Answer:
(A)[tex](-\infty, 2)(2, \infty)[/tex]
(−[infinity], 2) (2, [infinity])
Step-by-step explanation:
Given the rational function, f(x) such that:
[tex]f(x)=\dfrac{x+1}{x-2}[/tex]
The domain of the function are the values of x for which f(x) is defined.
A rational function is undefined when its denominator equals zero.
Denominator of f(x)=x-2
x-2=0
x=2
Therefore, f(x) is undefined at x=2.
The domain of f(x) is all therefore all real numbers excluding 2.
This is written in set notation as:
[tex](-\infty, 2)(2, \infty)[/tex]
The correct option is A.
Answer: A (-infinity,2) (2,infinity)
Step-by-step explanation:
In a school the the duration of primary section is 40 min and senior section is hour if the bell rings at 9 am together when will the next bell ring together
Answer:
11 a.m.
Step-by-step explanation:
Duration of Primary Period = 40 min
Duration of Senior Section =1 hour = 60 min
To find out when the next bell will ring together, we first determine the LCM of 40 and 60.
Multiples of 40 are: 40,80,120,160,...
Multiples of 60 are: 60, 120, 180, 240...
From the above, we observe that the bell will ring together exactly 120 Minutes after 9 a.m.
Therefore:
9+120 Min =9 +2 Hours =11 a.m.
Therefore, the bell of the primary section and senior section will ring together at exactly 11 am.
use
tiles
Algebra
factor for X^2-2x-3
Answer:
I hope it's correct
Caroline, Colin & Sarah share some money in the ratio 1 : 9 : 1.
In total, Caroline and Sarah receive £28.
How much does Colin get?
Answer:
Colin got £126
Step-by-step explanation:
Here we want to know how much Colin got from the sharing.
We can collapse the ratio to mean;
Colin : Caroline + Sarah
= 9:1 + 1 = 9:2
So total ratio is 9 + 2 = 11
If Caroline and Sarah got £28 we need to find the total money shared
Let the total money shared be £x
Thus;
2/11 * x = 28
2x = 11 * 28
x = (11 * 28)/2
x = 11 * 14 = £154
So the amount of money Colin got would be;
£154 - £28 = £126
Part 1 of 1 -
Question 2 of 50
2 Points
Solve the equation for x. x/3 -1 = -2
Copyright 2010-2020 edtell, LLC. All rights reserved. Portions of this software are copyrighted by other parties as described in the Acknov
Answer:
x = -3
Step-by-step explanation:
When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....
x/3 - 1 = -2
x/3 = -1 ( add 1 on both side)
x = -3 (x3 on both side)
Mrs. Sing invests $12,876 for her business at an annual interest rate of 7 percent for 3 years. Which number will Mrs. Sing substitute for r in the simple interest formula? I = p r t
Answer:
she wills substitute r with 7%.
Step-by-step explanation:
Just did it.
Answer:
R = 7%
Principal (P)
Rate (R)
Time (t)
Step-by-step explanation:
The full intrest rate formula is i=prt
You are looking for r
R is the interest rate 7%
So i = 12,876*7%*3years will be the full equation.
what's the product of 9 (-8)
Answer:
-72
Step-by-step explanation:
I googled it.
Answer:
-72
Step-by-step explanation:
You take the 9, multiply by the -8, and boom. You get -72.
And when you multiply two opposite signs together, it equals to a negative number.
Boom bam boom you became a bit smarter
F(x)3x+5/x what is f(a+2)
A: 3a+5/a+2
B:3(a+2)+5/a+2
C:3(f(a))+5/f(a)+2
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Arrange the proof of the given statement in correct order to show that R is an equivalence relation. (Prove the given relation is reflexive first, and then symmetric and transitive.)
Answer:
The given relation R is equivalence relation.
Step-by-step explanation:
Given that:
[tex]((a, b), (c, d))\in R[/tex]
Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.
To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.
1. First of all, let us check reflexive property:
Reflexive property means:
[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]
Here we need to prove:
[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]
As per the given relation:
[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.
[tex]\therefore[/tex] R is reflexive.
2. Now, let us check symmetric property:
Symmetric property means:
[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]
Here we need to prove:
[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]
As per the given relation:
[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]
[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]
Hence true.
[tex]\therefore[/tex] R is symmetric.
3. R to be transitive, we need to prove:
[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]
[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)
[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)
To prove:
To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]
Multiply (1) with (2):
[tex]adcf = bcde\\\Rightarrow fa = be[/tex]
So, R is transitive as well.
Hence proved that R is an equivalence relation.
The relation R is an equivalence if it is reflexive, symmetric and transitive.
