\(if a : b = 2 : 3 and b : c = 4 : 5 than find a :b c: \)
​

Answer:

height of the building = 36√3 m

Step-by-step explanation:

Answer:

62.4 m

Step-by-step explanation:

           |\----------------------------------------

           |    \   60°

           |        \

   h      |            \

           |                \

           |           60°    \

           ---------------------  A

                    36 m

Point A is 36 m from the foot of the building. The angle of depression above is 60°. m<A = 60°.

tan A = opp/adj

tan 60° = h/(36 m)

h = 36 * tan 60° m

h = 62.4 m

Answer: 62.4 m

The average distance of electric cars is 275.

The range of the data set is 300.

Given:

To find: Average distance of electric cars

Solution:

The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:

250, 250, 250, 400, 300, 300, 350, 100

To find the average distance of electric cars, we can use the formula:

Average = (Sum of all the data points) / (Number of data points)

Substituting the given values, we get:

Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8

Average = 2200 / 8

Average = 275

Therefore, the average distance of electric cars is 275.

Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.

Range = Maximum value - Minimum value

Range = 400 - 100

Range = 300

Therefore, the range of the data set is 300.

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Answer:

x² - 4x - 5 = ( x + 1)(x - 5)

Step-by-step explanation:

x² - 4x - 5 =

x² + x - 5x - 5 =

x(x + 1) - 5(x + 1) =

( x + 1)(x - 5)

Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.

Direct Materials: It includes the cost of raw materials used in manufacturing a product.

Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.

Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process

Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.

To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.

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There are 10 people running for the 7 seats in the school's student council. The number of different student council combinations is 120.

To calculate the number of different student council combinations, we can use the concept of combinations, specifically the formula for selecting r objects from a set of n objects without replacement. In this case, we have 10 people running for 7 seats, which means we need to select 7 people from the group of 10.

The formula for combinations is given by:

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

Plugging in the values, we have:

C(10, 7) = 10! / (7!(10 - 7)!)

= 10! / (7!3!)

Using factorials, we can simplify this calculation:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

3! = 3 x 2 x 1 = 6

Substituting these values back into the formula:

C(10, 7) = 3,628,800 / (5,040 x 6) = 120

There are 120 different student council combinations possible when 10 people are running for the 7 available seats. This means that out of the 10 candidates, any group of 7 can be chosen to form the student council in a total of 120 different ways.

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The lines are parallel because parallel means 2 or more lines that can go on and on without ever touching or meeting.

Answer:

about 5.5

Step-by-step explanation:

so 5cm. Just trust me i dont know how to explain but i know its right.

Answer:

C.8cm

Step-by-step explanation:

i took the test its correct

A and B are mutually exclusive, with P(A) is 0.7 and P(B) is 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

To find the probability of B given A, we can use the formula:

P(B|A) = P(A and B) / P(A)

Given:

P(A) = 0.5

P(B) = 0.1

P(A and B) = 0.3

P(B|A) = 0.3 / 0.5

= 0.6

Therefore, the probability that B will occur if A occurs is 0.6.

Given:

P(A) = 0.3

P(B) = 0.4

Since A happening guarantees that B must also happen, the events A and B are not independent. In this case, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.4 - 0.3

= 0.4

Therefore, the probability of A or B occurring is 0.4.

Given:

P(A) = 0.7

P(B) = 0.2

Since A and B are mutually exclusive events, they cannot occur together. In this case, we have:

P(A and B) = 0

Therefore, P(B|A) = P(BIA)

= 0.

P(BIA) = P(B)

= 0.2.

So, P(BIA) < P(B) is true.

When events A and B are mutually exclusive, with P(A) = 0.7 and P(B)

= 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

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Answer:

Stephan adds $12.50 per week to the amount he owes on the loan and will pay back the loan in 125 weeks.

Step-by-step explanation:

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a)

P (gold or silver) is 0.20

b)

P (not gold) is 0.95

c)

P (silver or bronze) is 0.70

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Color          gold   silver   bronze  white

Probability 0.05   0.15      0.55     0.25

Now,

The probability that the counter is

a)

P (gold or silver)

= 0.05 + 0.15

= 0.20

b)

P (not gold)

= 1 - 0.05

= 0.95

c)

P (silver or bronze)

= 0.15 + 0.55

= 0.70

Thus,

The probabilities are given above.

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Answer:

-2, 8/3

Step-by-step explanation:

You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...

 A = (1/2)(f(a) +f(4))(4 -a)

 = (1/2)((3a -1) +(3·4 -1))(4 -a)

 = (1/2)(3a +10)(4 -a)

We want this area to be 12, so we can substitute that value for A and solve for "a".

 12 = (1/2)(3a +10)(4 -a)

24 = (3a +10)(4 -a) = -3a² +2a +40

 3a² -2a -16 = 0 . . . . . . subtract the right side

 (3a -8)(a +2) = 0 . . . . . factor

Values of "a" that make these factors zero are ...

 a = 8/3, a = -2

The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.

Alternate solution

The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.

Answer:

Step-by-step explanation:

If you're tasked to do this mathematically, you have to complete the square to get it into vertex, or work, form. Do that by first setting the equation equal to 0 then moving over the constant:

\(3x^2+2x=8\) Next you have to have a +1 as the leading coefficient, and ours is a 3, so we factor it out:

\(3(x^2+\frac{2}{3}x)=8\). Now take half the linear term, square it, and add it in to both sides. Our linear term is 2/3. Half of 2/3 is 2/6 which reduces to 1/3. Squaring 1/3 gives us 1/9, so that's what we add in.

\(3(x^2+\frac{2}{3}x+\frac{1}{9})=8+\frac{1}{3}\) to the right of the equals sign we added in 3*1/9 which is 3/9, which reduces to 1/3. Now we clean up both sides. The right side is easy; the left side, not so much. The reason we do this (complete the square) is to get a perfect square binomial on the left. When we re-write the left side into that perfect square binomial, we get

\(3(x+\frac{1}{3})^2=\frac{25}{3}\) Now we move the constant back over and set the parabola back equal to y:

\(y=3(x+\frac{1}{3})^2-\frac{25}{3}\) which shows us that the vertex is

\((-\frac{1}{3},-\frac{25}{3})\)

Answer:

\(\dfrac 14\)

Step by step explanation:

\(~~~\cos (75^{\circ}) \cos (15^ \circ)\\\\=\dfrac 12 \cdot 2 \cos ( 75 ^\circ}) \cos( 15^\circ})\\\\\)

\(=\dfrac 12 \left[\cos \left( 75^ \circ + 15^ \circ \right) + \cos \left( 75^{\circ} - 15^{\circ} \right)\right]~~~~~~;[2 \cos a \cos b = \cos( a+b) + \cos(a-b)]\\\)

\(\\=\dfrac 12 \left( \cos 90^{\circ} + \cos 60^{\circ} \right)\\\\=\dfrac 12 \left(0+\dfrac 12 \right)\\\\=\dfrac 12 \cdot \dfrac 12\\\\=\dfrac 14\)

The cylinder is a three-dimensional shape and it has a radius, diameter and a height

Assume the square has the following dimensions:

Base dimensions = x

Height = h

Assume the cylinder has the following dimensions:

Radius  = r

Height = h

When the square is drilled out, the lateral surface area would be:

Lateral Area = Cylinder - Square

This gives

\(Lateral = 2\pi rh - 4xh\)

Factor out 2h

\(Lateral = 2h( \pi h - 2x)\)

Using the same dimensions in (a), we have:

Total surface Area = Cylinder - Square

This gives

\(Area = 2\pi r(r +h) - 2(2x^2 - xh)\)

Factor out 2

\(Area = 2[\pi r(r +h) - (2x^2 - xh)]\)

Using the same dimensions in (a), we have:

Base area = Cylinder - Square

So, we have:

\(Base = \pi r^2 - x^2\)

Using the same dimensions in (a), we have:

Volume = Cylinder - Square

So, we have:

\(Volume = \pi r^2h - x^2h\)

Factor out h

\(Volume = h(\pi r^2 - x^2)\)

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Is this the full question?

Answer:

The graph below

Step-by-step explanation:

Start at -2 on the y-axis and go up 1/2 every space you go on the x-axis

Hope this Helps

Answer:

x = \(\frac{c+d}{a-b}\)

Step-by-step explanation:

Given

ax - c = bx + d ( collect the terms in x together )

Subtract bx from both sides

ax - bx - c = d ( add c to both sides )

ax - bx = c + d ← factor out x from each term on the left side

x(a - b) = c + d ← divide both sides by (a - b )

x = \(\frac{c+d}{a-b}\)

Answer:

 x= c+d/a+e

Step-by-step explanation:

The required equation of the line using the given gradient and the points is given by y = (3/5)x - 7/5.

Points through which line passes are (x₁, y₁) = ( 4, 1 )

Gradient of the line = ( 3 / 5 )

Standard gradient-intercept form of a straight line is y = mx + c.

where 'm' is the gradient of the line

And 'c' is the y-intercept.

Point-slope form of a straight line is equal to,

y - y₁ = m(x - x₁)

Substitute the given values, we have,

⇒ y - 1 = ( 3/5 )( x - 4 )

Expanding the right-hand side we get,

⇒ y - 1 = (3/5)x - (3/5)4

⇒ y - 1 = (3/5)x - 12/5

Add 1 to both sides of the equation we get,

⇒ y = (3/5)x - 12/5 + 1

⇒ y = (3/5)x - 7/5

Therefore, the equation of the line that passes through the point (4,1) and has a gradient of 3/5 is y = (3/5)x - 7/5.

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The true statements are (A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

There are 30 people and each person is served soup in a 400 ml bowl, so the total amount of soup needed is 30 × 400 ml = 12,000 ml.

Option A is true

30 bowls of soup hold 30 × 400 ml = 12,000 ml, which is the same as 12 litres (since 1 litre = 1,000 ml).

Option B is true

Since 1 litre = 1,000 ml

Noah can multiply the number of bowls of soup by 1,000 to find the number of litres.

For example, 30 bowls of soup hold 12,000 ml = 12 litres.

Option C is true

If each family member has 2 bowls of soup, then the total amount of soup needed is

30 × 2 × 400 ml

= 24,000 ml, which is 24 litres (since 1 litre = 1,000 ml).

Option D is true.

Noah needs to make 24 litres of soup, and each pot contains 6 litres of soup.

Therefore, he would need to make 24 ÷ 6 = 4 pots of soup to serve each family member 2 bowls of soup.

Option E is false.

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Noah is making soup for a family reunion of 30 people. Each pot he makes contains 6 liters of soup. He uses bowl that 400mL to serve the soup to his family

Select all the true statements

(A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

(E) Noah would need to make 2 pots of soup for each family member to have 2 bowls of soup

To apply Green's Theorem to evaluate the given line integral, we need to express the integral as a double integral over the region bounded by the curve. In this case, the region is a triangle bounded by the lines x = 0, x + y = 1, and y = 0.

Green's Theorem states that for a vector field F = (P, Q) and a simple closed curve C oriented counterclockwise, the line integral of F around C is equal to the double integral of the curl of F over the region D bounded by C.

Let's calculate the curl of the vector field F = (y^2, x^2):

∂Q/∂x = 2x

∂P/∂y = 2y

The curl of F is given by ∂Q/∂x - ∂P/∂y:

curl(F) = 2x - 2y

Now, let's set up the double integral over the region D:

∬_D (2x - 2y) dA

To evaluate this integral, we need to express it in terms of the region D. The given region is a triangle bounded by the lines x = 0, x + y = 1, and y = 0.

We can rewrite the double integral using the limits of integration corresponding to the triangle:

∬_D (2x - 2y) dA = ∫_0^1 ∫_0^(1-x) (2x - 2y) dy dx

Evaluating the inner integral with respect to y:

∫_0^(1-x) (2x - 2y) dy = [2xy - y^2]_0^(1-x)

Plugging in the limits:

[2x(1-x) - (1-x)^2]_0^1

Simplifying:

[2x - 2x^2 - (1 - 2x + x^2)]_0^1

[2x - 2x^2 - 1 + 2x - x^2]_0^1

Combining like terms:

-3x^2 + 4x - 1

Therefore, the value of the line integral ∫ (y^2 dx + x^2 dy) over the triangle bounded by x = 0, x + y = 1, and y = 0 is -3x^2 + 4x - 1.

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Answer:

whats the question again???????????????????????????

Answer:

yall its 9 i got it right on the test in edg

Step-by-step explanation:

The value of the variable 'x' in the arithmetic sequence 6, 9, 12, 15, x, .... will be 18.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given as,

6, 9, 12, 15, x, .....

The common difference between the succession term remains constant. Then the equation is given as,

15 - 12 = x - 15

Simplify the equation, then we have

15 - 12 = x - 15

3 = x - 15

x = 15 + 3

x = 18

The value of the variable 'x' in the arithmetic sequence 6, 9, 12, 15, x, .... will be 18.

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The complete sequence is given below.

6, 9, 12, 15, x, ......

It is stated that y = 10x + 60 is the equation for the line of greatest fit for all of this data set. indicating that the third choice is the right one.

How can I get the formula for the best fit line?

It is stated that a linear function has the following slope-intercept definition:

y = mx + b.

which contains the following coefficients:

The slope, or m, shows how quickly the function's output changes in relation to its input.

The y-intercept, or b, represents the value that the input function assumes to be zero.

Since the function passes through the given point (0,60), the following is the line's b-intercept:

b = 60.

When x rises by two from zero to two, y rises by twenty from sixty to eighty.

Consequently, the slope m is determined as follows:

m = 20/2 = 10.

Therefore, the following is the line of fit:

y = 10x + 60.

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It is stated that y = 10x + 60 is the equation for the line of greatest fit for all of this data set. indicating that the third choice is the right one.

How can I get the formula for the best fit line?

It is stated that a linear function has the following slope-intercept definition:

y = mx + b.

which contains the following coefficients:

The slope, or m, shows how quickly the function's output changes in relation to its input.

The y-intercept, or b, represents the value that the input function assumes to be zero.

Since the function passes through the given point (0,60), the following is the line's b-intercept:

b = 60.

When x rises by two from zero to two, y rises by twenty from sixty to eighty.

Consequently, the slope m is determined as follows:

m = 20/2 = 10.

Therefore, the following is the line of fit:

y = 10x + 60.

Step-by-step explanation:

(2x + 3) (2-8)=0

2x( 2-8)+3(2-8)= 0

4x - 16x + 6 - 24 = 0

-12x - 18= 0

-12x= 18

x= -18/12

x = - 3/2

Answer:

x = 45, y = 115; 90, 90, 115, 65

Explanation:

One of the properties of a trapezoid is that adjacent angles of the legs of the trapezoid are supplementary, that is, they add up to 180 degrees.

Considering the above property, we'll have;

Still considering the above property, we have;

We can see that the measure of the four angles of the trapezoid are;

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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