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xz_007 [3.2K]
3 years ago
7

A dart is thrown at the board shown. it hits the board at a random point. find the probability that it will land in an unshaded

region. round to the nearest percent.
A. 25%
B.67%
C.75%
D.33%

Mathematics
2 answers:
aliina [53]3 years ago
8 0

Answer:

The correct option is C. The probability that it will land in an unshaded region is 75%.

Step-by-step explanation:

The given figure it square, which is divide into 4 equal square. Out of these two squares are half shaded.

If these 4 small square are divided in two equal parts, then total number of parts are 8. Out of 2 parts are shaded.

The probability that it will land in an unshaded region is

P=\frac{\text{Unshaded parts}}{\text{Total number of parts}}\times 100

P=\frac{6}{8}\times 100

P=\frac{3}{4}\times 100

P=75\%

Therefore probability that it will land in an unshaded region is 75%. Option C is correct.

kupik [55]3 years ago
6 0

Answer:

d

Step-by-step explanation:


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A 40-degree angle is translated 5 inches along a vector. What is the angle measurement, in degrees, of the Image?
vagabundo [1.1K]

Answer:

40°

Step-by-step explanation:

As clarified in an online document, a translation along a vector (which is a line in a plane) of a figure, is equivalent to a translation along a coordinate grid, and therefore, given that a translation is a form of rigid transformation, the the dimensions and inclinations of the rays forming the preimage are the same as those in the image and the angles measurement in the preimage and the image are equal.

Therefore, given that the angle measurement of the image is 40-degrees, the angle measurement of the image is also 40-degree (40°) angle.

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A pet store has 5 puppies, including 2 poodles, 2 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one p
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Answer:

1/4

Step-by-step explanation:

Rebecka already chose a retriever, so the puppies left for Aaron to pick are:

2 poodles

2 terriers

1 retriever

Total: 4

Number of retrievers left after Rebecka's pick: 1

p(Aaron picks retriever) = 1/4

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Step-by-step explanation:

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Chris is painting a wall with a length of 3 meters and a width of 1.6 meters
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Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv
Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

f_x = ycos(xy)

f_y = xcos(xy) - ze^{yz}

f_z = -ye^{yz}

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)  

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)

Where, again, the constant of integration depends on Z.

As a result,

f(x,y,z) = cos(xy) - e^{yz} + K(z)

if we derivate f over z, we obtain

f_z(x,y,z) = -ye^{yz} + d/dz K(z)

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0
3 years ago
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