a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:

Answer: Equation: 3x-2=4

               Solutoin: x=2

Step-by-step explanation:

[tex]x+x+x-1-1=1+1+1+1\\3x-2=4\\3x-2+2=4+2\\3x=6[/tex]

Divide both parts of the equation by 3:

[tex]x=2[/tex]

Answer: A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.

Step-by-step explanation:

Hope this helps you! :) have an amazing day! ^-^

Answer:

9

Step-by-step explanation:

6x+15=27

6x=27-15

6x=12

x=2

2x+5=(2)(2)+5

= 4+5

= 9

Answer:D

Step-by-step explanation:

Answer:B (8)

Step-by-step explanation:

OVER 50 means anything higher than 50, NOT OLDER THAN 70 means anything that's 70 or lower. So we have a range of 51-70. Now, when we look at the diagram, we can tell that there are 4 people who are 51-60 years old which fits to the range we are looking for. Same with the 4 people in the 61-70 range.

The length and width of the rectangle are: 10 inches and 5 inches.

Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Given:

To find: the length and width of the rectangle.

Finding:

Let the width of the rectangle be 'x'

Then the length of the rectangle = x + 5

Now, area of the rectangle = width (length)

=> 104 = x ( x + 5)

=> x² + 5x - 104 = 0

=> x² + 13x - 5x - 104 = 0

=> (x + 13) (x - 5) = 0

Since the lengths can't be negative, x = 5, i.e., the width of the rectangle = 5 inches

=> Length = 5 + 5 = 10 inches

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Answer:

100 times more

Answer:

B

Step-by-step explanation:

Answer:

m

Step-by-step explanation:

If the cost of car is $26000 and it depreciates by one half every 7 years, then the cost of car will reach to $8800 after 10 years.

Given that the cost of car is $26000 and it depreciates by one half every 7 years.

We are required to find the number of years after which the cost of car will reach $8800.

Because the method of depreciation is not given in question, so we will apply straight line method of depreciation.

Depreciation is the gradual or permanent decrease in the cost of asset due to passage of time and many factors.

Depreciation of 7 years=26000*R*7

13000=26000*R*7

R=13000/26000*7

=7.14%

The cost of car will be $8800,so the depreciation charged will be 26000-8800=$17200

17200=26000*7.14/100 *N

N=1720000/26000*7.14

=9.2652

Because it is slightly larger than 9 so we can approx it as 10 years.

Hence if the cost of car is $26000 and it depreciates by one half every 7 years, then the cost of car will reach to $8800 after 10 years.

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The value of the expression 3x + 5y will be 47.

It should be noted that an equation is used in Mathematics to show the relationship the exist between different variables.

The given equations are:

x - 4y = -10 ...... i

2x + 9y= -3 ....... ii

Multiply equation i by 2

Multiply equation ii by 1

2x - 8y = -20 ...... iii

2x + 9y = -3. ..... iv

Subtract equation iv from iii

(2x - 2x) (-8y - 9y) = (-20 + 3)

-17y = -17

Then, we have to divide by the coefficient.

y = -17/-17

y = 1

Since x - 4y = -10.

We will then put the value of y = 1 into the equation

x - 4(1) = 10

x = 10 + 4

x = 14

Therefore, 3x + 5y will be:

=3(14) + 5(1)

= 42 + 5

= 47.

In conclusion, the value of 3x + 5y is 47.

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Answer:

I think 7.5 answer is right

Answer:

2.5 cm.

Step-by-step explanation:

7.5 - 5

= 2.5

Answer: x=59 1/10     x=59.1

Step-by-step explanation:

Answer:

If the question is 5+4x(8-6)+2,then the answer is 15

Step-by-step explanation:

Median for the number of sick days of the employees is 5

A statistical phrase that splits the data into four quarters is called a quartile. On the number line, it essentially separates the data points into a data set into four quarters. It essentially serves as an extended middle. Data is divided into two equal parts by the median, and into four parts by the quartiles.

