Let [tex]c[/tex] denote the number of customers.
The number of customers that seek advice is [tex]0.3c[/tex].
The number of customers that do not seek advice is thusly [tex](1-0.3)c=0.7c[/tex]
40% of the customers that do seek advice buy a device, denoted with [tex]0.4\cdot0.3c=0.12c[/tex] that is 12% of the total customers here buy a device.
20% of the customers that do not seek advice buy a device, denoted with [tex]0.2\cdot0.7c=0.14c[/tex] so 14% of the total customers here buy a device.
Together, the percentage of customers that will buy an applicance on the end of the day is [tex]12\%+14\%=26\%[/tex].
So the probability from that follows that when a customer enters the shop there exists a 26% probability that the customer will end up buying a device.
Hope this helps :)
A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 9 meters and its width from left to right is 12 meters. If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex?
The telescope shape and the characteristic equations of the telescope parameters are the same as parabolic equations
The distance between the focus and the vertex, of the parabola is 3.375 meters
The process for obtain the above values is as follows:
The known parameters of the parabola are;
The location of the vertex of the parabola= The origin = (0, 0)
The height of the parabola = 9 meters
The width of the parabola = 12 meters
The unknown parameter;
The distance between the focus and the vertex
Method:
Finding the coordinate of the focus from the general equations of the the parameters of a parabola
The equation of the parabola in standard form is y = a·(x - h)² + k
From which we have;
(x - h)² = 4·p·(y - k)
The coordinates of the focus, f = (h, k + p)
Where;
(h, k) = The coordinates of the vertex of the parabola = (0, 0)
∴ a = 1/(4·p)
From the question, we have the following two points on the parabola,
given that the parabola is 12 meters wide at 9 meters above the origin and
it is symmetric about the y-axis;
Points on the parabola = (9, 6), and (9, -6)
Plugging in the values of the vertex, (h, k) and the two known points, in the equation, y = a·(x - h)² + k, we get;
6 = a·(9 - 0)² + 0 = 81·a
a = 6/81 = 2/27
p = 1/(4·a)
∴ p = 1/(4 × 2/27) = 27/8
The coordinate of the focus, f = (h, k + p)
∴ f = (0, 0 + 27/8) = (0, 27/8)
The coordinate of the focus f = (0, 27/8)
Given the vertex and the focus of the parabola have the same x-values of 0, we have;
The distance between the focus and the vertex, d = the difference in their y-values;
∴ d = 27/8 - 0 = 27/8 = 3.375
The distance between the focus and the vertex, d = 3.375 meters
Learn more about parabola here;
https://brainly.com/question/22404310
HELP UUUURRRRRRRGGGGGEEEEEENNNNTTTTT PLLLLZZZZZ IM BAD AT MATHHHHHHHH
Answer:
-1 8/9
Step-by-step explanation:
w + ( - x)
w = -5/9
z = 4/3
Input:
-5/9 + ( -4/3)
-5/9 - 4/3
-4/3 * 3/3 = -12/9
-5/9 - 12/9 = -17/9 = -1 8/9
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Suppose A and B are events with P(A) = 1/4, P(B) = 1/3 and P(A cup B)= 1 2 a ) Find P(A cap B) b) Find P(A|B)
Answer:
Step-by-step explanation:
I need to know about rounding the numbers up to 100
Step-by-step explanation:
Rounding number are important in world-problem. They help us in many ways like counting class, food, etc. It's the same thing as estimating.
Tens Place:
50-99: round to 100
100th place:
150-101: round to 100
There is still a lot I'm missing out on, but you could say does are the lowest group that can be round to 100. I'm not a expert, but I hope I could help! You can also ask for the other numbers, but it just depends on where you place or how you use the 100.
Help 50 point question
Answer:
1/3
Step-by-step explanation:
.444444444(repeating)- .111111111111(repeating)
.44444444......
-.11111111........
--------------------
.33333333........
Let x = .3333333.....
10x = 3.3333333.....
Subtract the first equation from the second
10x = 3.33333.....
