Answer:
the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)
Step-by-step explanation:
since the random variable X= time taken to make a grilled cheese sandwich is uniformly distributed, then the probability is governed by
P(a<X<b)= proportion of the time considered / total time range = (a-b)/(c-d) , where c is the maximum time and d is the minimum one
then
P(4<X<5) = (5-4)/(11-3) = 1/8 = 0.125
since we already know that takes less than 6 minutes , then
P(X<6)= P(3<X<6) = (6-3)/(11-3) = 3/8 = 0.375
then using the theorem of Bayes
P( 4<X<5 | X<6 ) = P ( 4<X<5 ∩ X<6 ) / P(X<6) = P(4<X<5)/P(3<X<6) = 0.125 /0.375 = 1/3 (33.33%)
therefore given that we already know that will take Michelle less than 6 minutes , the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)
Answer:
15 cm
Step-by-step explanation:
Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.
A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:
.
To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.
Answer:
BA = 25π,
LA = 25√2π,
TA = 25π + 25√2π,
V = 41 and 2 / 3π
Step-by-step explanation:
We need to determine the height here, as it is not given, and is quite important to us. The height is a perpendicular line segment to the radius, hence forming a 45 - 45 - 90 degree triangle as you can see. Therefore, by " Converse to Base Angles Theorem " the height should be equal in length to the radius,
( Height = 5 inches = Radius
______
Now knowing the height, let's begin by calculating the base area. By it's name, we have to find the area of the base. As it is a circle, let us apply the formula " πr^2 "
- Base Area = 25π
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The lateral area is simply the surface area excluding the base area, the surface area having a formula of " πr^2 + πrl. " Thus, the lateral area can be calculated through the formula " πrl, " but as we are not given the slant height ( l ) we have to use another formula, -
- Lateral Area = 25√2π
______
And the surface area is the base area + lateral area -
- Surface Area
______
The volume of a cone is 1 / 3rd that of a cylinder, with a simple formula of Base * height. Therefore, we can conclude the following -
- Volume = 41 and 2 / 3π
Answer:
6 is the ans
Step-by-step explanation:
Write a Pythagorean triplet whose one member is.
2m, m 2 − 1 , m 2 + 1 \mathrm{m}^{2}-1,
mathrm{m}^{2}+1 m2−1,m2+1 is a Pythagorean triplet.
∴ (6, 8, 10) is a Pythagorean triplet.
(2x + 3) and (x - 2)
Step-by-step explanation:
2x² - x - 6
f(x) = (2x + 3)(x - 2)