Kennedi paid $288 for 4 nights at a hotel.

To reduce bias in an estimator, (B) use random sampling and (C) increase the number of items included in the sample. Random sampling ensures that each member of the population has an equal chance of being selected, while increasing the sample size reduces sampling error and increases the representativeness of the sample.

To reduce bias in an estimator, it is important to use random sampling rather than nonrandom sampling. Random sampling ensures that every item in the population has an equal chance of being included in the sample, which helps to eliminate any potential bias. Additionally, increasing the number of items included in the sample can also help to reduce bias by providing a more representative sample. However, decreasing the number of items included in the sample can actually increase bias as it may not accurately represent the population. Therefore, it is important to use random sampling and include a sufficient number of items in the sample to reduce bias in an estimator.

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To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:∫CF.v dlWhere v = (x²+2yz)i + y²j and dl = dx i + dy j + dz kTherefore,∫CF.(x²+2yz) dx + y² dy … (1)Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴

The above line integral is the required value. So, we need to evaluate this integral. To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:

∫CF.v dl

Where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

Therefore,

∫CF.(x²+2yz) dx + y² dy … (1)

Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴ The above line integral is the required value. So, we need to evaluate this integral.The integral is a line integral of a vector field, with the curve path of integration is given by C as follows: C: (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1)In other words, we need to evaluate the integral of the dot product of the vector field v with the differential of the curve:

∫CF.v dl...

where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

We must split the curve C into three distinct segments before we can start evaluating the integral. The segments will be from (0,0,0) to (1,0,0), from (1,0,0) to (1,1,0), and from (1,1,0) to (1,1,1).Let's start with the first segment, from (0,0,0) to (1,0,0). We can set x = t, y = 0, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = dt, dy = 0, dz = 0. We have:∫(0,0,0)to(1,0,0)

vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(t²+0)dt + 0 + 0= [t³/3]0to1= 1/3

Now, let's evaluate the second segment, from (1,0,0) to (1,1,0). We can set x = 1, y = t, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = dt, dz = 0. We have:

∫(1,0,0)to(1,1,0)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+0)dx + t²dy + 0dz= 1∫0to1(t²)dt= [t³/3]0to1= 1/3

Finally, let's evaluate the third segment, from (1,1,0) to (1,1,1). We can set x = 1, y = 1, z = t, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = 0, dz = dt. We have:

∫(1,1,0)to(1,1,1)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+2(1)(t))dx + 1²dy + 0dz= ∫0to1(1+2t)dt + 1(0to1)+ 0= [t²+t]0to1+ 1= 3/2

Therefore, the line integral is the sum of the integrals along the three segments:

∫CF.v dl= 1/3+ 1/3+ 3/2= 2

Thus, the value of the line integral of the given function v = x²+2yzi + y²j from (0,0,0) the point (1,1,1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1) is equal to 2.

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Answer:

I can't tell what it says so I can't solve it

Answer:

I can't tell what that is , sorry

The expression representing height of kite from ground is Height = sin 50° × 40.

The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -

sin theta = perpendicular ÷ hypotenuse

Keep the values in mentioned trigonometric relation to find the expression -

sin 50 = height ÷ 40

Height = sin 50° × 40

Finding the height using formed equation -

Height = 0.77 × 40

Performing multiplication

Height = 30.64 meters

Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.

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The tickets sold to the students is 979 and the tickts sold to non students is 1481.

According to the statement

we have to find the equation which is linear  with the help of the given data.

So, For this purpose, we know that the

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

From the given statement

Let the students buy a ticket is x

And let the non students buy a ticket is y

Then from the information the equation become

x+y = 2460

And the

9x+14y = 29,545

put y = 2460 -x then

9x + 14(2460-x) = 29,545

9x -14x+ 34440 = 29,545

-5x = 29,545 -34440  

-5x = -4895

x = 979

And the y become

y = 2460 -x

y = 2460 -979

y = 1481.

So, The tickets sold to the students is 979 and the tickts sold to non students is 1481.

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Answer:

see explanation

Step-by-step explanation:

To find a , substitute the coordinates of the point on the curve into the equation, that is

(1)

y = ax² (3, 18)

18 = a × 3² = 9a ( divide both sides by 9 )

2 = a , then

y = 2x² is the equation

(2)

y = ax² (- 2, 30 )

30 = a × (- 2)² = 4a ( divide both sides by 4 )

7.5 = a , then

y = 7.5x² is the equation

(3)

y = ax² (4, 8 )

8 = a × 4² = 16a ( divide both sides by 16 )

\(\frac{8}{16}\) = \(\frac{1}{2}\) = a , then

y = \(\frac{1}{2}\) x² is the equation

(4)

y = ax² (- 1, - 2 )

- 2 = a × (- 1)² = a , then

y = - 2x² is the equation

(5)

y = ax² (2, - 12 )

- 12 = a × 2² = 4a ( divide both sides by 4 )

- 3 = a , then

y = - 3x² is the equation

(6)

y = ax² (- 3, - 3 )

- 3 = a × (- 3)² = 9a ( divide both sides by 9 )

\(\frac{-3}{9}\) = - \(\frac{1}{3}\) = a , then

y = - \(\frac{1}{3}\) x² is the equation

Answer:

circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

\( \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}\)

\( \large {\boxed{ \tt{p = 2 \times \pi \times r}}}\)

If the radius is 2 inches and

Use 3,14 for π So:

\( \tt{ {A = \pi \times {r}^{2} }}\)

\( \tt{A = (3.14 \times 2 \times 2)} \)

\( \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}\)

Answer:

Step-by-step explanation:

Your first two answers are incorrect. Radius = 5 km

Height = 12 km

volume of cone = πr²h/3 = π5²⋅12 = 300π km³

300π ≈ 942 km³

Answer:

Step-by-step explanation:

15

The number of miles for which the cost of Uber and Lyft is the same is 30.

How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.

Let the number of miles covered be = x
Given, the cost of travel = Pickup Fee + Cost per mile
Given, the pickup fee for Uber = $ 0
The cost per mile for Uber = $ 0.25
Again, the pickup fee for Lyft = $ 3
The cost per mile for Lyft = $ 0.15
Thus, the cost of travel for Uber = 0 + 0.25x -- (i)
Also, the cost of travel for Lyft = 3 + 0.15x -- (ii)
As per question, (i) and (ii) are equal.
Thus, 0 + 0.25x = 3 + 0.15 x ⇒ (0.25 - 0.15)x = 3 ⇒ 0.10x = 3
⇒ x = 3/0.10 ⇒ x = 30
Thus, for 30 miles  the cost of Uber and Lyft is the same.

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The points lie on the given inequality y ≥ 2x-4 are  (0,1) and (10,16)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that an inequality y ≥ 2x-4

We need to check whether the given points lie on the solution of the inequality or not,

1) (5, 4)

Put x = 5

2×5-4 = 10-4 = 6

4 ≥ 6, this is a contradiction which means (5, 4) do not lie on the solution,

2) (0, 1)

Put x = 0

2×0 - 4 = 0-4 = -4

1 ≥ -4, satisfying the condition hence lies on the solution.

3) (10, 16)

Put x = 10

2×10-4 = 20-4 = 16

16 = 16. satisfying the condition hence lies on the solution.

4) (2, -1)

Put x = 2,

2×2-4 = 4-4 = 0

-1 ≥ 0, this is a contradiction which means (5, 4) do not lie on the solution,

Hence, points lie in the solution set of the inequality are (0,1) and (10,16)

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A = old value = 3431

B = new value = 3732

C = percent change

C = [ (B-A)/A ] * 100%

C =  [ (3732-3431)/3431 ] * 100%

C = (301/3431) * 100%

C = 0.0877 * 100%

C = 8.77%

Note: if C was a negative value, then we'd have a percentage decrease

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

\(n=\frac{-km}{2k+3}\)

Step-by-step explanation:

\(n=-km/2k+3\)

Hope this helps!

The value of x and the sum of all the terms in an arithmetic progression (A.P.) with 25 terms, given the last three terms as 1/(x-4), 1/(x-1), and 1/x.

Let's assume the first term of the arithmetic progression is 'a' and the common difference is 'd'. The formula for the nth term of an A.P. is given by tn = a + (n-1)d.

Given that the 25th term is 1/(x-4), we can write:

a + (25-1)d = 1/(x-4)

Similarly, using the 24th and 23rd terms, we have:

a + (24-1)d = 1/(x-1)

a + (23-1)d = 1/x

We now have a system of three equations with three variables (a, d, and x). By solving these equations simultaneously, we can find the values of a, d, and x.

Once we find the values of a, d, and x, we can calculate the sum of the arithmetic progression using the formula Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms.

By substituting the values of a, d, and n = 25 into the sum formula, we can determine the sum of all the terms in the progression.

Note: Since the exact values of a and d are not provided in the question, we cannot provide a specific numerical answer without additional information.

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Answer:

answers

Step-by-step explanation:

A. Vertex at (−6, 1)

Answer:

There's no real solutions

Step-by-step explanation:

8x - 3 > 2(4x + 1 ) multiply inside the parenthesis with 2

8x - 3 > 8x + 2 transfer like terms to the same side of the inequation

8x - 8x > 3 + 2

0 > 5 this is not correct so we say there's no real solution to this inequation

Answer:

x=−5 and y=−7

Step-by-step explanation:

Step: Solve y=2x+3for y:

y=2x+3

Step: Substitute2x+3foryin4x−3y=1:

4x−3y=1

4x−3(2x+3)=1

−2x−9=1(Simplify both sides of the equation)

−2x−9+9=1+9(Add 9 to both sides)

−2x=10

−2x

−2

=

10

−2

(Divide both sides by -2)

x=−5

Step: Substitute−5forxiny=2x+3:

y=2x+3

y=(2)(−5)+3

y=−7(Simplify both sides of the equation)

Answer:

y = 2x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , then

y = 2x + c is the partial equation

To find c substitute (7, 2 ) into the partial equation

2 = 14 + c ⇒ c = 2 - 14 = - 12

y = 2x - 12 ← equation of line

From figure we have , ∠GFH = 80°  and ∠HGF = 60° , ∠GFH = 40° and ∠GFE = x°

Now,

In ∆HGF

Since Sum of the angles of a triangle is 180° :  

∠GFH + ∠HGF + ∠GFH = 180°

80° + 60° + 40° = 180°

14° + 40° = 180°

54° = 180° ………..(1)

∠GFH + ∠GFE = 180° [Linear pair]

80° + x° = 180°

x° = 180°-80°

x° = 100°

Hence the value of ∠x is 100°

Among the given options option (D) 100° is correct.

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Angle EFG and gfh are a linear pair the measure of EFG equals 4n + 25 and the measure of gfh equals 3n + 15 what are the measures of EFG and the measure of gfh...

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Answer:

37.68

Step-by-step explanation:

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Answer:

The answer is 37.68

Step-by-step explanation:

I took the test! :)

Answer:

(X - 10, y - 5)

Step-by-step explanation:

Just like walking

To solve this equation, we need to use trigonometric identities to simplify the left-hand side:

tan x + sec x csc x cos 2x = 1
(sin x / cos x) + (1 / (sin x cos x)) (cos x / sin x) (2cos^2 x - 1) = 1
(sin^2 x + 2cos^2 x - 1) / (sin x cos x) = 1
(sin^2 x + 2cos^2 x - 1) = sin x cos x

Next, we can use the identity sin^2 x + cos^2 x = 1 to substitute for sin^2 x:

(1 - cos^2 x + 2cos^2 x - 1) = sin x cos x
cos^2 x = sin x cos x

We can then divide both sides by cos x (assuming cos x ≠ 0) to get:

cos x = sin x

Using the identity sin^2 x + cos^2 x = 1, we can find that sin x = ±√(1 - cos^2 x). Since cos x = sin x, we have:

sin x = cos x = ±√(1/2)

Therefore, the solution set on the interval [0,2π) is {π/4, 5π/4, 3π/4, 7π/4}.
To solve the equation tan x + sec x csc x cos 2x = 1 on the interval [0, 2π), we can first rewrite the terms using their definitions in terms of sine and cosine.

tan x = sin x / cos x
sec x = 1 / cos x
csc x = 1 / sin x

Now, the equation becomes:

(sin x / cos x) + (1 / cos x)(1 / sin x)(cos 2x) = 1

To eliminate the fractions, multiply each term by sin x cos x:

sin^2 x + cos 2x = sin x cos x

Now, we can rewrite cos 2x using the double-angle formula:

cos 2x = 1 - 2 sin^2 x

Substitute this back into the equation:

sin^2 x + (1 - 2 sin^2 x) = sin x cos x

Combine the sin^2 x terms:

1 - sin^2 x = sin x cos x

Now, use the Pythagorean identity to replace 1 - sin^2 x with cos^2 x:

cos^2 x = sin x cos x

If cos x = 0, then there is no solution because sin x cos x would also be 0. However, if cos x ≠ 0, we can divide both sides by cos x:

cos x = sin x

Now, we need to find the angles in the interval [0, 2π) that satisfy this equation. Using the inverse trigonometric functions:

x = π/4, 5π/4

Therefore, the solution set on the interval [0, 2π) is {π/4, 5π/4}.

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Answer:

150 pennies were lost altogether

Step-by-step explanation:

Let the initial number of pennies owned by Dante be x pennies

Let the initial number of pennies owned by Mia be y pennies

Mathematically ;

x + y = 350 •••••••(i)

So after losing half, dante will have x/2 pennies left.

Mia lost 1/3 so she will have 2/3y left

So after all the losses, they both had equal amount of pennies

This means that;

x/2 = 2y/3

Cross multiply;

3x = 4y •••••••(ii)

Let’s solve both equations simultaneously;

From i , x = 350-y

Substitute this into equation ii

3(350-y) = 4y

1050-3y = 4y

7y = 1050

y = 1050/7

y = 150

since x = 350-y

x = 350-150 = 200

Now Dante loss x/2 = 200/2 = 100

Mia lost 1/3y = 1/3 * 150 = 50

Total pennies lost = 100 + 50 = 150

Answer:

x=3

Step-by-step explanation:

9 - 2x = 4x - 9
Add 9 to both sides
18-2x=4x
Add 2x to both sides to make x go on one side
18=6x
divide by 6 both sides
x=3
hope this helps

The possible number of books that could be on sale is option 1: (5, 15).

Let's evaluate each option using the given system of inequalities:

a. (5, 15)

x = 5 and y = 15

The first inequality, x + y < 20, becomes 5 + 15 < 20, which is true.

The second inequality, x < y, becomes 5 < 15, which is true.

Therefore, (5, 15) satisfies both inequalities.

b. (15, 5)

x = 15 and y = 5

The first inequality, x + y < 20, becomes 15 + 5 < 20, which is true.

The second inequality, x < y, becomes 15 < 5, which is false.

Therefore, (15, 5) does not satisfy the second inequality.

c. (10, 10)

x = 10 and y = 10

The first inequality, x + y < 20, becomes 10 + 10 < 20, which is true.

The second inequality, x < y, becomes 10 < 10, which is false.

Therefore, (10, 10) does not satisfy the second inequality.

Hence based on the analysis, the possible number of books that could be on sale is option 1: (5, 15).

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Answer:

True

Step-by-step explanation:

The length of each ray (hypotenuse) can be calculated using the Pythagorean theorem, which gives the square root of 33² + 56².

The problem describes a right triangle formed by Aurora, the top of the forest, and the sun rays. The height of the forest is given as 33 feet, and the sun rays shine 56 feet into the forest.

We can use the Pythagorean theorem to find the length of each ray (hypotenuse). By applying the theorem, we have: hypotenuse² = height² + distance².

Plugging in the given values, we get: hypotenuse² = 33² + 56². Simplifying the equation, we find that the length of each ray (hypotenuse) is the square root of 33² + 56², which can be calculated to obtain the exact value in feet.

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Answer:

So for x sandwiches, the cost would be 10 + 4.5x dollars.

Step-by-step explanation:

The cost for x sandwiches can be calculated by adding the delivery fee to the cost of the sandwiches:

Cost = Delivery fee + Cost of sandwiches

Cost = 10 + 4.5x