-x = .33333.....
--------------------------
9x = 3
x = 3/9
x = 1/3
---------------------------
PLEASE SHOW YOUR WORK! I NEED THIS QUICK! THANK YOU!! POINTS AND RATES WILL BE GIVEN!!
Answer:
3
Step-by-step explanation:
Y is given by sin(theta). sin(-60)=-sqrt(3)/2
find the surface area of the prism
Answer:
114 cm²
Step-by-step explanation:
Surface area of the rectangular prism,
2×(wl+hl+hw)
=2×(3×8+3×8+3×3)
= 2×(24+24+9)
= 2×(57)
=114 cm²
PLEASE JUST GIVE ME THE EQUATION
Answer:
y=4/3x-3
Step-by-step explanation:
Calculate the amount in an account after one year that starts
with the principal listed below and pays the specified annual
rate of interest compounded yearly.
Principal = $18,000, Rate = 3%
9514 1404 393
Answer:
$18,540
Step-by-step explanation:
When interest is compounded yearly, the amount of interest earned in one year is the same as the amount of simple interest earned. The account balance is ...
A = P(1 +r) = $18,000(1 +.03) = $18,540
Parallelogram QRST has vertices Q(- 4, 2) . R(-2,4),5(0)) draw and label the image after a counterclockwise rotation of 270 degrees about the origia.please I need help.
Answer:
gr,wrgñegetjj
Step-by-step explanation:
jyyjytjjttj
$88 tickets to the San Francisco 49ers game are offered at a 15%
discount. What is the sale price?
Answer:
74.80
Step-by-step explanation:
First find the discount
88 * 15%
88*.15
13.2
Subtract the discount from the original price
88-13.2
74.80
complete the equation describing how x and y are related.
Answer:
y=-2x+1
Step-by-step explanation:
The slope of the line is (y(2)-y(1))/(2-1)=(-3+1)/1=-2. The equation of the line is y=mx+(y intercept), y=-2x+1
The complete equation describes how x and y are related y=-2x+1.
We have given, the equation,
We have to determine the complete equation describing how x and y are related.
What is the formula for the slope?
The slope of the line is(m)=y2-y1/x2-x1
Where m is the slope,
Therefore we get,
(y(2)-y(1))/(2-1)
=(-3+1)/1
=-2.
The equation of the line is y=mx+(y-intercept), y=-2x+1.
To learn more about the slope visit:
https://brainly.com/question/3493733
#SPJ2
Natalie's team needs to make a decision on how to handle a big product recall. People on the team have a lot of strong opinions. Management wants everyone to come to a consensus and to find a solution that everyone can support. What's the best way to get to a consensus? a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Describe the translation y= (x-2) squared +5 -> y = (x+2) squared - 3
9514 1404 393
Answer:
A. T<-4, -8>
Step-by-step explanation:
To get the second equation, we had to replace x with x+4 (a translation left 4) and we had to add -8 to the function value (a translation down 8).
Left 4 and down 8 is the translation ...
T<-4, -8>
3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}
A.657
B.2433
C. -843
Answer:
657
Step-by-step explanation:
pemdas
The value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.
Hence option A is correct.
Given is an expression, 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}, we need to simplify it,
Let's break down the expression step by step:
First, let's simplify the expression inside the innermost parentheses:
8 - 2 x 3 = 8 - 6 = 2
Next, let's simplify the expression inside the brackets:
3 x 23 - 2 = 69 - 2 = 67
Now, let's substitute the simplified expression inside the brackets back into the original expression:
(300 - 70 ÷ 5) - 67
Next, let's simplify the expression inside the remaining parentheses:
70 ÷ 5 = 14
Now, let's substitute the simplified expression inside the parentheses back into the expression:
(300 - 14) - 67
Next, let's simplify the expression inside the remaining parentheses:
300 - 14 = 286
Now, let's substitute the simplified expression inside the parentheses back into the expression:
286 - 67
Finally, let's perform the subtraction:
286 - 67 = 219
Now, let's multiply the result by 3:
3 x 219 = 657
Therefore, the value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.
