Answers
Answer:
Step-by-step explanation:
Given expressions are,
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex] and [tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
Remove the radicals from the denominator from both the expressions.
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}} \times \frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{p}=\sqrt{\frac{(\sqrt{10}-\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{5}}[/tex]
[tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\times \frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{q}=\sqrt{\frac{(\sqrt{10}+\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}[/tex]
[tex]\sqrt{q}-\sqrt{p}-2\sqrt{pq}=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}-\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}}-2(\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}})(\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}})[/tex]
[tex]=\frac{1}{\sqrt{5}}(\sqrt{10}+\sqrt{5}-\sqrt{10}+\sqrt{5})-\frac{2}{5}[(\sqrt{10})^2-(\sqrt{5})^2)][/tex]
[tex]=\frac{1}{\sqrt{5}}(2\sqrt{5})-\frac{2}{5}(10-5)[/tex]
[tex]=2-2[/tex]
[tex]=0[/tex]
Related Questions
Lainey is looking for a new apartment and her realtor keeps calling her with new listings . The calls only take a few minutes , but a few minutes here and there are really starting to add up . She's having trouble concentrating on her work . What should Lainey do ? a ) Tell her realtor she can only receive text messages b ) Limit the time spent on each call c ) Turn off her phone until she is on a break d ) Call her realtor back when customers won't see her on the phone
Answers
Answer:
c ) Turn off her phone until she is on a break
A basketball player averages 22.5 points scored per game with a standard deviation of 6.2 points. In one game, the athlete scored 10 points. What is the z-score for the points scored in this game?
–2.02
–1.63
1.63
2.02
Answers
Answer:
Step-by-step explanation:
Z -2.02
x 10
µ 22.5
σ 6.2
A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 52 in^2 and a perimeter of 30in. Find the dimensions of the brochure. The longer side is _____in. The shorter side is ______ in.
Answers
9514 1404 393
Answer:
9.562 in5.438 inStep-by-step explanation:
The sum of side lengths of a rectangle is half the perimeter, so is 15 inches for this brochure. If x is one of the side lengths, then (15 -x) is the other one, and the area is ...
x(15 -x) = 52
x^2 -15x = -52 . . . . multiply by -1 and expand
(x -7.5)^2 = -52 +56.25 = 4.25 . . . complete the square
x = 7.5 ±√4.25 ≈ {5.438, 9.562} . . . inches
The longer side is 7+√4.25 ≈ 9.562 inches; the shorter side is 7-√4.25 ≈ 5.438 inches.
Find the surface area of the rectangular prism below.
Answers
Answer:
Option B
Step-by-step explanation:
This is the formula :
2(wl+hl+hw)
Step 1 : Take the length, width, and height and substitute the values in.
The required surface area of the rectangular prism is 461.02 square meters (m²).
What is surface area?Surface area is defined as the measure of a region or surface is called as surface area.
The surface area of a rectangular prism can be calculated by adding up the areas of all six faces. The formula for the surface area of a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Substituting the given values, we get:
Surface area = 2(12.3m x 4.3m) + 2(12.3m x 10.7m) + 2(4.3m x 10.7m)
Simplifying the expression gives:
Surface area = 461.02m²
Therefore, the surface area of the rectangular prism is 461.02 square meters (m²).
Learn more about the surface area here: https://brainly.com/question/2835293
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Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answers
Answer:
m=3*sqrt(2) and n=3
Step-by-step explanation:
tan(45)=3/n
1=3/n, n=3. As it's a right angled triangle, 3^2+3^2=m^2, m=3*sqrt(2)
The quotient of -8 and the sum of a and b
Answers
Hi! I'm happy to help!
To solve this, you need to know what all of the terms mean. Quotient means division, and sum means addition. Knowing this we can set up our expression.
Because there is an operation inside of an operation (addition inside of division) we use parenthesis.
-8÷(a+b)
I hope this was helpful, keep learning! :D
Select the statement that correctly compares two numbers. (GIVING BRAINLIEST)
4.13 = 4.130
5.16 < 5.06
6.28 < 6.08
7.09 > 7.19
Answers
Answer:
4.13=4.130
If there is a 0 at the end of a decimal then you can drop it.
The statement that correctly compares two numbers is 4.13 = 4.130. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
From the given options the correct expression which represents equality will be 4.13 = 4.130. The value of both the numbers is the same. There is not any significance of 0 at the end of the expression.
Therefore, the statement that correctly compares two numbers is 4.13 = 4.130. The correct option is A.
To know more about an expression follow
https://brainly.com/question/28040125
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The ratio of two numbers is 9 to 8, and their sum is 187. What are the numbers?
Answers
=========================================================
Explanation:
The ratio of the two numbers is 9 to 8, which we can write as shorthand into 9:8
Multiplying both parts by x gets us the ratio 9x:8x where x is nonzero.
The numbers 9x and 8x add up to 187, so,
9x+8x = 187
17x = 187
x = 187/17
x = 11
Which then means
9x = 9*11 = 998x = 8*11 = 88are the two numbers. Note how 9x+8x = 99+88 = 187 to help confirm the answers. Furthermore, note how 99:88 reduces to 9:8 after dividing both parts by the GCF 11.
