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abruzzese [7]
3 years ago
11

Laura can drive her car 260 miles on 10 gallons of gasoline. Michael can drive his car 280 miles on

Mathematics
1 answer:
Marianna [84]3 years ago
4 0
Michael

Michel Can travel 70 mile on one gallon which is 1400 miles on 20 gallons

Laura can only travel 26 miles on one gallon which is 520 miles on 20 gallons
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What is the slope of the line that passes through the points (9, 1) and (17, 2)
Wewaii [24]

Answer:

C

Step-by-step explanation:

Slope of a line that goes trough the points (x1=9, y1=1) and (x2=17, y2=2)

m= (y2-y1)/(x2-x1) = (2-1) / (17-9) = 1/8

3 0
2 years ago
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose t
andrezito [222]

Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:

f(x) = λ.e^{-\lambda.x}

and the cumulative distribution function, which describes the probability distribution of a random variable X, is:

F(x) = 1 - e^{-\lambda.x}

(a) <u>Probability</u> of distance at most <u>100m</u>, with λ = 0.0143:

F(100) = 1 - e^{-0.0143.100}

F(100) = 0.76

<u>Probability</u> of distance at most <u>200</u>:

F(200) = 1 - e^{-0.0143.200}

F(200) = 0.94

<u>Probability</u> of distance between <u>100 and 200</u>:

F(100≤X≤200) = F(200) - F(100)

F(100≤X≤200) = 0.94 - 0.76

F(100≤X≤200) = 0.18

(b) The mean, E(X), of a probability distribution is calculated by:

E(X) = \frac{1}{\lambda}

E(X) = \frac{1}{0.0143}

E(X) = 69.93

The standard deviation is the square root of variance,V(X), which is calculated by:

σ = \sqrt{\frac{1}{\lambda^{2}} }

σ = \sqrt{\frac{1}{0.0143^{2}} }

σ = 69.93

<u>Distance exceeds the mean distance by more than 2σ</u>:

P(X > 69.93+2.69.93) = P(X > 209.79)

P(X > 209.79) = 1 - P(X≤209.79)

P(X > 209.79) = 1 - F(209.79)

P(X > 209.79) = 1 - (1 - e^{-0.0143*209.79})

P(X > 209.79) = 0.0503

(c) Median is a point that divides the value in half. For a probability distribution:

P(X≤m) = 0.5

\int\limits^m_0 f({x}) \, dx = 0.5

\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx = 0.5

\lambda.\frac{e^{-\lambda.x}}{-\lambda} = -e^{-\lambda.x} + e^{0}

1 - e^{-\lambda.m} = 0.5

-e^{-\lambda.m} = - 0.5

ln(e^{-0.0143.m}) = ln(0.5)

-0.0143.m = - 0.0693

m = 48.46

6 0
3 years ago
Solid: What is the surface area of the pyramid? 7
baherus [9]

Answer:

i am so sorry if its wrong

Each of the triangles making up the sides and base have a base of 8 cm and a height of 6.9 cm. Then the area of the pyramid is that of 4 such triangles.

 A = 4×(1/2)×b×h

 A = 2×(8 cm)×(6.9 cm)

 A = 110.4 cm²Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
In the form of a paragraph, explain in complete sentences, your answers to the following questions. Include the final answer in
Yanka [14]
Lisa is an avid runner and is training for a marathon, so she runs everyday to achieve this purpose. In this way, she goes out to run for six days, so we have the following data set regarding the miles she runs:

1st day  = 3.2    miles
2nd day = 7.5    miles
3rd day  = 9.8    miles
4th day  = 11.5  miles
5th day  = 2.9    miles
6th day  = 3.5    miles

<span>Finally, she ran a total of:

3.2+7.5+9.8+11.5+2.9+3.5 = 38.4 miles

</span><span>What was the average distance of each run? 

This result can be get as the sum of each run (or the </span>total of miles she run<span>) divided by the numbers of days she ran.

</span>A=\frac{38.4}{6}=6.4mi

<span>Lisa's goal for this week is to run an average of 6 miles per day. How many miles does she need to run tomorrow (the 7th day) in order to achieve her goal of 6 miles per day for the week?

Let's name x the distance she must run tomorrow. Therefore, the equation for this purpose is given as follows:

</span>\frac{3.2+7.5+9.8+11.5+2.9+3.5+x}{7}=6

∴ \frac{38.4+x}{7}=6

Isolating x:

38.4+x=42

∴ x=42-38.4=3.6

Therefore, she need to run:

\boxed{3.6mi} in order to achieve the goal of 6 miles per day.

4 0
3 years ago
Can you please help me do this?!
Marianna [84]

Answer:

the and swer is 3x+9

hoped that helped

5 0
2 years ago
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