The amount of work done in a certain amount of time is called?

The value obtained for new correlation will be 0.1

What is Correlation ?

Correlation is a term which is used in statistics. It is a statistical measure that indicates the range to which the two or more variables fluctuate together.

There are mainly two type of correlation that is positive correlation in which variables increase or decrease partially in negative correlation if one variable  is increases then other decreases

Given :

n = 15 pairs

r = 0.20

According to the Question , If each of the X values is multiplied by 2

The value obtained for new correlation will be  [tex]r = \frac{0.2}{2}[/tex] =  0.1

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The vertices of a regular decagon can only ever give rise to a maximum of zero scalene triangles at any one time.

Generally, An isosceles triangle has two sides with the same length. There are 10 ways to choose the vertex that is common to the two equal sides, and for each of these choices, there are 5 ways to choose the other two vertices (since they must be distinct from the first). Therefore, there are a total of

10* 5*5=250 isosceles triangles.

To get the final count of scalene triangles, we use the principle of inclusion-exclusion by subtracting the number of isosceles triangles from the total number of triangles.

This gives us a final count of 120-250=-130.

However, since we cannot have a negative number of triangles, the final answer is 0.

Therefore, there are 0 scalene triangles that can be formed from the vertices of a regular decagon.

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The complete Question was not found

In the picture we can see the graph represents of the function f(x)=x²-2x+3 that is curve graph.

Given that,

We have to find the graph represents the function f(x)=x²-2x+3.

We know that,

The quadratic function is f(x)=x²-2x+3.

This is a vertical parabola open downward

The vertex is a maximum

We know,

A vertical parabola's equation in vertex form is equal to

y= a(x-h)²+k

where

a is a coefficient

(h,k) is the vertex

Here

a=1

(h,k)=(0,3)  is vertex

The y-intercept is the point (0,3) is value of y when the value of x is equal to zero (is the same point that the vertex)

The x-intercepts are the points is values of x when the value of y is equal to zero  

Therefore, In the picture we can see the graph represents of the function f(x)=x²-2x+3.

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The statement that characterizes the outcome of the game is option d;

All of the above are correct.

Given,

The statements;-

a. Both Firm A and Firm B have a dominant strategy to advertise.

b. There is a Nash equilibrium when both firms advertise.

c. Although both firms collectively would earn higher profits by maintaining the agreement not to advertise, self-interest will cause each firm to break the agreement.

d. All of the above are correct

We have to find the correct statement that characterize the outcome of this game.

Here,

All the statement will characterize the outcome of this game. So correct answer is option d, All of the above are correct

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The dimensions of the rectangle are:

Length = 10 m

Width = 6.5 m

Recall that the area of aa rectangle is given as, length × width.

Given the following:

Area of the rectangle = 65 m²

Let the width of the rectangle be represented as w.

Length of the rectangle = 2w - 3 m

Therefore:

(2w - 3)(w) = 65

Expand:]

2w² - 3w = 65

2w² - 3w - 65 = 0

Factorize:

w = 6.5 or w = -5

The width cannot be negative, therefore, the width = 6.5 m.

Length of the rectangle = 2w - 3 = 2(6.5) - 3 = 10 m

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Answer: No mistake

It seems that there are not any problems with these steps.

Answer:

26.74

Step-by-step explanation:

add the money John spends on the week days(13.75) to 12.99 and you get your answer

The nonprofit company charges $100 each ticket for the opportunity to win a $50,000 vintage Mustang. With four prizes and 1500 tickets sold, he expects to lose $54.53 on each one.

The chance of winning is multiplied by the bet multiplier to determine the mathematical anticipated value. Typically, expected value is estimated for a bet of one unit. To determine the predicted profit, multiply the win chance by the stake amount.

Chances of getting first prize = 1/1500

Chances of getting second prize = 1/1500

Chances of getting third prize = 1/1500

Chances of getting Fourth prize = 1/1500

Cost of one ticket = $100

Expected winning = -100 +1/1500 (56000 + 6600 + 4300 + 1300)

= -100 + 68200/1500

= - 54.53 dollars

There is an expected loss of $54.53.

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Answer:

I think Numerical and univariate

Step-by-step explanation:

Answer:

Step-by-step explanation:

This would be numerical and univariate because the information shown represents a stem and leaf plot.

Hope this helps! :)

95% confidence interval for the true mean breaking strength of the white wood is (71.66 MPA, 78.74 MPA)

The result above means that the lower limit of the true mean breaking strength of the white wood is 69.89 MPA and the upper limit is 81.51 MPA.

The definition says, "A confidence interval is a range of values ​​derived from a sample statistic that likely includes the value of an unknown population parameter."

To calculate the confidence interval, we need to know three parameters of the sample: the mean (average value) μ, the standard deviation σ, and the sample size n (number of measurements). Then you can calculate standard error and tolerance using the following formulas:

                      standard error = σ/√n

Given in the question:

Confidence interval = mean + or - Error margin (E)

Mean = 75.2 MPA

Standard deviation = 8.6 MPA

Sample size, n = 25

Now,

Degree of freedom = n - 1 = 25 - 1 = 24

Confidence level (C) = 95% = 0.95

Significance level = 1 - C

                              = 1 - 0.95

                              = 0.05 = 5%

Therefore, t-value corresponding to 24 degrees of freedom and 5% significance level is 2.06

Again,

E = t × sd/√n

  = 2.06 × 8.6/√25

  = 2.06 × 1.72

  = 3.54 MPA

Lower limit = Mean - E

                  = 75.7 - 5.81

                  = 69.89 MPA

Upper limit = Mean + E

                   = 75.7 + 5.8

                   = 81.51 MPA

95% confidence interval is (69.89 MPA, 81.51 MPA)

The result means that the true mean breaking strength of the white wood is between 69.89 and 81.51 MPA.

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The equation, in standard form, that  represents the relationship between the number of lunches, x is 5x + y = 100. Option A

An equation is a mathematical statement that illustrates the equality of two things.

The given parameters are

Amount spent = x

Amount that remains = y

Total amount spent = 100

The difference between the amount spend is 5

This implies that 5(x) + y (1) = 100

Opening the brackets to have 5x + y = 100

In this case, we conclude that the best equation  in standard form, represents the relationship between the number of lunches, x, is 5x + y = 100

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The area under the given curve is 77/60. SO the option B is correct.

In the given question we have to estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.

The given function is

F(x) = 1/x; [1,5]; n=4

The given options are:

A≈77/240

A≈77/60

A≈77/15

A≈25/3

A≈25/12

Since, f(x) =1/x

∆x = (b-a)/n

∆x = (5-1)/4

∆x =4/4

∆x = 1

Now the table is

x               1            2            3            4            5

f(x)            1            1/2          1/3         1/4          1/5

R(4) = [f(2)+f(3)+f(4)+f(5)]∆x

R(4) = [1/2+1/3+1/4+1/5]1

R(4) = (30+20+15+12)/60

R(4) = 77/60

Hence, the area under the given curve is 77/60. SO the option B is correct.

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The right question is given below:

The statement If B ⊂ A, then A U B = A is true.

From the question, we have the following parameters that can be used in our computation:

If BCA, then AUB=A.

When the above statement is represented properly, we have the following representation

If B ⊂ A, then A U B = A

The statement If B ⊂ A means that

The set B is a subset of the set A

In other words, the whole of set B is in set A

If this is true, then the union of both sets represented by A U B is set A

Hence, it is true that If B ⊂ A, then A U B = A

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Tamia will need 166 feet of fabric

Given that:

Tamia wants each curtain to be 24 inches long

At the fabric store, fabric is sold by the foot

Tamia's curtain company wants to make 83 curtains

1 curtain = 24 inches

83 curtains = 24×83 = 1992 inches

To convert inches to feet multiply by 1/12:

1992 inches =  1992 × 1/12 feet = 166 feet

Thus, she will need 166 feet

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You will pay a price of $72.31 if you wait to purchase tickets at the door

Discount is defined as a deduction from the usual cost of something. You will save 22% off the door price by prepay $56.40 per ticket now.

Let P represent the original price. We can write that:

P - 22% of P = $56.40. It should be noted that this can be rewritten as:

P - (22% × P) = 56.40

P - 0.22P = 56.40

Subtract

0.78P = 56.40

Divide through by 0.78

P = 56.40/0.78

P = $72.31

Therefore the price is $72.31.

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There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Answer:

dependent

Step-by-step explanation:

the probability of 0.697 is dependent upon Kaia scoring an 82, followed by an 85 on the other test

Check:  multiply 0.82 by 0.85 and your will get 0.697

On solving the provided question we go to know that - Graph with points- (2,1) (0,3) (4,3) (x,y).

In mathematics, a function is an expression, rule, or law that establishes the connection between two variables (the dependent variable).

a unique connection where every input only has one output. Where x is the input value, it is frequently expressed as yields a single output [tex]"x/2,"[/tex]indicating that it is a function:[tex]* f(2) = 1.[/tex]

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The propagated error in computing the area of the square is 6.01 cm

According to the question,

It is given that Length of side of square was found = 30cm

The possible error in measurement = 0.1cm

So, the length will be 30 + 0.1cm or 30 - 0.1cm

As we know that

Area of the square : A = x²

Where x is side of square

The differential of this equation =

=> dA/dx = 2x --------(1)

If dx is the error of the side length of the square

dA = 2(30)(0.1)

=> dA = 6

Therefore , The propagated Error = ΔA = (x + Δx)² - x²

=> (30 + 0.1)² - (30)²

=> 906.01 - 900

=>  6.01

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The dimensions of the rectangular package with the condition of maximum volume is equal to  x = 19inches and y = 38inches.

As given in the question,

Let us consider length of the cross section which is square be x

Perimeter of the cross section is 4x

And y be the length of the rectangular package

Maximum combined ( length + perimeter of the cross section ) = 114

y + 4x = 114

⇒ y = 114 -4x

Volume of the package 'V' = x²y

⇒V = x²(114 -4x)

⇒V = 114x² -4x³

Differentiate both the side of the equation with respect to x,

dV/dx = 228x - 12x²

For maximum Volume

dV/dx =0

228x -12x² = 0

⇒12x( 19 -x ) =0

⇒12x = 0 or 19 - x =0

⇒x =0 or x =19

x =0 is not possible

⇒x =19inches

y = 114 - 4(19)

  = 38inches

Therefore, the dimensions of the rectangular package with the given condition of volume is equal to x = 19inches and y = 38inches.

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If Roberta took two tests. She scored 10 points more on the second test. she score 70 on the second test.

Average score = (x+y)/2

he scored 10 points less on the second test than he did on the first.

y = x - 10

Replace y with x-10

(x + x - 10) / 2

(2x-10)/2

Average score on both tests is 75

(2x-10)/2 = 75

Multiply both sides of this equation by 2

2x-10 = 150

Add 10 to both sides

2x = 160

Divide both sides  by 2x

x = 160/2

x = 80 (She got 80 on the first test)

He got 80 - 10 = 70 (She got 70 on the second test)

(80+ 70) / 2 = 150/2 = 75 (She got average  of 75 on both tests)

Therefore she scored 70 on the second test is your solution.

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The amount Sally’s share would be;

⇒ $30,000

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

John, Sally and Jane form a partnership. They agree to distribute profits using a 2:3:2 ratio.

And, The profits are $70,000.

Now,

Since, The profits are $70,000.

Hence, We get;

⇒ 2x  + 3x + 2x = $70,000

⇒ 7x = $70,000

⇒ x = $10,000

So, The amount of Sally’s share would be;

⇒ 3x = 3 × 10,000

         = $30,000

Thus, The amount Sally’s share would be;

⇒ $30,000

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The coordinate pair of D that will make AB perpendicular to CD is ( 4,7)

The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1.

The slope of a line is given as ( y1-y2)/(x1-x2)

for AB and CD to be perpendicular

( y2-y1)/(x2-x1) × ( y4-y3)/(x4-x3) = -1

therefore (5-4)/-2-1 = ( y4-y3)/(x4-x3)

1/-3 ×(y4-4)/(x4-3) = -1

(y4-4)/(x4-3) = 3/1

therefore 3= y4-4 and 1 = x4-3

therefore y4 = 3+4= 7

and x4 = 1+3= 4

therefore the coordinate of D = (x4,y4) for AB perpendicular to CD = (4,7)

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Answer:

x = 13

x = 1

Step-by-step explanation:

The (x – 7)2 = 36 gives the value of x as 25.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

(x – 7)2 = 36

Now, dividing both side by 2

(x – 7)2/2 = 36 /2

(x – 7) = 18

Now, add 7 both side

x- 7+ 7= 18 + 7

x = 25

Hence, the value of x is 25.

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The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Let the missing number be 'x'. Then the equation is given as,

25 - x = 13

Simplify the equation, then the value of the variable 'x' will be given as,

25 - x = 13

x = 25 - 13

x = 13

The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.

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The rate of hiking is 4 miles per hour.  The rate of driving is 40 miles per hour.

What is the mile?

Mile, any of various units of distance, such as the statute mile of 5,280 feet (1.609 km). It originated from the Roman mile passus, or “thousand paces,” which measured 5,000 Roman feet.

We have given,

A camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods. The camper's speed while driving was ten times that of the hiker. Three hours were spent driving and hiking together.

We have to determine the camper's hiking speed.

We know that,

Let x represent the increasing rate and 10x represent the driving rate

Time equation is

80/10x + 4/x = 3

Simplify

8/x + 4/x = 3

12/x = 3

x = 12/3

x = 4

Therefore, Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.

Hence, the rate of hiking is 4 miles per hour.  The rate of driving is 40 miles per hour.

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Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

If 60% of the population supports massive federal budget cuts.

We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.

So, the probability is, 155 / 250 = 0.62

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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The non-zero orthogonal vector to the plane is 486i + 243j + 162j and the area of the triangle is 4374 unit squares.

The vertices of the triangle are P(9, 0, 0), Q(0, 18, 0), and R(0, 0, 27).

So, firstly we should find the vector PQ and PR,

Now,

PR = (0)i + (-18)j + (27)k

PR = -18j + 27j

And PQ,

PQ = (-9)i + (18)j + (0)k

PQ = -9i + 18j

Now, the normal vector which is also a non-zero orthogonal vector,

n = PQ x PR

n = 486i + 243j + 162j

Now, the area of the ΔPQR will be,

Ar(PQR) = [tex]\left[\begin{array}{ccc}9&0&0\\0&18&0\\0&0&27\end{array}\right][/tex]

Solving further,

Ar(PQR) = 4374 unit square.

So, the area of the triangle is 4374 unit square.

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Answer:

Step-by-step explanation:16x^2+9=25

                                             16x^2=16

                                               x^2=1

                                                 x=1 or -1

                                                   D