the length (in km) of a random sample of new zealand (nz) rivers that travel to the pacific ocean and the lengths (in km) of a random sample of new zealand rivers that travel to the tasman sea are given in the table below. do the data provide enough evidence to show on average that the rivers that travel to the pacific ocean are longer than the rivers that travel to the tasman sea?

The P-value is a measure of the strength of the evidence against the null hypothesis (H0). It represents the probability of obtaining a result as extreme or more extreme than the one observed, given that the null hypothesis is true.

In this case, the null hypothesis is that the proportion of customers who will ask for a straw is equal to 50%. The alternative hypothesis is that the proportion is less than 50%.

Based on the information provided, it is not possible to calculate the P-value. To calculate the P-value, you would need to know the specific results of the 150 trials of the simulation and how those results compare to the observed result of 43 out of 100 customers asking for a straw.

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If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

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Answer: 0.6 espero haberte ayuado

Step-by-step explanation:

y = C * x^6,

where C is an arbitrary constant.

To solve the differential equation dy/dx = 6y/x, x > 0, we can use separation of variables.

Step 1: Separate the variables:

dy/y = 6 dx/x.

Step 2: Integrate both sides:

∫ dy/y = ∫ 6 dx/x.

ln|y| = 6ln|x| + C,

where C is the constant of integration.

Step 3: Simplify the equation:

Using the properties of logarithms, we can simplify the equation as follows:

ln|y| = ln(x^6) + C.

Step 4: Apply the exponential function:

Taking the exponential of both sides, we have:

|y| = e^(ln(x^6) + C).

Simplifying further, we get:

|y| = e^(ln(x^6)) * e^C.

|y| = x^6 * e^C.

Since e^C is a positive constant, we can rewrite the equation as:

|y| = C * x^6.

Step 5: Account for the absolute value:

To account for the absolute value, we can split the equation into two cases:

Case 1: y > 0:

In this case, we have y = C * x^6, where C is a positive constant.

Case 2: y < 0:

In this case, we have y = -C * x^6, where C is a positive constant.

Therefore, the general solution to the differential equation dy/dx = 6y/x, x > 0, is given by:

y = C * x^6,

where C is an arbitrary constant.

Note: In the provided solution, C is used to denote the arbitrary constant without any negation or multiplication.

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The area of the rectangle will be 24sq, units.

To determine the area of various polygons, there exist specialized formulae. The general formula for rectangles is as follows:

A = width x length

Given, the coordinates of the rectangle are W(0,1), X(3,4), Y(-1, 8), Z(-4,5)

So the length of rectangle will be = distance between W and X will be -

⇒\(\sqrt{(3 - 0)^{2} + (4-1^{2}) }\)

⇒\(\sqrt{18}\)

The breadth of rectangle will be = distance between X and Y

⇒ \(\sqrt{(3 + 1)^{2} + (8-4)^{2} }\)

⇒ \(\sqrt{32}\)

Now, area of rectangle = length × breadth

⇒ \(\sqrt{18}\) × \(\sqrt{32}\)

⇒ 24 sq. units

So, the area of the rectangle will be - 24 sq. units

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The amount of plastic coating required to coat the surface of the chain link is 471 cm². So, the correct option is D. 471 cm².

The surface area of the cylinder can be found by using the formula SA = 2πrh + 2πr². O

ne link in a chain was made from a cylinder that has a radius of 3 cm and a height of 25 cm.

How much plastic coating would be needed to coat the surface of the chain link (use 3.14 for pi)?

To get the surface area of a cylinder, the formula SA = 2πrh + 2πr² is used.

Given the radius r = 3 cm and height h = 25 cm, substitute the values and find the surface area of the cylinder.  

SA = 2πrh + 2πr²SA = 2 × 3.14 × 3 × 25 + 2 × 3.14 × 3²SA = 471 cm²

Therefore, the amount of plastic coating required to coat the surface of the chain link is 471 cm². So, the correct option is D. 471 cm².

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If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is \(-16t^{2} +48t\).

We are required to find the time that the ball took to travel before returning the ground.

We know that speed is the distance a thing covers in a particular time period.

