Answer:
Yes it is an equivalence relation
Explanation:
An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.
Example, given set {x, y, z} where ~ means equivalence:
x ~ y if y ~ z means symmetric
since x ~ y and y ~ z, then x ~ z means transitive
x ~ x means reflexive
Equivalence relations share a common attribute or attributes(example, a satisfying condition)
The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.
On a coordinate plane, a line goes through points (negative 1, 0), (0, 1), and (1, 2). Which table goes with the graph?
Answer:
Table B
Step-by-step explanation:
correct on edge :)
The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)
Answer:
Area swept by the blade = 448[tex]in^{2}[/tex]
Step-by-step explanation:
The arc the wiper wipes is for 135 degrees angle.
So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.
Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.
So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]
Simplify it,
=216[tex]\pi[/tex]
Now, let's find area of sector with radius 14 inches
Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]
Simplify it
=73.5[tex]\pi[/tex]
So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]
Simplify it and use pi as 3.14.....
Area of swept =678.584 - 230.907
=447.6769
Round to nearest whole number
So, area swept by the blade = 448[tex]in^{2}[/tex]
Deon bought a desk on sale for $105.60. This price is 67% less than the original price. What was the original price?
Answer:
.33x = 105.60
$371
Step-by-step explanation:
Answer:
63.44
Step-by-step explanation:
its 63.44697 but you round so its 63.44
Convert 1.5% to decimal and a fraction. Show and explain your method.
Answer:
0.015
Step-by-step explanation:
1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015
Estimate 19.625-6.77 by first rounding each number to the nearest tenth.
Answer:
13
Step-by-step explanation:
1. Round 19.625 up to 20.
2. Round 6.77 up to 7.
3. Calculate the equation. Ans is 13.
For each of the following variables, identify the type of variable (categorical vs. numeric). (1) Temperature (in Fahrenheit) of an office building (11) Traffic congestion (e.g. light, medium, heavy)
1) (1) Numeric, and (II) Categorical
2) (1) Numeric, and (II) Numeric
3) (1) Categorical, and (II) Numeric
4) There is no correct match.
5) (1) Categorical, and (11) Categorical
Answer:
(a) Temperature: Numerical
(b) Traffic congestion: Categorical
Step-by-step explanation:
Required
Determine the variable type
(a) Temperature
Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.
Hence, the variable is numerical
(b) Traffic congestion
From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....
Hence, the variable is categorical
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Would you rather?
buy 2 lollypops for $2
buy 30 lollypops for $40
Answer:
Buy 2 lollipops for $2.
Step-by-step explanation:
If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
What is the value of x in the triangle?
Answer:b
Step-by-step explanation:
Ive done this
a number decreased by 22% is 117. What is the number?
Answer:
Old number = 150
Step-by-step explanation:
Given information;
Percentage decreased = 22%
New number obtain = 117
Find:
Old number
Computation:
Old number = New number obtain[100 / (100 - 22)]
Old number = 117[100 / (100 - 22)]
Old number = 117[100 / (78)]
Old number = 11,700 / 78
Old number = 150
A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.)
Answer:
1100 ft³
Step-by-step explanation:
Use the formula for the volume of a cylinder. For height, use the average of the minimum and maximum depths.
V = πr²h
r = d/2 = 20 ft/2 = 10 ft
h = (1 ft + 6 ft)/2 = 3.5 ft
V = π(10 ft)²(3.5 ft)
V = 1100 ft³
What is the common ratio of the sequence? -2, 6, -18, 54,...
a.-3
b.-2
c.3
d.8
Answer:
a. -3
Step-by-step explanation:
-2 turns into 6 by multiplying it by -3.
the same from 6 to -18, from -18 to 54, ...
so, an/an+1 = -3
Pls answer
Subtract -37 from -53
Answer:
-37 subtract -53
-53 subtract -37 = -16
Step-by-step explanation:
Answer:
The answer is 16
Step-by-step explanation:
-37-(-53) = -37 + 53
You can flip it to 53 - 37 which equals 16.
Hope this helps! :)
*Heads up you can also search this up* ^^
Blank DVD's are sold in packages of 50 for $17.95 if your company will need 2700 blank divide these next year how much money must your budget for blank dvd's
Answer:
Step-by-step explanation:
50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.
If f(x) is a linear function, what is the value of n?
х
_4
f(x)
---25
-10
-1
n
20
2
оооо
9
Step-by-step explanation:
You can simply plot these points on a graph and see where the line goes. It go
Hello, please help me!!
Answer:
0.14
Step-by-step explanation:
P(A|B) asks for the probability of A, given that B has happened. This is equal to the probability of A and B over the probability of B (see picture)
Here, the question is asking if someone is taking the bus given that they are a senior.
The probability of someone being a senior and taking the bus is 5/100, or 0.05 . The probability of someone being a senior is 35/100, or 0.35
Our answer is then 0.05/0.35 = 1/7 = 0.14
help please i don't know how to do this
Find the equation of the lines in problem 1 (0,0) slope =2.
Answer:
y = 2x
Step-by-step explanation:
Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,
[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]
What are the values of x for which the denominator is equal to zero for y=(x+3)/(x^2+4x)
9514 1404 393
Answer:
-4, 0
Step-by-step explanation:
The denominator is x^2+4x. This is zero when ...
x^2 +4x = 0
x(x +4) = 0
The zero product rule tells you the product is zero when the factors are zero.
x = 0
x +4 = 0 ⇒ x = -4
The denominator is zero for x=0 and x=-4.
it is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails and the probability for a flase positive is 5%. What is the probability that an email is detected as spam
Answer:
0.52 = 52% probability that an email is detected as spam.
