John and Jeremy are the local names for two lighthouses that guard a particularly dangerous part of the coast. John blinks every 6 seconds and Jeremy blinks every 4 seconds. They blink together at midnight. How many seconds will pass before they blink together again?
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plz help me so confused
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Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he 21) has 20 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?
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Let the short side be W
The half circumference of the semi-circle = .5 * pi *W
2Lengths + width + semicircle = 20 ft
2L + W + (.5*pi*W) = 20
2L + W + 1.57W = 20
Combine like terms
2L + 2.57W = 20
Simplify divide by 2
L + 1.285W = 10
L = (10 - 1.285W); for substitution:
Get the area equation:
Rectangle area + semicircle area
A = L * W + (.5*pi*(.5W) ^2)
A = LW + (1.57*.25W^2)
A = LW + .3925W^2
Replace L with (10-1.285W)
A = W(10-1.285W) + .3925W^2
A = -1.285W^2 + .3925W^2 + 10W
A = -.8925W^2 + 10W
Find W by finding the axis of symmetry of this equation a=-.8925, b=10
W = -10 / 2 * (-.8925)
W = -10 / -1.785
W = 5.60 is the width for max area
then we solve for the length
L = 10 - 1.285(5.60)
L = 10 – 7.20 = 2.8 ft is the length
Then, Check the perimeter
2(2.8) + 5.60 + 1.57(5.60) = 20ft
5.6 + 5.6 + 8.736 = 20ft
Rectangle: 2.8 by 5.60 has semicircle circumference 8.736 has a maximum area: (2.8*5.60)
+ (.5 * pi * 2.8 ^ 2)
=15.68 + 12.31
=28 sq/ft
given that 2/3a=16, which of the following illustrates how the multiplicative inverse property can be used to find the value of a?
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2/3a×3/2 = 16×3/2
a= 8×3 = 24
Step-by-step explanation:
We have been given that [tex]\frac{2}{3}a=16[/tex].
Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.
[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]
To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].
[tex]a=16\div \frac{2}{3}[/tex]
Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].
[tex]a=16\times\frac{3}{2}[/tex]
[tex]a=8\times 3[/tex]
[tex]a=24[/tex]
We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].
Let us verify our answer by substituting a=24 in our given equation.
[tex]\frac{2}{3}\times 24=16[/tex]
[tex]2\times 8=16[/tex]
[tex]16=16[/tex]
Hence, to find the value of a we used multiplicative inverse property.
Evaluate (1/2^-2) + 1/2
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Consider a point on the trans-australian highway, where two old wombats live. arrivals of cars at this point follow a poisson distribution; the average rate of arrivals is 1 car per 12 seconds.
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This is a Poisson distribution with a mean of 1 car every 12 seconds.
Part A:
The probability of a Poisson distribution is given by:
[tex]P(X=x)= \frac{e^{-\lambda}\lambda^x}{x!} [/tex]
Given tha one of the old wombats requires 12 seconds to cross the highway, and he starts out immediately after a car goes by.
The probability he will survive is the probability that no car passes through the point in the next 12 seconds.
[tex]P(x=0)= \frac{e^{-1}(1)^0}{0!} =e^{-1}=0.368[/tex]
Therefore, the probability that he will survive is 0.368
Part B:
Given that at the same point of the highway there is another old wombat, slower but tougher than in the previous exercise. He requires 24 seconds to cross the road, but it takes two cars to kill him. (A single car won’t even slow him down. The arrival rate of cars is still one car per 12 seconds.)
Since the arrival rate of cars is one car per 12 seconds, then, in 24 seconds the arrival rate is 2 cars. (i.e. λ = 2)
The probability that he survives is the probability that 2 cars did not pass through the point.
[tex]P(X\neq2)=1-P(X=2)=1- \frac{e^{-2}(2)^2}{2!} =1-0.135=0.865[/tex]
162x + 731 = −y − 9x-2 vertex form
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I am goint to solve this question assuming that the correct expression is 162x + 731 = - y - 9x^2
Now, you should know that the vertex form is y = a(x - h)^2 + k, where the vertex is (h,k).
So, we just must transform the quadratic function into that form. To do that you must complete squares. I will do it step by step
start: 162 x + 731 = - y - 9x^2
1) Transpose terms:
y = - 9x^2 - 162x + 731
2) extract common factor ot the two terms with x^2 and x.
y = - 9 (x^2 + 18x) + 731
3) complete squares for x^2 + 18x, which is (x + 9)^2 - 81
=> y = - 9 [ ( x + 9)^2 - 81 ] + 731
4) solve the square brackets
=> y = - 9 (x + 9)^2 - 9*81 + 731
=> y = - 9(x + 9)^2 -729 + 731
=> y = - 9 (x + 9)^2 + 2
Answer: y = - 9 (x + 9)^2 + 2
To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.
Explanation:To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2
Combine like terms: 171x + y = -733
Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2
Simplify: 171x + y + 7391/4 = 17113/4
Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4
Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4
What is 7 divided by 28
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7/28
To simplify this divide the numerator and the denominator by the greatest common factor. In this case, it is 7.
