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Alik [6]
2 years ago
10

Rewrite e^{x}= y into logarithmic form.

Mathematics
1 answer:
Aleksandr-060686 [28]2 years ago
6 0

Answer:

x=\ln{y}

Step-by-step explanation:

The natural logarithm function is the inverse of the natural exponential function.  

\text{power}=\text{base}^{\text{exponent}}\\\\\text{exponent} \: =\: \log_\text{base}{\text{power}

are equivalent.

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The proportion of households in a region that do some or all of their banking on the Internet is 0.31. In a random sample of 100
Alenkasestr [34]

Answer:

Approximate probability that the number of households that use the Internet for banking in a sample of 1000 is less than or equal to 130 is less than 0.0005% .

Step-by-step explanation:

We are given that let X be the number that do some or all of their banking on the Internet.

Also; Mean, \mu = 310/1000 or 0.31   and  Standard deviation, \sigma = 14.63/1000 = 0.01463 .

We know that Z = \frac{X-\mu}{\sigma} ~ N(0,1)

Probability that the number of households that use the Internet for banking in a sample of 1000 is less than or equal to 130 is given by P(X <= 130/1000);

 P(X <=0.13) = P( \frac{X-\mu}{\sigma}  <= \frac{0.13-0.31}{0.01463} ) = P(Z <= -12.303) = P(Z > 12.303)

Since this value is not represented in the z table as the value is very high and z table is limited to x = 4.4172.

So, after seeing the table we can say that this probability is approximately less than 0.0005% .

4 0
3 years ago
Ellie took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.50 plus $5 per mile. The total far
abruzzese [7]

Answer:

5x= 76.5-1.5

So, m=15m

Step-by-step explanation:

4 0
3 years ago
Numbers are numbers of the form...
Olenka [21]

Answer: Third option.

Step-by-step explanation:

In order to solve the given exercise it is important to remember that:

1. Rational numbers are defined as those numbers that can be wrriten as a  simple fraction.

2. The symbol for Rational numbers is: Q

3. Integers can be positive numbers, negative numbers and zero.

4. The symbol for Integers is: Z

5. Fractions have the following form:

\frac{a}{b}

Where:

 "a" is the numerator and "b" is the denominator.

The numerator "a" and the denominator "b" are both Integers ( and b\neq 0)

Therefore, based on the information given above, you can conclude that Rational numbers are numbers of the form \{\frac{a}{b}|a,b ∈ Z,b\neq0\}

4 0
3 years ago
Use the babylonian method to approximate square root of 24 to the nearest hundredth.
irina [24]
We will start with our guess of 12, since 12*2 = 24.
Divide 24 by 12; 24/12=2.  Average this answer with our guess:  (12+2)/2=7.  This is our new guess.
24/7=3.428571429.  Average this with our guess of 7:  (3.428571429+7)/2=5.214285715.  This is our new guess.
24/5.214285715=4.602739726.  Averaging with our guess:  (4.602739726+5.214285715)/2=4.90851272.  New guess!
24/4.90851272=4.889464766.  Averaging with our guess:  (4.889464766+4.90851272)/2=4.898988743.  New guess!  You can see as we go through our guesses are closer and closer to the same number...)
24/4.898988743=4.898970228.  Averaging:  (4.898970228+4.898988743)/2=4.898979486.  At this point our answer is the same every time down to the hundred-thousandth.  Our estimate to the nearest hundredth would be 4.90.
6 0
2 years ago
The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of itsâ height, and
storchak [24]

The question is incomplete.Here is the complete question.

The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its length, and inversely as the length of the beam. A beam 13 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?

Answer: It must be 392 inches or approximately 33 feet.

Step-by-step explanation: According to the question, the measures (width, length and height) of a beam and the weight it supports are in a relation of <u>proportionality</u>, i.e., if divided, the result is a constant.

For the first load:

width = 6in

height = 4in

length = 13ft or 156in

weight = 800lbs

Then, constant will be:

\frac{6.4^{2}}{156} k = 800

k=\frac{800.156}{96}

k = 1300

For the similar beam:

\frac{8.7^{2}}{L}1300=1300

L = 49.8

L = 392in or 32.8ft

A similar board will support 1300lbs if it has 392 inches or 32.8 feet long.

6 0
3 years ago
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