A rectangular paperboard measuring 20in long and 12in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.)

Answer:

f(g(x))=3x+8

g(f(x))=3x-2

Step-by-step explanation:

f(x)=3x-7, g(x)=x+5

f(g(x))=f(x+5)

=3(x+5)-7

=3x+15-7

=3x+8

g(f(x))=g(3x-7)

=3x-7+5

=3x-2

The standard form of the equation is (x + 3)² + (y - 4)² = 2.

A linear equation with two variables has the conventional form Ax + By = C, where A, B, and C are constants and where A and B are not equal to zero. The general form of a linear equation is another name for this format. When the line is plotted on the Cartesian plane, the constant term C and coefficient A in this form indicate the line's y-intercept and slope, respectively. When solving systems of linear equations and graphing linear equations, the standard form is helpful.

Complete the squares for the given equation: x² + y²+ 6x - 8y + 18=0.

Starting with the x terms, we add (b/2)² to both sides of the equation:

x² + 6x + 9 + y² - 8y + 18 = 9

For y terms by adding (c/2)² to both sides of the equation:

x² + 6x + 9 + y² - 8y + 16 = -2

The standard form is:

(x + 3)² + (y - 4)² = 2

Hence, the standard form of the equation is (x + 3)² + (y - 4)² = 2.

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Answer:

-12

Step-by-step explanation:

g(x)=3x,h(x)= x²-4

(g•h)(0)=g(h(0))

=g(0²-4)

=g(-4)

=3×(-4)

=-12

Option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.

A statistical metric called a correlation coefficient shows the degree and direction of the association between two variables. Its value falls between -1 and 1, with -1 being a perfect negative correlation, 0 denoting no connection, and 1 denoting a perfect positive correlation. If there is a positive correlation, it implies that as one variable rises, the other variable likewise tends to rise, and if there is a negative correlation, it means that as one variable rises, the other variable tends to fall. The letter r is frequently used to represent the correlation coefficient.

Comparing the scatter plot with the given equations we observe that the slope of option b and d are very large as compared to the given distribution.

Observing from the given graph, the y-intercept of the best fit line will be nearly less than 20.

Thus, option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.

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There is a 0.25 percent chance of choosing a sedimentary rock from John's collection based on laws of probability.

We must apply the following formula to determine the likelihood of choosing a sedimentary rock from John's collection:

Probability is calculated as the ratio of favourable outcomes to all other possible outcomes.

The best result in this situation is choosing a sedimentary rock, and the total number of outcomes is equal to the entire number of rocks in John's collection, which is:

Igneous rocks, sedimentary rocks, and metamorphic rocks together make up the total quantity of rocks.

a total of 15 + 9 + 12 stone.

There are 36 rocks in all.

As a result, the likelihood of choosing a sedimentary rock is:

Number of sedimentary rocks divided by the total number of rocks is the likelihood of choosing a sedimentary rock.

picking a sedimentary rock has a 9/36 probability.

25% or 0.25 of the time will a sedimentary rock be chosen.

So, there is a 0.25 percent, or 25%, chance that you will choose a sedimentary rock from John's collection. This indicates that 25% of all the rocks in John's collection are sedimentary rocks, and if one were to choose a rock at random from his collection, there is a one in four chance that they would be sedimentary rocks.

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Answer:

1.6

Step-by-step explanation:

it is this one trust me

Answer:

Step-by-step explanation:

Diameter = 7 cm, Radius = 1/2 diameter = 3,5 cm

Step-by-step explanation:

Radius is the line or length from the center of the circle to the side, and is half the diameter. Diameter is a line from one side of the circle to the other, passing through the center point, and is 2 times the radius. With this information we can see the diameter is 7cm and the radius would be half of that, with 3.5cm being the radius.

Answer:

x = 0 , x = 2

Step-by-step explanation:

y = x² - 2x + 3 ← substitute y = 3

3 = x² - 2x + 3 ( subtract 3 from both sides )

0 = x² - 2x ←  factor out x from each term on the right side

0 = x(x - 2)

equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

The measure of minor arc UT is equal to the measure of angle UWT, which is half the central angle ZWT. The measure of sector UST is equal to the measure of central angle ZST, which is 2*34 - 112 = -44 degrees. The measure of major arc UT is 360 - 17 = 343 degrees and the measure of segment UST is 343 - 316 = 27 degrees.

A circle is a geometric shape that consists of all the points in a plane that are equidistant from a given point called the center. It is a perfectly round shape and has a constant diameter, which is the distance between any two points on the circle passing through the center.

Given information:

Circle Z

VZ = ZW (equal chords)

SV = 21

m = 112

To find:

UT

WT

ST

Measure of minor arc UT

Measure of sector UST

Since VZ = ZW, we can conclude that SZ is the perpendicular bisector of VW. Therefore, SV = SW = 21.

a) Using the theorem of the perpendicular bisector, we can say that UT = WT = (1/2)VW. Since VZ = ZW, we have VW = VZ + ZW = 2VZ. Therefore, UT = WT = (1/2)2VZ = VZ = 2.

b) Similarly, WT = VZ = 2.

c) Since SV = SW, we can say that ST = SW - TW = 21 - WT = 21 - 2 = 19.

d) The measure of minor arc UT is equal to the measure of angle UWT, which is half the measure of the central angle ZWT. Since VZ = ZW, the central angle ZVW is an isosceles triangle, and the measure of angle ZVW is (180 - 112)/2 = 34 degrees. Therefore, the measure of minor arc UT is 1/2 * 34 = 17 degrees.

e) The measure of sector UST is equal to the measure of central angle ZST. Since VZ = ZW, the central angle ZVW is an isosceles triangle, and the measure of angle ZVW is (180 - 112)/2 = 34 degrees. Therefore, the measure of central angle ZST is 2*34 - 112 = -44 degrees (measured counterclockwise from ZV). However, since angles are usually measured in the range 0 to 360 degrees, we can add 360 to -44 to get 316 degrees. Therefore, the measure of sector UST is 316 degrees.

f) We have already found the measures of minor arc UT and sector UST. Therefore, we can say that the measure of major arc UT is 360 - 17 = 343 degrees, and the measure of segment UST is 343 - 316 = 27 degrees.

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Answer:

h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.

Step-by-step explanation:

Hence, it will take about 43.28 minutes for the population to reach 12,000 and  there are approximately 7742.85 people in the world after 105 minutes.

A exponential is an exponents or power in mathematics that must be increased from a given denominator to get a certain value. In other words, just as division is the opposite of multiplication,

the logarithm is the greater operating of exponentiation. The base 10-logarithm (written as log) or the beta coefficient (written as ln), which has a baseline of e, the mathematical constant roughly equal to 2.71828, are the two most widely used logarithms.

In many mathematical fields in science, engineering, and technology, logarithms are employed to facilitate calculations and express extremely big or extremely small values.

given

a) The culture's initial size is:

P(0) = [tex]500/e^{15415*15}[/tex]

≈ 98.90

b) We can easily enter t = 105 into the exponential growth model to determine the population after 105 minutes:

P(105)=98.9*[tex]e^{15415*105}[/tex]

≈ 7742.85

Hence, there are approximately 7742.85 people in the world after 105 minutes.

d) To determine the population's peak, we set P(t) = 12000 and solve for t as follows:

1200=98.9*[tex]e^{0.15415t(0.15415t)}[/tex]

By taking the natural logarithm and dividing both sides by 98.90, we arrive at:

ln(12000/98.90) = 0.15415t

To solve for t, we obtain:

t ≈ 43.28

Hence, it will take about 43.28 minutes for the population to reach 12,000 and  there are approximately 7742.85 people in the world after 105 minutes.

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y(y + 5) = 750, y² – 5y = 750, y(y – 5) + 750 = 0 are the equations that can be used to solve for y, the length of the room.

It is used to measure the size of two-dimensional shapes, such as circles, rectangles, and triangles, and is also used to measure the surface area of three-dimensional shapes, such as cubes, pyramids, and cylinders.

Option 1: y(y + 5) = 750

This equation can be used to solve for y, the length of the room. The area of a rectangular room is equal to the product of its length and width. Therefore, the equation for the area of the room can be expressed as Area = Length x Width.

Substituting y for Length and y+5 for Width, yields Area = y(y+5). Rearranging this equation to solve for y, yields y(y+5) = 750.

Option 2: y² – 5y = 750

This equation can be used to solve for y, the length of the room. This equation can be derived by substituting y for Length and y+5 for Width in the equation Area = Length x Width.

Rearranging this equation yields Area = y² – 5y. Substituting this equation with the given area of 750, yields y² – 5y = 750.

Option 3: y(y – 5) + 750 = 0

This equation can also be used to solve for y, the length of the room. This equation can be derived by substituting y for Length and y+5 for Width in the equation Area = Length x Width.

Rearranging this equation yields Area = y(y – 5).

To find the length of the room, the given area of 750 must be added to both sides of the equation. This yields y(y – 5) + 750 = 0.

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The rate of inflation used to make this calculation is 4%

The equation

y = 100(0.96)^x

represents the purchasing power of $100 after x years of inflation. In this equation, 0.96 is the inflation rate.

This means that the purchasing power of $100 decreases by 4% each year due to inflation.

To understand this better, let's take an example. Suppose you have $100 today and the inflation rate is 4%. This means that the purchasing power of $100 will be reduced by 4% after one year. So, after one year, the value of $100 will be $96. If the inflation rate remains the same, after two years, the value of

$100 will be $92.16 ($96 * 0.96)  and so on.

It is important to note that inflation rates can vary over time and across countries, and can have a significant impact on the economy and the purchasing power of consumers. Understanding inflation and its effects is crucial for making informed financial decisions.

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Using the area formula for rectangle, the largest area that can be enclosed by rope and wall = 450m².

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are many rectangular objects all around us. The two characteristics that distinguish each rectangle are its length and its breadth. A rectangle's longer and shorter sides are its width and length, respectively.

Here in the question,

The rope used here is 60m.

Now 60m of rope is forming 3 sides of the rectangle.

The adjacent sides cannot be equal to each other as it is a rectangle.

So, the sides of the rectangle can be given as such so that area will be maximum:

length = 30m

width = 15m

So, the rope includes one length and 2 widths of the rectangle.

As such (60m = 30m + 15m + 15m).

Now, area of the rectangle =

l × w

= 30 × 5

= 450m²

Therefore, the largest area that can be enclosed by rope and wall = 450m².

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Answer:

x = 29

Step-by-step explanation:

The whole circle is 360°.

Theorem regarding angles inside a circle says that the angle is one half of the arc it encompasses. So m∠S = 0.5 * arc PQR. Also m∠Q = 0.5 * arc PSR.

Think about this, arc PQS + arc RQS = 360°. We have a formula for each of these arc measurements in terms of x.

The arc that corresponds to ∠R is some part of the circle, and the arc that corresponds to ∠P is the other part of the circle.

(5x + 20) + (7x - 8) = 360

12x + 12 = 360

12x = 348

x = 29

Blank #1: 6
Blank #2: 2

The surface area of the rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft is 1376 square feet.

What is surface area?

The area is the space occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

To find the surface area of a rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft, we need to calculate the area of each face and then add them together.

First, let's calculate the area of the top and bottom faces, which are both rectangles with dimensions of 12 ft by 20 ft:

Area of top and bottom faces = 2 x (12 ft x 20 ft) = 480 square feet

Next, let's calculate the area of the front and back faces, which are both rectangles with dimensions of 12 ft by 14 ft:

Area of front and back faces = 2 x (12 ft x 14 ft) = 336 square feet

Finally, let's calculate the area of the left and right faces, which are both rectangles with dimensions of 14 ft by 20 ft:

Area of left and right faces = 2 x (14 ft x 20 ft) = 560 square feet

To find the total surface area, we add up the area of all six faces:

Total surface area = Area of top and bottom faces + Area of front and back faces + Area of left and right faces

Total surface area = 480 sq ft + 336 sq ft + 560 sq ft = 1376 sq ft

Therefore, the surface area of the rectangular prism with dimensions of 12 ft, 14 ft, and 20 ft is 1376 square feet.

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What is the percentage of values in a normal distribution between 16 and 21 with a mean of 16 and a standard deviation of 5, according to the 68-95-99.7 rule is approximately 68%.

How to calculate the percentage of values in a normal distribution?

According to the 68-95-99.7 rule, approximately 68% of the values in a normal distribution are within one standard deviation of the mean, approximately 95% are within two standard deviations of the mean, and approximately 99.7% are within three standard deviations of the mean.

In this case, we want to find the percentage of values in the distribution between 16 and 21.

The range from 16 to 21 is one standard deviation above the mean, since the mean is 16 and the standard deviation is 5. Therefore, approximately 68% of the values in the distribution will fall between 16 and 21.

So, the answer is approximately 68%.

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Since the dividend per share is computed as Quarterly Dividend Payment / Shares, $1.52 is the yearly dividend for each share of Merck.

One of the four crucial steps in the division process is the dividend. It is necessary to divide the entire into several equal sections. For instance, if the result of the division of 10 by 2 is 5, then 10 is the dividend, which is split into two equal pieces, and 2 is the divisor. The result of the division is 5, the quotient, and the remainder is 0.

Given: The following steps can be taken in order to obtain the dividend per share for the quarterly payment:

Dividend per share is determined using the formula Quarter Dividend Payment / Shares.

The dividend equals $0.38 per share when $1,140 is divided by 3,000 shares.

To calculate the annual dividend per share, multiply the dividend paid every three months per share times the number of quarters in a year:

The annual dividend per share is equal to the quarter dividend per company multiplied by the total number of quarters in a year.

The annual dividend per share is calculated as $0.38 multiplied by four quarters, or $1.52 per share.

Since the calculation for the dividend per share is Periodic Dividend Payment / Shares, the annual dividend for each share of Merck is $1.52.

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The measures of the angles are:

m ∠GAL = 90°

m ∠LAO = 71°

m ∠CAO = 109°

m ∠KAC = 71°

From the question, we are to determine the measure of the angles

m ∠GAL = 90° (Right angle)

m ∠LAO

m ∠LAO + m ∠GAL + 19° = 180° (Sum of angles on a straight line)

m ∠LAO + 90° + 19° = 180°

m ∠LAO = 180° - 90° - 19°

m ∠LAO = 90° - 19°

m ∠LAO = 71°

m ∠CAO

m ∠CAO = m ∠KAL (Vertically opposite angles)

m ∠KAL = m ∠GAL + 19°

m ∠KAL = 90° + 19°

m ∠KAL = 109°

Therefore,

m ∠CAO = 109°

m ∠KAC = m ∠LAO (Vertically opposite angles)

m ∠LAO = 71°

Therefore,

m ∠KAC = 71°

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Answer:

the answer is x=6

Step-by-step explanation:

Answer: 250

Step-by-step explanation: because i got it right

we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads.

What is meter?

A meter is a unit of length in the International System of Units (SI). It is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. The symbol for meter is "m".

To determine which option is less expensive, we need to compare the cost of laying pipes along the rural roads to the cost of laying pipes through the field.

Let's assume that we need to lay a water pipe that is 100 meters long. If we choose to lay the pipe along the rural roads, the cost would be:

Cost = length of pipe x cost per meter = 100 x $3.00 = $300.00

If we choose to lay the pipe through the field, the cost would be:

Cost = length of pipe x cost per meter = 100 x $4.50 = $450.00

Therefore, laying the pipe along the rural roads would be less expensive in this case, with a cost of $300.00 compared to $450.00 for laying the pipe through the field.

In general, we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads. Conversely, if the cost per meter of laying pipes through the field is less than the cost per meter of laying pipes along the rural roads, then it would be less expensive to lay the pipes through the field.

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Full question:

It costs $3.00 per meter for the water pipes to go along the rural roads and $4.50 per meter for the water pipes to go through the field. Which option is less expensive? Explain how you found your answer.

Answer:

Try restarting your computer or using a different web browser

Step-by-step explanation:

the company can pack 224 basketballs into each truck.

To calculate the number of basketballs that can be packed into the truck

Number of basketballs = Volume of truck / Volume of each basketball package

first calculate the volume of the truck

The volume of the truck is:

Volume = Length x Width x Height

Volume = 10.5 ft x 8 ft x 9 ft

Volume = 756 cubic feet

The volume of each basketball package  is:

Volume = Side x Side x Side

Volume = 1.5 ft x 1.5 ft x 1.5 ft

Volume = 3.375 cubic feet

Now, we can calculate the number of basketballs :

Number of basketballs = Volume of truck / Volume of each basketball package

Number of basketballs = 756 cubic feet / 3.375 cubic feet

Number of basketballs = 224

Therefore, the company can pack 224 basketballs into each truck.

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The statement and reason to complete the proof that TU² = TV · TW include the following:

Statement                                  Reason_____

TU² = TV · TW                        cross product.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to the given triangles after the definition of similarity step, we would cross-multiply as follows:

TU/TW = TV/TU                  definition of similarity

TU(TU) = TV(TW)                    cross product.

TU² = TV · TW                        cross product.

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The blend of minimum cost with an octane rating of at least 90 is 11.11% type A gasoline and 55.56% type B gasoline, with a cost per liter of $0.6917.

What is the blend of minimum cost with an octane rating of at least 90?

Let x be the fraction of type A gasoline and y be the fraction of type B gasoline in the blend.

Since we want the blend to have an octane rating of at least 90, we can set up the following equation:

80x + 92y ≥ 90(x + y)

Simplifying this equation,

10x ≥ 2y

y ≤ 5x

We also want to minimize the cost of the blend, which can be expressed as 0.83x + 0.98y

Now we can use the inequalities we've established to find the minimum cost.

We know that y ≤ 5x

So we can substitute y = 5x into the cost equation 0.83x + 0.98(5x)

Simplifying and we get,

5.85x

This is the cost per liter of the blend, so we want to minimize this expression. To do so, we can use calculus and take the derivative with respect to x,

d/dx (5.85x) = 5.85

Setting this equal to zero to find the minimum value of the expression, we get:

5.85 = 0

This is not possible, so we know that the minimum value occurs at the boundary of the feasible region. That is, either x = 0 or y = 5x.

If x = 0, then the cost per liter is simply 0.98y, which we want to minimize subject to the constraint that 92y ≥ 90y, or y ≥ 45. We also have the constraint that y ≤ 1 (since we can't have more than 100% type B gasoline in the blend). So the minimum cost occurs when y = 1, and the cost per liter is 0.98.

If y = 5x, then the cost per liter is 0.83x + 4.9x = 5.73x. We want to minimize this subject to the constraints that 80x + 460x ≥ 90(1 + 4x), or x ≥ 0.0278, and that x ≤ 1. We can also use the inequality y ≤ 1 to get,

5x ≤ 1

x ≤ 0.2

So the feasible range for x is 0.0278 ≤ x ≤ 0.2. We can now calculate the cost of the blend for each value of x in this range and choose the minimum. This is a straightforward calculation, and we find that the minimum cost occurs when x = 0.1111 and y = 0.5556, and the cost per liter is $0.6917.

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The value of the car is $30675.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: A new car is purchased for $33, 000 and over time its value depreciates by one-half every 4 years.

We have to find the value of the car to be $9, 300.

Then the value of the car is given by the linear equation. Then the line is passing through (0, $33,000) and (4, $9,300). Then we have

Let y be the value of the car and x be the number of years. Then we have

y - 33000 = (-9300/4)(x-0)

y + 2325x = 33000

Then the value of the car of a year after it was purchased, to the nearest hundred dollars will be

y + 2325(1) = 33000

y = 33000 - 2325

y = 30675

Hence, the value of the car is $30675.

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Answer:

We can use the definition of tangent to find the value of \tan\theta. Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle.

To find the value of \tan\theta, we need to first find the values of the adjacent and opposite sides of the triangle. We know that the terminal side of angle \theta passes through the point (-8,9) in the Cartesian plane. This means that the coordinates of the endpoint of the terminal side are (-8,9).

We can now draw a right triangle with the hypotenuse as the terminal side of angle \theta, and the adjacent and opposite sides as the x and y coordinates of the endpoint of the terminal side. We can use the Pythagorean theorem to find the length of the hypotenuse.

The length of the adjacent side is -8 (since it is to the left of the origin) and the length of the opposite side is 9 (since it is above the origin). Therefore, we have:

adjacent = -8

opposite = 9

hypotenuse = \sqrt{(-8)^2 + 9^2} = \sqrt{64 + 81} = \sqrt{145}

Now we can use the definition of tangent to find the value of \tan\theta:

\tan\theta = \frac{opposite}{adjacent} = \frac{9}{-8} = -\frac{9}{8}

Therefore, the exact value of \tan\theta is -\frac{9}{8} in simplest radical form.