Answer:
99 and 88
Step-by-step explanation:
Let the two number be 9x and 8x
Add together
9x+8x = 187
17x = 187
Divide by 17
17x/17 = 187/17
x = 11
The numbers are
9*11 = 99
and 8*11 = 88
The population p(t) of a culture of the bacterium Pseudomonas aeruginosa is given by ,p(t)= -1683t^2+75,000t+ 10,000 where is the time in hours since the culture was started. Determine the time the population was at its maximum. Round to the nearest hour.
Answers
Answer:
22hrs
Step-by-step explanation:
hope it is well understood?
James purchased five acres of land fo 75,000 what was the cost per acre
Answers
Answer:
$15,000
Step-by-step explanation:
James purchased a total of 5 acres of land for a total price of $75,000. To find the cost of each individual acre, simply divide the total cost with the total amount of acres purchased:
[tex]\frac{total price of land bought}{total amount of acres} = \frac{75000}{5} = 15000[/tex]
The cost per individual acre, assuming all of them cost the same, is $15,000.
~
Answer:
15000
Step-by-step explanation:
Since
5 acres = 75000
therefore,
the cost price per acre would be
total cost price ➗ 5
7500/5= 15000
HELP PLEASE!!!!
The median age for a first marriage in the United States for women was 25.9 in 2009 and 26.1 in 2010. Use an exponential model to predict the median age for women in 2019, where x is the number of years since 2009.
A) 23.9
B) 28.3
C) 28.0
D) 24.0
Answers
Answer:
29.1 Is the answer for 2009
Step-by-step explanation:
A family are going away for the weekend. They look at a road map to see where their hotel is.
The scale used is 1:250,000
The distance to their hotel measures 8.5 cm on the map.
What is the actual distance?
km
Answers
Answer:
106.25km
Step-by-step explanation:
8.5cm = 0.000085km
map:real life
1:1250000
0.000085km : 0.000085km * 1250000 = 106.25km
(0.5, -1)
(-1, 0.5)
(2, -4)
(1, -2)
Answers
Answer:
so your answer is (0.5,-1)
In a 4 day period, a delivery person delivered the following number of
packages per day: 1150, 1200, 1900 and 1350. The average number of
packages he delivered per day was _?_
Answers
Answer: 1400 packages
Step-by-step explanation:
1150+1200+1900+1350 divided by the 4 day interval means and average of:
1400 packages per day
Help needed!!!
Find the length of the segment indicated.
A. 12.1
B. 16.4
C. 13.3
D. 11.4
Answers
Answer:
A
Step-by-step explanation:
using the theorem of Pythagoras
x = sqrt* 19.6 ^2 - 15.4^2*
x = 7× sqrt* 3*
x = 12.1 units
Answer:
A.) 12.1
Step-by-step explanation:
I got it correct on founders edtell
The illustration below shows the graph of y as a function of x.
Complete the following sentences based on the graph of the function.
The y-intercept of the graph is the function value y=_____
The smallest positive x-intercept of the graph is located at x=_____
The greatest value of y is y=____ and it occurs when x=____
For x between x and x= 2 π the function value y___ 0
Answers
Answer:
below
Step-by-step explanation:
that is the solution above
I really need help with this
Answers
Answer:
G=21, F=9, M=6, L=7, E=20, D=15, B=10, R=12.5, T=16, N=13.5, W=18, H=36, Z=12
*I=5*
Step-by-step explanation:
I basically just found the scale factor/proportion from two given sides and then used that to find the remaining sides.
*I'm not sure about 'I' since the edge of the paper was cut off so I want sure if it was a 5 or a 15 on the left most problem in the third row. I assumed it was 15. If it's not, just shout it out in the comments and I'll fix it! :)*
You can fill the letters in at the bottom XD
I hope this helped! :D
Solve 6y - 9 + 2y - 5 = -8 y + 17 + 4y
Answers
Please Mark my answer brilliant
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three points. A random sample of 36 scores is taken and gives a sample mean of 68. Find a 85 % confidence interval estimate for the population mean exam score. Explain what the confidence interval means
Answers
this the answer of queastions
Step-by-step explanation:
67.18,68.82
Let mu be the true population mean of statistics exam scores. We have a large random samples of n=36 scores with a sample mean of 68.we know that the population standard deviation is sigma=3.A pivotal quantity is 3^sqrt(36)=(3/6)=68(1/2) which is approximately normally distributed. Therefore the 85%confidence interval is 68-(1/2)(1.6449), 68+(1/2)(1.6449) i.e (67.18,68.82)
Which function represents the graph below?
Answers
Answer:
The inequalities all need to be of the form a < x ≤ b. Only the first selection matches that requirement.
Step-by-step explanation:
Please help meeee
Find the value of d.
A. 47
B. 56
C. 75
D. 30
Answers
Answer:
56
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
75 = 1/2 (94+d)
Multiply by 2
75*2 = 94+d
150 = 94+d
Subtract 94 from each side
150-94 = d
56=d
Kayla parks her car at the corner of Ogilvie and Montreal Rd. She walks 80m East and then turns 30° to the left towards her office building and continues walking for another 100m until she reaches her building. She then takes the elevator to her office 60m above ground level and looks out the window. She can see her car from here. How far is it from where she is to her car in a direct line?
Answers
9514 1404 393
Answer:
184 m
Step-by-step explanation:
The direct distance from Kayla's car (C) to the door of her office building (B) can be found using the Law of Cosines. The interior angle of the triangle at the turning point is 180° -30° = 150°, so the distance is ...
t² = b² +c² -2bc·cos(T)
t² = 80² +100² -2·80·100·cos(150°) = 30256.406
The direct distance from her window to the car can be found from the Pythagorean theorem. The legs of the right triangle are the distance from the car to the building (CB) and the height from the building entrance to the window (BW).
CW = √(t² +60²) ≈ 184.001
The direct line distance from Kayla to her car is 184 meters.
_____
For the first computation, we used the usual notation for a triangle, where capital letters (CTB) are the vertices and angles, and corresponding lower-case letters are their opposite sides.
A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 millimeters and standard deviation 0.08 millimeter. (a) [5pts] What proportions of the diameters are greater than 25.4
Answers
Answer:
The proportions of the diameters that are greater than 25.4 millimeters is 5%.
Step-by-step explanation:
Given;
mean of the normal distribution, m = 25.1 millimeters
standard deviation, d = 0.08 millimeter
1 standard deviation above the mean = m + d = 25.1 + 0.08 = 25.18
2 standard deviation above mean = m + 2d = 25.1 + 2(0.08) = 25.26
3 standard deviation above the mean = m + 3d = 25.1 + 3(0.08) = 25.34
4 standard deviation above the mean = m + 4d = 25.1 + 4(0.08) = 25.42
To obtain a diameter greater than 25.4, we select data after 4 standard deviation above the mean.
Data within 4 standard deviation above the mean is 95%
Data outside 4 standard deviation above the mean is 5%
Therefore, the proportions of the diameters that are greater than 25.4 millimeters is 5%.
the mean salary if of 5 employees is $35900. the median is $37000. the mode is $382000. If the median payed employee gets a $3100 raise, then…
New median:
New mode:
Answers
Answer:
Step-by-step explanation:
New median:40100
New mode:385100
What temperature is 10 degrees les then 6 degrees Celsius
Answers
Answer:
-4
Step-by-step explanation:
you say 6-10
which is -4
What is the temperature if 10°C less than 6°C
Answer:-10°C less than 6°C is -4°C
Explanation:
So, if we start with 6°C, and we want a temperature 10°C less than that, then we can just subtract 10 from 6.
6-10 = -4
```````````````````````````````````````````````````````````Let the set A be defined as follows.
A={h,m,s,d,c}
(a) Find the total number of proper subsets of A.
(b) Find the total number of subsets of A.
Answers
Answer:
(a) 31
(b) 32
Step-by-step explanation:
We will do (b) first since it will help us do (a).
(b)
There are [tex]n(A)=5[/tex] elements in [tex]A[/tex]. Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is
[tex]2^{n(A)}=2^5=32[/tex]
(a)
A subset of [tex]A[/tex] is called proper if it does not equal [tex]A[/tex]. The only subset of [tex]A[/tex] that is not proper is [tex]A[/tex] itself, so simply subtract 1 from the number of subsets to get the number of proper subsets, which is
[tex]32-1=31[/tex]
look at the image for the question
Answers
Answer:
117.8
Step-by-step explanation:
surface area = πr²+πrl, where r = radius and l = slant height
so,
πr²+πrl
= π×3²+π×3×9.5
= 75π/2
= 117.8 (rounded to the nearest tenth)
How do I answer this
Answers
Answer:
11. Yes
12. No
Step-by-step explanation:
11. The x values only have 1 y value, so it makes it a function.
12. The x value 0 has 2 y values -4 and 4, therefore it is not a function, because in functions that x value can only have one y value,
Help please, but more importantly, I am really trying hard to figure out how, you arrive at the answer. Thanks in advance!
A recent social survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?ocial survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?
Answers
Answer:
Step-by-step explanation:
#1
A) P(FEMALE|APPLE)
apple total = 346
apple/female = 194
194/346 = .56 = 56 %
B) P(APPLE|MALE)
male total = 320
apple male = 152
152/320 = .475 = 47.5%
C) female prefer Microsoft
152:168 = 76:84 = 38:42 = 19:21
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a significance level of ? can be found as follows. In the expression
E=z?p1(1?p1)n1+p2(1?p2)n2?????????????????????????
we replace both n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, and p2, by 0.5 (because their values are not known). Then we solve for n, and get
n=(z?)22E2.
Finally, increase the value of n to the next larger integer number.
Use the above formula and Table C to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 99% confidence level and that the error is smaller than 0.07.
n=______.
Answers
Answer:
n= (z)22E2
n=10× 99%÷ 0.07
