Answer:
![A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153](https://tex.z-dn.net/?f=%20A%20%3D%201986%281%2B%20%5Cfrac%7B0.063%7D%7B12%7D%29%5E%7B12%2A8%7D%20%3D3283.153)
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
![I = 3283.153 -1986 = 1297.153](https://tex.z-dn.net/?f=%20I%20%3D%203283.153%20-1986%20%3D%201297.153)
Step-by-step explanation:
For this case we can use the formula for the future value using compound interest given by:
![A = P (1+ \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=%20A%20%3D%20P%20%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where P= 1986 the initial amount invested. r = 0.063 represent the interest rate. n=12 represent the number of times that the rate is compounded in a year. And t =8 years . Replacing the info we got:
![A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153](https://tex.z-dn.net/?f=%20A%20%3D%201986%281%2B%20%5Cfrac%7B0.063%7D%7B12%7D%29%5E%7B12%2A8%7D%20%3D3283.153)
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
![I = 3283.153 -1986 = 1297.153](https://tex.z-dn.net/?f=%20I%20%3D%203283.153%20-1986%20%3D%201297.153)
Answer:
Todd's Z-score is - 0.27
Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>Step(i)</em></u>:-
Given data A test is normally distributed with a mean of 70 and a standard deviation of 10.
<em>Mean of the population 'μ' = 70 </em>
<em>Standard deviation of the Population ' σ ' = 10</em>
<em>let 'x' be the random variable in normally distributed</em>
<u><em>Step(ii)</em></u>:-
<em>Given raw score 'x' = 55</em>
Todd's Z-score
![Z = \frac{x-mean}{S.D}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx-mean%7D%7BS.D%7D)
![Z = \frac{55-70}{55}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B55-70%7D%7B55%7D)
Z = -0.27
<u><em>Final answer</em></u>:-
<em>Todd's Z-score is - 0.27 </em>
Answer:11
Step-by-step explanation:Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*(x-5)-(18)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
3 • (x - 5) - 18 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
3x - 33 = 3 • (x - 11)
Equation at the end of step
3
:
3 • (x - 11) = 0
STEP
4
:
Equations which are never true:
4.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.2 Solve : x-11 = 0
Add 11 to both sides of the equation :
x = 11
One solution was found :
x = 11
Answer: 665,640 minutes
Step-by-step explanation:
Dimensional analysis: dividing out common units like dividing out common factors
<em>For ex: </em>3/5* 5/7= 3/7
cross out the fives and turn them into 1
For dimensional analysis you just cross out the units.
days-->hours-->minutes
462.25d/1* 24h/1d* 60m/1h= 665,640 minutes
Cross out the d's and h's.
You are left with minutes on the top and no units on bottom.
Just multiply across to get the answer 665,640 minutes
Answer:
<em>Option B</em>
Step-by-step explanation:
<u>Congruent Triangles</u>
The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both triangles are congruent, then the two triangles are similar.
The triangles
are congruent if the relation between LK and KN is the same as the relation between KN and MN, that is
![\displaystyle \frac{4}{2}=\frac{2}{MN}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B4%7D%7B2%7D%3D%5Cfrac%7B2%7D%7BMN%7D)
It means that
MN=1
Option B