Write the component form of the vector.

The value of x in the equation is 18. 98

Trigonometric identities are defined as mathematical equations relating to several trigonometric functions, holding true for all the values in the domain of the functions.

The several types of trigonometric identities includes;

It is important to note that the trigonometric ratios for major identities are;

sine = opposite/hypotenuse

tangent = opposite/adjacent

cosine = adjacent/hypotenuse

Given the equation;

x/25.75=sin47.5 degrees

Take the following steps to determine the value of 'x'

We have;

cross multiply

x = sin47.5  × 25. 75

Find the value of sin 47. 5 and substitute the value

x = 0. 7373 × 25. 75

multiply through

x = 18. 98

Hence, the value of x is  18. 98

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The complete question:

x/25.75=sin47.5 degrees

Find the value of x

It is observed that f is a subset of A×B

A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.

Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}

A={1,2,3}

B={7,8,9,10}

A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}

f={(1,7),(2,9),(3,8)}

A relation from a non-empty set  A to a non-empty set  B  is a subset of the Cartesian product A×B

It is observed that f is a subset of A×B

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Answer: 25 is divisible by 5, so it is composite

Step-by-step explanation:

Units change translation from cm to feets

1 cm is equivalent to 2.5 feets

triangle is a rectangular triangle suported with the bigger side

this means the height of triangle is 6cm

the base is 16 cm

the area is (base x height)/2

so then area= 16x 6/2= 48cm ^2

BUT because 1cm is equivalent to 2.5 feets then

multiply 48 x 2.5 x 2.5 = 48 x 6.25 = 300 ft^2

The absolute change or the car's value decreased by $1500.

The relative change: The value of the car decreased by 6.302 %.

The car's value dropped from $23,800 to $22,300 over the last year.

So, the initial price of the car is I = $23,800, and the final value of the car after a year is F = $22,300.

Therefore,

The Absolute change will be:

= I - F

= $23,800 - $22,300

= $1500

Hence, the car's value decreases by $1500.

Now, the relative change is the percentage by which the price decreased over the year.

So,

As the price decreased by $1500.

Let x be the relative change.

Then,

$ 23,800 × x/100 = $1500

238x = 1500

x = 6.302

Hence, the car's value decreased by 6.302% last year.

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The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%

To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room

The probability of an unlocked room being robbed is therefore:

= 0.75 x 0.03 x 0.842

= 0.0225 x 0.842

= 0.018945

= 1.89%

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The reciprocal of 3 7/8 is 8/31.

To find the reciprocal of a number, we invert the fraction by swapping the numerator and denominator.

Let's calculate the reciprocal of 3 7/8.

First, we need to convert the mixed number into an improper fraction. To do this, we multiply the whole number (3) by the denominator (8) and add the numerator (7). This gives us:

3 7/8 = (3 x 8 + 7) / 8 = 31/8

Now, to find the reciprocal, we invert the fraction:

Reciprocal of 31/8 = 8/31

Therefore, the reciprocal of 3 7/8 is 8/31.

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Answer: x = 7

Explanation - 4(5x-2)=2(9x+3)

20x-8=18x+6

20x-18x=6+8

2x=14

x=14÷2

x=7

Hello there!

Here we need to solve for x.

The first thing that we're going to do is this:

[tex]\implies\boldsymbol{4(5x-2)=2(9x+3)}[/tex]

[tex]\implies\boldsymbol{20x-8=18x+6}[/tex]

[tex]\implies\boldsymbol{20x=18x+14}[/tex]

[tex]\implies\boldsymbol{20x-18x=14}[/tex]

[tex]\implies\boldsymbol{2x=14}[/tex]

[tex]\implies\boldsymbol{x=7}[/tex]

Therefore x=7. I hope this helps you, feel free to comment if you have any queries :)

Given:

Center of circle: (-4, 7)

Endpoint on the circle: (8, -4)

Let's write the equation of the circle with the given information.

Apply the equation of a circle:

Where:

Center of circle: (h, k) ==> (-4, 7)

Radius = r

Substitute the values of (h, k) in the equation:

To find the radius, let's find the distance between the points (-4, 7) and (8, -4).

Apply the distance formula:

Given:

(x1, y1) ==> (-4, 7)

(x2, y2) ==> (8, -4)

Thus, we have:

Therefore, the radius is 16.3

Therefore, we have the equation of the circle as:

ANSWER:

The number of different samples possible when the shopper selects a sample of 4 apples from the bag is 126.

Combinations are a method of calculating the overall results of an event where the order of the results is irrelevant. From the information, the bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.

It should be noted that the question has to do with a combination. The number of different samples that are possible will be:

Number of apples = 9

Number to be selected = 4

= ⁹C₄

= 9! / (9 - 4)! 4!

= 9 × 8 × 7 × 6 / 4 × 3 × 2

= 126

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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. How many different samples are possible?

The actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.

