Simplify Exponential Expression: <br><br> 3= 27

PLEASE HELP ASAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER

mote1985 [20]

Answer:

c x = 10/3

Step-by-step explanation:

log (3x) =1

Take each side to 10 to the power. That will get rid of the base 10 log

10 ^(log (3x)) =10^1

3x = 10

Divide by 3

3x/3 = 10/3

x = 10/3

4 0

3 years ago

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Please help with ratios of the area of triangles.....thank you

harkovskaia [24]

Answer:

Part 1) The ratio of the areas of triangle TOS to triangle TQR is $\frac{4}{25}$

Part 2) The ratio of the areas of triangle TOS to triangle QOP is $\frac{4}{9}$

Step-by-step explanation:

Part 1) Find the ratio of the areas of triangle TOS to triangle TQR

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

The scale factor is equal to

TS/TR

substitute the values

6/(6+9)

6/15=2/5

step 2

Find the ratio of the areas of triangle TOS to triangle TQR

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

$(\frac{2}{5})^{2}=\frac{4}{25}$

Part 2) Find the ratio of the areas of triangle TOS to triangle QOP

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

The scale factor is equal to

TS/QP

substitute the values

6/9

6/9=2/3

step 2

Find the ratio of the areas of triangle TOS to triangle QOP

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

$(\frac{2}{3})^{2}=\frac{4}{9}$

4 0

3 years ago

Find the derivative u(x)=4\3x-1

amid [387]

The answer is X=3/4.

6 0

4 years ago

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Your friend approaches with three, fair 5-sided dice (labeled 1 to 5). You get to roll them and your friend gives you money base

k0ka [10]

Answer:

$1.68 per match

Average Fee = $1.69

Step-by-step explanation:

Given:

- Earnings for all 3 different number = $ 1

- Earnings for 2 same number = $ 2

- Earnings for 3 same number = $ 6

- Five sided fair dice = 3

Find:

- Expected pay-out

- What fee charged per match for 10 cent income

- Reason for change to new match

Solution:

- Construct a probability distribution table, where X: payout per match

X $1 $2 $6

P(X) 0.48 0.48 0.04

Case X = $1 : _ _ _ All three different numbers

No.outcomes 5 * 4 * 3 = 60

Total outcome 5 * 5 * 5 = 125

Hence, P(X= $ 1) = 60 / 125 = 0.48

Case X = $2 : S _ S two numbers are same

No.outcomes = 5 * 4 * 1 = 20 per combination

Total combinations = S _ S + S S _ + _ S S = 3

Total outcome = 3 * 20 = 60

Hence, P(X= $ 2) = 60 / 125 = 0.48

Case X = $6 : S S S two numbers are same

No.outcomes = 5 * 1 * 1 = 5 per combination

Total combinations = 1

Total outcome = 5 * 1 = 5

Hence, P(X= $ 2) = 5 / 125 = 0.04

- Expected Payout E(X):

E(X) = 1*0.48 + 2*0.48 + 6*0.04 = $1.68 per match

- To earn $0.01 on average the fee of match is:

Fee_avg = E(X) + $0.01 = $1.69

- With this new plan your friend would loose less. The expected payout of a match is $1.68 for which the probability X < $ 2 is around = 0.48. However, to gain a $2 or higher P ( X > 2 ) = 0.48 + 0.04 = 0.52. Hence, the week-payout for X > 2 is greater than 7*2 = $14. So probability of week's payout to be $14 is higher than to be $ 11.76 as per average pay per day.

7 0

4 years ago

A bag with 6 marbles has 1 blue marble and 5 yellow marbles. A marble is chosen from the bag at random. What is the probability

almond37 [142]

Answer:

0% because there isn't Red marbles

7 0

2 years ago

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Simplify Exponential Expression: 3= 27