The Probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
The probability that the light is red is given by the ratio of the time the light is red to the total cycle time:
P(red) = 15 / (15 + 5 + 30) = 0.375
Using the binomial distribution, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light is:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
where (8 choose 3) is the binomial coefficient, which represents the number of ways to choose 3 cars out of 8. Evaluating this expression gives:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
= (8! / (3! * 5!)) * (0.375)^3 * (0.625)^5
= 56 * 0.052734375 * 0.1787109375
≈ 0.268
Therefore, the probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
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Advanced algebra please help!!
o = 6.5 cm, ∠P=88° and ∠N=83°. Find the area of ΔNOP, to the nearest 10th of a square centimeter.
The area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side. It states that for any triangle ABC, the ratio of the length of a side to the sine of the angle opposite that side is constant, that is;
a/sinA = b/sinB = c/sinC
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.
angle m∠O = 180 - (83 + 88) {sum of interior angles of a triangle}
angle m∠O = 9°
Using the sine rule;
6.5/sin9 = ON/sin88
ON = (6.5 × sin88°)/sin9 {cross multiplication}
ON = 41.5
Area of the triangle = 1/2 × 6.5cm × 41.5cm × sin83
Area of the triangle = 133.9
Therefore, the area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.
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Helppppp pleaseeeeee
The reduced row echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&-7\\0&1&0&2\\0&0&1&4\end{array}\right][/tex]
How to obtain the reduced row echelon form?The row echelon form of a matrix contains the entire matrix except the last column in the format of an identity matrix, with the last column containing the solution to the system of equations represented by the matrix.
Considering the matrix, the system of equations is given as follows:
7x - y - 3z = -63.-6y - 2z = -20.y + z = 6.Multiplying the last equation by 2 and adding with the second equation, the value of y is obtained as follows:
-4y = -8
4y = 8
y = 2.
The value of z is given as follows:
z = 6 - y
z = 4.
The value of x is given as follows:
7x = -63 + y + 3z
7x = -63 + 2 + 14
7x = -49
x = -7.
Hence the row-echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&-7\\0&1&0&2\\0&0&1&4\end{array}\right][/tex]
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A real estate sells houses for Birr 200,000 plus Birr 400 per one square metre. a Find the function that represents the cost of the house that has an area of x m². Calculate the cost of the house that has an area of 80 m².
Step-by-step explanation:
Cost of house = Birr ( 200 000 + 400 x ) where x is square meters
for 80 m^2 cost = Birr ( 200 000 + 400(80)) = Birr 232000
To the nearest tenth, what is the value of x?
Answer:
34.1
Step-by-step explanation:
In this case we have supplementary information that is not required to find the length of [tex]x[/tex].
A screenshot is provided below with the other values.
Y-3=2(x-6) what point does this line pass through? What is the slope of this line ? Rewrite the equation in slope intercept form
Answer:
This line passes through (0, -9)
Slope = 2
y = 2x-9
Step-by-step explanation:
Slope intercept form is : y=mx+b (m = slope, b= y-intercept)
First, let's distribute the 2 to the (x-6).
y-3 = 2x-12
Second, set it into slope intercept form (y = mx+b) by adding 3 to both sides.
y = 2x-9
This will be the equation in slope intercept form.
After looking at the the slope intercept form, we know that m = the slope. So the since the 2 is in the place of m when in slope intercept form, m=2. this would mean that the slope = 2.
Y-intercept is the point when the line touches the y-axis. To find the y-intercept, x would have to equal 0. This would mean that the point would have to be (0, y). After looking at the slope intercept form, and comparing it with our equation in slope intercept form, we know that -9 is in the place of b. This would mean that b = -9. This would also mean that the y-intercept is equal to -9. Therefore, the point would be (0, -9).
please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The values of all the solutions are,
16) m QT = 142 deg
17) m ∠STR = 23 deg
18) m ∠RSQ = 19 deg
Given that;
A circle is shown.
