Scores are {72, 97, 82, x} where x is the unknown fourth score
They add up to 72+97+82+x = x+251
Divide this sum over four because there are four scores we want to average out. We end up with (x+251)/4 = M where M is the mean. Asa wants the mean to be 82, so make M = 82.
We can replace M with 82 and solve for x like so
(x+251)/4 = M
(x+251)/4 = 82
x+251 = 4*82
x+251 = 328
x = 328-251
x = 77
Asa needs a score of 77 on the fourth test so that the mean of the four tests is 82. If she scores higher than 77 on the fourth test, then the mean will be larger than 82.
-----------------------------------
Depending on what your teacher is looking for, the first step is to establish your variable. So you would say "let x = fourth score". However, that seems too easy. So perhaps your teacher is looking for the equation (x+251)/4 = 82 or some variant of it.
Answer: 28.33 Celsius and 301.483 Kelvin
83°F − 32) × 5/9 = 28.333°C
(83°F − 32) × 5/9 + 273.15 = 301.483K
a. The velocity t = 
b. v60 = 7164
<h3>How to solve for the velocity</h3>
mdv/dt = ck - mg
dv/dt = ck/m - mg/m
= ck/m - g
dv = 
Integrate the two sides of the equation to get
v 

b. fuel accounts for 55% of the mass
So final mass after fuel is burned out is = 0.45
c=2500
g=9.8
t=60
v = -2500ln0.45 - 9.8 x 60
= 7752 - 588
= 7164
<h3>Complete question</h3>
A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation where g is the acceleration due to gravity.
dv dt m =ck - mg
(a) Find v(t) keeping in mind that the mass m is a function of t.
v(t) =
m/sec
(b) Suppose that the fuel accounts for 55% of the initial mass of the rocket and that all of the fuel is consumed at 60 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]
v(60) =
m/sec [Round to nearest whole number]
Raed more on velocity here
brainly.com/question/25749514
#SPJ1
Answer: 24 and 37
Step-by-step explanation:
Let the numbers be x and y . Also let us pick x as the larger number.
From the first statement :
x + y = 61 ............................ equation 1
From the second statement :
x = y + 13 ............................equation 2
Solving the resulting linear equations by substitution method, substitute x = y + 13 into equation 1, then
x + y = 61 becomes
y + 13 + y = 61
2y + 13 = 61
2y = 48
y = 24
Substitute y = 24 into equation 2 , then
x = y + 3 becomes
x = 24 + 13
x = 37
Therefore the numbers are 24 and 37
I’m not 100% but l’ll say go for D