ucsd reddit A watermelon is thrown down from the 7th floor of Urey Hall at UCSD. If the initial height of the watermelon is 21.0 meters, and it is thrown straight downward with an initial downward velocity of 3.00 m/s. How far will the watermelon have fallen from its starting height after 1.50 seconds?

Answer:

a) Yes, it is a linear combination.

b) Impossible to write as a linear combination.

Step-by-step explanation:

Recall that given vectors u,v,w we say that w is a linear combination of u and v if there exists real numbers a,b such that

[tex]w=au+bv[/tex]

a) [tex] u = (2,19,-16, -4)[/tex]. So, we have the following

[tex] (2,19,-16, -4)=a(6,-7,8,6)+b(4,6,-4,1)[/tex]. Which give us the following equations

[tex]6a+4b = 2[/tex]

[tex]-7a+6b = 19[/tex]

[tex]8a-4b = -16[/tex]

[tex]6a+b =-4[/tex]

Note that if we add the first and the third equation, we get that [tex]14a = -14[/tex] which implies that a=-1. In the first equation, if a=-1, then [tex]4b=2+6[/tex] which implies that b=2. We must check that when (a,b) =(-1,2) the four equations are still valid.

So

[tex]6(-1)+4(2) = -6+8 = 2[/tex]

[tex]-7(-1)+6(2) = 7+12 = 19[/tex]

[tex]8(-1)-4(2) = -8-8 = -16[/tex]

[tex]6(-1)+(2) =-6+2 = -4[/tex]

Since all equations are met, we have written the desired vector u as the linear combination of the initial vectors.

b) Repeating the same analysis, we get

[tex](432 , 1134 , −18, 132)=a(6,-7,8,6)+b(4,6,-4,1)[/tex]

[tex]6a+4b = 432[/tex]

[tex]-7a+6b = 1134[/tex]

[tex]8a-4b = -18[/tex]

[tex]6a+b =132[/tex]

adding the first and third equation we get [tex]14a = 414[/tex] so a = 207/7. Replacing this value will give us that b=891/14.

However,

note that

[tex]-7\frac{207}{7}+6\frac{891}{14} = \frac{1124}{7}\neq 1134[/tex]. Then, it is impossible to write the linear combination.

The question seeks a linear combination of vectors from a given set 'S' that matches specified vectors. Using vector addition and scalar multiplication, it is possible to find a unique combination for each specified vector. If no combination can provide the required vector, 'IMPOSSIBLE' is the answer.

In this problem, you're asked to express a given vector as a linear combination of other vectors from the set 'S'. This involves using the properties of vector addition and scalar multiplication to define a unique way to represent each given vector. A linear combination of vectors involves adding or subtracting multiples of these vectors.

For instance, if we have the set S = {(6, -7, 8, 6), (4, 6, -4, 1)}, and we're asked to write the vector u = (2, 19, -16, -4), the correct linear combination would be -1 times the first vector in S plus 2 times the second vector (-1*(6,-7,8,6) + 2*(4,6,-4,1) = (2, 19, -16, -4)). This means vector 'u' would be expressed as u = -1 * S1 + 2 * S2. If no such combination is possible, the answer would be 'IMPOSSIBLE'.

Other important concepts related to this problem include vector addition, scalar multiplication, and the distributive property. Vector addition is both associative and commutative and vector multiplication by a sum of scalars is distributive. The direction and magnitude of vectors are also significant elements to consider while solving such problems.

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Answer:

0.0445937

Step-by-step explanation:

-Given that the sample statistic has a mean of 406 grams, standard deviation of sq root(225) and the null statistic is 411 grams.

-Assuming normal distribution, the test statistic is calculated as:

[tex]z=\frac{Sample \ statistic-Null \ statistic}{\sigma/\sqrt{n}}\\\\=\frac{406-411}{\sqrt{225/26}}\\\\=-1.6997[/tex]

-we then find the p-value of the test statistic from the z-tables:

P-value=0.0445937

I don't know how to do that. Only one angle is given and no relationships between the triangles or any lines are given.

