Adding Rational Expressions
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Related Questions
The table below shows the results of a survey in which 141141 men and 145145 women workers ages 25 to 64 were asked if they have at least one month's income set aside for emergencies. complete parts (a) through (d). men women total less than one month's income 6565 8484 149149 one month's income or more 7676 6161 137137 total 141141 145145 286286 (a) find the probability that a randomly selected worker has one month's income or more set aside for emergencies. the probability is nothing. (round to the nearest thousandth as needed.) (b) given that a randomly selected worker is a male, find the probability that the worker has less than one month's income. the probability is nothing. (round to the nearest thousandth as needed.) (c) given that a randomly selected worker has one month's income or more, find the probability that the worker is a female. the probability is nothing. (round to the nearest thousandth as needed.) (d) are the events "having less than one month's income saved" and "being male" independent or dependent? independent dependent
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Final answer:
The probability that a randomly selected worker has one month's income or more set aside for emergencies is approximately 0.479. Given that a randomly selected worker is a male, the probability that the worker has less than one month's income is approximately 0.460. Given that a randomly selected worker has one month's income or more set aside for emergencies, the probability that the worker is a female is approximately 0.446. The events 'having less than one month's income saved' and 'being male' are independent.
Explanation:
To find the probability that a randomly selected worker has one month's income or more set aside for emergencies, we need to divide the number of workers with one month's income or more by the total number of workers. According to the table, there are 76 men and 61 women with one month's income or more, for a total of 137 workers. The total number of workers is 286. So the probability is 137/286, which is approximately 0.479.
Given that a randomly selected worker is a male, we need to find the probability that the worker has less than one month's income set aside for emergencies. According to the table, there are 65 men with less than one month's income. The total number of men is 141. So the probability is 65/141, which is approximately 0.460.
Given that a randomly selected worker has one month's income or more set aside for emergencies, we need to find the probability that the worker is a female. According to the table, there are 61 women with one month's income or more. The total number of workers with one month's income or more is 137. So the probability is 61/137, which is approximately 0.446.
The events 'having less than one month's income saved' and 'being male' are independent. To confirm independence, we need to check if the probability of both events occurring is equal to the product of their individual probabilities. In this case, the probability of having less than one month's income saved is 65/286 and the probability of being male is 141/286. The probability of both events occurring is (65/286) * (141/286), which is approximately 0.126. This is equal to the product of their individual probabilities, confirming that the events are independent.
how much should Tabatha budget monthly for insurance that costs $956.89 for the entire year?
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i divided 956.89 in 12 so that was the answer
A farmer owns 42 acres of land, of the 42 acres, only 85% can be farmed. How many acres are available for farming?
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How?
Simple. An easy trick I use is by dividing the number by 100, and multiplying by the percent.
So 42/100 x 85 = 35.7
Evaluate the expression shown for x=12 -5/6×+7
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-5/6(12)+7
-10+7=-3
-3
Answer:
-3
Step-by-step explanation:
The given expression is
[tex]-\frac{5}{6}x+7[/tex]
We need to find the value of given expression for x=12.
Substitute x=12 in the given expression.
[tex]-\frac{5}{6}(12)+7[/tex]
Cancel out the common factors.
[tex]-5\times 2+7[/tex]
After multiplication, we get
[tex]-10+7[/tex]
After subtraction, we get
[tex]-3[/tex]
Therefore, the value of given expression for x=12 is -3.
what is the prime factorization of 2^3x3x5^2
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= 8 x 3 x 25
= 600
If I didn't try 600 As an answer bro!
bye
which of these is the absolute value parent function?
A. f(x) = |x| – 2
B. f(x) = |x|
C. f(x) = |2x|
D. f(x) = |x| + 1
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Answer:
The correct option is B. The absolute value parent function is f(x) = |x|.
Step-by-step explanation:
The absolute parent function is a function where
[tex]f(x)=x[/tex] and [tex]f(-x)=x[/tex]
The graph of absolute function is v-shaped and vertex of the function is (0,0).
According to these conditions the absolute value parent function is
f(x) = |x|
The function f(x) = |x| – 2 shifts 2 units down.
The function f(x) = |2x| stretch by factor 2.
The function f(x) = |x| + 1 shifts 1 units up.
Therefore the correct option is B.
Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.
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[tex]L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)[/tex]
which has partial derivatives (set equal to 0) satisfying
[tex]\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}[/tex]
This is a fairly standard linear system. Solving yields Lagrange multipliers of [tex]\lambda_1=-\dfrac{32}{11}[/tex] and [tex]\lambda_2=-\dfrac{104}{11}[/tex], and at the same time we find only one critical point at [tex](x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)[/tex].
