Answer: 0.2742531
Step-by-step explanation:
Let x denote the random variable that represents the driving times.
As per given we have,
![\mu = 38](https://tex.z-dn.net/?f=%5Cmu%20%3D%2038)
![\sigma = 5](https://tex.z-dn.net/?f=%5Csigma%20%3D%205)
Z-score value corresponds to x= 35,
![z=\dfrac{x-\mu}{\sigma}=\dfrac{35-38}{5}=-0.6](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cdfrac%7B35-38%7D%7B5%7D%3D-0.6)
Using z-value table ,
The probability that John’s drive to work will take less than 35 minutes:-
P(X<35)=P(z<-0.6)=1-P(z<0.6)=1-0.7257469=0.2742531
hence, the required probability = 0.2742531
a)
If the triangles are similar, the corresponding sides vary on the same proportion, so the ratios between the corresponding sides are equal.
For
![\frac{x}{20}=\frac{12}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B12%7D%7B16%7D)
To solve for x you have to multiply both sides of the expression by 20
![\begin{gathered} \frac{20x}{20}=(\frac{12}{16})\cdot20 \\ x=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B20x%7D%7B20%7D%3D%28%5Cfrac%7B12%7D%7B16%7D%29%5Ccdot20%20%5C%5C%20x%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5Ccdot20%20%5C%5C%20x%3D15%20%5Cend%7Bgathered%7D)
b)
Following the same logic, the ratio between x and 20 is the same as the ratio between 6 and 8
![\frac{x}{20}=\frac{6}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B6%7D%7B8%7D)
6/8 can be simplifies as 3/4. Then multiply both sides by 20 to determine the value of x.
![\begin{gathered} \frac{x}{20}=\frac{6}{8} \\ 20\cdot\frac{x}{20}=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B6%7D%7B8%7D%20%5C%5C%2020%5Ccdot%5Cfrac%7Bx%7D%7B20%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5Ccdot20%20%5C%5C%20x%3D15%20%5Cend%7Bgathered%7D)
As mentioned above, when two triangles are similar, the corresponding sides are always in the same ratio, that is why the results in a and b are the same.
The second box/whisker plot is correct.
First we have to put he data set in ascending order:
16, 17, 18, 20, 21, 22, 23, 25
The median (middle number or average of 2 middle numbers) = 20.5 The center line of the box needs to be at 20.5
The middle of the first half of the data is 17.5, (average of 17 & 18) so the left side of the box needs to be at 17.5
The middle of the second half of the data is 22.5, (average of 22 & 23), so the right side of the box needs to be at 22.5.
The “whiskers” are your bottom & top numbers...representing the full range of data. They should be at 16 & 25.
You would divide $29 by 7 batteries to get the price per battery.
29/7 = $4.14 per battery ..
! Check Your Work !
4.14 * 7 = $28.98
round 28.98 to the nearest tenth to get $29.00 even. Hope this helps!! :)
Answer:
The value of Liam's investment at the end of 4 years is £9069.764
Step-by-step explanation:
Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods of an investment.
We multiply the principal amount by one plus the annual interest rate to the power of the number of compound periods to get a combined figure for principal and compound interest.
4.5% in the first year;
4.5/100 = 0.045
(1 + 0.045) × 8000 =
1.045 × 8000 = £8360.
2.75% for all subsequent year;
2.75/100 = 0.0275
1 + 0.0275=1.0275
Number of years is;
4-1=3years
Therefore,
8360 × (1.0275)^3 =
8360 × 1.0849 = £9069.764