Answer:

The answer is 50.

Step-by-step explanation:

Answer:

Hi Gabbie,

   The answer to your question that was what is the expected value for the "under 21 and regularly use text messaging" cell is 82.

Please rate me good  :)

Step-by-step explanation:

The answer is 82 because the table that clearly defines the result  was in the question.

Answer:

-5,-4,-3,-2,-1,0,1,2,3,4,5

Step-by-step explanation:

The sample space for the two balanced dice, a red die, and a green die is given below in the pair (G,R)

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

For each pair, Y=G-R is presented below:

0 -1 -2 -3 -4 -5

1 (2,2) (2,3) (2,4) (2,5) (2,6)

2 (3,2) (3,3) (3,4) (3,5) (3,6)

3 (4,2) (4,3) (4,4) (4,5) (4,6)

4 (5,2) (5,3) (5,4) (5,5) (5,6)

5 (6,2) (6,3) (6,4) (6,5) (6,6)

The first column and row is representative of the values which will be obtained throughout the table.

Therefore, the possible values of the random variable Y are:

-5,-4,-3,-2,-1,0,1,2,3,4,5

The possible values of Y are its sample space, and the values are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1

The sample space of the green die is:

[tex]G= \{1,2,3,4,5,6\}[/tex]

The sample space of the red die is:

[tex]R= \{1,2,3,4,5,6\}[/tex]

When the numbers on both dice are combined, we have the following possible outcomes

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) , (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) , (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) , (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) , (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) , (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Subtract the second outcomes from the first, to get Y

(0) (-1) (-2) (-3) (-4) (-5) , (-1) (0) (-1) (-2) (-3) (-4) , (2) (1) (0) (-1) (-2) (-3) , (3) (2) (1) (0) (-1) (-2) , (4) (3) (2) (1) (0) (-1) , (5) (4) (3) (2) (1) (0)

List out the unique numbers:

(0) (-1) (-2) (-3) (-4) (-5) (5) (4) (3) (2) (1)

Hence, the possible values of Y are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1

Read more about sample space at:

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Answer:

[tex]y=\frac{x}{6.4}[/tex]

Step-by-step explanation:

The complete question in the attached figure

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem, we have a proportional relationship between the average speed (x) and the time (y)

Find the constant of proportionality k

Fox =32, y=5

[tex]k=\frac{5}{32}[/tex]

substitute

[tex]y=\frac{5}{32}x[/tex]

we have

[tex]\frac{5}{32}=\frac{1}{6.4}[/tex]

therefore

[tex]y=\frac{x}{6.4}[/tex]

Answer:

C(x)=16600+63x

R(x)=160x

Break-even Point, x=172

Step-by-step explanation:

Let x be the number of Toilets Produced.

Fixed cost = $16,600

Variable costs = $63 per toilet.

Total Cost, C(x)=16600+63x

The company expects to sell the toilets for $160.

Selling Price Per Toilet=160

Total Revenue for x Toilets, R(x)=160x

Next, we determine the break-even point.

The break-even point is the point where the Cost of Production equals Revenue generated.

i.e. C(x)=R(x)

16600+63x=160x

16600=160x-63x

16600=97x

x=171.13

The company needs to sell at least 172 Toilets to break even.

To formulate the functions C(x) and R(x) for the total cost and revenue of producing and selling x toilets, we can use the given information about fixed costs, variable costs, and selling price. By setting the total cost equal to the total revenue, we can find the number of toilets needed to break even, which is approximately 171.

