Answer:
37
Step-by-step explanation:
The first thing is to calculate critical z factor
the alpha and the critical z score for a confidence level of 90% is calculated as follows:
two sided alpha = (100% - 90%) / 200 = 0.05
critical z factor for two sided alpha of .05 is calculated as follows:
critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:
critical z factor = 2.58
Now we have the following formula:
ME = z * (sd / sqrt (N) ^ (1/2))
where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58
N the sample size and we want to know it, replacing:
6 = 2.58 * (14 / (N) ^ (1/2))
solving for N we have:
N = (2.58 * 14/6) ^ 2
N = 36.24
Which means that the sample size was 37.
Answer:
Step-by-step explanation:
Yes, it's reasonable.
What you are doing is solving the question by rounding. You come up with an answer. Suppose you loose the decimal somewhere and you get 0.36? Is that reasonable? Do you just write the answer in the provided blank and move on. What now?
You get it wrong?!!
But your estimate should be about 9/3 = 3. Now you look at your calculator with great misgivings, because it made a mistake. Did it or did you? Well ultimately you did, but you have to blame something. So the calculator takes the heat.
Who knows? Maybe the decimal doesn't work. It's stuck or something. In any event you should be aware that there's no way the answer could be 0.36 when you estimate it to be 3.
Domain means the values of independent variable(input) which will give defined output to the function.
Given:
The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function
Solution:
To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.
![To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)](https://tex.z-dn.net/?f=%20To%20%5C%3B%20find%20%5C%3B%20domain%3A%5C%5C%5C%5Ch%28t%29%20%5Cgeq0%5C%5C%5C%5C-16t%5E2%2B96t%20%5Cgeq%20%200%5C%5CFactoring%20%5C%3B%20-16t%20%5C%3B%20in%20%5C%3B%20the%20%5C%3B%20left%20%5C%3B%20side%20%5C%3B%20of%20%5C%3B%20the%20%5C%3B%20inequality%5C%5C%5C%5C-16t%28t-6%29%20%5Cgeq%20%200%5C%5CStep%20%5C%3B%201%3A%20Find%20%5C%3B%20Boundary%20%5C%3B%20Points%20%5C%3B%20by%20%5C%3B%20setting%20%5C%3B%20up%20%5C%3B%20above%20%5C%3B%20inequality%20%5C%3B%20to%20%5C%3B%20zero.%5C%5C%5C%5Ct%28t-6%29%3D0%5C%5CUse%20%5C%3B%20zero%20%5C%3B%20factor%20%5C%3B%20property%20%5C%3B%20to%20%5C%3B%20solve%5C%5C%5C%5Ct%3D0%20%5C%3B%20%28or%29%20%5C%3B%20t%20%3D%206%5C%5C%5C%5CStep%20%5C%3B%202%3A%20%5C%3B%20List%20%5C%3B%20the%20%5C%3B%20possible%20%20%5C%3B%20solution%20%5C%3B%20interval%20%5C%3B%20using%20%5C%3B%20boundary%20%5C%3B%20points%5C%5C%28-%20%5Cinfty%2C0%5D%2C%20%5C%3B%20%5B0%2C%206%5D%2C%20%5C%26%20%5B6%2C%20%5Cinfty%29%20)
![Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution](https://tex.z-dn.net/?f=%20Step%20%5C%3B%203%3APick%20%5C%3B%20test%20%5C%3B%20point%20%5C%3B%20from%20%5C%3B%20each%20%5C%3B%20interval%20%5C%3B%20to%20%5C%3B%20check%20%5C%3B%20whether%20%5C%5C%5C%3B%20makes%20%5C%3B%20the%20%5C%3B%20inequality%20%5C%3B%20TRUE%20%5C%3B%20or%20%5C%3B%20FALSE%5C%5C%5C%5CWhen%20%5C%3B%20t%20%3D%20-1%5C%5C-16%28-1%29%28-1-6%29%20%5Cgeq%20%200%5C%5C-112%20%5Cgeq%20%200%20%5C%3B%20FALSE%5C%5C%28-%5Cinfty%2C%200%5D%20%5C%3B%20is%20%5C%3B%20not%20%5C%3B%20solution%5C%5CAlso%20%5C%3B%20Logically%20%5C%3B%20time%20%5C%3B%20t%20%5C%3B%20cannot%20%5C%3B%20be%20%5C%3B%20negative%5C%5C%5C%5CWhen%20%5C%3B%20t%20%3D%201%5C%5C-16%281%29%281-6%29%20%5Cgeq%20%200%5C%5C80%20%5Cgeq%20%200%20%5C%3B%20TRUE%5C%5C%20%5C%3B%20%5B0%2C%206%5D%20%5C%3B%20is%20%5C%3B%20a%20%5C%3B%20solution%5C%5C%5C%5CWhen%20%5C%3B%20t%20%3D%207%5C%5C-16%287%29%287-6%29%20%5Cgeq%20%200%5C%5C-112%20%5Cgeq%20%200%20%5C%3B%20FALSE%5C%5C%20%5C%3B%20%5B6%2C%20-%5Cinfty%29%20%5C%3B%20is%20%5C%3B%20not%20%5C%3B%20solution%20)
Conclusion:
The domain of the function is the time in between 0 to 6 seconds
The height will be positive in the above interval.
For a.
Since there are already two angles given for the triangle, we can measure the last angle using this formula:
90 + 55 + a = 180
Now solve for "a".
90 + 55 + a = 180
145 + a = 180
a = 180 - 145
a = 35°
For b.
From the picture above, the two triangle's tip are touching and having to form <em>vertical angles. </em>This means that the angles are congruent to each other.
Now that we have two angles in the second triangle(35 and 120), we can use the same formula:
35 + 120 + b = 180
Now solve for "b":
35 + 120 + b = 180
155 + b = 180
b = 180 - 155
b = 25°
Answer:
What's the question?
Step-by-step explanation:
342 is the product of q and 214
