40 POINTS!!!
All integers are either odd or even. Conceptually, an integer is odd if it has a remainder of 1 when dividing by 2. And an integer is even if it has a remainder of 0 when dividing by 2.
But when proving something rigorously, mathematicians use more precise definitions, like these: an integer is odd if it can be written in the form 2k + 1, where k is some integer. An integer is even if it can be written in the form 2k, where k is some integer. For example, 13 is odd because 13 can be written as 2(6) + 1.
With these definitions, use complete sentences to explain why zero is an even number.
Answer:
[tex] = > 2k + 1 \\ when \: k = 0 \\ 2(0) + 1 \\ = 1 \\ \therefore \: zero \: is \: odd \\ \\ = > 2k \\ when \: k = 0 \\ 2(0) \\ = 0 \\ \therefore \: zero \: is \: not \: even \: because \: when \: divided \: by \: 2 \: \: remainder \: is \: zero[/tex]
the number of calls received by an office on Monday morning between 8:00am and 9:30 am has a mean of 3.Calculate the probability of getting no more than 3 calls between eight and nine in the morning.
Answer:
Step-bLet X be the number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM.
In mathematical terms,
X
∼
P
o
i
s
s
o
n
(
2
)
.
The PMF of the random variable X is given as,
P
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=
x
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−
2
×
2
x
x
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o
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x
=
0
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1
,
2
,
.
.
.
.
.
=
0
E
l
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The probability of getting no more than 3 calls between eight and nine in the morning is obtained by the following way,
P
(
X
≤
3
)
=
P
(
X
=
0
)
+
P
(
X
=
1
)
+
P
(
X
=
2
)
+
P
(
X
=
3
)
=
e
−
2
×
2
0
0
!
+
e
−
2
×
2
1
1
!
+
e
−
2
×
2
2
2
!
+
e
−
2
×
2
3
3
!
=
0
.13534
+
0
.27067
+
0
.27067
+
0
.18045
=
0
.85712
Hence the probability of getting no more than 3 calls between eight and nine in the morning is 0.85712.y-step explanation:
how do you do the probability section?
need help quickkkk!!
Answer:
1 + 1 = 1 is the correct answer ok
Answer:
1+1 is 2 it is wrong here in explanation it is good way to solve
Step-by-step explanation:
take 1 finger and 1 more finger how much is it 2 ! ok so bye do good work !!!
How do you find the perimeter of a rectangle with the dimensions
(x^2+2x-16) ft (length)
and (x+5) ft (width)
Answer:
(2x²+6x-22) ft
Step-by-step explanation:
l = (x²+2x-16) ft
and w = (x+5) ft
the Perimeter =
2(x²+2x-16) +2(x+5)
= 2x²+4x-32+2x+10
= 2x²+6x-22
Write an equation of a line in slope-intercept form with a slope of -12 and a y-intercept of 3.
a
y = 3x - 12
y = -12(3)+b
Ob
Ос
3= -12x + b
Od
y=-12x + 3
Answer:
y = -12x + 3
Step-by-step explanation:
The slope-intercept form of an equation can be written as y = mx + b where m is the slope and b is the y-intercept. We are given both values, so we can plug them into the equation to get:
y = mx + b
y = -12x + 3
Assuming the trend that exists in the data set below applies to all students, how long should Trevor study if
he want to get at least a 75% on the test?
Answer:
He should study for at least 88 minutes
Step-by-step explanation:
The missing parameters are:
[tex]y = 0.36805x + 42.6864[/tex] --- equation of trend
[tex]y \to grade[/tex]
[tex]x \to time[/tex]
Required
x when [tex]y = 75[/tex]
[tex]y = 0.36805x + 42.6864[/tex] becomes
[tex]75 = 0.36805x + 42.6864[/tex]
Collect like terms
[tex]0.36805x = 75 - 42.6864[/tex]
[tex]0.36805x = 32.3136[/tex]
Solve for x
[tex]x = \frac{32.3136}{0.36805}[/tex]
[tex]x = 87.80[/tex]
[tex]x \approx 88[/tex]
Question and choices are in the photo please explain the answer
Step-by-step explanation:
but sorry i can't get the answer of (2x-1) =3 (x+5) because the answer of this came -16
I don’t understand this equation. m= -3 and b = 3
can you please put the equation so i can answer it?
thank you!
