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1 year ago

2.) Simplify: 10x + 6y +4x = x(14) + 6y = 14x +6y

Mathematics

1 answer:

adelina 88 [10]1 year ago

5 0

Answer:

{x,y} = {1,1}

Step-by-step explanation:

[2] 6y = -14x + 20

[2] y = -7x/3 + 10/3

// Plug this in for variable y in equation [1]

[1] -10x - 6•(-7x/3+10/3) = -16

[1] 4x = 4

// Solve equation [1] for the variable x

[1] 4x = 4

[1] x = 1

// By now we know this much :

x = 1

y = -7x/3+10/3

// Use the x value to solve for y

y = -(7/3)(1)+10/3 = 1

Solution :

{x,y} = {1,1}

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The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is th

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Answer:

a) 0.0025

b) 0.9975

c) 23.03 minutes

d) 23.03 minutes

Step-by-step explanation:

Let X be the random variable that measures the time waited for a taxi.

If X is exponentially distributed with a mean of 10 minutes,then the probability that you have to wait more than t minutes is

$\large P(X>t) = e^{-t/10}$

1 hour = 60 minutes, so the probability that you wait longer than one hour is

$\large P(X>60)=e^{-6}=0.0025$

Due to the “memorylessness” of the exponential distribution, the probability that you have to wait 10 or less minutes after you have already waited for one hour, is the same as the probability that you have to wait 10 or less minutes

$\large P(X\leq 10)=1-e^{-6}=0.9975$

We want x so that

P(X>x)=0.1

$\large e^{-x/10}=0.1\rightarrow -x/10=ln(0.1)\rightarrow x=-10ln(0.1)=23.03\;minutes$

We want P(X<x)=0.9

$\large 1-e^{-x/10}=0.9\rightarrow e^{-x/10}=0.1\rightarrow x=-10ln(0.1)=23.03\;minutes$

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3 years ago

Identify the equivalent expression for each of the expression below 3√x

antiseptic1488 [7]

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3 years ago

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2 years ago

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Use the diagram to find the height of statue.round to the nearest tenth

jeyben [28]

Answer:

7.3 ft

Step-by-step explanation:

The information given represents a right angle triangle with the following:

reference angle = 52°

Adjacent side length = 5.7 ft.

Opposite side length = height of the statue = h

Applying the trigonometric ratio formula, we would have:

$tan(52) = \frac{h}{5.7}$

Multiply both sides by 5.7

$tan(52) \times 5.7 = \frac{h}{5.7} \times 5.7$

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2 years ago

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun

QveST [7]

Answer:

We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 31.7 milligrams

Sample mean, $\bar{x}$ = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s = 2.8 milligrams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}$

We use One-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429$

Now, $t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

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3 years ago