Answer:
yes
Step-by-step explanation:
A rational number is in the form p/q where p and q are both integers and the denominator q is not equal to zero. This means that the set of all real numbers are rational numbers.
Since q can be any integer apart from zero, it means that all integers are rational numbers i.e for q = 1.
Hence 2 which can be written as fraction as 2/1 is a rational number since the denominator (q = 1) is a non zero number
Answer:
Mark is not correct because a fraction is rational only if the numerator and the denominator are both integers.
Step-by-step explanation:
find the value of a in the equatuion 5 over a+3 =3 over a-2
Answer:
9.5
Step-by-step explanation:
5/(a+3)=3/(a-2)
5(a-2)=3(a+3)
5a-10=3a+9
5a-3a=9+10
2a=19
a=9.5
M
What x values would be good to use so she does not get fractions for her y values when making the table of ordered pairs.
Answer:
-3, 0, 3
Step-by-step explanation:
Given, [tex] y = -\frac{4}{3}x + 2 [/tex], the set of x values that will make Kayda not to get y values that are not fraction are -3, 0, 3.
This is so, because,
when x = -3, [tex] y = -\frac{4}{3}(-3) + 2 = \frac{12}{3} + 2 = 4 + 2 = 6 [/tex]
when x = 0, [tex] y = -\frac{4}{3}(0) + 2 = -0 + 2 = 2 [/tex]
when x = 3, [tex] y = -\frac{4}{3}(3) + 2 = \frac{-12}{3} + 2 = -4 + 2 = -2 [/tex]
The correct response is -3, 0, 3
Which number is the solution of the inequality 8-1/4b> 27
Answer:
B < -76
Step-by-step explanation:
You start out with writing out the equation
8-1/4b> 27
Then, you subtract 8 from each side, so the -1/4b can be by itself
-1/4b>27-8
-1/4b>19
After that, you want to get rid of that -1/4, so you multiply both sides by -4
This makes the > sign flip to <
So, this makes:
b < -76
You randomly draw a marble from a bag of marbles that contains 7777 blue marbles, 2222 green marbles, and 1111 red marble. What is P(not draw a blue marble)\text{P(not draw a blue marble})P(not draw a blue marble)start text, P, left parenthesis, n, o, t, space, d, r, a, w, space, a, space, b, l, u, e, space, m, a, r, b, l, e, end text, right parenthesis? If necessary, round your answer to 2222 decimal places.
Answer:
0.3
Step-by-step explanation:
There are:
Blue marbles = 7777Green marbles = 2222Red marbles = 1111Total marbles:
7777 + 2222 + 1111 = 11110Then:
P ( not blue) = (2222+1111)/11110 = 0.3Answer is: the probability of not draw a blue marble is 0.3
Find an equation for the linear function which has a slope of 8 and x intercept of 5
Answer:
y = 8x-40
Step-by-step explanation:
The slope intercept form of a line is
y= mx+b where m is the slope and b is the y intercept
We know the slope is 8 and the x intercept is 5 ( 5,0)
y = 8x +b
Substitute the point into the equation
0 = 8(5)+b
0 = 40+b
b=-40
The equation is
y = 8x-40
Write the equation of a line that is perpendicular to 6x - 3y - 15 = 0 and goes through the point (4, 6) in y-intercept form.
Answer:
y= -1/2(x) +8
gradient= -1/2
Intercept= 8
Step-by-step explanation:
Let's transform the equation to y -intercept form first
6x - 3y - 15= 0
-3y= -6x+15
Y= -6/-3(x) +(15/-3)
Y= 2x -5
Intercept c= -5
Gradient m =2
Rule of perpendicularity
mm'= -1
m'= -1/m
m' = -1/2
Equation of line of the point (4, 6)
(Y-Y1)/(x-x1)=m'
(Y-6)/(x-4)= -1/2
2(y-6)= -1(x-4)
2y -12 = -x +4
2y= -x +4+12
2y= -x+16
y= -1/2(x) +8
gradient= -1/2
Intercept= 8
A Holiday aircraft charters an aircraft to fly to Malta at a cost of $22000. It then sells 150 seats at $185 each and a further 35 seats at a 20% discount. calculate the profit made per seat if the plane has 200 seats.
Answer:
Hope it helped u if yes mark me BRAINLIEST pzllzllzl
-8-x=x-4x
Can anyone help please
Answer: x=4
Step-by-step explanation:
-8-x=x-4x
-8-x=-3x
-x+3x=8
2x=8
x=4
HELP! WILL GIVE BRAINLIESY.
Answer:
$1 for one tube
Step-by-step explanation:
Ratio is 10:10
if you keep on reducing it
you will eventually get to 1:1
Therefore, the answer is $1 for one tube
3x + 7x=
Combine like terms
Answer:
10x
Step-by-step explanation:
3x + 7x
= 10x
please assist me with this problem: part 11
Answer:
a² = b² -w² +2wx
Step-by-step explanation:
The algebra is pretty straightforward. Expand the expression in parentheses and add x².
b² -(w -x)² = e² = a² -x²
b² -(w² -2wx +x²) = a² -x² . . . . . expand the square
b² -w² +2wx -x² = a² -x² . . . . . . distribute the minus sign
b² -w² +2wx = a² . . . . . . . . . . . . add x²
Mathematics 25 points
Answer:
The angle from the centre of Ann's slice is 60 degrees.
Step-by-step explanation:
If the size of the slices is proportional to the ages of the children eating the cake, then the sum of their ages equal to 360 degrees (since the cake is a circle).
So to work out the angle of Ann's portion, we find a fraction for Ann's age over the total of all of their ages. So:
5/(5 + 10 + 15) = 5/30
Now since we know their ages are proportional to the slices of cake, we can find the same value for the fraction 5/30 that is out of 360 to work out the angle. Let's call the angle representing Ann's slice x. So know we can create an equation:
5/30 = x/ 360
5/30 * 360 = x
x = 60
Answer:
60 degrees.
Step-by-step explanation:
Calculus 2 master needed; evaluate the integral PLEASE SHOW STEPS IF IM WRONG [tex]\int{sin^3x/\sqrt{cosx} } \, dx[/tex] I split off the sin^3 so i can use the pythag identity and allows for u substitution u=cosx du=-sinx dx -du=sin dx [tex]\int{1-u^2/\sqrt{u}*-du }[/tex] I move the negative towards the outside of the integral. then i divide the terms by sqroot 2||| [tex]-\int{(1/\sqrt{u} - u^2/\sqrt{u} )} \, du[/tex] I eventually get to a=1/2 b =5/2 [tex]-2{cos^a x +2/5cos^b} \, dx[/tex] did I miss anything? Or is this the final answer?
Answer:
Your process is indeed correct!
The full solution is:
[tex]\displaystyle \int\frac{\sin ^3 x}{\sqrt{\cos x}}\, dx= \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int \frac{\sin^3(x)}{\sqrt{\cos(x)}}\, dx[/tex]
As you had done, we can rewrite our integral as:
[tex]\displaystyle =\int \frac{\sin(x)(\sin^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]
Using the Pythagorean Identity, this is:
[tex]\displaystyle =\int \frac{\sin(x)(1-\cos^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]
Now, we can make a substitution. Let u = cos(x). Then:
[tex]\displaystyle du = - \sin x \, dx[/tex]
Substitute:
[tex]\displaystyle = \int\frac{1-u^2}{\sqrt{u}} \, \left(- du\right)[/tex]
Simplify:
[tex]\displaystyle = -\int \frac{1}{\sqrt{u}} - \frac{u^2}{\sqrt{u}}\, du[/tex]
Rewrite:
[tex]\displaystyle = -\int u^{{}^{-1}\!/\!{}_{2}} - u^{{}^{3}\!/\!{}_{2}}\, du[/tex]
By the Reverse Power Rule:
[tex]\displaystyle = -\left(2u^{{}^{1}\!/\!{}_{2}} - \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}\right) + C[/tex]
Simplify:
[tex]\displaystyle = \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}-2u^{{}^{1}\!/\!{}_{2}} + C[/tex]
Back-substitute:
[tex]\displaystyle = \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]
Answer:
= - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x) + C
5
Step-by-step explanation:
∫ sin³ (x) dx
[tex]\sqrt{cos(x)}[/tex]
= ∫ sin² (x) sin (x) dx
[tex]\sqrt{cos(x)}[/tex]
= ∫ (1 - cos² (x) sin (x) dx
[tex]\sqrt{cos(x)}[/tex]
= ∫ - 1 - u² du
√u
= ∫ - 1 + u³/₂ du
√u
= - ∫ 1 du + ∫ u³/₂ du
√u
substitute it back
= - 2 √u + 2 cos⁵/₂ (x)
5
add constant, therefore
= - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x) + C
5
How do you solve 5+25:5x8-2
I hope I helped you
Step-by-step explanation:
First you solve: 25:5=?
After: the number you find×8=?
And:?+5=?
The number -2
One side of a triangle is 3 times the second side. The third side is 13 feet longer than the second side. The perimeter of a triangle is 68 feet. Find the length of each side.
Answer:
33, 11, 24 feet
Step-by-step explanation:
Let s represent the length of the second side. Then the length of the first side is 3s and the length of the third side is s+13. The perimeter is the sum of side lengths:
(3s) +(s) +(s +13) = 68
5s = 55 . . . . . subtract 13
s = 11 . . . . . . . divide by 5
The side lengths are ...
33, 11, 24 feet
Assuming that it takes 1.25 seconds for light to travel from the Moon to the Earth, how
many miles away is the Moon?
Answer:
238,900 miles away
Answer:
238,900
Step-by-step explanation:
Light travels at a speed of 186,282 miles per second, you multiply this number by 1.25 you get your answer.
Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers as a comma-separated list. Enter ∅ for the empty set.)
(a) What are the 16 outcomes in ?
(b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rate?
(c) Which outcomes are in the event that all four mortgages are of the same type?
(d) Which outcomes are in the event that at most one of the four is a variable-rate mortgage?
(e) What is the union of the events in parts (c) and (d)?
What is the intersection of these two events?
(f) What is the union of the two events in parts (b) and (c)?
What is the intersection of the two events in parts (b) and (c)?
Answer:
a)
{FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV,VVFV,FVVF,FFVF,VFVF,VVVF,FVFF,FFFF,VFFF,VVFF}
b)
{FFFV,FFVF,FVFF,VFFF}
c)
{FFFF,VVVV}
d)
{FFFV,FFVF,FVFF,FFFF,VFFF}
e)
{FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
{FFFF}
f)
{FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
{ }
Step-by-step explanation:
a)
The 16 outcomes for a sample of four home mortgages classified as fixed and variable rate are
Sr.No Outcomes
1 FVVV
2 FFVV
3 VFVV
4 VVVV
5 FVFV
6 FFFV
7 VFFV
8 VVFV
9 FVVF
10 FFVF
11 VFVF
12 VVVF
13 FVFF
14 FFFF
15 VFFF
16 VVFF
b)
Let A be the event that exactly three are fixed rate. Thus, event A consists of following outcomes
A={FFFV,FFVF,FVFF,VFFF}
c)
Let B be the event that all four are of same type. The event B consists of either all fixed rate or all variable rate. Thus, event B consists of following outcomes
B={FFFF,VVVV}
d)
Let C be the event that at most one of four is variable rate. The event C consists of less than and equal to one variable rate. Thus, event C consists of following outcomes
C={FFFV,FFVF,FVFF,FFFF,VFFF}
e)
Let union of part(c) and part(d) can be represented as BUC. The union represents all the outcomes in event B and event C.
B∪C={FFFF,VVVV}∪{FFFV,FFVF,FVFF,FFFF,VFFF}
B∪C={FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
Let intersection of part(c) and part(d) can be represented as B∩C. The intersection represents the common outcomes in event B and event C.
B∩C={FFFF,VVVV}∩{FFFV,FFVF,FVFF,FFFF,VFFF}
B∩C={FFFF}
f)
Let union of part(b) and part(c) can be represented as AUB. The union represents all the outcomes in event A and event B.
A∪B={FFFV,FFVF,FVFF,VFFF}∪{FFFF,VVVV}
A∪B={FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
Let intersection of part(b) and part(c) can be represented as A∩B. The intersection represents the common outcomes in event A and event B.
A∩B={FFFV,FFVF,FVFF,VFFF}∩{FFFF,VVVV}
A∩B={ }
So intersection of part(b) and part(c) is an empty set as there is no common outcome in these two sets.
Sample of four homes.
The sample of 4 homes is on a mortgage and has been classified as a fixed rate of F and a variable rate of V. The mortgage is thus an agreement between the lender of the money and the borrower. The lender has the right to take away the property.
Thus answer is given below.
The set of 16 outcomes of the variable and the fixed rates is given as {FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV, and VVFV,FVVF,FFVF,VFVF,VVVF,and the FVFF,FFFF,VFFF,VVFF}. The outcomes in the events that exactly is of 3 of the selected mortgages at a fixed rate is about {FFFV, FFVF,FVFF, VFFF}The outcomes of the events that all four mortgages are of the same type are about {FFFF, VVVV} The union of events in parts of c and d are as {FFFV, FFVF, FVFF, FFFF, VFFF}.Learn more about the sample of four homes.
brainly.com/question/14565659.
One megabyte of cell phone storage space is 2^{20} bytes. An app uses 4^4 megabytes of storage space. How many bytes of storage space does the app use? Write your answer as a power of 2.
Answer:
2²⁰ bytes
Step-by-step explanation:
Given
[tex]Phone\ Storage = 2^{20}\ bytes[/tex]
[tex]App\ Storage = 4^4\ megabytes[/tex] of phone storage space
Required
Determine the storage space of the app in bytes
To answer this, we simply multiply the app storage by the phone storage
This gives:
[tex]Total = 2^{20} * 4 ^4[/tex]
Express 4 as 2²
[tex]Total = 2^{20} * 2^2^* ^4[/tex]
[tex]Total = 2^{20} * 2^8[/tex]
Apply Laws of Indices
[tex]Total = 2^{20+8}[/tex]
[tex]Total = 2^{28}[/tex]
Hence, the storage space of the app is 2²⁰ bytes
I enter the bedroom. There are 34 people. You kill 30. How many people are in the bedroom?
Answer:
34
Step-by-step explanation:
The dead bodies are still in the room.
Which number has the greatest absolute value?
A) 0
B) −18
C) −31
D) −44
Answer:
D
Step-by-step explanation:
If the number is positive, the absolute value is the same as the number. If the number is negative, the absolute value is just a positive version of that number. So the absolute value of 0 is 0, -18 is 18, -31 is 31, and -44 is 44. Out if these, D has the greatest absolute value, so it would be D
Answer:
D. -44.
Step-by-step explanation:
Absolute value of -44:
= |-44| = 44
Point B is the midpoint of Line segment A C .
Answer:
Angle ABC is bisected by BD
BC =Half AC
2 mangle DBC =mangle ABC
How many integers satisfy the inequality 0<|x|<5
Answer:
4
Step-by-step explanation:
0</x/<5
0</1, 2, 3, 4/>5
(1,2,3,4) there are 4 numbers that are greater than 0 and less than 5.
Answer:
8
Step-by-step explanation:
All possible answers are 1,2,3,4,-1,-2,-3, and -4. Since we are using the absolute value here, the opposites of the positive values are also included.
Find sin(2A) if sin(A)=[tex]\frac{1}{4}[/tex] and [tex]0\leq A\leq \frac{\pi }{2}[/tex]
Step-by-step explanation:
sin(2A)
Use double angle formula:
= 2 sin(A) cos(A)
Use Pythagorean identity. 0 ≤ A ≤ π/2, so cos(A) > 0.
= 2 sin(A) √(1 − sin²(A))
Substitute and simplify.
= 2 (¼) √(1 − (¼)²)
= ½ √(¹⁵/₁₆)
= ⅛ √15
Abel currently has a balance of $10,986.50 in an account he has held for 25 years. He opened the account with an
initial deposit of $5,110. What is the simple interest rate on the account?
A. 4.0%
B. 2.1%
C.8.6%
D.4.6%
Which of the values in the set {3, 4, 5, 6} is a solution to the equation 4x + 2 = 22?
03
04
05
06
Find the midpoint of the line segment joining the points R(3,3) and S(-5,5).
Answer:
(-1,4)
Step-by-step explanation:
A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not replacing it, and then choosing a red marble?
Answer:
if its fractions then 1/4 if its percentage then 25%
Step-by-step explanation:
I know that the answer isn't x=0. Please help.
(2x+8)/6=1/3(x+4)
3(2x+8)=6(x+4)
6x+24=6x+24.
0=0.
∴There are no real solutions.
Help would be appreciated !!
Unit Rates: Tutorial
hours per acre
Part B.
Write a division problem that will help you solve for the unit rate. Write the problem from left to right using only mixed numbers. Include units
next to each mixed number
.)
A-A-DEZE
y
X
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Answer:
4 1/8hours ÷ 2 3/4
Step-by-step explanation: