(Look at photo)
54. Given that P is a positive number, N is a negative
number, and | P | > | N |, which of the following
expressions has the greatest value?
Answers
Answer: Choice G [tex]\left| \frac{p-n}{n} \right|[/tex]
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Explanation:
Pick a positive number for p, and a negative value for n. Make sure that p is further away from 0 than n is (so that [tex]|p| > |n|[/tex] is a true statement).
I'll go for these values
p = 5n = -2Replace every copy of p with 5, and replace every copy of n with -2. Then evaluate or simplify. Use your calculator if needed.
Let's start with choice F.
[tex]F = \left| \frac{p-n}{p} \right|\\\\F = \left| \frac{5-(-2)}{5} \right|\\\\F = \left| \frac{5+2}{5} \right|\\\\F = \left| \frac{7}{5} \right|\\\\F = \left| 1.4 \right|\\\\F = 1.4\\\\[/tex]
Now onto choice G
[tex]G = \left| \frac{p-n}{n} \right|\\\\G = \left| \frac{5-(-2)}{-2} \right|\\\\G = \left| \frac{5+2}{-2} \right|\\\\G = \left| \frac{7}{-2} \right|\\\\G = \left| -3.5 \right|\\\\G = 3.5\\\\[/tex]
Next up is evaluating the expression for choice H.
[tex]H = \left| \frac{p+n}{p-n} \right|\\\\H = \left| \frac{5+(-2)}{5-(-2)} \right|\\\\H = \left| \frac{5-2}{5+2} \right|\\\\H = \left| \frac{3}{7} \right|\\\\H \approx \left| 0.4286\right|\\\\H \approx 0.4286\\\\[/tex]
Then let's compute expression J.
[tex]J = \left| \frac{p+n}{p} \right|\\\\J = \left| \frac{5+(-2)}{5} \right|\\\\J = \left| \frac{5-2}{5} \right|\\\\J = \left| \frac{3}{5} \right|\\\\J = \left| 0.6 \right|\\\\J = 0.6\\\\[/tex]
Lastly, compute expression K.
[tex]K = \left| \frac{p+n}{n} \right|\\\\K = \left| \frac{5+(-2)}{-2} \right|\\\\K = \left| \frac{5-2}{-2} \right|\\\\K = \left| \frac{3}{-2} \right|\\\\K = \left| -1.5 \right|\\\\K = 1.5\\\\[/tex]
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To summarize, when plugging p = 5 and n = -2 into each expression, we got these results:
F = 1.4G = 3.5H = 0.4286 (approximate)J = 0.6K = 1.5Expression G leads to the largest output.
Therefore, [tex]\left| \frac{p-n}{n} \right|[/tex] has the largest value when p > 0 and n < 0.
The expression |(p-n)/n| has the greatest value. Therefore, option G is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, p is a positive number, n is a negative number, and |p| > |n|.
Let us consider p=5 and n=-2
Now,
F) |(p-n)/p|
= |(5-(-2))/5|
= |7/5|
= 1.4
G) |(p-n)/n|
= |(5-(-2))/(-2)|
= |7/(-2)|
= 3.5
H) |(p+n)/(p-n)|
= |(5-2)/(5-(-2))|
= |3/7|
= 0.43
J) |(p+n)/p|
= |(5-2)/5|
= |3/5|
= 0.6
K) |(p+n)/n|
= |(5-2)/2|
= |3/2|
= 1.5
The expression |(p-n)/n| has the greatest value. Therefore, option G is the correct answer.
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Related Questions
A
2.
-3
-2
-3
The midpoint of AB = ([?],[])
=PLEASE HELP I WILL MARK BRAINLIEST
Answers
Explanation:
The x coordinates of points A and B are 2 and -2 respectively. Add them up and divide by 2 and we would get (A+B)/2 = (2+(-2))/2 = 0/2 = 0.
The x coordinate of the midpoint is 0.
The y coordinate of the midpoint follows the same idea, but we focus on the y coordinates of course. You should find the y coordinate of the midpoint is 0.
The midpoint is at (0,0) as the diagram shows.
GET BRAINLIEST
There are 400 7th graders at your school. You sampled 35 of them and found that 14 students are in advanced math. How many 7th graders can you expect to be in advanced math at your school?
Answers
Answer:
160
Step-by-step explanation:
P(advance math | 7th grader) = 14/35 (sample size 35)
Estimated advance math 7th grader in school = 400 * 14/35
= 160
Answer: 160 people can be expected to be in advanced math
Step-by-step explanation:
14 ÷ 35 = 0.4
⇒ what is 40% of 400?
⇒ 0.4 × 400
⇒ 160 people
Find the area of the region which is inside the polar curve r=5sin(θ) but outside r=4. Round your answer to four decimal places
Answers
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be
Then the intersection point will be given as
[tex]\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214[/tex]
Then by the integration, we have
[tex]\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\[/tex]
[tex]\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\[/tex]
On solving, we have
[tex]\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75[/tex]
Thus, the area of the region is 3.75 square units.
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PLEASE HELP ME MI AMOR
Answers
Answer:
P(X > 8) = 5/18
P(X mod 5 ≠ 0) = 29/36
Step-by-step explanation:
You want various probabilities related to the sum of two dice.
Greater than 8Please refer to the attached chart of possible outcomes. There are 4 ways to roll a 9, 3 ways to roll a 10, 2 ways to roll 11, and one way to roll 12. That means there are 4+3+2+1 = 10 ways to roll a number greater than 8.
P(X > 8) = 10/36 = 5/18
Not divisible by 5It is easier to count results that are divisible by 5. Then the difference between that number and 36 will be the number of outcomes not divisible by 5.
5 can be rolled 4 ways, and 10 can be rolled 3 ways. A total of 4+3 = 7 of the 36 outcomes are divisible by 5. That means 36 -7 = 29 are not divisible by 5.
P(X not divisible by 5) = 29/36
<95141404393>
There are are 10 covered dishes to choose from 2 broccoli, 2 cake, 1 chicken, 2 fish, and 1 meatloaf
What is the probability of choosing a vegetable?
Answers
Based on the information marked in the diagram, ABC and DEF must be
congruent.
A. True
B. False
Answers
You start at (8, 6). You move left 6 units and right 8 units. Where do you end?
Answers
Answer:
(10,6)
Step-by-step explanation:
of you start at (8,6) X is left and right and Y is up and down so yoy move left 6 unites meaning your now at (2,6) then you move right so you go back again and now you have (10,6) Hope this helps
WILL GIVE BRAINLIEST
How would the median change if the number 71 replaced one of the 67's in the set?
71, 67, 67, 17, 69, 84, 21, 87
Question 5 options:
decrease
increase
no change
Answers
Answer:
increase
Step-by-step explanation:
Given data is: 71, 67, 67, 17, 69, 84, 21, 87Arranging in ascending order we find: 17, 21, 67, 67, 69, 71, 84, 87 Here N = 8 (Even number)N/2 = 4 and N/2 + 1 = 54th term = 67, 5th term = 69-> median = Sum of 4th and 5th term/2 = (67 + 69)/2 = 132/2 = 66Now, when one of the 67 is replaced by 71, the new data set in ascending order will be: 17, 21, 67, 69, 71, 71, 84, 87Here, 4th term = 69, 5th term = 71New median = (69 + 71)/2 = 140/2 = 70-> new median > initial medianCONCLUSION: Median will increase if the number 71 replaced one of the 67's in the set.
(WILL GIVE BRAINLIEST)
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common?
Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
Answers
Functions can be represented using equations and graphs Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
How to determine the key features?The domain of the function is defined as the set of the numbers we are allowed to put in the function while the range is the assumed data put in the function.
The functions are given as:
[tex]F(x)=e^{-x}\\\\\\g(x)=-\sqrt{x-4}[/tex]
Using a graphing calculator:
The domain of g(x) is [4, ∞)
The range of g(x) is [0, ∞)
The domain of f(x) is (–∞, ∞),
The range of f(x) is [0, ∞)
Both functions have positive values for their domains
By comparing the above highlights, the true statement between functions g(x) and f(x) is option 3
Read more about function domain and range at:
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Answer:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
I got it right on the test.
Which of the following fractions equal to 1/4
A. 12/60
B. 48/12
C. 36/108
D. 26/104
E. 17/50
Answers
Answer:
D
Step-by-step explanation:
A no = 1/5
B no = 4
C no = 1/3
D yes
E no = 17/50
26/104
Step-by-step explanation:the correct option is 26/104 because if 26 divides 26/104 it will give 1/4 because
26÷26= 1
104÷26=4
therefore, the correct option is 26/104
If one fourth of a square of positive number is 9, find the number.
Answers
Answer:
6
Step-by-step explanation:
1 /4 x^2 = 9 (Given) Multiply both sides of the equation by 4
x^2 = 36 sq rt both sides
x = 6
Help me find the Scale factor of these two rectangles!
Answers
Answer:
scale factor of 1/3 from the big rectangle to the small rectangle
Step-by-step explanation:
Hope this helps! Please mark me as brainliest:)
I really need help with this. I don’t understand it at all. It was due yesterday and I need to finish it. Please help.
Answers
if michaels score is 87, the class average is 82, and the standard deviation is 4. what is michaels z-score?
Answers
Answer:
Z = 1.25
Step-by-step explanation:
[tex]\displaystyle Z=\frac{\text{Observed Value}-\text{Mean of the Sample}}{\text{Standard Deviation of the Sample}}\\\\Z=\frac{x-\mu}{\sigma}\\ \\Z=\frac{87-82}{4}\\ \\Z=\frac{5}{4}\\ \\Z=1.25[/tex]
Hence, Michael's z-score is 1.25, which means that he scored 1.25 standard deviations above the class average.
help Mary ann and carlos are each saving for new scooters. Their savings are shown. Let x represent the number of hours each person works y represent the total earnings in dollars
after how many hours of work will mary ann and carlos have saved the same amount?
Answers
Answer:
4 hoursStep-by-step explanation:
Use a couple of ordered pairs on the graph and get the equation of the line:
(0, 2), (1, 10)The y-intercept is 2 and the slope is 10 - 2 = 8
The line is
y = 8x + 2Solve the system of equations by substitution to find the intersection
y = 6x + 10y = 8x + 26x + 10 = 8x + 28x - 6x = 10 - 22x = 8x = 4They will work 4 hours to get same amount of saving
Answer:
4 hours
Step-by-step explanation:
First, create a linear equation for Carlos using the graph.
Two points on the line: (0, 2) and (1, 10)
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{10-2}{1-0}=8[/tex]
Use the point-slope equation with the found slope and one of the points:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=8(x-0)[/tex]
[tex]\implies y=8x+2[/tex]
Now equate the equations for Mary Ann and Carlos, and solve for x:
[tex]\implies 6x+10=8x+2[/tex]
[tex]\implies 8=2x[/tex]
[tex]\implies x=4[/tex]
Therefore, Mary Ann and Carlos have saved the same amount after 4 hours work.
the table represents the number of minutes to walk to school find the mean 10 15 20 25
1221
Answers
Answer:
The answer is 258
Step-by-step explanation:
10+15+20+25+1221= 1291
1291 divided by 5 equals 258 with a remainder of 1
What is the length of side AB of parallelogram ABCD?
units
4g - 8
B
q+4
Answers
Answer:
8 units
Step-by-step explanation:
» Concepts
Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.
» Application
In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.
» Solving
Step 1: Subtract q from both sides.
[tex]4q-8-q=q+4-q[/tex] [tex]3q-8=4[/tex]Step 2: Add 8 to both sides.
[tex]3q-8+8=4+8[/tex] [tex]3q=12[/tex]Step 3: Divide both sides by 3.
[tex]3q/3 = 12/3[/tex] [tex]q=4[/tex]Step 4: Plug in the value of q for side AB.
[tex]4(4)-8[/tex] [tex]16-8[/tex] [tex]8[/tex]Therefore, the answer is 8 units.
What is the explicit formula for the sequence {3,8,13,18,…}?
Answers
Answer:
3+5(n-1)
Step-by-step explanation:
first term (a)=3
common difference (d)=5
they an=a+(n-1)d
=>3+(n-1)5
=>3+5(n-1)
Can anyone help me figure out what shape this is? 10th grade geometry
Answers
Answer:
I think option C is correct or it can be. B OPTION
As if we join B to C it will form a diagonal BC which will cut the shape into two right angled triangle
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
A television is on sale for $75 off. The price of the television with the sale is $300. If you use the equation n−75=300 to solve this problem, what does n represent?
Answers
Answer:
The original price
Step-by-step explanation:
I got it right
can you help me its worth 50
Answers
B. X is less than or equal to -4
A bag of candy contains five red four blue six green and three yellow candies what is the probability of randomly selecting one candy that is blue or yellow
Answers
Answer:7/18
Step-by-step explanation:
P(R) =4/18
P(Y)= 3/18
BOTH = 4/18 + 3/+18
Simplify the following expression
-2x^2 + 4 + 5x^2 - 11 - 12x
Write the steps, please
Answers
3x^2-12x-7
Pls help me, giving 10 points plus crown
Answers
Answer:
if u are talking about completing the table then that's easy
The diameter of a circle is 38 in. Find its area to the nearest whole number.
Answers
Answer:
1134
Step-by-step explanation:
Formula for diameter=2 x r
(π is 3.14)
Formula for area= π x r^2
So all you basically have to do is go backwords with the first one then plug the radius into the second one normally
38/2=19
Now just plug it into your second equation
π x 19^2=1134.11494795
And lastly round that to 1134, easy! :)
Simplify the expression. Write your answer as a power.
The simplified expression is
Answers
Answer:
view explanation, please
Step-by-step explanation:
If the variable is the same and you are multiplying: add the exponents.
[tex]Z^8 * Z^6 = Z^8+^6[/tex]
8+6=14
If the variable is the same and you are dividing: subtract the exponents.
[tex]Z^1^4-^8=Z^6[/tex]
Answer:
The answer is Z⁶
Step-by-step explanation:
Cancel the common factor, Z⁸
8x - 10
25
B
E
18
15
с
D
Solve for x
Answers
Step-by-step explanation:
the upper (smaller) triangle and the complete triangle are similar.
that means the angles in both triangles are the same. and the lengths of all corresponding pairs of sides correlate with the same scaling factor.
therefore,
(8x - 10) / (8x - 10 + 18) = 25 / (25 + 15)
(8x - 10) / (8x + 8) = 25 / 40 = 5/8
8(8x - 10) = 5(8x + 8)
64x - 80 = 40x + 40
24x = 120
x = 5
What is the equation of the line shown in this graph?
(3,-3) (-2,-3)
Answers
The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.
Answers
Answer:
centre : (4;-5)
radius : 2
Please help me on this!
Answers
Answer:
linear
Step-by-step explanation:
Answer:
bec97 is right it is linear
Step-by-step explanation:
y = 10 + 2x
Have a nice day! :)