A nursery owner buys 9 panes of glass to fix some damage to the greenhouse. The 9 panes cost ​$19.35. ​Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of​ glass?

The correct option : Both np and n(1 – p) are at least 10, for the a population with population proportion p.

A portion of a population that possesses a certain characteristic, given as a percentage, fraction, or decimal of the entire population.

For the stated data;

n = sample size of the population

p = population proportion

Then, for the sampling distribution of the sample proportion to be approximately normal both np and n(1 – p) are at least 10.

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14 9 12 18 19 15 13

I hope this helps. :)

Answer:

+4 then +1

Step-by-step explanation:

1,4,5,6,7,10,11

Answer

Option D is correct.

Magnitude of 3.7 is 3.7 because |3.7| = 3.7

Hope this Helps!!!

Answer:

No it is 12

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

6 ÷ 1/2 = 12

(1/2 = 0.5)

6 ÷ 0.5 = 12

Check you answer.

0.5 x 12 = 6

So Jordan is incorrect.

The correct answer is 12

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The equation represents the value of the car after 3 years is  V = 28900 (1 - 0.05)³

Price of the car = 28,900

Depreciation rate = 5%

Time period = 3 years

Calculating the amount of depreciation -

V = 28900 x (1 - 0.05)³

= 28900 x  (0.95)³

= 28900 x (0.857375)

= 24,827.75

Thus, the equation will be - V = 28900 (1 - 0.05)³ ( Depreciation means loss in value, thus the negative sign)

This equation accounts for the 5% yearly depreciation rate, which indicates that car value declines by 5% annually. The original cost of car must be multiplied by the depreciation factor (1 - 0.05) raised to the total time period (3 years) to get the car worth after three years.

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Complete Question:

A new car is purchased for 28,900 dollars. The value of the car depreciates at a rate of 5% per year. Which equation represents the value of the car after 3 years?

a. V = 28900 (1 + 0.05)^3

b. V = 28900 (1 - 0.05)^3

c. V = 28900 (0.05)^3

The predicted rate of growth 7 years from the present is approximately 8,484 people per year. The estimated population in 7 years will be around 159,821 people.

The rate of growth of the population is given by dp/dt = 1000t1.07.

(a) To determine the anticipated growth rate 7 years from now, we can simply substitute t = 7 into the equation:

dp/dt = 1000(7)^1.07 ≈ 8,484

Therefore, the predicted rate of growth 7 years from the present is approximately 8,484 people per year.

(b) To determine the anticipated population in 7 years from now, we need to integrate the growth rate from t = 0 (present) to t = 7:

∫dp = ∫1000t 1.07 dt

p = (1000/1.07) *\(t^(2.07)\) + C

Considering the initial supposition that there are 100,000 people living there at the moment (i.e., p(0) = 100,000), we can solve for the constant C:

100,000 = (1000/1.07) * \(0^(2.07)\) + C

C = 100,000

Therefore, the predicted population 7 years from the present is:

p(7) = (1000/1.07) * \(7^(2.07)\)+ 100,000 ≈ 159,821

Therefore, the predicted population 7 years from the present is approximately 159,821 people.

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Answer:

8= 24b

8/8=24b/8

b=3

Step-by-step explanation:

Based on my own learning

Answer:

3y +6

Step-by-step explanation:

8y + 10 − 4 − 5y

Combine like terms

8y-5y   +10-4

3y +6

Answer:

3y+6

Step-by-step explanation:

The question is incomplete. Here is the complete question.

(a) How many three-digit numbers can be formed from the digits 0,1,2,3,4,5 and 6, if each digit can be used only once?

(b) How many of these are odd numbers?

(c) How many are greater than 330?

Answer: (a) 180

              (b) 75

               (c) 105

Step-by-step explanation:

(a) In the group, there are 7 digits. A three-digit number can not start with zero, otherwise, it will be a 2-digit number. So:

For the hundreds position, there are 6 choices.

For the tens position, since the digit can be used only once, there are 6 choices.

For the unit position, there are 5 choices.

The total three-digit number formed is: 6*6*5 = 180

(b) To form an odd number, the unit position must be an odd digit, then:

unit position has 3 choices;

hundreds position has 5 choices;

tens position has 5 remaining choices.

The total three-digit odd number is: 3*5*5 = 75

(c) The number formed must be greater than 330, so:

If the number start with a 3, to be greater, there are 3 other choices (4, 5 and 6), so Tens position has 3 choices and Unit position has 5 choices.

Total number is: 3*5 = 15

Another possibility is the number starts with a digit bigger than 3 and so,  there are 3 choices.

Tens position has 6 choices;

Unit position has 5 choices;

Total possibilities are: 3*6*5 = 90

The total number of ways a three-digit number is greater than 330 is:

90 + 15 = 105

Answer:

D

Step-by-step explanation:

Lines EF and GH are already parallel. Translating them 2 units to the side without changing how far apart they are vertically means they won't intersect and will remain the same distance apart.

Answer:

D

Step-by-step explanation:

They are parallel lines

Answer:

63

Step-by-step explanation:

Make a ratio:

5 : 7 = 45 : x

x = 63

The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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Part A: The two possibilities for the x component are 59.7 units and -59.7 units.

Part B: The magnitude of the required vector is 104.9 units.

Part C: The direction of the vector -50.2 degrees, 50.2 degrees.

Part D: The magnitude of the resultant vector would be 80.0 units.

Part A:

The magnitude of the vector is given by:

|V| = sqrt(x^2 + y^2)

where x is the x component and y is the y component.

Substituting the given values, we have:

89.0 = sqrt(x^2 + (-66.0)^2)

Squaring both sides, we get:

7921 = x^2 + 4356

Solving for x, we get:

x = +/-sqrt(7921 - 4356)

x = +/-sqrt(3565)

x = +/-59.7

Therefore, the two possibilities for the x component are 59.7 units and -59.7 units.

Answer: 59.7, -59.7 units

Part B:

Let the magnitude of the required vector be V.

We need to find the x component of this vector, which we can denote by Vx.

The y component of this vector would be -66.0 units, since the original vector has a y component of -66.0 units and we want the resultant vector to point entirely in the negative y direction.

The magnitude of the resultant vector would be 80.0 units.

Using the Pythagorean theorem, we have:

\(|V + Voriginal| = sqrt((Vx + xoriginal)^2 + (-66.0)^2) = 80.0\)

Squaring both sides, we get:

\((Vx + xoriginal)^2 + (-66.0)^2 = 6400\)

Substituting the given values, we get:

\((Vx + xoriginal)^2 + 4356 = 6400\)

Solving for Vx, we get:

\(Vx = sqrt(6400 - 4356) - x\)

\(Vx = sqrt(2044) - x\)

\(Vx = 45.2 - xoriginal\)

Since we want Vx to be positive, we choose xoriginal to be -59.7 (the negative value from Part A), which gives:

Vx = 45.2 + 59.7 = 104.9

Therefore, the magnitude of the required vector is 104.9 units.

Answer: 104.9 units

Part C:

The direction of the vector can be found using the tangent function:

theta = arctan(y/x)

Substituting the given values, we get:

theta = arctan(-66.0/x)

Since we found two possibilities for x in Part A, we need to calculate two values of theta:

For x = 59.7:

\(theta = arctan(-66.0/59.7) = -50.2 degrees\)

For x = -59.7:

\(theta = arctan(-66.0/-59.7) = 50.2 degrees\)

The negative sign in the first answer indicates that the vector is below the negative x-axis, while the positive sign in the second answer indicates that the vector is above the negative x-axis.

Answer: -50.2 degrees, 50.2 degrees

Part D:

To find the magnitude of the vector that would give a resultant vector of 80.0 units in the negative y direction, we can use a similar approach as in Part B.

Let the magnitude of the required vector be V.

We need to find the x component of this vector, which we can denote by Vx.

The y component of this vector would be positive, since we want the resultant vector to point entirely in the negative y direction.

The magnitude of the resultant vector would be 80.0 units.

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The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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The area of the parallelogram will be 6cm²

The region in a two-dimensional plane that a parallelogram occupies is known as its area. A parallelogram is a form with four sides that has two dimensions in geometry. Because the opposing sides are equal and parallel, it is a unique example of a quadrilateral.

The space bounded by the four sides of a parallelogram is known as its area. A parallelogram's area is calculated as the sum of its length and height.

The given Base is 6cm

The height to the base is given is 1cm

So the are of the parallelogram is 6cm*1cm

= 6cm²

Hence, the area of the green parallelogram will be 6cm²

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Answer:

b*34

Step-by-step explanation:

an expression does not include an equal sign but an equation does

The relationship between the length of a side and the area is non proportional. so option C is correct.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a square, we need to find the relationship between the length of a side and the area.

The answer is non proportional because the side length is x, so is the other side lengths.

The side lengths are all equal and to find area you do x squared or x times x.

So they are not proportional because there will be different numbers for each.

For example. X= 2, area ( x squared ) is 4.

Hence, The relationship between the length of a side and the area is non proportional. so option C is correct.

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Answer:

the probability is 0.6

Step-by-step explanation:

The computation is shown below:

Let us assume the X would be the number appear on the top face

Now

= P(X = 1) ÷ P(X = 0)

= 0.3 ÷ 0.3 + 0.1 + 0.1

= 0.3 ÷ 0.5

= 0.6

hence, the probability is 0.6

For states, n = 1, 2, and 3 the probability of finding the particle at left 1/3rd of the box is P₁ = (3/4) * (2/L)²    P₂ = (1/4) * (2/L)²    and    P₃ = (1/3) * (2/L)²  respectively

a.

The wave function for the particle in a rigid box of length L for the state

n = 1, is given by:

|ψ₁(x)|² = (2/L)² * sin²(πx/L)

the wave function for the state n = 2,  is given by:

|ψ₂(x)|² = (2/L)² * sin²(2πx/L)

And the wave function for the state n = 3, is given by:

|ψ₃(x)|² = (2/L)² * sin²(3πx/L)

The graphs of |ψ₁(x)|², |ψ₂(x)|², and |ψ₃(x)|² is attached.

b.

The points of maximum probability density, which occur at x = 0 and       x = L for all three states are the positions at which the particle is most likely to be found.

c.

The points of minimum probability density, occur at x = L/2 for the state

n = 1, and at x = L/4 and x = 3L/4 for the state n = 2. For the state n = 3, the points of minimum probability density occur at x = L/3, x = 2L/3, and

x = L are the positions at which the particle is least likely to be found.

d.

Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 1 the probability of finding the particle in the left one-third of the box is greater than 1/3.

Since the probability density is highest at x = 0 and x = L, which are both outside the left one-third of the box for the state n = 2, the probability of finding the particle in the left one-third of the box is less than 1/3.

Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 3, the probability of finding the particle in the left one-third of the box is equal to 1/3.

e.

We need to integrate the probability density over the region of interest to calculate the probability that the particle will be found in the left one-third of the box for each of the states n = 1, n = 2, and n = 3.

the probability for the state n = 1,  is given by:

P₁ = ∫ |ψ₁(x)|² dx = (2/L)² * ∫ sin²(πx/L) dx

The probability for the state n = 2,  is given by:

P₂ = ∫ |ψ_2(x)|² dx = (2/L)² * ∫ sin²(2πx/L) dx

The probability for the state n = 3,  is given by:

P₃ = ∫ |ψ₃(x)|² dx = (2/L)² * ∫sin²(3πx/L) dx

Here all integrals have limits 0 and L/3

Solving these integrals gives:

P₁ = (3/4) * (2/L)²

P₂ = (1/4) * (2/L)²

P₃ = (1/3) * (2/L)²

Thus, the probabilities that the particle will be found in the left one-third of the box are:

P₁ = (3/4) * (2/L)²

P₂ = (1/4) * (2/L)²

P₃ = (1/3) * (2/L)²

for the states n = 1, n = 2, and n = 3, respectively.

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Answer:

An informal proof

Step-by-step explanation:

I just did this question

(It could be wrong though considering that they can be either formal or informal, it depends on the situation!)

The resulting differential function is f'(x) = 2x and g'(x) = 2x² + 1

The term function in statistics refers the expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here we have given that let f and g be functions that are differentiable for all real numbers.

And we have to find the solution for the function.

Let us consider f(x) =  x² and g(x) = x³ + 1

Then the differentiation function is calculated as,

As per the law of differentiation, it can be written like the following,

=> f'(x) = x² dx

Then it can be written as the following after differentiation

=> f'(x) = 2x

Similarly, the g(x) is differentiated like the following,

=> g'(x) = x³ + 1 dx

=> g'(x) = 2x² + 1

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The result of the number 1 trillion to the 10th power as required to be determined is; 10¹²⁰.

The result of the number 1 trillion to the 10th power is as follows;

Recall; 1 trillion = 1,000,000,000,000 = 10¹²

Hence; 1 trillion to the 10th power is; ( 10¹² )¹⁰.

From the laws of indices; we therefore have that;

= 10¹²⁰

Ultimately, the result is; 10¹²⁰.

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Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

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

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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The OLS estimate of the Bo parameter will tell us the difference in the likelihood of watching the movie between a student and a non-student, controlling for parental income, option C is correct.

The Bo parameter is the intercept, which is the value of the dependent variable when all the independent variables are equal to 0. In this case, the independent variables are Student and In(Parental Income), so when both of these variables are equal to 0, the person is not a student and their parents have an income of $0. The OLS estimate of the Bo parameter will tell us the likelihood of this person watching the movie.

The OLS estimate of the B1 parameter will tell us the difference in the likelihood of watching the movie between a student and a non-student, holding parental income constant. The OLS estimate of the B2 parameter will tell us the difference in the likelihood of watching the movie for every one-unit increase in parental income, holding student status constant.

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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Answer:

(-3,-1)

Step-by-step explanation:

Answer:

= 7x² + 5x - 9

Step-by-step explanation:

(9x + 1) - (-7x² + 4x + 10)

= 9x + 1 - ( -7x² + 4x + 10)

= 9x + 1 + 7x² - 4x - 10

= 7x² + 5x - 9

The number of different seating arrangements is an illustration of permutation

There are 151200 different seating arrangements

The number of seats (n) is given as:

n = 10

The number of people (r) is given as:

r = 6

So, the number of seating arrangements is:

\(^nP_r = \frac{n!}{(n - r)!}\)

This gives

\(^{10}P_6 = \frac{10!}{(10 - 6)!}\)

Simplify

\(^{10}P_6 = \frac{10!}{4!}\)

Evaluate the quotient

\(^{10}P_6 = 151200\)

Hence, there are 151200 different seating arrangements

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