Now, We can formulate;
16|) The value of m QT is,
m QT = 2 ∠QST
= 2 × 71
= 142 degree
17) The value of m ∠STR is,
m ∠STR = 1/2 m ∠SXR
= 1/2 × 46
= 23 deg
17) Since, ∠ RST = 90°
Then, We get;
m ∠RSQ = 90 - ∠QST
= 90 - 71
= 19 degree
Thus, The values of all the solutions are,
16) m QT = 142 deg
17) m ∠STR = 23 deg
18) m ∠RSQ = 19 deg
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5. Jordan is putting his
blocks away. He measures
one block and discovers it
is 5 cm long, 3 cm wide,
and 1 cm tall. If he is
planning to put all the
blocks into a bin that has a
volume of 370 cm³, how
many blocks will fit?
PLEASE HELP WILL MARK BRAINLIEST
Determine the number of real solutions:
1. y=-3x^2+x+12
Answer:
2
Step-by-step explanation:
To determine the number of real solutions of the quadratic equation `y = -3x^2 + x + 12`, we can use the discriminant formula `b^2 - 4ac`.
First, we identify the values of a, b, and c:
a = -3
b = 1
c = 12
Next, we substitute these values into the discriminant formula:
b^2 - 4ac = (1)^2 - 4(-3)(12) = 145
Since the discriminant is positive (and not equal to zero), the quadratic equation has two distinct real roots. Therefore, the number of real solutions is 2.
Calcula la medida de la altura de un triángulo equilátero del lado 6
The measure of the height of an equilateral triangle with a side length of 6 is 3√3.
We have,
In an equilateral triangle, all three sides are equal, and all three angles are also equal.
To calculate the height of an equilateral triangle, we can use the formula:
Height = (√3 / 2) x side
Given that the side length of the equilateral triangle is 6, we can substitute this value into the formula to find the height:
Height = (√3 / 2) x 6
Height = (√3) x 3
Simplifying, we have:
Height = 3√3
Therefore,
The measure of the height of an equilateral triangle with a side length of 6 is 3√3.
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The complete question.
Calculate the measure of the height of an equilateral triangle of side 6
You are standing 190 meters away from the base of a building. The angle of elevation to the top of the
building is 25°. What is the height of the building?
Answer:
Step-by-step explanation:here it is. you did not say which grade ...
but hoping ok method .
What is the interval in which both f (x) and g(x) are positive?
The interval in which both functions are positive is the one in option C.
(3, ∞)
In which interval are the two functions positive?First, when we have a graph, to identify when the function is positive we need to see when the graph of the function is above the horizontal axis.
So here we just need to see in which interval are both curves (orange one and blue one) are above the horizontal axis.
We can see that from x = 3 and above, both of the curves are above the horizontal axis, then the interval in which both functions are positive is:
(3, ∞)
So the correct option is C.
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name the leading coefficient and degree of the polynomial 12+5x^y+4x
Answer:
The leading coefficient is 5, the degree is y+1
Step-by-step explanation:
The polynomial 12+5x^y+4x has two terms, 12 and 5x^y+4x. The leading coefficient of the polynomial is 5, which is the coefficient of the term with the highest degree. The degree of the polynomial is y+1, which is the highest power of x in any term of the polynomial after like terms have been combined. The degree is determined by adding the exponents of the variables in the term with the highest degree, which is 5x^y in this case. The exponent of x is 1 and the exponent of y is y, so the degree is y+1. Therefore, the leading coefficient is 5 and the degree is y+1.
What is the function equation for the graph below?
Answer:
f(x)= - [x] + 3
Step-by-step explanation:
because it describes a negative slope and 3 units up from the origin
A geometric pattern is made using 17 triangles and squares. If the triangles and squares have a total of 64 sides how many triangles were used
Answer:
Let s be the number of squares and t be the number of triangles.
s + t = 17---->4s + 4t = 68
4s + 3t = 64---->4s + 3t = 64
----------------- -----------------
t = 4, s = 13
4 triangles, 13 squares
Express 0.01430 in Standard form
Answer:
1.430
Step-by-step explanation:
1.430 x 10^-2
what should be subtracted from -5/12 to get 1
Answer=
-17/12 should be subtracted from-5/12 to get the answer 1
Mark me as brainlist pls...
Please help on question! If answers correct I'll reward with five stars , a thanks and maybe even brainliest!
Bob the builder is making 480kg of a concrete mix. Concrete is made by mixing cement , said and gravel in ratio 1:3:4.
How much sand does he need?
Answer:
x = the number of kg of cement
3x = number of kg of sand
4x = number of kg of gravel
x + 3x + 4x = 480
8x = 480, so x = 60
60 kg of cement
3(60) = 180 kg of sand
4(60) = 240 kg of gravel
Bob will need 180 kg of sand.
All points of the step function f(x) are graphed. What is the domain of f(x)?
The domain of the step function f(x) is given as follows:
{x | -4 < x ≤ 4}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.For the function graphed at the end of the answer, we have that:
The lowest value of x is the open circle at x = -4.The highest value of x is the closed circle at x = 4.Hence the domain of the step function f(x) is given as follows:
{x | -4 < x ≤ 4}.
Missing InformationThe function is given by the image presented at the end of the answer.
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HI PLEASE HELPP REFER TO PICTURE STATISTICS
We are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
Hence, Using a t-distribution with 86 degrees of freedom (n-1), and a 95% confidence level (α=0.05), the critical value for the two-tailed test is 1.992.
The standard error can be calculated as:
SE = SD / √n = 15.6 / √100 ≈ 1.56
The margin of error (ME) can be calculated as:
ME = t x SE = 1.992 x 1.56 ≈ 3.11
The 95% confidence interval (CI) is then:
CI = mean ± ME = 5.9 ± 3.11 = (2.79, 9.01)
Therefore, we are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
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Solve using long division. 142/6 =
Answer: 23.666
(if you would like an explanation please let me know)
URGENT
A pyramid is
Group of answer choices
the total area of the surface of a solid figure.
a pattern of two-dimensional shapes that can be folded to make a model of a solid figure.
a solid figure with a base that is a polygon and sides that are triangles that meet at the top.
any one of the individual surfaces of a solid object.
A pyramid is a solid figure with a base that is a polygon and sides that are triangles that meet at the top.
Answer: A solid figure with a base that is a polygon and sides that are triangles that meet at the top.
Step-by-step explanation: A pyramid consists of a polygonal base and sides that are triangles. A polygon is a 2D shape that only has straight lines that enclose an area.
4(x - 7) in.
2(10 - x) in.
What is the value of x?
3 in. What is the value of X
The value of x, considering the rectangle given at the end of the answer, is given as follows:
x = 8.
How to obtain the value of x?From the rectangle given at the end of the answer, the bases are given as follows:
4(x - 7)2(10 - x).For a rectangle, the bases are congruent, meaning that they have the same measure.
Considering that the bases are congruent, the value of x is obtained as follows:
4(x - 7) = 2(10 - x)
4x - 28 = 20 - 2x
6x = 48
x = 48/6.
x = 8.
Missing InformationThe rectangle is given by the image presented at the end of the answer.
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Which measurement is the same for Charles and Jermod?
O median
Orange
Olower quartile
Oupper quartile
1
These dot plots show how many refutes Charles and Jermod spent on homework per day
for three weeks.
W
15 20 25 30 35 40 45 50 55 60
Charles's Homework (minutes per day)
..
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
The measurement that is the same for Charles and Jermod is the median
How to find the Which measurement is the same for Charles and Jermod?The dot plots show the distribution of the number of minutes that Charles and Jermod spent on homework per day for three weeks. To determine which measurement is the same for both of them, we need to compare the dot plots.
Looking at the dot plots, we can see that both Charles and Jermod have a dot at 35 minutes, indicating that they both spent 35 minutes on homework on at least one day.
Therefore, the measurement that is the same for Charles and Jermod is the median, since it is the middle value of the data when arranged in order. In this case, the median is not clearly identifiable from the dot plots
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how do you solve 3/(n-1) = 2n/(n+4)
Step-by-step explanation:
To solve the equation 3/(n-1) = 2n/(n+4), follow these steps:
Step 1: Cross-multiply to eliminate the fractions.
3 * (n + 4) = 2n * (n - 1)
Step 2: Distribute the terms on both sides.
3n + 12 = 2n^2 - 2n
Step 3: Move all terms to one side and set the equation to zero.
2n^2 - 5n - 12 = 0
Step 4: Factor the quadratic equation, if possible. In this case, we can factor by finding two numbers that multiply to -24 and add to -5.
(2n + 3)(n - 4) = 0
Step 5: Use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
2n + 3 = 0 or n - 4 = 0
Step 6: Solve for 'n' in each equation.
2n + 3 = 0 => n = -3/2
n - 4 = 0 => n = 4
So, there are two possible solutions for 'n': -3/2 and 4.
Answer: n= 4 , (-3/2)
Step-by-step explanation:
Your goal is to isolate n by getting it by itself
Multiply both sides by (n-1) to get 3 = ((2n)(n-1))/(n+4)
Use distributive property on the 2n * (n-1) to get 3 = (2n^2 - 2n)/(n+4)
Multiply both sides by (n+4) to get 3n + 12 = 2n^2 - 2n
Subtract 12 and 3n from both sides to get 2n^2 - 5n -12 = 0
Solve the quadratic using any method you like
Factoring would give you (n - 4)(2n + 3) = 0
So n= 4 and -3/2
Two lines AB and CD intersect each other at O.If angle AOD = 120 deg . BOC=3y. < BOD = 2x then find (x + y)
The value of x + y = 70 when 2 lines AB and CD intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.
Given that,
AB and CD 2 lines intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.
We have to determine the value of (x + y).
We know that,
In the picture we can see the two lines AB and CD intersect each other at O.
So,
From line AB a straight line has 180°.
Then ∠AOD + ∠DOB = 180°
120° + 2x = 180°
2x = 180° - 120°
2x = 60
x = [tex]\frac{60}{2}[/tex]
x = 30°
Then ∠DOB = 2x = 2(30) = 60°
And by vertically opposite angles ∠AOD = ∠COB
120° = 3y
3y = 120°
y = [tex]\frac{120}{3}[/tex]
y = 40°
Then ∠COB = 120°
So,
Now, x + y = 30 + 40 = 70
Therefore, The value of x + y = 70
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On average, Americans consume 13.9 pounds of ice cream per person over an entire year. Ben loves ice cream, but limits himself to one 3-ounce (oz) serving each week. Find the difference between the amount of ice cream that Ben consumes compared to the national average. (1 pound equals to 16 ounces and there are 52 weeks in a year.)
A class is presented with the following problem.
In a bag of marbles, the ratio of white marbles to red marbles is 2:3 and the ratio of red to black marbles is 6:11. What is the ratio of white to black marbles?
Connor, who likes using fractions, writes 2/3 *6/11 = 4/11 announces, without explanation, that the ratio of white to black marbles is 4:11. Explain why he is right. (Hint: taking the number of black marbles to be the whole unit, what fraction are red, and then what fraction are white?)
Answer:
Therefore, Connor is correct in his explanation that the ratio of white to black marbles is 4:11.
Step-by-step explanation:
Connor is correct in his reasoning. Let's break down the problem step by step to understand why.
Given:
Ratio of white marbles to red marbles = 2:3
Ratio of red marbles to black marbles = 6:11
To find the ratio of white to black marbles, we can follow these steps:
Step 1: Consider the black marbles as the whole unit.
Let's assume there are 11 black marbles (since the ratio of red to black marbles is 6:11).
Step 2: Determine the number of red marbles.
Since the ratio of red marbles to black marbles is 6:11, out of the assumed 11 black marbles, there are (6/11) * 11 = 6 red marbles.
Step 3: Determine the number of white marbles.
Using the ratio of white marbles to red marbles (2:3), we can find the number of white marbles. Since the ratio is 2:3, the number of white marbles would be (2/3) * 6 = 4.
Step 4: Find the ratio of white to black marbles.
Now that we have determined there are 4 white marbles and 11 black marbles, the ratio of white to black marbles is indeed 4:11.
The area of a circle is 81л m². What is the circumference, in meters? Express your
answer in terms of π.
Answer:
Step-by-step explanation:
Formulas:
A = (pi)(radius^2)
C = (pi)(Diameter)
Find the radius
81pi = pi * (r)^2
r^2 = 81
r = 9
Use radius to find diameter
D= 2r
D = 18
Use circumference formula
C = 18π
Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. 8 m 9 m 8 m 0|0 E 08 m² G m3
The value of the volume of this rectangular pyramid is,
⇒ V = 192 m³
We have to given that;
In rectangular pyramid,
Lenght = 8 m
Width = 9 m
Height = 8 m
Hence, The volume of this rectangular pyramid is,
⇒ V = 1/3 x Length x width x height
⇒ V = 1/3 × 8 × 9 × 8
⇒ V = 192 m³
Thus, The value of the volume of this rectangular pyramid is,
⇒ V = 192 m³
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