To formulate the function C(x) for the total cost of producing x new toilets, we need to consider the fixed cost and the variable cost. The fixed cost is $16,600, which remains constant regardless of the number of toilets produced. The variable cost is $63 per toilet, so we multiply it by x to account for the number of toilets produced. Therefore, the function C(x) can be expressed as:

C(x) = 16,600 + 63x

The function R(x) for the total revenue generated from the sales of x toilets can be found by multiplying the selling price of each toilet by the number of toilets sold. Since each toilet is sold for $160, the function is:

R(x) = 160x

To find the number of toilets needed to break even, we need to determine the value of x when the total cost is equal to the total revenue. In other words, we set C(x) = R(x) and solve for x:

16,600 + 63x = 160x

Subtracting 63x from both sides:

16,600 = 97x

Dividing both sides by 97:

x = 170.10

Therefore, the company needs to sell approximately 171 toilets to break even.

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Answer:

At 0.05 level of significance, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units

Step-by-step explanation:

We hypothesize that mean difference between abrasive wear of material 1 and material 2 is greater than 2.

So we write the null hypothesis [tex]H_0 : \mu_1 - \mu_2 >2[/tex],

and the alternative hypothesis [tex]H_1: \mu_1 - \mu_2 \leq 2[/tex].

We will find the T-score as well as the p-value. If the p-value is less than the level of significance, we will reject the null hypothesis, i.e. we will conclude that the abrasive wear of material 1 is less than that of material 2. Otherwise, we will accept the null hypothesis.

Since the variance is unknown and assumed to be equal, we will use the pooled variance

[tex]s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} = 20.05[/tex],

where [tex]n_1 = 12, n_2 =10, s_1 =4, s_2 = 5[/tex].

The mean of material 1 and material 2 are [tex]\mu_1 =85, \mu_2=81[/tex] respectively and mean difference [tex]d[/tex] is equal to 4. The hypothesize difference [tex]d_0[/tex] is equal to 2.

To find the T-score, we use the following formula

[tex]T = \frac{d - d_0}{\sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2} }}[/tex]

Substituting all the values into the T-score formula gives us [tex]T = 1.04[/tex], and the respective p-value is equal to 0.31. This means we have enough statistical evidence not to reject the null hypothesis, and at 5% significance level, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units.

Answer:

A. 24024

B. 364

Step-by-step explanation:

(a) There are 14*13*12*11 = 24024 ways to select the officers...

(b) Since the officers can also serve on the committee, the sampling

    is with replacement, so then there are (14 choose 3) ways to

    select the committee members... 364 ways to be exact

Answer:

a) [tex]P(R<95)=P(\frac{R-\mu}{\sigma}<\frac{95-\mu}{\sigma})=P(Z<\frac{95-100}{3.606})=P(Z<-1.387)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-1.387)=0.0827[/tex]

b) [tex]P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)[/tex]

And we can find this probability using the complement rule and the normal standard table or excel and we got:

[tex]P(z>2.774)=1-P(Z<2.774) = 1-0.9972 = 0.0028[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:

[tex]R \sim N(40+60 = 100,\sqrt{2^2 +3^2}= 3.606 s)[/tex]  

Where [tex]\mu=65.5[/tex] and [tex]\sigma=2.6[/tex]

We are interested on this probability

[tex]P(R<95)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{R-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(R<95)=P(\frac{R-\mu}{\sigma}<\frac{95-\mu}{\sigma})=P(Z<\frac{95-100}{3.606})=P(Z<-1.387)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-1.387)=0.0827[/tex]

Part b

[tex]P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)[/tex]

And we can find this probability using the complement rule and the normal standard table or excel and we got:

[tex]P(z>2.774)=1-P(Z<2.774) = 1-0.9972 = 0.0028[/tex]

Given Information:  

Mean = μ = 40 + 60 = 100 minutes  

Standard deviation = σ = 2² + 3² = 13 minutes  

Required Information:  

a. P(X < 95) = ?

b. P(X > 110) = ?

Answer:  

a. P(X < 95) = 0.0823

b. P(X > 110) = 0 .0028

Explanation:  

a)

Let random variable X represents the time in minutes of wheel throwing and firing.

