how many different samples of size 3 (without replacement) can be taken from a finite population of size 10?

So the image of the point (-9, -3) under the translation is (-7, -1).

Every point in the plane is translated by shifting it a predetermined distance in one direction to a new position. The translation moves the point (x1, y1) by the same horizontal and vertical distances to reach to point (x2, y2) if the image of the point (x1, y1) under a translation is (x2, y2) (x2, y2).

We can observe that the translation shifts the point -2 units to the right and 2 units up if we consider that the image of point (-3, -6) under a translation is (-1, -8).

By shifting the point -9 units to the right and -3 units up by 2 units, the image of the point (-9, -3) under the same translation may be found:

(-9 + 2, -3 + 2) = (-7, -1) (-7, -1)

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Answer:

Given data:

Arrange the numbers in the ascending order:

Identify the minimum and the maximum values:

Identify the median of the data set.

Since the number of data is even, the median is the average of the middle two numbers:

Identify the medians of the lower and upper regions.

For the lower region, the median- the first quartile is 14, for the upper region, the median - the third quartile is 83

We have all required numbers:

Attached is the example of the plot, this may be horizontal or vertical

A sample size of at the least 103 batteries should be randomly decided on and examined from the manufacturing run to make sure that the hypothesis test has a level of significance of 0.02 and that the possibility of erroneously accepting a batch with an average use life of much less than 400 hours isn't any more than 10%.

To determine the specified sample size for the hypothesis test, we want to apply the formulation for the sample size required for checking out a population mean, given by:

\(n = (zα/2 * σ / E)^2\)

in which:

In this example, the margin of error E may be calculated with the aid of subtracting the required minimum mean use life of 400 hours from the actual mean use existence of 384 hours, and taking the absolute value  

E = |384 - 400| = 16

The critical value zα/2 may be determined the usage of a standard normal distribution table or calculator, with a level of significance of 0.02:

zα/2 = 2.33

Substituting those values into the sample size method, we get:

\(n = (2.33 * 35 / 16)^2 = 72.43\)

Rounding up to the closest whole range, we get a recommended sample size of 73.

But, the production manager additionally needs a sampling procedure that only 10% of the time might show erroneously that the batch is suitable.

This requirement corresponds to the possibility of type I errors, or α, that's identical to 0.10. To make certain that the probability of kind I error is no more than 0.02, we need to modify the extent of significance and the critical price consequently:

zα/2 = 2.58 (from standard ordinary distribution table with α = 0.02)

Substituting this elements into the sample size formulation, we get:

\(n = (2.58 * 35 / 16)^2 = 102.07\)

Rounding as much as the closest entire number, we get a encouraged sample length of 103.

Thus, 103 sample size is recommended for the hypothesis test.

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Answer:

6/10 or 3/5

Step-by-step explanation:

Answer:

4 Groups

Step-by-step explanation:

2 1/2 can be written as 2.5, and since this is division, all we have to do is divide 10 by 2.5.

10/2.5=4

No, there is no commutative property of subtraction for rational numbers. The commutative property, which states that the order of operands does not affect the result of an operation, does not apply to subtraction for rational numbers.

The commutative property states that the order of the operands does not affect the result of an operation. For addition and multiplication, the commutative property holds true. However, for subtraction, the order of the operands does matter, and thus, the commutative property does not apply.

Let's consider an example to demonstrate this:

Take the rational numbers 3/4 and 1/2.

If we subtract 3/4 from 1/2, we have: 1/2 - 3/4 = (2/4) - (3/4)

= -1/4.

If we subtract 1/2 from 3/4, we have: 3/4 - 1/2 = (3/4) - (2/4)

= 1/4.

As you can see, the results are different when the order of subtraction is changed, indicating that subtraction does not follow the commutative property for rational numbers.

The commutative property, which states that the order of operands does not affect the result of an operation, does not apply to subtraction for rational numbers. Changing the order of subtraction changes the result, making subtraction non-commutative for rational numbers.

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The commutative property does not apply to the operation of subtraction with rational numbers. This is because changing the order of the numbers in a subtraction operation will give a different result.

In mathematics, the commutative property refers to the idea that the order in which numbers are used in an operation does not change the result of that operation. This property holds true for addition and multiplication but, unfortunately, it does not hold true for subtraction and division. For example, in subtraction, if we take two rational numbers such as 5 and 3, 5 - 3 is equal to 2, but 3 - 5 equals to -2. As you can see, changing the order of the numbers gives us different results, demonstrating that there is no commutative property of subtraction for rational numbers.

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Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

To find the length of the loop of the given curve, we need to use the formula for arc length: L = ∫√(dx/dt)² + (dy/dt)² dt.

where dx/dt and dy/dt are the derivatives of x and y with respect to t.
In this case, we have:

dx/dt = 12 - 12t²
dy/dt = 24t

Therefore,
(dx/dt)² + (dy/dt)² = (12 - 12t²)² + (24t)² = 144t⁴ - 96t² + 144
and √(dx/dt)² + (dy/dt)² = √(144t⁴ - 96t² + 144)
The loop of the curve occurs when y = 0, which implies 12t² = 0, i.e., t = 0.

So, we need to integrate from t = 0 to t = 2: L = ∫₀² √(144t⁴ - 96t² + 144) dt
This integral can be quite difficult to solve analytically, so we can use numerical methods to approximate the value of L. Using a numerical integration tool, we get: L ≈ 33.14

Therefore, the length of the loop of the given curve is approximately 33.14 units.

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Answer:

\(\boxed 3 \: h(x) = 14 {x}^{3} - 7 {x}^{2} + 12\)

Answer:

B. \(x>-17.5\)

C. \(x\leq-30\)

Step-by-step explanation:

B.)

\(\frac{-8}{14}x+22>32\\-8x+308>448\\-8x>140\\x>-17.5\)

C.)

\(0.9x+12\leq-15\\0.9x\leq-27\\x\leq-30\)

Hope this helped!! <3

Answer:it is 2 and 4

Step-by-step explanation:

Answer: 7/20

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

Answer:

Question 1 is G.

Question 2 is B

Question 3 is D

Question 4 is A.

Step-by-step explanation:

The correct representation of the inequality are:

1 ≥ 2x

6x ≥ 3 + 8x – 4

A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

6x ≥ 3 + 4(2x – 1)?

6x ≥ 3 + 8x - 4  ---- correct

6x - 8x ≥ 3 - 4

-2x ≥ - 1

1 ≥ 2x ----- correect

The number line would be A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

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L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

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Estimated  large sample size need to be selected for the 90%  of confidence level with standard deviation of $900 is equal to 24.

Standard deviation = $900

Confidence level = 90%

Estimate the required sample size,

Use the formula for the margin of error,

Margin of Error = Z × (standard deviation / √(sample size))

where Z is the z-score corresponding to the desired level of confidence.

Using attached z-score table,

For 90% confidence level, Z = 1.645.

Rearrange the formula to solve for the sample size,

Sample size = (Z × standard deviation / margin of error) ^ 2

Substituting the given values, we get,

⇒ Sample size = (1.645 × 900 / 300) ^ 2

⇒ Sample size = 24.35

Round up to the nearest whole number = 24

Therefore, need a sample size of at least 28 to ensure that it is large enough to achieve the desired level of confidence level.

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Answer:

The midpoint is ( 1,5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

( -4+6)/2 = 2/2 =1

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

( -4+14)/2 = 10/2 =5

The midpoint is ( 1,5)

The two sides of an inequality are not the same so inequality can never be true.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that the inequality is 2(3x - 1) +4> 6x + 2. The inequality will be solved as below;-

2(3x - 1) +4> 6x + 2

6x - 2 + 4 > 6x + 2

6x + 2 > 6x + 2

The two sides are equal so inequality can never be true.

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Answer:

True

Step-by-step explanation:

Actually, I'm pretty sure it can also be a reflection! :) Have a good day!!!

An equation is formed of two equal expressions. The solution of the equation √(x+12)=x is x=4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the equation √(x+12)=x can be done as,

\(\sqrt{x+12} = x\\\\\text{Square both the sides of the equation}\\\\x+12=x^2\\\\x^2-x-12=0\\\\x^2-4x+3x-12=0\\\\x(x-4)+3(x-4)=0\\\\(x-4)(x+3)=0\)

Equate each of the factors with 0,

\((x-4)=0\\x=4\\\\(x+3)=0\\x=-3\)

Now, if we substitute the value of x in the equation given, only the value of x as 4 will satisfy the equation.

Thus, the solution of the equation √(x+12)=x is x=4.

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Answer:

2A + 3W = 12 ---(1)

6A - 5W = 8 ---(2)

We can solve this system using the method of elimination or substitution. Let's use the method of substitution:

From equation (1), we can express A in terms of W:

2A = 12 - 3W

A = (12 - 3W) / 2

Substitute this value of A in equation (2):

6((12 - 3W) / 2) - 5W = 8

Simplify the equation:

6(12 - 3W) - 10W = 16

72 - 18W - 10W = 16

72 - 28W = 16

-28W = 16 - 72

-28W = -56

W = (-56) / (-28)

W = 2

Now that we have the value of W, we can substitute it back into equation (1) to find the value of A:

2A + 3(2) = 12

2A + 6 = 12

2A = 12 - 6

2A = 6

A = 6 / 2

A = 3

Therefore, in the given system of equations, the value of A is 3.

Step-by-step explanation:

2A + 3W = 12 ---(1)

6A - 5W = 8 ---(2)

We can solve this system using the method of elimination or substitution. Let's use the method of substitution:

From equation (1), we can express A in terms of W:

2A = 12 - 3W

A = (12 - 3W) / 2

Substitute this value of A in equation (2):

6((12 - 3W) / 2) - 5W = 8

Simplify the equation:

6(12 - 3W) - 10W = 16

72 - 18W - 10W = 16

72 - 28W = 16

-28W = 16 - 72

-28W = -56

W = (-56) / (-28)

W = 2

Now that we have the value of W, we can substitute it back into equation (1) to find the value of A:

2A + 3(2) = 12

2A + 6 = 12

2A = 12 - 6

2A = 6

A = 6 / 2

A = 3

Therefore, in the given system of equations, the value of A is 3.

Answer: a = 3; w = 2

Step-by-step explanation:

Multiply equation 1 by 3:

6a + 9w = 36

subtract equation 2 from 1:

9w - (-5w) = 36 - 8

14w = 28

w = 2

put w = 2 in equation 1

2a + 6 = 12

2a = 12 - 6

2a = 6

a = 3



The null hypothesis (H _0 ) is a statement that assumes there is no significant difference or effect in the population. In this case, the null hypothesis states that the variance of the production line is equal to or greater than 25. It serves as the starting point for the hypothesis test.

a. The null hypothesis (\(H_0\)) in this case would be that the variance of the production line is equal to or greater than 25.

b. The alternative hypothesis (\(H_1\) or \(H_a\)) would be that the variance of the production line is less than 25.

c. To compute the test statistic, we can use the chi-square distribution. The test statistic, denoted as \(\chi^2\), is calculated as:

\(\chi^2 = \frac{{(n - 1) \cdot s^2}}{{\sigma_0^2}}\)

where \(n\) is the sample size, \(s^2\) is the sample variance, and \(\sigma_0^2\) is the hypothesized variance under the null hypothesis.

d. The rejection region is the range of values for the test statistic that leads to rejecting the null hypothesis. In this case, since we are testing whether the variance is less than 25, the rejection region will be in the lower tail of the chi-square distribution. The specific numerical value depends on the degrees of freedom and the significance level chosen for the test.

e. To draw a conclusion, we compare the test statistic (\(\chi^2\)) to the critical value from the chi-square distribution corresponding to the chosen significance level. If the test statistic falls within the rejection region, we reject the null hypothesis. Otherwise, if the test statistic does not fall within the rejection region, we fail to reject the null hypothesis.

f. In terms of the problem situation, if we reject the null hypothesis, it would provide evidence that the variance of the production line is indeed less than 25. On the other hand, if we fail to reject the null hypothesis, we would not have sufficient evidence to conclude that the variance is less than 25.

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Answer:

Solution given

Cos I=adjacent/hypotenuse=16/34

8/17 is a required answer.

The value of the trigonometric ratio of cosI is 8/17 if the length of the side adjacent to the angle is 16 units and the length of the hypotenuse is 34.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle and the trigonometric ratio are defined as the ratio of the pair of sides of a right-angled triangle.

We have a right-angled triangle in the picture.

If we take ∠I to calculate the ratio of cosec.

We know the cos is the ratio of the side adjacent to the angle to the side opposite to the right angle.

The length of the side adjacent to the angle A = 16 units

The length of the side opposite to the angle H = 34 units

Then

\(\rm cosI = \frac{A}{H}\)

\(\rm cosI = \frac{16}{34}\)

\(\rm cosI = \frac{8}{17}\)

Thus, the value of the trigonometric ratio of cosI is 8/17 if the length of the side adjacent to the angle is 16 units and the length of the side opposite to the right angle is 34.

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0.17/30 = x/450 Use proportion

76.50 = 30x Cross multiply

2.55 = x Divide 30 both sides

7.5 minutes call would cost 2.55

Answer:

255 ¢ or 2.55$

Step-by-step explanation:

i counted like this

l    30 seconds   = 1

l    1 minute         = 2

l    1.5 minutes    = 3

l    2 minutes      =  4

l    2.5 minutes   =  5

l    3 minutes      =  6

l    3.5 minutes   =  7

l    4 minutes      =  8

l    4.5 minutes   = 9

l    5 minutes      = 10

l    5.5 minutes   = 11

l    6 minutes      =  12

l    6.5 minutes   = 13

l    7 minutes      = 14

l    7.5 minutes   = 15

 So then 17 ¢ x 15 = 255 ¢

If Colin wants to make 2 batches of Lavender soap and 2 batches of Vanilla soap, then he will need $9.57 for the oils

Here, Colin needs 1.5 ounces of Scented oil to make a batch of soap.

He wants to make 2 batches of Lavender soap and 2 batches of vanilla soap.

So, the amount of scented oil for 2 batches would be:

1.5 × 2 = 3 ounces

The cost of an ounce of Lavender oil is $1.54

So, using unitary method the cost of oil for the 2 batches of Lavender soap would be:

C₁ = 3 × 1.54

C₁ = 4.62 dollars

The cost of an ounce of Vanilla oil is $1.65

So,  using unitary method the cost of oil for the 2 batches of Vanilla soap would be:

C₁ = 3 × 1.65

C₁ = 4.95 dollars

Thus, the total cost would be,

C = C + C

C = 4.62 + 4.95

C = 9.57 dollars

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Answer:

An equivalent ratio in simplest term is: 3 : 5

The given system of equation is,

consider the equation (2),

consider the quation (3) and mulitply with 2,

then subract them,

Thus, the system of equation are, infinitely many solution.

The answer is (x,y) = (oo,oo).

The solution is, it represents a vertical translation, and value is (d)  k = 8.

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.

here, we have,

Translations of various kinds are often most easily seen by comparing points where the graph has a distinctive feature. On this graph, that is the vertex.

When looking at the graph we can discard 2 of the options, these are rotation (as they are parallel, it is impossible to find a rotation axis) and reflection. We can observe that it occur a translation. To know what kind of translation happened, let's look at the y intercept of both lines.

For f(x) the y intercept is 0 and for g(x) the y intercept is -4, it means it occured a vertical translation down 4 units.

so, we have,

The value k in the equation ...

 g(x) = f(x) +k

represents a vertical translation by k units.

The vertex coordinates for f(x) and g(x) are ...

 f(x): vertex = (-3, -3)

 g(x): vertex = (-3, 5)

This means ...

 f(-3) = -3

 g(-3) = 5 = f(-3) +k = -3 +8  

⇒   k = 8

Hence, The solution is, it represents a vertical translation, and value is (d)  k = 8.

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Answer:

13 u²

Step-by-step explanation: