By using the given scale, we will see that the real distance is 240km
What is the real distance between Cardiff and London?We know that the scale of the map is 1 cm to 12km, so we just need to take the distance in centimeters on the map, and multiply that number by 12 km.
We know that on the map, the distance between Cardiff and London is 20cm, then the real distance is 12km times that, so we will get:
real distance = 20*12km = 240km
The real distance between Cardiff and London is 240 kilometers.
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What is the 36th derivative of f(x)=cos2x?
The 36th derivative of f(x) = cos(2x) is \(2^{17}\)* cos(2x).
To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).
Let's start by finding the first few derivatives of f(x) = cos(2x):
f'(x) = -2sin(2x)
f''(x) = -4cos(2x)
f'''(x) = 8sin(2x)
f''''(x) = 16cos(2x)
We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.
Based on this pattern, we can see that the 36th derivative will be:
f^(36)(x) =\((-1)^{17} * 2^{17} *\) cos(2x)
Simplifying this expression, we have:
f^(36)(x) = \(2^{17} * cos(2x)\)
Therefore, the 36th derivative of f(x) = cos(2x) is\(2^{17\) * cos(2x).
It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.
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geometry need help asap
The value of angle LAF in the intersecting chords is determined as 104⁰.
What is the value of angle LAF?The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
m∠LAF = ¹/₂ (arc LF + arc YS)
From the diagram, we have arc LF = 160⁰ and YS = 48⁰
m∠LAF = ¹/₂ (160 + 48)
m∠LAF = 104⁰
Thus, the value of angle LAF is calculated by applying intersecting chord theorem.
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Estimate 71.91-56.423 by first rounding each number to the nearest whole number.
Answer:
16
Step-by-step explanation:
71.91 ~ 72
56.423 ~ 56
72-56=16
solve simultaneously 2x - y = - 10 and 3x + 2y = - 1
The solution to the system of equations is x = -3 and y = -4.
To solve the system of equations:
Equation 1: 2x - y = -10
Equation 2: 3x + 2y = -1
We can use the method of substitution or elimination to find the values of x and y.
Let's use the method of elimination:
Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:
2(2x - y) = 2(-10)
4x - 2y = -20
Now, we can eliminate y by adding Equation 2 and the modified Equation 1:
(3x + 2y) + (4x - 2y) = -1 + (-20)
7x = -21
x = -3
Substitute the value of x into Equation 1 to solve for y:
2(-3) - y = -10
-6 - y = -10
y = -10 + 6
y = -4
Therefore, the solution to the system of equations is x = -3 and y = -4.
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Which example shows the Identity Property of Multiplication?
26 +0= 26
26•0=0
26•1= 26
26-26 = 0
Answer:
26 times 1
Step-by-step explanation:
because its multiply
Answer:
It’s 26
Step-by-step explanation:
26 is used in each equation resulting in either 26 or 0
12/16•4/3 divided by 5/6
Answer: 1.2
Step-by-step explanation:
12/16 = 0.75
0.75 X 4/3 = 1
1/ (5/6) = 1.2
Answer:
I believe it is 1.2
Step-by-step explanation:
12/16x4/3
12x4=48
16x3=48
48/48=1
1 divided by 5/6=1.2
hope this helps :)
Which of the following is the value of sine Superscript negative 1 Baseline (StartFraction StartRoot 2 EndRoot Over 2 EndFraction)?
The value of sine Superscript negative 1 Baseline (StartFraction StartRoot 2 EndRoot Over 2 EndFraction) is π/4 radians or 45 degrees.
The value of sine Superscript negative 1 Baseline (StartFraction StartRoot 2 EndRoot Over 2 EndFraction) is π/4 radians or 45 degrees.What is inverse sine?
The inverse sine function or arc sine function is the inverse function of the sine function. It is defined as follows:If y = sin x, then x = sin-1 y, where x is the angle whose sine is y.
The range of the inverse sine function is from -π/2 to π/2 radians or from -90 to 90 degrees. It is denoted by sin-1 or arcsin.What is the value of sine Superscript negative 1 Baseline (StartFraction StartRoot 2 EndRoot Over 2 EndFraction)?
Given that the value of sine Superscript negative 1 Baseline (StartFraction StartRoot 2 EndRoot Over 2 EndFraction) is to be determined.
Using the formula, sin θ = opposite side/hypotenuse= (StartRoot 2) / 2= 0.707The angle whose sine is 0.707 can be found using a calculator or a unit circle.
The inverse sine of 0.707 is π/4 radians or 45 degrees.
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What is 90 divided by 10
Answer:
9
Step-by-step explanation:
Evaluate the expression: (–2)2 + (–42) + (18 – 23).
Hey there!
(-2)2 + (-42) + (18 - 23).
= -2(2) - 42 + 18 - 23
= -4 - 42 + 18 - 23
= -46 + 18 - 23
= -46 + (-5)
= -46 - 5
= -51
Therefore, your answer is: -51
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The experimental probability of not spinning a 1 is
Answer:
0.84 or 84%Step-by-step explanation:
As per graph we have:
Number 1 = 8Number 2 = 6Number 3 = 9Number 4 = 11Number 5 = 9Number 6 = 7Total number of spins:
8 + 6 + 9 + 11 + 9 + 7 = 50Number of spins excluding a 1:
50 - 8 = 42Required probability:
42/50 = 0.84 or 84%Answer:
The experimental probability of not spinning a 1 is
Saludos
In the 2012 Olympics a U.S. athlete Nathan Adrian finished the 100-meter freestyle swim in 47.52 seconds. If nathan swam the same pace in a regular 25-meter pool what would his time have been per lap?
Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.
Given that the time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle.
Here we will use the concept of proportionality.
Since the rate is constant while the distance varies, we can establish a ratio:
100 meters / 47.52 seconds = 25 meters / x seconds
Where x is the unknown time for one lap in the 25-meter pool.
To solve for x, we can cross-multiply:
100 meters × x seconds = 47.52 seconds × 25 meters
100x = 1188
Dividing both sides by 100, we get:
x = 11.88 seconds
Hence Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.
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I need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What’s the integral of 1/2
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles faster than the other. If the two buses are 640 miles apart after 5 hours, what is the rate of each bus?
If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Two buses leave a station at the same time and travel in opposite directions.
One bus travels 14 miles faster than the other.
Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).
If the two buses are 640 miles apart after 5 hours.
Then the rate of each bus will be
Then the relative speed of the buses will be
S = x + x + 14
S = 2x + 14
Then the value of x will be
2x + 14 = 640 / 5
2x + 14 = 128
2x = 114
x = 57 miles per hour
Then the speed of the other bus will be
⇒ 57 + 14
⇒ 71 miles per hour
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Match the dimensions of each rectangle with its corresponding area.
3 feet by 8 feet
90 square feet
5 feet by 7 feet
24 square feet
9 feet by 10 feet
64 square feet
13 feet by 2 feet
26 square feet
8 feet by 8 feet
35 square feet
Answer:
3x8= 24sf
5x7= 35sf
9x10= 90sf
13x2= 26sf
8x8= 64sf
Step-by-step explanation:
Help help help please in a hurry!!!!!!!!!!!!!!!!!!!
Answer:D
Step-by-step explanation:
please mark brainliest
Select the correct answer.
Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?
68% of the data points lie between 10 and 14.
68% of the data points lie between 8 and 12.
68% of the data points lie between 10 and 18.
68% of the data points lie between 10 and 16.
Answer:
68% of the data points lie between 10 and 18.
Step-by-step explanation:
one standard deviation to left of mean = 14 - 4 =10
one standard deviation to right of mean = 14 + 4 = 18
68% of data is in this region.
so the answer is 68% of the data points lie between 10 and 18.
using the unit circle what is the exact value of tanpi/6
Answer:
\( \frac{ \sqrt{3} }{3} \)
Step-by-step explanation:
\(\frac{1}{3} \div \sqrt{3} \)
(7 points) Briefly explain what perfect multicollinearity is and how it relates to what is often called the "dummy variable trap". This is where if you have multiple binary regressors (variables that are either 0 or 1) to represent a series of groups, you have to leave the variable that represents one of the groups out of the regression.
Find the given attachments
Find the exact value of tan(x-y) if sin x=8/17 cosy = 3/5
To solve the the question we proceed as follows:
From trigonometric laws
\((cos x)^2+(sin x)^2=1\)
\((cos x)^2+(sin x)^2=1\)
\(sin (x-y)=sin\) \(x\) \(sin\) \(y-sin\) \(y\) \(cos\) \(x\)
\(cos (x-y)=cos\) \(x\) \(cos\) \(y+sin\) \(x\) \(xin\) \(y\)
si \(x=\frac{8}{17}\)
\(cos\) \(x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(\frac{225}{289} )=\frac{15}{17}\)
\(cos\) \(y=\frac{3}{5}\)
\(sin\) \(x= sqrt(1- (cos x)^2)= sqrt(1-\frac{9}{25} )=sqrt(\frac{16}{25} )=\frac{4}{5}\)
thus
\(tan (x-y)=[sin (x-y)]/[cos (x-y)]\)
=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]
plugging in the values we obtain:
\([8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]\)
simplifying
\([24/85-60/85]/[45/85+32/85]\)
\(=-\frac{36}{77}\)
Solve
2
EX>8 or --X<4.
