for a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 115 min and 135 min? (round your answer to four decimal places.)

The average cost function is C(x) = 5000x + 20,000/x, where x is the number of machines used in the production. The critical value is C(x) = 20,000 and it happens when x = 2.

If we have a function f(x), the critical point happens when its first derivative is equal to zero.

             f '(x) = 0

In the given problem, the function is:

C(x) = 5000x + 20,000/x

Take the derivative:

C '(x) = 5000 - 20,000/x² = 0

5000 x² = 20,000

x² = 4

x = ±2

Since x is within the interval: 0<x<∞, the solution is x = 2

Substitute x = 2 into the function:

C(2) = 5000 (2) + 20000/2

C(2) = 10000 + 10000 = 20,000

Hence, the critical value is C(x) = 20,000 and it happens when x = 2.

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Answer:

5x + 10× - 30= 180 degree

15x =150

x= 10

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Answer:

Given, x²+y²+4X −2y= −1

⇒x²+4x+y²=−1

⇒(x²+4x+4)+(y² −2y+1) =−1+4+1

⇒(x+2)²+(y−1) = 2²

Clearly, = (−2,1)

Radius = 2

The radius of the circle is 2. Therefore, A) is the answer

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Given the equation of the circle as x² + y² + 4x - 2y = -1

Factorize the equation using the completing square:

x² + y² + 4x - 2y = -1

x² + 4x + (2)²  + y² - 2y + (-1)² = -1 + (2)² + (-1)²

(x+2)² + (y-1)² = -1 + 4 + 1

(x+2)² + (y-1)² = 4

(x+2)² + (y-1)² = 2²

Comparing this equation with (x-a)² + (y-b)² = r²:

r = 2

Thus, the radius of the circle is 2

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If a gardner plants 90 seedlings. the number of seedlings in each row is 3 more than twice the number rows then 43.5 number of rows are planted by the gardner.

Two or more expressions with an Equal sign is called as Equation.

Given,

Gardner plants 90 seedlings

The number of seedlings in each row is 3 more than twice the number rows.

We need to find the number of rows.

Let r be the number of rows

2r+3=90

Subtract 3 from both sides

2r=87

Divide both sides by 2

r=43.5

Hence, 43.5 number of rows are planted by the gardner.

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The matrices A and B are not inverse matrices

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

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

[tex]B = \left[\begin{array}{cc}1&-1&-1&2\end{array}\right][/tex]

To determine if the matrices are inverse matrices, we simply calculate the inverse of matrix A and then make the comparison.

The matrix A is given as

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

Calculate the determinant of the matrix A

So, we have the following representation

|A| = -2 * -2 + 3 * 2

Evaluate the sum of products

|A| = 10

The inverse is then calculated as

[tex]A^{-1} = \frac 1{10} * \left[\begin{array}{cc}-2&3&-2&-2\end{array}\right][/tex]

Evaluate

[tex]A^{-1} = \left[\begin{array}{cc}-\frac 1{5}&\frac 3{10}&-\frac 1{5}&-\frac 1{5}\end{array}\right][/tex]

When compared to matrix B, both matrices are different

Hence, the matrices are not inverse matrices

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The completed equation of complex numbers in the puzzle is presented as follows;

(5 - 6·i) × (2 + 4·i) = 34 + 8·i

Complex numbers are numbers that have a real number part and an number imaginary part.

The formula form the multiplication of two complex numbers is presented as follows;

(a + i·b) × (c + i·d) = (a·c - b·d) + i·(a·d + b·c)

The specified equation is; (_ + _i) × (_ + _i) = 34 + 8·i

Therefore; (a·c - b·d) = 34

(a·d + b·c) = 8

Making a the subject, we get;

(34 + b·d)/c = (8 - b·c)/d

34·d + b·d² = 8·c - b·c²

b·d² + b·c² = 8·c - 34·d

b = (8·c - 34·d)/(d² + c²)...(1)

Similarly, making c the subject, we get;

(34 + b·d)/a = (8 - a·d)/b

34·b + b²·d = 8·a - a²·d

b²·d + a²·d = 8·a - 34·b

d = (8·a - 34·b)/(b² + a²)...(2)

The values of b and d which are whole numbers larger than or equal to -9 and less than or equal to 9, obtained using MS Excel are;

-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8

Obtaining the whole number digit for b from equation (1) and plugging in the value of b in equation (2), to obtain the value of d with which the value of b was obtained, we should get;

a = 5, b = -6, c = 2, and d = 4

Which indicates that we get;

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The incorrect descriptor is :

The graph is centered around 0 , using the properties of graph of normal distribution of random variable.

What is normal distribution?

Normal distribution is continuous probability distribution of a real valued random variable.

Properties:

1.The curve is symmetric at center around the mean .

2. The curve shape is bell-shaped.

So, from above properties, we can say that the statement - "The graph is centered around 0" is incorrect.

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Answer: 8

Step-by-step explanation:

=(1) ^3×(2) ^3

=1×1×1×2×2×2

=1×8

=8

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P is the subject of the formula if we rewrite it as:

p = m*(nx - y²)/3n

The subject of a formula is the variable that is isolated, so here we only need to isolate the variable p.

The formula is:

m*(nx - y²)/p = 3n

First, we can multiply both sides by p to get:

m*(nx - y²) = 3n*p

Now we can divide both sides by 3n, then we will get:

m*(nx - y²)/3n = p

Now p is the subject of that formula.

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Answer:

Question 1: Calculate the coordinates of 2 points. You know that the value of the Y coordinate in a point is 4 times the value of the x in the same point. Once you figure out the points, put them on the graph and draw a straight line through them with a ruler.

Question 2: What number do you multiply 5 by to get 12? You multiply that same number by the 375 to get the value in the corresponding row. That's called proportion.

Question 3: You can find the proportion between the two values (distance and energy). Its how many times bigger (or smaller) the values are in relation to each other. You can use this proportion for the scale of the graph so that the location of points are easier understood in relation to each other and discernable all by your eye.

The proportions in this problem are given as follows:

1. a = 40.

2. t = 1.

3. q = 29.25.

4. g = 3.

5. m = 9.8.

6. v = 12.9.

7. w = 1.3.

8. n = 2.28.

9. n = 0.84.

10. k = 1.2.

11. t = 0.57.

12. z = 63.4.

The proportions are solved using these two steps presented as follows:

Then, for item a, the proportion is given as follows:

3/8 = 15/a

Applying cross multiplication, we have that:

3a = 15 x 8

Then, the variable a is isolating applying the division operation, as follows:

a = 15 x 8/3

a = 5 x 8 (as 15/3 = 5)

a = 40.

Then the second proportion is solved as follows:

t/2 = 6/12

12t = 12

t = 1.

And the same procedure is then applied to obtain any of the remaining 10 proportions. Some include operations with decimals, hence calculator used is recommended.

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The probability the researcher will make a type i error 0.10

The hypothesis testing, type I error involves rejecting true null hypothesis also referred to as 'false-positive' conclusion and type II error occurs when false null hypothesis is not rejected. It is also known as 'false negative' conclusion. And they are opposite to each other.

Here we have given that suppose a researcher plans to conduct a test of hypotheses at the 5% significance level. she designs her study to have power of 0.90 at a particular alternative value of the mean

And we need to find the probability the researcher will make a type i error

While looking into the given question,

We know that,

Significance level = 5%

alternative value of the mean = 0.90

Then the probability the researcher will make a type i error is calculated as,

mean = 1 - error

0.90 = 1 - error

=> error = 0.10

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The equation of the line passes through the point (6,2) and slope 1/3 is

X=3Y-3

Here the point is (6,2) and the slope is 1/3

Means,

x=6      y=2   and m=1/3

We know that the equation of a line is -

Y=mx+c

Putting these values in the above equation we get

⇒2=1/3×6+c

⇒2=6/3+c

⇒2=2+c

⇒c=1

Therefore we find that the intercept is 1

So after putting all these values in that equation y=mx+c we get

Y=1/3X+1

⇒X/3=Y-1

⇒X=3Y-3

The equation passes through the point (6,2) and the slope is  1/3 is x=3y-3

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Answer:

y < -1x + 2

y [tex]\geq \\[/tex] 2x + 4

Step-by-step explanation:

The steps taken to find the two inequalities are on the GraphInequalities worksheet.  The derived equations are graphed on DESMOS and attached, for comparison.

