(3x+2)+(4x+1)+(2x+1)=180
9x+4=180
9x = 45
X= 5
Answer: z < 36
Step-by-step explanation: To solve for <em>z</em> in this inequality, we multiply by 12 on both sides of the inequality to get <em>z < 36</em>.
We can write this in set notation as {z: z < 36}.
The volume of cone B is twice the volume of cone A.
Explanation:
For cone A,
Radius (r)= 2m
Height (h) = 3m
Volume of cone A (V1) = 1/3 Pi r^2 *h
=1/3 * 22/7 * 2^2 *3
=264/21
=88/7
=12.571,,
For cone B,
r= 2m
h= 6m
Volume of cone B (V2) = 1/3 Pi r^2*h
=1/3 * 22/7 * 2^2 * 6
=528/21
=176/7
=25.142,,
It is seen that,
V2= 2*V1
25.142 = 2*12.571
25.142 = 25.142, which is true.
Answer:
The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of
. So we have T = 1.7531
The margin of error is:
![M = T\frac{s}{\sqrt{n}} = 1.7531\frac{0.78}{\sqrt{16}} = 0.34](https://tex.z-dn.net/?f=M%20%3D%20T%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%201.7531%5Cfrac%7B0.78%7D%7B%5Csqrt%7B16%7D%7D%20%3D%200.34)
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 23.29 - 0.34 = 22.95 mpg
The upper end of the interval is the sample mean added to M. So it is 23.29 + 0.34 = 23.63 mpg
The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.
Answer:
BC = 15.01
Step-by-step explanation:
Solve this question using a trigonometry ratio, which you can remember them all with SohCahToa, which says:
sinθ = opp / hyp
cosθ = adj / hyp
tanθ = opp / adj
θ means the "angle of reference" (angle we are talking about).
In this problem, θ is A = 65°,
To decide which trig. ratio to use, find out which sides we want to use. We will use AC = 7 because we know it.
We also use BC because we need to find it.
In relation to ∠A or θ, <u>AC is adjacent</u> and <u>BC is opposite</u>.
The ratio with adjacent and opposite is tangent.
tanθ = opp / adj Substitute the variables for this question
tanA = BC / AC Substitute the values you know
tan65° = BC / 7 Rearrange this and isolate C
BC = 7tan65° Multiply 7 and tan65 to find the missing side
BC = 15.011548...... Exact answer on your calculator
BC ≈ 15.01 Round to nearest hundredth