Answer:
Let fertilizer be F
and peat moss be P
since F is proportional to P
F = kP
where, k = constant of proportionality
k = F/P
putting in the values,
k = (3/4) /12
k = 3/4 * 1/12
k = 1/16
Therefore the constant of proportionality is 1/16.
Answer:
108 units
Step-by-step explanation:
We are given that
Length of each office,l=10 units
Breadth of each office=b=8 units
Total number of office=3
We know that
Perimeter of rectangle=
Using the formula
Length of cable for 1 office=
Length of cable required for 3 offices=units
Hence, the required length of cable=108 units
and intersect
AD
at point M. Find the area of ΔBDM. What is the area of ABCD?
The diagram is attached below
The midpoint of AC is E. The ΔMAE is congruent to ΔBCE, and the sides MA = BC = 5 cm. Also MD = 17 -5 = 12 cm
From the figure we can see that the height of the trapezoid is 8cm
The height of trapezoid is the difference between the x axis and the BC that is 8cm
The triangle BDM has base 12 cm and height 8 cm.
Area of triangle =
A = = 48 cm²
2. The area of trapezoid ABCD formula is
A =
base 1= 17cm , base2= 5cm , height = 8cm
A =
A = 88 cm²
Answer:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
0.00885... < 0.01
The test statistic of 46 is significant
There is sufficient evidence to reject H₀ and accept H₁
Air bags are more effective as protection than safety belts
Step-by-step explanation:
821 crashes
46 hospitalisations where car has air bags
7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts
α = 0.01 or 1% ← level of significance
One-tailed test
We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;
The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;
So we are testing if hospitalisations in cars with air bags is less than 0.078;
So, firstly:
Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags
X~B(821, 0.078)
Null hypothesis (H₀): p = 0.078
Alternative hypothesis (H₁): p < 0.078
According to the information, we reject H₀ if:
P(X ≤ 46 | X~B(821, 0.078)) < 0.01
To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;
If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:
You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
Now, we need to consider if the condition for rejecting H₀ is met and recognise that:
0.00885... < 0.01
There is sufficient evidence to reject H₀ and accept H₁.
To explain what this means:
The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;
In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.
Answer:
I don't know the answer but I know the formula. Its I=prt
Step-by-step explanation:
Intrerest= principle amount, rate, and time.
Hope this helps!! :)