Express 3-2 log 4 as logarithm of single number

Solve for x a 2.2 b 5.4 c 6.5 d 7.2

Reika [66]

Answer:

D

Step-by-step explanation:

Given that the segment is an angle bisector then the ratio of sides and base are equal, that is

$\frac{10}{4}$ = $\frac{18}{x}$ ( cross- multiply )

10x = 72 ( divide both sides by 10 )

x = 7.2 → D

8 0

3 years ago

Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a

notsponge [240]

Answer:

$z=0.842$

And if we solve for a we got

$\mu=13.16 +0.842*3=15.69$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the hourly rates of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,3)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>13.16)=0.20$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$\mu=13.16 +0.842*3=15.69$

3 0

3 years ago

The median of a triangle divides it into two________.

Lelu [443]

The median of a triangle divides it into two equal triangles of equal areas.

Must click thanks and mark brainliest

5 0

3 years ago

A tape diagram. There are 175 Saturday tickets sold out of 100 Friday tickets sold. There are question mark Saturday tickets sol

ASHA 777 [7]

Answer:

the answer is 3,500

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Simplify the following surds : 1) 2√21 × √27 ÷ √343 2) 7√5 × √125 ÷ 2√27

ludmilkaskok [199]

Answer:

1) $\frac{18}{7}$

2) $\frac{175\sqrt{3}}{18}$

Step-by-step explanation:

* Lets explain how to simplify a square root

1)

∵ $2\sqrt{21}$ × $\sqrt{27}$ ÷ $\sqrt{343}$

∵ $\sqrt{21}=\sqrt{3}$ × $\sqrt{7}$

∴ $2\sqrt{21}$ = $2\sqrt{3}$ × $\sqrt{7}$

∵ $\sqrt{27}$ = $\sqrt{3}$ × $\sqrt{3}$ × $\sqrt{3}$

∵ $\sqrt{3}$ × $\sqrt{3}$ = 3

∴ $\sqrt{27}$ = $3\sqrt{3}$

∴ $2\sqrt{21}$ × $\sqrt{27}$ =

$2\sqrt{3}$ × $\sqrt{7}$ × $3\sqrt{3}$

∵ $\sqrt{3}$ × $\sqrt{3}$ = 3

∵ 2 × 3 × 3 = 18

∴ $2\sqrt{21}$ × $\sqrt{27}$ = $18\sqrt{7}$

∵ $\sqrt{343}$ = $\sqrt{7}$ × $\sqrt{7}$ × $\sqrt{7}$

∵ $\sqrt{7}$ × $\sqrt{7}$ = 7

∴ $\sqrt{343}$ = $7\sqrt{7}$

∵ $2\sqrt{21}$ × $\sqrt{27}$ ÷ $\sqrt{343}$ =

$18\sqrt{7}$ ÷ $7\sqrt{7}$

∵ $\sqrt{7}$ ÷ $\sqrt{7}$ = 1

∴ $2\sqrt{21}$ × $\sqrt{27}$ ÷ $\sqrt{343}$ =

$\frac{18}{7}$

2)

∵ $7\sqrt{5}$ × $\sqrt{125}$ ÷ $2\sqrt{27}$

∵ $\sqrt{125}$ = $\sqrt{5}$ × $\sqrt{5}$ × $\sqrt{5}$

∵ $\sqrt{5}$ × $\sqrt{5}$ = 5

∴ $\sqrt{125}$ = $5\sqrt{5}$

∴ $7\sqrt{5}$ × $\sqrt{125}$ =

$7\sqrt{5}$ × $5\sqrt{5}$

∵ $\sqrt{5}$ × $\sqrt{5}$ = 5

∴ $7\sqrt{5}$ × $\sqrt{125}$ = 7 × 5 × 5 = 175

∵ $2\sqrt{27}$ = $2\sqrt{3}$ × $\sqrt{3}$ × $\sqrt{3}$

∵ $\sqrt{3}$ × $\sqrt{3}$ = 3

∴ $2\sqrt{27}$ = $6\sqrt{3}$

∴ $7\sqrt{5}$ × $\sqrt{125}$ ÷ $2\sqrt{27}$ =

175 ÷ $6\sqrt{3}$ = $\frac{175}{6\sqrt{3}}$

∵ $\frac{175}{6\sqrt{3}}$ not in the simplest form because

the denominator has square root

∴ Multiply up and down by $\sqrt{3}$

∴ $\frac{175}{6\sqrt{3}}$ = $\frac{175\sqrt{3}}{6\sqrt{3}*\sqrt{3}}$

∴ $\frac{175}{6\sqrt{3}}$ = $\frac{175\sqrt{3}}{18}$

∴ $7\sqrt{5}$ × $\sqrt{125}$ ÷ $2\sqrt{27}$ =

$\frac{175\sqrt{3}}{18}$

7 0

3 years ago