Step-by-step explanation:
Probability that an email is detected as spam:
99% of 50%(are spam).
5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).
What is the probability that an email is detected as spam?
[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]
0.52 = 52% probability that an email is detected as spam.
What is the amount f rainfall that Miami receives, round to the nearest half or whole? 55 9/10"
Answer:
56"
Step-by-step explanation:
SOLVE PLS!! ILL MARK BRAINILEST!!
Answer:
73.3333....
Step-by-step explanation:
please mark me brainliest
Answer:
a: t=13.6 cm
b: h=12.9 mm
Step-by-step explanation:
Hi there!
Let's start with a
in a, we are given a right triangle (notice the right angle), the length of the hypotenuse (the side OPPOSITE from the right angle) as 18 cm, one acute angle given as 41° and the length of one of the legs (the legs are the sides that make up the right angle) as t
We're asked to use the primary trigonometric ratios
Those ratios are:
Sine, which is opposite/hypotenuse
Cosine, which is adjacent/hypotenuse
Tangent, which is opposite/adjacent
We will be basing the ratio off of the 41° angle, so let's find out which sides will be which in reference to that angle
The opposite side will be the other leg, the unmarked side
The adjacent side will be t
The hypotenuse will be the side marked as 18 cm
So let's use cos(41) in this case
cos(41)=t/18
Plug cos(41) into your calculator, and remember to have the calculator in degree mode
cos(41)≈0.8 (rounded to the nearest tenth)
0.8=t/18
multiply both sides by 18
13.6 cm=t
It's already rounded to the nearest tenth :)
b.
We are given a right triangle, and the lengths of the legs as h and 9 mm, as well as one acute angle as 35°
We'll be basing our ratio off of the 35 degree angle, so let's find which sides will be which in reference to that angle
The opposite side will be the leg marked as 9 mm
The adjacent side will be the leg marked as h
The hypotenuse will be the unmarked side
Since we are given the lengths of the opposite and the adjacent, let's use tan(35)
tan(35)=9/h
Plug tan(35) into your calculator, and remember to have it in degree mode
tan(35)≈0.7
0.7=9/h
multiply both sides by h
0.7h=9
divide both sides by 0.7
h=12.9 mm (rounded to the nearest tenth)
Hope this helps!
i’ll give brainliest to the right answer
Answer:
First one , 0.0000805
Step-by-step explanation:
With negative exponents the decimal is moved to the left the amount of the exponent. The spaces are filled with zeros.
With positive exponents the opposite occurs. The decimal moves to the right.
(URGENT!!) Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
2nd Graph
Step-by-step explanation:
Bases off the graphs, you gave me, I assume your the equation is
[tex]f(x) = - 4(2) {}^{x} [/tex]
The parent equation of this function is
[tex]f(x) = b {}^{x} [/tex]
Let say x=0
Using the rules of exponets, the y value must be 1 so a critical point is
(0,1)
The function is multiplied by -4.
This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be
(0,-4).
The base 2 the function will get compressed by 1/2.
The best graph that represents this is the second graph
need help with algebra problem
Answer:
[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]
Step-by-step explanation:
Multiplication,
[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]
in a school there are 650 girls. It is 26% of the whole students, how many boys are there in the school?
Answer:
Step-by-step explanation:
Frt7v6c87buhinjomp,l.;
In the xy-plane, the slope of the line y = mx − 4 is
less than the slope of the line y = x − 4. Which of the
following must be true about m?
[Show Workings}
I will give brainlist to the person with the right
If the slope of the line y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.
The general formula for calculating an equation of a line is expressed as:
[tex]y = mx + b[/tex] where:
m is the slope of the line
Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:
[tex]mx=1x\\[/tex]
Divide through by x
[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]
Hence the slope of the line y = x - 1 is 1.
According to the question, since we are told that the slope of the line
y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
Learn more about the slope of a line here: https://brainly.com/question/16949303
Answer:
Step-by-step explanation:
A strawberry farmer in Poteet knows that 1/8 of his strawberries are typically not fit to sell at the market (either because they went bad or are too unusually shaped). The farmer takes a random sample of 156 strawberries to inspect for the upcoming farmer's market and finds that 24 are unfit to sell. If he were to go back and pick 1000 more strawberries to inspect for the market, how would the standard deviation of the sample proportion be affected
Answer:
It would be smaller.
Step-by-step explanation:
Given that :
The number of the strawberries that are unfit for sell, x = 24
The total number of the strawberries to inspect, n = 156
Total number of the strawberries to be picked = 1000 strawberries
Therefore,
[tex]$\widehat p =\frac{x}{n}$[/tex]
[tex]$=\frac{24}{156}$[/tex]
= 0.1538
[tex]$\widehat p =\frac{x}{n}$[/tex]
[tex]$=\frac{24}{1000}$[/tex]
= 0.024
Therefore, the standard deviation of the sample proportion would be smaller.
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 528 hours. Round your answer to four decimal places.
Answer:
0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours.
This means that [tex]\sigma = 15, \mu = 520[/tex]
Find the probability of a bulb lasting for at most 528 hours.
This is the p-value of Z when X = 528. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{528 - 520}{15}[/tex]
[tex]Z = 0.533[/tex]
[tex]Z = 0.533[/tex] has a p-value of 0.7031
0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.
