Answer: Paul gets £186
Step-by-step explanation:
Paul has 1/2 as much as Malachy, and Brian has 1/3 as much Paul, therefore Brian has 1/6 as much as Malachy.
1/2 * 1/3 = 1/6
So Malachy’s amount equals 1 in this equation, Paul’s amount equals 1/2 in this equation, and Brian’s amount equals 1/6 in this equation.
1 + 1/2 + 1/6 = 1 + 3/6 + 1/6 = 1 4/6
Now, divide 620 by 1 4/6 to find Malachy’s amount.
620/1 4/6 = 372
Now, divde 372 by 2 to get Paul’s amount.
372/2 = 186
Answer each question and explain your reasoning.
How long is 75% of 60 minutes?
Answer:
45 minutes
Step-by-step explanation:
75% is the same as [tex]\frac{3}{4}[/tex]. This means that we can multiply 60 by [tex]\frac{3}{4}[/tex] to find 75% of 60.
[tex]60*\frac{3}{4} \\\\\frac{180}{4} \\\\\frac{90}{2}\\\\45[/tex]
Answer:
45 minutes
Step-by-step explanation:
Of means multiply
75% * 60
Change to a decimal
.75 * 60
45
45 minutes
What is the average rate of change for this exponential function for the
interval from x = 2 to x = 4?,
A. -12
B. 12
C. -6
D. 6
Answer:
Option (D).
Step-by-step explanation:
In the figure attached,
An exponential function has been graphed with certain points marked on it.
To find the average rate of change for this function between the given interval we will use the formula,
Average rate of change = [tex]\frac{f(x_2)-f(x_1)}{y_2-y_1}[/tex]
where [tex]f(x_2)[/tex] = value of the function at x = 4
[tex]f(x_1)[/tex] = value of the function at x = 2
By substituting these values in the formula,
Average rate of change = [tex]\frac{16-4}{4-2}[/tex]
= [tex]\frac{12}{2}[/tex]
= 6
Therefore, Option D will be the answer.
√10·√8 is this equal to the √80?
Answer: yes
Step-by-step explanation:
They are both equal to 4/5
Mr Hassan gave his Y7 class a test on Friday. Can anyone answer C correctly?
Answer:
you are assuming that everyone in the class took the test. 33 people took the test but there could be more in the class but they were just not there for the test.
Calculate the probability of all three events occurring.
Answer:
even = 1/2
prime = 1/2
multiple of 5 = 1/6
Step-by-step explanation:
probability is the chances of obtaining a certain result out of many attempts.
when rolling a die, the maximum number of results you can get is 6
Then, calculate how many times each of the occurrences appear(even, prime or multiples of 5)
Even = There are only 3 even numbers from 1 to 6
Prime: There are only 3 primes from 1 to 6
Multiples of 5 = There is only one multiple of 5.
Now you present each of this out of 6:
Even: 3/6 = 1/2
Prime: 3/6 = 1/2
Multiple of 5 = 1/6
This can also be presented as a decimal or percentage:
Even: 50% = 0.5
Prime: 50% = 0.5
Multiple of 5 = 16.67% = 0.16
Hope this helps.
Good Luck
If
x = 3,
y = -5 and z-7, find
x +yz +xyz.
Answer:
143
Step-by-step explanation:
Since the values of x y and z are given
Substitute the value in the polynomial, so it'll become,
x+yz+xyz
= (3)+(-5)*(-7)+(3)*(-5)*(-7)
= 3+35+(3)*(-7)*(-5)
{Two negatives when multiplied becomes positive}
=3+35+3*35
= 3+35+105
=143
Scheels received a shipment of 400 water bottles. 30% were yellow.
How many yellow water bottles were in the shipment?
_________________________________
Solution,
30% of 400
= 30/100*400
=120
120 yellow water bottles were in the shipment.
Hope it helps
Good luck on your assignment
__________________________________
For which rational expressions is 5 an excluded value? Select two options.
X+5/X-5
x²-5/x² +5
X-3/x² - 25
2 x + 1/x2 + 25
X-5/
x² + 5x
Answer:
first one and the second one.
Step-by-step explanation:
nothing ：)
Answer:
this is right
Solve for x 3x - 5 = 2x + 6.