The basic steps are to find the slopes of the two lines and to identify the y-intercepts from the graph.  The inequalities can be assigned based on the darkened areas and presence of either a solid or dashed line.  All are outlined in the worksheet.

The slope of the line is  4/3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

In the slope marked,

vertical length = change in y values = number of unit squares = 4

Horizontal length = change in x values = number of unit squares = 3

Slope= ( change in y values  )/ ( change in x values ) = 4/3

Thus, the slope = 4/3

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The correct answer is (a) 10-15, 15-20. This is an example of a Discontinuous class.

In the context of statistical data and classification, a class is a group of observations or data points that share certain characteristics. Classes can be either continuous or discontinuous, depending on whether the values or categories they represent are continuous or not.

A discontinuous class is a set of values or categories that are not continuous, meaning there are gaps or breaks between them. In this case, the classes 10-15 and 15-20 are discontinuous because there is a gap between them at 15. In contrast, the classes 5-9 and 10-14 are continuous because there are no gaps between them, and 0-5 and 10-15 are also continuous because the lower bound of the second class is equal to the upper bound of the first class.

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The triangle should have 4.35 metres of wire, which means the square should have 6.978 meters

Let "x" is the cutting distance from one end of the wire.

Then, area of square would be ,

 Area =  (x/4)²

The side of equilateral triangle would be,

 L=(10-x)/3

height would be (10-x)/3*√(3)/2

=> (10-x)√(3)/6

So, the area of triangle is

Area of triangle= ((10-x)/3)² ×√(3)/4

=> (10-x)² ×√(3)/36

So, the total area is ,

A = (x/4) + (10 - x)²/36√3

Differentiating Area w.r.t x

dA/dx=x/8-2 ×√(3)/36(10-x)

=> x/8+20× √(3)/36-2 × √(3)/36x

Putting the expression equal to 0,

x/8+20× √(3)/36-2 × √(3)/36x = 0

=> x(1/8+ √(3)/18

=> 10√(3)/18

x*0.22122 = 0.96225  

 x=4.35

Substituting the value of x

This corresponds to minimum area which is:

 A(4.35)=(4.35/4)^2+(10-4.35)^2 × √(3)/36=1.183+1.536

=> 2.719m²

Thus , the minimum area is 2.71 square meters when x=4.35 m. As a result, the wire should be cut such that the dimension of the square is formed by the piece having a length of 4.35 m, and the equilateral triangle is formed by the piece having a length 5.65 m.

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3, possibilities are there for the digit that was written.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Not a multiple of 3, 7+5+7+0=19

Not a multiple of 3, 7+5+7+1=20

Multiple of three: 7+5+7+7+2=21

Not a multiple of 3, 7+5+7+3=22

Not a multiple of 3, 7+5+7+4=23

Multiple of three: 7+5+7+7+5=24

Not a multiple of 3, 7+5+7+6=25

Not a multiple of 3, 7+5+7+7=26

7+5+7+8=27 multiple of 3

Not a multiple of 3, 7+5+7+9=28

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Answer:

[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]

Step-by-step explanation:

See picture below :)

If f:RR, then Munkres' definition (f′(a) is a 11 matrix) is the definition of the derivative as it is presented in elementary calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value).

Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.

The function closest to that input value is best approximated linearly by the tangent line. Because of this, the derivative is

According to our question-

The linear mapping Dfa:RmRn that obeys limh0f(a+h)f(a)Dfa(h)h2=0 is typically used to compute the derivative (or "total derivative") of a function f:RmRn at some point aRm.

both are true. If f:RR, then Munkres' formulation (f′(a) is an 11 matrix) is the definition of the derivative as taught in introductory calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.

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Answer: It takes 3 cups of sugar for 4 cups of cranberry

Step-by-step explanation:

12 cups of sugar, 16 cups of cranberry

Divide both numbers by 4

12/4=3

16/4=4

It takes 3 cups of sugar for 4 cups of cranberry

Answer: The correct answer is C

Step-by-step explanation: Let's find each equation without any inequalities first. We have a dotted line at y = 1, so we can already remove A and B. Now, a dotted line represents exclusivity and hence; it should not include the = sign.

Answer:

To solve this problem, we can set up a system of two equations to represent the given information:Let A be the cost of an apple and B be the cost of a banana.Then the first equation is: 4A + 3B = 4.48

The second equation is: 3A + 4B = 4.76To find the values of A and B, we can solve this system of equations using substitution or elimination.Using substitution, we can solve for A in the first equation and substitute that expression into the second equation:4A + 3B = 4.48

A = (4.48 - 3B)/4Substituting this expression for A into the second equation gives:3((4.48 - 3B)/4) + 4B = 4.76

3(4.48 - 3B) + 4B = 4.76

13.44 - 9B + 4B = 4.76

4.44 - 5B = 4.76

-5B = -0.32

B = 0.064Now that we have found the value of B, we can substitute it back into the first equation to find the value of A:4A + 3(0.064) = 4.48

4A + 0.192 = 4.48

4A = 4.288

A = 1.072Therefore, the cost of an apple is £1.072 and the cost of a banana is £0.064.

Step-by-step explanation:

Answer:

The answer is below

Solving the given equations using substitution method we get (x,y) as (2, -1) i.e option (2) is correct answer.

Substitution method

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Given: 4x + 2y = 6      --------- (1)

            x = 2y + 4        ----------(2)      

Put the value of x from the 2nd equation in the 1st equation

4(2y+4) +2y = 6

8y + 16 + 2y = 6

10y + 16 = 6

10y = 6-16

10y = -10

y = -1 --------------- (3)

put the value of y in the (2) from (3)

x = 2(-1) + 4

x = -2+4

x = 2

Therefore, its solution is (2, -1)

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Answer: B

Step-by-step explanation: Did the test

Answer:

[tex]y > 3+\frac{x}{2}[/tex]

Hope this helps!

Answer: x<2y-6

Step-by-step explanation:

x-2y<-6

=(x-2y)+6<-6+6

=x-2y+6<0

=(x-2y+6)+(2y-6)<2y-6

=x-2y+6+2y-6<2y-6

=x-2y+2y+6-6<2y-6

=x<2y-6

Answer: m=4

Step-by-step explanation:

3m−7=5

3m = 12

m= 4

Answer:

m = 4

Step-by-step explanation:

The tree statements of the circle are

1) The radius of the circle is 3 units.

2) The center of the circle lies on x-axis.

3) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is center of a circle?

A circle's center is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.

Given equation of circle is

x² + y² - 2x - 8 =0

x² - 2x + 1 - 1 + y² - 8 =0

(x - 1)² - 1 + y² - 8 =0

(x - 1)² + y² - 9 =0

(x - 1)² + y² = 3²

Compare the equation above equation with (x - h)² + (y - k)² = r²:

h = 1, k=0, r=0

The radius of the circle is 3 units. The center of the circle is (1,0) which lies on the x-axis.

Rewrite the equation of circle x² + y² = 9:

x² + y² = 3²

The radius of the circle is 3 units:

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The total number of possible ways to complete the test would be 2048.

Total number of questions = 11

Each equation has two possible answers (either true or false).

We need to find the total number of ways in which the test can be​ completed.

the total number of possible ways to complete the test= 2×2×2×2×2×2×2×2×2×2×2

the total number of possible ways to complete the test=

2¹¹

Therefore the total number of possible ways to complete the test is 2048.

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