The thickness of eight pads designed for use in aircraft engine mounts are measured. The results, in mm, are 41.8, 40.9, 42.1, 41.2, 40.5, 41.1, 42.6, and 40.6. Assumed that the thicknesses are from a normal distribution. Can you conclude that the mean thickness is greater than 41.0 mm a) State your hypotheses. b) Test your hypotheses at .01 significance level. c) Your conclusion (in the context of this problem)

Answer:

angle B is 45 degree.

Step-by-step explanation:

since both radius are equal in a circle the triangle formed is ann isosceles triangle.

base angle of an isosceles triangle are equal

angle B be x

angle A = angle B (being base angles of a triangle)

then angle A is also x

angle A + angle B + angle C =180 degree (sum of interior angles of a triangle)

x + x + 90=180

2x =180-90

x=90/2

x=45 degree

Answer:

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have that:

The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].

Sample of n games:

This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Answer:

3 miles

Step-by-step explanation:

5-1+2=3

From the calculation done using the pythagoras theorem, the distance from Sarah's apartment is 12m

This theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Using the pythagoras theorem

BC² = AB² + AC²

The sides of the triangle are x, x - 1 and 5

x² = (x-1)² + 5²

x² = (x-1)(x-1) +25

x² = x²-x-x -1 + 25

collect like terms

2x = 24

divide through the equation by 2

x = 24/2

= 12m

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Answer:

c is equal to e

Step-by-step explanation: a

Answer:

x=3

Step-by-step explanation:

Answer:

1/2( 110+42)

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)

<<XYZ = 1/2( 42+110)

Answer:

Step-by-step explanation:

Answer:

The time-mean speed of the minivans is of 105.8 seconds.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the number of values.

Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.

Thus, the mean is:

[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]

The time-mean speed of the minivans is of 105.8 seconds.

Answer:

(A) 89 (B) 91 (C) 92 (D) 95 4.If |x−2| = p, where x < 2, then x+1 equals (A) −2 (B) 3− p (C) |2p−2| (D) 2p−2 5.A

Step-by-step explanation:

Following are the calculation to the find the value of x:

Given:

Please find the question.

To find:

x=?

Solution:

[tex]\frac{71}{7} <\frac{x}{9} < \frac{113}{11}\\\\10 <\frac{71}{7} < 11 \\\\10< \frac{113}{11}<11\\\\\frac{x}{9} >10\\\\x>90\\\\\text{When}\ x=91 \\\\\frac{71}{7} > \frac{91}{9}\\\\x=92\\\\ \frac{71}{7}< \frac{92}{9} <\frac{113}{11}\\\\[/tex]

so, x= 92 \\\\

by compare score value x= 92

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Answer:

to put the equation into standard for we must multiply the terms on the right side of the equation. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Step-by-step explanation:

y

=

(

x

−

13

)

(

x

−

12

)

becomes:

y

=

(

x

×

x

)

−

(

x

×

12

)

−

(

13

×

x

)

+

(

13

×

12

)

y

=

x

2

−

12

x

−

13

x

+

156

We can now combine like terms:

y

=

x

2

+

(

−

12

−

13

)

x

+

156

y

=

x

2

+

(

−

25

)

x

+

156

y

=

x

2

−

25

x

+

156

Answer:

Given:

Cost = £ 800

Tax = 20%

To find:

The total cost

Solution:

Total cost = Cost + Tax

Tax = 20 % of cost

20 / 100 * 800

Tax = £ 160

Hence,

Total cost =  £ 800 + £ 160

Total cost = £ 960

Answer:

Thirty rounded to the nearest whole number percent is 30% (%=percent)

Step-by-step explanation:

Well, you see that if you have 30 out of one hundred then that's when all you have to do is go with the same number and just add percent or % to the end.

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Hope this Helps

This is just evidence

Answer:

(a) The mean is 0

(b) The median is -30

(c) The mode is unimodal

Step-by-step explanation:

Given

[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]

Solving (a): The mean.

This is calculated using:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]

[tex]\bar x =\frac{0}{8}[/tex]

[tex]\bar x =0[/tex]

Solving (b): The median

First, arrange the data

[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]

There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.

[tex]Median = \frac{-4-2}{2}[/tex]

[tex]Median = \frac{-6}{2}[/tex]

[tex]Median = -3[/tex]

Solving (c): The mode

The item that has occurs most is -10.

Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).

Answer:

y = -x + 8

Step-by-step explanation:

First, plug in the slope.

y = mx + b

y = -1x + b

y = -x + b

Then, plug in the point.

