Answer:
Step-by-step explanation:
The aim of this question is to prove that the product of two rationals is rational.
To proof:
If [tex]\mathbf{x \ and \ y}[/tex] are arbitrary rational numbers.
Thus, going by the definition of rational, there exist integers
a, b, ≠ 0, c, and d ≠ 0 ; [tex]x = \dfrac{a}{b} \ and \ y = \dfrac{c}{d}[/tex]
Hence, [tex]xy = (\dfrac{a}{b})(\dfrac{c}{d}) = \dfrac{ac}{bd}[/tex]
Since a and c are integers, then e = ac appears to be an integer as well.
Also, provided that b and d are non-zero integers;
f =bd appears to be a non-zero integer.
Therefore, [tex]xy = \dfrac{e}{f}[/tex], and going by the definition of rational, xy is rational.
Hence, from the complete question:
The order of the statement is:
7,6,3,5,2,4
The statements that should not be used in the proof are:
1 N
8 N
9 N
10 N
11 N
Anyone know this?
Y=-3x+4
X | Y
-4
-2
0
2
Answer:
16
10
4
-2
.....................
Answer:
Y=10
Step-by-step explanation:
Y=3(2)+4
y= 6+4
y= 10
x= +2
why?
because if you add two at -4 you have -2 and you add 2 and u get 0 and u add two again and u get 2.
The figure has an area of 42 yd? Which equation can be
used to find the value of x?
A 13x + 1 = 42
B 14x = 42
C 15x -1 = 42
D 16x=42
Answer:
B. 14x = 42
Step-by-step explanation:
The figure is composed of a rectangle and a trapezium
(L*W) + [½(a + b)h] = Area of the figure
Where,
Area = 42
L = 2x
W = 3
a = 3 + 4 = 7
b = 9
h = x
Plug in the values
(2x*3) + [½(7 + 9)x] = 42
6x + [½(16x)] = 42
6x + 8x = 42
14x = 42
HELLPPPPP AGAIN PLSSSSSSS COME ON MATHS
Step-by-step explanation:
according to question triangle is concurrent so two traingle= 1rectangle
so finally ans is 6×2(12+2)=168
Papi has 148 slices of pizza in his shop. He sells 56 slices. How many slices does Papi have left? Draw a math Mountain to solve each word problem.
Answer:
92
Step-by-step explanation:
148 - 56 = 92
Hope this helped
Answer:
The answer is 92
Step-by-step explanation:
148 - 56 = 92
f(1)=25
f(n)= f(n-1)(-1/5)
f(3)=
Answer: f(3):1
Step-by-step explanation:
A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 4.5? (5 points)
Perimeter = 46 cm, area = 131.25 cm2
Perimeter = 126 cm, area = 972 cm2
Perimeter = 46 cm, area = 972 cm2
Perimeter = 126 cm, area = 131.25 cm2
Perimeter = 46 cm, area = 131.25 cm2
Perimeter = 126 cm, area = 972 cm2
Perimeter = 46 cm, area = 972 cm2
Perimeter = 126 cm, area = 131.25 cm2
Answer:
Perimeter = 126cm
Area = 972cm^2
Step-by-step explanation:
6*4.5 = 27
8*4.5 = 36
Perimeter = 27*2+36*2= 126 cm
Area = 27*36 = 972 cm^2
Hope this helped!
Answer:
Perimeter = 126 cm, area = 972 cm2
Step-by-step explanation:
Rectangle perimeter:
P = 2(w + l)Rectangle area:
A = wlWhen scaled, the perimeter will change by same factor but the area by the square of same factor.
Applying to the given rectangle
Perimeter:
P = 2(6 + 8)(4.5) = 126 cmArea:
A = 6*8*4.5² = 972 cm²Correct choice is B
A fair die is rolled 10 times. Find the expected value of:a) the sum of the numbers in the ten rolls;b) the number of multiples of three in the ten rolls;c) the number of different faces that appear in the ten rolls. (Hint:Use the indicator method.LetAibe the event that theith face appears at least once.)
