
Answer:
15c + 19d
Step-by-step explanation:
Here to simplify we have to add like-terms
3c + 14d + c + 11c + 5d = ( 3c + c + 11c) + ( 14d + 5d) = 15c + 19d
Glad to Help