There are two containers out of which one can hold 31/2 litres of oil while the other can hold 22/3 litres of oil. Suppose there are 4 containers of the first type and 9 containers of the second type. The volume of oil required to fill both the containers is litres.



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The angle between two parallel lines is zero, we can prove it by putting the value of tanθ as 0.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

As we know, parallel lines in geometry are co-planar straight lines that do not cross at any point. Parallel planes are planes that never meet in the same three-dimensional space. Curves that do not touch or contact each other and maintain a constant minimum distance are known as parallel curves.

We know that the angle between two parallel lines is zero degrees.

[tex]\rm tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]

tanθ = 0

m1 = m2

Thus, the angle between two parallel lines is zero we can prove it by putting the value of tanθ as 0.

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The midterm score of 45 is the 3rd decile, meaning that 42% of the Senior High School students scored below this test.

Deciles are a type of percentile that divides data into groups of 10%. That is, each decile comprises 10% of the dataset.

To determine the decile, sort the data from lowest to highest. Now, divide the result by ten. This number reflects the no. of observed values within each decile.

Sorting the data from lowest to highest, we have:

= 14/10

= 1.4

Thus, each decile contains only a 1.4 score.

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Step-by-step explanation:

a general line equation is

y = ax + b

"a" being the slope is the line, "b" being the y-intercept (the y value when x = 0).

we see from the 2 marked points (by we could choose any points on the line) that

y changes by 2 units, when x changes by 3 units.

so the slope is 2/3.

we use one point (1, 2) to solve for b

2 = 2/3 × 1 + b = 2/3 + b

6/3 = 2/3 + b

4/3 = b

and the full equation is

y = 2/3 x + 4/3

Answer:

The median of the data is 12.

Step-by-step explanation:

The median is really just another word for the average. To find that, you add all of the numbers and divide that sum by the number of numbers there are.

9+15+17+18+6+20+8+5+18+18+10+5+14+12+10+7=192

There are 16 numbers in this data set. So, we will divide the sum by 16.

192÷16=12

I hope this helps!! :)

Answer:

the image should help.

Step-by-step explanation:

image explains everything.

Answer:

  73 cm²

Step-by-step explanation:

Areas and volumes of composite figures are found by dividing the figure into shapes you have formulas for. Sometimes that will be a sum of shapes, and sometimes it will involve the difference of shapes.

__

This shape can be decomposed into two rectangles by extending the horizontal line. (This is the dashed line shown in the attachment.)

The width of the top rectangle will be the sum of the lengths of the labeled horizontal segments:

  4 cm + 5 cm + 3 cm = 12 cm

The height of the top rectangle, and the dimensions of the bottom rectangle (square) are shown in the given figure.

The area of each rectangle is the product of its width and height.

  A = WH

__

  top rectangle area = WH = (12 cm)(4 cm) = 48 cm²

  bottom rectangle area = WH = (5 cm)(5 cm) = 25 cm²

  Area = top rectangle area + bottom rectangle area = (48 cm²) +(25 cm²)

  Area = 73 cm²

The area of this composite shape is 73 cm².

_____

Additional comment

The figure will fit into a rectangle that is 9 cm high by 12 cm wide. From that rectangle, a rectangle 5 cm high and 4 cm wide is removed from the lower left, and a rectangle 5 cm high and 3 cm wide is removed from the lower right. Figuring the area this way, we find it to be ...

  figure area = bounding rectangle area - removed areas

  = (9 cm)(12 cm) -(5 cm)(4 cm) -(5 cm)(3 cm) = 108 cm² -20 cm² -15 cm²

  = 73 cm²

Circumference = 2 x radius x PI

Circumference = 2 x 3.8 x 3.14

Circumference = 23.86

answer: the closest one is A. 23.8 FT.

Answer:

Hendecagon

Step-by-step explanation:

a hendecagon has 11 sides

Answer:

Hendecagon

Step-by-step explanation:

It has 11 sides, 11 corners, and 11 angles inside the shape that equal to 1620 degrees

Answer:

The value of m in the figure is 28.

Step-by-step explanation:

When we look at the figure, we see that 6 and 21, are connected with parallel lines to 8 and m. We can also see that 21 is dilated from 6. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind)                

To get m, we can do the same that we did to get 21, from 6.

To get 21 from 6, you must divide 21 by 6. So when we do the same thing to 8, we should get m.

21 / 6 = 3.5

Now that we have the dilation of 3.5, we simply multiply that by 8.

3.5 * 8 = 28

The value of x in the figure is 28.

[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{21}{6}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{7}{2}[/tex]

[tex]\\ \rm\dashrightarrow 2m=56[/tex]

[tex]\\ \rm\dashrightarrow m=28[/tex]

Differentiating each function, we have for all x, unless otherwise indicated,

[tex]h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0[/tex]

[tex]g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0[/tex]

[tex]f(x) = -3x+7 \implies f'(x) = -3 < 0[/tex]

[tex]j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4[/tex]

and only h(x) has a strictly positive derivative. (A)

Answer: 3360 ft squared

Step-by-step explanation:

Short side : 30 x 14 = 420

Long side 30 x 3 x 14 = 1260

420 + 420 + 1260 + 1260 =  3360

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The area of the trapezoid is 284.31 square inches

The area of a trapezoid is:

Area = 0.5 * (Sum of parallel sides) * height

Using the given figure, we have:

Area = 0.5 * (17 + 31.6) * 11.7

Evaluate

Area = 284.31

Hence, the area of the trapezoid is 284.31 square inches

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Answer:

D

Step-by-step explanation:

-1.5(-6m+8n) = 9m-12n

3(3m -4n) = 9m - 12n

9m -12n = 9m -12n

-6(-1.5m +2n) = 9m - 12n

-2(-4.5m+ 4n) = 9m - 8n

Answer: D. -2(-4.5m + 4n)

Step-by-step explanation:

   First, let us simplify -1.5(-6m+8n).

Given:

-1.5(-6m + 8n)

Distribute:

9m - 12n

[A] ✗

   9 /3 = 3 and 12 / 3 = 4

   This means that 3(3m - 4n) = 9m - 12n = -1.5(-6m+8n)

Option A is not our answer.

[B] ✗

   Using this simplified version we did above, option B is not our answer as 9m - 12n = 9m - 12n and 9m - 12n = -1.5(-6m+8n).

[C] ✗

   We will distribute option C to see if we reach the same expression. Seeing below, we do, so option C is not our answer.

-6(-1.5m + 2n)

9m - 12n

[D] ✓

   Since none of the other options are correct, the answer to your question D because it is not equivalent.

                Answer:

          D. -2(-4.5m + 4n)

Answer:

Hi,

a=b+3

Step-by-step explanation:

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

a=b+3

The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation. See the attached image for details.

Rotation in math refers to the change in the angle of a geometric shape around a central axis on a point on the geometric plane such that it's original coordinates are modified but it's size or shape.

Hence, it is correct to state that The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation.

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The inequality which represents this is x ≥ 22 , Option C is the right answer.

When two algebraic expressions are equated using an inequality operator, <, > etc then the expression formed is called Inequality.

IT is given in the question that

There is a number line , with points marked for eighteen, nineteen, twenty, twenty one, twenty two, twenty three.

The twenty two point is marked with an open circle pointing left

The inequality which represents this is

x ≥ 22 , Option C is the right answer.

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Answer:

The answer to this is 9.

Step-by-step explanation:

First of all, you wrote the expression wrong, but that's okay. It's supposed to be written as (-3)².

Second of all, since multiplying two negatives makes a positive and squaring is just multiplying the integer to itself, then -3×-3=9. I hope this helps! :)

The equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5

The equation of a line in pint slope form is expressed as:

y - y1 = m(x-x1)

where

m is the slope = -7

(x1, y1) = (7, -54 ) is the point on the line

Substitute

y + 54 = -7(x -7)

Write in slope intercept form

y + 54 = -7(x -7)

y + 54 = -7x + 49
y = -7x - 5

Hence the equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5

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This is a means of reducing the cost of a goods or an asset over time. The value of the car after 9 years is approximately $888

This is a means of reducing the cost of a goods or an asset over time.

Mathematically, the cost of goods after a particular year is expressed as:

P(t) = P0e^-rt

Given

Substitute

P(17) = 41000r^0.17(9)
P(17) = 4100(0.21653)

P(17) = 887.79

Hence the value of the car after 9 years is approximately $888

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Answer:

Step-by-step explanation:

we know that

Solve for x

so

therefore

The number of pounds of apples is 4.5 and the number of pounds of grapes is 2.5

Answer:

what is your from my from is province philippines

Answer:

23.292°

Step-by-step explanation:

see the attachment photo.

The value of x to the nearest tenth is 23.3°.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given is a triangle ABC.

Using the law of sines,

AB / Sin C = BC / Sin A

We have to find the angle A.

Substituting,

18 / sin 22 = 19 / sin x

18 × sin(x) = 19 × sin (22°)

sin(x) = (19 × sin (22°)) / 18

sin x = 0.3954

x = 23.29° ≈ 23.3°

Hence the value of x is 23.3°.

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Answer:18

Step-by-step explanation:

Answer:

C. 16

Explanation:

[tex]\rightarrow \sf \dfrac{9}{4} = \dfrac{x+2}{8}[/tex]

cross multiply

[tex]\rightarrow \sf \dfrac{9(8)}{4} = x + 2[/tex]

simplify integers

[tex]\rightarrow \sf 18 = x + 2[/tex]

exchange sides

[tex]\rightarrow \sf x =18-2[/tex]

subtract integers

[tex]\rightarrow \sf x =16[/tex]

Answer:

x = 4.2

Step-by-step explanation:

14.1² + x² = 14.7²

198.81 + x² = 216.09

216.09 - 198.81 = 17.28

√17.28 = 4.15

x = 4.15

Round to nearest tenth

x = 4.2

Answer:

  g(x) = -√(x+6)

Step-by-step explanation:

The inverse of the function y = f(x) can be found by solving for y the relation x = f(y).

__

  x = f(y)

  x = y^2 -6

  x +6 = y^2 . . . . . . add 6

  -√(x +6) = y . . . . . negative square root

The negative root produces y ≤ 0, equivalent to x ≤ 0 for f(x).

The inverse of f is g(x) = -√(x +6).

_____

Additional comment

The graph of a function and its inverse are mirror images of each other across the line y=x. This is shown in the attachment for the f(x) and g(x) in this problem.

After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have:

If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.

We know the exponential decay can be given as:

D = a(1 - r)ⁿ

a is the starting value and n is the number of hours.

D = 75(1 - 0.20)⁶

D = 19.66 milligrams

Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

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Answer: a. 720

Step-by-step explanation:

       You have 6 different sticks to choose from for the first stick. Then there are 5 for the second (6 - 1 = 5), then 4 for the third (5 - 1 = 4), etc all the way to the last stick.

       Mathematically, this can be shown with 6!. In other words, 6 factorial.

                      6 * 5 * 4 * 3 * 2 * 1 = 720

      The answer to our question is:

                      a. 720

Answer:

d = 3

Step-by-step explanation:

6*3=18
2d*6=12d
54-18 = 12d
36/12 = 12d/12
d = 3

Answer:

d = 3

Step-by-step explanation:

6 ( 3 + 2d ) = 54

First, solve the brackets.

18 + 12d = 54

Take 18 to the right side.

12d = 54 - 18

12d = 36

Divide both sides by 12.

d = 3