Answers
The proof of the expression 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated for pqr = 1.
What is defined as the indices?The small floating number which shows up after a number or letter is known as an index or power. Indices represent the number of times a number or word has indeed been multiplied by itself.For the given expression;
pqr = 1. Then pq = 1/r; qr = 1/p; pr = 1/q.
OR, pq = r⁻¹ ; qr = p⁻¹ ; pr = q⁻¹ .
The given expression is;
1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1
Consider LHS part;
= 1/(1+p+pr) + 1/(1+q+pq) + 1/(1+r+qr)
Multiply and divide q in the first part;
= q/(q+qp+qpr) + 1/(1+q+pq) + 1/(1+r+qr)
Put prq = 1 (given)
= q/(q+qp+1) + 1/(1+q+pq) + 1/(1+r+qr)
Add 1st and 2nd part;
= (q+1)/(q+qp+1) + 1/(1+r+qr)
Multiply and divide r in the first part;
= (q+1)r/(rq+rqp+r) + 1/(1+r+qr)
Put prq = 1 (given)
= (qr+r)/(rq+1+r) + 1/(1+r+qr)
Add both
= (qr+r+1)/(rq+1+r)
Both will be cancelled;
= 1 = RHS
Therefore, proof for 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated.
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The complete question is-
If pqr = 1, then prove that 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1
Answer:
pqr = 1
Step-by-step explanation:
Related Questions
find a vector a with representation given by the directed line segment ab−→−, where a(−6,0,1) and b(1,6,−2) .
Answers
vector representation of the given vectors will be AB(5,6,-3).
What is vector, explain by giving example?A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
The vector representation will be -
A(x1,x2,x3), B(x1,x2,x3) so, AB will be - (x2 - x1, y2 - y1, z2 - z1)
So, given,
A(−6,0,1)
B(1,6,−2)
AB(1+6, 6-0, -2-1)
AB (5,6,-3)
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Complete the following proof.
Given: y+2 /3=3
Prove: y=7
Proof:
b. Statement: 3(y+2 / 3)=3(3) Reason: ____________
Answers
Using the multiplication and the subtraction property, we can prove that the value of y in the equation given is: 7. (see proof below).
How to Solve an Equation?Given the equation, y + 2/3 = 3, to prove that y = 7, we have to solve the given equation in other to find the value of y which must be equal to 7.
(y + 2)/3 = 3 [given]
3 × (y + 2)/3 = 3 × 3 [multiplication property of equality]
y + 2 = 9
y + 2 - 2 = 9 - 2 [subtraction property of equality]
y = 7
Thus, using the multiplication and the subtraction property, we can prove that the value of y in the equation given is: 7.
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Jean makes a 15% commission on any clothing that she sells. Jean sold $50.00 worth of clothes to a customer. How much was her commission?
Answers
Answer:
$7.50
Step-by-step explanation:
15% of $50 is 7.50, so she or he made $7.50 from that piece of clothing
3x, 4x-2 solve for x
Answers
Answer: x=2
Step-by-step explanation:
3x=4x-2
3x-4x=4x-4x-2
-x=-2
x=2
O is between M and P, MO= x^2-3, OP=4x-1 and MP= 8x+1. Find length of each story segment.
MO=
OP=
MP=
Answers
MO=4-3=1
OP=8-1=7
MP=16+1=17
Given:
MO= [tex]x^2-3,[/tex]
OP=[tex]4x-1[/tex]
MP= 8x+1
O is the midpoint of MP so
MO=OP
[tex]x^2-3[/tex]=[tex]4x-1[/tex]
[tex]x^2-4x-4=0[/tex]
[tex]X^2-2x-2x-4=0\\x(x-2)-2(x-2)\\(x-2)(x-2)\\x=2[/tex]
MO=4-3=1
OP=8-1=7
MP=16+1=17
A line segment's midpoint is a point that is halfway between two points. The midpoint is the same distance between the two ends.
This calculator can be used to find the midpoint, the distance between two points, or an endpoint given the midpoint and the other endpoint. Solutions for Midpoint and Endpoint Calculators
Enter two points in the form of numbers, fractions, mixed numbers, or decimals. The midpoint calculator displays the work to be done:
midpoint of two given points
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Drag each label to the correct location on the image.
Find the sum of each pair of rational numbers. plelz help
Answers
The addition of the given fractions are;
1) -3³/₅ + -1¹/₅
= -4⁴/₅
2) (-3.5) + (-4)
= -7.5
3) 4.5 + (-3)
= 1.5
4) -5³/₅ + 3¹/₅
= - 2²/₅
How to add fractions?
1) We want to add the fractions as follows;
-3³/₅ + -1¹/₅
= -3³/₅ - 1¹/₅
= -18/5 - 6/5
= -24/5
= -4⁴/₅
2) (-3.5) + (-4)
= -3.5 - 4
= -7.5
3) 4.5 + (-3)
= 4.5 - 3
= 1.5
4) -5³/₅ + 3¹/₅
= -28/5 + 16/5
= - 2²/₅
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Assessment
42. Marco goes on a recreational scuba diving
expedition. What is a possible diving depth for
his expedition?
A0 meters
B40 meters
400 meters
D-40 meters
Answers
Was lulu related to the cubs? cite three (3) pieces of specific evidence here to support your answer:
Answers
Yes, Lulu was associated to one of the cubs. Cub #711 because It was discovered it in data set 5 for her parentage.
Why is genetics needed for lion research?They discovered that there is evident genetic evidence of current population fragmentation, which occurs when teams of a species are isolated from each other, by trying to compare the DNA of lions presently to lions from 100 years ago.
This fragmentation could have a long-term effect on the iconic species' genetic health.
What were the advantages for Lulu (#630) in raising the cubs who were not hers?Raising the children together has an evolutionary advantage because it makes sure that Lulu's genetic data is passed down.
Because her cub is one of many, there is safety in numbers.
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What is the value of x if e squared 3x+6=8
Answers
Step-by-step explanation:
there is explanation in the answer
Geologic time is divided into units based upon evidence from
Answers
Answer:
Fossils
Step-by-step explanation:
Hope this helps.
could 10 to the 0 power =10 ? to show wether it upholds the prpety xm time xn = xm+n
Answers
Answer:
11
Step-by-step explanation:
Answer:
no. 10^0=
Step-by-step explanation:
payton wants to buy kiwi and cherries to make a fruit tart. Kiwi cost $2.25 per pound and cherries cost $4.25 per pound. How many pounds of fruit does she buy if she buys 3 pounds of kiwi and 1.5 pounds of cherries? How many pounds of fruit does she buy if she buys xx pounds of kiwi and yy pounds of cherries?
Answers
If Payton buys 3 pounds of Kiwi and 1.5 pounds of cherries, then the pounds of fruit Payton bought at 4.5 pounds.
If Payton buys x pounds of Kiwi and y pounds of cherries, the number of pounds of fruit purchased is x + y.
How much fruit did Payton buy?Payton bought 3 pounds of kiwi and 1.5 pounds of cherries. The total fruits bought is therefore:
= 3 + 1.5
= 4.5 pounds of fruit
If Payton bought x pounds of kiwi and y pounds of cherries, again the total pounds purchased is:
= x + y
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when bonding teeth, orthodontists must maintain a dry field. a new bonding adhesive has been developed to eliminate the necessity of a dry field. however, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. tests on a sample of extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of mpa and a standard deviation of s mpa. orthodontists want to know if the true mean breaking strength is less than mpa, the mean breaking strength of the
Answers
When we compare the p-value and the significance level is given [tex]\alpha=0.01[/tex], we can see that [tex]p_v < \alpha[/tex], so we can conclude that we have enough evidence to reject the null hypothesis, which is less than 5.7 Mpa at 1% significance.
Given:
[tex]\bar{X}=5.07[/tex] display the sample means = 0.46 represent the standard deviation of the samplen = 10 size of the sample[tex]\mu_o=5.7[/tex] represent the value under consideration[tex]\alpha=0.01[/tex] represent the hypothesis test's significance levelThe statistic would be represented by t. (variable of interest)[tex]p_v[/tex] represent the test's p-value (variable of interest)Identify the null and alternative hypotheses.
We need to test a hypothesis to see if the true mean is less than 5.7 Mpa; the hypothesis system would be:
Null hypothesis: [tex]\mu \geq 5.7[/tex]Alternative hypothesis: [tex]\mu < 5.7[/tex]If the sample size is 30 and we don't know the population deviation, we should use a t-test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{X-\mu_0}{\frac{s}{\sqrt{n}}}[/tex] ......(1)The t-test: "Is one of the most common tests for determining whether the mean is (higher, lower, or not equal) to a specified value."
