A rectangular storage container with an open top is to have a volume of 26 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 4 dollars per square meter. Find the cost of materials for the cheapest such container.
Total cost = ...

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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Answer:

c

Step-by-step explanation:

A rose garden is formed by rectangular and semi-circular parts. If the gardener wants to build a fence around the garden, then total 134.95 feet of fence are required.

The perimeter is defined as calculating the outer length of boundaries of shape.

We have a rose garden is formed by joining a rectangle and a semicircle, as present in above figure. We have to determine the feet of fence are required to build a fence around the garden.

From the above figure, length of rectangular part, l = 34 ft

Width of rectangular part, w = 26 ft.

Also, diameter of semi-circular part, d

= 26 ft

Radius of of semi-circular part, r = d/2

= 26/2 ft = 13 ft

So, the perimeter of semi-circular part, Pₛ= π× r = π× 13 ft

= 40.95 ft.

Here, the fence required for the rectangle shape is three sides that two long sides and one wide side. The fourth side of the width is already covered by the semi-circular part. So, the perimeter formula for the rectangle shape, Pᵣ = 2l + w. Therefore, perimeter of garden

= Pₛ + Pᵣ

= 40.95 ft + 2×34 ft + 26 ft

= 68 ft + 26 ft + 40.95 ft

= 134.95 ft.

Hence, required value is 134.95 feet.

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Complete question:

The above figure complete the question. a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 34 feet long and 26 feet wide. if the gardener wants to build a fence around the garden, how many feet of fence are required? (use the value for , and do not round your answer. be sure to include the correct unit in your answer.)

Answer:

Step-by-step explanation:

\(x^2-5=-2x+3\\\\x^2+2x-8=0\\\\a=1\,,\ b=2\,,\ c=-8\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot(-8)}}{2\cdot1}=\dfrac{-2\pm\sqrt{4+32}}{2}=\dfrac{-2\pm\sqrt{36}}{2}=\dfrac{-2\pm6}{2}\\\\x_1=\dfrac{-2-6}2=\dfrac{-8}2=-4\\\\y_1=-2x_1+3=-2(-4)+3=8+3=11\\\\(-4\,,\ 11)\\\\x_2=\dfrac{-2+6}{2}=\dfrac{4}2=2\\\\y_2=-2x_2+3=-2\cdot2+3=-4+3=-1\\\\(2\,,\ -1)\)

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Explanation:

Refer to the diagram below.

A small rectangle has its longer side equal to 10 and its shorter side is x, which is some real number on the interval 0 < x < 10.

Across the top, the two sides of length 10 add to 20. So the larger rectangle has a horizontal dimension of 20 units.

The vertical side of the larger rectangle is x+10+x = 2x+10 units

The area would be

area = length*width = 20(2x+10) = 40x+200

Each of the nine smaller rectangles has area of length*width = 10x. Since we have 9 identical copies, the smaller rectangle areas must add to 9*10x = 90x

---------------

Equate those two expressions and solve for x

90x = 40x+200

90x-40x = 200

50x = 200

x = 200/50

x = 4

So each smaller rectangle has area of 10*x = 10*4 = 40 square units. In total, the nine smaller rectangles combine to an area of 9*40 = 360 square units

Note how x = 4 leads 40x+200 to result in 360 as well.

Answer:

Step-by-step explanation:

x - 9/12 + 8/12 = 17/12

x - 1/12 = 17/12

x = 18/12= 3/2 = 1 1/2

Value of x = (4 / 3) which makes the given equation true.

" Variable is defined as the value which changes as per the condition act on it."

According to the question,

Given equation,

x - (3/4) + (2/3) = (17 / 12)

Convert all fraction into like fractions we get,

  x - (3/4) ×(3/3) +(2/3)×(4/4) = (17 /12)

⇒x - (9/12) + (8 /12) = (17 /12)

⇒x - (1/12) = (17 /12)

⇒x = (17/12) +(1/12)

⇒x= (18 /12)

⇒x= (3/2)

Hence, Value of x = (4 / 3) which makes the given equation true.

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we have the following:

John's rate = x mph

William's rate = x -20 mph

d = d, therefore:

John's rate = 40 mph

Willams's rate = 40 - 20 = 20 mph

Answer:

Kaylee drove her scooter for 2h and Sophia drove her scooter for 3h.

Step-by-step explanation:

From the graph shown below, we can see that the intersection point is (2,3). When using the graphing method to solve a system of equations, the intersection point is the answer. In this case, x = 2 and y = 3.

Thus, Kaylee drove her scooter for 2h and Sophia drove her scooter for 3h.

Kaylee drove her scooter for 2 hour and Sophia drove her scooter for 3 hours.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Kaylee drove her scooter at an average speed of 15 miles per hour. Sophia drove her scooter at an average speed of 10 miles per hour.

This can be represented with the system x+y=5 and 15x+10y=60 , where x represents the number of hours Kaylee drove her scooter and y represents the number of hours Sophia drove her scooter.

From the graph shown, we can see that the intersection point is (2,3).

When using the graphing method to solve a system of equations, the intersection point is the answer.

In this case, x = 2 and y = 3.

Thus, Kaylee drove her scooter for 2 hour and Sophia drove her scooter for 3 hours.

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Answer:

missing side.

AB²=AC²+CB²

AC²= 5²+4²

AC = √41

The type of sampling used in the given scenario is stratified random sampling.

Stratified random sampling is a probability sampling approach in which the population is divided into subgroups, known as strata, based on characteristics that are relevant to the study. For instance, a population may be divided into strata based on gender, socioeconomic status, age, or geographic location.

The strata are then randomly chosen to ensure that each stratum is represented in the sample. This technique can be more reliable than basic random sampling because it enables researchers to ensure that the sample is representative of the whole population.

Therefore, the type of sampling used in the scenario presented is stratified random sampling because the population was divided into ten groups or strata, and three of them were chosen at random.

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Let's find the equivalent equation to:

4x + 2y = 12

2y = 12 - 4x

Dividng by 2 at both sides:

2y/2 = 12/2 - 4x/2

y = 6 - 2x

We can see that choices B and C are not correct because the signs.

If we multiply by 2 at both sides, we have:

2y = 12 - 4x

We can see that if we change the order at the right side of the equation, we have:

2y = -4x + 12

I think now you are ready to select the correct choice, Deppreso.

Answer:

50

Step-by-step explanation:

Answer:

x = 50

Step-by-step explanation:

Move all terms containing x to the left, all other terms to the right.

Divide each side by '0.2'.

x = 50

The equation that the speed of an object is speed = distance/time

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

Parameter = Object

Argument = Speed

By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object

Mathematically, this can be represented as

Speed = Distance : Time

Express as fraction

Speed = Distance/Time

Hence, the equation is Speed = Distance/Time

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Answer:

25

Step-by-step explanation:

Answer:

We are given that:

- f(x) = x² - 2x - 4

- g(x) = x - 1We want to find fx for which f(x) = g(x) - 4, or in other words:

- f(x) = x - 1 - 4

- f(x) = x - 5

We can solve forTo find the value of x for which f(x) = g(x) - 4 (which is what I assume you meant by "f(x) = (x) = m - 4"), we can set up the following equation:

f(x) = g(x) - 4

Substituting the given expressions for f(x) and g(x), we get:

x² - 2x - 4 = x - 1 - 4

Simplifying, we have:

x² - 3x - 3 = 0

We can solve for x using the quadratic formula:

x = (-(-3) ± sqrt((-3)² - 4(1)(-3))) / (2(1))

x = (3 ± sqrt(21)) / 2

Therefore, the two values of x for which f(x) = g(x) - 4 are:

- x = (3 + sqrt(21)) / 2

- x = (3 - sqrt(21)) / 2

Answer:

kaya ko yan. Ano fb mo HAHAHA

Answer:

The answer is A.

Step-by-step explanation:

The possible advance in the field of biology that would be a result of the stem cell research is: Creation of a novel cancer cell line to test anticancer agents.

This is a type of research that is carried out by biogical researchers. The function of this type of research is to manipulate the different cells that are in the human body.

This research is done in order to specialize some body cells that can be used to treat different diseases.

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The nearest tenth of a foot, the thickness T of the cantilever at x = 6 feet is 7.6 feet.

The given equation for the bottom edge of the cantilever is y = 2Vx, where V is the height of the cantilever. Therefore, the height of the cantilever is:

V = y / (2x)

At x = 6 feet, the value of y is:

y = 2Vx = 2(3.2) = 6.4 feet

To find the thickness T at x = 6 feet, we can use the Pythagorean Theorem:

T² = b² - y²

where b is the height of the cantilever. We have already calculated V to be 3.2 feet, so:

b = 3.2 + y = 3.2 + 6.4 = 9.6 feet

Substituting these values into the equation for T², we get:

T² = (9.6)² - (6.4)² = 57.76

Taking the square root of both sides, we get:

T ≈ 7.6 feet

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Answer:

1) c. 5

2) 1.29

Step-by-step explanation:

1. To calculate the standard deviation, we first need to find the variance. The variance is the average of the squared differences from the mean.

Step 1: Find the differences from the mean:

15 - 21 = -6

21 - 21 = 0

17 - 21 = -4

16 - 21 = -5

26 - 21 = 5

18 - 21 = -3

29 - 21 = 8

Step 2: Square the differences:

(-6)^2 = 36

0^2 = 0

(-4)^2 = 16

(-5)^2 = 25

5^2 = 25

(-3)^2 = 9

8^2 = 64

Step 3: Find the average of the squared differences:

(36 + 0 + 16 + 25 + 25 + 9 + 64) / 7 = 175 / 7 = 25

Step 4: Take the square root of the variance to find the standard deviation:

√25 = 5

Therefore, the standard deviation is 5.

2. To calculate the standard deviation for the set of numbers 2, 3, 4, 4, 5, 6:

Step 1: Find the mean:

(2 + 3 + 4 + 4 + 5 + 6) / 6 = 24 / 6 = 4

Step 2: Find the differences from the mean:

2 - 4 = -2

3 - 4 = -1

4 - 4 = 0

4 - 4 = 0

5 - 4 = 1

6 - 4 = 2

Step 3: Square the differences:

(-2)^2 = 4

(-1)^2 = 1

0^2 = 0

0^2 = 0

1^2 = 1

2^2 = 4

Step 4: Find the average of the squared differences:

(4 + 1 + 0 + 0 + 1 + 4) / 6 = 10 / 6 ≈ 1.67

Step 5: Take the square root of the variance to find the standard deviation:

√1.67 ≈ 1.29

Therefore, the standard deviation is approximately 1.29

Answer:

(f · g)(x) = 4x³ + x² - 20x - 5

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 1

g(x) = x² - 5

(f · g)(x) is f(x)g(x)

Step 2: Find (f · g)(x)

We know that,

\( \Large \underline{\boxed{\sf{ (f . g)(x) = f(x) \times g(x) }}}\)

By substituting values :

\( \sf : \implies (f . g)(x) = (4x+1) \times (x^{2} -5)\)

\( \sf : \implies (f . g)(x) = 4x(x^{2} -5) +1(x^{2} -5)\)

\( \sf : \implies (f . g)(x) = 4x^{3} - 20x + x^{2} -5\)

\( \sf : \implies (f . g)(x) = 4x^{3} + x^{2} - 20x -5\)

Hence, answer is :

\(\underline{\boxed{\sf{(f . g)(x) = 4x^{3} + x^{2} - 20x - 5}}}\)

Answer:

x = 121°

Step-by-step explanation:

the angle at the vertex = 360° - 304° = 56°

the base angle = 180° - 115° = 65°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 56° + 65° = 121°

The angle opposite to 304° has measure:-

The angle aside 115° has measure

Now

Sum of two interiors=Exterior

If you select one card from a standard deck of playing cards, the probability of selecting a Queen is 1/13. This is because there are 4 Queens in the deck and a total of 52 cards.

So, the probability is calculated by dividing the number of favorable outcomes (4) by the total number of possible outcomes (52). Therefore, the probability of selecting a Queen is 4/52, which simplifies to 1/13. If you select one card from a standard deck of playing cards, the probability of selecting a Queen or a King is 8/52. This is because there are 4 Queens and 4 Kings in the deck, making a total of 8 favorable outcomes. Again, the total number of possible outcomes is 52. By dividing the number of favorable outcomes (8) by the total number of possible outcomes (52), we get the probability of 8/52.

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Answer: x = 0, 2 or 3/2 (look at the image for the solution)

Step-by-step explanation:

Given:

A recipe uses 4 pounds of rice and 5 quarts of boiling water.

To find:

The rate of rice to quarts of water for this recipe.

Solution:

We need to divide the amount of rice by amount of water to get the rate of rice to quarts of water for this recipe.

\(\text{Required rate}=\dfrac{\text{Rice in pounds}}{\text{Water in quarts}}\)

\(\text{Required rate}=\dfrac{4}{5}\)

\(\text{Required rate}=0.8\)

Therefore, the  rate of rice to quarts of water for this recipe is 0.8.

Answer:

-x + 23y

Step-by-step explanation:

-2(3x - 4y) + 5(x+3y)

Expand the brackets.

-6x + 8y + 5x + 15y

Rearrange.

- 6x + 5x +8y + 15y

Add or subtract like terms.

- 1x + 23y

Answer:

\( - x + 23y\)

Step-by-step explanation:

\( - 2(3x - 4y) + 5(x + 3y) \\ - 6x + 8y + 5x + 15y \\ - 6x + 5x - 8y + 23y \\ = - x + 7y\)

Answer:

Solution is invalid

Step-by-step explanation:

Let the time when they will have the same water content be x hours

At x hours;

For the first tank, the content will be;

50 + 10x

For the second;

29 + 3x

Equating both, will give us x

29 + 3x = 50 + 10x

We will get x as a negative number here

Since number of hours can not be negative, the solution is invalid

Answer:

the long one because of the friction and you can gain speed the second way

Step-by-step explanation:

Answer:

love how all our accounts got deleted. smh

Step-by-step explanation: