Assume √41 is rational, so that there exist integers p, q such that
[tex]\sqrt{41} = \dfrac pq[/tex]
and p/q is irreducible. Taking squares, this would mean
[tex]41 = \dfrac{p^2}{q^2} \implies p^2 = 41q^2[/tex]
This tells us that 41 is a factor of p², which in turn means 41 is a factor of p because 41 is prime. We can consequently write p = 41n for some integer n. But then
[tex]p^2 = (41n)^2=41q^2 \implies 41n^2 = q^2[/tex]
which says 41 also divides q² and hence divides q as well. In other words, p/q is reducible, so we have a contradiction.
If 1/5 of those in a high school are freshmen, and 40% of the freshmen are women, and 3/5 of those in the other grades are women, how many men are enrolled in the high school, given that there are 600 students altogether? a. 240.
b. 264.
c. 300.
d. 336.
e. 360
There are 264 male students in the high school containing 600 students.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
There are 600 students altogether, hence:
Number of freshmen = (1/5) * 600 = 120
Number of other graders = 600 - 120 = 480
Number of male freshmen = 120 - (0.4 * 120) = 72
Number of male other graders = (1 - 3/5) * 480 = 192
Total number of male = 72 + 192 = 264
There are 264 male students in the high school containing 600 students.
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what are these shapes called?
Pyramid, rectangular prism, and triangular prism?
Answer:
the nets are for 3Dshapes
Step-by-step explanation:
the drawing shown are nets
What was the experimental probability of choosing a blue marble from a bag?
Answer:
7/20
Step-by-step explanation:
There were 20 tries, and 7 of them(blue picks) were desired outcomes.
The forecast for Wednesday is literally changed to a high 70 without calculating the new mean describe have the changes that mean high temperature for the next five days
Heating and Cooling Degree Days
Degree days are based on the assumption that when the outside temperature is 65°F, we don't need heating or cooling to be comfortable. Degree days are the difference between the daily temperature mean, (high temperature plus low temperature divided by two) and 65°F. If the temperature mean is above 65°F, we subtract 65 from the mean and the result is Cooling Degree Days. If the temperature mean is below 65°F, we subtract the mean from 65 and the result is Heating Degree Days.
Step-by-step explanation: Example 1: The high temperature for a particular day was 90°F and the low temperature was 66°F. The temperature mean for that day was:
( 90°F + 66°F ) / 2 = 78°F
Because the result is above 65°F:
78°F - 65°F = 13 Cooling Degree Days
Example 2: The high temperature for a particular day was 33°F and the low temperature was 25°F. The temperature mean for that day was:
( 33°F + 25°F ) / 2 = 29°F
Because the result is below 65°F:
65°F - 29°F = 36 Heating Degree Days.
The calculations shown in the two examples above are performed for each day of the year and the daily degree days are accumulated so that we can compare months and seasons.
What is the distance between A(7, 4) and B(2, -8)?
Answer:
13 units
Step-by-step explanation:
Distance formula:
d = [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
In this problem,
d = [tex]\sqrt{(7 - 2)^2 + (4 - -8)^2}[/tex]
d = [tex]\sqrt{(5)^2 + (12)^2}[/tex]
d = [tex]\sqrt{25 + 144}[/tex]
d = [tex]\sqrt{169}[/tex]
d = 13
Someone pls help me answer this pls
Answer:
5^15
Step-by-step explanation:
Using the laws of powers, you can multiply 5^3 out of its bracket and get 5^27. Then, once again, using the laws of powers, you can get 5^15 by subtracting the powers.
Answer:
(5^3)^9/5^12 is equivalent to 5^15
Step-by-step explanation:
Begin by simplifying (5^3)^9
To make it much easier, apply the power rule. (a^x)^y = a^xy)
Multiply 3 x 9 = 27... so we get 5^27
Next, instead of dividing 27/12, which will result in a decimal..you must do 27-12, which is applying the quotient rule. (a^x / a^y = a^x-y)
5^27/5^12 = 5^27-12 = 5^15
( When I use /, it signifies to divide.)
