Divide through everything by b :
[tex]\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}[/tex]
Since a/b < c/d, it follows that
[tex]\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}[/tex]
Multiply through everything on the right side by b/d to get
[tex]\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd[/tex]
and so (a + c)/(b + d) < c/d.
For the other side, you can do something similar and divide through everything by d :
[tex]\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}[/tex]
and a/b < c/d tells us that
[tex]\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}[/tex]
Then
[tex]\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab[/tex]
and so (a + c)/(b + d) > a/b.
Then together we get the desired inequality.
brainiest to whoever right
Answer:
The area is 7.5 square units
Any mathematician am giving brainliest for this question
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Answer:
(x, y) = (1/2, 1)
Step-by-step explanation:
Subtract twice the second equation from the first to eliminate the x-variable.
(2/x +3/y) -2(1/x -4/y) = (7) -2(-2)
11/y = 11 . . . . . . . simplify
y = 1 . . . . . . . . multiply by y/11
__
Substituting into the second equation gives ...
1/x -4/1 = -2
1/x = 2 . . . . . . add 4
1/2 = x . . . . . . multiply by x/2
The solution is (x, y) = (1/2, 1).
_____
Additional comment
The attached graph seems to show that the graphs of the two equations also intersect at (x, y) = (0, 0). However, careful consideration of these equations leads to the conclusion that x=0 and y=0 are not in the domain of either equation. (Division by 0 is undefined.) So, the only solution is (x, y) = (1/2, 1).
If you were to multiply both equations by xy to eliminate fractions, you would, indeed, arrive at the conclusion that (x, y) = (0, 0) is a solution. As we noted, that "solution" is extraneous. Whenever you multiply an equation by an expression that can have the value 0, you need to be careful to exclude any "solution" that makes that expression 0.
Help please due today
Answer:
the scale factor is greater than 1
hope this helps!:)
HELP ASAP I WILL GIVE BRAINLIEST
Answer:
20 x 6
Step-by-step explanation:
23 x 6 = 138
We already have 3 x 6 on the right side, however, so subtract 3 x 6 or 18 from 138:
138 - 18 = 120
Now we have to fill in the blank with an answer that, when multiplied, equals 120 so that the equality is true.
The only option that works out to 120 is the second option, 20 x 6.
Answer:
(20×6)
Step-by-step explanation:
23×6=(20×6)+(3×6)
138=120+18
138=138
Match the line described on the left with the slope of the line on the right. y = 3‐--------------------------------------undefined 9x – 3y = 18.--------------------------,------- - 2 the line through (5, 7) and (5, – 8) -------0 the line through ( – 4, – 1) and (-1,–7)--- 3.
Answer:
y=3, 0; 9x-3y=18, 3; line through (5, 7) and (5, – 8), undefined; the line through ( – 4, – 1) and (-1,–7), -2;
Step-by-step explanation:
y=3 is a horizontal line so the slope is 0
9x-3y=18 can be written as 3y=9x-18 or y=3x-6 so the slope is 3
the line through (5,7) and (5,-8) is a vertical line since the x value didnt change between the two points so the slope is undefined
we have to find the slope of the line through ( – 4, – 1) and (-1,–7). to do this use the formula (y_2-y_1)/(x_2-x_1)=(-7-(-1))/(-1-(-4))=(-7+1)/(-1+4)=-6/3=-2 so the slope is -2
Can someone please help me (giving brainliest to whoever is right)
Write the equation of the line that passes through (6,8 ) and (2,4).
Answer:
y = x + 2
Step-by-step explanation:
The slope of the given points (6, 8) and (2, 4) is m = 1.
The y-intercept found through the slope, m = 1, is b = 2.
So, m = 1 and b = 2, right?
Let's put this together into the formula y = mx + b, we'll get: y = x + 2
Blue whales eat an average of 5,000 pounds of fish daily, with a standard deviation of 850 pounds. Approximately what percentage of blue whales eat more than 5,850 pounds of fish?
