For hi birthday Kameron received 18 toy car. He plan to tart collecting more car and i going to buy 2 more every month. Write the number of car to go with the month 0:18 in ratio form
The ratio of the number of cars to the month's 0:18 is 1:3.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
18 toy automobiles were given to Kameron.
And he intends to begin accumulating more automobiles, planning to purchase two more each month.
Month 0 finds him with 18 automobiles.
At the end of the 18th month, he will possess:
(18 + (218) vehicles = (18 + 36) cars = 54 cars
The ratio of month 0 to month 18 will therefore be as follows:
18:54 = 1:3
HENCE, the ratio form for the number of cars to accompany the month 0:18 is 1:3.
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what is the rate of change for the equation y = 2x+ 40
Answer: 2
Step-by-step explanation: When we talk about rate change, we are talking about the slope!
The slope is 2x which means the rate change is rise 2 and run over 1.
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If x – y = 6 and x is twice the value of y, what is the value of x + y ?
Answer:
18
Step-by-step explanation:
x - y = 6
Given: 2x - x = 6 since x is twice the value of y.x = 6
2x = 6 · 2 = 12
12 + 6 = 18
x is twice the value of y can be written as:
x= 2y
then we replace x with 2y in the given equation
x - y = 6
2y - y = 6
y = 6
then to find x we replace y with 6 in either of the equations
x = 2y
x = 2(6) = 12
or
x - 6 = 6
x= 6 + 6 = 12
now find value if x + y
12 + 6 = 18
Please help me i have no clue how to do this thanks
The weights of Alma and Bella are in the ratio 5:7 respectively.
When they sit 18 feet apart on a seesaw how far from the fulcrum must Alma sit
in order to balance the seesaw
Alma should sit 7.5 feet apart from the fulcrum, In order to balance the seesaw.
What is Ratio ?
A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons.
Given, The weights of Alma and Bella are in the ratio 5:7 respectively.
∴ Alma's weight = 5/12 and Bella's weight = 7/12.
they are sitting 18 feet apart on a seesaw.
It means the distance between Alma and Bella is 18 feet.
Now, Alma should sit feet far from the fulcrum in order to balance the seesaw :
= Distance between Alma and Bella × Weight of Alma
= 18 feet × 5/12
= 7.5 feet.
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A minivan is traveling at 80.5 kilometers per hour. Cargo is strapped to the roof at a height of 1.75 meters. The car hits a concrete barrier, and the cargo is ejected from the roof. Use the following two equations to determine how long it takes for the cargo to hit the ground and how far it travels in the horizontal direction. Let y represent height in meters, x represent horizontal distance in meters, and t represent time in seconds. Equation 1: y = -4.9t2 + 1.75 Equation 2: y = -0.0081x2 + 1.75
The time taken for the cargo to hit the ground will be 0.6 seconds and it travels in the horizontal direction for around 14.69 feet.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
The calculations are attached in images.
To calculate t we will use that is y because at the moment of cargo will have a height 0, so we get,
= −4.9t² +1.75
-1.75=-4.9t²
t²=-1.75/-4.9
t²=√0.3571
=0.6 seconds
Now we will calculate x, then y = 0
because since the cargo will be on the ground it will no have height, so
0= -0.0081x²+1.75
-1.75 =-0.0081x²
x²=-1.75/-0.0081
x= √216.04 = 14.69 feet
It will take the cargo 0.6 seconds to hit the ground, and it will travel 14.69 feet in a horizontal direction.
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given the equation y = 3x, complete the table of values.
(just give me the output numbers)
given the equation y = 3x, complete the table of values.
x = -2
y = 3x
y = 3(-2)
y = -6
______________________
x = -1
y = 3x
y = 3(-1)
y = -3
______________________
x = 0
y = 3x
y = 3(0)
y = 0
______________________
x = 1
y = 3x
y = 3(1)
y = 3
______________________
x = 2
y = 3x
y = 3(2)
y = 6
______________________
suppose the roots of the equation 2x 2 − 5x − 6 = 0 are α and β. without explicitely solving for the roots, find the quadratic equation with roots 1 α and 1 β
The quadratic equation with the roots 1/α and 1/β using the given equation is equal to
As given in the question,
Given equation is:
2x²−5x−6=0
Roots of the given equations are α and β
Compare with standard quadratic equation:
ax² + bx + c = 0
a = 2 , b= -5 , c = -6
Sum of the roots are:
α + β = -b/a
= -( -5/2)
= 5/2
Product of the roots
αβ = c/a
= -6/2
= -3
Now ,
( α + β )/ αβ = (5/2) / -3
⇒1/ β + 1/α = -5/6
⇒ 1/α + 1/β = -5/6
And ,
1/αβ = -1/3
Quadratic equation with roots 1/α and 1/β is given by:
x² - ( 1/α + 1/β)x + 1/αβ =0
⇒x² - (-5/6)x + (-1/3) = 0
⇒x² + (5/6)x -(1/3) =0
Therefore, the quadratic equation with roots 1/α and 1/β is equal to
x² + (5/6)x -(1/3) =0
The complete question is :
Suppose the roots of the equation 2x²−5x−6=0 are α and β.Find the quadratic equation with roots 1/α and 1/β.