The probability that a piece of pottery will be finished within 95 minutes means,

P(X < 95) = P(Z < (x - μ)/√σ)  

P(X < 95) = P(Z < (95 - 100)/√13)  

P(X < 95) = P(Z < -1.39)  

The z-score corresponding to -1.39 is 0.0823

P(X < 95) = 0.0823

Therefore, there is 8.23%  probability that a piece of pottery will be finished within 95 minutes.

b)

P(X > 110) = 1 - P(X < 110)  

P(X > 110) = 1 - P(X < (x - μ)/√σ)

P(X > 110) = 1 - P(X < (110 - 100)/√13)

P(X > 110) = 1 - P(X < 2.77)

The z-score corresponding to 2.77 is 0.9972

P(X > 110) = 1 - 0.9972

P(X > 110) = 0 .0028

Therefore, there is 0.28%  probability that a piece of pottery will take longer than 110 minutes.

Answer:

0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 990 kWh

Standard Deviation, σ = 198 kWh

We are given that the distribution of energy consumption levels is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(September energy consumption level is between 1100 kWh and 1250 kWh)

[tex]P(1100 \leq x \leq 1250)\\\\ = P(\displaystyle\frac{1100 - 990}{198} \leq z \leq \displaystyle\frac{1250 -990}{198}) \\\\= P(0.5556 \leq z \leq 1.3131)\\\\= P(z \leq 1.3131) - P(z < 0.5556)\\\\= 0.9054- 0.7108= 0.1946[/tex]

0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

Answer:

Check the explanation

Step-by-step explanation:

Period, X  Actual , Y

1                        6

2                       11

3                       9

4                       16

5                       17

Y= intercept + slope*x

Answer a and b:

INTERCEPT(known Y's,known X's)          Slope(known Y's,known X's)

                      3.7                                                           2.7

Simple linear regression equation is

Forecast, Y= 3.7+ 2.7*x

Period, X  Actual , Y  linear          Absolute           squared

                                   trend         deviation=         deviation=

                                Forecast,      |Forecast -        (absolute          

                            Y= 3.7+ 2.7*x      Actual|            deviation)^2

1                  6            6.40                  0.4                      0.2

2                 11            9.10                   1.9                       3.6

3                 9            11.80                  2.8                       7.8

4                16           14.50                  1.5                       2.3

5                17           17.20                  0.2                       0.0

6                              19.90  

                                                                                      2.78

                                                                                      MSE

Answer c: MSE= 2.78

Answer d: Forecast for x= 6= 19.90

Step-by-step explanation:

[tex] {5}^{17} \times {5}^{2} [/tex]

Now adding powers

[tex] {5}^{17 + 2} [/tex]

[tex] {5}^{19} [/tex]

Hope it will help :)

Answer:

5x1^19

Step-by-step explanation:

Basically, the only way to have the 5 be to the power of 1 in this equation is to put it in scientific notation, or in other words, multiply 5 by 1 to the power of 19.

Answer:

2 (2x - 3) x (2x + 3)

Answer:

The correct explanation is:

D. Statistical significance means that the result observed in a sample is unusual when the null hypothesis is assumed to be true.

Step-by-step explanation:

The statistical significance gives a threshold to measure if a sample result or observed effect is due only to a sampling or it really reflects a characteristics of the population we are studying.

The level of statistical significance is usually 0.05 or 5%, depending on how strong the evidence needs to be and the consequences of the conclusions of the study, taking into account the Type I and Type II errors.

Thus the response above i.e., "option D" is appropriate.

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Answer:

C

Step-by-step explanation:

The correct option is option C , that is the rule which describes the translation is (x, y) → (x + 4, y - 3).

What do you mean by translation ?

The modification of an existing diagram to create a different version of the following diagram is known as translation.

The translated triangle is moved along the x-axis by 4 units, to the right. The numbers get more positive as one moves to the right along the x-axis, hence an additional 4 units should be added to the x-coordinate. So , the coordinate would be x + 4.

Along the y-axis, the triangle is also pushed downward by 3 units. More negative numbers are produced as the axis moves below, hence 3 should be subtracted. So , the coordinate should be y - 3.