Answer:
a) 3.5
b) 3.33
c) [tex]6 - 6\left(\begin{array}{ccc}5\\6\end{array}\right)^{10}[/tex]
Step-by-step explanation:
As given,
A fair die is rolled 10 times
a)
Expected value of Sum of the number in 10 rolls = [tex]\frac{1}{6}(1+2+3+4+5+6) = \frac{21}{6}[/tex]
= 3.5
∴ we get
Expected value of Sum of the number in 10 rolls = 3.5
b)
Ley Y : number of multiples of 3
Y be Binomial
Y - B(n = 10, p = [tex]\frac{2}{6}[/tex] )
Now,
Expected value = E(Y) = np = 10×[tex]\frac{2}{6}[/tex] = 3.33
c)
Let m = total number of faces in a die
⇒m = 6
As die is roll 10 times
⇒n = 10
Now,
Let Y = number of different faces appears
Now,
Expected value, E(Y) = m - m[tex]\left(\begin{array}{ccc}m-1\\m\end{array}\right)^{n}[/tex]
= [tex]6 - 6\left(\begin{array}{ccc}6-1\\6\end{array}\right)^{10} = 6 - 6\left(\begin{array}{ccc}5\\6\end{array}\right)^{10}[/tex]
In this exercise we have to use probability knowledge to calculate the times the numbers of a roll, in this way we have to:
a) [tex]3.5[/tex]
b) [tex]3.33[/tex]
c) [tex]6-6\left[\begin{array}{cc}5\\6\2\end{array}\right] ^{10}[/tex]
Given that a fair die is rolled 10 times:
a) Expected value of Sum of the number in 10 rolls :
[tex]\frac{1}{6} (1+2+3+4+5+6)= \frac{21}{6} = 3.5[/tex]
b) Using the formula of the binomial that is represented by:
[tex]Y - B(n = 10, p = \frac{2}{6})[/tex]
Expected value: [tex]E(Y) = np = (10)(\frac{2}{6} ) = 3.33[/tex]
c) Looking at the 10 times the roll does, we have that it will be. Let m = total number of faces in a die that represents m = 6, as die is roll 10 times that represents n = 10. Now, Expected value:
[tex]= E(Y) = m - m \left[\begin{array}{cc}m-1\\m\\ \end{array}\right] \\= 6-6\left[\begin{array}{cc}5\\6\2\end{array}\right] ^{10}[/tex]
See more about probability at brainly.com/question/795909
Lydia is saving money for her vacation. So far she has $82.50. Each week she sets aside 25% of her paycheck for the vacation. After 8 weeks, Lydia has $338.50 saved for vacation. What is the amount of Lydia's weekly paycheck
Answer:
$128
Step-by-step explanation:
338.50 - 82.50 = 256
256/8= 32
25%= 1/4
4 x 32= 128
Chang has nine new magazines to read
Let M be the number of magazines he would have left to read after reading R
of them
Answer:
Step-by-step explanation:
M=9-R is the equation for it
What are the values of s and t?
Answer:
I think t is 72, because the angle looks equal to the known degree, which is 72. And since all the degrees have to add up to 180, 72+72 is 144 and 180-144 is 36. So angle s is 36 degrees.
Need help On question 1. for geo
Classify by angle = obtuse (one angle in the triangle is obtuse)
Classify by sides = isosceles (has two equivalent sides)
Triangle 2 :Classify by angles = right (an angle in the triangle is equal to 90°)
Classify by sides = scalene (none of the sides in this triangle is equal)
How long does it take an account with a principal of $500 to earn $75 in interest at a simple annual interest rate of 3%?
Answer:
about 5 years
Step-by-step explanation:
year 1)500*0.03= 15
year 2)515*0.03= 15.45+515=530.45
year 3)530.45*0.03= 15.91+530.45=546.36
year 4)546.36*0.03=16.39+546.36=562.75
year 5)562.75*0.03=16.88+562.75=579.63
use prime factorization to find the greatest common factor of 56 and 84
Answer:
28
Step-by-step explanation:
Hope this helped.
Which list correctly orders A, B, and C from least to greatest when A=-8, B = |-61, and C = 11|?
d
A, B, C
C, A, B
BA, C
C, B,A
Decrease 60 by 0.75 of itself
Answer:
15
Step-by-step explanation:
(0.75 of 60)
0.75 * 60 = 45
(decrease 60 by answer)
60 - 45 = 15
Swimming pool was 9 meters wide with an area of 90 square.What is the length of the pool?
Answer:
If the area is 90 square meters then, the answer is 10 meters long (length.)
Step-by-step explanation:
5x-8y=29 find y when x= -1
Answer:
-4.25
Step-by-step explanation:
When x = -1, the equation is 5(-1) - 8y = 29. This simplifies to -5 - 8y = 29. Add 5 to both sides to get -8y = 34. Divide -8 from both sides to get y = -4.25.
Hope it helps!
Desmond is rolling a standard six-sided number cube. He plans to roll it 72 times. About how many times would you expect him to roll an even number? Why?
Answer:
Step-by-step explanation:
3 even numbers are on a number cube. So, 1/3.
1/3 x 72 = 24
Desmond would roll an even number 24 times.
Tara has $320 in her savings account and plans to put all of the money that she earns this
week [m] into her account. Complete the equation to represent the amount of money in
Tara's savings account (S) after she gets paid. Do not use $ in the equation.
Answer: 320
Step-by-step explanation:
simplyfly
x+3/x-5 - x+5/x-3
Answer:
-8x - 8
_____
8
Step-by-step explanation:
Answer:
16/(x-3)(x-5)
Step-by-step explanation:
The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page. Assume that the numbers of typos on different pages are independent. (a) Find the probability that there are at most 2 typos on a page. (b) Find the probability that there are exactly 10 typos in a 5-page paper. (c) Find the probability that there are exactly 2 typos on each page in a 5-page paper. (d) Find the probability that there is at least one page with no typos in a 5-page paper. (e) Find the probability that there are exactly two pages with no typos in a 5-page paper.
Answer:
a) 0.8088 = 80.88% probability that there are at most 2 typos on a page.
b) 0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.
c) 0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.
d) 0.717 = 71.7% probability that there is at least one page with no typos in a 5-page paper.
e) 0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page.