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there are 3 seniors and 15 juniors in mrs. gillis’s math class. three students are chosen at random from the class. a. what is the probability that the group consists of a senior and two juniors? b. if the group consists of a senior and two juniors, what is the probability that stephanie, a senior, and jan, a junior, are chosen?
a) is 0.386 and of b) is 0.017
What is Probability?
One use of probability theory is calculating the odds that experiments will succeed or fail. Probabilities can be used to determine, for example, the possibility of flipping a coin and obtaining heads or tails, or the likelihood of making a research error. Understanding the formula for estimating probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together, is essential to understanding this area of mathematics.
Given that:
no of seniors = 3
no of juniors = 15
a) probability that a group consist of a senior and two juniors:
[tex]=\frac{^{3} C_{1} *^{15} C_{2 }}{^{18} C_{3}}\\\\=\frac{3 * 105}{316} \\\\=0.386[/tex]
b) if the name of a student given then there is only one way to select it
For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by [tex](^{14}C_{1} =14)[/tex] different ways.
[tex]=\frac{1 *1*{^{14} C_{1}}}{^{18} C_{3}}} \\\\= \frac{14}{316} \\\\= 0.017[/tex]
Hence, The answer of a) is 0.386 and of b) is 0.017
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nic and tim each purchased one raffle ticket. if a total of 10 raffle tickets are sold and two winners will be selected, what is the probability that both nic and tim win?
The probability of both Nic and Tim winning the raffle at the same time is 1/100.
Probability is a mathematical measurement of a likelihood of an event to happen. Given that both Nic and Tim each purchase one raffle ticket out of 10 tickets and that there will be two winners selected, the odds of either Nic or Tim winning the raffle out of 10 ticket is 1/10.
Since the odds of either Nic or Tim winning the raffle ticket is 1 out of 10 or 1/10, we can then calculate the mathematical probability of two events occurring at the same time with a multiplication rule formula as follows:
1/10×1/10=1/100
Hence, the odds of both Nic and Tim winning at the same time is 1 out of 100 or 1/100.
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question content area top part 1 in a fraternity with 36 members, 18 take mathematics, 5 take both mathematics and art history, and 8 take neither mathematics nor art history. how many take art history but not mathematics?
With the help of set relation and function the number of members taking art history but not mathematics is 12
what is set ?
Sets are collections of clearly defined objects, relations show the connections between the elements of two sets A and B, and functions are a special kind of relation where each element in A has exactly one relationship (or no more than one) with an element in B.
solution:
Total members (A + B + C + D)= 38
B + C = 18
C = 5
A = 8
Work from the end to the beginning:
A = 8
C = 5
B = 13 [from clues 3 and 2]
D = 12 [use clue 1 and above info]
Therefore, The member of taking art history but not mathematics D = 12
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a rectangle has perimeter 52 km, and its area is 165 sq-km. find the dimensions of this rectangle. (for purposes of this problem only, the width is shorter than the length.)
The dimensions of the rectangle: length = 15 km and width = 11 km
Let l be the length of rectangle and w be the width of the rectangle.
A rectangle has perimeter 52 km
Using the formula of the perimeter of rectangle we get an equation,
2(l + w) = 52 ............(1)
And its area is 165 sq-km.
Using the formula of the area of rectangle we get an equation,
l * w = 165 ............(2)
From equation (1),
l = 26 - w
Subatitute above value of l in equation (2),
(26 - w) * w = 165
26w - w² = 165
w² - 26w + 165 = 0
(w - 15)(w - 11) = 0
w = 15 or w = 11
For w = 15,
l = 26 - 15
l = 11
For w = 11,
l = 26 - 11
l = 15
But as we know, the length of rectangle is always greater than the width,
l = 15 and w = 11 is true .
Therefore, the length of rectangle = 15 km and width of rectangle = 11 km
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How many 4-digit numbers can be formed if the number must be divisible by 2 and digits can be repeated?
Answer:
4500
Step-by-step explanation:
This can be solved in more than one way. One method is to use permutations and see which digits can appear how many times in which position in the possible list of even numbers between 1000 and 9999
However, I think approaching this from an arithmetic progression perspective is easier to explain.
An arithmetic progression or sequence is a sequence of numbers such that there is a common difference between consecutive numbers.
For example, 2, 4, 6, 8, 10... is an arithmetic sequence with a common difference.
Given the first term in the sequence, we can find the nth term using the formula:
[tex]a_n = a_0 + (n-1)\cdot d[/tex]
where
[tex]a_n[/tex] is the nth term,
[tex]a_0[/tex] is the first term
[tex]d[/tex] is the common difference
Treating the even numbers from 1000 to 9999 as an arithmetic sequence, we get the following:
[tex]a_0 = 1000[/tex]
[tex]a_n = 9998[/tex] (since the last number has to be even
[tex]d = 2[/tex]
Let [tex]n[/tex] be the number of possible values
Plug this into the formula and solve for [tex]n[/tex]
9998 = 1000 + (n-1)2
9998 = 1000 + 2n - 2
9998 = 998 + 2n
9998-998 = 2n
9000 = 2n
Switch sides:
2n = 9000
Divide by 2 to get
n = 9000/2 or
n = 4500
Giselle’s father is 3 times as old as her. After 10 years his age will be 5 more than twice her age. Which equation can be used to find Giselle’s age?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equation that can be used to find Giselle's age is
3x + 10 = 5 + 2 (x + 10)
Giselle's age is 15 years.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Giselle's age = x
Father age = 3x
Now,
After 10 years his age will be 5 more than twice her age.
This can be written as,
3x + 10 = 5 + 2 (x + 10)
Solve for x.
3x + 10 = 5 + 2x + 20
3x - 2x = 5 + 20 - 10
x = 15
Thus,
The equation that can be used to find Giselle's age is
3x + 10 = 5 + 2 (x + 10)
Giselle's age is 15 years.
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(Angle Relationships
Which angle is supplementary to LPM?
O. KPL
NPI
ONPL
OMPN
44. 2 80. 2
55. 6
P
124. 4°
55. 6°
The ∠MPN is supplementary to ∠NPI.
What is the supplementary angles?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because the sum of 130° and 50° is equal to 180°.
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, The ∠MPN is supplementary to ∠NPI.
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Note : Given question is incomplete, the complete question is:
Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
three points are chosen randomly and independently on a circle. what is the probability that all three pairwise distances between the points are less than the radius of the circle?
The probability that all three pairwise distances between the points are less than the radius of the circle is 1/12.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Since it doesn't matter where the first point is picked, it can be placed anywhere on the circle.
The following point must be within an arc of 60 degrees on either side, providing a total of 120 degrees and a chance of 1/3. The final point must be situated within 60 degrees of the first two.
If the first two points are apart by 60 degrees, the third point can be placed within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6. If the first two points are the same, the third point can be placed with a maximum degree of freedom of a 120 degree arc and a 1/3 probability.
The chance changes linearly with increasing distance from the first point, up to a maximum of 60 degrees.
As a result, we may find 1/4, the average likelihood we can position the third point based on a fluctuating second point, by averaging the probabilities at either end.
Total probability is 1 × 1/3 × 1/4 = 1/12.
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The portions of gold in three bracelets are shown. Which bracelet has the highest portion of gold? A. 62% B. 3/5 C.0.65
The portion of gold in three bracelets that are shown. The bracelet that has a portion of gold is 0.65. The correct option is c.
What is gold?Gold is actually a very soft metal. Rings constructed of pure gold would bend and disfigure over time. Other elements are added to strengthen the ring. 100% gold is far too soft and far from as durable as it should be.
Gold is a pure element. It is found in the earth's crust when making jewellery from gold, and some other metals like copper or silver is mixed with it.
Therefore, the correct option is c. 0.65.
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A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least one of each type.
(a) Give an interval (a, b) such that (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?
a= μ-3.16*σ , b= μ+3.16*σ if each fish caught is equally likely to be any one of these 4 distinct types.
What is meant by Chebyshev inequality?Chebyshev's inequality is a probability theory that ensures that, over a vast range of probability distributions, no more than a particular proportion of values would be present within a selected limits or range as from mean. In other words, only a certain fish caught will be discovered within a given range of the distribution's mean.
The formula for which no more than a particular number of values can exceed is 1/K2; in other words, 1/K2 of a distribution's values can be more than or equal to K standard deviations away from the distribution's mean. Furthermore, it asserts that 1-(1/K2) of a distribution's values must be within, but not include, K standard deviations of the distribution's mean.
How to solve?
from Chebyshev's inequality for Y
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
where
Y = the number of fish that need be caught to obtain at least one of each type
μ = expected value of Y
σ = standard deviation of Y
P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean
k= parameter
thus for
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16
then
P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
using one-sided Chebyshev inequality (Cantelli's inequality)
P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)
P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ
then for
P(Y≥ μ+3*σ ) ≥ 0.90
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USE MODELS Immediately after take-off, a jet plane consistently climbs 20 feet for every 40 feet it moves horizontally. The graph shows the trajectory of the jet.
The slope-intercept equation that represents the proportional relationship in this problem is given as follows:
y = 0.5x.
How to obtain the equation?The slope-intercept representation of a linear function is defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the rate of change of the function.b is the y-intercept of the function.A proportional relationship is a linear function with an intercept of zero, hence the equation is defined as follows:
y = mx.
The variables in this problem are given as follows:
Variable x: horizontal movement.Variable y: vertical movement.The plane consistently climbs 20 feet for every 40 feet it moves horizontally, hence the slope is obtained as follows:
m = 20/40
m = 0.5.
As the slope is given by the vertical movement divided by the horizontal movement, and hence the equation is given as follows:
y = 0.5x.
Missing InformationThe problem asks for the slope-intercept equation that represents the proportional relationship in this problem.
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the ratio of buses to cars entering the lot was 2 to 11. if 650 vehicles entered the lot altogether. how many were cars?
The number of cars were are, 550.
What is Vehicle?
A device, typically with wheels and an engine, used to move people or things, particularly on land: Yesterday evening, a truck driver was killed when his car flipped over. Buses, trucks, and other road vehicles are included. A farm vehicle is a tractor.
Wagons, bicycles, motorized (cars, trucks, buses, mobility scooters for the disabled), railed (trains, trams), amphibious (screw-propelled, hovercraft), watercraft, and aircraft are all examples of vehicles (airplanes, helicopters, aerostats)
The ratio of buses to cars entering the lot was 2 to 11.
650 vehicles entered the lot altogether.
Base on the given information,
650 x 11 ÷ (2 + 11)
Simplifying,
7150 ÷ 13
⇒ 550
Hence, the number of cars were are, 550.
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how many ways are there to pick five people for a committee if there are six (different) men and eight (different) women and the selection must include at least one man and one woman?
The number of ways there to pick five people for a committee is if there are six men and eight women, and the selection must include at least one man and one woman 1940.
What is the combination?
Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.
There are 6 different men and 8 different women.
The committee must include at least 1 man and 1 woman.
Thus let us first see the possible cases where this condition does not satisfy.
We select 5 men and no women = (6C5)(8C0) = (6)(1) =6
We select 5 women and no men = (8C5)(6C0) = 56
Total no.of possibilities of selecting 5 people in any way = 14C5 = 2002
So the no.of possibilities with at least 1 man and 1 woman = 2002 - 6 - 56 = 1940.
Hence, the number of ways there to pick five people for a committee is if there are six men and eight women, and the selection must include at least one man and one woman 1940.
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an inverted cylindrical cone, 44 ft deep and 22 ft across at the top, is being filled with water at a rate of 11 ft3/min. at what rate is the water rising in the tank when the depth of the water is:
The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
Explain the term rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.The rate of change of volume is-
dV/dt = 11 ft3/min.
Volume of cylindrical cone = (1/3)πr²h
As we're trying to find dh/dt, we need to calculate the volume within terms of just one variable, h.
Diameter = 22 ft
Thus, radius is 11 ft
By using height and radius of a water in the tank, we may calculate h using similar ratios.
11/44 = r/h
1/4 = r/h
r= h/4
Put into volume;
V = (1/3)π(h/4)h²
V = (1/3)(π)h³ / (16)
dV/dt = [(1/3)(3)(π)(h)² / 16](dh/dt)
V = [(π)(h)² / 16](dh/dt)
Solve for (dh/dt) ;
dh/dt = (dV/dt)(16) / [((π)(h)²]
Now, the change in volume is dV/dt = 11 ft³/min
dh/dt = (11 ft³/min)(16) / [((π)(h)²]
For h = 1 ft,
dh/dt = (11 ft³/min)(16) / [((π)(1 ft)²]
dh/dt ≈ 56.05 ft/min
Thus, the rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
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An arrow is shot with an initial upward velocity of 100 feet per second from a height of 5 feet above the ground. The equation h= -16t^2 + 100t + 5 models the height in feet t seconds after the arrow is shot. After the arrow passes its maximum height, it comes down and hits a target that was placed 20 feet above the ground. About how long after the arrow was shot does it hit its intended target?
