any probability statement involving a normal random variable can be converted to an equivalent statement involving a standard normal random variable through the process of

Work Shown:

If cos(x) = 8/17, then sin(x) = 15/17. Use the identity [tex]\sin^2(\text{x}) + \cos^2(\text{x}) = 1[/tex] to determine this.

If cos(y) = 3/5, then sin(y) = 4/5 using that same identity.

So,

sin(x-y) = sin(x)cos(y) - cos(x)sin(y)

sin(x-y) = (15/17)*(3/5) - (8/17)*(4/5)

sin(x-y) = 45/85 - 32/85

sin(x-y) = (45 - 32)/85

sin(x-y) = 13/85

AO in terms of P and/or Q is OA = Q = Q

OB in terms of P and/or Q is OB = P =Q

EB in terms of P and/or Q is EB = 2P =2Q

A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any basic hexagon has a total internal angle of 720°.

In a regular hexagon, all sides are equal

Which means:

AB= BC

5p + q -5p = 6p-5p

q = p

So, every side of the hexagon is p = q

Which means that AB = BC = CD = DE = EF = FA = p =q

Recall that at the center, each side forms an angle

There are six sides in a hexagon.

Total angle = 360°

6x= 360°

x= 60°.

By the symmetry of regular hexagon, OA = OB

<OAB = <OBA

<AOB = x = 60°

Sum of all angles in a triangle is 180°

We add the values

<OAB = 60°.

<OAB is an equilateral triangle, thus every side is equal

Hence,

a. OA = Q = Q

b. OB = P =Q

c. EB = 2P =2Q.

From the figure, <BOE= 180° which makes it a straight line.

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Answer:

[tex]\frac{x}{x+(x-2)}[/tex] = [tex]\frac{10}{16}[/tex]

[tex]\frac{x}{2x-2}[/tex] = [tex]\frac{5}{8}[/tex]

5(2x-2) = 8x

10x - 10 = 8x

2x = 10

x = 5

Value of expression 5 - 3 is 2

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Given expression,

5 - 3 = ?

we need the difference of 5 and 3

5 - 3 = 2

Hence, 2 is value of expression 5 - 3

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Answer:

1) 2/5

2) 4/13

3) 1/8

4) 25/4 or 6 + 1/4

Step-by-step explanation:

1) 5/2 * x = 1

x = 1 / (5/2)

x = 2/5

2) (3 + 1/4) * x = 1

13/4 * x = 1

x = 1 / (13/4)

x = 4/13

3) 8 * x = 1

x = 1/8

4) (2/5)^2 * x = 1

2^2 / 5^2 * x = 1

4/25 * x = 1

x = 1 / (4/25)

x = 25/4

x = 6 + 1/4

The table for the values when x = 0,5,8,10, will be:

x (minutes) y (altitude in feet)

0                                    1500

5                                1450

8                                1420

10                                1400

30                                  1200

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

When x = 0, y will be:

-10x + 1500

= -10(0) + 1500

= 1500

When x = 5 y will be:

= -10(5) + 1500

= 1500 - 50

= 1450

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Answer:

  (a)  -1/2x +3 = 3x -4

Step-by-step explanation:

Given a graph of two lines, you want to know which equation it is showing the solution for.

The blue line has a slope of -3/6 = -1/2, and a y-intercept of +3, so its slope-intercept equation is ...

  y = -1/2x +3

This expression is seen on the left side of the equal sign for the first choice, and is not seen anywhere else.

By way of confirmation, the red line has slope 3/1 = 3 and a y-intercept that is a negative value less than -2. It is reasonable to say its slope-intercept equation is ...

  y = 3x -4

This expression matches the right side of the equal sign for the first choice.

The solution to the system of these two equations might reasonably be found by equating the expressions for y:

  -1/2x +3 = 3x -4

The area of the triangle is calculated to be equal to 7.5 square inches.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

we have the base of the triangle to be 6 inches and the height as 2.5 inches, so we solve for the area as follows:

1/2 × 6 inches × 2.5 inches

6 inches can be divided by 2 to give;

3 inches × 2.5 inches

7.5 square inches

Therefore, the area of the triangle is calculated to be equal to 7.5 square inches

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Answer:

n = 12

Step-by-step explanation:

Solve for n

3 ( n -5 ) = 21

Divide each side by 3.

3/3 ( n -5 ) = 21/3

n-5 = 7

Add 5 to each side.

n-5+5 = 7+5

n = 12

Step-by-step explanation:

jaubslsjsolqmaiBaokmaalo

Answer:

width=71km, length=177.5km

Step-by-step explanation:

Let x be the width of the farm.

Then the length of the farm will be 2.5x.

perimeter of farm in terms of x=2.5x+2.5x+x+x=7x

perimeter of farm in terms of x=perimeter of farm

7x=497

x=71

width=71km

length=71×2.5=177.5

Answer:

[tex] \sin( \alpha ) = \frac{16}{ \sqrt{281} } [/tex]

Step-by-step explanation:

Greetings!!!

Firstly, remember the sin trigonometric equation

[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} [/tex]

Assuming the image as this question and solve

If you have any questions or unclear ideas tag on comments

Hope it helps!!!

The value of the indicated trigonometric ratio sin( α ) is (16√281 )/281.

The figure in the image is a right triangle.

To find sin(α), we use trigonometric ratio.

Sine = Opposite / Hypotenuse

Plug in the values

sin( α ) = 16/√281

To simplify further, we rationalize the denominator

Multiply both the numerator and denominator by √281

sin( α ) = (16 × √281 ) /(√281 × √281 )

sin( α ) = (16 × √281 ) / 281

sin( α ) = (16√281 )/281

Therefore, the value of sin( α ) is (16√281 )/281.

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The highest number obtainable by multiplying the numbers 1-9 is 40,320. To obtain this result, you need to arrange the numbers in a specific order.

The problem is to find the highest number that can be obtained by multiplying the numbers 1-9, where each number can only be used once. To obtain the highest possible number, it's important to arrange the numbers in a specific order. One possible arrangement is 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This arrangement results in the highest product of 40,320. It's worth mentioning that different arrangements of the numbers may result in different products, but the arrangement mentioned above gives the highest possible product. Understanding the order of operations and how to manipulate the numbers is key to solving this problem and finding the highest number.

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The correct answers is (a). False (b). False (c). False (d).True

(A). False

If Mrs. Smith and Mr. Smith drive 80 miles each, then the total miles they drive is 80 + 80 = 160 miles. That means James will have to drive 240 - 160 = 80 miles, which is 1/3 of the round-trip distance, not 13/3.

(B). False

If Mrs. Smith and Mr. Smith drive 90 miles each, then the total miles they drive is 90 + 90 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{1}{4})[/tex] of the round-trip distance, not [tex]\frac{12}{4}[/tex].

(C). False

If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then the total miles they drive is 90 + 50 = 140 miles. That means James will have to drive 240 - 140 = 100 miles, which is [tex](\frac{1}{2} )[/tex] of the round-trip distance, not [tex](\frac{5}{12} )[/tex].

(D). True

If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then the total miles they drive is 60 + 120 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{7}{12} )[/tex] of the round-trip distance.

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Answer:

Your answer should be: TRUE FALSE TRUE FALSE

Answer:

0.0002

Step-by-step explanation:

She divides by 10.

The area of the piece of paper left after cutting out the circle is 29.76 in².

Area of a figure:

The amount of unit squares that completely encircle the surface of a closed figure is its area. Area is measured in square units like cm² and m². A shape's area is a two-dimensional measurement. The term “area” refers to the space inside the boundary or perimeter of a closed shape.

You need to first determine the rectangle's area.

8x10=80 in²

determine the circle's overall area.

The diameter is 8 in so you would use 4 as the radius

A=πr²

A=3.14x4²

A=3.14x16

A=50.24 in²

The area of the circle must then be subtracted from the area of the rectangle.

80-50.24=29.76

The area of the piece of paper is 29.76 in ².

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Answer:

Nov 27 at 14:24 hours

Step-by-step explanation:

57.6 days equates to 57 days, 14 hours, 24 minutes (using a calculator)

Adding to Oct 1 at 12:00:00 we get this as Nov 27 at 14:24 hours

In multiple regression, we have 4 assumptions listed and explained below. They are valid.

Following are assumptions for multiple regression model:

1. Linear connection: Each predictor variable and the responder variable have a linear relationship.

Making a scatter plot of each predictor variable and the response variable is the simplest technique to check if this premise is true.

2. Lack of Multicollinearity: There is no significant correlation between any of the predictor variables.

Calculating the VIF value for each predictor variable is the quickest approach to see if this premise is true.

3. Independence: Each observation has its own validity.

The Durbin-Watson test, a formal statistical test that informs us whether or not the residuals (and consequently the observations) exhibit autocorrelation, is the easiest approach to find out if this assumption is true.

4. Homoscedasticity: At every point in the linear model, the residuals' variance is constant.

The simplest technique to check if this premise is true is to plot the standardized residuals against the expected values.

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Answer:

Below

Step-by-step explanation:

6 C 2  =   6! /(4! 2!) = 15 outcomes

5- Perimeter of the new rectangle is 48 cm.

6- Area of the new triangle is 9 cm².

5- A rectangle that has a perimeter of 16 cm has been dilated with a scale factor of 3. To find the perimeter of the new shape, we need to multiply the original perimeter by the scale factor:

16 cm * 3 = 48 cm

So the perimeter of the new shape is 48 cm.

6- A triangle that has an area of 36 squared cm has been dilated with a scale factor of 0.5. To find the area of the new triangle, we need to multiply the original area by the square of the scale factor:

36 cm² * (0.5)²

= 36 cm² * 0.25

= 9 cm²

So the area of the new triangle is 9 cm².

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The test is determined whether the population variance is less than 7.

The hypothesis formulation-

‘H0: σ² ≥ 7’

‘H1: σ² < 7’

Now let us solve this question options-wise:

Option a is incorrect because we should always contain the ‘=’ or ‘≥’ or ‘≤’ sign, and in the null hypothesis, and also this option denotes the standard deviation, not the variance.

Option b is correct because it contains a ‘≥’ sign and it is the right complement to the alternative hypothesis.

Option c is incorrect because it measures the standard deviation instead of the variance.

Option d is incorrect because it has the lower limit of the variance as 49 instead of 7

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full question:

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ< 7.

b.σ^2≥7.

c. σ< 49.

d.σ^2≥ 49

The result is obtained by using the formula for a triangle.

Simply we count the number of grids representing a certain unit.

We have a flag in coordinate system can be seen in the picture.

Each grid represents a foot. Kenna will make five flags.

The flag is a triangle with the base at y-axis.

The base length is 3 ft and the height is 2. The area of the triangle is

Area of a flag = ½ bh

Area of a flag = ½(3)(2)

Area of a flag = 3 ft²

Area of five flags = 5(3 ft)

Area of five flags = 15 ft²

Hence, Kenna will need the material of 3 ft² for one flag and 15 ft² for five flags.

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Arithmetic overflow error converting numeric to data type numeric can be solved by increasing the precision and the scale, storing number in different data type or use user-defined datatype.

An "arithmetic overflow error converting numeric to data type numeric" error occurs when you try to store a number in a numeric column that is too large to be represented by the specified precision and scale. To resolve this error, you have a few options:

Increase the precision and scale of the numeric column, you can increase the precision and scale of the numeric column so that it can store larger numbers.

If you don't need the precision and scale of a numeric column, you can store the number in a different data type, such as float or big int.

 If the number is too large to be represented in the numeric column, you can round it to a smaller value before inserting it into the database.

 If the number is still too large to be represented in a numeric column or a different data type, you can create a custom data type in SQL Server to store the number.

It's important to choose the right solution based on your requirements and the specific use case. You may also need to consider the performance implications of each solution, especially if the data being stored is very large or complex.

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Answer:

Step-by-step explanation:

The Pythagorean Theorem will be applied:

[tex]c^{2} = a^{2} + b^{2}[/tex]

Substituting the values provided in the question:

[tex]7^{2} = 6^{2} + b^{2}[/tex]

[tex]= 49 = 36 + b^{2}[/tex]

[tex]= 49 - 36 = b^{2}[/tex]

[tex]= b^{2} = 13[/tex]

Taking the square root on both sides to get rid of the square:
[tex]= \sqrt{b^{2}} = \sqrt{13}[/tex]

[tex]= b = \sqrt{13}[/tex] yards

= b = 3.6 yards (Rounded to the nearest tenth)

1.) The "(≠)" means that all of the points on the line will satisfy the inequality.

2.) The solution set for the inequality is the entire region (shaded or unshaded portion) shown in the graph. The shaded region represents the set of all points that satisfy the inequality, while the unshaded region represents the set of all points that do not satisfy the inequality.

What is linear inequality?

A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.

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Answer: The expression that represents the amount of money John has collected is:

5 * m

This expression calculates the amount of money John collects by multiplying the number of members (m) by the amount of money collected per member ($5).

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

y varies directly with  x  means

y = k x

now with y = -93 and x = -3

   -93  =  k (-3)      shows k =  30

so   y = 30 x

now with x = -2

    y = 30 (-2) = -60