The minimal amount of coordinates required to specify any point within a mathematical space (or object) is known as the dimension in physics and mathematics. As a result, a line has one dimension (1D), since only one coordinate is required to specify a point on it, such as the point at 5 on a number line.

A surface, like the perimeter of a cylinder or sphere, has two dimensions (2D) because two coordinates are necessary to specify a point on it. For instance, both a latitude and a longitude are necessary to pinpoint a point on the surface of a sphere.

The dimensions are 3cm by 5 cm meaning length = 5cm and breadth = 3cm

Given that ½ cm = 2 ft, that is

1 cm = 4 ft

Using the conversion method

3 cm = 3 × 4

        = 12 ft

5 cm = 5 × 4

        = 20 ft

Actual area = 20 × 12 ft

                    = 240 square ft

Thus, the actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.

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If the following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.  The percent of those who do not have diabetes test negative for the disease is: B. 56.8%.

Probability can be defined as the tendency or likelihood that something will happen.

Hence,

Percentage of people  do not have diabetes and test positive is 5.2%

Percentage of people  do not have diabetes and test negative is  56.8%

Total percentage of people who tested positive and negative is 62%

Based on the above analysis for people who does not have a diabetes we can see that the Percentage of people  do not have diabetes and test negative is  56.8%.

Therefore the correct option  is B.

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As per the given matrix [tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex], Option (C) is not true.

Matrix:

The matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Given,

[tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex]

Here we need to find which of the option is not true.

To find the incorrect options first we have to calculate the |A| and A⁻¹.

And we have also check whether is matrix has inverse or skew symmetric matrix.

First, we have to calculate the value of |A|,

|A| = (2 x 1) - (-1 x 2)

|A| = 2 - (-2)

|A| = 2 + 2 = 4

Therefore, option (A) is true.

Now we have to check this matrix has inverse,

It can be calculated using the formula,

[tex]A^{-1} =\frac{1}{|A|} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]

So, the inverse of the matrix is,

[tex]A^{-1} =\frac{1}{4} \left[\begin{array}{ccc}1&-2\\-(-1)&2\end{array}\right][/tex]

Which is equal to,

[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-2/4\\1/4&2/4\end{array}\right][/tex]

When we simplify it then we get,

[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-1/2\\1/4&1/2\end{array}\right][/tex]

Through this we have conclude that Option (B) and (D) are true.

We know that,

In the skew-symmetric matrix, a matrix whose transpose is equal to its negative.

So, the transpose of the given matrix is,

[tex]A^{T}=\left[\begin{array}{ccc}2&-1\\2&1\end{array}\right][/tex]

So, the given matrix is not a skew-symmetric matrix.

Therefore, the incorrect option is (c).

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Answer:

Your leading coefficient is 2

The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.

As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.

We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:

Where (t,C) is any point on the line, m is the slope and b is the C-intercept.

By replacing the know values we can solve for b:

Therefore,

Answer:

a: undefined

b: -15

c: 20

d: 25

Step-by-step explanation:

a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined

b: look at x 0 on graph, there is open dot at -15 meaning the limit is there

c: look at x -7 on graph, there is open dot at 20 meaning the limit is there

d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)

Domain and Range of Functions

Given a function y = f(x), the domain of f is

The range of f is the

We are given the function:

It's required to find the domain and range of the inverse function.

We must recall that, if the inverse function exists, its domain is the range of f, and its range is the domain of f.

Since f(x) is a rational function, it may not exist for the values of x where the denominator is 0.

Concretely, for x=0, the denominator is 0 and the function does not exist, thus the domain of f consists of every real number except x=0.

This can be written as (-∞,0) U (0,∞). This is also the range of the inverse function.

Now let's find the inverse function. We must solve for x the equation:

Adding 3:

Multiplying by x and dividing by y+3:

Swapping letters:

This is the inverse function of f.

Thus the domain of the inverse is:

-3-3

And the range:

Answer: Choice d

The prices p that would yield a revenue of 7110 dollars are;

Lowest price = $0.895

Highest price = $119.105

We are told that the total revenue obtained by producing and selling x units is given by; R = xp.

Now, we are told that the demand equation for a certain product is given by p = 120 - 0.015x.

where;

p is the unit price (in dollars) of the product.

x is the number of units produced.

At a revenue of $7110, we will have;

(120 - 0.015x)x = 7110

120x - 0.015x² = 7110

0.015x² - 120x + 7110 = 0

Using quadratic equation calculator, we have;

x = 59.695 and 7940.305

Thus;

Lowest price = 120 - 0.015(7940.305) = $0.895

Highest price = 120 - 0.015(59.695) = $119.105

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1) Dividing the given formula by W we get:

2) We know that:

Therefore:

Then:

Substituting W=3/4ft and L=18ft in the given formula we get:

Answer:

1)

2)

4 Tangerines will balance 1 apple.

Given that

Weight of Apple is represented by: a

Weight of tangerine is represented by: t

Weight of Grapefruit is represented by: g

Weight of Banana is represented by: b

Consider 1st picture:

1 apple and 1 tangerine balance 1 grapefruit.

⇒ a+t = g                  ...(1)

Consider 2nd picture:

1 banana and 1 tangerine balance 1 apple.

⇒ b+t = a                  ...(2)

Consider 3rd picture:

2 grapefruits balance 3 bananas.

⇒ 2g = 3b

g = 1.5b                     ...(3)

The system of equations are:

First balance: a+t = g  

Second balance: b+t = a  

Third balance: g = 1.5b  

Putting the value of g from equation (3) to equation (1), we get

a+t = 1.5b                   ...(4)

Now, putting the value of b from equation (2) to equation (4), we get

a+t = 1.5(a-t)

1.5a - 1.5t = a+t

0.5a = 2t

a = 4t

Hence, one apple is balanced by 4 tangerines.

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nswer:

Explanation:

ere, we want to solve the given composuite function

What we have to do is to replace the x in f(x) with the entirety of g(x)

We have that as:

Now, we replace x in f(x) with 2x+9 as stated

We have that as:

Answer:

I'm not so very sure but I really need points

The estimated value of 3√28 using linear approximation is 82/27 which is answered in form of fraction.

A general function can be approximated using a linear function in mathematics using the term "linear approximation" (more precisely, an affine function). They are frequently utilised in the finite difference method to create first order approaches for resolving or approximating solutions to equations.

We need to find the approximate value of ∛28 using linear approximation

Let f(a) =  ∛a

then F(27) =  ∛27 = 3

We compute the derivative of f(a) as being

[tex]f(a)=a^{\frac{1}{3}}[/tex]  ⇒  [tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex]

Hence,

[tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex] = [tex]\frac{1}{3}(3)^{-2}=\frac{1}{3}(\frac{1}{9})=\frac{1}{27}[/tex]

Recall the equation of a line is given by

⇒ y - b = m(x - a)

⇒ [tex]y-3=\frac{1}{27}(x-27)[/tex]

⇒ [tex]y=\frac{1}{27}x-1+3[/tex]

⇒ [tex]y=\frac{1}{27}x+2[/tex]

So the approximation at  x= 27.5 would be

⇒  [tex]y=\frac{1}{27}(28)+2[/tex]

⇒ y = 82/27

⇒ y = 3.037

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The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275

The given parameter is in the attached figure

Also from the question, we have:

House price decreases by approximately every mile

The above implies that the relationship is an approximately linear relationship

From the table, we have

Coefficient constant = 301.7

Coefficient distance = -2.158

This means that

y-intercept = 301.7

Slope = -2.158

So, the equation is

y = y-intercept + slope * x

This gives

y = 301.7 - 2.158x

The interpretation of the slope and y-intercept in context are:

Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7

Here, we have

Residual =  -2.962

Miles = 11

This means that

Predicted price = 301.7 - 2.158 * 11

Evaluate

Predicted price = 277.96

So, we have

residual = actual - predicted

This gives

actual = residual + predicted

So, we have

actual = -2.962 +  277.96

Evaluate

actual = 275

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The g graph exhibits a four-fold vertical stretch.

The graph of f (x)=[tex]x^{2}[/tex] is translated up to two units, then reflected in the X-axis.

The rule for g.

Identify the vertex​

The g graph exhibits a four-fold vertical stretch.

=> g = 4f(x) (x)

an X-axis reflection

=> g = - 4f(x) (x)

(X-axis reflection of (X, Y) is (x , - y)

a conversion two units higher

=> g = -4f(x) + 2

f(x) = x²

=> g = - 4x² + 2

Vertex is at  ( 2, 0)

What is a vertical stretch?

When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.

How to vertically stretch a function?

When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:

Ensure that the values for x remain the same, so the base of the curve will not change.

This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.

Take note of the new critical points, such as the new maximum point of the graph.

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Answer: Smooth muscle contractions

The ratio of appaloosa to mustang horses is 12:40

The total number of horses is given as 52.

Number of white horses =12

Let the number of black horses be x

This means that ratio of white: black horses is 12 : x

Using the ratio above, we can find the number of black horses as follows:

[tex]\frac{x}{12+x} of 52 = x[/tex]

[tex]\frac{52x}{12+x} = x[/tex]

52x = x(12 + x)

[tex](12x + x^{2} ) = 52x[/tex]

[tex]x^{2}[/tex] + 12x - 52x = 0

[tex]x^{2}[/tex] - 40x = 0

Taking out the common factor x from equation we have:

x(x - 40) = 0

This gives us with two solution:

x = 0 and x = 40

Since the question said there are some black horses, the x=0 value can be ignored. So we have x = 40

Hence,  The ratio of appaloosa to mustang horses is 12:40

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Answer:  31y2 + 6

Step-by-step explanation:

61 y2 + 1 y2 = 62 y2  

7y + -7y = 0

6+6 =12

62y2 + 12  then divide by 2 and it's  31y2 + 6