The order to options required to show that R is an equivalence relation are;
((a, b), (a, b)) ∈ R since a·b = b·aTherefore, R is reflexiveIf ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ RTherefore, R is symmetricIf ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·cMultiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈RTherefore R is transitiveFrom the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.Reasons:
Prove that the relation R is reflexive
Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)
The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c
By multiplication property of equality; a·b = b·a
Therefore;
((a, b), (a, b)) ∈ R
The relation, R, is reflexive.Prove that the relation, R, is symmetric
Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c
Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R
((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.
Therefore, the relation, R, is symmetric.Prove that R is transitive
Symbolically, transitive property is as follows; If x = y, and y = z, then x = z
From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c
Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e
By multiplication, a·d × c·f = b·c × d·e
a·d·c·f = b·c·d·e
Therefore;
a·f·c·d = b·e·c·d
a·f = b·e
Which gives;
((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.Therefore;
R is an equivalence relation, since R is reflexive, symmetric, and transitive.
Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.
Learn more about equivalent relations here:
https://brainly.com/question/1503196
the tax rate is 3.9%. What is the tax on $42?
Answer:
$43.64
Step-by-step explanation:
Answer:
1.64
Step-by-step explanation:
To find the tax, multiply the cost by the tax rate
42 * 3.9%
Change to decimal form
42 *.039
1.638
Round to the nearest cent
1.64
A genetic experiment involving peas yielded one sample of offspring consisting of 437437 green peas and 129129 yellow peas. Use a 0.050.05 significance level to test the claim that under the same circumstances, 2727% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.
Answer:
The null hypothesis: [tex]\mathbf{H_o: p=0.27}[/tex]
The alternative hypothesis: [tex]\mathbf{H_1: p \neq 0.27}[/tex]
Test statistics : z = −2.30
P-value: = 0.02144
Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.
Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27
Step-by-step explanation:
From the given information:
Let's state the null and the alternative hypothesis;
Since The claim is that 27% of the offspring peas will be yellow.
The null hypothesis state that the proportion of offspring peas will be yellow is equal to 0.27.
i.e
[tex]\mathbf{H_o: p=0.27}[/tex]
The alternative hypothesis state that the proportion of offspring peas will be yellow is not equal to 0.27
[tex]\mathbf{H_1: p \neq 0.27}[/tex]
The test statistics:
we are given 437 green peas and 129 yellow apples;
Hence;
[tex]\hat p = \dfrac{x}{n}[/tex]
where ;
[tex]\hat p[/tex] = sample proportion
x = number of success
n = total number of the sample size
[tex]\hat p = \dfrac{129}{437+129}[/tex]
[tex]\hat p = \dfrac{129}{566}[/tex]
[tex]\mathbf{\hat p = 0.2279}[/tex]
Now; the test statistics can be computed as :
[tex]z = \dfrac { \hat p -p }{\sqrt {\dfrac{p(1-p)}{n} } }[/tex]
[tex]z = \dfrac {0.2279 -0.27 }{\sqrt {\dfrac{0.27(1-0.27)}{566} } }[/tex]
[tex]z = \dfrac {-0.043 }{\sqrt {\dfrac{0.27(0.73)}{566} } }[/tex]
[tex]z = \dfrac {-0.043 }{\sqrt {\dfrac{0.1971}{566} } }[/tex]
[tex]z = \dfrac {-0.043 }{\sqrt {3.48233216*10^{-4} } }[/tex]
[tex]z = \dfrac {-0.043 }{0.01866} }[/tex]
z = −2.30
C. P-value
P-value = P(Z < z)
P-value = P(Z< -2.30)
By using the P-value method and the normal distribution as an approximation to the binomial distribution.
from the table of standard normal distribution
move left until the first column is reached. Note the value as –2.0
move upward until the top row is reached. Note the value as 0.30
find the probability value as 0.010724 by the intersection of the row and column values gives the area to the left of
z = -2.30
P- value = 2P(z ≤ -2.30)
P-value = 2 × 0.01072
P - value = 0.02144
Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.
Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27
Which answer needs to be true to be able to use the SSS Congruence Postulate to prove △ABC≅△DBC? AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ and ∠ACB≅∠DCB ∠ACB≅∠DCB and ∠A≅∠D AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ or AC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Answer:
The correct option is;
[tex]\overline{AB}\cong \overline{DB}[/tex] and [tex]\overline{AC}\cong \overline{DC}[/tex]
Step-by-step explanation:
The steps to prove that ΔABC ≅ ΔDBC with the SSS Congruence postulate
We have;
Statement, Reason
BC ≅ BC, Reflexive property
[tex]\overline{AB}\cong \overline{DB}[/tex], Option selected
[tex]\overline{AC}\cong \overline{DC}[/tex], Option selected
ΔABC ≅ ΔDBC, SSS Congruency Postulate
Therefore, whereby all three sides of the triangles ABC and DBC are congruent, then ΔABC is congruent to ΔDBC.
Answer:
AC≅DF
AB≅DE
Step-by-step explanation:
took the test :)
which linear inequality is represented by the graph?
