Researchers are investigating the effectiveness of leg-strength training on cycling performance. A sample of 7 men will be selected to participate in a training program that lasts for one month. Peak power during cycling will be recorded for each man both before training and after training. The mean difference in times will be used to construct a 95 percent confidence interval for the mean difference in the population.

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:

They will accept the $50,000 maximum offered by your insurance company

In this scenario, with $50,000 liability insurance, if you cause a $75,000 accident, the other party is likely to accept the $50,000 from your insurance (Option C) but could also sue you for the remaining $25,000 (Option D).

In this scenario, if you cause an accident resulting in $75,000 in damage to the passengers in another car, your liability insurance has a maximum coverage limit of $50,000 per accident. Typically, insurance policies cover up to the policy limits, and the insurance company would pay out up to $50,000 to the injured parties.

The most likely outcome in this situation would be that the injured parties may initially pursue a claim with your insurance company, and the insurance company would pay up to its policy limit of $50,000. However, since the damages exceed the policy limit, the injured parties may still have the option to sue you personally for the remaining $25,000 to cover their damages.

So, the answer could be a combination of options C and D: They may accept the $50,000 maximum offered by your insurance company but could also potentially sue you for the remaining $25,000 if they believe it's necessary to cover their damages. The actual outcome may vary depending on the specific circumstances, local laws, and the decisions made by the injured parties and their legal advisors. It's crucial to notify your insurance company as soon as an accident occurs so they can handle the situation accordingly.

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Let U={a,b,c,d,e,f,g,h}

A={a,c,d}

B={b,c,d}

C={b,e,f,g,h}

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: no

Step-by-step explanation:

Answer:

The expected value is 0.87.

Step-by-step explanation:

a) To calculate the expected value X we will first see the posible outcomes. So could take value of 0,1,2,3. We will calculate the probability of each outcome. To do so, we will introduce the following notation. Consider the following tuple (A,B,C) where A is the number of butterflies found by Alice, B the number found for by Bob and C the number found by C. To calculate the probability of the tuple (A,B,C) we will do as follows. If the entry of the tuple is 1, then we will multiply by the probability of the person that found the butterfly. So, if A =1, we will multiply by 0.17(Alice finds a butterfly with probability 0.17). On the other side, if the entry of the tuple is 0, we will multiply by (1-p) where p is the probability of the person that found the butterly. So, if A=0, we will multiply by 0.83. So, for example, consider the tuple (1,0,1). The probability of having this result is 0.17*0.75*0.45 (Alice and Charlotte found a butterfly, but Bob didn't). We can do this since we are said that their probabilities of success don't affect others' probabilities.

We will see the total number of butterflies and the tuples associated to that number. That is

X number of butterflies - tuples

0 butterflies - (0,0,0)

1 butterfly - (1,0,0) or (0,1,0) or (0,0,1)

2 butterflies - (1,1,0) or (1,0,1) or (0,1,1)

3 butterflies - (1,1,1)

To find the probability of the value of X, we will sum up the probability of the associated tuples. The values of the probabilities are as follows

(0, 0, 0) =  0.342375

(0, 0, 1 ) = 0.280125

(0, 1, 0)  = 0.114125

(0, 1, 1 ) = 0.093375

(1, 0, 0)  = 0.070125

(1, 0, 1 ) = 0.057375  = 0.17*0.75*0.45

(1, 1, 0)  = 0.023375

(1, 1, 1)  = 0.019125

In this case,

P(X=0) =  0.342375 ,

P(X=1) = 0.464375  = 0.280125 +0.114125+ 0.070125

P(X=2) = 0.174125

P(X =3 ) = 0.019125

So, the expected value of X is given by

0*  0.342375 +1 * 0.464375 +2* 0.174125+3*0.019125 = 0.87

b)Let X1 be the number of butterflies found by Alice, X2 the number found by Bob and X3 the number found by Charlotte. Then X = X1+X2+X3. Using the expected value properties and the independence of X1, X2 and X3 we have that E(X) = E(X1)+E(X2)+E(X3).

Recall that each variable is as follows. Xi is equal to 1 with probability p and it is 0 with probability (1-p). Then, the expected value of Xi is

[tex]1\cdot p + 0\codt (1-p)=p[/tex]. Note that the value of p for X1,X2 and X3 is 17%, 25% and 45% respectively.

Then E(X) = 17%+25%+45%= 0.87.

So the expected number of butterflies is 0.87.

Final answer:

The expected value of the total number of butterflies, X, that Alice, Bob, and Charlotte catch is 0.87. This is found by summing their independent probabilities of catching a butterfly (0.17 for Alice, 0.25 for Bob, and 0.45 for Charlotte). X is also represented as the sum of three indicator random variables X1, X2, and X3, leading to the same expected value.

Explanation:

Expected Value of the Number of Butterflies Caught

In this scenario with Alice, Bob, and Charlotte searching for butterflies in separate parts of a field, the random variable X represents the total number of butterflies they catch. The expected value of X, or E(X), is calculated by adding the individual probabilities of finding a butterfly, since their probabilities are independent.

To find the expected value of X:

Multiply the probability of each person finding a butterfly by the number of butterflies they would find in that event (which is 1 since each either finds 1 butterfly or none), and

Add these products together.

The expected value is thus 0.17 + 0.25 + 0.45 = 0.87 butterflies. We can also express X as X1 + X2 + X3, where each Xi is an indicator random variable for whether Alice (X1), Bob (X2), or Charlotte (X3) found a butterfly.

The expected value for each indicator variable is the same as the person's probability of success. So, E(X1) = 0.17, E(X2) = 0.25, and E(X3) = 0.45. By the linearity of expectation, E(X) = E(X1) + E(X2) + E(X3), which also equals 0.87 butterflies.

Step-by-step explanation:

The given expression in word problem can be translated as:

Six more than half of a number is 20

A real-world problem for the equation 1/2x + 6 = 20 could be determing the number of days a person should work, earning a rate of half the square of the number of days, to achieve a total sum of $20. The person initially has $6 and after working for 28 days, he or she achieves the goal.

Consider a real-world example represented by the equation 1/2x + 6 =20. Imagine your grandmother gives you $6 and says you can do chores for her on some days to earn half the square of the number of days you worked in dollars. If you want to accumulate $20 in total, how many days should you work? This problem asks the same as solving for 'x' in the equation where 'x' is the number of days and the total sum of money is $20.

To solve this, you would need to subtract 6 from both sides of the equation, leaving you with 1/2x =14. Then, you multiply both sides by 2 to get x = 28, so it takes 28 days of work.

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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

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:

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:

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

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

Answer:

Over the boundary: maximum:13, minimum:12

Over D: maximum:13, minimum:0

Step-by-step explanation:

We are given that [tex]f(x,y) = 12x^2+13y^2[/tex] and D is the disc of radius one. Namely, [tex]x^2+y^2\leq 1[/tex].

First, we want to find a critical point of the function f. To do so, we want to find the values(x,y) such that

[tex] \nabla f (x,y) =0[/tex].

Recall that [tex] \nabla f (x,y) = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})[/tex].

So, let us calculate [tex] \nabla f (x,y)[/tex] (the detailed calculation of the derivatives is beyond the scope of the answer.

[tex]\frac{\partial f}{\partial x} = 24x[/tex]

[tex]\frac{\partial f}{\partial y} = 26y[/tex]

When equalling it to 0, we get that the critical point is (0,0), which is in our region D. Note that the function f is the sum of the square of two real numbers multiplied by some constants. Hence, the function f fulfills that [tex]f(x,y)\geq 0[/tex]. Note that f(0,0)=0, so without further analysis we know that the point (0,0) is a minimum of f over D.

