what is the answer for ¼ +6 ⅓
Answer:
Step-by-step explanation: ¼ +6 ⅓;
= [tex]\frac{1}{4}[/tex] +[tex]\frac{19}{3}[/tex];
= [tex]\frac{3+76}{12}[/tex];
= [tex]\frac{79}{12}[/tex];
= 6[tex]\frac{7}{12}[/tex]
Step-by-step explanation:
Well to add fractions, you should make the denominator (denominator means the lower part for example 4 in ¼) the same for all numbers.
Forget the 6 for now, take only ¼ and ⅓ into consideration, make it have the same denominator
For 1/4 you multiply both up and down by 3 so it will become 3/12
For 1/3, multiply both by 4, so it becomes 4/12
You now have 3/12 and 4/12, let's not forget about the 6 now.
How do you obtain 6 if you have to make 12 denominator? (If you do 12×6 you get 72 right?) so 6 = 72/12
Your answer will be obtained like this
1/4 + 6 + 1/3 = 3/12 + 72/12 + 4/12 = 79/12 and you can make it a whole number if you can.
Ans : 79/12 which is also equal to 6 and 7 over 12 (6 7/12)
and with a solution pls thanks
Answer:
you didn't say which process to use while solving so I have used graphical method but I hove it's useful
Find g(x), where g(x) is the translation 3 units left of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
We can conclude after answering the provided question that Therefore, function g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.
what is function?In mathematics, a function appears to be a connection between two sets of numbers in which each member of one set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from a set and produces output from another. The variable x has now been frequently sometimes used represent the inputs, and the flexible y is used to represent the outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 represents a linear model in which each x-value yields a unique value of y.
So, g(x) = f(x + 3) = (x + 3)² = x² + 6x + 9.
g(x) = x² + 6x + 9
= 1(x² + 6x + 9)
= 1(x² + 6x + 9 + 9 - 9)
= 1((x + 3)² + 9 - 9)
= 1(x + 3)² + 0
Therefore, g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.
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From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (show working too)
The area of remaining sheet is 536 cm²
Since, we know that the area of circle [tex]=\pi \times r^2[/tex]
Area of bigger circle [tex]=\dfrac{22}{7} \times14\times14[/tex]
[tex]=44\times14[/tex]
[tex]=616 \ \text{cm}^2[/tex]
Thus, the area of bigger circle is 616 cm²
Similar way, the area of 2 smaller circles [tex]=2\pi r^2[/tex]
[tex]=2\times\dfrac{22}{7} \times3.5\times3.5[/tex]
[tex]=44\times0.5\times0.5[/tex]
[tex]=77 \ \text{cm}^2[/tex]
Thus, the area of 2 smaller circle is 77 cm²
[tex]\text{Area of rectangle}=\text{Length}\times\text{Breadth}[/tex]
[tex]=3\times1=3 \ \text{cm}^2[/tex]
Thus, the area of rectangle is 3 cm²
Now, remaining area of sheet = Area of bigger circle − Area of both smaller circle − Area of rectangle
[tex]=616-77-3=536 \ \text{cm}^2[/tex]
Hence, area of remaining sheet is 536 cm²
1. The ball bin at the local pizza shop has
3,600 balls. Jamie randomly grabbed 20 balls and
threw them out of the bin. The results are in the
table below. How many of each color do you
predict are in the bin?
Blue
4
Red
6
Green
2
Orange
3
Yellow
5
There are approximately 720 blue balls, 1080 red balls, 360 green balls, 540 orange balls, and 900 yellow balls in the bin.
How many of each color do you predict are in the bin?To predict how many of each color are in the bin, we can assume that the ratio of each color in the bin is the same as the ratio in the sample of 20 balls.
First, we calculate the total number of each color in the sample:
Blue: 4 balls
Red: 6 balls
Green: 2 balls
Orange: 3 balls
Yellow: 5 balls
Next, we calculate the total number of balls in the sample:
4 + 6 + 2 + 3 + 5 = 20
Now, we can set up proportions to estimate the number of each color in the bin:
Blue: (4/20) * 3600 = 720
Red: (6/20) * 3600 = 1080
Green: (2/20) * 3600 = 360
Orange: (3/20) * 3600 = 540
Yellow: (5/20) * 3600 = 900
Therefore, we predict that there are approximately 720 blue balls in the bin.
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For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one-to-one, give an example showing why.
(a) Let A be defined to be the set {1, 2, 3, 4, 5, 6, 7, 8}. f: P(A) → P(A). For X ⊆ A, f(X) = A-X. Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A. Prove with a proof.
(b) A = {a, b, c}, h: P(A) → P(A). For X ⊆ A, h(X) = X ⊕ {a}.
the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
To determine if the function f: P(A) → P(A), where f(X) = A-X, is onto, one-to-one, neither, or both, we need to consider the following:
Onto: A function is onto if every element in the codomain has a corresponding preimage in the domain. In other words, for every Y in P(A), there exists an X in P(A) such that f(X) = Y.
Let Y be any subset of A. Then, we need to find an X such that f(X) = Y. Since f(X) = A-X, we need to find an X such that A-X = Y. Solving for X, we get X = A-Y. Therefore, we can choose X = A-Y, and we have f(X) = A-(A-Y) = Y. Hence, f is onto.
Next, we need to prove that f is not one-to-one. To do this, we need to find two different sets X1 and X2 such that f(X1) = f(X2).
Hence, the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.
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What is the smallest number of cars that can tailgate in a straight line at a football game so that one car is in front of two cars,one car is behind two cars,and one car is in between 2 cars ?
Answer:
The smallest number of cars that can tailgate in a straight line at a football game is 12.
Step-by-step explanation:
Smallest Tailgate Cars Number
This can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.
This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.
Answer:
3
Step-by-step explanation:
basicly one car will be in the back one in the middle and one in the front. if I'm correct then it should be 3
what is the value of 63,798 divided by 49?]
Answer:
1302
Step-by-step explanation:
Use the Standard Normal Table or technology to find the Z-score that corresponds to the following cumulative area.0.952
The cumulative area corresponds to the z-score is 1.67
What is the cumulative area?
The likelihood that a real-valued random variable, X, will assume a value less than or equal to x is represented by the cumulative distribution function of X, or simply by the distribution function of X, assessed at x.
Here, we have
Given: the following cumulative area is 0.952.
We have to find the Z-score that corresponds to the following cumulative area.
p(z<z)=0.952
p(z<1.67)=0.952
z=1.67 (from the standard normal table)
Hence, The cumulative area corresponds to the z-score is 1.67
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6.In a survey, it was found that 62 families bought milk in the following quantities in a p articular month. 19 16 22 9 9 6 12 10 23 14 23 25 22 17 18 23 8 24 16 18 7 7 33 13 24 20 21 10 5 30 23 34 22 37 16 14 18 13 11 36 17 19 28 20 22 21 32 21 31 39 25 24 29 15 27 17 21 12 20 28 26 15
A. Construct grouped frequency distribution for the above data.
B. Draw histogram, frequency polygon, less than and more than cumulative freq uency curve
A. To construct a grouped frequency distribution for the given data, we first need to determine the range of the data:
Range = Maximum value - Minimum value
Range = 39 - 5
Range = 34
Next, we need to decide on the width of each class interval. A common rule is to choose the number of classes to be between 5 and 20, and then choose a class width that is a convenient number. In this case, we will choose 8 classes and a class width of 5.
Class width = Range / Number of classes
Class width = 34 / 8
Class width ≈ 4.25
We can round up the class width to 5 to get a convenient number. The class intervals are:
5 - 9.99
10 - 14.99
15 - 19.99
20 - 24.99
25 - 29.99
30 - 34.99
35 - 39.99
40 - 44.99
Next, we count the number of observations that fall into each class interval. This gives us the frequency of each interval. The grouped frequency distribution is:
Class Interval Frequency
5 - 9.99 5
10 - 14.99 8
15 - 19.99 9
20 - 24.99 16
25 - 29.99 7
30 - 34.99 6
35 - 39.99 1
40 - 44.99 0
B. To draw the histogram, frequency polygon, and cumulative frequency curves, we first need to calculate the cumulative frequencies. The less than cumulative frequency is the running total of the frequencies up to each class interval, while the more than cumulative frequency is the running total of the frequencies from each class interval to the end.
Class Interval Frequency Less than Cumulative Frequency More than Cumulative Frequency
5 - 9.99 5 5 62
10 - 14.99 8 13 57
15 - 19.99 9 22 49
20 - 24.99 16 38 40
25 - 29.99 7 45 24
30 - 34.99 6 51 17
35 - 39.99 1 52 11
40 - 44.99 0 52 10
Now we can draw the graphs:
Histogram:
20 |
| __
| | |
| __ | |
| | | | |
| | | | |
| | | | |
|___|__|___|__|__
5 10 15 20
Frequency polygon:
25 |
| __
| | | __
| | | | |
| | | | |
| | |
Divide f(x) by d(x). Your answer
should be in the following format:
f(x) = Q(x) +
R(x)
d(x)
f(x) 3x³ + 20x² + 3x + 6
d(x)
x+7
R(x) = [?]
The quotient using a synthetic method of division is 3x² - x + 10 - 64/(x + 7)
How to evaluate the quotient using a synthetic methodThe quotient expression is given as
(3x³ + 20x² + 3x + 6) divided by x + 7
Using a synthetic method of quotient, we have the following set up
-7 | 3 20 3 6
|__________
Bring down the first coefficient, which is 3:
-7 | 3 20 3 6
|__________
3
Multiply 3 by -7 to get -21, and write it below the next coefficient and repeat the process
-7 | 3 20 3 6
|____-21__7_-70____
3 -1 10 -64
So, the quotient is 3x² - x + 10 and the remainder is -64
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The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
Let x= the number of busses and y= the number of vans
Create an equation representing the number of vehicles needed.
Preview Change entry mode
Create an equation representing the total number of seats in vehicles for the orchestra members.
The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.
The system of equations to find the smallest number of busses the orchestra can rent is,
The total number of buses :
b + v ≤ 6
The total number of passengers.
25b + 12v ≥ 111 - - - - (2)
Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
for the following exercise, consider the following scenario: the weight of a newborn is 11 pounds. the baby gained one-half pound a month for its first year. find the linear function that models the baby's weight, w , as a function of the age of the baby, in months, t .
w(t) = _____
The linear function that models the baby's weight, w, as a function of the age of the baby, in months, t, is equals to the w(t) = 11 + (1/2)t.
The a straight line graph represents linear function. The linear function form is, y = f(x) = a + bx. It has an independent variable and a dependent variable. There is independent and dependent variables are x and y respectively. We have provide a scenario which consists the following informations,
The weight of new born baby = 11 pounds
The weight gained by new born baby in one month = 1/2 pounds
We have to determine a linear function which models the baby's weight (w pounds), as a function of the baby's age, in months (t). From the definition of linear function, we see here weight of baby is an dependent variable and month in first year is independent. So, the linear function of weight of baby is written as w(t) = 11 + (1/2)t , where t represents months in baby's first year. Hence, required function is w(t) = 11 + (1/2)t.
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Find the experimental probability that only 1 of
4 children in a family is a boy.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT HTTH TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
Experimental Probability = [?]%
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In which of the following scenarios will conducting a paired
-test for means be appropriate? CHECK ALL THAT APPLY.
A. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.
B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.
C. To test if the mean annual income of Ontarians is higher than that of British Columbians.
D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.
E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.
F. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
G. None of the above
The appropriate scenario to conduct a paired t-test for means is when we have two related samples, and we want to test whether there is a significant difference in the means between the two samples. Hence, B, D, and E are the appropriate responses.
What is a t-test?A t-test is a statistical test used to determine whether two sets of data are significantly different from each other, based on their means. It is a parametric test, meaning it makes certain assumptions about the data, such as that it is normally distributed and that the variances of the two groups being compared are equal.
There are several types of t-tests, including the independent samples t-test, which is used when comparing two groups that are not related to each other, and the paired samples t-test, which is used when comparing two groups that are related or paired, such as before-and-after measurements from the same individuals.
B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.
D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.
E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.
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48. Graph the vertical line x = -2. Then name its intercept.
Answer:
There is no y intercept because the graph does not cross the y axis.
The x intercept is (-2,0)
Step-by-step explanation:
Helping in the name of Jesus.
Tests show that the lives of light bulbs are
normally distributed with a mean of 750 hours
and a standard deviation of 75 hours. Find
the probability that a randomly selected light
bulb will last between 750 and 900 hours.
675 750 825 900 975
P = [? ]%
Hint: use the 68 - 95 - 99.7 rule.
525 600
Enter
Therefore, the probability that a randomly selected light bulb will last between 750 and 900 hours is 0.4772, or 47.72%.
What is deviation?
The degree to which anything deviates from a norm or expected value is referred to as its deviation. The deviation of a collection of data from the average or mean value in statistics is a measurement of how dispersed the data are. Absolute deviation and standard deviation are the two different types of variance.
We may determine that, according to the 68-95-99.7 rule, 68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations.
Here, we're trying to determine the likelihood that a randomly chosen light bulb would live between 750 and 900 hours. One standard deviation to two standard deviations above the mean define this range.
First, we need to standardize the values using the formula:
z = (x - μ) / σ
where x is the value, we want to standardize, μ is the mean, and σ is the standard deviation.
For x = 750
z = (750 - 750)/75 = 0
For x = 900
z = (900 - 750)/75 = 2
Now we need to find the area under the standard normal distribution curve between z = 0 and z = 2. We can use a table or calculator to find this area, which is approximately 0.4772.
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Complete question:
Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 750 and 900 hours.
525, 600, 675, 750, 825, 900, 975.
What will be the value of P = [? ]%
Hint: use the 68 - 95 - 99.7 rule.
pls help fast!! 47 Points and Brainliest!
Answer:
a) (720 - 12xp) p
b) (960 - 17xp) p
Step-by-step explanation:
240 pence = 1 pound
Eliot's change
= 240x3 - (x × 12p)
= 720 - (x × 12p)
= 720 - 12xp
Maya's change
= 240 x 4 - ( x × 17p)
= 960 - ( x × 17p )
= 960 - 17xp
f(x)-x^2+10x-22
What is the y-intercept of this quadratic function
The y intercept of this quadratic equation is (0, -22)
How do functions work?Any subset of a Cartesian product is a relation.
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B. Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set). As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A graph, which is a collection of all ordered pairs (x, f (x)), is the only way to represent a function.
As you can see from these definitions, every function is a relation to X.
To find the y intercept, set x =0 and solve for y
f(0)=-0²+10×0-22
= -22
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Find the distance covered by a wheel of radius 1.4 m, if it makes 250 revolutions. show working too
Answer:
The distance covered by a wheel is given by the formula:
distance = circumference of the wheel x number of revolutions
The circumference of the wheel can be found using the formula:
circumference = 2πr
where r is the radius of the wheel.
Substituting the given values, we get:
circumference = 2π(1.4) = 2π(1.4) = 2(22/7)(1.4) = 8.8 meters
Therefore, the distance covered by the wheel in 250 revolutions is:
distance = 8.8 x 250 = 2200 meters
So, the wheel covers a distance of 2200 meters if it makes 250 revolutions.
Answer:
[tex]\text{Radius} = 1.4 m[/tex]
[tex]\text{Distance covered in One revolution} = 2\pi r[/tex]
[tex]2\pi r =[/tex]
[tex]2\times22=\dfrac{1.4}{7}[/tex]
[tex]= 8.8 \ \text{m}[/tex]
[tex]\text{Distance covered in 250 revolutions}[/tex]
[tex]= 8.8 \ \text{m}\times 250[/tex]
[tex]\bold{= 2200 \ m}[/tex]
[tex]\it{Hope \ this \ is \ the \ answer \ you \ were \ looking \ for.}[/tex]
cos(3x - 180°)=ー√3/2, where 0 < x180°
Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
cos(3x - 180°) = cos(180° - 3x)
cos(180° - 3x) = -√3/2
-cos(3x) = -√3/2
cos(3x) = √3/2
3x = π/6
x = π/18
Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.
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Which expression is represented by the model below? pleaseeeee help!!! 30 points!!!!
4. In 2018, Apple's net worth was $945 billion. What does that mean?
How much the company pays its' employees.
How much debt the company has.
The money the company wants to make one day.
The value of the company.
Therefore , the solution of the given problem of unitary method comes out to be Option '' value of money" is correct.
What is an unitary method?To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.
Here,
The phrase "In 2018, Apple's net worth was $945 billion" refers to the company's valuation in that particular year.
So, the appropriate choice is:
the company's market worth.
Option : '' value of money" is correct.
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7. Gretchen makes pillows using *
15 yards of fabric per pillow.
She has 814 yards of fabric. What
is the greatest number of pillows
Gretchen can make?
O A 4
OB 5
C 6
OD 8
coordinate points: (-5,-3),(-7,-11),(4,-13). give the coordinate of the fourth vertex
The coordinate of the fourth vertex is determined as (13,-23).
What is the coordinate of the fourth vertex?To find the fourth vertex of the parallelogram, we need to use the fact that opposite sides of a parallelogram are parallel and equal in length.
Let's start by finding the vectors for two sides of the parallelogram. We can use the given coordinate points to find the vectors:
Vector AB = (xB - xA, yB - yA) = (-7 - (-5), -11 - (-3)) = (-2, -8)
Vector BC = (xC - xB, yC - yB) = (4 - (-7), -13 - (-11)) = (11, -2)
Since opposite sides of a parallelogram are parallel, we know that these two vectors are parallel.
To find the fourth vertex, we can add the vector AB to the endpoint of vector BC:
Vector CD = Vector BC + Vector AB = (11, -2) + (-2, -8) = (9, -10)
Now we can add this vector to point C to find the coordinates of point D:
Point D = (xC + CDx, yC + CDy) = (4 + 9, -13 - 10) = (13, -23)
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I need help with all 3 task
The volume of the cylinders are;
1. 602. 88 cm³
2. 56.52 cm³
3. 141. 3 cm³
How to determine the volumeThe formula for calculating the volume of an open cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volume of the cylinder.r is the value of the radius.h is the height of the cylinder.Then, we have;
Substitute the values
1. Volume = 3.14 × 4² × 12
Multiply the values after finding the square
Volume = 602. 88 cm³
2. Substitute the values
Inner radius, r = 2cm
Volume =3.14 × 1.5 ² × 8
Multiply the values, we get;
Volume = 56.52 cm³
3. Substitute the values
Inner radius = 2cm
Volume = 3.14 × 3² × 5
Multiply the values
Volume = 141. 3 cm³
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The probability of flipping a coin and having it land on heads is 1/2. If a coin is tossed 4 times, how many times can you expect it to land on heads?
You can expect the coin to land on heads 2 times when it is tossed 4 times, on average.
help pls show ur work
Answer:
For #17:
This is a 45-45-90 triangle. Therefore, the missing side length (x) is equal to the other leg of the triangle, which is 6.
For #18:
This is a 30-60-90 triangle. Therefore, the missing side length (m) is equal to the hypotenuse (18) divided by 2, or 9.
For #19:
This is a 30-60-90 triangle. Therefore, the missing side length (y) is equal to the hypotenuse (12) multiplied by the square root of 3, or 12√3.
For #20:
This is a 30-60-90 triangle. Therefore, the missing side length (u) is equal to the short leg (5√3) multiplied by 2, or 10√3.
For #21:
This is not a right triangle because the angles do not add up to 180 degrees.
For #22:
This is a right triangle because the angles add up to 180 degrees and one of the angles is 90 degrees.
Step-by-step explanation:
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Given: T=X=U=Y
Prove: TUV ~ XYZ
The triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
What is congruent?In mathematics, congruent means that two shapes or objects have the same size and shape. They match exactly when superimposed on each other. Congruence also applies to angles, where two angles are said to be congruent if they are equal in measure. Congruence can also refer to the equality of two expressions, where two expressions are congruent when they have the same value. In other words, congruence is a term used to describe a relationship between two objects or shapes that are exactly the same size and shape.
In order to prove that two triangles are similar, we need to show that their corresponding angles are congruent. Given that angles T, X, and U are all equal, and angles X, U, and Y are all equal, we can therefore conclude that angles T and Y are also equal. This means that triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
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The corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write : TUV ~ XYZ
What is congruent?
Congruent is a term used in geometry to describe two figures or objects that have the same shape and size. In other words, if two figures are congruent, they are identical in every way, except that they may be oriented differently or located in different positions in space.
To prove that TUV ~ XYZ, we need to show that the two triangles are similar, which means that their corresponding angles are congruent and their corresponding sides are in proportion.
Given that T=X=U=Y, we can conclude that angle TUV and angle XYZ are congruent, and angle TVU and angle YXZ are also congruent. These two angles are the corresponding angles that are congruent in the two triangles.
To show that the corresponding sides are in proportion, we need to compare the ratios of the corresponding side lengths. We can start by comparing the ratio of the lengths of TU and XY:
TU / XY = (TU / TX) * (TX / XY) (by the transitive property of equality)
TU / TX = 1 (because T = X)
TX / XY = 1 (because U = Y)
Therefore, TU / XY = 1 * 1 = 1.
Similarly, we can compare the ratio of UV and YZ:
UV / YZ = (UV / UY) * (UY / YZ) (by the transitive property of equality)
UV / UY = 1 (because U = Y)
UY / YZ = 1 (because T = X)
Therefore, UV / YZ = 1 * 1 = 1.
Therefore, the corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write:
TUV ~ XYZ
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The probability that it is going to rain tomorrow is 1/7. What are the odds in favor of it raining tomorrow
The odds in favor of it raining tomorrow are 1 to 6.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
To find the odds in favor of it raining tomorrow, we need to calculate the ratio of the probability that it will rain to the probability that it won't rain. The probability that it won't rain is 1 - 1/7 = 6/7.
So, the odds in favor of it raining are:
Probability of raining / Probability of not raining
= (1/7) / (6/7)
= 1/6
Therefore, the odds in favor of it raining tomorrow are 1 to 6.
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