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 2 , will he have enough paint to cover the tank with one layer of paint? [take = 3.142]
Answer:
He will have enough paint to cover the tank with one layer of paint
Step-by-step explanation:
To calculate the area of the surface that has to be painted, we will have to calculate the lateral surface of the cylinder
Lateral surface of the cylinder is given by
A=2πrh
Where,
π=3.142
r=1.1/2m=
h=1.4m
A=2πrh
=2*3.142*1.1/2*1.4
=4.84m^2
He uses 250ml to cover 1m^2
To cover 4.84m^2, he will use
4.84m^2 × 250ml of paint
=1,210ml of paint is needed
He has 2 litres of paint
2litres =2000ml
Tublu has 2000ml of paint but needs 1210ml of paint
Therefore,
He has an excess of 2000-1210
=790ml
The answer is yes, he will have enough paint to cover the tank with one layer of paint.
55=2.7[tex]55=2.7\sqrt{x} +14[/tex] what is the value of x
Answer:
230.59
Step-by-step explanation:
55 = 2.7sqrt(x) + 14
41 = 2.7sqrt(x)
15.185=sqrt(x)
x = 15.185^2
x=230.59
Which statement explains how the lines x+y=2 and y=x+4 are related?
(1) They are parallel.
(2) They are perpendicular.
(3) They are the same line.
4) They are not related.
Answer:
(2)They are perpendicular.
Step-by-step explanation:
Select the correct answer. Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs. If you assume he takes an equal amount of time to compose each song and graph this relationship with the number of weeks on the x-axis and the number of songs on the y-axis, what is Wayne's unit rate for composing a song?
Answer:
3 weeks for one song
Step-by-step explanation:
The function would be y = 3x + b
Answer:
it is 1/3 of a song per week for all you people that cant do math
Step-by-step explanation:
Helppp!!!! please!!!
Answer:
B. 24700
Step-by-step explanation:
Answer:
b. 24700 cm³
Step-by-step explanation:
[tex]\frac{lwh}{3} \\\\65*30*38/3 = 24700 cm^3[/tex]
Hope this helps! :)
plzz helpp mee in this question!!!
Answer:
Please see attached picture for full solution.
describe the transformations of how the graph y=x^2 can be transformed into y= -1/5 (x-4)^2 + 2
Answer:
Reflected over the x-axis, vertically shrunk by a factor of 1/5, moved right 4 units and up 2 units.
Step-by-step explanation:
Parent Graph: f(x) = a(bx - h)² + k
a is vertical stretch (a > 1) or shrink (a < 1) and reflection over x-axis
b is horizontal stretch or shrink and reflection over y-axis
h is horizontal movement left (if positive) or right (if negative)
k is vertical movement up (if positive) or down (if negative)
Now that we have our rules, we simply apply it to y = -1/5(x - 4)² + 2
a = -1/5, so reflection over x-axis and vertical shrink of 1/5 (1/5 < 1)
Nothing has changed b, so no horizontal stretch/shrink
h = -4, so horizontal movement right 4 units
k = 2, so vertical movement up 2 units
An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years
Answer:
y = 7,595.96(1.02)x
Step-by-step explanation:
y = 7,595.96(1.02)x
a normal linear equation is basically y = x + b
in this case,
y = amount of money in the bank accountx = number of yearsb is not required because there are no new deposits or withdrawals from the accountSince the accounts earns 2% interest per year, then you need to multiply the original amount by 1.02. As more years pass, the account will increase by 1.02, so the account increases by 1.02x. Since the original amount is $7,595.96, that will be our starting point.
Answer:
C y = 7,595.96(1.02)x
Step-by-step explanation:
At the deli, Alberto paid $24.33 for 7.4
pounds of sliced ham. What was the
price of one pound of sliced ham?
Answer:
About $3.28
Step-by-step explanation:
Divide 24.33 by 7.4
Answer:
3.28783783784...
Step-by-step explanation:
You're description could turn into 24.33 : 7.4.
You turn 7.4 into 1, and divide 7.4 / 1.
(It is 7.4)
Then, you divide 24.33 / 7.4.
It is 3.28783783784.......
or, If you want you're answer close to an natural number, It is 3.
not quite sure of the answer. help me out???
Answer:
C = pi * d
Step-by-step explanation:
C = 2 * pi *r
We can replace 2 * r with d since the diameter is twice the radius
C = pi * 2*r
C = pi * d
Step 1: Calculate the measures of center for Mrs. Hampton's data in the dot plot (round your answer to the nearest tenths place). Show your work and briefly explain each step. (Measures of Center are the Mean and Median of a data set)
*dot plot is shown in the attachment below
Answer:
Mean = 6.3
Median = 6
Step-by-step explanation:
Measures of centre, mean and median, can be calculated as follows:
First, bear in mind that each dot represents a value in the data set.
==>Mean:
Mean is the sum of all values in the data set divided by the number of data set we have.
The sum can be calculated as follows:
0 (1) = 0
4 (3) = 12
5(8) = 40
6(3) = 18
7(1) = 7
8(5) = 40
9(2) = 18
10 (3) = 30
Sum = 0+12+40+18+7+40+18+30 = 165
No of data set = 26
Mean = 165/26 = 6.346 ≈ 6.3 (nearest tenth place)
==>Median: this is the middle value in the data set. Since the number of data set is even number (26) , the middle value lies between the 13th and 14th data points. The average of the 13th and 14th data points will give us the median value.
Thus, the 13th and 14th values are both 6.
Therefore, median = (6+6) ÷ 2 = 6
Answer:
The mode is 5, because 5 occurs 8 times, which is more than any other numbers occurring more than once. The median is 6, and this is because when you line up the numbers in order and cross them off to find the middle number, it is 6. I rounded to the mean to about 6.4. I got this by adding all of the numbers up, or by doing 12 + 40 +18 +7, etc, and got the total of 165. Because there is a total of 26 data points, I divided those numbers and got 6.3461, which ends up rounding to 6.4.
Step-by-step explanation:
change wording
Suppose that p partners equally share the profits from a sale of $3,600. Which algebraic expression represents this situation?
Given : p partners equally share the profits from a sale of $3,600
To find : Which algebraic expression represents this situation
Solution:
Number of Partners = p
Total Profit = $ 3600
Profit of Each Partner = Total Profit / number of Partners
=> Profit of Each Partner = 3600 / p
Hence is algebraic expression that represent the Share of each partner
Answer:
D
Step-by-step explanation:
100% on quiz
Factor x2 – 3x – 28. An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Identify the values that should be written to complete the X diagram. On the top: On the bottom: On the sides: Rewrite the expression using the numbers on the sides of the X diagram. Use double grouping to factor the four terms. x2 – 3x – 28 =
Answer:
(x - 7)(x + 4)
Step-by-step explanation:
Note that 4 times 7 is 28, and that -7x + 4x = -3x.
Therefore, x^2 - 3x - 28 factors into (x - 7)(x + 4)
The factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).
What is a quadratic equation?
It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Writing a number or any mathematical object as the result of several factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
The factorization will be done as below:-
x² – 3x – 28
Split the middle term as 7 and 4.
x² – 7x + 4x – 28 = 0
x ( x - 7 ) + 4 ( x -7 ) = 0
Take x-7 common from the whole equation.
( x - 7 ) ( x + 4 ) = 0
Therefore, the factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).
To know more about quadratic equations follow
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What is the length Y in this picture ?
Answer:
5
Step-by-step explanation:
The triangle pictured is a 45-45-90 triangle, meaning both legs are the same length, 5.
I don't understand???? I'll give the brainliest!!!!!
Answer:
37Option A is the correct option.
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} - 2ab \: \cos \: c \: = {c}^{2} \\ a = 4 \\ b = 5 \\ c = 2 \\ \\ 2ab \: cos \: c = {a}^{2} + {b}^{2} - {c}^{2} \\ \: \: \: \: \: \: \: \: = {(4)}^{2} + {(5)}^{2} - {(2)}^{2} \\ \: \: \: \: \: \: \: \: = 16 + 25 - 4 \\ \: \: \: \: \: \: = 41 - 4 \\ \: \: \: \: \: \: = 37[/tex]
Hope this helps...
Good luck on your assignment...
How many times would you have to cross the Golden Gate Bridge in order to travel the exact distance between Wolverhampton and Birmingham?
Answer:
Hey!
Well...the distance from Birmingham to Wolverhampton in about 12 miles (19km)
The length of the Golden Gate bridge is 2,737m OR 2.737 km...in miles it's 1.701
So you will have to cross it about 11.2 times (3 sf)
Step-by-step explanation:
19 km / 1.701km = 11.16990005878895
Rounded up to a degree of accuracy = 3 sf
= 11.2
Hope this helps!
10. 80 machines can produce 4800 identical pens in 5 hours. At this rate
a) how many pens would one machine produce in one hour?
b) how many pens would 25 machines produce in 7 hours?
Answer:
a) 12 (Simply divide 4800/5 to get 960. Then divide 960/80 to get 12)
b) 2100 (Simply multiply 12 by 25 by 7)
Hope it helps <3
6TH GRAD LE MATH PLEASE HELP ME
Answer: 6
Step-by-step explanation: I think..... this is a division sign, nvm... so 4 divided by 8/12 is basically 4 x 12/8 which is 48/8 simplified is/equals 6!
Answer:
6
Step-by-step explanation:
4 / 8/12 = 4 * 12/8 = 4 * 3/2 = 6