Check the Hessian for [tex]f(x,y,z)[/tex], given by
[tex]\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}[/tex]
[tex]\mathbf H[/tex] is positive definite, since [tex]\mathbf v^\top\mathbf{Hv}>0[/tex] for any vector [tex]\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top[/tex], which means [tex]f(x,y,z)=x^2+y^2+z^2[/tex] attains a minimum value of [tex]\dfrac{480}{11}[/tex] at [tex]\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)[/tex]. There is no maximum over the given constraints.
Let x be a random variable that takes values from 0 to 9 with equal probability 1=10. find the pmf of the random variable y = x mod (3).
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[tex]y=\begin{cases}0&\text{for }x\in\{0,3,6,9\}\\1&\text{for }x\in\{1,4,7\}\\2&\text{for }x\in\{2,5,8\}\end{cases}[/tex]
[tex]\implies\mathbb P(Y=y)=\begin{cases}\dfrac4{10}=\dfrac25&\text{for }y=0\\\\\dfrac3{10}&\text{for }y=1\\\\\dfrac3{10}&\text{for }y=2\end{cases}[/tex]
The pmf of the random variable y = x mod (3) is: P(y=0) = 0.4, P(y=1) = 0.3, and P(y=2) = 0.3.
Explanation:The random variable y can take on the values 0, 1, and 2, since those are the possible remainder values when x is divided by 3. We need to find the probability mass function (pmf) of y, which represents the probabilities of each possible value of y. The pmf of y can be calculated by finding the probability of each possible value of y based on the probability distribution of x and dividing it by the total number of possible values of x. Since x takes values from 0 to 9 with equal probability, the pmf of y is:
P(y=0) = P(x=0) + P(x=3) + P(x=6) + P(x=9) = 1/10 + 1/10 + 1/10 + 1/10 = 4/10 = 0.4
P(y=1) = P(x=1) + P(x=4) + P(x=7) = 1/10 + 1/10 + 1/10 = 3/10 = 0.3
P(y=2) = P(x=2) + P(x=5) + P(x=8) = 1/10 + 1/10 + 1/10 = 3/10 = 0.3
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3x+y=5
y=2x
Substitution method
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3x + y = 5
3x + 2x = 5
5x = 5
x = 1
Now, substitue 1 as x into one of the two equations:
y = 2x
y = 2(1)
y = 2
Hope this helps!
order the set of numbers from least to greatest
11/20, 1/2, 0.51
a. 0.51, 11/20, 1/2
b. 1/2, 0.51/, 11/20
c. 1/2, 11/20, 0.51
d. 0.51, 1/2, 11/20
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1/2 = 50/100 = 0.50
0.51
1/2. 11/20, 0.51 (least to greatest)
C is your answer
hope this helps
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
[tex]\frac{11}{20},\frac{1}{2},0.51[/tex]
Now, we have to arrange the set of numbers from least to greatest.
So, for this we have to make the denominator same ,
[tex]\frac{11\times 5}{20\times 5}=\frac{55}{100}[/tex]
Similarly,
[tex]\frac{1\times 50}{2\times 50}=\frac{50}{100}[/tex]
Similarly,
[tex]\frac{51}{100}[/tex]
Numbers In increasing order :
[tex]\frac{50}{100},\frac{51}{100},\frac{55}{100}\\\\\frac{1}{2},0.51,\frac{11}{20}[/tex]
Hence, Option 'b' is correct.
Joan can type 50 letters in three hours. When Jill helps, they can do the job in one hour. How long would it have taken Jill to do the job alone?
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Answer:50 in 1.5 hours.
Step-by-step explanation:
If Joan can do 50 in 3 hours, then in 1 hour, that’s 50/3.
Jill completes the rest of the 50, so 50-(50/3) is how many letters Jill can type in an hour.
50-(50/3)=(150/3)-(50/3)=100/3 letters in an hour. If Jill can write 100 letters in 3 hours, then she can write 50 in 1.5 hours.
