It takes Bob 3 hours and 30 minutes to drive from Albuquerque to Las cruises which is 360 km away?

Find the missing lengths: HI=7 and LH=9, find LK.

Katarina [22]

Answer:

LK=12

Step-by-step explanation:

From the given figure, HI=7 and LH=9, and we know that

$(KH)^{2}=(IH)(HL)$

$(KH)^{2}=7{\times}9$

$(KH)^{2}=63$ (1)

Now, from ΔKHL, we have

$(OH)^{2}=(OK)(OL)$

and from ΔOKH,

$(KH)^{2}=(OH)^{2}+(OK)^2$

$(OK)^2=(KH)^2-(OH)^2$

$(OK)^2=63-(OK)(OL)$

$(OK)^2+(OK)(OL)=63$

$OK(OK+OL)=63$

$OK(KL)=63$ (2)

Also, ΔIKL is similar to ΔOHL, therefore

$\frac{OL}{KL}=\frac{9}{16}$

$\frac{KL-OK}{KL}=\frac{9}{16}$

$1-\frac{OK}{KL}=\frac{9}{16}$

$\frac{7}{16}=\frac{OK}{KL}$

Using equation (2), we get

$\frac{7}{16}=\frac{63}{(KL)^2}$

$(KL)^2=\frac{1008}{7}$

$(KL)^2=144$

$KL=12$

Thus, the value of LK is 12.

8 0

3 years ago

A store pays $450 for a computer the markup is 20%. Find the amount of the markup

nalin [4]

Answer:

The amount of the markup is $90

Step-by-step explanation:

20% of 450 = 90

7 0

2 years ago

What is -7 – 4 – (-6)

Temka [501]

Answer:

-5

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

The average number of minutes Americans commute to work is 27.7 minutes. The average commute time in minutes for 48 cities are a

dolphi86 [110]

Answer:

a) $\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X = 27.2$

b) For this case we have n =48 observations and we can calculate the median with the average between the 24th and 25th values on the dataset ordered.

20.4 20.4 20.5 21.7 22.3 23.3 23.6 23.7 23.7 23.7 23.9 23.9 24.1 24.3 24.7 24.9 25.1 25.1 25.1 25.2 25.3 25.6 26.1 26.1 26.4 26.5 26.7 27.1 27.1 27.4 27.6 28.4 28.6 28.6 28.7 28.8 28.8 29.6 31.0 32.0 32.0 32.4 32.5 32.9 33.1 34.5 38.4 44.1

For this case the median would be:

$Median = \frac{26.1+26.4}{2}=26.25 \approx 26.3$

c) $Mode= 23.2, 25.1$

And both with a frequency of 3 so then we have a bimodal distribution for this case

Step-by-step explanation:

For this case we have the following dataset:

23.6, 26.5, 28.6, 28.6, 23.7, 25.3, 24.9, 28.7, 26.7, 32.4, 20.4, 23.9, 32.0, 32.5, 23.7, 26.1, 21.7, 26.1, 38.4, 24.1, 20.5, 25.2, 31, 26.4, 27.1 ,25.1, 25.1, 23.7, 23.9, 32.9, 28.8, 25.6, 28.8, 28.4, 32, 27.6, 29.6, 44.1, 27.1, 24.7, 22.3, 24.3, 23.3, 27.4, 20.4, 25.1, 34.5, 33.1

Part a

We can calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X = 27.2$

Part b

For this case we have n =48 observations and we can calculate the median with the average between the 24th and 25th values on the dataset ordered.

20.4 20.4 20.5 21.7 22.3 23.3 23.6 23.7 23.7 23.7 23.9 23.9 24.1 24.3 24.7 24.9 25.1 25.1 25.1 25.2 25.3 25.6 26.1 26.1 26.4 26.5 26.7 27.1 27.1 27.4 27.6 28.4 28.6 28.6 28.7 28.8 28.8 29.6 31.0 32.0 32.0 32.4 32.5 32.9 33.1 34.5 38.4 44.1

For this case the median would be:

$Median = \frac{26.1+26.4}{2}=26.25 \approx 26.3$

Part c

For this case the mode would be:

$Mode= 23.2, 25.1$

And both with a frequency of 3 so then we have a bimodal distribution for this case

4 0

3 years ago

What's the answer to 4x + 6 = 2 ( 3x - 4 )

Tcecarenko [31]

4x+6=2(3x−4)

Step 1: Simplify both sides of the equation.
4x+6=2(3x−4)

4x+6=(2)(3x)+(2)(−4)(Distribute)
4x+6=6x+−8

4x+6=6x−8

Step 2: Subtract 6x from both sides.
4x+6−6x=6x−8−6x

−2x+6=−8

Step 3: Subtract 6 from both sides.
−2x+6−6=−8−6

−2x=−14

Step 4: Divide both sides by -2.
−2x−2=−14−2

x=7

8 0

3 years ago

Read 2 more answers

It takes Bob 3 hours and 30 minutes to drive from Albuquerque to Las cruises which is 360 km away?​

It takes Bob 3 hours and 30 minutes to drive from Albuquerque to Las cruises which is 360 km away?