The time it will take for the block of ice to melt if the temperature is 45 degrees is 3 hours.
The cost to travel 22 miles is 55 dollars.
<h3>How to find how long for the ice to melt?</h3>
let
time it takes for ice to melt = x
air temperature = y
Therefore,
x ∝ 1 / y
x = k / y
when x = 2.5 hours and y = 54 degrees
Hence,
k = 2.5 × 54
k = 135
The time it will take for the block to melt at 45 degrees = 135 / 45 = 3 hours
<h3>How to find equation that relates the cost to the number of miles?</h3>
It costs $35 for a ride from the city centre to the airport, 14 miles away.
where
c = cost
m = number of miles
Therefore, the equation is as follows:
35 / 14 = 2.5
c = 2.5m
Hence, when you travel 22 miles,
c = 22(2.5)
c = 55 dollars
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Question:
The square of a number decreased by 3 times the number is 28 find all possible values for the number
Answer:
The possible values of number are 7 and -4
Solution:
Given that the square of a number decreased by 3 times the number is 28
To find: all possible values of number
Let "a" be the unknown number
From given information,
square of a number decreased by 3 times the number = 28
Let us solve the above quadratic equation
Using the above formula,
Thus the possible values of number are 7 and -4
Answer:
For the first one: 2+3(1) = 5
Second one: 5=5
Third one: 1 = -2 + 3
Last one: 1=1
Step-by-step explanation:
Answer:
The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.
Step-by-step explanation:
This is a problem of optimization.
We have to minimize the time it takes for the lifeguard to reach the child.
The time can be calculated by dividing the distance by the speed for each section.
The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.
Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:
Then, the time (speed divided by distance) is:
To optimize this function we have to derive and equal to zero:
![\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\](https://tex.z-dn.net/?f=%5Cdfrac%7Bdt%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B4%7D%2B%5Cdfrac%7B1%7D%7B1.1%7D%28%5Cdfrac%7B1%7D%7B2%7D%29%5Cdfrac%7B2x-120%7D%7B%5Csqrt%7Bx%5E2-120x%2B5200%7D%7D%20%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bdt%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B4%7D%20%2B%5Cdfrac%7B1%7D%7B1.1%7D%20%5Cdfrac%7Bx-60%7D%7B%5Csqrt%7Bx%5E2-120x%2B5200%7D%7D%20%3D0%5C%5C%5C%5C%5C%5C%20%20%5Cdfrac%7Bx-60%7D%7B%5Csqrt%7Bx%5E2-120x%2B5200%7D%7D%20%3D%5Cdfrac%7B1.1%7D%7B4%7D%3D%5Cdfrac%7B2%7D%7B7%7D%5C%5C%5C%5C%5C%5C%20x-60%3D%5Cdfrac%7B2%7D%7B7%7D%5Csqrt%7Bx%5E2-120x%2B5200%7D%5C%5C%5C%5C%5C%5C%28x-60%29%5E2%3D%5Cdfrac%7B2%5E2%7D%7B7%5E2%7D%28x%5E2-120x%2B5200%29%5C%5C%5C%5C%5C%5C%28x-60%29%5E2%3D%5Cdfrac%7B4%7D%7B49%7D%5B%28x-60%29%5E2%2B40%5E2%5D%5C%5C%5C%5C%5C%5C%281-4%2F49%29%28x-60%29%5E2%3D4%2A40%5E2%2F49%3D6400%2F49%5C%5C%5C%5C%2845%2F49%29%28x-60%29%5E2%3D6400%2F49%5C%5C%5C%5C45%28x-60%29%5E2%3D6400%5C%5C%5C%5C)
As 
, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.
Answer:
(a) yes
(b) 1/36
(c) 1/36
(d) 1/18
Step-by-step explanation:
(a) yes they are independent as the outcome of one does not affect the outcome of the other.
(b) As the dice are fair, each possible number (1 through 6) has the same probability of being rolled.
P(1 on green die) = 1/6
P(2 on red die) = 1/6
Therefore, P(1 on green die) AND P(2 on red die) = 1/6 × 1/6 = 1/36
(c) Again, as the dice are fair, each possible number (1 through 6) has the same probability of being rolled.
P(2 on green die) = 1/6
P(1 on red die) = 1/6
Therefore, P(2 on green die) AND P(1 on red die) = 1/6 × 1/6 = 1/36
(d) p[(1 on green die and 2 on red die) OR (2 on green die and 1 on red die)
= 1/36 + 1/36
= 2/36
= 1/18
