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yanalaym [24]
3 years ago
6

Rewrite the expression with the given base. 25^3x with a base of 5

Mathematics
2 answers:
spin [16.1K]3 years ago
6 0
\bf 25=5^2\qquad \qquad 25^{3x}\implies (5^2)^{3x}\implies 5^{2\cdot 3x}\implies 5^{6x}
blondinia [14]3 years ago
5 0
Use\ (a^n)^m=a^{nm}\\\\25^{3x}=(5^2)^{3x}=5^{2\cdot3x}=5^{6x}
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In order for two lines to be perpendicular, their gradients must multiply together to get -1

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if the humpback whales had traveled at the same rate for 32 days,how many more miles would the have traveled than the grey whale
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Answer:

192 miles more than the gray whales.

Step-by-step explanation:

first, get the rate of each whale per day. To put it in simpler terms, divide 2,240 miles by 28 to find how much the humpback whales travel in a day. next, do the same for the gray whales. I got that the humpback whales traveled 80 miles in a day and the gray whales traveled 74 in a day. Multiply 80 miles by 32 days to get the distance the humpback whales travel in 32 days (2,560 miles). Since you know the distance the Gray whales traveled in 32 days, you do not need to solve for it. Subtract 2,560-2,368 and you get 192 miles.


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The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (according to GolfWeek). Assume th
Usimov [2.4K]

Answer:

a) f(x) = \frac{1}{25.9}

b) 0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

P(X < x) = \frac{x - a}{b - a}

The probability of finding a value between c and d is:

P(c \leq X \leq d) = \frac{d - c}{b - a}

The probability of finding a value above x is:

P(X > x) = \frac{b - x}{b - a}

The probability density function of the uniform distribution is:

f(x) = \frac{1}{b-a}

The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards.

This means that a = 284.7, b = 310.6.

a. Give a mathematical expression for the probability density function of driving distance.

f(x) = \frac{1}{b-a} = \frac{1}{310.6-284.7} = \frac{1}{25.9}

b. What is the probability the driving distance for one of these golfers is less than 290 yards?

P(X < 290) = \frac{290 - 284.7}{310.6-284.7} = 0.2046

0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards

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