The height of the ball after t seconds is as follows:

h(t)=\(-16t^{2} +48t\)

It is at ground at the instants of t.

Hence,

\(-16t^{2} +48t\)=0

-16t(t-3)=0

We want value of t different of 0, hence :

t-3=0

t=3.

Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

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Answer:

B. t=3

Step-by-step explanation:

i took the test and got it right

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

initial money = $8

final money = $11

percent of change = ?

Step 02:

percent of change

percent of change = ( final money - initial money ) / initial money * 100

= ( 11 - 8 ) / 8 * 100

= 3/8 * 100

= 0.375 * 100 = 37.5 %

The answer is:

The percent of change is 37.5 %

Answer:

I THINK** it's 115°

hope it helps ya...!

sorry if it's wrong :(

Answer:

Taking back all the points you took from me and did nothing.

Step-by-step explanation:

Answer:  –145 is the 25th term in this series where each term is 7 less than the preceding term.

Step-by-step explanation:  Find the difference between the numbers given.

They are decreasing by 7.

The requested term is 25. Subtract -1 . = 24  (n-1)

Multiply 24 × -7 = -168

Add that to to first term

23 + (-168) = the 25th term

–145 is the 25th term in this series where each term is 7 less than the preceding term.

Answer:

(3,1)

Step-by-step explanation:

To find the sum of 6k by adding each term together, we can simply add 6k + 6k + 6k + 6k + 6k + 6k which gives us a total of 36k.

To verify this result using the summation capabilities of a graphing utility, we can use the sigma notation (Σ) to represent the sum. The sigma notation is defined as Σ6k where k starts at 1 and goes up to 6. This means we are adding 6k, six times.

To input this into a graphing utility, we can use the summation feature. For example, on a TI-84 calculator, we can press the "Math" button, select "1:sum(", and enter the expression "6k" followed by a comma and then the values of k that we want to sum from (1) and to (6). This gives us the result of 36k, which matches our previous calculation.

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Answer:

The bond yield is 6.80%.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

You purchase a bond with a coupon rate of 8.5% and par value of $2,000. The value of the bond rose to $2,500. What is the bond yield?

The bond can now be calculated as follows:

Coupon payment = Coupon rate * Bond per value = 8.5% * $2,000 = $170

Bond yield = Coupon payment / Current value of the bond = $170 / $2,500 = 0.068, or 6.80%

Therefore, the bond yield is 6.80%.

Answer:

3rd option

Step-by-step explanation:

(f(x) + g(x)

= - 2x² + 3x - 6 + 5 - 4x - 8x² ← collect like terms

= - 10x² - x - 1

The equation of the plane through the origin and the points (2, –4, 6) and (5, 1, 3) is - 9x + 12y + 11 x = 0.

The general equation of a plane through (0, 0, 0) is a(x - 0) + b(y - 0) + c(z - 0) = 0

Since the plane passes though the origin, the equation of the plane is given by ( x, y, z ) = 0. Simplify it so that you write the equation of the plane in the form a x + b y + c z = 0

ax + by + cx = 0...(1)

It will pass through B(2, -4, 6) and C(5, 1, 3) if

a(2) + b(-4) + c(6) = 0

2a - 4b + 6c = 0

a - 2b + 3c = 0 ...(2)

a(5) + b(1) + c(3) = 0

5a + b + 3c = 0 ... (3)

Solving (2) and (3) by cross-multiplication, we have

\(& \frac{a}{-6-3}=\frac{b}{15-3}=\frac{c}{1+10} \\\)

\(& \Rightarrow \frac{a}{-9}=\frac{b}{12}=\frac{c}{11}=\lambda\) (say) }

\(& \Rightarrow\) a = - 9 \(\lambda\), b = 12 \(\lambda\)  and c = 11 \(\lambda\)

Substituting the values of a, b and c in (1), we get

- 9 \(\lambda\) x + 12 \(\lambda\) y + 11 \(\lambda\) x = 0

- 9x + 12y + 11 x = 0

which is the required equation of the plane.

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Answer:

x = 9/2

Step-by-step explanation:

The outside triangle is also a right triangle, with hypotenuse 8 and side 6.

The missing side can be calculated with pythagoras as:

\(\sqrt{8^2-6^2} = \sqrt{28}\)

Now for the vertical line, lets call it y, which is a side for two "back to back" triangles, you can do pythagoras twice:

left triangle: \(y^2 + (8-x)^2 = 28\)

right triangle: \(y^2 + x^2 = 6^2\)

Eliminating y², you can solve:

\(28 - (8-x)^2 = 36 - x^2\)

\(28 -x^2 + 16x - 64 = 36 - x^2\)

\(16x = 36 + 64 - 28\)

\(x = \frac92\)

The maximum value of the sine function is 1, the angle corresponding to sin^(-1)(1) is π/2 or 90 degrees.

The principal value of sin^(-1)(1) is π/2 or 90 degrees.

The function sin^(-1)(x), also known as arcsin(x) or inverse sine, represents the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is 1.

Since the sine function oscillates between -1 and 1, the angle corresponding to sin^(-1)(1) is the maximum value where the sine is equal to 1.

This occurs at π/2 or 90 degrees, making it the principal value for sin^(-1)(1).

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When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

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As per the given statement by solving with Simplex method The maximum value of z is 6, and it occurs when x₁ = 4 and x₂ = 9.

To solve the given linear programming problem using the Simplex method, we start by introducing slack variables to convert it into standard form. The initial Simplex tableau is set up with the objective function and constraints.

By selecting the most negative coefficient in the objective row as the pivot column and finding the pivot row based on minimum non-negative ratios, we perform row operations to pivot on the selected element. This process is iterated until the final tableau indicates the optimal solution.

In this case, the maximum value of z is 14, achieved when x₁ = 4 and x₂ = 2. These values satisfy the given constraints and maximize the objective function. Therefore, the maximum value of z is 6, and it occurs when x₁ = 4 and x₂ = 9.

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The optimal solution we get after solving the linear problem is z = 26 when x₁ = 0 and x₂ = 19.

To solve the given linear programming problem using the Simplex method, we will first convert it into standard form by introducing slack variables.

The initial tableau is as follows:

| BV | x₁ | x₂ | s₁ | s₂ | RHS |
|----|----|----|----|----|-----|
| s₁ | -1 | -1 |  1 |  0 |  6  |
| s₂ | -2 | -1 |  0 |  1 | 13  |
| z  | -2 | -2 |  0 |  0 |  0  |

We will apply the Simplex method to optimize the objective function.

1. Identify the most negative coefficient in the bottom row, which is -2 in this case. This indicates that x₁ should enter the basis.
2. Calculate the ratio of the RHS to the pivot column values for each row. The minimum ratio determines the variable to exit the basis. In this case, s₁ has the minimum ratio of \(\frac{6}{1}\) = 6.
3. Perform row operations to make the pivot element 1 and eliminate other coefficients in the pivot column. Multiply Row 1 by -2 and add it to Row 3, and multiply Row 1 by -1 and add it to Row 2. The new tableau is as follows:

| BV | x₁ | x₂ | s₁ | s₂ | RHS |
|----|----|----|----|----|-----|
| x₁ |  1 |  1 | -1 |  0 | -6  |
| s₂ |  0 |  1 |  2 |  1 | 19  |
| z  |  0 |  0 |  2 |  0 | 12  |

4. Repeat steps 1-3 until all coefficients in the bottom row are non-negative. In the next iteration, x₂ will enter the basis, and x₁ will exit.
5. Continue iterating until all coefficients in the bottom row are non-negative. The final tableau is as follows:

| BV | x₁ | x₂ | s₁ | s₂ | RHS |
|----|----|----|----|----|-----|
| x₂ |  1 |  0 | -1 | -1 | -7  |
| s₂ |  0 |  1 |  2 |  1 | 19  |
| z  |  0 |  0 |  4 |  2 | 26  |

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Step-by-step explanation:

Your going to want to subtract 3/2 from 10 then multiply that number by 20 then simplify and thats your answer

Answer:

5/9

step by step follow up

The total amount of money Christina spent on streaming music service in a year is $36

Total yearly cost = One time payment + Cost of each song(Number of songs)

= 18 + 1.20(15)

= 18 + 18

= $36

Therefore, the total amount of money Christina spent on streaming music service in a year is $36

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=========================================================

Let's go through the answer choices one by one

Answer:

The df values for the A x B interaction are also 3,40

Step-by-step explanation:

The F-value for Factor A has df = 1, 40

The F-value for Factor B has df = 3, 40.

The df values for the A x B interaction are also 3,40

This is because the source of variation between columns has ( c- 1); rc(n-1) degrees of freedom and  the source of variation between  rows has (r-1); rc(n-1) degrees of freedom and the  source of variation of interaction

(between rows and columns)  has ( c-1) ( r-1); rc(n-1) degrees of freedom.

Therefore

Factor A:  ( c- 1); rc(n-1)    = 1,40

Factor B:    (r-1); rc(n-1)     = 3,40

Interaction : ( c-1) ( r-1); rc(n-1)   =  3*1,(40)= 3,40

where c refers to columns , r refers to rows and n refers to the total sample size.

Answer:

A=1 B=2 C=7

Step-by-step explanation:

Look at the graph!!!!

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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The confidence interval for the mean is (10.7485, 11.6515)

Given Data:

n = 225

×= 11.2

s = 4.1

Note that, Population standard deviation(\(\alpha\)) is unknown. So we use t distribution.

Our aim is to construct a 90% confidence interval.

c = 0.90

\(\alpha\) = 1- c = 1- 0.90 = 0.10

\(\alpha\)/2 = 0.10/2 = 0.05

Also, d.f = n - 1 = 225 - 1 = 224

t\(\alpha\)/2.d.f- = t\(\alpha\)/2.n-1 = t0.05,224 = 1.652

( use t table or t calculator to find this value..)

The margin of error is given by

E = t\(\alpha\)/2,d.f. * (s / \(\sqrt{n}\))

= 1.652 * (4.1/ √225)

= 0.4515

Now , confidence interval for mean(\mu) is given by:

(× - E ) <  μ< x + E)

(11.2 - 0.4515) < μ < (11.2 + 0.4515)

10.7485 < μ< 11.6515

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Answer:

Area of Top Bottom- L x W = Area so 8 x 5= 40 sq ft

Area of Front Back- L x W = Area so 3 x 8 = 24 sq ft

Area of Left side/ Right side L x W = Area so 3 x 5 = 15

Total Surface Area-  X + Y + Z = Total SA so 40 + 24 + 15 = 79

Volume- L x W x H = Volume so 8 x 5 x 3 = 120 cubic feet

Step-by-step explanation:

L being length

W being width

H being Height

Answer:

C and D

Step-by-step explanation:

C). With the X right by the 100 means that it could be anything there, so you would put a 3 at the end so then 100 x 3 = 300.
D). The value is already 300 so no need to do work there.

Using Multiplication, 100 × 3 is this expressions could be the one daisy estimated.

Multiplication is an "operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers".

According to the question.

Daisy estimated a certain expression to have a value is 300 using Multiplication we have,

100 × x =300

x = 300/100

x = 3.

Hence, 100 × 3 is this expressions could be the one daisy estimated using Multiplication.

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To determine function could have created a specific graph, it is crucial to have additional information, such as the shape, key points, or other characteristics of the graph.

Without the specific functions provided, it is challenging to determine which function could have created the graph with certainty.

I can offer some insights on how different types of functions can produce various types of graphs.

Linear Functions:

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Linear functions create straight lines.

The graph of a linear function can be determined if you have two points on the line.

Quadratic Functions:

A quadratic function has the form f(x) = ax² + bx + c a, b and c are constants.

The graph of a quadratic function is a parabola.

The specific shape of the parabola depends on the values of a, b and c.

Exponential Functions:

An exponential function has the form f(x) = abˣ, where a and b are constants.

The graph of an exponential function can take various shapes, such as exponential growth or decay.

Trigonometric Functions:

Trigonometric functions include sine, cosine, tangent, etc.

They have periodic behavior and produce repetitive wave-like patterns.

Other Types of Functions:

There are many other types of functions, such as logarithmic, rational, polynomial and more.

Each type of function has its own unique characteristics and can produce different graph shapes.

Without this information, it is not possible to accurately identify the function that corresponds to the graph.

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