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Diano4ka-milaya [45]
3 years ago
10

Use Natural Logarithms to solve the equation

Mathematics
1 answer:
Rus_ich [418]3 years ago
7 0

Answer:

A) 0.106

Step-by-step explanation:

8e^3x + 4 = 15

Subtract 4 from each side

8e^3x + 4-4 = 15-4

8e^3x  = 11  

Divide each side by 8

8/8e^3x = 11/8

e^(3x) = 11/8

Take the natural log of each side

ln(e^(3x)) = ln(11/8)

3x = ln(11/8)

Divide by 3

3x/3 = 1/3 ln(11/8)

x = 1/3 ln(11/8)

x =.106151244

To the nearest thousandth

x = .106

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In a study of exercise, a large group of male runners walk on a treadmill for six minutes. Their heart rates in beats per minute
Vera_Pavlovna [14]

Answer:

a) 1.88% percent of the runners have heart rates above 130.

b) 50% percent of the nomrunners have heart rates above 130.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) What percent of the runners have heart rates above 130?

In a study of exercise, a large group of male runners walk on a treadmill for six minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104,12.5) distribution. This means that \mu = 104, \sigma = 12.5.

This percentage is 1 subtracted by the pvalue of Z when X = 130.

Z = \frac{X - \mu}{\sigma}

Z = \frac{130 - 104}{12.5}

Z = 2.08

Z = 2.08 has a pvalue of 0.9812.

This means that 1-0.9812 = 0.0188 = 1.88% percent of the runners have heart rates above 130.

(b) What percent of the nonrunners have heart rates above 130?

The heart rates for male nonrunners after the same exercise have the N(130, 17) distribution. This means that \mu = 130, \sigma = 17.

This percentage is 1 subtracted by the pvalue of Z when X = 130.

Z = \frac{X - \mu}{\sigma}

Z = \frac{130 - 130}{17}

Z = 0.00

Z = 0.00 has a pvalue of 0.5000.

This means that 1-0.50 = 0.50 = 50% percent of the nomrunners have heart rates above 130.

4 0
3 years ago
Someone please help me I need it
umka21 [38]

When x = -1, y = - 3 ((-1)^2-4)

When x = 0, y = -4 ((0)^2-4)

When x = 5, y = 21 ((5)^2-4)

When x = 13 y = 165 ((13)^2-4)

You just substitute the values of X into the equation

4 0
3 years ago
The school production of​ 'Our Town' was a big success. For opening​ night, 391 tickets were sold. Students paid ​$4.00 ​each, w
drek231 [11]

Answer:

280 students

111 non students

Step-by-step explanation:

number of students (S)

number of non students (N)

S+N=391     S=391-N

4S+6N=1786

substitute S

4(391-N)+6N=1786

1564-4N+6N=1786

subtract 1564 from each side

2N=222

N=111

S=391-111=280

3 0
3 years ago
Can someone explain to me how to do this please
castortr0y [4]

Answer:

look at the attachment (p.s you could also use desmos to find the vertex)

6 0
3 years ago
In which number does the 5 represent a value 10 times the value represented by the 5 in 35,187
blagie [28]
It would be 50,000 since the 5 in the other number is in the thousands place so just multiply that by 10 in place value.
3 0
2 years ago
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