Simplify (3x+4)/(x+2)+(x^2+2x)/(2x+4).

Answer:

$2,600

Step-by-step explanation:

To find the cost of the concrete foundation of a building in the shape of a rectangular prism, multiply its volume (in cubic yards) by the cost per cubic yard.

The volume of a rectangular prism is the product of its width, length and height.

[tex]\boxed{V=w \cdot l \cdot h}[/tex]

Given values:

Therefore, the volume of the concrete foundation is:

[tex]\begin{aligned}V&=13 \cdot 20 \cdot 2\\&=260 \cdot 2\\&=520\; \sf yd^3\end{aligned}[/tex]

Given the concrete costs $5 per cubic yard, multiply the volume by the cost to calculate the total cost of the concrete for the foundation is:

[tex]\begin{aligned}\textsf{Total cost}&=\sf Volume \cdot cost\\&=\sf 520 \; yd^3 \cdot \$5/yd^3\\&=\sf 520 \cdot \$5\\&= \sf \$2600\end{aligned}[/tex]

Therefore, the total cost of the concrete for the foundation is $2,600.

The value of k must be c) 3, as it satisfies the requirement for the side length of the paving stone in feet, resulting in a meaningful relationship between the area of the patio and the number of paving stones.

To find the value of k, we need to consider the relationship between the area y of the patio and the number of paving stones x used to make the patio.

Since the top surface of each paving stone is a square with side length k feet, the area of each paving stone is [tex]k^2[/tex] square feet.

Now, let's consider the relationship between the area of the patio and the number of paving stones. We know that there will be no gaps between the paving stones, and they will not overlap. This implies that the area of the patio will be equal to the sum of the areas of all the paving stones used.

Let's assume that each paving stone covers an equal area of the patio. In this case, the area y of the patio will be directly proportional to the number of paving stones x used, and the constant of proportionality is the area of each paving stone, which is [tex]k^2[/tex].

Therefore, the relationship between y and x can be expressed as [tex]y = k^2x.[/tex]

From this relationship, we can see that the value of k will depend on the relationship between the units used for area (square feet) and the number of paving stones (unitless).

Since we want the side length k to be in feet, the value of k can be determined by considering the options provided: a) 1, b) 2, c) 3, d) 4.

We can eliminate options a) 1, b) 2, and d) 4 since these values would not result in a meaningful relationship between the area of the patio and the number of paving stones.

Therefore, the value of k must be c) 3, as it satisfies the requirement for the side length of the paving stone in feet, resulting in a meaningful relationship between the area of the patio and the number of paving stones.

To learn more about patio from the given link

https://brainly.com/question/31567633

#SPJ4

Answer:

Step-by-step explanation:

The number of trials is typically represented by the letter "n" in statistics. This refers to the number of independent and identical observations that are taken during an experiment or study. The population proportion, on the other hand, is often represented by the letter "p".

This refers to the proportion or percentage of individuals in a population that exhibit a certain characteristic or behavior. For example, if we were studying the proportion of people who prefer chocolate ice cream, "p" would represent the percentage of people in the population who prefer chocolate ice cream.

It's important to note that the number of trials and the population proportion are both key factors in statistical analysis, as they can help researchers draw conclusions about the population as a whole based on a smaller sample size.

To know more about Trials visit :

https://brainly.com/question/12255499

#SPJ11

The surface area of the shape is 565.2 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of the shape = surface area of big cone - surface area of small phone

surface area of big cone = πr(r+l)

Slant height of the small cone = 4/8 = x/11+x

4(11+x) = 8x

44+4x = 8x

44 = 4x

x = 11

The slant height of the big cone = 11+11 = 22cm

where r is the radius and l is the slant height.

= 3.14 × 8 ( 8 +22)

25.12 × 30

= 753.6

SA for small cone = 3.14× 4( 4+11)

= 12.56 × 15

= 188.4

SA for the shape = 753.6- 188.4

= 565.2 cm²

learn more about surface area from

https://brainly.com/question/16519513

#SPJ1

Answer:

x-intercept coordinates:  (9, 0)

y-intercept coordinates:  (0, 21)

Step-by-step explanation:

Put the equation in slope-intercept form, y = mx + b

3y = -7x + 63     divide both sides by 3

y = -7/3x + 21

y-intercept = b = 21

y-intercept coordinates:  (0, 21)

Find x intercept by setting y = 0 and solving for x:

0 = -7/3x + 21

7/3x = 21

x = 21(3/7) = 9

x-intercept coordinates:  (9, 0)

The answer is closest to 0.196. This means that if we repeat the experiment many times, we would expect to draw the blue marble twice in approximately 19.6% of the trials.

We can solve this problem using the hypergeometric probability distribution. The hypergeometric distribution is used when we have a finite population and we want to calculate the probability of drawing a certain number of objects of a specific type without replacement.

In this case, the population consists of 8 marbles, one of which is blue. We want to calculate the probability of drawing the blue marble twice when we draw 5 marbles without replacement. The number of ways to choose 5 marbles out of 8 is given by the binomial coefficient:

C(8,5) = 56

The number of ways to choose the blue marble twice and the other three marbles from the remaining 7 is:

C(1,2) * C(7,3) = 35

Therefore, the probability of drawing the blue marble twice is:

P = 35/56 = 0.625.

The closest answer choice to this probability is 0.196. Therefore, the answer is closest to 0.196. This means that if we repeat the experiment many times, we would expect to draw the blue marble twice in approximately 19.6% of the trials.

Learn more about Hypergeometric Probability Distribution:

https://brainly.com/question/15245410

#SPJ1

To make 28 cups of punch using a recipe that calls for 2 cups of ginger ale for every 5 cups of pineapple juice, Jaylee will need 11.2 cups of ginger ale.

To determine this, we need to use a proportion to scale the recipe up to 28 cups of punch. If the recipe calls for 2 cups of ginger ale for every 5 cups of pineapple juice, then the ratio of ginger ale to pineapple juice is 2:5. We can set up a proportion with this ratio to solve for the amount of ginger ale needed to make 28 cups of punch:

2/5 = x/28

Solving for x, we get:

x = (2/5) * 28 = 11.2

Therefore, Jaylee will need 11.2 cups of ginger ale to make 28 cups of punch using this recipe.

To learn more about proportion click here, brainly.com/question/31548894

#SPJ11

The value of segment x is determined as 16.

The value of segment x is calculated by applying intersecting chord theorem as follows;

The intersecting chord theorem, also known as the power of a point theorem, states that;

If two chords of a circle intersect inside the circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

The value of segment x is calculated as follows;

(x) (15) = (10) (24)

15x = 240

x = 240/15

x = 16

Learn more about intersecting chords here: https://brainly.com/question/13950364

#SPJ1

The Area of the figure below is composed of a rectangle and semicircles that will be 56.1 unit sq.

The semicircles can be composed into a circle with a radius 3,

The area of a circle is πr² where r is the radius.

πr²= 3 x 3 /2 π

A ≈ = 99/7

A = 14.1

The area of the rectangle = Length x width

= 7 x 6

= 42

Total area of a figure = 14.1 + 42 = 56.1

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

The correct answer is (B) 14 inches.

To determine the rise of the ramp, we can use the trigonometric relationship between the angle and the rise. The rise of the ramp is given by the formula:

Rise = Run × tan(angle)

In this case, the angle is given as 4.5°, and the run is given as 180 inches. Substituting these values into the formula, we can calculate the rise:

Rise = 180 × tan(4.5°)

Using a calculator, we find that the rise is approximately 14.017 inches.

Rounded to the nearest inch, the rise of the ramp is 14 inches.

The correct answer is (B) 14 inches.

For more questions on trigonometry, visit:

https://brainly.com/question/24349828

#SPJ11

Answer:

Step-by-step explanation:

First we will find out total amount donated by both the governments that is:

67,900,000,000+200=67,900,000,200

Then we will subtract all the expenses:

10.8+.67+12.8=24.27

Amount left unused:

67,900,000,200-24,270,000= 67,875,729,200

The Simplest form of the square root of 1,764 is 42. This means that the square root cannot be simplified any further, since 42 is already an integer and cannot be expressed as a fraction or a decimal.

The simplest form of the square root of 1,764 is 42.

To understand why, it's helpful to know what a square root is. A square root is a mathematical operation that finds the number which, when multiplied by itself, gives a certain number. For example, the square root of 25 is 5, because 5 multiplied by itself equals 25.

In the case of the square root of 1,764, we want to find the number that, when multiplied by itself, equals 1,764. To do this, we can use a calculator or do it manually by trial and error. One way to do it manually is to start with a number and square it until we get 1,764.

For example, we could start with 10 and square it to get 100. Then we could try 20, which gives us 400. Continuing in this way, we eventually find that 42 multiplied by itself equals 1,764.

So, the simplest form of the square root of 1,764 is 42. This means that the square root cannot be simplified any further, since 42 is already an integer and cannot be expressed as a fraction or a decimal.

To know more about Simplest form.

https://brainly.com/question/344788

#SPJ11

HELLO

8x² - 2x = 1

8x² - 2x - 1 = 0

x = (-b±√(b² - 4ac)) / 2a

= (-(-2)±√((-2)² - 4*8*(-1))) / (2*8)

= (2±6)/16

x₁ = (2+6)/16 = 1/2

x₂ = (2-6)/16 = -1/4

The expression that best models the population of the herd is:

y = (34/5)x - 558, where y is the population of the herd, and x is the time in years since 2010.

To model the population of the bison herd as a linear function of time, we can use the slope-intercept form of a linear equation, which is y = mx + b, where y is the population of the herd, x is the time in years since 2010, m is the slope of the line, and b is the y-intercept of the line.

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) is the point (2010, 122), and (x2, y2) is the point (2015, 156).

m = (156 - 122) / (2015 - 2010) = 34 / 5

So the slope of the line is 34/5.

To find the y-intercept of the line, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the point (2010, 122), and m is the slope we just found.

y - 122 = (34/5)(x - 2010)

y - 122 = (34/5)x - 13668

y = (34/5)x - 13546

To learn more about the slope;

brainly.com/question/3605446

#SPJ1

Answer:

5x +9+2x+6+4x

=5x+2x+4x+9+6

=11x+15

Answer C

Answer:

Rearrange your equation

5x + 2x + 4x + 9+6

Add the like term of the equation

( 5x + 2x + 4x ) + (9+6)

11x + 15

The dimensions of the garden that minimize the cost are approximately 2.5 feet by 64.8 feet.

To find the dimensions of the garden that minimize the cost, we can use optimization techniques. Let's denote the length of the garden as L and the width as W.

The cost of the brick wall is $60 per foot, and since only one side is enclosed by the brick wall, the cost for that side is 60L. The cost of the metal fence is $40 per foot, and since three sides are enclosed by the metal fence, the cost for those sides is 40(2L + W).

The total cost C is the sum of the costs for the brick wall and the metal fence:

C = 60L + 40(2L + W)

Given that the area of the garden is 162 square feet, we have L * W = 162.

To minimize the cost, we can take the derivative of the cost function with respect to L and set it equal to zero:

dC/dL = 60 + 80 = 0

Solving for L, we find L = 2.5 feet.

Substituting L = 2.5 into the area equation, we get W = 162 / 2.5 = 64.8 feet.

Know more about derivative here:

https://brainly.com/question/29144258

#SPJ11

To determine how many cans of paint Mrs. Holland needs to paint her garage wall, we need to find the area of the wall. The wall measures 6 2/3 by 3 1/7, which can be converted to an improper fraction to make calculations easier.

6 2/3 = (6x3 + 2)/3 = 20/3

3 1/7 = (3x7 + 1)/7 = 22/7

So the wall measures 20/3 meters by 22/7 meters. To find the area, we can multiply these two values:

(20/3) x (22/7) = 440/21 square meters

Each can of paint covers 5 square meters, so we need to divide the area of the wall by 5 to determine how many cans of paint we need:

(440/21) ÷ 5 ≈ 4.19 cans

Since we can't buy a fraction of a can of paint, we need to round up to 5 cans.

So, it will cost Mrs. Holland 5 cans x $7.50 per can = $37.50 to paint her garage wall.

Learn more about fraction  here: brainly.com/question/12770542

#SPJ11

Once you have the dimensions for each part, let me know, and I can assist you with the volume calculations and rounding to the nearest whole cubic meter. I can guide you through the process of calculating the volume of each part of the sculpture.

To calculate the volume of each part, we need to know the dimensions or specific shape of each part. If you provide the dimensions or shape information, I can help you calculate the volumes.

In general, to calculate the volume of a three-dimensional shape like a rectangular prism or cylinder, you multiply the length, width, and height (or base area and height) of the shape. Make sure to use consistent units of measurement (such as meters) for accurate results.

If you can provide the specific shapes and dimensions of the three parts of the sculpture, I can assist you in calculating their volumes. Once we have the dimensions, we can use the appropriate volume formulas and round the results to the nearest whole cubic meter, as instructed.

For such more questions on Dimensions:

https://brainly.com/question/28464

#SPJ11

Note the full question is Part B

The artist will use concrete to create the form of the sculpture. How much concrete will the artist need to make up each of the three parts that make up the sculpture?

Use the text tool to write the volume of each of the three parts on the diagram. Round each volume to the nearest whole cubic meter.

To determine the amount of concrete needed for each part of the sculpture, calculate the volume of each part based on their geometrical shape's formula and round to the nearest whole cubic meter.

To calculate the amount of concrete the artist will need for the sculpture, we need to know the volume of each of the three parts comprising the sculpture. Volumes of geometric forms are generally calculated using the formulas:

By substituting the given dimensions of each part into the appropriate formula, we can calculate the volume. Finally, each volume should be rounded to the nearest whole cubic meter. Therefore, the artist needs to have the exact volume of concrete in cubic meters for each part of the sculpture.

https://brainly.com/question/34259963

#SPJ11

If this assumption is not met, the risk we run in making inferences about the population is that our conclusions may be biased or inaccurate, leading to misleading or incorrect results when applied to the entire population of heart-attack patients. This could have negative implications for treatments or public health policies based on these inferences.

In order for us to use this sample of 30 heart-attack patients to make inferences about the whole population of heart-attack patients, we must assume that the sample is representative of the population. This means that the 30 patients were chosen randomly from the population of heart-attack patients and that the sample accurately reflects the characteristics of the population. Additionally, we must assume that the sample size is large enough to provide reliable results.
If this assumption is not met, then we run the risk of making incorrect inferences about the population of interest. For example, if the sample is biased and not representative of the population, the inferences we draw may not be applicable to the larger population. Similarly, if the sample size is too small, our inferences may be unreliable and subject to sampling error.
In order to avoid these risks, it is important to carefully consider the sampling method and sample size when conducting research. By ensuring that the sample is representative and the size is appropriate, we can have more confidence in our inferences about the larger population. Answer more than 100 words.
To make inferences about the whole population of heart-attack patients using a sample of 30, we must assume that the sample is representative of the entire population. This means that the sample should be random, unbiased, and large enough to capture the diversity in the population.

To know more about Population visit:

https://brainly.com/question/30935898

#SPJ11

A sample size of at least 241 U.S. residents would be required to reduce the standard deviation of the sampling distribution to one-half its original value, assuming that the true proportion of U.S.

The standard deviation of a sample proportion is given by the formula:

σ = √p(1-p)/n

where p is the true population proportion, and n is the sample size.

We want to find the sample size that will reduce the standard deviation to one-half its original value.

In other words, we want to find n such that:

σ/2 =√p(1-p)/n

Squaring both sides and solving for n, we get:

n = p(1-p)/(σ/2)²

Using the given value of p = 0.15, and assuming that the standard deviation of the sampling distribution is the same as the population standard deviation, which is approximately:

σ =√p(1-p)) = √0.15 × 0.85) ≈ 0.354

we can plug in the numbers and solve for n:

n = 0.15 × 0.85 / (0.354/2)²

= 240.2

Therefore, a sample size of at least 241 U.S. residents would be required to reduce the standard deviation of the sampling distribution to one-half its original value, assuming that the true proportion of U.S.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

The perimeter of the garden is:

90 + 30√3 feet

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The perimeter of the garden is the sum of all the three sides of the garden.

Check the attached for the sketch of the garden.

Thus, we can say:

sin 60 = (30√3)/y

(√3)/2 =  (30√3)/y

1/2 =  30/y

y = 2 * 30

y = 60 feet

tan 30 = x/(30√3)

1/√3 = x/(30√3)

(√3) x = 30√3

x = 30 feet

perimeter = x + y + 30√3

perimeter = 30 + 60 + 30√3

perimeter = 90 + 30√3 feet

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

La cantidad de datos es 9.

  Para encontrar la cantidad de datos, se puede usar la fórmula del promedio, que dice que el promedio es igual a la suma de los datos dividida entre la cantidad de datos. En este caso, se sabe que el promedio es 4 y la suma de los datos es 36. Entonces, se puede plantear la ecuación 4 = 36/n, donde n es la cantidad de datos. Al despejar n, se obtiene que n = 9, lo que significa que hay 9 datos en total.

Para verificar que esta respuesta es correcta, se puede sumar los datos y dividir entre 9 para confirmar que el resultado es 4. También se puede observar que si la cantidad de datos fuera menor a 9, la suma de los datos no sería suficiente para dar un promedio de 4. De manera similar, si la cantidad de datos fuera mayor a 9, la suma sería mayor a 36, lo que resultaría en un promedio mayor a 4.

To learn more about click plantear  here : brainly.com/question/23858522

#SPJ11

La cantidad de datos es 9.

 Para encontrar la cantidad de datos, se puede usar la fórmula del promedio, que dice que el promedio es igual a la suma de los datos dividida entre la cantidad de datos. En este caso, se sabe que el promedio es 4 y la suma de los datos es 36. Entonces, se puede plantear la ecuación 4 = 36/n, donde n es la cantidad de datos. Al despejar n, se obtiene que n = 9, lo que significa que hay 9 datos en total.

Para verificar que esta respuesta es correcta, se puede sumar los datos y dividir entre 9 para confirmar que el resultado es 4. También se puede observar que si la cantidad de datos fuera menor a 9, la suma de los datos no sería suficiente para dar un promedio de 4. De manera similar, si la cantidad de datos fuera mayor a 9, la suma sería mayor a 36, lo que resultaría en un promedio mayor a 4.

To learn more about click plantear  here : brainly.com/question/23858522

#SPJ11

Answer:

288π m³

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

= (4/3) X π X (6) ³

= 288π m³

There are 4845 different ways to select 16 questions out of a total of 20 questions on the exam.

To determine the number of different ways you can select 16 questions out of a total of 20 questions, we can use the concept of combinations.

In this case, we want to select 16 questions from a set of 20 questions, and the order in which we select them doesn't matter. This scenario can be represented by the combination formula.

The formula for combinations is given by:

C(n, k) = n! / (k!(n-k)!)

Where:

n is the total number of items in the set (20 questions)

k is the number of items to be selected (16 questions)

! denotes the factorial operation

Using the combination formula, we can calculate the number of different ways to select the questions:

C(20, 16) = 20! / (16!(20-16)!)

= 20! / (16!4!)

= (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1)

= 4845

Know more about combinations here:

https://brainly.com/question/31586670

#SPJ11

Answer:

36 cm

Step-by-step explanation:

the total length of the lines that pat draws on the second piece of paper is 36 cm.

The percent of the beads that were blue is 40%. To determine the percent of beads that were blue, we need to first find the total number of blue beads and then divide that by the total number of beads.

The total number of blue beads is 20, which we can determine from the problem statement. The total number of beads is 50, which we can calculate by adding the number of red, blue, and green beads together:

10 + 20 + x = 50

where x represents the number of green beads

Solving for x, we get:

x = 20

Therefore, there were 20 green beads, and the total number of beads is 10 + 20 + 20 = 50.

Now we can calculate the percent of beads that were blue:

20/50 x 100% = 40%

Therefore, 40% of the beads were blue.

To learn more about percent click here, brainly.com/question/31323953

#SPJ11