7 = -(1) + b

7 = -1 + b

8 = b

Answer:19.82

Step-by-step explanation:

Got it right i did it on a test

Answer:

The answer is 0.5

Answer:

rhe answer is r= .50

Step-by-step explanation:

125-75=50

Answer:

[tex]x\approx 5.48[/tex]

Step-by-step explanation:

Draw a line from the center of the circle O to the end of either side of the line marked as 4. This line represents two things:

In this case, both are important. Since [tex]x[/tex] is also a radius of the circle, the line must be equal to [tex]x[/tex], since all radii of a circle are equal. To find the length of this line, use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

Since we're solving for the hypotenuse and the two legs are 5.1 and 2, we have:

[tex]5.1^2+2^2=c^2,\\26.01+4=c^2,\\c^2=30.01,\\c=5.47813836992\approx \boxed{5.48}[/tex] (round as necessary).

Answer:

P = 7.7 C + 1.1 XC

Step-by-step explanation:

From the question, it is noted that the price of helium required to fill each of the balloons would increase by 10%. Let the current price of helium be C, so that;

10% of C = 0.1 C

The price of helium next year = C + 0.1 C

                        = 1.1 C

Cost of 7 small balloons = 1.1 C * 7

                         = 7.7 C

Cost of X large balloons = 1.1 C * X

                         = 1.1 XC

The total price, P for helium next year = 7.7 C + 1.1 XC

Thus, the equation to find the total price of helium that would fill the balloons next year is;

P = 7.7 C + 1.1 XC

Answer:

The amount of interest he paid at the end of the loan is $ 311.85.

Step-by-step explanation:

Given that Juan borrowed $ 1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%, to determine what is the amount of interest he paid at the end of the loan, the following calculation must be performed:

(1500 x 0.0297) x 7 = X

44.55 x 7 = X

311.85 = X

Therefore, the amount of interest he paid at the end of the loan is $ 311.85.

Answer:

This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].

For the proof, make use of the fact that:

[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and

[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].

Step-by-step explanation:

Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.

Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:

[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].

Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:

[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].

Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].

Answer: x=3

Step-by-step explanation:

First we're going to get rid of the fraction by multiplying both sides by the square root of x-2

Now square both sides

[tex](\sqrt{3x })^2=3^2(\sqrt{x-2 })^2\\3x=9(x-2)[/tex]

Next use the distributive property

[tex]3x=(9)(x)-(9)(2)\\3x=9x-18[/tex]

Now subtract 9x from both sides

[tex]3x-9x=9x-18-9x\\-6x=-18[/tex]

Finally divide -6 on both sides

[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\x=3[/tex]

Answer:

165°

Step-by-step explanation:

Find the interior angle measure by using the formula, ((n - 2) x 180°) / n

Plug in 24 as n:

((n - 2) x 180°) / n

((24 - 2) x 180°) / 24

(22 x 180°) / 24

3960 / 24

= 165

So, the measure of each angle is 165°

Answer:

163.6

Step-by-step explanation:

180•(22-2)=180•20 =3600

3600/22= 163.636363…

Answer:

40.2667

Step-by-step explanation:

P(X=36)= 36/120

P(X=40)= 40/120

P(X=44)=44/120

E(X) = 36(36/120)+40(40/120)+44(44/120)=1208/30=40.2667

hope this helps

If a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A school class of 120 students is driven in 3 buses to a symphonic performance.

There are 36 students on one of the buses, 40 on another, and 44 on the third bus.

From the data given:

Let X be the total number of passengers on the bus carrying that randomly selected student,

Total number of students = 120

Let:

Probability:

P(X = 36) = 36/120

Probability:

P(X = 40)= 40/120

Probability:

P(X = 44)=44/120

E(X) = 36(36/120) + 40(40/120) + 44(44/120)

E(X) = 1208/30

E(X) = 40.26

Therefore, if a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.

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Answer:

Yes, this graph represents a function

Step-by-step explanation:

The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.

Answer:

The graph does represent a function

Step-by-step explanation:

The function is at about 30y = x^3

Answer:

The answer is C

Step-by-step explanation:

3    :    4

^          ^

II          II

red    blue

Answer:

1,736 chocolate cover peanuts

Step-by-step explanation:

do 28×62 hope this helps

Answer:

1736 chocolate-covered peanuts

Step-by-step explanation:

[tex]\frac{1}{62} :\frac{28}{y}[/tex]

1 · y = 62 · 28

y = 1736

Answer:

10

Step-by-step explanation:

5

C

3

5!/(3!(5-3)!)

5!/(3!x2!)

120/12

10

In 10 ways can a supermarket manager display 5 brands of cereals

in 3 spaces on a shelf.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

Total brands of cereals= 5

Using Combination, C(n, r)

= n!/ r! (n- r)!

So, the number of ways

= C(5, 3)

= 5!/(3!(5-3)!) 5

= 5 x 4 x 3! / 3! x 2!

= 5 x 4 /2

= 10

Thus, the total number of ways is 10.

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