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5 days ago

In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.5 mm. Someone says that th

e mean thickness is less than 8.2 mm. With what level of confidence can this statement be made? (Express the final answer as a percent and round to two decimal places.)

Mathematics

Further explanation

Dividing the function by 2 results in all the y-values being halved as well. Thus, to determine the new point, we take the y-value (-1) and halve it to arrive at -1/2. Hence, the new point is (4,-1/2).
When 2 is subtracted from the function's input, it shifts all x-values up by 2. Therefore, to adjust the x-value (4), we add 2 to get 2. Thus, the new point is (2,-1).
Making the function's input negative alters each x-value by multiplying by -1. Consequently, to find the new point, we take x-value (4) and apply -1 to get -1. Therefore, the new point is (-1,-1).
Multiplying the function's input by 4 results in each x-value being divided by 4. To find the new x-value from 4, we divide by 4 to get 1. Hence, the new point becomes (1,4).
When multiplying the entire function by 4, each y-value is increased fourfold. Thus, the original value of 4 becomes -4, making the new point (4,-4).
By multiplying the entire function by -1, each y-value is also multiplied by -1. As a result, the new y-value becomes 1, leading to the new point (-12,1).

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Answer details

Grade: 9

Subject: mathematics

Chapter: corresponding point

Keywords: corresponding point, the graph, point on the graph

3 0

3 months ago

Read 2 more answers

This picture of a wall hanging is made of congruent 30° − 60° − 90° triangles with height 6 cm and hypotenuse 12 cm. What is the

Svet_ta [12734]

Answer:

28.4 cm

Step-by-step explanation:

The perimeter of the triangular wall is determined by adding all sides of the right triangle.

The triangle's height is given as 6 cm.

The hypotenuse measures 12 cm.

Using the Pythagorean theorem to find the third side:

Hypotenuse² = opposite² + adjacent²

Assigning the height as opposite = 6 cm, we find:

12² = 6² + adj²

Thus, adj² = 12² - 6²

Which gives us adj² = 144 - 36

So, adj² = 108

Leading to adj = √108

Thus, adj = 10.39 cm

The perimeter totals = 6 cm + 12 cm + 10.39 cm

= 28.39 cm

= 28.4 cm when rounded to the nearest tenth.

6 0

3 months ago

In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and

babunello [11817]

Answer:

(b)E(x)=1.3087

(c)Variance of x =1.7119

(d)E(y)=2.0447

Step-by-step explanation:

The random variable x refers to the average number of cups of coffee consumed daily.

The total number of respondents equals 1014

(a) Probability distribution for x.

$\left|\begin{array}{c|cccccc}x&0&1&2&3&4\\\\P(x)&\dfrac{365}{1014}&\dfrac{264}{1014}&\dfrac{193}{1014}&\dfrac{91}{1014}&\dfrac{101}{1014} \end{array}\right|$

(b) Expected value for x

$E(x)=\left(0\times\dfrac{365}{1014}\left)+\left(1\times\dfrac{264}{1014}\left)+\left(2\times\dfrac{193}{1014}\left)+\left(3\times\dfrac{91}{1014}\left)+\left(4\times\dfrac{101}{1014}\right)$

E(x)=1.3087

Variance $=\sum (x-\mu)^2P(x)$

$\left|\begin{array}{c|cccccc}x&0&1&2&3&4\\(x-\mu)^2&1.7167&0.0953&0.4779&2.8605&7.2431\\\\P(x)&\dfrac{365}{1014}&\dfrac{264}{1014}&\dfrac{193}{1014}&\dfrac{91}{1014}&\dfrac{101}{1014} \\\\(x-\mu)^2P(x)&0.6179&0.0248&0.0910&0.2567&0.7215\end{array}\right|$

$Variance, \sum (x-\mu)^2P(x)=1.7119$

(d)

$\left|\begin{array}{c|cccccc}y&1&2&3&4\\\\P(y)&\dfrac{264}{649}&\dfrac{193}{649}&\dfrac{91}{649}&\dfrac{101}{649} \end{array}\right|$

$E(y)=\left(1\times\dfrac{264}{649}\left)+\left(2\times\dfrac{193}{649}\left)+\left(3\times\dfrac{91}{649}\left)+\left(4\times\dfrac{101}{649}\right)$

E(y)=2.0447

The expected value for y surpasses that of x.

6 0

2 months ago