Each section of the spinner shown has the same area. Find the probability of the event. Express your answer as a simplified fraction. Picture of spin wheel with twelve divisions and numbered from 1 to 12. An arrow points toward 2. The colors and numbers of the sectors are as follows: yellow 1, red 2, 3 green, 4 blue, 5 red, 6 yellow, 7 blue, 8 red, 9 green, 10 yellow, 11 red, and 12 blue. The probability of spinning an even number or a prime number is .
Answers
The probability of spinning an even number or a prime number is 5/6.
How to calculate the probabilityThe total number of possible outcomes is 12 since there are 12 sections on the spinner.
Therefore, the probability of spinning an even number or a prime number is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 10 / 12
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
Probability = (10 / 2) / (12 / 2)
Probability = 5 / 6
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Related Questions
A random variable is said to be continuous if it: ______________ a. can have decimal values. b. is measured over an interval. c. has a countably infinite number of values.
d. has a countable number of values.
Answers
A random variable is said to be continuous if it is measured over an interval. Option b. "is measured over an interval" correctly describes a continuous random variable.
A continuous random variable can take on any value within a given interval, including decimal values. It represents measurements that can be infinitely divided and can take on an uncountable number of values. Examples of continuous random variables include the height of individuals, the time it takes to complete a task, or the temperature of a room. These variables are not restricted to specific discrete values and can vary continuously.
On the other hand, discrete random variables (options a, c, and d) can only take on a countable number of distinct values. Discrete random variables represent outcomes that are distinct and separate, such as the number of students in a class, the number of cars passing by, or the number of heads obtained when flipping a coin.
These variables do not have decimal values and cannot be measured over a continuous range.
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sixty more than nine times a number is the same as two less than ten times the number. What’s the number
Answers
Step-by-step explanation:
the number unknown=x
9x+60=10x-2
Bring all right hand side of the equation to the left side
9x+60-10x+2=0
-x+62=0
-x=-62
answer x=62
I have a) down but the rest I dont understand please help!!!
(20 points and brainly!!!)
Answers
B. 9.67
C. 90.33
I’m not sure if C is correct because I might not of been working by the correct equation
a graphic artist has a picture that is 5 in by 10 in the picture needs to be in large so the larger side is 30 in the ratio of the sides lengths will remain the same how long will the shorter side be after the enlargement
Answers
Answer:15
Step-by-step explanation:
the ratio is 1:2 so 5 is half of 10 and if 10 becomes 30 it’s tripled so you would then have to triple 5 getting 15 , i hope this is right if not i’m sorry
I have to finish this before next week because of grades please thanks
Answers
Answer:
D
Step-by-step explanation:
Here are the first five terms of an arithmetic sequence. 2 6 10 14 18 Write down an expression, in terms of n, for the nth term of this sequence.
Answers
Answer:
Step-by-step explanation:
Use the formula
a
n
=
a
1
+
d
(
n
−
1
)
a
n
=
a
1
+
d
(
n
-
1
)
to identify the arithmetic sequence.
a
n
=
4
n
−
2
The nth term of given series is an = 4n - 2
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.
We have
a = 2
Common difference (d):
= 6 - 2 = 4
= 10 - 6 = 4
= 14 - 10 = 4
Common difference (d) = 4
According to the question
We know the formula nth term of arithmetic sequence,
an = a + (n – 1)d
an = 2 + (n - 1)4
an = 2 + 4n - 4
an = 4n - 2
Hence, nth term of given series is an = 4n - 2
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I need Help ASAP PLEASE! I'm stuck on this one question
Answers
The measure of ∠s is 22 degrees according to corresponding and straight line angle.
We will use the rrelation between angles to find the measure of each. We see that ∠158 degree and angle r are corresponding angles and hence they will be equal. Thus, it can be said that angle r = 158 degree.
Now, angle r and angle s is present on same line. It means the sum of these two angles will be 180 degree. Using the relation to find angle s.
158 + angle s = 180
Angle s = 180 - 158
Subtract the values
Angle s = 22 degrees
Hence, ∠s measures 22 degrees.
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Consider the following NLP: min s.t. 2x12+2x1x2+x22−10x1−10x2
x12+x22≤5
3x1+x2≤6
x1,x2≥0 (a) Aside from regularity and the given constraints, what are the first order necessary conditions for this problem? (Be as specific as possible.) (b) Find a solution by assuming the first Lagrangian multiplier constraint is active and the second one is inactive. (c) Does this satisfy the first order necessary conditions? Explain.
Answers
The first-order necessary conditions for the given NLP problem involve the KKT conditions, and a specific solution satisfying these conditions needs further analysis.
(a) The first-order necessary conditions for constrained optimization problems are defined by the KKT conditions. These conditions require that the gradient of the objective function be orthogonal to the feasible region, the constraints be satisfied, and the Lagrange multipliers be non-negative.
(b) Assuming the first Lagrangian multiplier constraint is active means that it holds with equality, while the second one is inactive implies that it does not affect the solution. By incorporating these assumptions into the KKT conditions and solving the resulting equations along with the given constraints, a solution can be obtained.
(c) To determine if the solution satisfies the first-order necessary conditions, one needs to verify if the obtained values satisfy the KKT conditions. This involves checking if the gradient of the objective function is orthogonal to the feasible region, if the constraints are satisfied, and if the Lagrange multipliers are non-negative. Only by performing this analysis can it be determined if the solution satisfies the first-order necessary conditions.
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15Pts An automobile manufacturer has discovered that 20% of all the transmissions it installed in a particular style of truck one year are defective. It has contacted the owners of these vehicles and asked them to return their trucks to the dealer to check the transmission. The Friendly Auto Mart sold seven of these trucks and has two of the new transmissions in stock. What is the probability that the auto dealer will need to order more new transmissions?
Answers
The probability that the auto dealer will need to order more new transmissions is the sum of the probabilities of having 3, 4, 5, 6, or 7 defective transmissions among the seven trucks sold.
To calculate the probability that the auto dealer will need to order more new transmissions, we can use the binomial probability formula.
Given that the probability of a defective transmission is \(20\%\) (or 0.2), and the dealer has sold seven trucks with two new transmissions in stock, we want to find the probability of having more than two defective transmissions among the seven sold.
Let's denote X as the number of defective transmissions among the seven sold. We need to calculate \(\(P(X > 2)\).\)
Using the binomial probability formula, we can calculate the probability of X using the following formula:
\(\[P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k}\]\)
Where:
\(- \(\binom{n}{k}\)\) is the number of combinations of choosing \(\(k\)\) items from a set of n items.
- p is the probability of success (defective transmission).
- n is the total number of trials (number of trucks sold).
To calculate \(\(P(X > 2)\),\) we need to sum the probabilities of having 3, 4, 5, 6, or 7 defective transmissions.
\(\[P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)\]\)
Now let's calculate each term and sum them:
\(\[P(X = 3) = \binom{7}{3} \cdot (0.2)^3 \cdot (0.8)^{7 - 3}\]\[P(X = 4) = \binom{7}{4} \cdot (0.2)^4 \cdot (0.8)^{7 - 4}\]\[P(X = 5) = \binom{7}{5} \cdot (0.2)^5 \cdot (0.8)^{7 - 5}\]\[P(X = 6) = \binom{7}{6} \cdot (0.2)^6 \cdot (0.8)^{7 - 6}\]\[P(X = 7) = \binom{7}{7} \cdot (0.2)^7 \cdot (0.8)^{7 - 7}\]\)
Finally, we sum these probabilities to get the desired result:
\(\[P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)\]\)
Calculating these probabilities will yield the probability that the auto dealer will need to order more new transmissions.
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In the diagram below, find the value of y....
Answers
Answer:
y = 130
Step-by-step explanation:
(4x+8) + (3x-19) + (x+7) = 180
4x + 8 + 3x - 19 + x + 7 = 180
(4x + 3x + x) + (8 -19 + 7) = 180
8x - 4 = 180
8x -4 +4 = 180 +4
8x = 184
8x/8 = 184/8
x = 23
3(23) - 19 = 50
50 + y = 180
180 - 50 = y
y = 130
what is a types of quadrilaterals?
Answers
Types of quadrilaterals are parallelograms, rectangles, squares, rhombi, trapezoids, kites, and isosceles trapezoid.
A polygon having four sides and four angles are called a quadrilateral. Quadrilaterals come in a wide variety of forms, each with its own set of qualities and attributes.
Some of the most typical varieties are listed below:
Parallelogram - A quadrilateral has opposing sides that are equally long and parallel.
Rectangle - A parallelogram with all angles at 90 degrees is referred to as a rectangle.
Square - A rectangle with equally long sides.
Rhombus - A parallelogram with equal-length sides is referred to as a rhombus.
Trapezoid - A quadrilateral with just one set of diagonally opposed sides is called a trapezoid.
Kite - A quadrilateral has two sets of adjacent sides that are of equal length or a kite.
Isosceles trapezoid - An isosceles trapezoid is one with equally long non-parallel sides.
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A crane is being set up on a slope of. If the base of the crane is. 0 ft wide, how many inches should the downhill side of the base be raised in order to level the crane?
Answers
The downhill side of the crane base should be raised by approximately 4.53 inches to level the crane on a 2.5° slope.
We can use trigonometry here. Let x be the length (in inches) that the downhill side of the base should be raised. The slope of the ground is given to be 2.5°,
tan(2.5°) ≈ 0.0436
Now, using the equation,
x / 12 = 9tan(2.5°)
Here, we converted the base's width from feet to inches (by dividing by 12) and calculated the crane's required vertical displacement (inches) using the angle's tangent. When we simplify this equation, we obtain,
x = 9tan(2.5°)12
x ≈ 4.53 inches
Therefore, the downhill side of the base should be raised by about 4.53 inches to level the crane.
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Complete question - A crane is being set up on a slope of 2.5 degrees. If the base of the crane is 9.0 ft wide, how many inches should the downhill side of the base be raised in order to level the crane?
What is 3 + 3?
I'm really stuck on this
Answers
Answer:
3 + 3 = 6
Step-by-step explanation:
I hope this helped!
Sara uses ribbon to make hair bows. The length of each ribbon Sara uses is represented by the line plot shown. What is the difference, in feet, between one of the pieces of ribbon that has the longest length and one of the pieces that has the shortest length?
Answers
Answer:
1
Step-by-step explanation:
because if you do 1 1/2 - 1/2 = 1
use integrals test, comparisons tests to determine the convergence or divergence for an alterning series
Answers
To determine the convergence or divergence of an alternating series, you can use the Alternating Series Test. This test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.
Additionally, if the terms do not approach zero, the series diverges.
To apply the Alternating Series Test, you need to check two conditions:
1. The terms of the series must alternate in sign.
2. The absolute value of the terms must decrease or approach zero.
If both conditions are satisfied, you can conclude that the alternating series converges. However, if either condition fails, the series diverges.
If you want to determine the convergence or divergence more precisely, you can use the Integral Test or the Comparison Test. The Integral Test allows you to compare the convergence or divergence of a series to the convergence or divergence of an improper integral. If the integral converges, the series converges, and if the integral diverges, the series diverges.
The Comparison Test is another method to determine the convergence or divergence of a series. It involves comparing the given series with a known series whose convergence or divergence is already known. If the known series converges and the terms of the given series are less than or equal to the corresponding terms of the known series, then the given series also converges. Conversely, if the known series diverges and the terms of the given series are greater than or equal to the corresponding terms of the known series, then the given series also diverges.
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For 0 ≤ x ≤ 2pi, solve the equation:tanx = 4sec^2x-4
Answers
Given the equation;
\(\tan x=4\sec ^2x-4\)We start by moving all terms to the left side of the equation;
\(\tan x-4\sec ^2x+4=0\)Now we re-write this using trig identities;
\(4+\tan x-4\sec ^2x=0\)Note that;
\(\sec ^2x=\tan ^2x+1\)Input this into the last equation and we'll have;
\(4+\tan x-4(\tan ^2x+1)=0\)Simplify the parenthesis;
\(\begin{gathered} -4(\tan ^2x+1) \\ =-4\tan ^2x-4 \end{gathered}\)We now refine the last equation;
\(\begin{gathered} 4+\tan x-4\tan ^2x-4 \\ =4-4+\tan x-4\tan ^2x \\ =\tan x-4\tan ^2x \end{gathered}\)The equation now becomes;
\(\tan x-4\tan ^2x=0\)We now represent tan x by letter a.
That means;
\(a-4a^2=0\)We shall apply the rule;
\(\begin{gathered} \text{If} \\ ab=0 \\ \text{Then} \\ a=0,b=0 \end{gathered}\)Therefore;
\(\begin{gathered} a-4a^2=0 \\ \text{Factorize;} \\ a(1-4a)=0 \end{gathered}\)At this point the solutions are;
\(\begin{gathered} a=0 \\ \text{Also;} \\ 1-4a=0 \\ 1=4a \\ \frac{1}{4}=a \end{gathered}\)If we now substitute a = tan x back into the equation, we would have;
\(\begin{gathered} \tan x-4\tan ^2x=0 \\ \tan x=0,\tan x=\frac{1}{4} \end{gathered}\)Where tan x = 0;
\(\begin{gathered} \tan x=0 \\ x=\pi \end{gathered}\)Where tan x = 1/4;
\(\begin{gathered} \tan x=\frac{1}{4} \\ x=\arctan (\frac{1}{4}) \\ x=0.24497\ldots \end{gathered}\)ANSWER:
\(\begin{gathered} x=\pi \\ x=0.245 \end{gathered}\)Select all terms that are like terms 5 yx2 -8 x2 1.25 x2 1/2 x2 -3.4 x3 4 x 5 3/8
Answers
The volume (in cubic inches) of a shipping box is modeled by v=2x^3 - 19x^2 + 39x, where x is the length (in inches). Determine the values of x for which the model makes sense. Explain your reasoning.
a. x < 0
b. x ≥ 0
c. x > 0
d. x ≤ 0
Answers
The volume (in cubic inches) of a shipping box is modeled by \(v=2x^3 - 19x^2 + 39x\), The correct answer is option (b).
where x is the length (in inches). Determine the values of x for which the model makes sense.
The cubic volume of a box should always be positive for it to make sense in this context.
Since the length of a box is always a non-negative value, the length 'x' must be greater than or equal to zero.
Therefore, the correct answer is option b) x ≥ 0
In this case, we are dealing with the volume of a shipping box, which cannot have negative dimensions. Therefore, the length of the box, represented by x, must be non-negative.
Hence, the correct answer is:
b. x ≥ 0
This means that the model makes sense for values of x greater than or equal to zero, as negative lengths are not physically meaningful in the context of a shipping box.
Therefore, we can break down this equation into the following cases:
Case 1: x > 0 (positive value)
For x > 0, all factors of the inequality are positive.\(2x^2 - 19x + 39 > 0\)
This is always true when x > 0 because all factors are positive.
Therefore, this case holds.Case 2: x = 0 (value zero)
The left side of the equation is 0, and the right side is positive.
Therefore, this case does not hold.
Case 3: x < 0 (negative value)
The inequality is false when x < 0 because x is always negative.
Therefore, this case does not hold.
Therefore, the only valid case is x > 0, or x ≥ 0.
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\(\frac{t}{6} \ \textgreater \ -7\)
Answers
t > -42
Step-by-step explanation:
t/6 > -7
Multiply 6 by -7
-42/6 > -7
-7 > -7
so t > -42
The question is 3(2x +4) = 6x + 10
Answers
Answer:
no solution
Step-by-step explanation:
when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.
Answer:
The answer is False meaning it's no solution
Step-by-step explanation:
1. Distribute 3 through the parentheses which will be 6x+12=6x+10
2.Cancel equal terms on both sides of the equation and you will get 12=10 which isn't a true statement.
Which problem can be solved using this equation?
0.15m+35=0.25m+20
Answers
Answer:
The last problem.
150 minutes.
Step-by-step explanation:
0.15m+35=0.25m+20
15 = 0.10m
m = 150.
Answer:
What the guy on the top said, there right.
Step-by-step explanation:
David is the caption of the school soccer team. Last year, the team won four more games than it lost. If the team won 46 games, how many games did it lose?
Answers
Answer:
C
Step-by-step explanation:
Games lost=Games won - 4
Games lost=46-4=42
Find the solution of the system of equations.
10x+6y= 16
−10x+5y= 50
Answers
Answer:
( − 2 , 6 )
x = − 2
y = 6
Step-by-step explanation:
A triangle has a 35° angle, a 55° angle, and a side 6 centimeters in length,
Select True or False for each statement about this type of triangle.
True
False
The triangle might be an isosceles triangle.
The triangle might be an acute triangle.
The triangle must contain an angle measuring 90°.
O
Answers
Answer:
f
f
v
Step-by-step explanation:
True or
False?
A binary predictor variable is tested for significance using a different test statistic than used for a quantitative predictor variable.
Answers
Answer:
it is False
Step-by-step explanation:
Consider the probability that greater than 99 out of 160 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 64%.
Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answers
The approximate probability that greater than 99 out of 160 students will pass their college placement exams is 0.2831.
To approximate the probability using the normal distribution, we can use the concept of the binomial distribution approximation to the normal distribution. In this case, we have a large sample size (160 students) and a probability of success (passing the exam) that is not extremely small or large (64%).
To calculate the probability that greater than 99 out of 160 students will pass the exam, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is given by μ = n * p, and the standard deviation is given by σ = sqrt(n * p * (1 - p)), where n is the sample size and p is the probability of success.
In this case, n = 160 and p = 0.64.
Therefore, the mean is μ = 160 * 0.64 = 102.4,
and the standard deviation is σ = sqrt(160 * 0.64 * (1 - 0.64)) ≈ 5.1055.
Now, we can calculate the probability using the normal distribution. We want to find the probability of having more than 99 students pass the exam out of 160, which is equivalent to finding the probability that the number of successes is greater than 99.
We can standardize the value using the z-score formula: z = (x - μ) / σ, where x is the desired number of successes. In this case, x = 99.5 (to account for continuity correction, as we're dealing with a discrete distribution).
z = (99.5 - 102.4) / 5.1055 ≈ -0.565
Using a standard normal distribution table or a calculator, we can find the probability corresponding to the z-score of -0.565, which is the probability of having more than 99 students pass the exam.
Looking up the z-score of -0.565 in the standard normal distribution table, we find that the probability is approximately 0.2831.
Rounding the answer to four decimal places, the approximate probability that greater than 99 out of 160 students will pass their college placement exams is 0.2831.
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A car travels a distance of 170 miles in a time of 3.6 hours.
What is its average speed rounded to 1dp?
Answers
Answer:
47mph
Step-by-step explanation:
S=d/t
s=170/3.6
s=47.2
Find all the critical points (equilibrium solutions). Gb. Use an appropriate graphing device to draw a direction field and phase portrait for the system. c. From the plot(s) in part b, determine whether each critical point is asymptotically stable, stable, or unstable, and classify it as to type. d. Describe the basin of attraction for each asymptotically stable critical point. 4. dx/dt = x - xy, dy/dt = y + 2xy 5. dx/dt = 1 + 2y, dy/dt = 1 - 3x2 6. dx/dt = 2x + x2 - xy, dy/dt = 3y - 2y? – 3xy 7. dx/dt = -(2+ y)(x + y), dy/dt = -y(I – x) 8. dx/dt = y(2 - x - y), dy/dt = -x - y - 2xy 9. dx/dt = (2+ x)(y - x), dy/dt = y(2 + x - x?) 22
Answers
The critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).
What is the system of equations?
A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.
To find the critical points (equilibrium solutions) of the given systems of differential equations, we need to set both derivatives equal to zero and solve for x and y.
dx/dt = x - xy, dy/dt = y + 2xy
Setting dx/dt = 0, we have:
x - xy = 0
x(1 - y) = 0
This gives us two critical points: (0, y) and (1, y), where y can take any value.
Setting dy/dt = 0, we have:
y + 2xy = 0
y(1 + 2x) = 0
This gives us two critical points: (x, 0) and (x, -1/2), where x can take any value.
Therefore, the critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).
Regarding the stability and classification of each critical point, we need to analyze the eigenvalues of the Jacobian matrix at each point. The stability of a critical point is determined by the sign of the real parts of the eigenvalues.
To describe the basin of attraction for each asymptotically stable critical point, we would need to perform further analysis of the system's behavior near each critical point.
Hence, the critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).
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use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answers
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
8.4 = -t/6.5
solve for t. thanks!
Answers
Answer:
t=-54.6
Step-by-step explanation:
on this picture below hope this helps :)