If we restrict to the boundary, we have the following equation [tex] x^2+y^2=1[/tex]. Main idea is to replace the value of one of the variables n the function f, so it becomes a function of a single variable. Then, we can find the critical values by using differential calculus:

Case 1:

Let us replace y. So, we have that [tex]y^2=1-x^2[/tex]. So, [tex]f(x,y) = 12x^2+13(1-x^2) = -x^2+13[/tex].

So, we will find the derivative with respect to x and find the critical values. That is

[tex] \frac{df}{dx} = -2x=0[/tex]

Which implies that x =0. Then, [tex] y =\pm 1[/tex]. So we have the following critical points (0,1), (0,-1). Notice that for both points, the value of f is f(0,1) = f(0,-1) = 13.  If we calculate the second derivative, we have that at x=0

[tex] \frac{d^2f}{dx^2} = -2<0[/tex]. By the second derivative criteria, we know that this points are local maximums of the function f.

Case 2:

Let us replace x. So, we have that [tex]x^2=1-y^2[/tex]. So, [tex]f(x,y) = 12(1-y^2)+13y^2 = y^2+12[/tex].

So, we will find the derivative with respect to y and find the critical values. That is

[tex] \frac{df}{dx} = 2y=0[/tex]

Which implies that y =0. Then, [tex] x =\pm 1[/tex]. So we have the following critical points (-1,0), (1,0). Notice that for both points, the value of f is f(1,0) = f(-1,0) = 12.  If we calculate the second derivative, we have that at y=0

[tex] \frac{d^2f}{dx^2} = 2>0[/tex]. By the second derivative criteria, we know that this points are local minimums of the function f.

So, over the boundary D, the maximum value of f is 13 and the minimum value is 12. Over all D, the maximum value of f is 13 and the minimum value is 0.

Final answer:

The critical point of f(x, y) on the disk D is (0, 0). f(x) restricted to the boundary of D is f(x) = 12x^2 + 13(1 - x^2) with the domain [-1, 1]. The absolute maximum and minimum values of f(x, y) over all of D are 25 and 0, respectively.

Explanation:

To find the critical point of the function f(x, y) = 12x2 + 13y2 on the disk D: x2+y2 ≤ 1, we need to set the partial derivatives of f with respect to x and y equal to zero.

The partial derivative with respect to x is 24x, and setting it to zero gives x = 0. Similarly, the partial derivative with respect to y is 26y, which implies y = 0. Therefore, the critical point is (0, 0).

On the boundary of D, where x2+y2 = 1, we can solve for y2 as y2 = 1 - x2. Substituting into f, we get a function of a single variable x: f(x) = 12x2 + 13(1 - x2) with the closed interval domain [-1, 1].

The maximum value on the boundary occurs at x = ±1, giving a maximum of f(±1) = 25. The minimum on the boundary is at x = 0, which gives f(0) = 13.

Across the entire disk D, the absolute minimum is at the critical point (0,0), with f(0, 0) = 0, and the absolute maximum is the same as the boundary maximum, f(x) = 25.

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:

There is no sufficient evidence

Step-by-step explanation:

See attached files

Answer:

A) i) the probability it is brown = 60%.  (ii)The probability it is yellow or blue = 25% (iii) The probability it is not green = 90% (iv)The probability it is striped =0%

B) i)The probability they are all brown = 21.6%.  (ii) Probability the third one is the first one that is​ red = 4.51% (iii) Probability none are yellow = 51.2% (iv) Probability at least one is green = 27.1%

Step-by-step explanation:

A) The probability that it is brown is the percentage of brown we have.  However, Brown is not listed, so we subtract what we are given from 100%. Thus;

100 - (20 + 5 + 5 + 10) = 100 - (40) = 60%. 

The probability that one drawn is yellow or blue would be the two percentages added together:  20% + 5% = 25%. 

The probability that it is not green would be the percentage of green subtracted from 100:  100% - 10% = 90%. 

Since there are no striped candies listed, the probability is 0%.

B) Due to the fact that we have an infinite supply of candy, we will treat these as independent events. 

Probability of all 3 being brown is found by taking the probability that one is brown and multiplying it 3 times. Thus;

The percentage of brown candy is 60% from earlier. Thus probability of all 3 being brown is;

0.6 x 0.6 x 0.6 = 0.216 = 21.6%

To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100% - 5% = 95% = 0.95

Now, for the first two and the probability that it is red = 5% = 0.05

Thus for the last being first one to be red = 0.95 x 0.95 x 0.05 = 0.0451 = 4.51%.

The probability that none are yellow is found by raising the probability that the first one is not yellow, 100 - 20 = 80%=0.80, to the third power:

0.80³ = 0.512 = 51.2%.

The probability that at least one is green is; 1 - (probability of no green). 

We first find the probability that all three are NOT green:

0.90³ = 0.729

1 - 0.729 = 0.271 = 27.1%.

Final answer:

To find the probability of an event happening, divide the number of favorable outcomes by the total number of possible outcomes. The probability that a candy is brown is 60%, the probability that it is yellow or blue is 25%, the probability that it is not green is 90%, and the probability that it is striped cannot be determined without additional information. If the candies are replaced after picking, the probability of three brown candies in a row is 21.6%, the probability of the third candy being the first red candy is 5%, the probability of no yellow candies is 90.25%, and the probability of at least one green candy is 27.1%.

Explanation:

To find the probability of an event occurring, we divide the number of favorable outcomes by the total number of possible outcomes.

a) The probability of picking a brown candy is 100% - (20% + 5% + 5% + 10%) = 60%. The probability of picking a yellow or blue candy is 20% + 5% = 25%. The probability of not picking a green candy is 100% - 10% = 90%. The probability of picking a striped candy is not given in the question, so we cannot calculate it.

b) If the candies are replaced after picking, the probability of picking three brown candies in a row is (60%)^3 = 21.6%. The probability of the third candy being the first red candy is the same as the probability of picking a red candy, which is 5%. The probability of none of the candies being yellow is (100% - 5%)^2 = 90.25%. The probability of at least one candy being green is 1 - (100% - 10%)^3 = 27.1%.

Answer:

2 hours if they go to school.

10 hours if they dont go to school.

Step-by-step explanation:

add up the hours.

9/2+5/2=14/2=7hours +7 hour of sleep= 14 hours.

if they go to school for 8 hours then add 8. then it =22 hours witch gives you 2 hours

if they dont go to school then you got 24-14 hours=10 hours.

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 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.

Learn more about statistical significance here:

https://brainly.com/question/15873779

Answer:

10 people

Step-by-step explanation:

Given:

Colors of shirts: 3 (red, blue, and purple)

Colors of pants: 3 (black, brown, or white)

Total number of outfits ( both shirts and pants) =

3 * 3 = 9

The minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits will be:

Total number + 1

= 9 + 1

= 10 people

Answer:

A.y=2x^5 + c1+ c2x + c3x^5

B. Y = 2x² + 9+7x+2x^5

Step-by-step explanation:

See attached file

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:

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:

x +21

Step-by-step explanation:

13+(x+8)=

Combine like terms

x +13+8

x +21

Alternate angles in a transversal are congruent.

The value of x is 13

See attachment for the image of the transversal,

Where [tex](9x + 2)[/tex] and [tex]119[/tex] are alternate angles

This means that:

[tex]9x + 2 = 119[/tex] ---- alternate angles are equal

Collect like terms

[tex]9x = 119 - 2[/tex]

[tex]9x = 117[/tex]

Divide both sides by 9

[tex]x = 13[/tex]

Hence, the value of x is 13

Read more about alternate angles at:

https://brainly.com/question/22580956

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:

256 m2

Step-by-step explanation:

- First, know the formula A = (a+b/2)h

- Using this, we will fill the equation in with our variables. For example...

A = ((13+19)/2)16

A = (32/2)16

A = (16)(16)

A = 256 m2

- Hope this helps! If you need a further explanation or step by step practice please let me know.

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]