A random sample of n = 16 scores is obtained from a normal population with m = 40 and s = 8. what is the probability that the sample mean will be within 2 points of the population mean?

Step-by-step explanation:

[tex] \frac{ \cot(x) - 1 }{ \cot(x) + 1} \\ \cot(x) = \frac{1}{ \tan(x) } \\ (\frac{1}{ \tan(x) } - 1) \div ( \frac{1}{ \tan(x) + 1} ) \\ multiply \: though \: by \: \tan(x) \\ \tan(x) \times ( \frac{1}{ \tan(x) } - 1 ) \div \tan(x) \times ( \frac{1}{ \tan(x) } + 1) \\ = 1 - \tan(x) \div 1 + \tan(x) \\ \frac{ \cot(x) - 1}{ \cot(x) + 1 } = \frac{1 - \tan(x) }{1 + \tan(x) } [/tex]

Answer:

<f = 132°

Step-by-step explanation:

360 - 56 - 106 = f + g

f = 2g

198 = 3g

g = 66

f = 2g

f = 2(66)

f = 132

The bases of a trapezium are parallel to each other.

The line x is parallel in this trapezium.

Hence,

Given two sides

I think you should provide extra information for correct answer.

that the angles etc.

Answer:

Step-by-step explanation:

The sum of the squares of the shorter sides is equal to the square of hypotenuse!

The area of one circle is 48 in² if the butcher paper is 24 inches long.

The area of a two-dimensional figure is the total area it takes up. It is the quantity, in other words, that counts the number of unit squares that cover the surface of a closed figure.

Square units—commonly expressed as square inches, square feet, etc.—are the accepted unit of area.

Given that:

3 congruent circles are perfectly fitted in the rectangular banner of length 24 inches,

⇒ diameter of each circle =  length of rectangular banner/3

⇒ d =  24/3

⇒ d =  8

⇒ r =  8/2

⇒ r =  4

Area of circle, A = π r²

A = 3× 4 × 4        (used pi as 3 as instructed in the question)

A = 48 in²

Thus, the area of one circle is 48 in² if the butcher paper is 24 inches long.

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No, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side for a triangle to be formed.

In order to determine whether 7 cm, 8 cm, and 11 cm can form a triangle, we must first consider the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side in order for a triangle to be formed. Therefore, in order for 7 cm, 8 cm, and 11 cm to form a triangle, the sum of any two sides must be greater than 11 cm. Since

7 cm + 8 cm = 15 cm,

which is less than 11 cm, 7 cm, 8 cm, and 11 cm cannot form a triangle.

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No, standard form does not have to be between 1 and 10. Standard form refers to a way of writing a number in which the number is expressed as a decimal between 1 and 10, multiplied by a power of 10.

Standard form, also known as scientific notation, is a way of writing a number that is a product of a decimal between 1 and 10, and a power of 10. The decimal part is called the coefficient, and the power of 10 is called the exponent.

For example, 12,000 can be written in standard form as 1.2 x 10⁴. Here, the coefficient is 1.2 (a decimal between 1 and 10) and the exponent is 4, indicating that the number is being multiplied by 10 raised to the power of 4 (10,000).

It is important to note that standard form is not limited to positive numbers and decimals between 1 and 10. A negative number or decimal less than 1 can also be written in standard form, but it would be multiplied by a power of 10 that is less than 1.

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Therefore ,as a result, ABC is equivalent with XYZ, which is the answer to the triangle problem that was presented.

Given its three sides and three vertices, a triangular is a polygon. This geometric shape is fundamental. Triangle ABC is a triangle that has the points A, B, and C as its corners. In geometric shapes, when four pieces are not collinear, a single plane and triangle are obtained. Polygons include triangles since they have three sides and a top right corner.

Here.

Therefore,

∠ A = ∠X because ABC is identical with XYZ.

∠B and ∠Y have the same meaning.

∠Z equals ∠C, and

Line ab has the same value as xy.

Line bc and yz are interchangeable.

Line ac corresponds to xz.

Cpct was employed to find a solution.

Triangle segments that are congruent are matched.

As a result, ABC is symmetrical with XYZ is the answer to the presented triangle problem.

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Complete question is: Are triangles ABC and XYZ similar?

Answer: -24x+18y

Step-by-step explanation:

6(-4x+3y)

=6*(-4x)+6*(3y)

=-24x+18y

Answer:

6(-4x + 3y)

Step-by-step explanation:

-24x + 18y

6(-4x + 3y)

Answer: ok ok... If this is like pick one ima go for A. = b

Step-by-step explanation: i hope this helps<3

Answer:

Step-by-step explanation:

One 1/12 is equal to 1/12, so you do not need to add any other fractions of 1/12 to get 1/12.

1/12 + 0 = 1/12

You can think of it in another way, if you want to add a certain number of fractions to obtain 1, you just need to add 12 of 1/12s to get 1, not one.

Answer:

Step-by-step explanation:

translate

Answer:

x² + 6² = 17²

6² + x² = 17²

Step-by-step explanation:

Pythagoras Theorem defines the equation of opposite² + adjacent² = hypotenuse². To make it simple, it's basically base² + height² = slope². Therefore:

[tex] \displaystyle{ {x}^{2} + {6}^{2} = {17}^{2} }[/tex]

Or you can also form as

[tex] \displaystyle{ {6}^{2} + {x}^{2} = {17}^{2} }[/tex]

Therefore, there are two correct answers here.

The equation of the line is y = -3x + 16

The general equation of a line is expressed as;

y = mx + c

Given that;

From the diagram shown, the coordinates of the line is expressed as;

(3, 7) and (2.5, 3)

The intercept. c = -3

Substitute the values

7 = -3(3) + c

expand the bracket

7 = -9 + c

collect like terms

c = 7 + 9

c = 16

The equation of the line is then given as;

y = -3x + 16

Hence, the equation is y = -3x + 16

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The equation into standard form is x = 4

From the question, we have the following parameters that can be used in our computation:

0 = x - 4

A linear equation in standard form is represented as

Ax + By = C

So, we have

0 = x - 4

Rewrite as

x - 4 = 0

Add 4 to all sides

x = 4

hence, the equation is x = 4

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The equation of variation is xy = 96. The value of y when x = 18 is 16/3 and the value of x when y = 8 is 12.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

y inversely varies as x.

That means, y ∝ 1/x.

So, y = kx, where k constant of variation.

Then, x × y = k

When y = 16, x = 6.

k = 6 × 16 = 96

So, the equation of variation is xy = 96.

When x = 18,

18y = 96

⇒ y = 96/18

⇒ y = 16/3

When y = 3.2,

3.2(30) = 96

When y = 8

8x = 96

⇒ x = 12

Therefore, the values are  y = 16/3 and  x = 12.

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Answer:

final cost of 42" TV after deducting 15% discount and adding 6.5% sales tax will be $1163.56

Step-by-step explanation:

final cost of 42" TV after deducting 15% discount and adding 6.5% sales tax will be $1163.56

The final cost of the TV would be $1,063.50.

To calculate this:

First, calculate the discount by multiplying the original price of the TV ($1,250) by 15% (0.15). This equals $187.50.

Subtract the discount from the original price of the TV ($1,250 - $187.50 = $1,062.50)

Next, calculate the sales tax by multiplying the price after the discount ($1,062.50) by 6% (0.06). This equals $63.75

Finally, add the sales tax to the price after the discount ($1,062.50 + $63.75 = $1,063.50)

Answer:

$1.49

Step-by-step explanation:

17.88/12 = 1.49

Answer:

each eraser cost $1.49

Step-by-step explanation:

take how much it cost 17.88

divide by how much you have 12

get how much one unit or 1 of what you have

17.88/12=1.49

Answer:

50%

Step-by-step explanation:

Divide the number of glass beads by the total number of beads:

75 glass beads / 150 total beads =

75 glass beads / 150 beads =

75/150 =

1/2 =

0.5 =

0.5 * 100% =  ==> 100% = 1

50%

Answer:

A. 106

Step-by-step explanation:

Use the correct order of operations.

(8 + 2)² + (6 − 4) × 3 =

= 10² + 2 × 3

= 100 + 6

= 106

The additive inverse of 2 9 is -2 9. This means that if you add -2 9 to 2 9, the result will be zero. This is because any number plus its opposite will equal zero.

2 9 + (-2 9) = 0

20 + (-20) = 0

The additive inverse of a number is the opposite of that number. This means that the inverse of 2 9 would be -2 9. When you add a number and its inverse together, the result is always zero. This is because any number plus its opposite will equal zero. For example, if we take 2 9 and add it to its inverse -2 9, the result will be 0. This is because 20 + (-20) = 0. The same concept can be applied to other numbers as well. For instance, if we take 3 4 and add it to its inverse -3 4, the result will be 0 because 34 + (-34) = 0. This shows that the additive inverse of a number is the opposite of that number, and when a number and its inverse are added together, the result is always zero.

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The relationship in this problem is a function, as each input is mapped to a single output.

A relation represents a function when each input value is mapped to a single output value.

From the table, we have that:

Each input is mapped to a single output, hence the table represents a function.

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The value of 'x' is not same in both cases, so this is a empty set.

step1

Because here square of element of set should be 4 then element should be 2 or -2 but when 2 or -2 multiplied by 3 gives 6 or - 6 which is not equal to 9. So, no element exists which can satisfy both conditions.

A={x x 2}=4 and 3x=9 is not empty set because there is no element we can say that is an empty set but there is an element, so it is not an empty set.

step2

X^2=4

Therefore only 2's square is 4

In first equation X=2

But in second equation

3x=9

Therefore here X=3

One variable has only one value

Therefore it is an empty set

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Answer:

-12<=n<=-7

Step-by-step explanation:

Answer:

x=-4/5, y=-6/5. (-4/5, -6/5).

Step-by-step explanation:

y-1/4x=-1

y-2=4x

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

y=4x+2

4x+2-1/4x=-1

4x-1/4x=-1-2

16/4x-1/4x=-3

15/4x=-3

x=-3/(15/4)

x=(-3/1)(4/15)

x=-12/15=-4/5

y-2=4(-4/5)

y-2=-16/5

y=-16/5+2

y=-16/5+10/5

y=-6/5

Answer: 3

Step-by-step explanation:

32 x 3 = 96

In the equation for total cost c = 1.5x + 6.99, 1.5 represents the cost of per song downloaded.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equation for total cost per month is c = 1.5x + 6.99.

Where x represents the number of songs Kaj downloads and c represents the total cost, in dollars and cents.

So, c and x are variable components of the equation.

There are only two fixed components in the equation 1.5 and 6.99.

Since number of songs downloaded x is multiplied by 1.5, so 1.5 is the cost of per song downloaded.

Hence, 6.99 becomes the fixed monthly membership cost of the music service.

Therefore, 1.5 is cost of per song downloaded.

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For the given data, ∅ is the given angle in standard position, terminal side passes through (21, -20) then the exact value of cot ∅= ( - √41/ 20 ) in simplest radical form.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( 21, -20 )

( 21, -20) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = 21

Altitude = -20

Using Pythagoras theorem,

Hypotenuse² = (21)² + (-20)²

⇒ Hypotenuse = √41

Cot ∅    = - √41/20 ( simplest radical form )

Then the exact value of

Cot ∅  = ( - √41/ 20 )  in simplest radical form.

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Answer:

The sum of the exterior angles is 360.  360/14 = 25.7 would be the measure of one exterior angle.

The sum of the interior angles is 1260.  1260/14 = 154.3 would be the measure of on interior angle.

Step-by-step explanation:

(n-2)180

n  is the number of sides

(14-2)180

12(180) 1260

This is the sum of the interior angles of the polygon.  

1260/14 = 154.3  Is the measure of one angle.

Percent of land planted with wheat  is 50% of total land.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

a farmer planted

320 acres of one variety of wheat

160 acres of a second variety of wheat.

He also planted 40 acres of milo,

and he has 440 acres that will lie fallow

Total land farmer has = 320 + 160 + 40 + 440 = 960 acres

Land planted with wheat = 320 + 160 = 480 acres

Percentage of land with wheat

= (land planted with wheat/ total land)× 100

= 480/960 × 100

= 0.5 × 100

= 50%

Hence, 50% of total land is planted with wheat.

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