Based on the above information, we can conclude that another way to write the given rule by translation is (x, y) → (x + 4, y - 3) .

Therefore , the correct option is option C , that is the rule which describes the translation is (x, y) → (x + 4, y - 3).

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Answer:

28

Step-by-step explanation:

3/4x= 21

x= 21(4/3)

x= 28

Check! (optional)

28 x 3/4 = 21

Check correct!!!!!!

Answer:

the number is 28

Step-by-step explanation:

I know this because 21 is 3/4 of a number. 21 divided by 3 is 7, you do this to find what 1/4 of the number is. so then you add 7 to 22 and you get 28!

Answer:

1. 564 tractor trailers

2. (0.2919, 0.4339)

3. It should be noted that there is 90% confidence that the true population proportion lies between 0.2919 and 0.4339.

Step-by-step explanation:

1)

Proportion= P = 0.8333333333333 (1/12)

Margin error= 0.06/2 = 0.03

Confidence level= 99

Significance level = α= (100 - 99)%= 1%= 0.01

α/2 = 0.01/2 = 0.0005

Sample size= n

= p(1 - p) (Z*/E)

=0.8333333333333 x (2.576/0.03)^2

=563.15

Approximately

=564

2) Sample size n= 124

Sample number of event x =45

Sample proportion = p= x/n

=45/124

= 0.3629

Standard error =√p(1 - p) /n

√(0.3629× (1 - 0.3629)/ 124

= 0.0432

Confidence level= 90

Significance level α= (100-90)% =0.01

Critical value Z* = 1.645

Margin of error = Z×Standard error= 1.645 × 0.0432= 0.07103

Lower limit = p- margin error= 0.3629 - 0.07103= 0.2919

Upper limit = p+margin error= 0.3629 + 0.07103= 0.4339

The answer is (0.2919, 0.4339)

3) It should be noted that there is 90% confidence that the true population proportion lies between 0.2919 and 0.4339.

Answer:

The maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight is of 3.46 ounces.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this problem:

[tex]\sigma = 13.3, n = 40[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.645*\frac{13.3}{\sqrt{40}}[/tex]

[tex]M = 3.46[/tex]

The maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight is of 3.46 ounces.

Final answer:

The maximal margin of error for a 90% confidence interval for the mean watermelon weight is calculated using the z-score for the confidence level, the known population standard deviation, and the sample size, resulting in 3.463 ounces.

Explanation:

To find the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight when the mean weight of the watermelons is 66 ounces, the population standard deviation is 13.3 ounces, and the sample size is 40, we use the formula for the margin of error E = z * (σ / sqrt(n)), where z is the z-score corresponding to the confidence level, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is approximately 1.645. Plugging in the values, we get:

E = 1.645 * (13.3 / sqrt(40))
= 1.645 * (2.105)
= 3.463 ounces.

The maximal margin of error is therefore 3.463 ounces, which means the interval is 66 ± 3.463 ounces for the true population mean weight of watermelons with 90% confidence.

Answer:

1/3

Step-by-step explanation:

For the 1st fraction, since 4 × 3 = 12,

3 /4  =  3 × 3/  4 × 3 =  9/ 12

Likewise, for the 2nd fraction, since 12 × 1 = 12,

5 /12  =  5 × 1 /12 × 1  =  5 /12

Subtract the two fractions: 9 /12  -  5 /12  =  9 - 5 /12  =  4 /12

So next you simplify the answer how many 4 go in 4 and how many go in 12 the simplified answer is the answer is  1/3

Hope this helps

Answer:

229.23 feet.

Step-by-step explanation:

The pictorial representation of the problem is attached herewith.

Our goal is to determine the height, h of the tree in the right triangle given.

In Triangle BOH

[tex]Tan 60^0=\dfrac{h}{x}\\h=xTan 60^0[/tex]

Similarly, In Triangle BOL

[tex]Tan 50^0=\dfrac{h}{x+60}\\h=(x+60)Tan 50^0[/tex]

Equating the Value of h

[tex]xTan 60^0=(x+60)Tan 50^0\\xTan 60^0=xTan 50^0+60Tan 50^0\\xTan 60^0-xTan 50^0=60Tan 50^0\\x(Tan 60^0-Tan 50^0)=60Tan 50^0\\x=\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0} ft[/tex]

Since we have found the value of x, we can now determine the height, h of the tree.

[tex]h=\left(\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0}\right)\cdotTan 60^0\\h=229.23 feet[/tex]

The height of the tree is 229.23 feet.

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

µ = 75

For the alternative hypothesis,

µ ≠ 75

Since the number of samples is 20 and no population standard deviation is given, the distribution is a student's t.

Since n = 20,

Degrees of freedom, df = n - 1 = 20 - 1 = 19

t = (x - µ)/(s/√n)

Where

x = sample mean = $69.46

µ = population mean = $75

s = samples standard deviation = $9.78

t = (69.46 - 75)/(9.78/√20) = - 2.53

We would determine the p value using the t test calculator. It becomes

p = 0.01

Since alpha, 0.05 > than the p value, 0.01, then the null hypothesis is rejected.

Therefore,

The value of the test statistic is -2.53; therefore, the null hypothesis is rejected for level of significance = 0.05

Answer:

A)  (33/5, 0, 44/5)

B) - 11

C) (28/5, 2, - 54/5)

D) 11, 12.83

Step-by-step explanation:

A)

Given the vectors

b= (1, 2,-2)

a= (-3, 0, 4)

Projection of the vector b onto the line along vector a as p=ˆxa

Calculating ab,

ab= a1b1 + a2b2 + a3b3

a1= - 3, a2=0, a3=4, b1=1, b2=2, b3= - 2

ab= (-3)(1) + (0)(2) +(4)(-2)

ab= - 3 + 0 +(-8)

ab= - 11

Vector projection which is

( ab÷ /vector a/^2) × vector a

= - 11/√(-3)^2 + (0)^2 + (4)^2

= - 11/ √9 +16

=-11/√25

= - 11/5× (-3, 0, - 4)

= (33/5, 0, 44/5)

B) When p= pb

It will be a scalar projection and will be written as:

ab÷ /a/

-11/√1

= - 11

C) Given the vector that form P to b in

e= b - p

=b- ˆxa

e= (1, 2,-2) - (33/5, 0, 44/5)

= (1 - 33/5, 2- 0, -2 - 44/5)

=(5-33/5, 2, - 10- 44/5)

= (28/5, 2, - 54/5)

D.

Length of the projection vector:

/e/ = √(33/5^2 + 0 + 44/5^2)

/e/= √33^2/25 + 0 + 44^2/25

/e/= √33^2/25 +44^2/25

/e/= √121

/e/= 11

Length of error vector

/e/ = √(28/5)^2 + 2^2 + (-54/5)^2

/e/= √28^2/25 +4 +(-54^2/25)

/e/= 12.83

Answer:

a) and b) p= (33/25, 0, -44/25)

c) e = (-8/25, 2, -6/25)

d) p = 11/5 = 2.2

e) e = (2/5)√26 = 2.039

Step-by-step explanation:

Given

b = (1, 2, −2)

a = (−3, 0, 4)

a)  and b) We use the formula

p = (at*b)/(at*a)*a

⇒ p = ((−3, 0, 4)*(1, 2, −2)/((−3, 0, 4)*(−3, 0, 4)))*(−3, 0, 4)

[tex]p=\frac{at*b}{at*a}*a\\ p=\frac{(-3, 0, 4)*(1, 2,-2)}{(-3, 0, 4)*(-3, 0, 4)} *(-3, 0, 4)\\ p=\frac{-3+0-8}{9+0+16}*(-3, 0, 4)\\ p=-\frac{11}{25} *(-3, 0, 4)\\ p=(\frac{33}{25} ,0,-\frac{44}{25})[/tex]

c)