Learn more about expression click;
https://brainly.com/question/28170201
#SPJ2
Find the x-and y-intercepts of the graph of 4x + y = 28. State your answers as
whole numbers or as improper fractions in simplest form.
Answer:
at x-intercept, y = 0
4x = 28
x = 7
x intercept = (7,0)
at y-intercept, x = 0
y = 28
y intercept = (0,28)
Use the distributive property to remove the parentheses.
I’m so bad at math so I need help :/
4 l to 250 miles ratio
Answer:
See below.
Step-by-step explanation:
Are you sure it's 4 liters to 250 miles, and not 4 liters to 250 milliliters?
If it is 4 liters to 250 miles, then it equals
0.016 liter : 1 mile
If it is 4 liters to 250 ml, then it is
4 liters : 250 ml
4 liters : 0.25 liter
16 liters : 1 liter
16 : 1
Solve the equation on the interval [0,2pi) 7sec x-7=0
Answer:
2π or 0π are the only points that satisfy the expression, but since the restriction is 0 <= x < 2π
the answer would be 0π
The solution of the equation on the interval [0,2π) is 0.
To find Solution of the equation.
What is equation?A statement that the values of two mathematical expressions are equal.
The given equation is :
7secx-7=0 on the interval [0,2π)
7secx-7=0
7secx=7
sec x =1
∴ x=0
So, the solution of the equation on the interval [0,2π) is 0.
Learn more about equation here:
https://brainly.com/question/24366859
#SPJ2
If two numbers differ by 9 the same of their squares is 653. What are the numbers?
Answer:
Two numbers differ by 9 and the sum of their square is 653. What are the numbers?
Well,that's a mathematical question from algebra and it's quite difficult to answer such questions by writing through the circumstances offered by apps like quora.
However,I have tried to answer your question in an understandable way.Hope you may not find it difficult to analyze.
Let the numbers be x and (9+x)
Therefore,according to given,
x^2 + (9+x)^2 =653
=>x^2 + (9)^2 + x^2 + 2×(9)×(x)=653 (Applying the formula of (a+b)^2)
=>x^2 + 81 + x^2 + 18x =653
=>2x^2 + 18x + (81-653)=0
=>2x^2 + 18x - 572=0
=>2x^2 + (44x - 26x) - 572=0
=>2x^2 + 44x - 26x - 572=0
=>2x(x + 22) - 26(x + 22)=0
=>(x + 22)(2x - 26)=0
But since the number can't be negative
Therefore, x=13
Hence,the required numbers are 13 and 22.
Step-by-step explanation:
in first hope you like it
If two people are splitting a total rent number of $1,120 a month, it would be $560 split evenly. However, if one roommate pays $60 more than the other, how much would that roommate be paying per month?
$560-$500
=$500
therefore, other roommate will be paying $500 per month
How do you write it in digits
27 million, 200
Answer:
27,000,200
Step-by-step explanation:
Going by basic math you know a million has six 0's.
So; one million is represented as 1,000,000.
Hence twenty-seven million as 27,000,000.
Using you tens, hundreds and thousands you'll know 200 will fall into the last area.