So, (5^3)^9/5^12 is equivalent to 5^15! Hope this helps! :D
The table below represents the data collected at a sandwich shop for the last six months with respect to the type of bread people ordered (sourdough or wheat) and whether or not they got cheese on their sandwich.
Are the events “sourdough” and “with cheese” independent events? Explain why or why not using probabilities. Show all work to receive full credit.
Answer:
First, add totals to the table (see attachment)
Let S = Sourdough
Let C = With cheese
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(S)=\dfrac{1225}{3125}=\dfrac{49}{125}[/tex]
[tex]\implies \sf P(C)=\dfrac{2000}{3125}=\dfrac{16}{25}[/tex]
[tex]\implies \sf P(S \cap C)=\dfrac{800}{3125}=\dfrac{32}{125}[/tex]
For independent events S and C,
[tex]\sf P(S \cap C)=P(S)P(C)[/tex]
[tex]\sf\:As\quad P(S) \cdot P(C)=\dfrac{49}{125} \cdot \dfrac{16}{25}=\dfrac{784}{3125}[/tex]
[tex]\sf And\quad \dfrac{32}{125} \neq \dfrac{784}{3125}[/tex]
[tex]\sf Then \quad P(S \cap C)\neq P(S)P(C)[/tex]
So the events are NOT independent
Point m lies between points l and n on line segment l n . the space between l and m is 10 x 8. the space between m and n is 5 x minus 4. if ln = 12x 16, what is the length of line segment l n in units? 16 units 40 units 48 units 64 units
The length of line segment l n on which point m lines in between is 64 units. Option 4 is the correct option.
What is the length of line segment?Length of a line segment is the distance of both the ends of it.
Point m lies between points l and n on line segment l n .
The space between l and m is 10x 8. The space between m and n is 5x -4.The value of line segment LN is,
[tex]LN = 12x +16[/tex]
The sum of LM and LN is equal to the line segment LN. Thus,
[tex]LM+MN=LN\\10x +8+(5x-4)=12x+ 16\\10x +8+5x-4=12x+ 16\\10x+5x-12x=16 -8+4\\3x=12\\x=\dfrac{12}{3}\\x=4[/tex]
Put this value of x in the equation of line segment LN,
[tex]LN = 12(4) +16\\LN=48+16\\LN=64\rm\; units[/tex]
Thus, the length of line segment l n on which point m lines in between is 64 units. Option 4 is the correct option.
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(09.06 MC) A mechanic gives a survey to all of his customers asking them to rate the quality of the service they received. He then keeps track of how many customers return to the shop for additional services during the next six months. Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services. What conclusion can be drawn from this study? (6 points)
Answer: Most customers who rate their service as high quality return for additional services.
Step-by-step explanation: just took the test :)
The act of collecting data that are representative of the population data is called _________.
Answer: Random Sampling
Step-by-step explanation:
The act of collecting data that are representative of the population data is called random sampling.
maribel surveyed 55 people to find out their favorite types of music. the results are shown in the bar graph. what percent of the people like country and opera combined?
15 people liked country, and 10 people liked opera, so 10+15 = 25.
25 people combined
4 over 11 of 77 ( 4 over 11 is supposed to be a fraction)
Answer:
28
Step-by-step explanation:
4 x 77 / 11 x 1 = 308 / 11
308/11 = 28 11/11 = 1
the answer is 28 / 1
Hey there!
4/11 of 77
= 4/11 * 77/1
= 4(77) / 11(1)
= 77(4) / 1(11)
= 77 + 77 + 77 + 77 / 11
= 154 + 154 / 11
= 308 / 11
= 28
Therefore, your answer is: 28
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Convert.
pints = 61 quarts
A bag contains 6 red marbles, 8 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the
nearest 1000th, that both marbles drawn will be blue?
Please help if you can!!!
Answer:
0.111
The probability of two blue marbles being drawn from the bag to all marbles is [tex]\frac{2}{18}[/tex], and [tex]\frac{2}{18}~-- > ~0.111[/tex] rounded to nearest thousandth.
Questions?Ask in the comments box.
