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Lerok [7]
3 years ago
15

What is the value of x in the equation (5^x)^5=5^35

Mathematics
1 answer:
Arada [10]3 years ago
6 0

\bf (5^x)^5=5^{35}\implies 5^{x\cdot 5}=5^{35}\impliedby \begin{array}{llll} \textit{same bases}\\ \textit{same exponents} \end{array}\implies 5x = 35 \\\\\\ x = \cfrac{35}{5}\implies x=7

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An athlete plains to run 3 miles. Each lap around th school yard is 3/7 miles how many laps will the athlete run
kati45 [8]

Answer: 7 laps

Step-by-step explanation:

The athlete planned to run 3 miles

1 lap = 3/7 miles

x laps = 3 miles

by proportion :

x × 3/7miles = 3 miles

x = 3 ÷ 3/7

x = 3 x 7/3

x = 7

Therefore: the athlete will run 7 laps

3 0
3 years ago
Chase consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Chase's body
PIT_PIT [208]

Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

(c) The amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720

(a)

Compute the 5-hour decay factor as follows:

5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720

Thus, the 1-hour decay factor is 0.8720.

(c)

The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)<em>ⁿ</em>

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

4 0
3 years ago
What is the area of this figure
konstantin123 [22]

Answer:

108

Step-by-step explanation:

add all of the numbers together and thats what you get :)

4 0
2 years ago
Find last​ year's salary​ if, after a 4 % pay​ raise, this​ year's salary is $ 33,280.
son4ous [18]

Answer: 31,948.80

Step-by-step explanation: I thin it his is correct. I multiplied the original amount by .04 then subtracted that from the original number.

6 0
3 years ago
What is x divided by 7=9?
Arturiano [62]
Multiply 7 by 9 and you will get 63 which is x.
3 0
3 years ago
Read 2 more answers
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