 [tex]e=b-p\\ e=(1, 2, -2)-(\frac{33}{25} ,0,-\frac{44}{25})\\ e=(-\frac{8}{25} ,2,-\frac{6}{25} )[/tex]

d) We use the formula

[tex]p=\sqrt{(\frac{33}{25} )^{2} +(0)^{2} +(\frac{-44}{25} )^{2}} =\frac{11}{5}[/tex]

e) Applying the same formula we have

[tex]e=\sqrt{(\frac{-8}{25} )^{2} +(2)^{2} +(\frac{-6}{25} )^{2}} =\frac{2}{5}\sqrt{26} =2.039[/tex]

Complete Question:

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with ? = 0.001 millimeters. A random sample of 15 rings has a mean diameter of \bar{X}= 74.106. Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter.

(Round your answers to 3 decimal places.)

(Calculate the 99% two-sided confidence interval on the true mean piston diameter.

Answer:

99% true sided confidence Interval on the true mean Piston diameter = (74.105, 74.107)

Step-by-step explanation:

Check the attached file for the complete solution

Answer:

42.86%

Step-by-step explanation:

3/7 as a decimal is 0.4286... and to convert that into a decimal, you move the decimal point right twice.

0.4286 = 42.86%

I hope this helped!

Final answer:

To convert the fraction 3/7 into a percent, divide 3 by 7 to get the decimal 0.4286, then multiply by 100 to get 42.86%.

Explanation:

Converting a Fraction to a Percent

To convert a fraction like 3/7 into a percent, follow these steps:

Therefore, 3/7 as a percent is 42.86%.

A percent (or per cent) is a way of expressing a number as a fraction of 100. The term "percent" comes from the Latin per centum, which means "by the hundred." It is often represented by the symbol "%."

Answer:

There is no sufficient evidence

Step-by-step explanation:

See attached files

Answer:

2/9

Step-by-step explanation:

The ratio is 12/54 which can be simplified by dividing the numerator and denominator by 6 to get 2/9

Step-by-step explanation:

To find the sum of first 20 terms,

a = 6, r = 3

By formula, [tex]S_{n} = \frac{a(r^{n}-1) }{r-1}[/tex]

substitute the values in the above formula, the equation becomes,

[tex]S_{20} = \frac{6(3^{20}-1) }{3-1}[/tex]

[tex]S_{20} = \frac{6(3^{20}-1) }{2}[/tex]

[tex]S_{20}[/tex] = [tex]{3(3^{20}-1) }[/tex]

Step-by-step explanation:

[tex] - 18 - \frac{3}{4v} = 3[/tex]

[tex] - \frac{3}{4v} = 3 + 18[/tex]

[tex] - \frac{3}{4v} = 21[/tex]

Now doing cross multiply

-3 = 21 * 4v

[tex]v = - \frac{3}{21 \times 4} [/tex]

Therefore

[tex]v \: = \frac{1}{28} [/tex]

Hope this helps.

Answer:

a) H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

The P-value is less than the significance level.

Therefore, Reject the null hypothesis

In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Step-by-step explanation:

(a) From the information given, we can identify the null hypothesis and alternative hypothesis.

H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

(b) n1 which is size of sample 1 = 279

p1 which is proportion of sample 1= 0.60

n2 which is size ofsample 2 = 279

p2 which is proportion of sample 2 = 0.14

P=n1p1+n2p2 / n1+n2

=279 × 0.60+279 × 0.14/279+279

=0.37

Q = 1- P = 0.63

SE= √PQ(1/n1+1/n2)

= √ 0.37 × 0.63(1/279+1/279)=0.0409

So,

Test statistic is:

Z = (p1 - p2) /SE

= (0.60 - 0.14)/0.0409

= 11.3049

(c) The able of Area Under Standard Normal Curve gives the following area =

0.5 approximately.

So,

P-value = 0.5 - 0.5 nearly =0 nearly

(d)From the information derived, the P-value is less than the significance level.

Therefore, Reject the null hypothesis

In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.