Since the question specified that the arrow had to reach the height only after reaching its maximum altitude, then the only correct answer is 6.096 seconds.
What is the equation referred to as?A mathematical expression with the equals sign is referred to as an equation. Algebra is frequently used in equations. When performing calculations but not knowing the precise number, algebra is used.
Give,
[tex]20 = -16t^{2} + 100t + 5[/tex]
[tex]= > -16t^{2} + 100t - 15 = 0[/tex]
[tex]= > t = \frac{-100 ± \sqrt{100^{2} - 4(-15)(-15) } }{2(-16)} \\\\= > t = \frac{-100 ± \sqrt{9040} }{-32} \\\\Here, \sqrt{9040} = 4\sqrt{565} \\ \\= > t = \frac{-100 ± \ 4sqrt{565} }{-32} \\\\= > t = \frac{-25 ± \ sqrt{565} }{-8} \\\\= > t_{1} = 6.096 sec \\ = > t_{2} = 0.154 sec[/tex]
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It says that Complete the pattern and find the rule and I haven't done this in a really long time so I kind of just like forgot how to do it so that's why I'm asking for your help so I really need this for my grade
The pattern of the value is given as aₙ = 2aₙ₋₁, where n is a set of natural numbers,
Given that,
We have to determine the pattern of the given series of numbers.
Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
Given series,
2, 4, 8,16, 32, .... so on
From observation, it is to be determined that each proceeding value is twice the previous value.
So,
The pattern is given as,
aₙ = 2aₙ₋₁
Thus, the pattern of the value is given as aₙ = 2aₙ₋₁, where n is a set of natural numbers,
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how to find the points?
As described in the analytic geometry, the points are(1.1, -5 )
What is analytic geometry?The area of algebra known as analytical geometry uses an ordered pair of numbers known as coordinates to determine the position of a point on a plane. It is utilized to model many plane objects, including points, lines, and others. The terms Coordinate geometry and Cartesian geometry are both used to refer to analytical geometry.
We have to locate the point where the line is through the x line and y line coordinates
Therefore the point is (1.1, -5 )
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Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y = -5 x=3
Answer: Perpendicular
Reason:
y = -5 is horizontal
x = 3 is vertical
A horizontal line is always perpendicular to a vertical line. The two lines form a 90 degree angle.
11. If two million is the dividend and two hundred is the LE divisor, what is the quotient?
Answer:
bacon sotda
Step-by-step explanation:
I remember thejnwnenenenensenenenejee
Of the 52 plays attributed to a playwright, 19 are comedies, 19 are tragedies, and 14 are histories. If one play is selected at random, find the odds against selecting a tragedy.
There are 19 tragedies out of 52 plays, so the probability of selecting a tragedy is 19/52. Therefore, the odds against selecting a tragedy are 33/52
What is meant by Probability?Probability is a way of selecting how likely something random is to happen. It is a mathematical idea that is used to estimate the probability of an event occurring given a collection of circumstances or results. Probability is commonly expressed as a fraction or decimal, with a value of 1 representing an event that is certain to occur and a value of 0 representing an event that is impossible to occur. In order to generate predictions and to assist in making decisions based on the possibility of various events, probability might be utilized. It is a crucial instrument in a variety of disciplines, such as physics, economics, and statistics.
How to solve?
probability of selecting a tragedy = 19/52.
The odds against selecting a tragedy = 1 - 19/52 = 33/52
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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 25 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
The measure of the largest angle of the triangle is 93°, while the measure of the smallest and the third angle is 31° and 56° respectively. Considering that the measure of the third angle is 25 degrees more than that of the smallest angle.
Sum of interior angles of a triangleIn any given triangle, the sum of its interior angles is equal to 180°.
Let the smallest angle be represented by x, so that the other angles are 3x and x + 25.
thus
x + 3x + x + 25 = 180° {collect like terms}
5x + 25° = 180°
5x + 25° - 25° = 180° - 25° {subtract 25° from both sides of the equation}
5x = 155°
x = 155°/5 {divide through by the coefficient of x}
x = 31°
thus the other angles are derived by substituting the value 31° for x as follows;
3(31) = 93°
31° + 25° = 56°
Therefore, the largest angle of the triangle 93°, the smallest angle is 31° and the measure of the third angle is 56°.
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Which of these fractions will always result in a terminating decimal no matter what the whole-number numerator is?
A ?/9
B ?/200
C ?/60
D ?/120
Answer:
B
So convert the number over 200