3
3
.
Steps:
See attachment.
Description:
The first step is to simplify the equation step by step and to simplify an equation you can first multiplying the factors and use the exponent rules to remove the parentheses. After that you need to combine it a terms. Then you will get your answer.
For more steps and graph see the attachment.
Answer: x>1.471518 or x<4.33
Hope this helps.
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed random variables with parameter 2 for component A, and parameter 3 for component B. The system fails at the first component failure.
(a) - Read section 1.5.2 in the textbook.
(b) - What is the mean time to failure for component A and for component B
Answer:
\(E(x) = \frac{1}{2}\) -- Component A
\(E(x) = \frac{1}{3}\) -- Component B
Step-by-step explanation:
Given
Distribution = Exponential
\(\lambda = 2\) --- Component A
\(\lambda = 3\) --- Component B
Solving (a): The mean time of A
The mean of an exponential distribution is:
\(E(x) = \frac{1}{\lambda}\)
We have:
\(\lambda = 2\) --- Component A
\(E(x) = \frac{1}{2}\)
Solving (b): The mean time of B
The mean of an exponential distribution is:
\(E(x) = \frac{1}{\lambda}\)
We have:
\(\lambda = 3\) --- Component B
\(E(x) = \frac{1}{3}\)
pls help ty will mark brainiest
Answer:
No, because 60 degrees is not valid to do so
Step-by-step explanation:
Given the unit circle what is the value of x
Given the figure, we can deduce the following information:
1. The two given points are:
(1,0)
(x,-7/10)
To determine the value of x, we must note first that the x value on the first quadrant is 1 so the radius of the circle must be equal to 1.
Next, we apply the equation for unit circle:
\(x^2+y^2=1\)Then, we plug in y=-7/10 into x^2+y^2=1:
\(\begin{gathered} x^2+y^2=1 \\ x^2+(-\frac{7}{10})^2=1 \\ x^2+\frac{49}{100}=1 \\ \text{Simplify and rearrange} \\ x^2=1-\frac{49}{100} \\ x^2=\frac{51}{100} \\ x=\pm\sqrt[]{\frac{51}{100}} \\ x=\pm\frac{\sqrt[]{51}}{10} \end{gathered}\)But since the point is in the third quadrant, the value of x must be negative. Therefore, the answer is:
\(x=-\frac{\sqrt[]{51}}{10}\)Which of the following is true regarding the sequence below?
71
12'6
12
4' 3
The sequence is arithmetic because there is a common difference of
5
12
The sequence is arithmetic because there is a common difference of 1.
The sequence is not arithmetic because there is no common difference between the values of n.
The sequence is not arithmetic because there is no common difference between the values of an
Answer:
Option A
Step-by-step explanation:
Let's find common difference
\(\\ \sf\longmapsto \dfrac{7}{12}-\dfrac{5}{12}\)
\(\\ \sf\longmapsto \dfrac{7-5}{12}\)
\(\\ \sf\longmapsto \dfrac{2}{12}\)
\(\\ \sf\longmapsto \dfrac{1}{6}\)
Hence verified
2 1/7 - 1 2/5 give your awenser as a mixed number
Answer:
dunno la saya , gak bisa bahasa ingeris
which is an irrational number
Answer:
C
Step-by-step explanation:
A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals. What dimensions should
be used so that the enclosed area will be a maximum?
Length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
What is Area of Rectangle?The area of Rectangle is length times of width
Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.
Here, the dimensions of the rectangles are the same.
The width of the two rectangles is W=2W+2W=4W
The length of the two rectangles is L=L+L+L=3L
Because the adjacent side has a common length.
3L+4W=200
3L=200-4W
Divide both sides by 3
L=(200-4W)/3
Let us form an equation using the area of rectangle formula:
A=2LW
=2(200-4W)/3.W
A=400-8W²/3
Let us differentiate to get the area to be maximized dA/dW=0
1/3×(400-8W²)=0
1/3(400-16W)=0
400-16W=0
400=16W
Divide both sides by 16
W=25
The width is 25 feet.
Substitute W value in equation to get L value:
L=200-4×25/3
=200-100/3
=100/3
=33.33
The length is 33.33 feet.
Now let us find the maximum area
A=2LW
=2×33.33×25
=1666.66
Hence, length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
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At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answer:
yes
Step-by-step explanation: