The original equation (10x + 25) / (3x + 12) = 5x / (x + 4) has no valid solutions.
We have,
To determine the number of valid solutions for the equation
(10x + 25) / (3x + 12) = 5x / (x + 4), we need to solve the equation and check if there are any values of x that satisfy the equation while not causing any division by zero.
Let's solve the equation step by step:
(10x + 25) / (3x + 12) = 5x / (x + 4)
Cross-multiply to eliminate the fractions:
(10x + 25)(x + 4) = (3x + 12)(5x)
Expand both sides:
10x² + 40x + 25x + 100 = 15x² + 60x
Combine like terms:
10x² + 65x + 100 = 15x² + 60x
Subtract 10x² + 60x from both sides:
5x² + 5x + 100 = 0
Now we have a quadratic equation.
To solve it, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
For the equation 5x² + 5x + 100 = 0, a = 5, b = 5, and c = 100.
Calculating the discriminant (b² - 4ac):
Discriminant = (5²) - (4 x 5 x 100)
Discriminant = 25 - 2000
Discriminant = -1975
Since the discriminant is negative (-1975), the quadratic equation has no real solutions.
Therefore,
The original equation (10x + 25) / (3x + 12) = 5x / (x + 4) has no valid solutions.
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In triangle ABC, AB measures 25 cm and AC measures 35 cm. The inequality < s < represents the possible third side length of the triangle, s, in centimeters. The inequality < p < represents the possible values for the perimeter, p, of the triangle, in centimeters.
Answer:
The inequality 10 < s < 60 represents the possible third side length of the triangle, s in centimeters.
The inequality 70 < p < 120 represents the possible values for the perimeter p, of the triangle in centimeters.
Step-by-step explanation:
Firsts one The lower number has to be the difference between the bigger number and smaller number. In this case 35 - 25 = 10 and the s < 60 has to be the sum of both numbers.
Second one. I'm assuming it's just the sum of the two numbers to the first answer, and the second number is just the second number from the previous one, but multiplied by 2. Sorry that I couldn't go into too much detail about this one
The inequality that represents the possible third side length
\(10cm<s<60cm\)
The inequality that represents the possible values for the perimeter
\(70cm<P<120cm\)
Given :
In triangle ABC, AB measures 25 cm and AC measures 35 cm.
For any triangle , we know that the sum of measures of two sides is greater than the third side
Let 's' be the third side length
\(25+35>s\\60>s\\\\Also , s+25>35\\s>35-25\\s>10\\Inequality\; is \;\\10<s<60\)
Now we find the perimeter when s=10
Perimeter = sum of all the sides
\(s=10\\P=25+35+10=70\\s=60\\P=25+35+60=120\)
\(70<P<120\)
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Se lanza al mismo tiempo un dado y una moneda. ¿Cuál es la probabilidad de obtener 5 y sol?
Usando conceptos de probabilidad, se encuentra que hay una probabilidad de 1/12 de de obtener 5 y sol.
---------------------------------
Una probabilidad es el número de resultados deseados dividido por el número de resultados totales Si dos eventos, A y B, son independientes, la probabilidad de que ambos sucedan juntos es la multiplicación de las probabilidades de que ambos sucedan, o sea:\(P(A \cap B) = P(A)P(B)\)
---------------------------------
Dado y moneda son independientes.En el dado, uno de los seis lados es 5, o sea, \(P(A) = \frac{1}{6}\).En la moneda, uno de los dos lados es sol, o sea, \(P(B) = \frac{1}{2}\)Entonces, la probabilidad deseada viene dada por
\(P(A \cap B) = P(A)P(B) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}\)
Probabilidad de 1/12 de de obtener 5 y sol.
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Which expression is equivalent to 25x â€" 45y?
A. 25(5x â€" 20y)
B. 5(5x - 9y)
C. 70(x â€" y)
D. 10(15x â€" 35y)
Answer:
D
Step-by-step explanation:
Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica
Which set of values contains no integers?
A. {-5, 9/3, 7.2}
B. {2.2361, 4, 7.8}
C. {-12, -3.33, 2.6458}
D. {-23/5, 2.4495, 5.1}
Answer:
D
Step-by-step explanation:
Integers found in:
A: -5, 9/3 = 3
B: 4
C: -12
Hope this helped! ^^
What is the difference of the two polynomials?
(9x2 + 8x) – (2x2 + 3x)
7x2 + 5x
7x2 + 11x
11x2 + 5x
11x2 + 11x
Answer:
The answer is 7x²+5x
Step-by-step explanation:
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♛┈⛧┈┈•༶♛┈⛧┈┈•༶
HELP PLSSSSSSS
NO LINKS
Answer:
Is there anything else to this like a description or a sentence?
Step-by-step explanation:
Sorry I need more than this
You give me answer=BRAINLIEST
Answer:
A. 2
Step-by-step explanation:
Well let’s first graph the following,
\(x^2 + y = 8\)
\(x=y\)
So on the graph the system of equations only have 2 real solutions which are
(-3.272, -3.272) (2.372,2.372)
A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people
By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.
To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.
Since a van can ferry a maximum of 12 people, we can write the inequality as:
12v ≥ 80
Now, let's solve for "v":
Divide both sides of the inequality by 12.
v ≥ 80/12
Simplify the inequality.
v ≥ 6.67
Since we cannot have a fraction of a van, we need to round up to the nearest whole number:
v ≥ 7
Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.
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use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z)
The divergence theorem provides a useful tool to calculate the surface integral of a vector field across a closed surface by relating it to the volume integral of the divergence of the vector field. The specific calculation requires determining the divergence of the given vector field and performing the necessary integration over the enclosed volume.
To calculate the surface integral using the divergence theorem, we need both the vector field f(x, y, z) and the surface S across which we want to calculate the flux. However, the specific vector field f(x, y, z) and surface S are not provided in your question.
The divergence theorem states that the flux of a vector field across a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface. Mathematically, it can be expressed as:
∬S f · ds = ∭V (∇ · f) dV
Where:
∬S denotes the surface integral over the closed surface S.
f represents the vector field.
ds represents the outward-pointing vector normal to the surface element dS.
∭V denotes the triple integral over the volume V enclosed by the surface.
∇ · f represents the divergence of the vector field f.
In summary, the divergence theorem provides a useful tool to calculate the surface integral of a vector field across a closed surface by relating it to the volume integral of the divergence of the vector field. The specific calculation requires determining the divergence of the given vector field and performing the necessary integration over the enclosed volume.
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Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate the flux of F across S. F(x, y, z) = xyezi + xy2z3j − yezk, S is the surface of the box bounded by the coordinate plane and the planes x = 3, y = 6, and z = 1.
please help im freaking out because this is due in 5 minutes
Step-by-step explanation:
12:8
24:16
36:24
48:32
Girl hurry and submit it
Which of the following can be found on a credit report?
A Personal Social Security Number
B Checking Account Balance
C Late Payments to Lenders
D Credit Card Balances
B and D Only
A Only
Not here
A, C, and D Only
Answer:
A, C, & D only
Step-by-step explanation:
All of the following are listed on your credit report except option B) your checking account balance.
Which equation has the least steep graph?
A. y=-x-9
X-
B. y = -7x-2
C. y= x+6
6
D. y = 2x + 1
to add 0.01 0.02 ... 1.00, what order should you use to add the numbers to get better accuracy?
To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is recommended to add the numbers in ascending order (from smallest to largest) to minimize the accumulation of rounding errors and maintain higher precision during intermediate calculations. Thus, starting with 0.01 and ending with 1.00 would provide better accuracy.
To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is generally recommended to use an order that minimizes the accumulation of rounding errors. In this case, it is advisable to start with the smaller numbers and progress towards the larger ones.
By adding the numbers in ascending order (from 0.01 to 1.00), the rounding errors at each step will have a smaller impact on the overall result. This is because adding smaller numbers together first helps maintain a higher level of precision during intermediate calculations.
Therefore, to achieve better accuracy, you should add the numbers in ascending order, starting with 0.01 and ending with 1.00.
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Consider the following vector field.
F(x, y, z) =
9ex sin(y), 2ey sin(z), 8ez
sin(x)
(a)
Find the curl of the vector field.
curl(F) =
(b)
Find the divergence of the vector field.
div(F) =
The curl of the vector field
curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
The divergence of the vector field
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.
(a) Curl of F:
The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:
curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k
In this case, we have:
P(x, y, z) = 9ex sin(y)
Q(x, y, z) = 2ey sin(z)
R(x, y, z) = 8ez sin(x)
Taking the partial derivatives, we get:
∂P/∂y = 9ex cos(y)
∂Q/∂z = 2ey cos(z)
∂R/∂x = 8ez cos(x)
∂R/∂y = 0 (no y-dependence in R)
∂Q/∂x = 0 (no x-dependence in Q)
∂P/∂z = 0 (no z-dependence in P)
Substituting these values into the curl formula, we have:
curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k
= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
Therefore, the curl of the vector field F is given by:
curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k
(b) Divergence of F:
The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:
div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z
In this case, we have:
∂P/∂x = 9e^x sin(y)
∂Q/∂y = 2e^y sin(z)
∂R/∂z = 8e^z
Substituting these values into the divergence formula, we have:
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
Therefore, the divergence of the vector field F is given by:
div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z
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Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form.
The indefinite integral, \(\int {sin(9x)} \, dx\) = \(\frac{-1}{9} cos(9x) + C\)
We have to find the indefinite integral,
\(\int {sin(9x)} \, dx\)
using the substitution 9x = u.
So we need to change the variable of integration from x to u using this substitution.
9x = u ⇒ 9 dx = du
So \(\int {sin(9x)} \, dx\) = \(\frac{1}{9} \int{sin(u) \ du\)
= 1/9 (- cos(u)) + C, [ Since integral of sin(u) = -cos(u) ]
where C is the integration constant which is often put when evaluating indefinite integrals.
Now replacing u with x to get the final answer,
1/9 (- cos(u)) + C = -1/9 cos(9x) + C
Therefore, \(\int {sin(9x)} \, dx\) = \(\frac{-1}{9} cos(9x) + C\)
The question is incomplete. Find the complete question below:
Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form. \(\int {sin(9x)} \, dx\), 9x = u.
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A university professor does not believe that there is really a difference between the GPA of male and female scholarship athletes, so he looks into how the sample was collected. His investigation shows that the study was given to all of the athletes on the basketball teams exclusively. Based on this information, should the university administration trust the results from this study?
a. Yes, because the results were significant
b. Yes, because a large enough sample was taken
c. No, because not every scholarship athlete part of the study
d. No, because the study was not taken from a random sample of scholarship athletes
Answer: d. No, because the study was not taken from a random sample of scholarship athletes.
Step-by-step explanation:
Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.
7. What factors may be involved in a fit person achieving steady-state and full recovery sooner than an unfit person? 8. Finally, graph/plot RQ as a function of time, noting rest, PA, and recovery phases. Does its variation make sense? Why or why not?
A person's cardiovascular fitness, age, weight, gender, and the severity of the activity performed may all play a role in how fast a person attains steady-state and fully recovers. When an individual is fit, they tend to have a lower resting heart rate than an unfit person. Furthermore, a fit person's heart rate is less likely to climb to high levels during activity, and their muscles are more efficient, requiring less oxygen to function. Finally, fit people tend to have better cardiovascular health and are more capable of removing waste products from their muscles, allowing for a quicker recovery time.
RQ stands for respiratory quotient and represents the ratio of carbon dioxide produced to oxygen consumed. During exercise, RQ rises because the body is using more carbohydrates than fats to generate energy, which increases carbon dioxide production. During the recovery period, RQ decreases as the body switches back to using fat as its primary energy source and oxygen consumption increases.The graph/plot of RQ as a function of time during rest, physical activity, and recovery phases should show a steady increase during physical activity and a decline during recovery. This variation makes sense because during exercise, the body's demand for energy increases, and RQ increases as a result. Conversely, during recovery, the body switches back to using fat as its primary energy source, resulting in a decrease in RQ.
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Find all missing angles?
20 ÷ ____ = 5 need your help
Answer:
4
Step-by-step explanation:
PLZ HELP IM GIVING YOU 100 POINTS
solve for x
2 1/4 = 1 2/7 divided by x
Answer:
x = 4/7 or 0.571428571
Step-by-step explanation:
HURRY PLEASEEE
Q. 6
What is the equation of the rational function g(x) and its corresponding slant asymptote?
Rational function with one piece increasing from the left in quadrant 3 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line x equals 2 and another piece increasing from the left in quadrant 3 asymptotic to the line x equals 2 and passing through the point 3 comma 0 and going to the right
A. g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x + 2
B. g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x + 2
C. g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x – 2
D. g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x – 2
The slant asymptote of the function is y = x - 2. The correct option is D.
Given a rational function with one piece increasing from the left in quadrant 3 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line x equals 2 and another piece increasing from the left in quadrant 3 asymptotic to the line x equals 2 and passing through the point 3 comma 0 and going to the right.
The equation of the rational function g(x) and its corresponding slant asymptote are to be determined.
A rational function is a type of function in which both the numerator and denominator of the function are polynomials.
The equation of a rational function with one piece increasing from the left in quadrant 3 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line x equals 2 and another piece increasing from the left in quadrant 3 asymptotic to the line x equals 2 and passing through the point 3 comma 0 and going to the right can be given as follows:g(x) = (x² - 9) / (x - 2) (x + 2)The domain of the given function is x ≠ ±2 and the vertical asymptotes are at x = 2 and x = -2.
The slant asymptote can be found by performing a polynomial division. Divide the numerator by the denominator, then we get (x) = x - 2 - (5 / (x - 2)(x + 2))
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will mark brainliest! question in the picture
Answer:
+9r+
Step-by-step explanation:
You can see the attached photo for the answer.
If g(x) = -25, then x =
argumento sobre el medio ambiente
El medio ambiente es un tema crucial para la supervivencia de todas las especies del planeta, incluyendo los seres humanos. La actividad humana ha tenido un impacto significativo en el medio ambiente, lo que ha llevado a la degradación de los ecosistemas, la pérdida de biodiversidad y el cambio climático.
Es importante que tomemos medidas para proteger el medio ambiente. Podemos hacer esto reduciendo nuestra huella de carbono, utilizando fuentes de energía renovable, reduciendo nuestro consumo de recursos naturales y siendo más conscientes de nuestras acciones en relación con el medio ambiente.
Además, la educación es clave para la protección del medio ambiente. Si todos estamos educados sobre los problemas ambientales y las soluciones, podemos trabajar juntos para encontrar formas de proteger y preservar nuestro planeta para las generaciones futuras.
En resumen, el medio ambiente es esencial para nuestra supervivencia y debemos tomar medidas para protegerlo. La educación y la acción son necesarias para abordar los desafíos ambientales que enfrentamos como sociedad.
verify that the pair x(t), y(t) is a solution to the given system. Sketch the trajectory of the given solution in the phase plane. dx/dt = 3y^3 , dy/dt = y ; x(t) =e^3t , y(t) = e^t dx/dt = 1 , dy/dt = 3x^2 ; x(t) = t + 1, y(t) = t^3 + 3t^2 +3t
The pair x(t) = e^3t, y(t) = e^t is a solution to the given system.
Is the given pair (x(t), y(t)) a solution?The given system consists of two differential equations: dx/dt = 3y^3 and dy/dt = y. We are given the pair x(t) = e^3t and y(t) = e^t. To verify if this pair is a solution, we need to substitute these values into the differential equations and check if they hold true.
Substituting x(t) = e^3t and y(t) = e^t into the first equation, we have dx/dt = 3(e^t)^3. Simplifying, we get dx/dt = 3e^(3t).
Similarly, substituting x(t) = e^3t and y(t) = e^t into the second equation, we have dy/dt = e^t.
We can see that both sides of the differential equations match the given pair (x(t), y(t)). Hence, x(t) = e^3t and y(t) = e^t satisfy the given system of differential equations.
To sketch the trajectory of the given solution in the phase plane, we can plot the points (x(t), y(t)) for different values of t. The trajectory would represent the path traced by the solution in the phase plane.
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How to find a quadratic equation with y-intercept and vertex? Explain with examples.
To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.
To find a quadratic equation with the y-intercept and vertex, we can follow these steps:
Step 1: Identify the coordinates of the y-intercept. The y-intercept has the form (0, c), where c is the y-coordinate.Step 2: Identify the coordinates of the vertex. The vertex has the form (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic equation.Step 3: Substitute the coordinates of the y-intercept and vertex into the general form of the quadratic equation, y = ax^2 + bx + c.Step 4: Solve the resulting system of equations to find the values of a, b, and c.Step 5: Substitute the values of a, b, and c back into the general form of the quadratic equation to obtain the final equation.For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:
3 = a(0)^2 + b(0) + c
1 = a(-2)^2 + b(-2) + c
Simplifying these equations, we get:
c = 3
4a - 2b + c = 1
By substituting c = 3 into the second equation, we can solve for a and b:
4a - 2b + 3 = 1
4a - 2b = -2
2a - b = -1
By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:
y = x^2 + x + 3
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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.
Start with the standard form of a quadratic equation: y = ax^2 + bx + c, where a, b, and c are constants.Use the vertex form of a quadratic equation: y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Substitute the vertex coordinates (h, k) into the equation to obtain the equation in vertex form.Use the y-intercept to find another point on the curve. The y-intercept has the form (0, c), where c is the value of y when x is zero.Substitute the coordinates of the additional point into the equation to obtain a system of two equations. Solve the system to find the values of a, b, and c.Substitute the determined values of a, b, and c into the standard form of the quadratic equation to obtain the final equation.Example:
Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).
Using the vertex form, we have y = a(x - 2)^2 - 1.Substituting the y-intercept coordinates, we get 4 = a(0 - 2)^2 - 1, which simplifies to 4 = 4a - 1.Solving the equation above, we find a = 1.Substituting the values of a and the vertex coordinates into the vertex form equation, we have y = 1(x - 2)^2 - 1.Expanding the equation and simplifying, we get y = x^2 - 4x + 3.The final quadratic equation with the given y-intercept and vertex is y = x^2 - 4x + 3.To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.
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7776^{-4x+4}=
7776
−4x+4
=
\,\,46656^{-5x+9}
46656
−5x+9
you have been doing this what is wrong about it will not make any difference for you guys that will take you in my arms to be in my arms forever to make any difference and to the fact it has a very high end basis as it does the work is very easy but not to do that much at least for 200m years so that we have more presents than the one you are using it is not just your favorite part in all your music from my head off and you of your love is very true for 170m you will not have the courage for 200m your child for the same thing you are for 170m 9999 255 and I is you to to get into in place in and day and Golden for is and and the Golden one was the first one I have ever used in this course for my head so that we will give a better little for our next trip and with and the
Solve the equation:
3/4x - 12 = 12
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
please help me on this
Answer:
I got 5/16 as my answer
Step-by-step explanation:
I used a calculator to solve the equation :/
PLEASE HELP
Sit-up
Push-up
Plank
Arm
circles
V-stretch
which event has a theoretical probability
of?
A. spinner landing on either sit-up
or V-stretch
B. spinner landing on push-up
c. spinner landing on either sit-up.
plank, or arm circles
D. spinner not landing on sit-up
Answer:
A
Step-by-step explanation:
Answer A has two of the five possibilities, and each section is equal so there is an equal probability for each. Add up the two possibilities for 2/5.