Determine the statistic
We can substitute the following information in formula (1):
[tex]t=\frac{5.07-5.7}{\frac{11.40}{\sqrt{30}}}=-4.33[/tex]P-value:
The first step is to compute the degrees of freedom, which in this case are:
[tex]d f=n-1=10-1=9[/tex]Because this is a one-sided lower-tailed test, the p-value would be:
[tex]p_v=P\left(t_{(9)} < -4.33\right)=0.00095[/tex]Therefore, when we compare the p-value and the significance level given [tex]\alpha=0.01[/tex], we can see that [tex]p_v < \alpha[/tex], so we can conclude that we have enough evidence to reject the null hypothesis, which is less than 5.7 Mpa at 1% significance.
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The complete question is given below:
When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called "Smartbond") has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. ( Trends in Biomaterials & Artificial Organs, Jan. 2003.) Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x = 5.07 Mpa and a standard deviation of s = 0.46 Mpa, where Mpa = megapascal, a measure of force per unit area. Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive. Conduct the appropriate analysis for the orthodontists. Use alpha= 0.01. What is the p-value?
25 points plus brainliest
Answers
Answer:
3
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other
so negative reciprocal of -1/3 is 3
Use the equation below to answer correctly fill in the blanks.
y = 3x + 2
Since linear lines are represented by the equation y = mx + b, I know that the slope (m) is
. The b value is
. This means the line is
3 to each figure when the starting value is
.
Answers
Answer:
this is sure confusing to me
you are leaving for a concert that starts in 5 hours and is 305 miles from your house. what average speed (in miles per hour) would allow you to arrive at the concert on time? miles per hour school starts in 37 minutes and you live 17 miles from school. what average speed (in miles per hour) would allow you to arrive at school on time? miles per hour
Answers
The average speed required to reach the concert in time is 61 miles per hour.
The average speed required to reach school in time is 27.567 miles per hour.
What is the average speed?
The average speed of an object is defined as the total distance travelled by an object in a particular interval of time or average time. Mathematically, average speed = total distance / total time taken. Its SI unit is m/s.
Calculation of the average speed
We are given that a concert starts in 5 hours and is 305 miles away from the house, i.e. time = 5 hours and distance 305 miles
Then the average speed in miles per hour is given by total distance / total time
Average speed = 305 / 5
= 61 miles per hour
Further, the time taken to reach school is 37 minutes which when converted to hours becomes 37 / 60 hour
The distance between school and home is 17 miles
So, the average speed = total distance / total time
= 17 / (37 / 60)
= (17 × 60) / 37
= 27.567 miles per hour
Hence, the average speed required to reach the concert in time is 61 miles per hour.
The average speed required to reach school in time is 27.567 miles per hour.
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Determine the solutions of the equation:
Absolute value of the quantity one third times x plus 9 end quantity minus 3 equals 21.
x = −11 and x = 5
x = −81 and x = 45
x = −99 and x = 45. <<<< THIS IS IT
x = −99 and x = 99
PLEASE HELP!!!
Answers
The solutions to the absolute value equation given by the word phrase; Absolute value of the quantity one third times x plus 9 end quantity minus 3 equals 21 are; x = −99 and x = 45.
What are the solutions of the absolute value equation as given in the task content?It follows from the task content that the solutions to the absolute value equations as given by the word phrase are to be determined.
Given;
| (1/3)x + 9 | - 3 = 21
Add 3 to both sides;
| (1/3)x + 9 | = 24
Hence, the result equations are; (1/3)x + 9 = 24 OR (1/3)x + 9 = -24.
Therefore, we have;
(1/3)x + 9 = 24
(1/3)x = 24 - 9
(1/3)x = 15
x = 45.
Also, considering the other equation;
(1/3)x + 9 = -24
Subtract 3 from both sides;
(1/3)x = -33
Multiply both sides by 3;
x = -99.
Ultimately, the solutions of the equation are;
x = −99 and x = 45.
Therefore, the solutions to the absolute value equation given by the word phrase; Absolute value of the quantity one third times x plus 9 end quantity minus 3 equals 21 are; x = −99 and x = 45.
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Help please I will give brainliest
Answers
Answer:
Option #1, #4 & #5
Step-by-step explanation:
It's rise over run which is y-axis/intercept (up and down) over x-axis/intercept (left or right).
Hope this helps.
4. Which of the following is true based on the congruence statement triangle △SUN≈ △FOG
Answers
Based on the congruence statement triangle △SUN ≈ △FOG, the true statement is SU is Congruent to side FO.
Congruence of the triangle:
Two triangles are said to be congruent if one can be placed over the other so that they coincide (fit together). This means that congruent triangles are exact copies of each other and when fitted together the sides and angles which coincide, called corresponding sides and angles, are equal.
For example,
△ABC ≈ △DEF
then,
Side AB corresponds to DE,BC corresponds to EF , and AC corresponds to DF .
Given,
The congruence statement triangle
△SUN ≈ △FOG
Based on the congruence of the triangle rule,
Here the option
SU is Congruent to side FO.
is the correct option.
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Kerry paid $8 for his admission ticket to the fair and bought 14 ride tickets.
He spent a total of $43 on admission and ride tickets. Write and solve an
equation to find the cost of one ride ticket. Put the cost of one ticket in the
answer space.
Answers
Answer: answer is 4 multiplied by eleven minus one is fourty three
Step-by-step explanation:
Solve the following system of equations graphically. Select the graph that shows the correct solution of the system.
x + y = 2
x = 1
Answers
Answer:
First one
Step-by-step explanation:
rearrange x + y = 2 in the form y = mx + c
y = -1x + 2
means gradient is -1 and y-intercept is 2. such line is shown in the first graph
see where x = 1 and draw a straight line. Such line is also only shown in the first graph.
it should be the first graph
Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+by=mx+b.
xx yy
11 1111
22 2222
33 3333
Answers
Answer:
gjj uijh
Step-by-step explanation:
Sarah bought a drink for $4 and bought 8 candy bars. She spent a total of 44 dollars. How much did each candy bar cost?
Answers
Answer:here is ur answer
4+8x=20 8x=20-4 8x=16 x=$2.00 for a candy bar
Step-by-step explanation: i really hope this helps pls lmk if i am wrong have a good day/night (: <3
Answer:
One per candy bar: 5$
8 candy bars: 40$
Step-by-step explanation:
Take four dollars away from the drink and you end up with 40$. And, then you'll go and divide 40 divided by 8 equals 5. So, per 1 candy bar is 5$.
Joseph had the following scores for a four-day tournament. day: 1, 2, 3, 4 score : -1 ,2, -2, -3 what was his total score for the tournament? write your answer as an integer.
Answers
The total score of Joseph for four days of the tournament is -4 .
Joseph had the following scores for a four-day tournament,
For the first day i.e., day 1 of the tournament the total score is -1 . For the second day i.e., day 2 of the tournament the total score is 2 . For the third day i.e., day 3 of the tournament the total score is -2 . For the fourth day i.e., day 2 of the tournament the total score is -3 .
To calculate the total score of four days of the tournament we need to add the score of first, second, third and fourth day.
The total score of four days of the tournament = ( -1 ) + ( 2 ) + ( -2 ) + ( -3 )
The total score of four days of the tournament = -4
The total score of Joseph for four days of the tournament is -4 .
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Only 5/8 of the class completed 1/2 of their homework. What is the rate of the homework per class?
Answers
Solve the system by substitution or elimination
y= 2x + 8
y= 3x - 1
Answers
Answer: x=9, y=26 (9,26)
DOGS On average, a male bulldog weighs 15 pounds less than a male
golden retriever. If the average male bulldog weighs 50 pounds, write
and solve an equation to find the average weight of a male golden
retriever.
A. 50= w-15; 65 pounds
B. 50=w+15; 35 pounds
C. 50= w-15; 35 pounds
D. 50=15-w; 65 pounds
Answers
differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are .
Answers
The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.
What is statistical significance?Statistical significance can be used to determine whether a result is more likely the consequence of chance or an important element.Significant results simply imply that you can be sure they are true rather than that you were fortunate (or unfortunate) in the sample you used.Now,
It can be presumed that the test mentioned is the t-test since it uses two samples. A t-t-value, test's which it generates, is what determines its statistical significance. The likelihood that a difference is statistically significant increases with increasing t-value. By dividing the mean difference between two samples by the square root of the sum of the variances of each sample, then by the size of each sample, one may determine the t-value.The likelihood that the difference between two means is statistically significant therefore increases if:a significant mean difference;the samples are substantial;The samples' standard deviations are lower.Hence, The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.
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Which ratios are equivalent to 8:12
Answers
Answer:
Step-by-step explanation:
2:3
Answer:
2:3.
Step-by-step explanation:
If you turn 8:12 into a fraction (8/12), then make it simplest form, it would be 2/3.
2/3 as a ratio is 2:3. Therefore, 2:3 is equivalent to 8:12.
Evaluate ab 0.5b when a = 1 and b = 5.
Answers
Answer:
Step-by-step explanation:
Calculate the formula weights.
mass of
1
mole of
a
b
⋅
(
0.5
b
)
=
0
g