Can someone help me with this? Use f and g to preform the following operations and match them to correct answer

The measure of angle U is given as follows:

m < U = 66º.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:

c² = a² + b² - 2abcos(C)

Hence the length of side v is obtained as follows:

v² = 22² + 79² - 2 x 22 x 79 x cosine of 51 degrees

v² = 4537.48

[tex]v = \sqrt{4537.48}[/tex]

v = 67.36.

By the law of sines, we have that:

sin(51º)/67.36 = sin(U)/79

Hence the measure of angle U is obtained as follows:

sin(U) = 79 x sine of 51 degrees/67.36

sin(U) = 0.9114

m < U = arcsin(0.9114)

m < U = 66º.

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Answer:

Step-by-step explanation:

Let the angle be x

then its supplementary angle be 180 - x

x - ( 180 - x )  =  14.2

2x = 194.2

x = 97.1

angle = 97.1

supplementary angle = 180 - 97.1

                                      = 82.9

Answer:

Step-by-step explanation:

Let’s assume the original price of the item is “x.” Then, using the first statement, the list price of the item is 80% of the original price, or 0.8x. If there is a discount applied, let’s say “d,” then the discounted price would be (1-d)(0.8x).

Using the second statement, if the price of the item has been reduced by 80%, then the discounted price would be 0.2x. This can be expressed as (1 - 0.8)(x).

So, we have the following two equations:

(1 - d)(0.8x) = 0.2x

0.64x - 0.8dx = 0.2x

Simplifying this equation, we get:

0.44x = 0.8dx

d = 0.55

This means that the discount applied in the first statement is 55%, not 80%.

The calculation for change in percentage (increase or decrease) involves finding the difference between two values and expressing it as a percentage of the original value. This is different from multiplying by percentages, which involves finding a percentage of the original value and subtracting or adding it to the original value.

The wording of percentage problems is important because it can affect the way the problem is interpreted and the calculation that is used to solve it. For example, the phrase “increased by 50%” could be interpreted as multiplying the original value by 1.5, while the phrase “increased to 50%” could be interpreted as finding 50% of the original value and adding it to the original value.

Examples:

A shirt is on sale for 30% off its original price of $50. The discounted price is (1-0.3)($50) = $35.

A company’s revenue increased from $100,000 to $120,000. The percentage increase in revenue is ((120,000 - 100,000) / 100,000) x 100% = 20%.

The area that Michaela will need to cover up with blue paint would be 396. 11 in ²

The area of the decorative box that needs to be covered is the entire outside of the shape.

The box is a pentagonal prism which means the area will be the area of a pentagonal prism which can be found by the formula :

= 5 a h + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) a ²

Where a is the side of the pentagon and h is the height.

The area is:

= 5 (7 ) ( 6. 5 ) + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) )  ( 7 )²

= 396.10679

= 396. 11 in ²

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Answer:

[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]

Step-by-step explanation:

A translation is a transformation that moves every point of a figure the same distance and in the same direction. This means that the size, shape, and orientation of the figure are preserved, but its position is changed.

From inspection of the given diagram, we can see that the size, shape and orientation of the graph of function g is the same as that of the graph of function f, but its position has changed.  Therefore, the transformation is a translation.

We can use the vertex of both graphs to determine the translation.

Therefore, the graph of function f has been moved 3 units left and 6 units down to create the graph of function g.

When we move "a" units left, we add the value of "a" to the x-value of the function.

When we move "a" units down, we subtract the value of "a" from the function.

Therefore:

[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]

The first plan has a higher rate of change compared to the second plan based on the given information.

To identify which function has the greater rate of change, we need to compare the rate at which the cost increases for each function. Given the table of values, let's analyze the rates of change for both functions.

First Plan:

The first plan charges a rate of $5 per day, regardless of the number of days. In this case, the rate of change is constant at $5 per day, meaning the cost increases by $5 for each additional day.

Second Plan:

The table of values provided doesn't directly represent the second plan. We need the values for the number of days and their corresponding costs for the second plan to determine its rate of change.

However, since we're comparing the rates of change between the two functions, we can calculate the average rate of change for the second plan using the given values. Let's find the average rate of change between the first and last points:

Change in cost = 102 - 24 = 78

Change in days = 20 - 2 = 18

The average rate of change = Change in cost / Change in days

= 78 / 18

≈ 4.3333

The average rate of change for the second plan is approximately 4.3333 dollars per day.

Comparing the rates of change:

The rate of change for the first plan is $5 per day, while the average rate of change for the second plan is approximately $4.3333 per day. Therefore, the first plan has a greater rate of change.

In conclusion, the first plan has a higher rate of change compared to the second plan based on the given information.

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Answer:

Step-by-step explanation:

Hi, im gonna try my best to explain.
First we solve what X could be, since it doesnt say; we make x = 1
3 x 1 = 3.
now we take both 3's and multiply which would be 9
2 to the power of 3 is 8.
8 + 9 is 17
then, minus 2 is 15
and lastly; 15 + 1 = 16

(hope this helped!)

The probability of someone being a right-handed chess player is 0.962, or approximately 0.96

Now, We have to given that;

The probability of being right-handed (R) is 0.9 and the probability of playing chess (C) given that someone is left-handed (L) is 0.6.

And, We are also told that dominant hand and playing chess are independent, so this means that the probability of playing chess is the same regardless of whether someone is left-handed or right-handed.

Hence, the probability of someone being a right-handed chess player, we can use the following formula:

P(R and C) = P(R) x P(C)

We know that P(R) = 0.9,

and since playing chess is independent of handedness,

P(C) = P(C|L) + P(C|R) = 0.6 + P(C|R).

We want to find P(C|R), the probability of playing chess given that someone is right-handed.

We can use the fact that the probabilities must add up to 1 to solve for P(C|R):

P(C|R) = 1 - P(not C|R)

We know that;

P(not C|R) = 1 - P(C|R),

so we can substitute to get:

P(C|R) = 1 - (1 - P(C|R)) = 2P(C|R) - 1

Now we can substitute this back into the original formula and solve for P(R and C):

P(R and C) = P(R) x P(C) P(R and C) = 0.9 x (0.6 + P(C|R))

P(R and C) = 0.54 + 0.9P(C|R)

Finally, we use the fact that the probabilities must add up to 1 to solve for P(C|R):

P(C|R) = 1 - P(not C|R) P(C|R)

= 1 - P(no C and R) / P(R) P(C|R)

= 1 - P(R and not C) / P(R) P(C|R)

= 1 - (0.1 x 0.4) / 0.9

P(C|R) = 0.5333

Now we can substitute this back into the equation for P(R and C) to get:

P(R and C) = 0.54 + 0.9(0.5333...)

P(R and C) = 0.962

Therefore, the probability of someone being a right-handed chess player is 0.962, or approximately 0.96

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Answer:

[tex]w=\frac{82}{17}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Decimal form: 4.82352941

having a great day and thx for your inquiry :)

The null hypothesis is given as follows:

[tex]H_0: \mu = 175[/tex]

The alternative hypothesis is given as follows:

[tex]H_1: \mu \neq 175[/tex]

The claim in the context of this problem is given as follows:

"The mean weight of male aerobics instructors in a certain city is equal to 175 lbs".

At the null hypothesis, we test if there is not enough evidence to verify if the claim is false, that is:

[tex]H_0: \mu = 175[/tex]

At the alternative hypothesis, we test if there is enough evidence to verify if the claim is false, that is:

[tex]H_1: \mu \neq 175[/tex]

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Here,

We know that,

[tex] \large \bf \: Distance= \sqrt{(x_2 - x_ 1) {}^{2} + (y_ 2 -y_1) {}^{2} } [/tex]

So ,

Putting the value of x and y in the given formula

We get,

[tex]\large\sf{ \: = \sqrt{ \{ \: - 1 - ( - 9) \} {}^{2} + (8 - 8) {}^{2} } \: }[/tex]

[tex]\large\sf{ = \sqrt{(8) {}^{2} + (0) {}^{2} } }[/tex]

[tex]\large\sf{ \: = \sqrt{64 + 0} }[/tex]

[tex]\large\sf{ = \sqrt{64} }[/tex]

[tex]\large\bf \blue { = 8 \: unit}[/tex]

Thus,

[tex] {\underline {\underline{ \rule{200pt}{8pt}}}}[/tex]

The value of GH is 6.42

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

GH is the hypotenuse and 3 is the adjascent to angle 65°

therefore;

tan65 = x/3

2.14 = x/3

x = 2.14 × 3

x = 6.42

therefore the value of GH is 6.42

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The value of the h while simplifying the given equation 2.46(h+9) - (-0. 2) = 2.66 as -8.

We need to determine the value h from the following linear equation. We can determine the value of h by using simple equation methods. To solve for h in the equation 2.46(h+9) - (-0.2) = 2.66, we can follow these steps:

2.66 = 2.46(h+9) - (-0. 2)

= 2.46(h+9) - (-0.2)

= 2.46h + 22.14 + 0.2

= 2.46h + 22.34

2.46h + 22.34 = 2.66

2.46h = 2.66 - 22.34,

2.46h = -19.68

h = -19.68/2.46

h = -8

Therefore, The value of the h is -8.

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If owners of a recreation area are filling a small pond with water.  The  total amount of water after 13 minutes is 1016 liters.

Let the total amount of water in the pond = W

Let the total number of minutes that water has been added = T

The equation relating W to T Is:

W = 600 + 32T

Where:

600=  initial amount of water in the pond

32T = additional water added over time

Now let find the  total amount of water in the pond after 13 minutes

Substitute T = 13 into the equation:

W = 600 + 32(13)

W = 600 + 416

W = 1016

Therefore the total amount of water is 1016 liters.

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We can conclude that cosθ = sin(90° - θ) for any right triangle with angle θ and its complementary angle (90° - θ).

To prove that cosθ = sin(90° - θ), we can use the properties of right triangles and their angles.
Consider a right triangle ABC, where angle A is θ, angle B is (90° - θ), and angle C is 90°.
According to the definition of trigonometric functions in a right triangle:
- cosθ = adjacent side (AB) / hypotenuse (AC)
- sin(90° - θ) = opposite side (AB) / hypotenuse (AC)
From the given definitions, we can see that both cosθ and sin(90° - θ) have the same ratio of side lengths, which is AB/AC.
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The given equation is true when a and b are integers and x is not equal to 0.

The statement "xᵃ + xᵇ = x⁽ᵃ⁺ᵇ⁾ " is always true when a=b.

In this case, the exponents of x on both sides of the equation are equal, and the equation simplifies to xᵃ + xᵃ = x²ᵃ , which holds true.

When a=b, the exponents are the same, and the equation is satisfied.

However, the statement is not always true for all values of a and b. If a and b are not equal, then the equation does not hold true in general.

The statement is also not true when a=0 and b=0, as both sides of the equation become 1, but the equation becomes 1 + 1 = 1, which is not true.

Therefore, the statement "xᵃ + xᵇ = x⁽ᵃ⁺ᵇ⁾ " is always true when a=b, but not true in general for all values of a and b.

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Answer:

The is is 1

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Net worth is a combination of everything you own.

This includes the amount of money you have, or have ever made, plus your house, vehicle, belongings, etc.

Answer:

Perimeter is 20.57 yards.

Step-by-step explanation:

Perimeter is the distance around the outside of a shape. This shape is a semicircle, that is, half of a circle.

We can calculate the circumference of the circle (that's the distance around the whole circle) and then cut it in half. Then add on the flat, straight side.

