a confidence interval for the true population correlation coefficient (p) is (0.62, 0.98). in this case, we would: _______

The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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Answer:

Step-by-step explanation:

First, we know a 45-45-90 triangle has two legs that are the same because two angles are the same, so we can say that:

\($a^2+b^2=c^2=a^2+a^2=c^2$\)

Remember that \(a^2\) and \(a^2\) are the legs, which are the same length, so we can do this. Now, we solve the equation.

\(a^2+a^2=c^2\\2a^2=5\sqrt{7}\\2a=(5\sqrt{7})^2\\2a=5\\a=\frac{5}{2}\)

HOPE THIS HELPS :D

The Pythagoras is the sum of the square of two sides equal to the square of the longest side. Then the exact measure of each leg is 9.4 ft.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A right-angle 45-45-90 triangle with the hypotenuse measuring 5√7 feet.

We know that if two angles of any triangle are the same then their opposite sides are also the same.

Let each side length of x ft. Then by the Pythagoras theorem. we have

\(\begin{aligned} x^2 + x^2 &= (5\sqrt7)^2\\\\2x^2 &= 25 \times 7\\\\x^2 &= \dfrac{175}{2}\\\\x^2 &= 87.5\\\\x &= 9.354 \approx 9.4 \ \rm ft \end{aligned}\)

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The outcomes of A ∪ B are {1, 2, 3, 5, 7, 9, 11, 13, 17, 19} and the outcomes of A ∩ B are {3, 5, 7, 11, 13}.

The set A represents the prime numbers less than 20, while the set B represents the odd numbers less than 15.

Listing the outcomes of A ∪ B (union of A and B) will provide all the elements present in both sets without duplication.

On the other hand, listing the outcomes of A ∩ B (intersection of A and B) will give the common elements between the two sets.

Set A: {2, 3, 5, 7, 11, 13, 17, 19}

Set B: {1, 3, 5, 7, 9, 11, 13}

To find the outcomes of A ∪ B, we need to combine all the elements from sets A and B without duplication.

Taking the union of A and B gives us the following elements: {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}.

Therefore, the outcomes of A ∪ B are {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}.

These numbers represent all the prime numbers less than 20 and all the odd numbers less than 15, combined without duplication.

To find the outcomes of A ∩ B, we need to identify the elements that are present in both sets A and B.

In this case, the common elements between A and B are {3, 5, 7, 11, 13}.

Therefore, the outcomes of A ∩ B are {3, 5, 7, 11, 13}.

These numbers represent the prime numbers less than 20 that are also odd numbers less than 15.

The intersection of A and B shows the elements that satisfy both conditions simultaneously.

By finding the outcomes of A ∪ B and A ∩ B, we have identified the elements that belong to both sets without duplication and the elements that are common between the sets, respectively.

This helps in understanding the combined elements and the overlapping elements between sets A and B.

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The complete question is:

A = {prime numbers less than 20} B = {odd numbers less than 15}

List the outcomes of A ∪ B and explain?

List the outcomes of A ∩ B and explain?

Answer:

Step-by-step explanation:

Let "t' be the number of t-shirts bought.

Let "c" be the number of CDs bought.

Let b" be the total cost.

15t + 5c = b

We buy 10 t-shirts so t = 10.

We buy 25 CDs so c = 25.

We are trying to find b.

15t + 5c = b

15(10) + 5(25) = b

150 + 125 = b

275 = b

Best of Luck!

Answer:

Step-by-step explanation:

t-shirts for $15 = t

cd's for $5 = c

let tp = total profit

the algebraic expression would be:

15t + 5c = tp

-------------------------

evaluate the expression 15t + 5c = tp

for t = 10 and c = 25

plugin values into the formula:

15(10) + 5(25) = tp

tp = 150 + 125

tp = 275

therefore, the total profit is $275

The length of the segment joining the points which are given is  \(\sqrt{10}\)

To measure the distance between these two given points

The given coordinates are

Let P = P(5,-3) and Q = Q(8,-2)

By using the distance formula we get;

the distance formula is used to calculate the length of the segment when points are given as in this question

thus the distance formula is :

\(\sqrt{(x2-x1)^2 + (y2 - y1)^2}\)

here x2 = 8 and x1 = 5

and y2 = - 2 and y1 = - 3

thus on substituting the values we get

\(\sqrt{(8-5)^2 + ( -2 +3)^2}\)

= \(\sqrt{3^2 + 1^2}\)

= \(\sqrt{10}\)

Thus the length of the segment is  \(\sqrt{10}\) units

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Answer:

1740 N

Step-by-step explanation:

To find the force, you need to multiply the mass by the acceleration.

(60.0 kg) × (29.0 m/s²) = 1740 N

The force will be 1740 N.

Answer:

26.93 feet ladder

Step-by-step explanation:

Answer:

h = sqrt( aa + bb )

L = sqrt( 9^2 + 26^2 )

L = 27.5 ft

Step-by-step explanation:

This is my first time using Brainly, lol. I trust it so I believe this is the answer, I'm new.