7 ÷ 7/ 28÷ 7
1/4
Hope this helps!
7 divided by 28 is 1/4 or 0.25.
To calculate 7 divided by 28.
What is simplification?
Simplification is defined as solving mathematical problems using arithmetic operators.
7 divided by 28 = 7/28
= 1/4
= 0.25
Thus, 7 divided by 28 is 1/4 or 0.25.
Learn more about simplification here:
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P(4,13);Q(13,13) find the slope
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A circle with a central that measures 1° has a radius of 10 inches. Find the length of the intercepted .
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Abe is going to plant 54 oak trees and 27 pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
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greatest number of trees Abe can have in each row =?
54 = 2 x 27
27 = 1 x 27
Now 27 is the common in both numbers and also is the greatest number
So, there are 2 rows of oak trees and 1 row of pine trees and all the rows have 27 number of trees.
Answer:
27 trees in each row
Step-by-step explanation:
Abe is going to plant 54 oak trees and 27 pine trees
greatest number of trees Abe can have in each row =?
54 = 2 x 27
27 = 1 x 27
Now 27 is the common in both numbers and also is the greatest number
So, there are 2 rows of oak trees and 1 row of pine trees and all the rows have 27 number of trees.
Help Dana find the sum 346 421 152
For numbers 13a-13d, select yes or no to tell Dana when to regroup
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346
421
+152
We start on the ones place 6 + 1 + 2 = 9, the sum of the digits in the ones place is not up to 10, we will not regroup this ones place.
So, basically the answer to 13a is NO.
Since we are not able to regroup the ones place there is no regrouped tens to add, therefore the answer to 13b is also NO.
Next is the tens place, 4 +2 +5 = 11, the sum of the digits in the ones place is up to 10 so we regroup the tens place.
Thus, the answer to 13c is YES.
Since, we regrouped the ones place, we add the regrouped hundred, thus the answer to 13d is YES.
Finally, for the hundred place, 1 + 3 + 4 + 1 = 9
Therefore, the sum of
346
421
+ 152
is 919
If x = -2 and y = 2, then which of the following statements is false?
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After a power failure, the temperature in a freezer increased an average rate of 2.5 Fahrenheit per hour. The total increase was 7.5 Fahrenheit. Right and solve any Quetion to find the number of hours until the power was restored.
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hope this helps!
There are 46 kids in the After-school Club. Today they're going to the pool at the Community Center. If each minivan can take 6 kids, they'll need 8 minivans for all the kids. Do you agree or disagree? Explain your thinking.
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you have to have enough buses for each person, and none of them are walking, and so you will need 8 minivans
hope this helps
) find the solution of y"+2y'=64sin(2t)+64cos(2t) with y(0)=9 and y'(0)=9
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Clearly people
Can the leaves of an ordered rooted tree have the universal address 1.1, 1.2.1, 1.2.2, 1.2.3, 2.1, 2.2.1, 2.3.1, 2.3.2, 2.4.2.1, 2.4.2.2, 3.1, 3.2.1, 3.2.2? if so, identify such an ordered rooted tree.
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For the function f(x) = x + 4, what is the ordered pair for the point on the graph when x = 3p? a. (x, x + 4) b. (x, 3p + 4) c. (3p, x + 4) d. (3p, 3p + 4)
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since x=3p then(3p,f(3p)) f(x)=x+4 so f(3p)=3p+4
therefore the point will be D.(3p,3p+4)
which simplified fraction is equal to 0.17...?
A. 9/17
B. 8/45
C. 17/9
D. 16/90
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8/45 = .17777 (the seven repeats)
17/9 = 1.8888 (the eight repeats)
16/90 = .17777 (the seven repeats)
While B and D both equal approximately 1.7. B is the simplified form, So B is the answer
Brainliest would be fantastic :) Have a nice day.
In order to find the simplified fraction that equals to 0.17, we need to take all the options given and start dividing them until we find the one that equals to 0.17
So, let's get started....
A) 9/17 = 0.52 So this NOT the answer
B) 8/45 = 0.17 This is the answer
C) 17/9 = 1.88
D) 16/90 = 8/45 = 0.17
Here is where the trick is. You see that B and D has the same final answer. Well, they ask for the simplified fraction. D or 16/90 was not simplified until we simplified it. But the others were already simplified. So, that's why we eliminated D.
So, the correct answer is option B
Good luck!
Which function has a vertex at the origin?
f(x) = (x + 4)^2
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x^2
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Answer:
fdx = x-4 2
Step-by-step explanation:The test was right
in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761
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The 6 in 600 has a value one tenth the value of the 6 in 34, 761.
Explanation:The question asks in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761.
To find the answer, we need to compare the place value of the 6 in both numbers. In 34, 761, the 6 is in the thousands place, and its value is 6,000. To have a value that is one tenth of 6,000, the 6 would need to be in the hundreds place in the other number.
So, the number in which the 6 has a value one tenth the value of the 6 in 34, 761 would be 600.
Final answer:
The number 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.
Explanation:
The number 6 in 34,761 has a value that is one-tenth the value of the 6 in the number 2,001.06.
To find this, we can compare the place values of the two 6's. The 6 in 34,761 is in the ones place, while the 6 in 2,001.06 is in the tenths place.
Since the tenths place is one place to the right of the ones place, the value of the 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.
There is a value of $a$ such that subtracting $a-4$ from $4a+16$ gives an answer of $-25$. What is that value of $a$?
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4a + 16 - a + 4 = -25
3a + 20 = -25
3a = -45
A = -15
Answer:
a = -15
Step-by-step explanation:
Let's rewrite the exercise in math language.
We have to subtract a-4 from 4a+16 to get -25, that is
4a+16 - (a-4) = -25
The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.
4a + 16 - a + 4 = -25
Now we can associate the terms with an a between them and the terms without it from the left side of the equation.
3a + 20 = -25
Let's subtract 20 on both sides.
3a + 20 - 20 = -25 - 20
3a = -45
Finally, we divide by 3 on both sides
3a/3 = -45/3
a = -15
A school employs 30 teachers.how many will there be if there is a 10% reduction
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If a school has 30 teachers and there is a 10% reduction, there will be 27 teachers remaining.
Explanation:If a school employs 30 teachers and there is a 10% reduction, we can calculate the number of teachers after the reduction by multiplying the initial number of teachers by (100% - 10%) = 90%. So, there will be 30 * 0.90 = 27 teachers after the reduction.
Learn more about Percentage Reduction here:https://brainly.com/question/31387045
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can anyone help me in pre-cal
tan^2 x = tan x
sin^2 x = sin x
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Samuel order four did from an online music stores. Each dvd cost 9.99$. He has a 20% discount code and sales tax is 6.75%. What is the total cost of the order
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Then you need to remember the 20% discount $39.96 - 20%= $39.96 x .20= 7.99 (if you need to show your work) Then subtract $7.99 from $39.96=$31.97
Next you have to factor in the tax. $31.97 + 6.75% = $31.97 + 2.16= $34.13 for Samuel's total order
multiply 4 by 9.99 for cost of the 4 dvd's
9.99 *4 = 39.96
20% discount is: 39.96 *0.20 = 7.99
39.96 - 7.99 = 31.97
now add the sales tax:
31.97 * 1.0675 = 34.13
total cost is $34.13
a picnic start at 12:10 pm .kevin arrives at 1:40 pm the picnic continues until 3 pm.how much time elapsed betwwen the picinic and keven arrivals
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1 hour 20 minute
Final answer:
To determine the time elapsed between the start of the picnic and Kevin's arrival, subtract the start time (12:10 pm) from Kevin's arrival time (1:40 pm), which results in 1 hour and 30 minutes.
Explanation:
To find out the amount of time that elapsed between the start of the picnic and Kevin's arrival, we subtract the start time of the picnic from the time Kevin arrived. The picnic started at 12:10 pm and Kevin arrived at 1:40 pm.
Step-by-step calculation:
Convert the times into a 24-hour format to avoid any confusion.12:10 pm is 12:10 in 24-hour format.1:40 pm is 13:40 in 24-hour format.Subtract the start time of the picnic from Kevin's arrival time.13:40 - 12:10.Calculate the difference in hours and minutes.Kevin arrived 1 hour and 30 minutes after the picnic started.
Find the greatest common factor of 36 and 72
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Answer:
36
Step-by-step explanation:
36 is a factor of both numbers
_____
If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.
If there is a remainder, replace the larger number with that and repeat the process.
Marcel is planning a vacation. The travel agent says the average high temperature at the resort is 20 degrees Celsius. What is the equivalent Fahrenheit temperature
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The equivalent Fahrenheit temperature for 20 degrees Celsius is 68 degrees Fahrenheit.
Explanation:To convert Celsius to Fahrenheit, you can use the formula: F = (C × 9/5) + 32
Using this formula, we can calculate the equivalent Fahrenheit temperature for 20 degrees Celsius:
F = (20 × 9/5) + 32 = 68 degrees Fahrenheit
Derivative of y = cos(x-1)/(x-1)
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Answer:
[tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative 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]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{\cos (x - 1)}{x - 1}[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{\Big( \cos (x - 1) \Big)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1) - \cos (x - 1)}{(x - 1)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which property is represented by the number sentence shown below?
6+(4+5) = (6+4)+5
A. Commutative property of multiplication
B. Associative property of addition
C. Commutative property of addition
D. Associative property of multiplication
If you can also explain how you got the I’ll appreciate it.
Answers
This means that no matter where you put the parenthesis, you will get the same solution.
Hope this helps!
find f(-2) for f(x)=2×3^x
a.-18
b.1/18
c.-36
d.2/9
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f(-2)= 2• 1/ (3^2)
f(-2) = 2/9
Answer is d.