Beth has just received an inheritance of $500,000 and would like to be able to make quarterly withdrawals over the next 20 years. She decides on an annuity that pays 6.4%, compounded quarterly. How much will her quarterly payments be to draw the account down to zero at the end of 20 years? Quarterly Payments =
The amount Beth would be able to withdraw quarterly from her inheritance over the next 20 years is Quarterly Payments ≈ $11,124.53
The given parameters in the question;
Present value of inheritance, PV = $500,000
The number of years of withdrawal, n = 20 years
Interest rate, i = 6.4%
The required parameter;
The amount Beth would be able to withdraw quarterly over the next 20 years to draw the account down to zero, given a quarterly interest rate of 6.4%
Method
The required parameter is given by the payment formula
The question is related with annuity given that withdrawals will be made quarterly
The question seeks to find how much she can withdraw so as to exhaust the balance in 20 years
The amount she can withdraw quarterly is given by the payment formula as follows;
[tex]\mathbf{PMT = PV \times \dfrac{i}{1 - \left(1 + i\right)^{-n}}}[/tex]
Where;
PMT = The amount of quarterly payments
PV = The present value of the investment = $500,000
i = The interest rate = 6.4%
n = The number of years = 20 years
Therefore, we get;
[tex]\mathbf{PMT = 500,000 \times \dfrac{\dfrac{0.064}{4} }{1 - \left(1 + \dfrac{0.064}{4} \right)^{-4 \times 20}} \approx 11,124.53}[/tex]
The amount she can withdraw quarterly for the next 20 years ≈ $11,124.53
Quarterly payment, PMT = $11,124.53
Learn more about annuity here;
https://brainly.com/question/20796802
In a café, I order a cup of tea and a piece of cake and it costs £1.10. The next time I order 2 cups of tea and one piece of cake and it costs £1.70. Find the cost of a piece of cake.
Answer:
£0.50
Step-by-step explanation:
t = one cup of tea
c = one piece of cake
t + c = £1.10
2t + c = £1.70
the cost increases by £0.60 (£1.70 - £1.10) when you order one more cup of tea which means that one cup of tea costs £0.60
substitute £0.60 into t + c = £1.10
£0.60 + c = £1.10
rearrange to get c = £1.10 - £0.60 = £0.50
so one piece of cake costs £0.50
If Ahmad’s balance is $85, what will the minimum payment be?
Find the probability
A bag contains 6 red marbles, 8 blue marbles, and 9 green marbles. What is the probability of choosing a blue marble?
Answer is in a box.
The bag contains 6 red marbles, 8 blue marbles and 9 green marbles, that is 23 marbles.
The probability that one of the 23 marbles will be picked is 1 or 100%, we are picking a marble for sure.
So what is the probability you will pick for example one of the 6 red marbles? It is 6 out of 23 but since we need percentages multiply by 100,
[tex]\frac{6}{23}\cdot100\approx26.09\%[/tex]
The probability to pick a blue marble is,
[tex]\boxed{\frac{8}{23}}\cdot100\approx34.78\%[/tex]
And the probability to pick a green marble is,
[tex]\frac{9}{23}\cdot100\approx39.13\%[/tex]
To check that everything is right you can sum all the probabilities; the probability that it will be either red, blue or green is 100% so the individual probabilities must sum to 100%, and they do,
[tex]26.09\%+34.78\%+39.13\%=100\%[/tex]
Hope this helps :)
At what rates did she invest?
$1400 invested at ____%
$900 invested at ____%
9514 1404 393
Answer:
$1400 at 8%$900 at 10%Step-by-step explanation:
The 1-year interest is simply the invested amount times the interest rate.
Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...
1400r + 900(r +.02) = 202
2300r +18 = 202 . . . . . . . . . .simplify
2300r = 184 . . . . . . . . . .subtract 18
r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r
$1400 was invested at 8%.
$900 was invested at 10%.
Write 2.71 repeating as a simplified fraction.
271/100 is wrong
Answer:
269/99
Step-by-step explanation:
Explain why this quadrilateral is not a parallelogram.
Answer:
because this figure does not have two parallel sides
I'm Sorry for by bad English but I am italian
Proceed as in Example 4 in Section 6.1 and find a power series solution y = [infinity] n = 0 cnxn of the given linear first-order differential equation. (Give your answer in terms of c0.) y' = xy
Let y be a solution to the given differential equation,
[tex]y' = xy[/tex]
where
[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]
Substituting these series into the DE gives
[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]
Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,
[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]
We have
[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]
so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while
[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]
and so on, with the general n-th coefficient being
[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]
Then the power series solution is
[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]
but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.
More concisely: let n = 2k for integers k ≥ 0. Then
[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]
and as a bonus, it's easier to get an exact solution for this DE,
[tex]y(x) = c_0e^{x^2/2}[/tex]
