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Zigmanuir [339]
3 years ago
14

Anna is in a cave 39 feet below the cave entrance. She descends 19 feet, then ascends 25 feet. Find her new position relative to

the cave entrance.
Mathematics
1 answer:
Ne4ueva [31]3 years ago
6 0

-40-13=-53

-53+18=-35

35 feet below the cave entrance

You might be interested in
If y varies directly with x, and y = 2 when x = −4, what is the value of y when x = 20
Klio2033 [76]

Answer:

y = - 10

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 2 when x = - 4, that is

2 = - 4k ( divide both sides by - 4 )

= k, that is

k = -  

y = -  x ← equation of variation

When x = 20, then

y = -  × 20 = - 10

3 0
3 years ago
Avoiding an accident while driving can depend on reaction time. Suppose that reaction time, measured from the time the driver fi
Nadya [2.5K]

Answer:

2.5% of drivers have a reaction time more than 2.14 seconds

16% of drivers have a reaction time less than 1.78 seconds

84% of drivers have a reaction time less than 2.02 seconds

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

In this problem, we have that:

Mean = 1.9s

Standard deviation = 0.12

What percentage of drivers have a reaction time more than 2.14 seconds?

2.14 = 1.9 + 2*0.12

So 2.14 is two standard deviations above the mean.

Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, so, below 2.14. The other 5% is above.

0.05*0.5 = 0.025

2.5% of drivers have a reaction time more than 2.14 seconds

What percentage of drivers have a reaction time less than 1.78 seconds?

1.78 = 1.9 - 0.12

So 1.78 is one standard deviation below the mean.

Of the 50% of the measures that are below the mean, 68% are within one standard deviation of the mean, that is, greater than 1.78.

100 - 68 = 32

0.32*50 = 0.16

16% of drivers have a reaction time less than 1.78 seconds

What percentage of drivers have a reaction time less than 2.02 seconds?

2.02 = 1.9 + 0.12

So 2.02 is one standard deviation above the mean.

Of the measures that are below the mean, all are below 2.02.

Of those that are above, 68% are below 2.02.

0.5 + 0.68*0.5 = 0.84

84% of drivers have a reaction time less than 2.02 seconds

5 0
3 years ago
Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, California (based on data from SigAlert
adell [148]

Answer:

Option (B) is the correct answer to the following question.

Step-by-step explanation:

Step-1: We have to find the Mean of the series.

The series is Given in the question 62 61 61 57 61 54 59 58 59 69 60 67.

Mean(\overline{x})=\frac{62+61+61+57+61+54+59+58+59+69+60+67}{12} = 60.67

Step-2: We have to find the Standard Deviation.

Let Standard Deviation be x.

Formula of Standard Deviation is: s= \sqrt{\frac{\sum(x_{i}+\overline{x})}{n-1}}

Put value in formula of Standard Deviation,

s= \sqrt{\frac{(62+60.67)^{2}+(61+60.67)^{2}+(61+60.67)^{2}+(57+60.67)^{2}+....(67+60.67)^{2}}{n-1}} = 40.75

Step-3: Then, we have to find the critical value by chi-square.

X_{1-\alpha/2}^{2}=3.82

X_{1-\alpha/2}^{2}=21.92

Then, find the confidence interval which is 95%.

\sqrt{\frac{(n-1).s^2}{X_{\alpha/2}^{2}} } = \sqrt{\frac{12-1}{21.92}.(4.075)^2 }\approx2.8868 \\ i.e 2.9

\sqrt{\frac{(n-1).s^2}{X_{\alpha/2}^{2}} } = \sqrt{\frac{12-1}{3.816}.(4.075)^2 }\approx6.9188 \\ i.e 6.9

5 0
3 years ago
Using the binomial theorem , obtain the expansion of :
andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1  6  15  20  15  6  1

Decreasing powers of 1 from 1^{6} to 1^{0}

Increasing powers of 3x from (3x)^{0} to (3x)^{6}

1+3x)^{6}

= 1.1^{6}(3x)^{0} + 6.1^{5}(3x)^{1} + 15.1^{4}(3x)^{2} + 20.1^{3}(3x)^{3} + 15.1²(3x)^{4} + 6.1^{1}(3x)^{5} + 1.1^{0}(3x)^{6}

= 1 + 18x + 135x² + 540x³ + 1215x^{4} + 1458x^{5} + 729x^{6}

--------------------------------------------------------------------------------------

(1-3x)^{6}

= 1.1^{6}(-3x)^{0} + 6.1^{5}(-3x)^{1} + 15.1^{4}(-3x)^{2} + 20.1^{3}(-3x)^{3} + 15.1²(-3x)^{4} + 6.1^{1}(-3x)^{5} + 1.1^{0}(-3x)^{6}

= 1 - 18x + 135x² - 540x³ + 1215x^{4} - 1458x^{5} + 729x^{6}

----------------------------------------------------------------------------------

Collecting like terms from both expressions

(1+3x)^{6} + (1-3x)^{6}

= 2 + 270x² + 2430x^{4} + 1458x^{6}

----------------------------------------------------

(2)

Using Pascal's triangle with n = 5

1  5  10  10  5  1

Decreasing powers of 1 from 1^{5} to 1^{0}

Increasing powers of 2x from (2x)^{0} to (2x)^{5}

(1+2x)^{5}

= 1.1^{5}(2x)^{0} + 5.1^{4}(2x)^{1} + 10.1^{3}(2x)^{2} + 10.1^{2}(2x)^{3} + 5.1^{1}(2x)^{4}+ 1.1^{0}(2x)^{5}

= 1 + 10x + 40x² + 80x³ + 80x^{4} + 32x^{5}

8 0
3 years ago
The population of a community is known to increase at a rate proportional to the number of people present at time t. If the popu
Lady bird [3.3K]

Answer:

P(t) = P(0)e^{0.0693t}

Step-by-step explanation:

The population of a community is known to increase at a rate proportional to the number of people present at time t.

This means that the population growth is modeled by the following differential equation:

\frac{dP(t)}{dt} = rP(t)

Which has the following solution:

P(t) = P(0)e^{rt}

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The population has doubled in 10 years

This means that P(10) = 2P(0). We use this to find r.

P(t) = P(0)e^{rt}

2P(0) = P(0)e^{10r}

e^{10r} = 2

\ln{e^{10r}} = \ln{2}

10r = \ln{2}

r = \frac{\ln{2}}{10}

r = 0.0693

So the equation that will estimate the population of the community in t years is:

P(t) = P(0)e^{0.0693t}

6 0
3 years ago
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