The correlation coefficient tells that every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.
Using technology
The mean= x bar = 26.4667
The mean = y bar= 0.86
The standard deviation= Sx= 0.2251
The standard Deviation Sy= 0.0438
The Correlation Coefficient= r = -0.8111
The slope= b= r* Sy/Sx= -0.15789
The intercept is 5.0389
(d)<u><em> Every increase </em></u>in sea <u><em>surface temperature</em></u> of one degree Celsius will result in an average of <em><u>0.1578 fewer</u></em> centimeters of <em><u>coral growth</u></em> per year.
Here the independent variable is X the sea surface temperature and dependent variable is the Y coral growth.
As the temperature decreases which is along x- axis the growth increases along y axis.
From the given options the option d is the best answer according to the question given.
The same values are calculated using different technology .
brainly.com/question/24183059
Answer:
the rate of change of height when the water is 1 meter deep is 21 m/min
Step-by-step explanation:
First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)
here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).
As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:
this can be substituted back in the volume equation
the rate of the water flowing in is:
The question is asking for the rate of change of height (m/min) hence that can be denoted as: 
Using the chainrule:
the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h
reciprocating
plugging everything in the chain rule equation:
L = 12, and h = 1 (when the water is 1m deep)
the rate of change of height when the water is 1 meter deep is 21 m/min
Answer:
-4
Step-by-step explanation:
Answer:
0.0918
Step-by-step explanation:
We know that the average amount of money spent on entertainment is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.
The mean and standard deviation of average spending of sample size 25 are
μxbar=μ=95.25
σxbar=σ/√n=27.32/√25=27.32/5=5.464.
So, the average spending of a sample of 25 randomly-selected professors is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.
The z-score associated with average spending $102.5
Z=[Xbar-μxbar]/σxbar
Z=[102.5-95.25]/5.464
Z=7.25/5.464
Z=1.3269=1.33
We have to find P(Xbar>102.5).
P(Xbar>102.5)=P(Z>1.33)
P(Xbar>102.5)=P(0<Z<∞)-P(0<Z<1.33)
P(Xbar>102.5)=0.5-0.4082
P(Xbar>102.5)=0.0918.
Thus, the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.5 is 0.0918.
The perimeter of the entire rectangle is 12 cm.
