Answer:Perimeter of a rectangle is 2*the length plus 2*the width
P = 2L + 2W and P = 130, so
L + W = 65
Three times the length is equal to 10 times the width, giving
3L = 10W
Substituting into the above for L = 65 – W,
3(65 – W) = 10W
195 – 3W = 10W
195 = 13W
W = 195/13 = 15
W = 15 yards,
And L = (10/3)W = (10/3)*15 = 50
L = 50 yards
Step-by-step explanation:
Part b c and d please help
Answer:
b) Y =5.73X +4.36
C) =5.73225*(21)X +4.359
124.73625
D) 163.728 = 5.73X +4.36
X = (163.728 - 4.36)/5.73
X = 27.81291449
Year would be 2027
Step-by-step explanation:
x1 y1 x2 y2
4 27.288 16 96.075
(Y2-Y1) (96.075)-(27.288)= 68.787 ΔY 68.787
(X2-X1) (16)-(4)= 12 ΔX 12
slope= 5 41/56
B= 4 14/39
Y =5.73X +4.36
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
From a club of 24 people, in how many ways can a group of four members be selected to attend a conference?
Answer:
255,024
Step-by-step explanation:
24 x 23 x 22 x 21
24 options for the first member
23 options for the second member
22 options for the third member
21 options for the last member
A professor wondered if there was a difference in the proportion of students who dropped math classes between females and males. The professor randomly selected 20 math classes around campus and recorded the gender of the individual and whether or not a student enrolled in the class at the beginning of the term dropped the class at some point during the term. Assuming all conditions are satisfied, which of the following tests should the researcher use? Choose the correct answer below.
a) Chi-square goodness of fit test
b) two-sample z-test for proportions C
c) paired t-test
d) one-sample z-test for proportions
e) two-sample t-test
Answer:
b) two-sample z-test for proportions
Step-by-step explanation:
The most appropriate test to use for the research hypothesis stated above is the two sample z-test for proportions, this is because, the experiment has two independent groups (male and female) with the result of each group not affecting the result of the other. The experiment clearly stses that, it is to estimate the difference in proportion, hence, it is a test of proportions rather than mean. Also when performing, a two sample tests of proportion, the Z distribution is used.
Damaged items are marked down 25% to 40%. A newspaper coupon holder; to an additional 10% markdown of the new price due to the damage. What is the lowest price of a damaged item that was originally marked GHC100?
A GHC 35.60
B GH 5000
C. GHC 18.00
D. GHC 40.80
E GHC 23.40
Markdown is the difference (at sale) between the price an item is placed at for retail sale, and the actual price the item is sold
The correct option is; B. GHC 50.00
The reason for choosing option B is as follows;
The known parameters
The percentage by which damaged items are marked down = 25% to 40%
The percentage markdown offered by the newspaper coupon = 10%
The original marked price of the item = GHC 100
Strategy:
Apply the damaged items and coupon markdown percentages to the original marked price of GHC100 sum the results to find the total markdown
Solution:
Markdown due to damage:
Given that the item is damaged, to have the lowest price, we apply the largest markdown of 40%;
40% is removed from the price to which the item marked down due to damage, as follows;
The markdown due to damage = 40/100 × GHC 100 = GHC 40
Markdown due to Coupon Holder:
The markdown the coupon holder is to get = 10% off the retail price
Given that the damage is not mentioned in the newspaper, we have;
∴ The markdown the coupon holder is to get = 10/100 × GHC 100 = GHC 10
Total markdown:
The total markdown is therefore equal to GHC 40 + GHC 10 = GHC 50
The Lowest Price of A Damaged Items marked GHC100:
The lowest price of the item = Original price - Maximum markdown
The lowest price of the item = GHC 100 - GHC 50 = GHC 50
Learn more about markdown and markup concepts here;
https://brainly.com/question/20705786
PLSSS HELP IM STRUGGLING SO HARD !!! ———————
Answer:
C)
Step-by-step explanation:
Just see the length of the R line, A and B are almost the same large when you add them.
Which of the following graphs represents the line that passes through (–2, –3) and has a slope of 2/3?
Answer:
Step-by-step explanation:
what is the least common multiple between 25 and 8
Answer:
200
Step-by-step explanation:
Break down 25 = 5*5
Break down 8 = 2*2*2
They have no common factors
The least common multiple is
5*5*2*2*2 = 25*8 = 200
Answer:
200
Step-by-step explanation:
list the factors of 25: 5,5
factors of 8:2,2,2,
In ΔABC, if AB = 10 and BC = 6, AC can NOT be equal to
Answer:
Step-by-step explanation:
4
The salt content in snack bags of pretzels is Normally distributed, with a mean of 180 mg and a standard deviation of 15 mg. Eighty four percent of bags have a salt content higher than which value?
Find the z-table here.
165.2 mg
179.2 mg
187.0 mg
194.9 mg
I think its (A), 165.2mg
Answer: Yes you are correct. The answer is choice A
============================================================
Explanation:
If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.
So by symmetry, P(Z > -1) = 0.84 approximately as well.
We'll convert the z score z = -1 into its corresponding x score
z = (x-mu)/sigma
-1 = (x-180)/15
-15 = x-180
x-180 = -15
x = -15+180
x = 165
We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.
I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.
Answer:
194.9
Step-by-step explanation:
ON EDG
Solve for Y equals -2 over 3x minus 1
Answer:
y=-\frac{2}{3}\approx -0.666666667
Which is the sum of the sequence {5*1, 5*8, 5*27, 5*64, 5*125, 5*216}?
Answer:
2160
Step-by-step explanation:
I find that it is easier to split the sequence into smaller, more manageable sections. For numbers beyond 13, the simplest way is to split it up into place values.
Note: * is a multiplication symbol
5*1 = 5
5*8 = 40
5*27 = (5*20) + (5*7) = 100+35 = 135
5*64 = (5*60) + (5*4) = 300+20 = 320
5*125 = (5*100) + (5*20) + (5*5) = 500+100+25 = 625
5*216 = (5*200) + (5*10) + (5*6) = 1000+50+30=1080
Now you can add all of the totals up!
135+320+625+1080 = 2160
A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $12 the average attendance has been 25000. When the price dropped to $9, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.
Required:
a. Find the demand function p(x), where x is the number of the spectators.
b. How should ticket prices be set to maximize revenue?
Answer:
We need to assume that the relationship is linear.
a) Remember that a linear relation is written as:
y = a*x + b
then we will have:
p(x) = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:
y = (d - b)/(c - a)
In this case, we know that:
if the ticket has a price of $12, the average attendance is 25,000
Then we can define this with the point:
(25,000 , $12)
We also know that when the price is $9, the attendance is 29,000
This can be represented with the point:
(29,000, $9)
Then we can find the slope as:
a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075
Then the equation is something like:
y = (-$0.00075)*x + b
to find the value of b we can use one of the known points.
For example, the point (25,000 , $12) means that when x = 25,000, the price is $12
then:
$12 = (-$0.00075)*25,000 + b
$12 = -$18.75 + b
$12 + $18.75 = b
$30.75 = b
Then the equation is:
p(x) = (-$0.00075)*x + $30.75
b) We want to find the ticket price such that it maximizes the revenue.
The revenue will be equal to the price per ticket, p(x) times the total attendance, x.
Then the revenue can be written as:
r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )
r(x) = (-$0.00075)*x^2 + $30.75*x
So we want to find the maximum revenue.
Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.
Remember that for an equation like:
y = a*x^2 + bx + c
the x-value of the vertex is:
x = -b/2a
Then in our case, the x-value will be:
x = -$30.75/(2*(-$0.00075)) = 20,500
Then the revenue is maximized for x = 20,500
And the price for this x-vale is given by:
p( 20,500) = (-$0.00075)*20,500 + $30.75 = $15.375
which should be rounded to $15.38
Use the compound interest formula to find the annual interest rate, r, if in 2 years an investment of 4,000 grows to 4410 The rate is %.
Answer:
5%
Step-by-step explanation:
Bank amount=PA*(1+r/100)^t
4410=4000*(1+x/100)^2
1.05=(1+x/100), x=5%
help me please !
4,5 and 6
9514 1404 393
Answer:
4a. ∠V≅∠Y
4b. TU ≅ WX
5. No; no applicable postulate
6. see below
Step-by-step explanation:
4.a. When you use the ASA postulate, you are claiming you have shown two angles and the side between them to be congruent. Here, you're given side TV and angle T are congruent to their counterparts, sides WY and angle W. The angle at the other end of segment TV is angle V. Its counterpart is the other end of segment WY from angle W. In order to use ASA, we must show ...
∠V≅∠Y
__
b. When you use the SAS postulate, you are claiming you have shown two sides and the angle between them are congruent. The angle T is between sides TV and TU. The angle congruent to that, ∠W, is between sides WY and WX. Then the missing congruence that must be shown is ...
TU ≅ WX
__
5.The marked congruences are for two sides and a non-included angle. There is no SSA postulate for proving congruence. (In fact, there are two different possible triangles that have the given dimensions. This can be seen in the fact that the given angle is opposite the shortest of the given sides.)
"No, we cannot prove they are congruent because none of the five postulates or theorems can be used."
__
6.The first statement/reason is always the list of "given" statements.
1. ∠A≅∠D, AC≅DC . . . . given
2. . . . . vertical angles are congruent
3. . . . . ASA postulate
4. . . . . CPCTC
find the value of x²-6x+13 when x=3+2i
Answer:
18
Step-by-step explanation:
x squared -6 +13
5 squared-6×3+2+13
25-20+13
5+13
=18
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate
Answer:
YWX = DFE
Step-by-step explanation:
AAS means angle angle side. so, we need 2 angles and 1 side.
we have 1 side and one angle confirmed.
so, we need one of the other two angles (W or Y vs. F or D) confirmed.
they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.
PLEASE HELP ME !!!!
How many solutions does the system of equations below have?
y = x - 3
3y-3x = -9
A. Exactly 1 solution
B. At least 1 solution
C. More than 1 solution
D. No solution
9514 1404 393
Answer:
C. More than 1 solution
Step-by-step explanation:
Divide the second equation by 3.
y -x = -3
Add x.
y = x -3
This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."
PLEASE HELPPPPPPPPP!!!!!!!!!!!
If ABCD is dilated by a factor of 3, the
coordinate of D' would be:
4
с
3
B
2
1
-5
-4
-3
-2
-1 0
1
N
3
4
5
DAN
- 1
-2
D
-3
D' = ([?], [ ]
Enter
Pls help me
Answer:
(6,-6)
Step-by-step explanation:
First let's identify the current coordinates of D
It appears that D is located at (2 , -2)
Now let's find the coordinate of D if it were dilated by a scale factor of 3.
To find the coordinates of a point after a dilation you simply multiply the x and y values of the pre image coordinates by the scale factor
In this case the scale factor is 3 and the coordinates are (2,-2)
That being said let's apply the dilation rule
Current coordinates: (2,-2)
Scale factor:3
Multiply x and y values by scale factor
(2 * 3 , -2 * 3) --------> (6 , -6)
The coordinates of D' would be (6,-6)
72a^7/-9 as a monomial
Answer:
− 8 a ^7
Step-by-step explanation:
See picture for steps :)
T
On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
TE
$
(S
9514 1404 393
Answer:
$3277.23
Step-by-step explanation:
The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...
A = P(1 +r/2)^(2t)
where P is the principal value.
For the given rate and time, this is ...
A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23
The value of the CD at maturity will be $3277.23.
A restaurant interest survey of 230 citizens in a town showed that 80 want a new Chili's, 120 want a new Red Lobster, and 20 want both. Determine the probability that:
...
Answer:
2/23
6/23
5/23
Step-by-step explanation:
60 only want chilis
20 wants both
100 only want red lobster
50 want neither
The right solution to the given question is "[tex]\frac{2}{23}[/tex]", "[tex]\frac{6}{23}[/tex]" and "[tex]\frac{5}{23}[/tex]".
According to the question,
[tex]a+b+c+d = 230[/tex][tex]b = 20[/tex][tex]a+b = 80[/tex]By putting the value of "b", we get
[tex]a+20=80[/tex][tex]a = 80-20[/tex]
[tex]a = 60[/tex]
[tex]b + c=120[/tex]By putting the value of "b", we get
[tex]20+c=120[/tex]
[tex]c = 120-20[/tex]
[tex]c = 100[/tex]
[tex]d = 230-60-100-20[/tex]By putting the values of "a", "b", "c" and "d", we get
[tex]d = 50[/tex]
(a)
P(both Chili's and Red lobster),
= [tex]\frac{b}{a+b+c+d}[/tex]
= [tex]\frac{2}{23}[/tex]
(b)
P(only chili's),
= [tex]\frac{a}{a+b+c+d}[/tex]
= [tex]\frac{6}{23}[/tex]
(c)
P(neither),
= [tex]\frac{d}{a+b+c+d}[/tex]
= [tex]\frac{5}{23}[/tex]
Learn more about probability here:
https://brainly.com/question/24269622
Factorise: 25x^2 - 1/49
Answer:
[tex] (5x + \frac{1}{7} )(5x - \frac{1}{7} )[/tex]Step-by-step explanation:
Given,
[tex] {25x}^{2} - \frac{1}{49} [/tex]
[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]
Since,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Then,
[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]
Find y' for the following.
Answer:
[tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{\sqrt{x} + 1}{\sqrt{y} + 1} = y^2[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx} \bigg[ \frac{\sqrt{x} + 1}{\sqrt{y} + 1} \bigg] = \frac{dy}{dx}[ y^2][/tex]Quotient Rule: [tex]\displaystyle \frac{(\sqrt{x} + 1)'(\sqrt{y} + 1) - (\sqrt{y} + 1)'(\sqrt{x} + 1)}{(\sqrt{y} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Rewrite: [tex]\displaystyle \frac{(x^\Big{\frac{1}{2}} + 1)'(y^\Big{\frac{1}{2}} + 1) - (y^\Big{\frac{1}{2}} + 1)'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Basic Power Rule [Addition/Subtraction, Chain Rule]: [tex]\displaystyle \frac{\frac{1}{2}x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - \frac{1}{2}y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Factor: [tex]\displaystyle \frac{\frac{1}{2} \bigg[ x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1) \bigg] }{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{2(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}= 4yy'(y^\Big{\frac{1}{2}} + 1)^2[/tex]Isolate y' terms: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = 4yy'(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}[/tex]Factor: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = y' \bigg[ 4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} \bigg][/tex]Isolate y': [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1)}{4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} = y'[/tex]Rewrite/Simplify: [tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Help once again thanks! !!!!!!!
Consider an urn initially containing n balls, numbered 1 through n, and suppose that balls will be randomly drawn from the urn, one by one, and without replacement (so that after n draws, it is empty). Letting X be the number of successes that will occur, where a success is considered to occur on the ith draw if the ball obtained is numbered i or smaller, give the expected value of X. (E.g., if n = 5, and the balls are drawn in the order 3, 1, 5, 4, 2, then x = 3, because the 2nd, 4th, and 5th draws result in successes, but the 1st and 3rd draws don’t.)
(b) How much the selling price should be fixed for pulse bought for Rs.70 per kg. to earn a profit of Rs.6 after allowing a 5 % discount?
Answer:
Rs. 80
Step-by-step explanation:
Given that :
Purchase price = 70
Profit = 6
Discount = 5%
Let selling price = x
Selling price * (1 - discount) = (purchase price + profit)
x * (1 - 5%) = (70 + 6)
x * (1 - 0.05) = 76
x * 0.95 = 76
0.95x = 76
x = 76 / 0.95
x = 80
Hence, selling price = Rs. 80
14/50 as as a percent?
Answer:
The answer would be 28%!
Step-by-step explanation:
14/50 is 0.28. To change a decimal to a percentage, we multiply it by 100 which we can do by moving the decimal two numbers to the right.
Conan puts tennis balls into tubes after gym class. There are 17 tennis balls, and each tube holds 3 balls. How many tubes does Conan completely fill? How many tennis balls are left?
