Answer:
D)
center of dilation.
Step-by-step explanation:
The answer
Answer:
D center of dilation
Step-by-step explanation:
dilation is the only invariant point
double the second number, the sum is 34."
a. Write an equation that represents this clue. Then, find two possible pairs of
numbers Diego could be thinking of.
b. Diego then says, "If we take half of the first number and double the second, the
sum is 14."
Write an equation that could represent this description.
c. What are Diego's two numbers? Explain or show how you know. A coordinate
plane is given here, in case helpful.
20
18
16
14
12
second number
10
8
6
4
2
2 4 6 8 10 12 14 16 18 20
first number
Answer:
a.) 3x+2y=34 is the equation. 2 pairs could be 10,2 and 8,5.
b.) .5x+2y=14
c.) 8,5
Step-by-step explanation:
because both 8 and 5 work in both equations 3(8)+2(5)=34
.5(8)+2(5)=14
Pls help me on this due in 10 mins
Answer:
A, E, G
Step-by-step explanation:
Answer:
A
E
G
Step-by-step explanation:
When you divide A, E, and G with the common factor, they all equal 5 : 9
Find the area of the region enclosed by the graphs of these equations. (CALCULUS HELP)
Answer:
[tex]\displaystyle A = \frac{20\sqrt{15}}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Area - Integrals
U-Substitution
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
F: y = √(15 - x)
G: y = √(15 - 3x)
H: y = 0
Step 2: Find Bounds of Integration
Solve each equation for the x-value for our bounds of integration.
F
Set y = 0: 0 = √(15 - x)[Equality Property] Square both sides: 0 = 15 - x[Subtraction Property of Equality] Isolate x term: -x = -15[Division Property of Equality] Isolate x: x = 15G
Set y = 0: 0 = √(15 - 3x)[Equality Property] Square both sides: 0 = 15 - 3x[Subtraction Property of Equality] Isolate x term: -3x = -15[Division Property of Equality] Isolate x: x = 5This tells us that our bounds of integration for function F is from 0 to 15 and our bounds of integration for function G is 0 to 5.
We see that we need to subtract function G from function F to get our area of the region (See attachment graph for visual).
Step 3: Find Area of Region
Integration Part 1
Rewrite Area of Region Formula [Integration Property - Subtraction]: [tex]\displaystyle A = \int\limits^b_a {f(x)} \, dx - \int\limits^d_c {g(x)} \, dx[/tex][Integral] Substitute in variables and limits [Area of Region Formula]: [tex]\displaystyle A = \int\limits^{15}_0 {\sqrt{15 - x}} \, dx - \int\limits^5_0 {\sqrt{15 - 3x}} \, dx[/tex][Area] [Integral] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle A = \int\limits^{15}_0 {(15 - x)^{\frac{1}{2}}} \, dx - \int\limits^5_0 {(15 - 3x)^{\frac{1}{2}}} \, dx[/tex]Step 4: Identify Variables
Set variables for u-substitution for both integrals.
Integral 1:
u = 15 - x
du = -dx
Integral 2:
z = 15 - 3x
dz = -3dx
Step 5: Find Area of Region
Integration Part 2
[Area] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle A = -\int\limits^{15}_0 {-(15 - x)^{\frac{1}{2}}} \, dx + \frac{1}{3}\int\limits^5_0 {-3(15 - 3x)^{\frac{1}{2}}} \, dx[/tex][Area] U-Substitution: [tex]\displaystyle A = -\int\limits^0_{15} {u^{\frac{1}{2}}} \, du + \frac{1}{3}\int\limits^0_{15} {z^{\frac{1}{2}}} \, dz[/tex][Area] Reverse Power Rule: [tex]\displaystyle A = -(\frac{2u^{\frac{3}{2}}}{3}) \bigg|\limit^0_{15} + \frac{1}{3}(\frac{2z^{\frac{3}{2}}}{3}) \bigg|\limit^0_{15}[/tex][Area] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = -(-10\sqrt{15}) + \frac{1}{3}(-10\sqrt{15})[/tex][Area] Multiply: [tex]\displaystyle A = 10\sqrt{15} + \frac{-10\sqrt{15}}{3}[/tex][Area] Add: [tex]\displaystyle A = \frac{20\sqrt{15}}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Area Under the Curve - Area of a Region (Integration)
Book: College Calculus 10e
Question 3 (5 points)
(02.01 MC)
Which of these is a positive externality of carpooling with friends to work?