Solution:

Stem and leaf plot from Minitab of the number of sick days of the employees is,

2, 3, 3, 5, 7, 10, 10, 7, 5, 3, 2

Arrange the numbers in the ascending order,

2, 2, 3, 3 ,3, 5, 5, 7, 7, 10, 10

Here,

[tex]number\;of\;data=10[/tex]

We know that the Quartile 2 is spilt the data in to two like median,

[tex]Q_{2}=(\frac{n+1}{2}) ^{th\;term}[/tex]

[tex]Q_{2}=(\frac{11+1}{2}) ^{th\;term}[/tex]

[tex]Q_{2}=(\frac{12}{2}) ^{th\;term}[/tex]

[tex]Q_{2}=6 ^{th\;term}[/tex]

Therefore, the 6th term is, 5

Median = 5

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Answer:

14

Step-by-step explanation:

If O is the midpoint of LN and P is the midpoint of MN and if OP = 31 - 2x, and LM = 38 + 4x, then the measure of LM = 88

As per the question statement, Triangle LMN where O is the midpoint of LN and P is the midpoint of MN and if OP = 31 - 2x, and LM = 38 + 4x, we are supposed to find the measure of LM.

As O is the mid point of LN and P is the midpoint of OP the using the Mid point theorem, we can say that in Triangle LMN

[tex]OP=\frac{LM}{2}[/tex]

Substituting values,

[tex]31-2x=\frac{38+4x}{2} \\2(31-2x)=38+4x\\62-4x=38+4x \\8x = 100\\x=12.5[/tex]

LM =  38 + 4x

[tex]LM = 38 + 4(12.5)\\LM=38 + 50\\LM=88[/tex]

Hence value of LM is 88

This question is a classic example of how to solve linear equations.

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Answer:

Step-by-step explanation: His final position relative to ground level should be -3. If he starts out 6 feet under ground that is a negative number. So we have -6. Then he climbs up 14 feet. So we are going to add -6+14 which equals 8. Next it says he climbs down 11 feet. So we have a -11 and we will do 8-11=-3.

So -3 is the answer

Hope this helps.

For the given line segment, the value of variable d is 2 units and the value of YZ is 16 units.

Given that, Y is between X and Z.

We need to find the value of the variable and YZ.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Given that, XY=11d, YZ=9d-2, XZ=5d+28

Here, the line segment XZ is sum of XY and YZ

That is, XZ=XY+YZ (∵Y is between X and Z)

⇒5d+28=11d+9d-2

⇒5d+28=20d-2 (Add like terms that is 11d+9d=20d)

⇒20d-5d=28+2

⇒15d=30

⇒d=2

So, YZ=9d-2

=9×2-2=18-2

=16

Therefore, the value of variable d is 2 units and the value of YZ is 16 units.

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Nora needs to visit at least 11 times in order to earn a free movie ticket .

Let the number of visit to the movie theater be " x " .

According to the question She earns 12.5 points for each visit to the movie theater .

Total number of points in " x " number of visit will be [tex]=12.5x[/tex]

She also receives 20 rewards points just for signing up.

Total points will be [tex]=20+12.5x[/tex]

She needs at least 155 points for a free movie ticket which means minimum to minimum she needs 155 points .

   [tex]20+12.5x\geq 155[/tex]

On simplifying the above inequality , we get

 [tex]12.5x\geq 155-20\\12.5x\geq135\\x\geq 10.8[/tex]

As , visits can't be in point so , on rounding off Nora needs to visit 11 times to the movie theater.

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Answer:

m = 0.5

Step-by-step explanation:

Step 1 : Take the cube root of it.

Basically what this means is that you multiply the reciprocal of it to the 0.125

Like this:

m^3 = 0.125   --------->       m = 0.125 (1/3)

Step 2: Solve

m = 0.125 (1/3)

m = 0.5

I hope this helps!

The length of line segment RT is 8 units

The given triangles are similar triangles

So, we have the following similarity ratio

RS : RT = QC : QY

Substitute the known values in the above equation

4 : RT = 3 : 6

Express as fractions

RT/4 = 6/3

Multiply through by 4

RT = 4 * 6/3

Evaluate

RT = 8

Hence, the length of RT is 8 units

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Step-by-step explanation:

The coordinate of A is 0. It is given that AR = 17. AR represents the distance from point A to point R. Remember that distance is always positive. So, from here we have two possibilities.

Point R is on Right side of A i.e. at coordinate 17

Point R is on Left side of A i.e. at coordinate -17

In both of these cases AR which is the distance from A to R will be 17.

So, if R is on Right side of A, the midpoint of AR would be:

0+17

  ÷      =  17/2  = 8.5

  2

Or if R is on Left side of A, the midpoint of AR would be:

0-17

  ÷      =  -17/2  = -8.5

  2

Thus, the possible coordinates of the midpoint of AR are 8.5 and -8.5

The number of blue marbles in the jar are 8.

Given,  the total number of marbles in the jar = 24.

therefore, total number of all possible outcomes = 24.

Let the number of green marbles in Jar be x.

therefore, the number of favourable outcomes = x.

The probability that the marble drawn is green  = x/24

But we have the probability of drawing a green marble = 2/3

x/24 = 2/3

3x = 2 (24)

x = 16

Thus , the number of green marbles in the jar = 16

The number of blue marbles = 24 - 16 = 8

Hence, the number of blue marbles in the jar is 8.

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Your question is incomplete.Please find the missing content below.

There are 24 marbles in a jar out of them some are green and remaining are blue. If a marble is drawn from the jar at random, the probability that the green marble drawn is 2/3.Find the number of blue marbles in the jar.

I think that it is the 2nd one and the 5th one.

I hope that this helps! :)

Water main valves should be located at frequent intervals in a grid system.

The flow and temperature in pipes and plumbing fittings are controlled by water valves. The valves regulate steady flow and volume when they are correctly placed and used. Water valves are made of brass, plastic, stainless steel, bronze, cast iron, and galvanised pipe, among other materials.

The master cutoff valve for the house will typically feature a wheel (a gate valve) or a straight handle (ball valve). The wheel on gate valves (seen on the right) is turned clockwise until the water is shut off. To turn off the water, turn the handle of a ball valve a quarter turn in the opposite direction. Every house has two main water shutoff valves: one inside and one near the intersection of your property and the street.

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Step-by-step explanation:

f=ma

force=mass×acceleration

=32×2

=64N

Algebra is a universal language used in communicating ideas, and it therefore improves how people can teach or learn ideas from others

Algebra is the mathematics representation of ideas, problems, situation or solutions using mathematical expressions.

Algebra makes use of numbers, variables, and operators to give value or convey information.

Algebra is therefore an indispensable communication tool that is used in all walks of life to improve understanding of disseminated information, from the original source, to the intended destination and beyond, without, losslessly losing any substance, value or understanding.

With algebra, a doctor speaking a foreign language in a remote location can perform complex and emergency operational procedures based on guidance from another doctor communicating through the internet to his exact location and a local robot that is able translate verbal information into action based on algebraic relationships.

Algebra allows the foreign doctor to obtain or look for specific health metrics and indicators.

It allows the foreign doctor to understand the cost implications as well as to avoid dangerous situations and risk factors which are best specified by algebraic relation, that is understandable to all languages, given that it is based on numbers and variables.

Algebra therefore is one of the main means through which one person can teach another or communicate ideas.

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Answer:

s = 4 m

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 16 m² , then

s² = 16 ( take square root of both sides )

s = [tex]\sqrt{16}[/tex] = 4 m

Answer:

4m

Step-by-step explanation:

All the sides of a square are equal lengths. So 2 numbers that are the same must equal 16m^2.

A number times itself is known as a square number. The value of this square number is 16 m².

It can be shown like this:

a²= 16 m² or a×a = 16 m²

The reverse of squaring numbers is square root. To find the value of one side you can do √16. √16 = 4. We can check this by substituting (replacing) 4 in the place of 'a' to see if the answer is 16.

a×a = 16 m²

4 × 4 = 16

Therefore, the length of one side of the square equals to 4m.

Answer:

7,000

Step-by-step explanation:

6,842 is more than 6,500 so u round to 7,000

Emmy's actual score in the exam is 64.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given,

class average =  76

standard deviation = 8

Z- score = -1.50

The formula of Z-score is -

z = (x-μ)/σ

Where x is the actual score,

μ is the mean,

σ is the standard deviation.

Now putting the values in the formula we get,

-1.50 = (x- 76) / 8

⇒ on solving, we get x = 64

So the actual score of Emmy = 64

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