1. Jack buys small tins of tomatoes every week. They usually cost 50¢ each. Last week,
however, Jack saw that the shop was selling six large tins of tomatoes plus a bag of
pasta for $7.50. He worked out that the pasta was normally $2. Jack decided that he
could use one large tin of tomatoes instead of two small tins so he bought 18 large tins
of tomatoes together with three bags of pasta.
This week, however, the small tins of tomatoes are on offer at $1.60 for a pack of four.
How much more did Jack pay last week for tinned tomatoes than if he had bought them
this week?
Answer is in what unit?

Integer Numbers

It can be defined as the number that can be written without a fractional (decimal) component.

Integers can be positive, negative, or 0.

From the numbers on the list only -4, 0, and 2 are integers. The rest of the numbers cannot be written without a decimal component.

For example:

-2/3 = -0.666

π = 3.14

The square root of 6 is 2.45

4.111... has an evident decimal component.

Answer: -4, 0, and 2

If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

Total number of registered voters in Central city = 29791 voters

Total number of voting centers = 93 voting centers

The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers

Substitute the values in the equation

The number of population serves by each center = 29791/93

= 320.33

≈ 320

Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

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Answer:

126

Step-by-step explanation:

90 ÷ 10 = 9

9 × 4 = 36

90 + 36 = 126

Answer:

d. y= 2x³

Step-by-step explanation:

All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.

The volume of blocks = 27n³cm3.

volume of the cube box = 216n⁹ cm3.

Here given,

6n³cm is the length of the cube-shaped box's side.

3n cm is the side length of the cube-shaped blocks.

We must calculate the volume of the box and the blocks.

The formula for cube volume is,

S³ = V

where s is the cube's side length

by substituting the values,

(6n³)³ cm3 box volume

= 216 n⁹ cm³

(3n)³ cm3 is the volume of the blocks.

= 27n³ cm³

As a result, the volume of the blocks is 27n³cm3 and the volume of the box is 216 n⁹ cm³.

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Answer:

A)  Volume of one block = 27n³  cm³

     Volume of the box = 216n⁹  cm³

B)  8n⁶ blocks will fit in one box.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cube}\\\\$V=s^3$\\\\where:\\ \phantom{ww}$\bullet$ $V$ is the volume. \\\phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]

The side length of the cube-shaped block is 3n cm.

Substitute the given side length into the formula to find the volume of the block:

[tex]\begin{aligned}\implies \textsf{Volume of one block}&=(3n)^3\\&=3^3 \cdot n^3\\&=27n^3\;\sf cm^3\end{aligned}[/tex]

The side length of the cube-shaped box is 6n³ cm.

Substitute the given side length into the formula to find the volume of the box:

[tex]\begin{aligned}\implies \textsf{Volume of one box}&=(6n^3)^3\\&=6^3 \cdot (n^3)^3\\&=216n^9\; \sf cm^3\end{aligned}[/tex]

To find the number of blocks that will fit in the box, divide the volume of the box by the volume of one block:

[tex]\begin{aligned}\implies \textsf{Number of blocks}&=\dfrac{\textsf{Volume of box}}{\textsf{Volume of block}}\\\\& = \dfrac{216n^9}{27n^3}\\\\&=\dfrac{216}{27} \cdot \dfrac{n^9}{n^3}\\\\&=8 \cdot n^{9-3}\\\\&=8n^6\end{aligned}[/tex]

Answer:

k = ± [tex]\sqrt{\frac{2A-3t\p}{\pi } }[/tex]

Step-by-step explanation:

2A = πk² + 3t ( subtract 3t from both sides )

2A - 3t = πk² ( isolate k² by dividing both sides by π )

[tex]\frac{2A-3t}{\pi }[/tex] = k² ( take square root of both sides )

± [tex]\sqrt{\frac{2A-3t}{\pi } }[/tex] = k

The number of two pt problems are 30 and 5 pt problems are 8.

Two or more expressions with an Equal sign is called as Equation.

Let x= one type of question

Let x-22= the other type of questions

100=2x+5(x-22) Distribute

100=2x+5x-110

100=7x-110

100+110=7x

210=7x

Divide both sides by 7

one type 30=x

second type 30-22=8

Hence the number of two pt problems are 30 and 5 pt problems are 8.

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The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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The equations of the lines are:

7. y = 3/2x - 3/2

8. y = -1/3x - 8/3

The equation that represents a line, in slope-intercept form is, y = mx + b.

7. Find the slope (m) between (5, 6) and (1, 0):

Slope (m) = (6 - 0)/(5 - 1) = 6/4

Slope (m) = 3/2

Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:

0 = 3/2(1) + b

-3/2 = b

b = -3/2

To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:

y = 3/2x - 3/2

8. Find the slope (m) between (-5, -1) and (1, -3):

Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6

Slope (m) = -1/3

Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:

-3 = -1/3(1) + b

-3 = -1/3 + b

-3 + 1/3 = b

-8/3 = b

b = -8/3

To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:

y = -1/3x - 8/3

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a. np = 8.91 and nq = 18.09 where n = 27 and p = 0.33

b. np = 3.75 and nq = 21.25 where n = 25 and p = 0.15

c. np = 9.68 and nq = 34.32 where n = 44 and p = .22

a. Given n =  27

          p = 0.33

np = 27 x 0.33

     = 8.91

nq = 27 x (1 - 0.33)

    = 18.09

For the approximation of binomial distribution, the sample size must be greater than 10 for both the products np and n(1-p) to approximate the binomial distribution by a normal distribution.

Since here np < 10 approximation is not applicable.

μp = np = 27 x 0.33  

             = 8.91

σp = √npq = √(27)x (.33) x (1 - 0.33)

              = 2.443

b.  n = 25 and p = 0.15

   np = 25 x 0.15

         = 3.75

   nq = 25 x (1 - 0.15)

    = 21.25

Approximation is not possible because np < 10.

c. n = 44 and p = .22

   np = 44 x 0.22

         = 9.68

   nq = 44 x (1 - 0.22)

    = 34.32

Since here np< 10 approximation is not possible.

μp = np = 44 x 0.22  

             = 9.68

σp =√npq = √(44)x (.22) x (1 - 0.22)

              = 2.747

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A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

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The value of x in the triangle is 3.

The exterior angle of the triangle is VBC.

Using the exterior angle theorem, the value of x can be found in the triangle.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Therefore,

m∠D = 9x - 2

m∠C = 40°

m∠VBC = 20x + 5

Hence,

20x + 5 = 9x - 2 + 40

20x + 5 = 9x + 38

20x - 9x = 38 - 5

11x = 33

x = 33 / 11

x = 3

Therefore,

x = 3

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Hey there!

2v - 7 - 12v + 15
COMBINE the LIKE TERMS

= (2v - 12v) + (-7 + 15)

= 2v - 12v - 7 + 15

= -10v + 8

Therefore, your answer should be:

-10v + 8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: Relation

Step-by-step explanation: it is a relation because if you take any number on the x axis and look at its points there are two points on multiple parts

Answer:

Length in inches → 11

1 inch = 2.5 centimeters

Length in Centimetres → 11 × 2.5 → 27.5 cm

letter D is the answer

For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is

and the line equation will be:

For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:

and the line equation will be:

For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero

Answer:

The perimeter is 12 units.

Step-by-step explanation:

The answer would be 12 units because each side is 1 unit. If you count all the sides together, you get 12 units.

Answer: 12 units

Step-by-step explanation:

       The perimeter is the length around a 2D shape. We will count the units that make up this shape's outline. See attached. Please note that as long as you count every side for this shape, it doesn't matter the order you count.

       The perimeter is 12 units, the last option.

Answer:

-16

Step-by-step explanation:

fog(18)=f(g(18))

g(18)=[tex]\sqrt{18-9} =\sqrt{9} =3[/tex]

f(3)=-8(3)+8

=-16

Using ratio and proportion, Louie is correct.

Ratio is defined as the relationship between two quantities. On the other hand, proportion is defined as the equality between two or more ratios.

From the given graph (see attached photo), the coordinates of Point F and Point G is (4, 8) and (-6, -7).

If the ratio of FP to PG is 4 to 1, then the ratio of the horizontal distance and vertical distance between the two endpoints is also 4 to 1.