01
O-1
O 11
0-11
Answer:
X= 11
Step-by-step explanation:
Move constant to the right side and change its sign
Find the simplest pattern and fill in the missing number. 45, 30, 18, 9, ... 0
Answer:
3 the patten is the previous subtracted about decrease by 3
Step-by-step explanation: the pattern decrease the number subtracted by 3 so it starts with 15 and goes to 12 then to 9 so the last one would be six and 9 - 6 = 3
What’s the answer ??? Help
Answer:
It's B. (2x+5) (x+4)
Answer:
b
Step-by-step explanation:
2x²+13x+20
You can just try all the answers if you'd like and see which one equals 2x²+13x+20.
Using FOIL for all of them:
a. (2x-5)(x-4) = 2x²-8x-5x+20 = 2x²-13x+20
b. (2x+5)(x+4) = 2x²+8x+5x+20 = 2x²+13x+20
c. (2x+2)(x+10) = 2x²+20x+2x+20 = 2x²+22x+20
d. is obviously not correct since we already have an answer.
Our answer is b. (2x+5)(x+4)
Find the sum of the first 44 terms of the following series, to the nearest integer. 10, 14,18,...
Answer:
4224
Step-by-step explanation:
Here, we want to calculate the sum of the first 44 digits
Term a which is first digit is 10
common difference which is difference of terms = 14-10 = 18-14 = 4
Now the nth term of an arithmetic sequence is
a + (n-1)d
44th term means n = 44
10 + (44-1)4
10 + 43(4)
10 + 172 = 182
To find the sum, we use the formula
Sn = n/2[a + L]
where a is the first term and L is the 44th term
Sn = 44/2 (10 + 182)
Sn = 22(192)
Sn = 4,224
the area that lies between Z= - 0.42 and Z= 0.42 is
Answer:
the answer is 0.84
Step-by-step explanation:
assume the two numbers are on a number line and take the absolute value of their difference
Let $z$ and $w$ be complex numbers satisfying $|z| = 4$ and $|w| = 2$. Then enter in the numbers\[|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \]below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark.
Answer:
a) |z+w|² cannot be uniquely determined from the information provided.
b) |zw|² = [|z| × |w|]² = (4×2)² = 64.
c) |z+w|² cannot be uniquely determined from the information provided.
d) |z/w|² = [|z|/|w|]² = (4/2)² = 4
Step-by-step explanation:
z & w are complex numbers with magnitudes
|z| = 4
|w| = 2
We are the told to find
|z + w|²
|zw|²
|z - w|²
|z/w|²
Let the complex numbers be
z = x + iy
w = a + ib
|z| = √(x² + y²) = 4
|w| = √(a² + b²) = 2
|z|² = x² + y² = 16
|w|² = a² + b² = 4
z+w = (x + iy) + (a + ib) = (x + a) + i(y + b)
|z+w|² = (x + a)² + (y + b)² = x² + 2ax + a² + y² + 2by + b²
= (a² + b²) + (x² + y²) + 2ax + 2by
= |w|² + |z|² + 2ax + 2by
= 4 + 16 + 2ax + 2by
= 20 + 2(ax + by)
This cannot be determined from the information provided.
zw = (x + iy)(a + ib) = ax + i(bx + ay) - by
= (ax - by) + i(bx + ay)
|zw|² = a²x² + b²y² - 2abxy + b²x² + a²y² + 2abxy
= a²x² + b²y² + b²x² + a²y²
= a²(x² + y²) + b²(x² + y²)
= (a² + b²)(x² + y²)
= |w|² × |z|²
= 4×16
= 64
c) z-w = (x + iy) - (a + ib) = (x - a) + i(y - b)
|z-w|² = (x - a)² + (y - b)²
= x² - 2ax + a² + y² - 2by + b²
= (a² + b²) + (x² + y²) - 2ax - 2by
= |w|² + |z|² - 2ax - 2by
= 4 + 16 - 2ax - 2by
= 20 + 2(ax + by)
This cannot be determined from the information provided.
d) z/w = (x + iy)/(a + ib)
Rationalizing by multiplying numerator and denominator by (a - ib)
(z/w)= [(x + iy)(a - ib)/(a + ib)/(a - ib)]
= [ax - by + i(ay - bx)]/(a² + b²)
|z/w|² = [(ax + by)² + (ay - bx)²]/(a² + b²)²
= [a²x² + b²y² + 2abxy + b²x² + a²y² - 2abxy]/(a⁴ + b⁴ + 2a²b²)
= [a²x² + b²y² + b²x² + a²y²]/[(a² + b²)² - 2a²b² + 2a²b²]
= [(a² + b²)(x² + y²)]/[(a² + b²)²]
= [(x² + y²)/(a² + b²)]
= |z|²/|w|²
= (4/2)²
= 4
Hope this Helps!!!
Find the perimeter of a rectangle whose length is (4a+b)cm and width (a+6)cm
Answer:
P = 10a +2b+12
Step-by-step explanation:
P = 2 (l+w) for a rectangle
P = 2 ( 4a+b + a+6)
Combine like terms
P = 2(5a+b+6)
Distribute
P = 10a +2b+12
Answer:
Given below
Hope it helps
Step-by-step explanation:
Perimeter= 2(l+b)
= 2(4a+b+a+6)
= 2(5a+b+6)
= 10a+2b+12 cm^2
Find the surface area.
The ratio of the sides of EBD to the sides of ABC is 3:4. Calculate the side lengths of ABC (Round to the nearest hundredth)
Answer:
The side lengths of triangle ABC are 6, 6.67 and 5.33
Step-by-step explanation:
In this question, we are interested in calculating the lengths of triangle ABC
ED: AC = 3:4
4.5:AC = 3:4
4.5/AC = 3/4
3AC = 4 * 4.5
3AC = 18
AC = 18/3 = 6
EB:AB = 3:4
5/AB = 3/4
3AB = 4 * 5
3AB = 20
AB = 20/3 = 6.67
DB:CB = 3/4
4/CB = 3/4
3CB = 4 * 4
CB = 16/3 = 5.33
In how many ways can you
select a group of 6 friends to
invite over from a group of
22 friends?
Answer:74613
Step-by-step explanation:
n!/r!(n-r)!
22!/6!(22-6)!
=74613
4x2 + 25y2
factor the following
Answer:
see explanation
Step-by-step explanation:
This polynomial is irreducible, that is cannot be factored.
4x² + 25y² ← is a prime polynomial
Answer:
1, the polynomial itself
Step-by-step explanation:
This is a prime polynomial since the terms have no common factor. The only factors it has are 1 and 4x2+25y2 (the number itself)
The lengths of a lawn mower part are approximately normally distributed with a given mean Mu = 4 in. and standard deviation Sigma = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.? 34% 68% 95% 99.7%
Answer:
b) 68%
The percentage of the parts will have lengths between 3.8 in. and 4.2 in
P( 3.8 ≤ x ≤ 4.2) = 0.6826 = 68 %
Step-by-step explanation:
Let 'X' be the normally distributed
mean 'μ'= 4 inches
standard deviation 'σ' = 0.2 inches
Case(i):-
when x₁ = 3.8 inches
[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{3.8-4}{0.2} = -1[/tex]
Case(ii):-
when x₂= 3.8 inches
[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{4.2-4}{0.2} = 1[/tex]
The probability of the parts will have lengths between 3.8 in and 4.2 in
[tex]P( 3.8\leq x\leq 4.2) = P(-1\leq z\leq 1)[/tex]
= P(Z≤1) - P(Z≤-1)
= 0.5 +A(1) -(0.5-A(1)
= 2 A(1)
= 2×0.3413
= 0.6826
Conclusion:-
The percentage of the parts will have lengths between 3.8 in. and 4.2 in
P( 3.8 ≤ x ≤ 4.2) = 0.6826 = 68 %
Answer:
B
Step-by-step explanation:
E2020
A closed box has a square base with side length feet and height feet given that the volume of the box is 34 ft.³ express the surface area of the box in terms of length only
Answer:
[tex]\dfrac{2s^3+136}{s}[/tex]
Step-by-step explanation:
Let the side length of the square base =s feet
Let the height of the box = h
Given that the volume of the box = [tex]34$ ft^3[/tex]
Volume of the box =[tex]s^2h[/tex]
Then:
[tex]s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}[/tex]
Surface Area of a Rectangular Prism =2(lb+bh+lh)
Since we have a square base, l=b=s feet
Therefore:
Surface Area of our closed box[tex]= 2(s^2+sh+sh)[/tex]
[tex]S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}[/tex]
In a grade 11 class, 40% of the students are taking Geography, 30% are taking History and 10% are taking both. If 40 students are enrolled in the grade 11 class, how many students are taking neither Geography or History?
I put the wrong answer
Find the circumference of the circle.
Use 3.14 for Pi
c=2pi r
13 cm
Give your answer to the nearest hundredth.
Answer:
81.64
Step-by-step explanation:
2(3.14)=6.28
6.28*13=81.64
Plug r into the equation provided...
c = 2(3.14)(13)
c = 81.64cm
The height, h in feet, a ball with reach when thrown in the ais is a function of time, t, in seconds,given by the equation h(t)=-16t2+35t+10. Find, to the nearest tenth, the maximum height, in feet, the ball will reach. The time when it reached its maximum height. How many seconds after the ball is thrown it will hit the ground?
Answer:
The maximum height the ball will reach is 29,141 feet.
The time when it reached its maximum height is 1.094 seconds.
2,443 seconds after throwing the ball, it will touch the ground.
Step-by-step explanation:
The function h (t) = - 16t² + 35t + 10 is a quadratic function of the form f (x) = ax² + bx + c, where a = -16, b = 35 and c = 10. To calculate the maximum height, you must then find the maximum of the function. In other words, Quadratic functions have a maximum (if a <0) or a minimum (if a> 0). This point is the vertex of the parabola.
The vertex coordinate on the x axis can be calculated by:
[tex]x=\frac{-b}{2*a}[/tex]
The value of the vertex on the y axis is obtained by substituting the value of "x vertex" in the function f (x), that is, by calculating f ([tex]\frac{-b}{2*a}[/tex]).
In this case, where h ([tex]\frac{-b}{2*a}[/tex]) is the maximum height:
[tex]t=\frac{-b}{2*a}=\frac{-35}{2*(-16)} =1.09375[/tex]≅ 1.094 seconds
So: h(1.094)= -16*1.094² + 35*1.094 + 10
h(1.094)=29.151
The maximum height the ball will reach is 29,141 feet.
The time when it reached its maximum height is 1.094 seconds.
To calculate the number of seconds after the ball is thrown it will hit the ground, you must calculate the roots of the quadratic function. For this you must apply:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]
where x1, x2 are the two roots of the function f(x)=a*x² +b*x + c
In this case:
[tex]t1,t2=\frac{-35+-\sqrt{35^{2}-4*(-16)*10 } }{2*(-16)}[/tex]
Solving, you get t1=-0.256 and t2=2.443
Since the time cannot be negative, 2,443 seconds after throwing the ball, it will touch the ground.
Please help!- this is 20% of my grade so I can pass 7th grade
Convert y = 8x^2-80x-32 to vertex form by completing the square.
Answer:
y = 8(x-5)^2 -232
Step-by-step explanation:
Factor out the 8 to get
y = 8(x^2-10x-4)
y = 8(x-5)^2 -232
Answer:
y = 8 (x - 5)^2 - 232
Step-by-step explanation:
Dividing the whole equation by 8, we get:
y = 8 (x^2 - 10x - 4)
y = 8 (x - 5)^2 - 232
Hope this helps!
Factor out the GCF from the following polynomials.
1) 45m^5-25m^4-20m^2-35m=? 2) 35x^2-15x^3+5x^4=? 3) 6ab^6-14a^2b^4+2a^5b^3=?
Answer:
Step-by-step explanation:
i hope
the the answer is 2ab3(a4+3b3−7ab)
hope it helps.
sorry if it wrong
-Delilah
I need help with this question
Answer:
133
Step-by-step explanation:
Answer is 133
[tex]answer \\ = 133 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
ANSWER THIS AND I WILL FRIEND YOU!!! What is x? 2x(3+4x) *2 -5
Answer:
Step-by-step explanation:
[tex]2*(3+4x) *2 -5\\6+8x*2-5\\16x =-6-5\\16x = -11\\x = 11/16[/tex]
b2 - 7b + 12 = 0
Factored equation: ( ) ( ) = 0
ANSWERS: b = ____, and b = ____
Answer: (b - 4)(b - 3); b = 4 and 3
Step-by-step explanation:
ima assume these are exponents since you didnt care to correctly write the equation.
What two numbers multiply to equal 12, but add to equal -7? That's -4 and -3
So the factored form of this trinomial is (b - 4)(b - 3) = 0. Make each of these expressions equal to 0 in order to get your answer.
