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3 years ago

Looking the area in the triangle

Mathematics

1 answer:

TEA [102]3 years ago

7 0

There’s nothing there..?

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Historically, these bolts have an average thickness of 10.1 mm. A recent random sample of 10 bolts yielded these thicknesses:

Akimi4 [234]

Answer:

a) Sample mean = 9.99

Sample standard deviation = 0.3348

b) -1.0389

c) 0.1631

Step-by-step explanation:

We are given the following in the question:

9.7, 9.9, 10.3, 10.1, 10.5, 9.4, 9.9, 10.1, 9.7, 10.3

a) sample mean and standard deviation

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{99.9}{10} = 9.99$

Sum of squares of differences = 1.009

$S.D = \sqrt{\dfrac{1.009}{9}} = 0.3348$

b) observed value of the t-statistic

Formula:

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

Putting all the values, we have

$t_{stat} = \displaystyle\frac{9.99 - 10.1}{\frac{0.3348}{\sqrt{10}} } = -1.0389$

c) probability of these statistics (or worse) if the true mean were 10.1 mm

Degree of freedom = n - 1 = 9

Calculating the value from the table

$P(x < 9.99) = 0.1631$

0.1631 is the the probability of these statistics (or worse) if the true mean were 10.1 mm

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3 years ago

How to do expanded form and word for for 119 000 003

kiruha [24]

Expanded- 100000000+10000000+9000000+4

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3 years ago

Determine the type and number of solutions of 4x^2-5x+1=0

MA_775_DIABLO [31]

4x^2-5x=-1

$\sqrt{4x^2-5x} = \sqrt{-1}$ 4x^2-5x+1=0

4x+2.24x=1

6.24x=1

x= 0.16025641025641025641025641025641

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3 years ago

Solve the following equation on the interval [0,2 \pi)<br> Cot(3x)=\sqrt{3}

Orlov [11]

Cot(3x)=3^(1/2)

cot(x)= cos(x)/sin(x)

cot(3x)= cos(3x)/sin(3x)

look at a unit circle chart

find a value for cos that has sqrt(3) in it

which one will reduce so that the cos/sin will equal sqrt(3)?

pi/6 radians

now cot(3x) implies that x is one third this value

pi/18 is the answer

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3 years ago

Mr. and Mrs. Carlo want to buy a new car, but they do not have enough money in their bank account to pay the entire cost after t

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The answer is B. They get a loan and pay each month, because then they have time to get the money to pay it back while still getting the car.

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