1.59%
15.87%
31.74%
84.13%
Answer:
31.74%
Step-by-step explanation:
..........................
Answer:
B) 15.87%
I got full points on this question!! It's correct!
A town has received about 49 inches of rainfall each year for the last 122 years. About how many inches of rain is this?
Answer:
5,978 inches
Step-by-step explanation:
you multiply 49 inches of rainfall by how many years it's been doing it for and you get 5,978
Select the TRUE statement below regarding aggregate supply in the long and short run.
O if production is below the LRAS, it will eventually have to fall back.
In the long run, changes in price will affect output.
O In the short run, there is no relationship between price level and RGDP.
O The discovery of new resources can cause the LRAS curve to move.
C. ....................
Regarding aggregate supply in long and short run (C) is the correct option.
What is aggregate supply ?The whole supply of goods and services produced within an economy at a certain overall price in a given period is known as aggregate supply, also known as total output.
What is the TRUE statement below regarding aggregate supply in the long and short run ?
During short run there is no relationship between price level and RGDP.
The intersection of the aggregate demand and short-run aggregate supply curves determines real GDP and price level in the short run. However, keep in mind that in the near run, sticky pricing may impede the economy from attaining its natural level of employment and output.
Hence we can say that In the short run, there is no relationship between price level and RGDP , (c) option is the correct answer.
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Solve UW. how do I get the answer?
Answer:
UW = 67
Step-by-step explanation:
UW = 6x - 35
VW = 4x - 20
UV = 19
So that means
4x - 20 + 19 = 6x - 35
4x - 1 = 6x - 35
-1 = 2x - 35
34 = 2x
x = 17
6(17) - 35
102 - 35 = 67
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Step-by-step explanation:
19 + ( 4x - 20 ) = 6x - 35
4x - 1 = 6x - 35
2x = 34
x = 17
UW = 6(17) - 35 = 67
All the applicants chose at least one of the three countries Egypt, Ghana and South Africa. A total of 2417 applicants chose Egypt as their favorite destination; 3500 applicants chose Ghana or South Africa as their favored destination. Of those that chose Egypt, 1233 also chose Ghana. 1031 applicants chose Ghana and South Africa, while 2014 chose Egypt or South Africa but not Ghana. Only 565 applicants indicated their preference for Egypt and Ghana but not South Africa. If 1803 did not indicate Egypt as their preferred destination, obtain the following:
The total number of applicants assessed. (5 marks)
The number of applicants who chose each of the three destinations only. (3 marks)
The most popular of the three destinations. (2 marks)
Answer:
hard quiz
Step-by-step explanation:
in a survey of 120 people it was found that 65 people like Messi and 60 like Ronaldo while 20 donot like both. by drawing Venn diagram find the number of people who like both Messi and Ronaldo
Answer:
15.
(P.S: Messi is the greatest footballer of all time) :)
To get the number of people who like both Messi and Ronaldo, you will add the two figures and the remain 20 that is not in the box minus x =120
I need help ASAP thanks!
The decimal for the first one is 0.4, and the fraction is 2/5.
The second one is also 0.4 and 2/5.
Yes, this means that both of these models are equal to each other. This is because Model 1 is equal to 4/10, while Model 2 is equivalent to 40/100. 4/10 is the same thing as 40/100, though. It's just a little bit more simplified, but the fully simplified answer would be 2/5.
So, therefore, the final answer is that both of these models are equal.
Anyways, I hope that this has helped you.
A sample of single celled marine algae from the Giant Stairs site provided an estimate of 100,000 cells on the initial sampling date. Ten days later, the population size was estimated to be 600,000 cells. Calculate the per capita rate of increase (r) for the population.
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Answer:
r ≈ 19.6% per day
Step-by-step explanation:
The growth of the population can be modeled by ...
P = P0 × (1 +r)^t
where P0 is the initial population, r is the growth rate (per day), and t is the number of days. Using the given numbers, we can find r to be ...
600,000 = 100,000 × (1 +r)^10
6^(1/10) = 1 +r
r = 6^0.1 -1 ≈ 0.196231
The growth rate per day is about 19.6%.
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Water flows out of a hose at a constant rate. After 2 1/3 minutes, 9 4/5 gallons of water have come out of the hose. At what rate, in gallons per minute, is water flowing out of the hose?
Time taken: 2[tex]\frac{1}{3}[/tex] minutes = 7/3 minutes
Water released: 9[tex]\frac{4}{5}[/tex] gallons = 49/5 gallons
Rate of water flowing out:
Rate(in gallons/minute) = Water released (in gallons) / Time Taken (in minutes)
plugging the given values
Rate = [tex]\frac{\frac{49}{5} }{\frac{7}{3} }[/tex] = [tex]\frac{49}{5} * \frac{3}{7}[/tex]
Rate = 21/5 = 4.2 gallons/minute
Answer:
Time taken: 2\frac{1}{3}
3
1
minutes = 7/3 minutes
Water released: 9\frac{4}{5}
5
4
gallons = 49/5 gallons
Rate of water flowing out:
Rate(in gallons/minute) = Water released (in gallons) / Time Taken (in minutes)
plugging the given values
Rate = \frac{\frac{49}{5} }{\frac{7}{3} }
3
7
5
49
= \frac{49}{5} * \frac{3}{7}
5
49
∗
7
3
Rate = 21/5 = 4.2 gallons/minute
Step-by-step explanation:
i hope it helps
Ernie writes this problem:
525 divided by 1500
Which expressions represent Ernie's problem?
Select each correct answer.
1500|525
525
____
1500
525Divied by 1500
525|1500
1500
____
525
Answer:
Pretty sure it would be 525/1500
Step-by-step explanation:
Read the problem outloud and you would hear that 525 is divided BY 1500, so 525 goes on top of the line since it is being divided by 1500. hope this helps!
Answer:
525 ÷ 1500
1500/525
525
-------
1500
are the correct answers.
Step-by-step explanation:
What expression is this equivalent to -4x^2 + 2x - 5(1 + x)
Answer:
-4x^2 -3x - 5
Step-by-step explanation:
-4x^2 + 2x - 5(1 + x)
Distribute
-4x^2 + 2x - 5 -5x
Combine like terms
-4x^2 -3x - 5
Which equation should be used to graph [tex]y=sec^{-1} (x)[/tex] on a calculator?
[tex]y = \frac{1}{sec(x)} \\y=\frac{1}{cos^{-1} (x)} \\y=sec(\frac{1}{x} )\\y=cos^{-1} (\frac{1}{x} )[/tex]
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Answer:
(d) y = arccos(1/x)
Step-by-step explanation:
You are given y = arcsec(x), which means sec(y) = x = 1/cos(y). Then ...
cos(y) = 1/x
y = arccos(1/x) . . . . . matches choice D
497 + 184
A. 581
B. 671
C.681
D.571
Answer:c
Step-by-step explanation:
Helppppppp pleaseeee
whats 1+(3x3)???? HELP I WILL GIVE BRAINLIEST !!!!
Answer:
[tex]1 + (3 \times 3) = 1 + 9 = 10 \\ thank \: you[/tex]
Answer:
its 10
Step-by-step explanation:
1+(3x3)
1+(9)
10
plz give brainliest im tryna level up
When analyzing an argument, the first task is to identify its premise or premises and its conclusion. Conclusion indicators are words or phrases that can help you identify which statement in an argument is the conclusion.Each argument shown next uses a conclusion indicator. Identify the conclusion indicator and the argument's conclusion. Type the indicator word or phrase into the space provided, and then select which statement best represents the argument's overall conclusion.Argument ASilver cars are more likely to be pulled over than any other kind of car. This is because there are more silver-colored cars on the road than any other kind of car. Kari drives an average-looking silver car to and from work everyday. We may infer that Kari is more likely to be pulled over.From this argument, type the conclusion indicator word or phrase here:Which statement best represents the conclusion of the argument?Kari is more likely to be pulled over.Kari drives an average-looking silver car to and from work everyday.Silver cars are more likely to be pulled over than any other kind of car.There are more silver-colored cars on the road than any other kind of car.Argument BScissors are not a toy. If you run with scissors, then you could get hurt. You could poke your eye out or cut yourself with the scissors if you fall. For these reasons, you should never run with scissors.From this argument, type the conclusion indicator word or phrase here:Which statement best represents the conclusion of the argument?You could poke your eye out or cut yourself with the scissors if you fall.If you run with scissors, then you could get hurt.Scissors are not a toy.You should never run with scissors.Argument CWe know that the natural world is governed by scientific laws of regularity. Those laws express predictable relationships that do not allow any wiggle room for variant outcomes. So, humans do not have free will. This is because the human body is as much a part of the natural world as any other physical object.From this argument, type the conclusion indicator word or phrase here:Which statement best represents the conclusion of the argument?Humans do not have free will.The natural world is governed by scientific laws of regularity.The human body is as much a part of the natural world as any other physical object.Scientific laws express predictable relationships that do not allow any wiggle room for variant outcomes.
In Argument A the conclusion indicator is "we may infer that" and the conclusion is Kari is more likely to be pulled over.
In Argument B the conclusion indicator is "For these reasons" and the conclusion is You should never run with scissors.
In Argument C the conclusion indicator is "So" and the conclusion is Humans do not have free will.
To identify the conclusion of each argument, we can either separate the premises (examples of the author's opinion) from the entire argument or we can identify the conclusion indicators.
Some conclusion indicators include:
therefore, thus, hence, so, for these reasons, we may infer, as a result,consequently, etcArgument A:
conclusion indicator = we may infer thatConclusion = Kari is more likely to be pulled over.
Argument B:
conclusion indicator = For these reasons,Conclusion = You should never run with scissors
Argument C:
conclusion indicator = So,Conclusion = Humans do not have free will
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Kelsey solved the following equation:
7x − one over two (8x + 2) = 6
Step Work Justification
1 7x − 4x − 1 = 6
2 3x − 1 = 6
3 3x = 7
4 x = 7 over 3
Which of the following has all of the correct justifications Kelsey used to solve this equation?
Question 8 options:
1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
1. Multiplication property of equality 2. Combine like terms 3. Addition property of equality 4. Division property of equality
1. Distributive property 2. Combine like terms 3. Subtraction property of equality 4. Division property of equality
1. Multiplication property of equality 2. Combine like terms 3. Subtraction property of equality 4. Division property of equality
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Answer:
(a) 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
Step-by-step explanation:
Replacement of -1/2(8x +2) by -4x -1 is use of the distributive property, eliminating choices B and D.
In step 3, addition of 1 to both sides of the equation is use of the addition property of equality, eliminating choice C. This leaves only choice A.
_____
Additional comment
This problem makes a distinction between the addition property of equality and the subtraction property of equality. They are essentially the same property, since addition of +1 is the same as subtraction of -1. The result shown in Step 3 could be from addition of +1 to both sides of the equation, or it could be from subtraction of -1 from both sides of the equation.
In general, you want to add the opposite of the number you don't want. Here, that number is -1, so we add +1. Of course, adding an opposite is the same as subtracting.
In short, you can argue both choices A and C have correct justifications. The only reason to prefer choice A is that we usually think of adding positive numbers as addition, and adding negative numbers as subtraction.
Answer:1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
Step-by-step explanation:
Can someone please show me how to solve (-6)=-x+b with steps?
Answer:
x = 6+b
Step-by-step explanation:
-6 = -x+b
Subtract b from each side
-6-b = -x+b-b
-6-b = -x
Multiply each side by -1
6+b = x
An insurance company’s records indicate that the mean compensation paid to clients claiming on motor insurance is R10 800 with standard deviation R2 500. Suppose that 50 claims are made within one week. What is the probability that the mean compensation paid is less than R10 200?