Circumference is:

C = pi•d

C = pi•8

C = 25.1327

This is the distance around the whole circle. For the curved part of our shape, we only need half of that.

25.1327/2

= 12.56637

Lastly, we add on the straight side, which was given as 8 yds.

12.56637 + 8

= 20.56637

Round to two decimal places.

20.57

The perimeter is 20.57yds.

The problem asks to convert a volume of 8000 [tex]cm^3[/tex] to [tex]m^3[/tex] which is 0.008 [tex]m^3[/tex].

Unit conversion is the process of converting a quantity expressed in one unit of measurement into another equivalent quantity expressed in a different unit of measurement.

To do this conversion, we need to use the fact that 1 m = 100 cm (or equivalently, 1 cm = 0.01 m) and that volume is a cubic measure.

So, first we need to convert the volume from cubic centimeters to cubic meters. To do this, we can divide the volume in [tex]cm^3[/tex] by the number of [tex]cm^3[/tex] in 1 [tex]m^3[/tex].

1 [tex]m^3[/tex] = (100 cm)^3 = 1,000,000 [tex]cm^3[/tex]

Therefore,

8000 [tex]cm^3[/tex] / 1,000,000 [tex]cm^3/m^3[/tex] = 0.008 [tex]m^3[/tex]

Thus, the volume of 8000 [tex]cm^3[/tex] is equal to 0.008 [tex]m^3[/tex].

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The number that belongs in the green box is 45.65

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

The triangle

If the number that belongs in the green box is x, then we have

6.78/sin(29) = 10/sin(x)

Take the inverse of both sides

sin(29)/6.78 = sin(x)/10

This gives

sin(x) = 10 * sin(29)/6.78

Evaluate

sin(x) = 0.7151

Take the arc sin of both sides

x = 45.65

Hence, the number that belongs in the green box is 45.65

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The distance from the town in SC to Washington DC is,

⇒ 32.6 units

We have to given that;

Washington DC is the midpoint of Maine and South Carolina. If a town in SC is located at (-2,-20) and a town in Maine is located at (18,42),

Since, We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, We get;

The coordinate for Washington is,

⇒ (18 - 2)/2, (- 20 + 42) / 2

⇒ (8, 11)

The distance from the town in SC to Washington DC is,

⇒ d = √ (8 - (- 2))² + (11 - (- 20))²

⇒ d = √10² + 31²

⇒ d = √100 + 961

⇒ d = √1061

⇒ d = 32.6 units

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Answer:

Step-by-step explanation:

You first do 190cm x 90cm then we divide each dimension by 50

190cm ÷ 50 = 3.8cm

90cm ÷ 50 = 1.8cm

So the scaled size is  3.8cm x 1.8cm

By converting the real measurements of the bed and room into a 1:50 scale, we can draw a floor plan and visualize the possibilities of where the bed can fit.

This question is about scale drawing and understanding measurements in everyday situations. Given the size of the bed (190cm x 90cm) and the scale of the plan (1:50), we first need to translate the actual measurements into the scale for the drawing.

A ratio of 1:50 means that 1cm on the drawing represents 50cm in real life. So, for the bed which is 190cm long and 90cm wide, we have to divide each value by 50. That gives us a bed representation of 3.8cm (190cm/50) by 1.8cm (90cm/50) on the drawing.

Then, we can use the same technique to draw a floor plan. With the room being 3m (300cm) long and 2.5m (250cm) wide, it translates to a drawing of 6cm (300cm/50) by 5cm (250cm/50). By comparing these dimensions, we can see different possibilities of where the bed can fit into the room on the floor plan.

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The Eric's time can be represented by the equation t = (d/60) - 2.

To create a second equation showing how long it would take Eric to travel the same distance as Noah, we can use the formula distance = speed x time. Let's call the distance that both Noah and Eric travel "d" (since we don't know the actual distance).

We know that Noah's speed is 135 mph and Eric's speed is 60 mph. We also know that Eric takes two hours longer to travel the same distance as Noah.

So, if we let "t" be the time it takes Noah to travel "d" distance, then Eric's time can be represented as "t + 2" hours. Putting all of this together, we can create the following equation: d = 135t (for Noah) and d = 60(t + 2) (for Eric).

From this second equation, we can solve for Eric's time by dividing both sides by 60, which gives us t + 2 = d/60.

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The percentage of the marbles that are red is 22%

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

Red = 500

Green = 750

White = 1000

Using the above as a guide, we have the following:

Percentage of red =Red/Total * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage of red =500/(500 + 750 + 1000) * 100%

Evaluate

Percentage of red = 22%

Hence, the percentage of red is 22%

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1. Point D is located in quadrant 2.

2. The coordinates of point A are (2, 3).

3. The coordinates of point C are both negative. It is located in quadrant

1. Point D is located in quadrant 2, which is the quadrant where the x-coordinates are negative and the y-coordinates are positive. This means that the x-coordinate of point D, which is -6, is negative and the y-coordinate, which is 2, is positive.

2. The coordinates of point A are (2, 3). This means that the x-coordinate of point A is 2, and the y-coordinate is 3. Point A is located in the first quadrant, which is the quadrant where both the x-coordinate and y-coordinate are positive.

3. The coordinates of point C are both negative. It is located in quadrant 3, which is the quadrant where the x-coordinates are negative and the y-coordinates are also negative. This means that the x-coordinate of point C, which is -0.5, is negative and the y-coordinate, which is -3, is also negative.

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Answer:

Step-by-step explanation:

To determine the time it takes for the same hose to fill the larger aquarium, we need to compare the volumes of the two aquariums and consider the rate at which the hose fills the smaller one.

The volume of a rectangular prism (such as an aquarium) is given by the formula: Volume = length × width × height.

Let's calculate the volume of the two aquariums:

For the first aquarium:

Volume = 9 inches × 13 inches × (height not given)

For the second (larger) aquarium:

Volume = 24 inches × 30 inches × 34 inches

Since the height of the first aquarium is not provided, we cannot directly compare the volumes. However, we can determine a proportion between the two based on the known measurements.

If the time it takes to fill the first aquarium is 2 minutes, we can establish a ratio:

(9 inches × 13 inches × height of the first aquarium) / (24 inches × 30 inches × 34 inches) = 2 minutes / x minutes

To find the value of x, the time it takes to fill the larger aquarium, we rearrange the equation:

x = (24 inches × 30 inches × 34 inches) / (9 inches × 13 inches × height of the first aquarium) * 2 minutes

Without knowing the height of the first aquarium, we cannot determine the exact time it takes to fill the larger aquarium.

The dollar value of the stock that Raquel wants to purchase is $1,833.33.

If the margin requirement is 55%, then the amount of cash wanted is 45% of the total value of the inventory.

Consequently, we will set up the following equation like this:

0.45x = 825

Wherein:

x is the dollar value of the stock Raquel wants to purchase.

To solve for x, we are able to divide both aspects of the equation by way of 0.45:

x = 825 ÷ 0.45

x = $1,833.33

Therefore, the dollar value of the stock that Raquel wants to purchase is $1,833.33.

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The probability the point will be in the region labeled A is 2/15 if  point is selected at random inside the given figure.

Given that a point is selected at random from inside the given figure.

We are to find the probability that the point will be in the region labeled B.

From the figure, we note that the regions A, B and D are rectangles and the region C is a square.

The areas of all the regions are calculated as follows:

Area of region A is 5×(3+4) =35 sq in

Area of region B is 3×4  = 12 in

Area of region C is 4² = 16 sq in

Area of region D is 3×(4+5)= 27 sq. in

Therefore, the probability that the randomly chosen point will lie in the region B is given by P

P = 12/35+12+16+27

=12/90

=2/15

Hence,  the probability the point will be in the region labeled A is 2/15

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