Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared plus 2 times x minus 3 end quantity and g(x) = x + 2, evaluate (g – f )(2).

The area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the Total area is 44 square units.

1. The rectangle, which has a length of 8 units and a width of 4 units.

2. The two triangles, which are identical and have a base of 4 units and a height of 3 units.

To find the area of the rectangle, we can use the formula:

Area = Length x Width

Area = 8 x 4 = 32 square units

To find the area of each triangle, we can use the formula:

Area = 1/2 x Base x Height

Area = 1/2 x 4 x 3 = 6 square units

So, the total area of both triangles is:

Total area = 6 + 6 = 12 square units

Now, to find the total area of the figure, we can add the areas of the rectangle and the two triangles:

Total area = Area of rectangle + Total area of triangles

Total area = 32 + 12 = 44 square units

Therefore, the area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the total area is 44 square units.

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Answer:

904.78 [tex]in^{3}[/tex]

Step-by-step explanation:

The volume formula for a sphere is the following:
[tex]v=\frac{4}{3} \pi r^{3}[/tex]
[tex]d = 2r[/tex]
Replace with values and the answer is 904.78

The regression line predict y will equal 531 when x equals 3

log(y) = 2.725

To undo the logarithm, we can use the exponential function:

y = 10^(2.725)

Using a calculator, we find:

y ≈ 530.8

We have to approximate this to 531

Rounding to the nearest whole number, the regression line predicts that y will equal 531 when x equals 3.

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Answer:

Step-by-step explanation:

yea the checks are not correct

Answer:

1,2

4,-1

5,-3

6,-5

Step-by-step explanation:

the question is unclear but if you put it in desmos this is what you get

The Probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.

The probability that the light is red is given by the ratio of the time the light is red to the total cycle time:

P(red) = 15 / (15 + 5 + 30) = 0.375

Using the binomial distribution, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light is:

P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5

where (8 choose 3) is the binomial coefficient, which represents the number of ways to choose 3 cars out of 8. Evaluating this expression gives:

P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5

        = (8! / (3! * 5!)) * (0.375)^3 * (0.625)^5

        = 56 * 0.052734375 * 0.1787109375

        ≈ 0.268

Therefore, the probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.

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Answer:

Step-by-step explanation:

f(x) = x + 3

g(x) = 2x + 1

g(g(-3)) = g(-5) = -9

f(g(x) = f(2x + 1) = 2x + 1 + 3 = 2x + 4

g(f(x) = g(x + 3) = 2(x + 3) + 1 = 2x + 7

The product of sin B and tan C is c/a.

The product of sin C and tan B is b/a.

Given is a right triangle, ABC, we need to find the product of sin B and tan C and the product of sin C and tan B,

So, we know,

Sine = Opposite ÷ Hypotenuse.

Cosine = Adjacent ÷ Hypotenuse.

Tangent = Opposite ÷ Adjacent.

Therefore,

Sin B = b/a

Tan C = c/b

Sin B x Tan C = b/a x c/b = c/a

And,

Sin C = c/a

Tan B = b/c

Sin C x Tan B = c/a x b/c = b/a

Hence the products are c/a and b/a.

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The complete is attached.

The value of x is 780 and 830 + 50 equals 880

The number of coaches is 17 and the total cost is £5850

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

830 + 50 gives the same answer as x + 100

This means that

830 + 50 = x + 100

So, we have

x = 830 + 50 - 100

Evaluate

x = 780

Also, we have

830 + 50 = 880

So, the value of x is 780 and 830 + 50 equals 880

Here, we have

People = 830

People per coach = 50

So, we have

Coaches = 830/50

Evaluate

Coaches = 16.6

Approximate

Coaches = 17

The total cost of hiring 13 coaches is

Cost = 450 * 13

Evaluate

Cost = 5850

Hence, the number of coaches is 17 and the total cost is £5850

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Answer: 20.4

Step-by-step explanation:

Answer:

it's is D

This is because equation 1 to 3 results in only a constant but D x will be 1

Answer: 4x - 10 = -2(-2x + 5)

Step-by-step explanation:

An equation has an infinitely many solutions when both sides are equal to each other.

-2(-2x+5) expands to become (-2*-2)*x + 5*(-2) = 4x - 10

Since the other side of the equation is also 4x - 10, both sides of the equation are identical and thus the equation has infinitely many solutions.

The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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A contradiction in the given clues and it is not possible to find a valid code with the given information.

The code to open the treasure chest can be determined using a few simple steps.
Firstly, we know that the last digit is half of 18, which is 9.

This means that the code ends with the number 9.
Next, we are given the information that the sum of the two middle digits is 10.

This tells us that the two middle digits must be 4 and 6, as they add up to 10.
Thirdly, we know that the third and fourth digits are the same.

Since we already know that the last digit is 9, this means that the third digit must also be 9.
Finally, we are told that the first digit is double the second digit.

Since we know that the second digit is 4, we can determine that the first digit must be 8.
Therefore, the code to open the treasure chest is 8469.

Mr Brainiac can now use this code to unlock the chest and discover the treasures inside.
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The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units

From the graph, the vertices of the land are

A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)

Calculate the distance between adjacent vertices

So, we have

AB = √[(0 - 25)² + (20 - 19)²] = 25.02

BC = √[(20 - 25)² + (2 - 19)²] = 17.72

DC = √[(20 - 5)² + (2 - 0)²] = 15.13

AD = √[(0 - 5)² + (20 - 0)²] = 20.62

The perimeter of the plot land is

P = 25.02 + 17.72 + 15.13 + 20.62

P = 78.49 units

This is calculated as

Area = Plot land - Building - Parking lot

Using the vertices, we have

Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]

This gives

Area = 295 -  45 - 40

So, we have

Area = 210

Hence, the area is 210 square units

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Answer:

10%

Step-by-step explanation:

P(reading paper 'given' that they are <40)

= P(reading paper AND < 40) / P(< 40)

= (4/80) / (40/80)

= 4/40

=1/10

=0.1

=10%

x=1/3

33x-1=10

add 1 on both sides

33x=11

divide 33 on both sides

and it should equal 1/3

The equation of the line is y = 2x - 8.

The equation of a line in slope-intercept form (y = mx + b) is determined by the slope (m) and the y-intercept (b).

Given that the point (3, -2) lies on the line and the slope is 2, we can substitute these values into the slope-intercept form to find the y-intercept.

Using the point-slope formula:

y - y1 = m(x - x1)

Substituting (3, -2) and m = 2:

y - (-2) = 2(x - 3)

Simplifying:

y + 2 = 2x - 6

Rearranging to slope-intercept form:

y = 2x - 8

The equation of the line containing the point (3, -2) with a slope of 2 in slope-intercept form is y = 2x - 8.

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Answer:

  C)  25°

Step-by-step explanation:

You want the base angles in an isosceles triangle with vertex angle 130°.

The base angles of an isosceles triangle are congruent. If each is represented by 'b', then the sum of angles in the triangle is ...

  2b +130° = 180°

  2b = 50° . . . . . . . . subtract 130°

  b = 25° . . . . . . . divide by 2

The base angles of the triangle are 25°, choice C.

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Answer:

To find the new balance, we'll start with the initial balance on May 20 and then perform the transactions in chronological order.

Step-by-step explanation:

Initial balance on May 20: $189.75

Deposit on May 22: +$112.45

To calculate the balance after the deposit, we add the deposit amount to the initial balance:

New balance after deposit = $189.75 + $112.45 = $302.20

Check written on May 29: -$75.68

To calculate the balance after writing the check, we subtract the check amount from the previous balance:

New balance after check = $302.20 - $75.68 = $226.52

ATM withdrawal on June 1: -$50.00

To calculate the final balance after the ATM withdrawal, we subtract the withdrawal amount from the previous balance:

Final balance after ATM withdrawal = $226.52 - $50.00 = $176.52

Therefore, the new balance after all the transactions is $176.52.

The probability that either event will occur is given as follows:

P(A or B) = 0.82 = 82%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of events in this problem is given as follows:

23 + 18 + 9 = 50.

The events are given as follows:

Hence the number of desired outcomes is given as follows:

23 + 18 = 41.

And the probability is of:

p = 41/50 = 0.82 = 82%.

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[tex]y^3 - 6y^2 = 0\\y^2(y-6)=0\\y^2=0 \vee y-6=0\\y=0 \vee y=6[/tex]

When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.

How to know what is formed from a line intersecting a cone?

The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.

This means the intersecting line forms a right angle with the base of the right circular cone.

Therefore, from this interaction is a pair of intersecting lines.

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Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

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

c=[tex]\sqrt{28^2+96^2}[/tex]

c=[tex]\sqrt{10,000}[/tex]

c=100

Therefore, the length of the hypotenuse is 100.

The lateral area of the pyramid is 512√3 in.

Area is the region bounded by plane shape.

To calculate the area of the pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these value into equation 1

Hence, the right option is D. 512√3 in.

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Step-by-step explanation:

Each ordered pair on the line represents the weight of an astronaut with the shuttle space suit, given in pounds, and the total weight of the shuttle space suit and life support system, also given in pounds.

Let x represent the weight of the astronaut without the shuttle suit, and let y represent the weight of the astronaut with the shuttle suit and life support system. Then the equation for the relationship shown in the graph is: y = x + 310.

No, this is not a proportional relationship because the slope of the line is not constant. In a proportional relationship, the ratio of y to x would always be the same, but in this case, the ratio changes depending on the value of x.

No, not all the points on the line make sense in the context of the problem situation. For example, the point (0, 310) would represent an astronaut with no weight without the shuttle suit, which is not physically possible. Also, the point (480, 790) would represent an astronaut with a weight of 480 pounds without the suit, which is also not physically possible. Therefore, we need to restrict the domain of the equation to make sense in the context of the problem situation.

To determine the weight of an astronaut without the shuttle suit, we need to solve the equation y = x + 310 for x, given that y = 480. Substituting y = 480 into the equation, we get: 480 = x + 310. Solving for x, we get: x = 170. Therefore, the weight of the astronaut without the shuttle suit is 170 pounds.

On July 20, the company recorded a journal entry debiting cash for $4,140, crediting treasury stock for $3,780, and crediting paid-in capital from treasury stock for $360.

To record the reissuance of treasury stock on July 20, the following journal entry should be made:

Date: July 20

Debit: Cash ($46 * 90) $4,140

Credit: Treasury Stock ($42 * 90) $3,780

Credit: Paid-In Capital from Treasury Stock $360

Explanation:

The debit to Cash represents the amount received from the reissuance of 90 shares at $46 per share, totaling $4,140.

The credit to Treasury Stock reduces the balance of the treasury stock account by the cost of the 90 shares, which is $42 per share, totaling $3,780.

The credit to Paid-In Capital from Treasury Stock accounts for the difference between the cost of the treasury stock and the amount received from its reissuance, which is $46 - $42 = $4 per share, totaling $360.

This journal entry properly reflects the increase in cash from the reissuance of the shares, reduces the treasury stock account balance, and recognizes the gain in paid-in capital resulting from the reissuance at a higher price than the repurchase cost.

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The length of the arcs are calculated to the nearest hundredth as:

12. 14.03 meters      13. 6.91 meters

The formula used to find the length of a an arc is: length of arc = ∅/360 * 2πr, where ∅ is the central angle measure and r is the radius of the circle.

Length of arc XW:

∅ = m<XZW = 180 - 113

∅ = 67 degrees

r = 24/2 = 12 meters

Plug in the values:

length of arc XW = 67/360 * 2 * π * 12 ≈ 14.03 meters

Length of arc XW:

∅ = m<YVU = 180 - 67 - 80

∅ = 33 degrees

r = 24/2 = 12 meters

Plug in the values:

length of arc YVU = 33/360 * 2 * π * 12 ≈ 6.91 meters

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Answer:

perimeter = 28 units. area = 45 square units.

Step-by-step explanation:

perimeter = (6 - -3) + (7 -2) + (6 - -3) + (7 - 2)

                = 9 + 5 + 9 +5

                 = 28 units.

area = (6 - -3) X (7 -2)

        = (6 + 3) X 5

         = 9 X 5

         = 45 square units

Check the picture below.

Answer:

148 in²

Step-by-step explanation:

The box is made up of two triangles and three rectangles.  The formula for the rectangles is length times width.  The formula for the triangles is one-half base times height.

RECTANGLES: (lxw)

7x2=14

12.5x2=25

12.5x2=25

TRIANGLES: (1/2bh)

1/2x12x7=42

1/2x12x7=42

Add together to get the sum of the surface area:

14+25+25+42+42=148 inches squared

Where the rules is  is y = |x|  the graph for y+x and y = -x will become the graph for y+x and y = x. Because x has to become an absolute (positive) value.

In discrete mathematics, and more particularly in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way.

Distances between locations are often measured using the absolute value function. The absolute value function can also be used to address applied issues such as ranges of feasible values.

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