Find the minimum and maximum of f(x, y, z) = y + 4z subject to two constraints, 2x + z = 4 and x2 + y2 = 1. g
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[tex]L_x=2\lambda_1+2\lambda_2 x=0\implies\lambda_1+\lambda_2x=0[/tex]
[tex]L_y=1+2\lambda_2y=0[/tex]
[tex]L_z=4+\lambda_1=0\implies\lambda_1=-4[/tex]
[tex]L_{\lambda_1}=2x+z-4=0[/tex]
[tex]L_{\lambda_2}=x^2+y^2-1=0[/tex]
[tex]\lambda_1=-4\implies \lambda_2x=4\implies\lambda_2=\dfrac4x[/tex]
[tex]1+2\lambda_2y=0\implies\lambda_2y=-\dfrac12\implies8y=-x[/tex]
[tex]x^2+y^2=1\implies (-8y)^2+y^2=65y^2=1\implies y=\pm\dfrac1{\sqrt{65}}[/tex]
[tex]y=\pm\dfrac1{\sqrt{65}}\implies x=\mp\dfrac8{\sqrt{65}}[/tex]
[tex]2x+z=4\implies z=4\pm\dfrac{16}{\sqrt{65}}[/tex]
We have two critical points to consider: [tex]\left(-\dfrac8{\sqrt{65}},\dfrac1{\sqrt{65}},4+\dfrac{16}{\sqrt{65}}\right)[/tex] and [tex]\left(\dfrac8{\sqrt{65}},-\dfrac1{\sqrt{65}},4-\dfrac{16}{\sqrt{65}}\right)[/tex].
At these points, we respectively have a maximum of [tex]16+\sqrt{65}[/tex] and a minimum of [tex]16-\sqrt{65}[/tex].
Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of change of money in his savings account per week?
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What is the relationship between 0.04 and 0.004?
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hope this helps
Hope this helped!
Simplify.
9y+11z+7y−4z
What is the answer?
A. 23yz
B. 2y + 7z
C. 16y + 7z
D. 16y + 15z
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Answer:
C. (16y + 7z)
Step-by-step explanation:
9y + 11z + 7y - 4z
1. Simplify the y's: 9y + 7y = 16y
16y + 11z - 4z
2. Simplify the x's: 11z - 4z = 7z
16y + 7z
Answer:
16y+7z
Step-by-step explanation: no thanks im good
What is the equation of the line that passes through
(10, 4)
and is perpendicular to
5x−y=3
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5x - y = 3
-y = -5x + 3
y = (-5x + 3)/(-1)
y = 5x - 3
The slope for this equation is 5.
The slope of the equation we want is the negative reciprocal of 5.
Let m = slope of equation we want.
m = -1/5
We are given the point (10,4).
Plug both into the point-slope formula.
y - 4 = (-1/5)(x - 10)
y - 4 = (-1/5)x + 2
y = (-1/5)x + 2 + 4
The equation we want is
y = (-1/5)x + 6
Did you follow?
Danny charges 35 dollars for 3 hours of swimming lessons. Martin charges 24 dollars for 2 hours of swimming lessons. Who offers a better deals?
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Samir works 15 hours for every 19 hours that Mitul works. If x represents the number of hours that Mitul works and y represents the hours that Samir works, which equation correctly models this relationship?
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15/19
y=15/19x
Answer:
[tex]y=\frac{15}{19}x[/tex]
Step-by-step explanation:
Let
x-----> the number of hours that Mitul works
y-----> the hours that Samir works
by proportion
[tex]\frac{x}{y}=\frac{19}{15}\\ \\19y=15x\\ \\y=\frac{15}{19}x[/tex]
The ruby- throated hummingbird has a wing beat of about 200 beats per second. About how many wings beats would a huming bird have in 3 minutes
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200 beats per second
200 x 60 = 12000 beats per minute
Then multiply 12000 by 3
36000 wing beats in 3 minutes
hope this helps
Texasxhic101.
I am adding you to help me
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The median of the data is not 3. It's four, because both sides are symmetrical and therefore the number in the very center is the median, or 4.
The mean of the data is not 3, as again, it is symmetrical, so therefore the number in the very center is the mean, 4 again.
The range is the max - min, or 4, which is not 5.
If we count the total number of observations, 2 + 3 + 5 + 3 + 2 = 15, then we know the last one is correct.
A triangle has the side lengths 5, 7, and 11. Which term best describes the triangle? A) acute B) equiangular C) equilateral D) obtuse
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Answer:
D) Obtuse
Step-by-step explanation:
Write the expression as the sine, cosine, or tangent of an angle. cos 8x cos 2x - sin 8x sin 2x
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cos(8x+2x)=cosαcosβ-sinαsinβ
cos(10x)=cosαcosβ-sinαsinβ
Answer:
cos (A - B) = cos 6 x
Step-by-step explanation:
given equation,
= cos 8 x . cos 2 x - sin 8 x . sin 2 x
using identity
cos (A - B) = cos (A) . cos(B) - sin (A) . sin(B)...................(1)
cos 8 x . cos 2 x - sin 8 x . sin 2 x......................................(2)
comparing both the equation (1) and (2)
we get ,
A = 8 x B = 2 x
hence, from the above identity we can see that
cos (A - B) = cos (8 x - 2 x)
cos (A - B) = cos 6 x
Kelly read 30 pages of her 300 page book on 6 hours at this rate how long will it take her to read the entire book
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300 / 30 = 10
Now multiply this by the number of hours required to read the initial 30 pages.
10 x 6 = 60
So, since it takes Kelly 6 hours to read 30 pages, it should take Kelly 60 hours to read the 300 page book.
You have 900-grams of an an unknown radioactive substance that has been determined to decay according to D ( t ) = 900 e − 0.002415 ⋅ t D ( t ) = 900 e - 0.002415 ⋅ t where t t is in years. How long before half of the initial amount has decayed?
It will take __ years for half of the initial amount to decay. (Round to 1 decimal place)
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so, how long will it be, for D(t) to turn to 450 grams?
[tex]\bf D(t)=900e^{-0.002415t}\implies 450=900e^{-0.002415t} \\\\\\ \cfrac{450}{900}=e^{-0.002415t}\implies \cfrac{1}{2}=e^{-0.002415t}\\\\ -------------------------------\\\\ \textit{Logarithm Cancellation Rules}\\\\ log_{{ a}}{{ a}}^x\implies x\qquad \qquad {{ a}}^{log_{{ a}}x}=x\\\\ -------------------------------\\\\[/tex]
[tex]\bf log_e\left( \frac{1}{2} \right)=log_e\left( e^{-0.002415t} \right)\implies log_e\left( \frac{1}{2} \right)=-0.002415t \\\\\\ \cfrac{ln\left( \frac{1}{2}\right)}{-0.002415}=t\implies 287.0174661 \approx t[/tex]
T Shirt sore keeps 7 white T-Shirts on the shelves for every 3 purple T- Shirts on the shelve how many white T-Shirts on the shelve if 15 purple T-Shirts on the shelve. Show how you get the answer in long form
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[tex]15 \div 3 = 5 \\ 5 \times 7 = 35[/tex]
THE OTHER WAY I DID IT WAS;
[tex]3 + 3 + 3 + 3 + 3 = 15 [/tex]
I ADDED IT 5 TIMES AND GOT 15
[tex]7 + 7 + 7 + 7 + 7 = 35[/tex]
I ADDED IT 5 TIMES AND GOT 35
True or false. If (7x+4) is a factor of some polynomial function F, then 4/7 is a zero of F. Please help!
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False, If (7x+4) is a factor of some polynomial function F, then - 4/7 is a zero
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zer then it is confirmed that x - a = 0 is a factor.
Given (7x + 4) is a factor of a polynomial function F.
Then, 7x + 4 = 0.
7x = -4.
x = - 4/7 is a root of the polynomial F or a zero of the polynomial F.
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How much force is required to push a 54-pound sofa across a carpeted floor?
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compare the decimals <, >, or = 0.73 ___ 0.7300
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0.73 = 0.7300 is our answer.
Given,
0.73 and 0.7300
We have to compare these decimal numbers.
What is the inequality used to compare two numbers?< = less than
> = greater than
= means equal
≤ = less than or equal to
≥ = greater than or equal to
We have,
0.73 = 73 / 100
There are two numbers after the decimal point.
We divide it by 100.
0.7300 = 7300/1000 = 73/100
There are four numbers after the decimal point.
We divide it by 10000.
We see that both the decimal numbers are equal.
Thus 0.73 = 0.7300
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Find each percentage decrease. round to the nearest percentage from 16 bagels to 0 bagels
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To solve this problem:
The formula would be: New Value – Old Value)/Old Value] x 100 or in the form of variable it would be: [(B-A)/A] x 100 = Answer.
So plugging in the information given in our problem it would be:
0 – 16 / 16 x 100 = percent of change
0/16 x 100 = 0%
The answer is 0%
a plumber charges a base fee of $55 for a service call plus $35 per hour for each hour worked during the service call the relationship between the total price of the service called and the number of hours worked
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The relationship between the total price and the number of hours worked can be represented by a linear equation. The equation is y = 35x + 55, where y represents the total price and x represents the number of hours worked.
Explanation:The relationship between the total price of the service call and the number of hours worked can be represented by a linear equation. We can use the formula y = mx + b, where y represents the total price, x represents the number of hours worked, m represents the hourly fee, and b represents the base fee.
In this case, the plumber charges a base fee of $55 and $35 per hour. So the equation that expresses the total price is y = 35x + 55.
The independent variable in this situation is the number of hours worked, which is x. The dependent variable is the total price, which is y. The y-intercept of the equation is 55, which represents the base fee. The slope of the equation is 35, which represents the hourly fee. The y-intercept (b) is the point where the line intersects the y-axis, and the slope (m) determines how steep the line is.