Mr. K needs to hire an electrician. The electrician charges $82 for making a house call and an additional $55.00 per hour of labor. If Mr. K only budgeted $300 for the electrical repair, write, solve, and graph an inequality that shows the maximum amount of hours of labor Mr. K can afford to hire the electrician.
Answer:
[tex] \displaystyle4 \: \text{hours}[/tex]
Step-by-step explanation:
we are given that,
The electrician charges $82 for making a house call an additional $55.00 per hour of laborMr. K only budgeted $300 for the electrical repairlet the hours be h
from the first condition we obtain:
[tex] \displaystyle 82[/tex]
from the second condition we ge:
[tex] \displaystyle 82+ 55h[/tex]
from the final condition we acquire:
[tex] \displaystyle 82 + 55h \leqslant 300[/tex]
to figure out the hour we have to solve the equation to do so
cancel 82 from both sides:
[tex] \displaystyle 55h \leqslant 215[/tex]
divide both sides by 55:
[tex] \displaystyle h \leqslant 3.9636 \dots[/tex]
since 3.96.... is very close to 4 he can maximum afford 4 hours of labor
[tex] \displaystyle h = 4[/tex]
refer the attachment
cotA + tanA= secAcosecA
Step-by-step explanation:
cotA + tanA
= cosA / sinA+ sinA/ cosA
= cos2A + sin2A / sinA* cosA
= 1 / sinA* cosA
=1/ sinA * 1/ cosA
= cosecA *secA
=secAcosecA
[tex]\frac{cos^2A + sin^2A}{sinAcosA}[/tex]Answer:
Step-by-step explanation:
cotA + tanA = secAcosecA
LHS=cotA + tanA
=[tex]\frac{cosA}{sinA}[/tex] + [tex]\frac{sinA}{cosA}[/tex]
take lcm of the denominator
=[tex]\frac{cosA*cosA + sinA*sinA}{sinAcosA}[/tex](COS^2A + sin^2A =1)
=[tex]\frac{1}{sinAcosA}[/tex]
=1/sinA * 1/cosA
=cosecA*secA
=secAcosecA
therefore LHS=RHS
hence proved.
MATH WIZZES, PLEASE HELP ME OUT HERE!! I NEED THIS PROBLEM DONE SOON, BECUASE IT'S DUE IN LIKE 2 MINUTES HELLPPPPPPP
The equations in this system were added to solve for y. What is the value of y?
x + 6 y = 10. -x + 3 y = -15. = 9 y = -5.
Answer:
y=-5/9
Step-by-step explanation:
it says 9y=-5
divide both sides by 9
y=-5/9
What is a carbon footprint? What are some actions you can take to reduce your carbon footprint?
Find the value of x.
6 3 2 x
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
To solve this problem, one must use the angle bisector theorem. This theorem provides a proportion between the sides formed by an angle bisector. One can apply this theorem here by forming the following proportion,
[tex]\frac{BA}{BC}=\frac{AD}{DC}[/tex]
Substitute,
[tex]\frac{x}{6}=\frac{2}{3}[/tex]
Cross products,
[tex]3(x)=2(6)[/tex]
Simplify,
[tex]3x=12[/tex]
Inverse operations,
[tex]3x=12\\\\x = 4[/tex]
Sympathetic Division function
Answer this equation
1 . Y/-7 = -7
Step-by-step explanation:
Y/-7= -7
Cross multiple
-7× -7 =Y
49 =Y
Answer:
y = 49
Step-by-step explanation:
y ÷ - 7 = - 7
y ÷ - 7 × - 7 = - 7 × - 7
y = 49
Help please !! Thank u
Answer:
parallel = same slope (-2x)
so it's y=-2x + b
let's find b by plugging in 1 for x and 3 for y (the coordinates)
3 = -2*1 + b
3 = -2 + b
5 = b
there you have it:
y = -2x +5
brainliest would really be appropriated (possible when someone else also leaves an answer)
please help find x!! asap
Answer:
x = 60
Step-by-step explanation:
The angle 30 is on the same vertical line as the angle that is adjacent to the missing angle x. they form 90 degrees.
SUPER URGENT: Find secθ.
Answer:
B
Step-by-step explanation:
√((-20)²+21²)=√(400+441)=√841=29
cos θ=-20/29
sec θ=-29/20
i think of a number, multiply it by 3, add 4 and square the answer
Step-by-step explanation:
I can read your mind you know
just ask me how
and see the magic
think of any number,
add it by 3 then by 5 then by 1.
multiply it by two
divide it by two
subtract the first number you thought of from your current number
your answer will be 9
I'm I correct ?
Answer:
2 x 3 = 6 + 4 = 10 squared = 100
Step-by-step explanation:
The square of a number is the number that can be multiplied by itself to get that specific number, for example 10 x 10 = 100
Find the gradient of the line segment between the points (-4,4) and (0,12).
gradient = 12-4 ÷0-(-4)=8÷4=2
Answer:
gradient = 2
Step-by-step explanation:
Calculate the gradient m using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 4) and (x₂, y₂ ) = (0, 12)
m = [tex]\frac{12-4}{0+4}[/tex] = [tex]\frac{8}{4}[/tex] = 2
Collins middle school's basketball team won 75% of their games if they lost the board games how many games did they win?
The phrase in the original question is:
....if they lost 12 games......
not
....if they lost board games......
Answer:
36 games won
Step-by-step explanation:
Given
[tex]\%Win = 75\%[/tex]
[tex]Lost = 12\ games[/tex]
Required
Number of games won
Give that: [tex]\%Win = 75\%[/tex]
The percentage loss is:
[tex]\%Loss = 100\% - \%Win[/tex]
So, we have:
[tex]\%Loss = 100\% - 75\%[/tex]
[tex]\%Loss = 25\%[/tex]
Calculate the number of games (n) using:
[tex]Lost = \%Loss * n[/tex]
[tex]12 = 25\% * n[/tex]
Make n the subject
[tex]n = \frac{12}{25\%}[/tex]
[tex]n = 48[/tex]
So, the games won is:
[tex]Win = n - Lost[/tex]
[tex]Win = 48 - 12[/tex]
[tex]Win = 36[/tex]
Question
Solve the inequality b – 27 > 3 and write the solution in interval notation, using improper fractions if necessary.
Answer:
(30, ∞)
Step-by-step explanation:
b – 27 > 3
Add 27 to both sides
b > 30
In interval notation
(30, ∞)
Answer:
(30,∞ )
Step-by-step explanation:
b> 27+3
b> 30
Please help this is due today!!
Answer:
c is the answer
Step-by-step explanation:
Graphs really aren't my thing but I really feel like it is c
GOOD LUCK HOPEFULLY YOU GET A GOOD GRADE
Find the breadth of a rectangular park whose area is 54.6 sq m and 15.6 m long
Answer:
breadth = 3.5 m
Step-by-step explanation:
length = 15.6 m
Area of rectangle = 54.6 sqm
breadth = [tex]\frac{Area}{length}[/tex]
[tex]= \frac{54.6}{15.6}\\\\= \frac{54.6*10}{15.6*10}\\\\=\frac{546}{156}\\\\= 3.5[/tex]
What is the approximate area covered by the label?
Find the length x
Plz help ASAP
Answer:
Step-by-step explanation:
factorise fully the expression 2d^2-7d
Answer:
d(2d-7)
Step-by-step explanation:
2d^2 -7d
take common
=d(2d-7)
[tex] \large \boxed{ \rightarrow d(2d - 7)}[/tex]
Solution :[tex] \rightarrow2d {}^{2} - 7d[/tex]
[tex] \rightarrow d(2d - 7)[/tex]
[tex] \mathfrak{hope \:it \: helps \: you.....}[/tex]
(b) In a continuous series the average weight of some students is 75 kg and the sum of the weights is 6000 kg. Find the number of students.
Answer:
the number of students is 80
Which of the following is a solution set to the equation x^2-10x+16=0
Answer:
x=2. or. x=8
Step-by-step explanation:
x^2-10x+16=0. s=-10
x^2-8x-2x+16=0. p=16
x(x-8)-2(x-8)=0. [-8,-2]
(x-2)(x-8)
x=2. or. x=8