оа
Reduced commute time
Ob
Reduced driving focus
Ос
Reduced traffic on the road
Od
Reduced time to socialize
Answer:
reduced traffic on the road
Step-by-step explanation:
just took the test :)
Answer: C) Reduced traffic on the road
Step-by-step explanation: Ive taken this test
Round to the nearest hundredth 94.855
Assume that each time a metal detector at an airport signals, there is a 25% chance that the cause is change in the passenger's pocket. During a given hour, 15 passengers are stopped because of a signal from the metal detector. a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets. b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket
Answer:
a) 0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.
b) 0 is less than 2.5 standard deviations from the mean, so it would not be unusual.
Step-by-step explanation:
For each passenger, there are only two possible outcomes. Either they will have been stopped due to a change in the pocket, or not. Passengers are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A measure is considered unusual if it is more than 2.5 standard deviations of the mean.
25% chance that the cause is change in the passenger's pocket.
This means that [tex]p = 0.25[/tex]
During a given hour, 15 passengers are stopped because of a signal from the metal detector.
This means that [tex]n = 15[/tex]
a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets.
This is
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134[/tex]
[tex]P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668[/tex]
[tex]P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.2361 = 0.7639[/tex]
0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.
b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket
First we find the mean and the standard deviation:
[tex]E(X) = np = 15*0.25 = 3.75[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15*0.25*0.75} = 1.68[/tex]
3.75 - 2.5*1.68 = -0.45
0 is less than 2.5 standard deviations from the mean, so it would not be unusual.
(30)Points
Which Statement is true
A,
B.
C.
D.
Answer:
The first answer one is true
8. A bakery is collecting data to investigate how changing the price charged for a loaf of bread
affects the bakery's daily profit. The graph shows the data the bakery has collected.
Bread Price vs. Daily Profit
1000
800
600
.
Daily Profit (Dollars)
.
.
400
.
.
200
0
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00
Price for One Loaf of Bread (Dollars)
Which quadratic function is the BEST model for the data?
A
8(1-4) - 800
В.
86
4) - 800
С
20001 - 1) --- 800
D
3000
4)- 800
The function that best models for the data is y = -200 (x-4)^2 + 800.
What is a function?A function is a mathematical expression that describes how factors are related. In this case, how the price is related to the profit.
How to determine if a function models the data?The best way to determine this is to solve the expression and verify if the answer is correct.
For example, we know that at 4 (x) dollars, the daily profit is $800 (y). Let's now the different options:
A.
y= -8 (x+4)^2 + 800y= -8 (4+4)^2 + 800y= -8 (8)^2 + 800y= -8 (36) + 800y=-8 (288) + 800y= -2304 + 800y= -1504B.
y= -8 (x-4)^2 + 800y= -8 (4-4)^2 + 800y= -8 (0)^2 + 800y= -8 (0) + 800y= 0 + 800y= 800C.
y= -200 (4+4)^2+ 800y= -200 (8)^2 + 800y= -200 (36) + 800y= -200 (36) + 800y= -7200 + 800y= -6400D.
y= -200 (x-4)^2 + 800y= -200 (4-4)^2 + 800y= -200 (0)^2 + 800y= -200 (0) + 800y= 0 + 800y= 800This means B and D are possible options, however, when verified with other results such as $6 the correct one is option D.
Learn more about bakery in: https://brainly.com/question/16421624
The quadratic equation is given by y = -200x² + 1600x - 2400.
Quadratic equation formulaThe standard form of the quadratic equation is:
y = ax² + bx + c
Where a,b,c are constants.
Let y represent the daily profit for x bread price.
At point (2, 0):
0 = a(2)² + b(2) + c
4a + 2b + c = 0 (1)
At point (4, 800):
800 = a(4)² + b(4) + c
16a + 4b + c = 800 (2)
At point (6, 0):
0 = a(6)² + b(6) + c
36a + 6b + c = 0 (3)
From all the equations:
a = -200, b = 1600, c = -2400
The quadratic equation is given by y = -200x² + 1600x - 2400.
Find out more on quadratic equation at: https://brainly.com/question/1214333
Find the area of the figure.
Answer:
180 sq.cm
Step-by-step explanation:
A = 10 x 10 + 16 x 5 x 1/2 x 2
A = 100 + 16 x 5
A = 100 + 80
A = 180 square cm
Hope that helps!
The perimeter of a rectangular backyard is 192 feet. The yard is 43 feet wide. How long is it?
Answer:
53 feet.
Step-by-step explanation:
2(Width)+2(Length)=Perimeter
--> 2(43)+2(Length)=192
--> 86+2(Length)=192
--> 2(Length)=106
Length = 53
What is the probability of getting a vowel if you randomly pick a letter from the English alphabet?
E is directly proportional to f.it E is 24 then f is 6 what is E when f is 24
Answer:
E = 96
Step-by-step explanation:
Given the following data;
E = kf .......equation 1.
When E = 24, f = 6
First of all, we would have to find the constant k;
Substituting the values into eqn 1, we have;
24 = k6
k = 24/6
k = 4
To find the value of E, when f = 24
E = kf
Substituting into the equation, we have;
E = 4*24
E = 96
Evaluate the expression if a = -2, b= 7. and c= -3
ac + b=
Answer:
13
Step-by-step explanation:
plug in the numbers
-2(-3) + 7 = ?
6 + 7 = ?
13
Hope this helped! Have a nice day! Plz mark as brainliest!!!
-XxDeathshotxX
PLEASE HELPPPPPPPP !!!!!!!!!!!!!!1
Answer:
-8.45, 0.95, 8.25
Step-by-step explanation:
The easiest way to do this is to convert the fraction to a decimal, and then compare the values.
8 8/32 is equal to 8 and 1/4. Because 1/4 = 0.25, 8 and 8/32 equals 8.25.
Now, let's compare values.
Numbers we need to compare: -8.45, 0.95, 8.25
The smallest number is -8.45, then 0.95, and lastly, 8.25.
Thus the answer is
-8.45, 0.95, 8.25
Find the 9th term of the geometric sequence 8, 32, 128, ...
Answer:
524,288
Step-by-step explanation:
Hope this helps!
you have $63.50. you earn additional money by raking leaves. you purchase a sweatshirt $44.99 and you have $53.51 left. how much money did you earn raking leafs?
868 ÷ 14 = ?? i need help lol
Answer:
**********************868/14=62********************
Step-by-step explanation:
Answer:
+*~868 ÷ 14 = 62~*+
(Hope this helps! Btw, I answered first. Brainliest please! :D)
please help!!! thank you!!!
uhm... I’m sorry I don’t actually know the answer to your question but I’m trying to get some points...
What is the missing polynomial -(20-4x-5x2)=20-7x2
Answer:
? – (20 – 4x – 5x2) = 20 – 7x2, so ? = 20 – 7x2 + (20 – 4x – 5x2)
? = 20 – 7x2 + (20 – 4x – 5x2)=20-7x²+20-4x-5x²=40-12x²-4x
the answer is 40-4x-12x^2
Step-by-step explanation:
Answer:
40-4x-12x^2
Step-by-step explanation:
so 29 is a monomial also
Answer:
yes, 29 is a monomial
Step-by-step explanation:
There are 3 boxes for green chips and 5 boxes for red chips. each box has the same number of chips in it. if there are a total of 16 chips complete the tape diagram showing the number of chips in each box.
Answer:
2 in each box of courseg= green chips r= red chips
3 boxes of green chips meaning for each box there are 2 chips so there are 6 green chips. 5 boxes of red chips meaning for each box there are two chips so there are 10 red chips and 6 g + 10r = 16 chips in total
Step-by-step explanation:
2x+ 20 + 3x +40 =
60 + 5X
write a multiplication equation and a division equation that represents the question how many 3/8 are in 5/4
Answer: 3
Step-by-step explanation: double the 5 and the 4(to have the same denominator as the 8)
HELP ITS TIMEDDDDDDDDDDDDDDDDD
Answer:
100
Step-by-step explanation:
6.5 ÷ ___________ = 0.065
Answer: 6.5 ÷ 100 = 0.065
help me and thank you
Answer:
15.736
Step-by-step explanation:
Please help and look at the others
Answer:
no
Step-by-step explanation:
pls give brainliest :)
Need help with this one:)
Answer:
1024 sq inches
Step-by-step explanation:
Surface area is the area of all added together.
So: 2(24 * 10 + 10 * 8 + 24 * 8)
2(240 + 80 + 192)
Answer: 1024
PLS HELP.I WILL MARK BRAINLIEST!!
Answer:
Answer in attachment photo
Find the equation of the line
Use exact numbers
I thank you very very much in advance!
Answer:
y = 3/4x -2
Step-by-step explanation:
Points on the graph: (4, 1) and (0, -2)
Slope:
m=(y2-y1)/(x2-x1)
m= (-2-1)/0-4)
m=(-3)/(-4)
m = 3/4
Point-slope:
y - y1 = m(x - x1)
y - 1 = 3/4(x - 4)
y - 1 = 3/4x - 3
y = 3/4x -2