FP : PG = 4 : 1

FP/PG = 4/1 = 4

x-coordinate of P

(4 - x)/(x - -6) = 4

(4 - x) = 4(x + 6)

4 - x = 4x + 24

-5x = 20

x = -4

y-coordinate of P

(8 - y)/(y - -7) = 4

(8 - y) = 4(y + 7)

8 - y = 4y + 28

-5y = 20

y = -4

Hence, the coordinates of Point P is (-4, -4).

Therefore, Louie is correct, while Nicky is mistaken probably while setting up the proportion and solving for the coordinates.

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Answer:

Step-by-step explanation:

Substitute and calculate:

We have that:

then, in this case, we have:

therefore, the velocity of the cart is 0.9 meters per second.

The number of sheets of toilet paper that have not been used is 193473.

Multiplication simply has to do with the product of numbers.

From the information, the roll had 969696 sheets when it was new and the person used 999 sheets of toilet paper each day for 777 days.

Therefore, the sheet left will be:

= Number in the new roll - Sheets used

= 969696 - (777 × 999)

= 969696 - 776223

= 193473

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Answer:

Inconsistent: parallel lines.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]

Use arithmetic operations to isolate y in the second equation:

[tex]\implies -12x+3y+12x=3+12x[/tex]

[tex]\implies 3y=12x+3[/tex]

[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]

[tex]\implies y=4x+1[/tex]

Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.

The solution to a system of linear equations is the point of intersection.

As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.

A)

If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:

B)

If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):

Answer:

4:2 and 14:7

Step-by-step explanation:

The ratios equivalent to 8:4 would be:

4:2

14:7

5:10 wouldn't be equivalent because if you simplify that, it is 1/2 and if you simplify 8/4, it is 2. 1/2 and 2 are not the same.

:D

Answer:

They are all equivalent except for 5:10

Step-by-step explanation:

You can write ratios as fractions

[tex]\frac{8}4}[/tex]   [tex]\frac{4}{2}[/tex]  [tex]\frac{14}{7}[/tex]   [tex]\frac{5}{10}[/tex]  If I simplify each fraction, I can see that they all equal 2 expect for the the last one.

2   2   2   1/2

The value of x = -12.

Define Function.

A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")

The given expression is

H(x)=-5/6 x

also, H(x) = 10

so, put H(x) value in given expression,

10 = -5/6 x

Now, solve for 'x'

-5x = 60

x = 60/(-5)

x = -12

Therefore, the value of x = -12

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The distance between the translated points C and D is 5 units

From the question, the coordinates are given as

A (-2,3) , B (3,3) , C (4,6) , and D (-1 , 6)

The sequence of transformations is given as

The above sequence of transformations are rigid transformations.

This means that the lengths are preserved

In other words,

CD = C'D'

So, we have the distance to be

Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]

Where

(x, y) = C (4,6) , and D (-1 , 6)

So, we have

Distance = √[(4 + 1)² + (6 - 6)²]

Evaluate

Distance = 5

Hence, the distance is 5 units

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The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).

Linear equation:

Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.

Given,

Here we have the following system of linear equations.

2x + 3y = 6

-3x + 5y = 10

Now, we need to find the solution for the equations.

Here we have to use the substitution method to solve this one,

To do the substitution method we have to follow the following steps:

Step 1) Solve anyone of the equations either for the variable x or y

Step 2) Now, substitute the value obtained from step 1 to the other equation

Step 3) Finally, solve the equation to find the value of the remaining variable.

Here we have to take the equation (2), and we have to solve it for the value of y,

For that we have to rewrite the equation as,

5y = 10 + 3x

y = (10 + 3x)/5

Apply the value of y on the equation (1), in order to get the value of x,

So,

2x + 3(10 +3x)/5 = 6

2x + (30 + 9x)/5 = 6

(10x + 9x + 30)/5 = 6

19x + 30 = 30

19x = 0

x = 0

Now, apply the value of x on the equation in order to get the value of y,

y = (10 + 3(0))/5

y = 10/5

y = 2.

Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).

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Answer:

y = 5

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

AB = CD , that is

7y = 3y + 20  ( subtract 3y from both sides )

4y = 20 ( divide both sides by 4 )

y = 5