Answer:
The equation of the line is y = 4x + 13
Step-by-step explanation:
In this question, we want to write the equation of the line using the point slope form.
Mathematically, the point slope form can be represented as;
(y-y1) = m(x - x1)
where x1 = -2 , y1 = 5 and m which is the slope is 4
Plugging these values into the equation, we have;
(y-5) = 4(x - (-2))
y-5 = 4(x + 2)
y -5 = 4x + 8
y = 4x + 8 + 5
y = 4x + 13
Answer:
a. V = (20-x)
b . 1185.185
Step-by-step explanation:
Given that:
- The height: 20 - x (in )
- Let x be the length of a side of the base of the box (x>0)
a. Write a polynomial function in factored form modeling the volume V of the box.
As we know that, this is a rectangular box has a square base so the Volume of it is:
V = h *
<=> V = (20-x)
b. What is the maximum possible volume of the box?
To maximum the volume of it, we need to use first derivative of the volume.
<=> dV / Dx = -3 + 40x
Let dV / Dx = 0, we have:
-3 + 40x = 0
<=> x = 40/3
=>the height h = 20/3
So the maximum possible volume of the box is:
V = 20/3 * 40/3 *40/3
= 1185.185
Answer:
(b) 0.30 atm
Step-by-step explanation:
Given data
Initial pressure= 1.2atm
Initial volume= 1.0L
Final volume= 4.0L
Final pressure= ???
Let us apply the gas formula to find the Final pressure
P1V1= P2V2
Substitute
1.2*1= x*4
Divide both sides by 4
1.2/4= x
x= 0.3atm
Hence the final pressure is 0.3 atm
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 5000
For the alternative hypothesis,
H1: µ > 5000
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5000
x = 5430
σ = 600
n = 40
z = (5430 - 5000)/(600/√40) = 4.53
Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001
Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.