Answer:

2 hours

Step-by-step explanation:

you can use factors to communicate or solve the question hope it helps!

Answer:

Step-by-step explanation:

This number would be between 3,300 and 3,400.  Which number would 3387 be closer to?  3350 would be right in the middle and 3387would be larger than 3350 so 3387 is closer to 3400.

Answer:

Segment QR is the shortest

Answer:

qr

Step-by-step explanation:

To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.



To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:

1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.

2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.

3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.

Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.

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The measure of each angle is 43.25 and 46.75

The attached image represents the missing piece in the question.

From the image, we can see that:

3x - 13 + 5x - 47 = 90 ---- complementary angles

Evaluate the like terms

8x = 150

Divide by 8

x = 18.75

Substitute x = 18.75 in the given angles

3x-13 = 3 * 18,75 - 13 = 43.25

5x -47 = 5 * 18.75 - 47 = 46.75

Hence, the measure of each angle is 43.25 and 46.75

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Step-by-step explanation:

cot(θ) = 1/tan(θ)

tan(θ) = sin(θ) / cos(θ)

Given cos(θ) = 15/17, we can find sin(θ) using the Pythagorean identity:

sin(θ) = sqrt(1 - (cos(θ))^2) = sqrt(1 - (15/17)^2) = 4/17

So, tan(θ) = 4/15

And, cot(θ) = 1/tan(θ) = 15/4

Answer: 15/8

Step-by-step explanation: We know that sin(0) will equal 8 by the 8,15,17 triangle. We using the restricted domain value for theta and using the pythagorean identities to get cot(0) as cos(0)/sin(0) and substitute the values. The denominators cancel and the result is 15/8.

The type of square that has a movable head and can be used to lay out both 45° and 90° angles is called a combination square.

A combination square is a versatile measuring tool commonly used in woodworking, metalworking, and construction. It consists of a ruler or blade with a movable head that can be locked at different angles, typically 45° and 90°. The head of the square usually has a spirit level or bubble level attached to ensure accurate measurements and alignments.

The movable head allows the user to set and measure angles other than 45° and 90° as well, making it a versatile tool for various applications. The square is often used for marking and checking right angles, marking 45° angles, measuring and transferring distances, and checking the flatness or alignment of surfaces.

The combination square derives its name from the fact that it combines multiple functions in a single tool, making it convenient and efficient for tasks that require different angle measurements. It is a common and essential tool in many trades and professions where accurate and precise measurements are required.

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Answer:

0

Step-by-step explanation:

-5 + 7 - 6 - (-4)

-11 + 7 - (-4)

-11 + 7 +4

-11 + 11

= 0

Answer: 0

Step-by-step explanation:

-5 + 7 -6-(-4)    

-5 + 7 -2

-5+ 5 = 0

x=-1/10 is the value of x in the given expression 5(-3x+5x)+1

An expression is combination of variables, numbers and operators.

The given expression is 5(-3x+5x)+1

In the given expression x is the variable

Plus and minus are the operators.

-3x and 5x are the like terms because each term has same variable x.

5(-3x+5x)+1

5(2x)+1

10x+1

10x=-1

Divide both sides by 10

x=-1/10

Hence, x=-1/10 is the value of x in the given expression 5(-3x+5x)+1

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Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

The orthogonal projection of vector v onto the subspace spanned by u₁ and u₂ is (-1/18, 1/18, 19/18).

What is vector?

A vector is a mathematical object that represents both magnitude and direction. It is commonly represented as an ordered set of numbers, known as components or coordinates, arranged in a specific order.

To find the orthogonal projection of vector v onto the subspace spanned by vectors u₁ and u2, we can use the formula:

proj_w(v) = ((v · u₁) / (u₁ · u₁)) * u₁ + ((v · u₂) / (u₂ · u₂)) * u₂

where "·" represents the dot product.

First, let's calculate the dot products and the norms squared:

v · u₁ = 12 + 2(-2) + 41 = 2 - 4 + 4 = 2

u₁ · u₁ = 22 + (-2)(-2) + 11 = 4 + 4 + 1 = 9

v · u₂ = 1 * (-1) + 21 + 44 = -1 + 2 + 16 = 17

u₂ · u₂ = (-1)(-1) + 11 + 4 * 4 = 1 + 1 + 16 = 18

Now, we can substitute these values into the formula:

\(\rm proj_w\)(v) = (2/9) * u₁ + (17/18) * u₂

To simplify further, we can perform scalar multiplication:

\(\rm proj_w\)(v) = (2/9) * (2, -2, 1) + (17/18) * (-1, 1, 4)

\(\rm proj_w\)(v) = (4/9, -4/9, 2/9) + (-17/18, 17/18, 17/9)

Combining like terms:

\(\rm proj_w\)(v) = (4/9 - 17/18, -4/9 + 17/18, 2/9 + 17/9)

\(\rm proj_w\) (v) = (-1/18, 1/18, 19/18)

Therefore, the orthogonal projection of vector v onto the subspace spanned by u₁ and u₂ is (-1/18, 1/18, 19/18).

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Answer:

A. 40°

Step-by-step explanation:

As we can see it is an isosceles triangle because two sides are equal. so Base angles of an isosceles triangle are equal. Then Now.,

70° + 70° + <X = 180° {Being sum of angles of triangle }

140° + < X = 180°

< X = 180° - 140°

< X = 40°

Hope it will help :)❤

Answer:

See explanation

Step-by-step explanation:

f(x)=x² + x + 2 and g(x) = 2x² - 7

f(2) g(2)=

((2)² + (2) + 2)(2(2)² - 7)=

(4 + 2+ 2)(2(4) - 7)=

(8)(8 - 7)=

8*1=8

2 fg(2)=

2 f(g(2))=

2 f(2(2)² - 7)=

2 f(2(4)-7)=

2 f(8-7)=

2 f(1)=

2(1² + 1 + 2)=

2(1+3)=

2(4)=8

8=8

2 fg(2)=f(2) g(2) √

I hope it is helpful for you ....

Answer:

y = -2x + 5

Step-by-step explanation:

Looking at the line, every time it moves one unit to the right, it goes down two units. Therefore, the slope is -2. Since the y-intercept is 5, the equation of this line is y = -2x+5.

I hope this helped!

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Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal.

To prove the given equation, we will differentiate both sides with respect to θ and simplify the expression.

Differentiating V cotθ + V^3cosecθ with respect to θ:

d/dθ(V cotθ + V^3cosecθ) = d/dθ(V cotθ) + d/dθ(V^3cosecθ)

Applying the differentiation rules:

= V (-cosec^2θ) + 3V^2cosecθ(-cosecθcotθ)

= -V cosec^2θ - 3V^2cosec^2θcotθ

Now, we need to express the right-hand side of the original equation in terms of dV/dθ:

V cotθ + V^3cosecθ = V(cotθ + V^2cosecθ)

                      = V(cotθ + cotθV^2)

                      = Vcotθ(1 + V^2)

Taking the derivative of the right-hand side with respect to θ:

d/dθ(Vcotθ(1 + V^2)) = V(−cosec^2θ)(1 + V^2) + Vcotθ(0)

                           = -Vcosec^2θ(1 + V^2)

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal. Therefore, we have proved that dV/dθ = V cotθ + V^3cosecθ.

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We assume that the outcomes of successive trials in a binomial experiment are c) identical from trial to trial.

The correct answer is:

c. identical from trial to trial

In a binomial experiment, the outcomes of successive trials are assumed to be identical from trial to trial. This means that each trial has the same probability of success or failure, and the outcome of one trial does not affect the outcome of the subsequent trials. Each trial is considered independent and does not depend on the previous or future trials.

Option a is incorrect because the outcomes in a binomial experiment are not random numbers between 0 and 1. They are discrete outcomes, usually represented as success or failure, or yes or no.

Option b is incorrect because the outcomes in a binomial experiment are assumed to be independent, not dependent. The probability of success or failure in one trial does not affect the probability in subsequent trials.

Option d is incorrect because it mistakenly states that the outcomes are probabilistically independent. The correct term is "independent," without the term "probabilistically."

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Answer:

M (- 5, 2 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = A (- 2, 8 ) and (x₂, y₂ ) = B (- 8, - 4 ) , then

midpoint = ( \(\frac{-2-8}{2}\) , \(\frac{8-4}{2}\) ) = ( \(\frac{-10}{2}\) , \(\frac{4}{2}\) ) = (- 5, 2 )

Jeff's golf score was 1 stroke under par.

Let's first find out what was Mike's golf score.

We know that Mike's score was 2 strokes more than Sam's score, so if Sam's score was 2 over par, then Mike's score must have been:

2 + 2 = 4 over par

We also know that Jeff's score was 5 strokes less than Mike's score. Therefore, Jeff's score relative to par would be:

4 + (-5) = -1 over par

So Jeff's golf score was 1 stroke under par.

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The integral evaluated using Green's theorem is 0.

Green's theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve.

In this case, we are asked to evaluate the integral \(\int_c (3yx dx + 2x dy),\)where c represents the boundary of a region denoted as 0.

Using Green's theorem, we can rewrite the given integral as the double integral of the curl of the vector field F = (3y, 2x) over the region 0.

The curl of F is obtained by taking the partial derivative of its second component with respect to x and subtracting the partial derivative of its first component with respect to y.

Since the partial derivative of 2x with respect to x is 2 and the partial derivative of 3y with respect to y is 3, the curl of F is equal to 2 - 3 = -1.

Therefore, according to Green's theorem, the given line integral is equal to the double integral of -1 over the region 0.

The value of a double integral of a constant over a region is simply the constant multiplied by the area of that region.

Since the constant in this case is -1 and the region 0 has an area of zero, the result of the integral is 0.

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