While mining, Joan found a large metal bar that weighed 20 ounces. Joan was also able to determine that the bar contained 65% tin. How many ounces of tin are in the metal bar? Round your answer to the nearest whole number if necessary.
(I will mark brainliest if you answer+explain)
Answer: 13 ounces
Step-by-step explanation:
To answer this question, we will find 65% of 20. A percent divided by 100 becomes a decimal that can be used to solve.
65% / 100 = 0.65
0.65 * 20 = 13
There are 13 ounces of tin in the metal bar.
Answer:
The metal bar contains 13 ounces of tin.
Step-by-step explanation:
Multiply '20 ounces' by 0.65, obtaining 13 ounces.
The metal bar contains 13 ounces of tin.
Brianna is graphing the function f(x) = x2 6x 5. what x-intercepts should brianna use to graph f(x)? –5 and –1 –5 and 1 –1 and 5 1 and 5
The value of the x of the equation x² + 2x = 24 is negative 5 and negative 1, then the correct option is A.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The expression equation is given below.
f(x) = x² + 6x + 5
On factorization, we have
x² + 6x + 5 = 0
x² + 5x + x + 5 = 0
(x + 5)(x + 1) =0
x = -1, -5
The value of x is –5 and –1.
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Answer:
A) -5 and -1
Step-by-step explanation:
Got it right on edge!
What is the solution to the equation shown below ?
6=-2/5 ( p-5)
Answer:
p=-10
Step-by-step explanation:
6=-2(p-5)/5
6=-2p+10/5
x5 to both sides to get rid of denominator
30=-2p+10
-10 from both sides to get rid of it on the right
20=-2p
divide by -2 from both sides to get p by itself to know its value
20/-2=-10 so....
p=-10
PLEASE HELP ILL GIVE BRAINLIEST!!!
Gio is solving the quadratic equation by completing the square. 5x2 15x – 4 = 0 what should gio do first? isolate the constant. factor 5 out of the variable terms. isolate the variable x. add 9 to both sides of the equation.
The complete square of the given polynomial is
[tex](x+\frac{3}{2})^2=\frac{43}{12}[/tex]
What is the completing the square method?For solving the quadratic equation by completing the square, we first need to ensure that the constant of the square variable is unit.
Following are the steps involved
[tex]5x^2+15x-4=0[/tex]
divide both side by 5
[tex]x^2+3x-\frac{4}{3}=0[/tex]
add 9 on both sides of the equations
[tex]x^2+3x-\frac{4}{3}-9/4+ 9/4=0[/tex]
[tex]x^2+3x+ 9/4=\frac{4}{3}+9/4\\(x+3/2)^2=43/12[/tex]
Therefore we the complete square of the given polynomial is
[tex](x+\frac{3}{2})^2=\frac{43}{12}[/tex]
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Answer:
A
Step-by-step explanation:
please answer this two math question.
Answer:
haha hut dog hahah ayoko nga
How can we determine the difference between a pyramid and a prism? Select all that apply.
The number of vertices is always equal to the number of sides for a prism but not a pyramid.
There is only one base for a pyramid.
The faces of prisms are triangles.
The faces of pyramids are triangles.
The faces of prisms are rectangles.
The faces of pyramids are rectangles.
Answer:
B. There is only one base for a pyramid.
D. The faces of pyramids are traingles.
E. The faces of prisms are rectangles.
Step-by-step explanation:
The difference between a pyramid and a prism is:
There is only one base for a pyramid.
The faces of pyramids are triangles.
The faces of prisms are rectangles.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The number of vertices is always equal to the number of sides for a prism but not a pyramid.
The faces of pyramids are triangles while the faces of prisms are rectangles.
A prism has two parallel bases and its other faces are rectangles.
A pyramid has a single base and its faces are triangles.
A prism also has the same number of vertices as its number of sides, but this is not true for a pyramid.
Thus,
The difference between a pyramid and a prism is:
There is only one base for a pyramid.
The faces of pyramids are triangles.
The faces of prisms are rectangles.
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Write an example problem(s) for area.
Answer:
Example 1.
A square with side lengths of 5.
5*5 = 25.
So the area would be 25 units ^2
Example 2.
A rectangle with a length of 9 and a width of 4
9*4 = 36
So the area is 36 units ^2
ANSWER THIS!!!!!!!! PLEASEEEEEE!!!!! CLICK ON THIS ONE!!
The line looks like it is around 6, the square root of 61 is 7.810249675906654, so that would be the closest to our estimate.
Answer:
I think the answer is 11
Step-by-step explanation:
because if u count under the lines from one point to another u get 6
then count up from where ur at and u get 5
and then ig just add it up
6+5
look
This is math. Please help due soon.
Answer:
A (0,6) B (6, 1) C (2,2)
Step-by-step explanation:
A (4, 4)
[-4, 2]
Subtract 4 - 4 = 0 and then add 4+2 since both of them are positive. Do it for all of the coordinates
Image Coordinates:
A----->A¹(0,6)
B----->B¹(2,3)
C----->C¹(-2,4)
19. True or false: If the n columns of S (eigenvectors of A) are independent, then (a) A is invertible. (b) A is diagonalizable. (c) S is invertible. (d) S is diagonalizable
When n columns of S (eigenvectors of A) are independent, then:
(a) A is invertible is a false statement.
(b) A is diagonalizable is a true statement
Why is A not invertible?Others are:
(c) S is invertible true statement.
(d) S is diagonalizable false statement.
Note that if n columns of S (eigen vectors of A) are said to be independent.
One can deduce or see that the eigen vector that is similar to the eigen value is said to be = 0 and one can say it is linearly independent when viewed with the other eigen vectors of A.
But because to the zero eigen value of A, we see that the determinant of A is the output of eigen values of A which is = 0 and as such, A is not invertible.
So, the linear independence of eigen vectors will not be able to find the invertibility of A and as such A is diagonalizable.
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How many packs of dvds can u but with 165 if one costs 15 dollars
Answer: You can buy 11 DVD’s with $165
Step-by-step explanation:
165 divided by 15= 11
Wich equation shows ax - w = 3 solved for w
Answer:
Answer depends on the value you put
Step-by-step explanation:
let's say a= 3 and x =4 then,
or 3*4 -w = 3
or 12 - w = 3
or -w = 3- 12
or -w = -9
or w = 9
just put any value in a and x and you will get the answer
Which is the BEST estimate for the value of x?
You are a payroll supervisor. You need to summarize work hours for an employee. The number of hours the
employee worked each week for seven consecutive weeks were 38, 37. 5, 38. 25, 35. 75, 39. 5, 39. 5, and 38. 5.
What, approximately, is the mean number of hours this employee worked each week for the seven weeks?
O 37. 63
O 37. 92
O 38. 14
O 38. 25
39. 5
Answer:C. 38.14
Step-by-step explanation:
The required mean of the given data is given as the employee worked 38.14 hours through 7 weeks.
Given that,
The number of hours the employee worked each week for seven consecutive weeks was 38, 37. 5, 38. 25, 35. 75, 39. 5, 39. 5, and 38. 5.
The mean of the values is the ratio of the total sum of values to the number of values.
here,
According to the question,
Mean = Sum of the working hours/number of weeks
Mean = 38 + 37. 5 + 38. 25 + 35. 75 + 39. 5 + 39. 5 + 38. 5 / 7
Mean = 267/7
Mean = 38.14
Thus, the required mean of the given data is given as the employee worked 38.14 hours through 7 weeks.
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if I made 136$ and gave 35% to my brother how much would he get
Answer:
47.6
Step-by-step explanation:
35% x 136
= (35/100)*136
_________________
Step 1: In the given case Output Value is 136
Step 2: Let us consider the unknown value as x
Step 3: Consider the output value of 136 = 100%
Step 4: In the same way, x = 35%
Step 5: On diving the pair of simple equations we got the equation as under
136 = 100% (1).
x = 35% (2).
(136%)/(x%) = 100/35
Step 6: Reciprocal of both the sides results in the following equation
x%/136 = 35/100
Step 7: Simplifying the above obtained equation further will tell what is 35% of 136
x = 47.6%
Therefore, 35% of 136 is 47.6