Answer:
10800
Step-by-step explanation:
The average price of a 0.5- carat round diamond is $3700 and the average price of a 0.75- carat diamond is $4950. If the weight and the price of the diamond is linearly related, how much will a 2.5 -carat round diamond cost?
Since the problem stated the weight and price are in a linear relationship, we can use y=mx+b.
First, let's calculate our slope.
m = (4950-3700)/(0.75-0.5) = 5000
Now, let's solve for b.
3700 = 5000(0.5) + b
Simplify the right side of the equation.
3700 = 2500 + b
Subtract 2500 from both sides
1200 = b
Now our equation looks like this:
y = 5000x + 1200
Let's plug 2.5 in for x to solve for the diamond cost.
y = 5000(2.5) + 1200
Simplify the right side.
y = 13700
The average price of a 2.5 carat diamond is $13700
turn 5/9 into a decimal.
5/9 to a decimal would be .5 repeated
The answer is .5 repeated
Do not put your answer as .5 because .5 is 5/10
A proper answer can be something like "0.5 repeated, 0.5555..., or .5 with a line over the 5"
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
| m^2+n^2 |
When m= -5 and n= 3, the value of the expression is ____.
**I answered 16 and it was wrong**
The value of the expression | m^2+n^2 | at m = -5 and n = 3 is 34.
Given,
| m^2+n^2 |
We need to find the value of this expression at m = -5 and n = 3.
What is the modulus of x?The modulus of x is given as |x|.
The modulus of a negative x is also positive.
|-x| = x
How do we find an expression at a given point?Example:
x + 2 at x = 1
= 1 + 2
= 3
Find the value of | m^2+n^2 | at m = -5 and n = 3.
| m^2+n^2 |
= | (-5)² + (3)² |
= | 25 + 9 |
= | 34 |
= 34
Thus the value of the expression | m^2+n^2 | at m = -5 and n = 3 is 34.
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HELP PLS!! D:
The net of a rectangular prism is shown below. What is the total surface area of this prism?
A. 112 cm²
B. 142 cm²
C. 105 cm²
D. 71 cm²
=========================================================
Explanation:
Think of unwrapping a present and doing so without any unnecessary tearing. That means there aren't any little small pieces thrown away. There are many ways to unwrap a 3D box, and this diagram shows one of many ways. This flat layout is the 2D version of the 3D surfaces.
To find the surface area of the 3D figure, we simply need to find the area of each rectangle in this 2D flat net. Once we know all the little areas, we add them up to get the surface area.
------------------------------
The lowest rectangle is 3 cm by 5 cm, so its area is 3*5 = 15 cm^2. Let A = 15 so we can use it later.
Let's move to the middle row of four rectangles. From left to right, we have these four rectangular areas
3*7 = 21 cm^25*7 = 35 cm^23*7 = 21 cm^25*7 = 35 cm^2I'll call these results B,C,D,E in the order given above. So B = 21, C = 35, etc.
The rectangle up top has area of 3*5 = 15 cm^2. I'll let F = 15
Lastly, we'll add up the sub-areas to get the grand total
A+B+C+D+E+F = 15+21+35+21+35+15 = 142 cm^2 is the surface area
------------------------------
Another pathway to the answer:
If you can picture how this flat diagram would fold up, then you would see that we'd get a 3D block with the following dimensions
L = 7 cmW = 5 cmH = 3 cmThe order of L,W,H doesn't really matter.
Then we can use the 3D block surface area formula like so
SA = 2*(LW + LH + WH)
SA = 2*(7*5 + 7*3 + 5*3)
SA = 2*(35 + 21 + 15)
SA = 2*71
SA = 142 cm^2 is the surface area
As you can see from the third step, we have "35", "21" and "15" show up again. The 2 out front is because we have 2 copies of each item mentioned.