This means that [tex]\mu = 1.5n[/tex], in which n is the number of pages.
(a) Find the probability that there are at most 2 typos on a page.
One page, which means that [tex]\mu = 1.5[/tex]
This is
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231[/tex]
[tex]P(X = 1) = \frac{e^{-1.5}*(1.5)^{1}}{(1)!} = 0.3347[/tex]
[tex]P(X = 2) = \frac{e^{-1.5}*(1.5)^{2}}{(2)!} = 0.2510[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2231 + 0.3347 + 0.2510 = 0.8088[/tex]
0.8088 = 80.88% probability that there are at most 2 typos on a page.
(b) Find the probability that there are exactly 10 typos in a 5-page paper.
5 pages, which means that [tex]n = 5, \mu = 5(1.5) = 7.5[/tex].
This is P(X = 10). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 10) = \frac{e^{-7.5}*(7.5)^{10}}{(10)!} = 0.0858[/tex]
0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.
(c) Find the probability that there are exactly 2 typos on each page in a 5-page paper.
Two typos on a page: 0.2510 probability.
Two typos on each of the 5 pages: (0.251)^5 = 0.001
0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.
(d) Find the probability that there is at least one page with no typos in a 5-page paper.
0.2231 probability that a page has no typo, so 1 - 0.2231 = 0.7769 probability that there is at least one typo in a page.
(0.7769)^5 = 0.283 probability that every page has at least one typo.
1 - 0.283 = 0.717 probability that there is at least one page with no typos in a 5-page paper.
(e) Find the probability that there are exactly two pages with no typos in a 5-page paper.
Here, we use the binomial distribution.
0.2231 probability that a page has no typo, so [tex]p = 0.02231[/tex]
5 pages, so [tex]n = 5[/tex]
We want P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.2231)^{2}.(0.7769)^{3} = 0.2334[/tex]
0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.
The graph of the function F(x)= x2
is shown above. Which of the functions below would be a reflection of AX) across the x-axis?
Answer:
d is the answer of graph function
1. 2a+b-c
A. O
B. 1
C. 3
D. 4
Answer:
i think C correct me if im wrong pls
Step-by-step explanation:
Angelo's yearly salary increased from $18,575 to $21,000 What was the monthly increase? Round your answer to the nearest dollar?
Answer:
The answer is 1750 dollars more than his other yearly salary.
Step-by-step explanation:
I am super sorry if it is wrong. It might be.
1.7 m+ 3.7 m +3.7 m +3 m +5.9 m
answer:
18 m
step-by-step explanation:
simply add up all the numbers given1.7 + 3.7 + 3.7 + 3 + 5.9 = 18 then, put the units givenAnswer:
18m
Step-by-step explanation:
(1.7 + 3.7 + 3.7 + 3 + 5.9)m = 18m
Hope that helps!
can you please help me
Answer:
90 degrees
Step-by-step explanation:
A triangle equals 180
180 - 60
= 120
120 - 30
= 90
Also you can easily get the answer without doing any math because you can see the angle is a right angle
Right angles equal 90
Hope this helps dude
Find the value of x y and m
Answer:
x = 33
y = 66
m<BGK = 71°
Step-by-step explanation:
✔️(2x + 5) + (3x + 10) = 180° (consecutive interior angles)
Solve for x
2x + 5 + 3x + 10 = 180
Add like terms
5x + 15 = 180
5x = 180 - 15 (subtraction property of equality)
5x = 165
Divide both sides by 5
x = 33
✔️(2x + 5) = (y + 5) (alternate interior angles are congruent)
Plug in the value of x
2(33) + 5 = y + 5
66 + 5 = y + 5
71 = y + 5
71 - 5 = y
66 = y
y = 66
✔️m<BGK = (y + 5) (vertical angles)
Plug in the value of y
m<BGK = (66 + 5)
m<BGK = 71°
If Johnny had 20 complete living room outfits, disregard color scheme, how many different sets of five complete outfits could be arranged?
Answer:
the answer would be 5.
Step-by-step explanation:
ty for reading :P
The number of ways five complete outfits could be arranged if Johnny had 20 complete living room outfits is 1,860,480 ways
Permutation has to do with arrangement.
Since Johnny had 20 complete living room outfits, for him to arrange different sets of five complete outfits, he can do it in 20P5 number of ways.
The permutation formula is as shown below:
[tex]^n P_r =\frac{n!}{(n-r)!}[/tex]
Hence:
[tex]^{20}P_5=\frac{20!}{(20-5)!}\\ ^{20}P_5=\frac{20!}{(15)!}\\^{20}P_5=\frac{20\times19\times 18 \times 17 \times 16 \times 15!}{15!}\\^{20}P_5=20\times19\times 18 \times 17 \times 16 \\^{20}P_5=1,860,480ways[/tex]
Hence the number of ways five complete outfits could be arranged if Johnny had 20 complete living room outfits is 1,860,480 ways.
Learn more on permutation here: https://brainly.com/question/23779115
Please help me with just the first two questions
Simplify the fractions using the greatest common factor and division 4/8 =
Answer:
2/4
Step-by-step explanation: