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Simplify the imaginary number...

The age of Marcus now is 20 years as 8 years ago Marcus was 12 years old.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.

Let his age now be x.

x-8=12

x=20

Marcus is currently 20 years old, although he was 12 years old eight years ago.

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A system of linear inequalities that represents this scenario is given by:

p + s ≥ 10

5.50p + 3.50s ≤ 117

An inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In order to write a system of linear inequalities to represent the scenario, we would assign variables to the cost of the beginner class and advanced class, and then translate the word problem into algebraic equation as follows:

Since Latisha cannot buy more than (≥) 10 vegetables, the inequality to represent this is as follows:

p + s ≥ 10

Since Latisha's budget cannot exceed (≤) $117, the inequality to represent this is as follows:

5.50p + 3.50s ≤ 117

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The fraction of 1/6 is equivalent to this following decimal number:

0.166.

A fraction is represented by the division of a term x by a term y, as follows:

Fraction = x/y.

The terms that represent x and y are given as follows:

In this problem, the fraction is given as follows:

1/6.

1 is less than 6, hence the equivalent decimal can be obtained as follows:

0.10/6.

10 divided by 6 is one with a remainder by 4, hence 1.4/6 = 1.6667.

Thus the equivalent decimal representing the fraction 1/6 is given as follows:

1/6 = 0.1666.

The problem asks for which decimal number the fraction 1/6 is equivalent.

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The correct result would be (x, y) = (5, 17); because both lines pass through this point.

Given,

In the question:

Two lines. C and D are represented by the equations.

We have :

Line C. y = x + 12

Line D. y = 3X + 2

Now, According to the question:

y = x + 12

y = 3X + 2

Substitute into one of the equations

x + 12 = 3x + 2

Solve the equation:

Combine like terms:

x - 3x = 2 - 12

-2x = -10

x = -10/-2

x = 5

Put the value of x in equation of Line C

y = x + 12

y = 5 + 12

y = 17

Hence, The correct result would be (x, y) = (5, 17); because both lines pass through this point.

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The equation that has x = -11 as the solution is given by -

y = x + 11

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following equation that has a variable on both sides and x = -11 as a solution.

An equation of a straight line can be used to depict the problem given. We can write the equation as -

y = x + 11

Therefore, the equation that has x = -11 as the solution is given by -

y = x + 11

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Answer: 25 cents i am sorry if this is wrong

Step-by-step explanation: 3 dimes are 30 cents plus 50 is 80 plus 35 is $1.15 so then when she removers 3 nickles she is getting rid of 15 cents which would leave $1.00 finally when you remove 75 cents you have 25 cents

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

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You started with a total of 28 muffins

From the question, the given parameters are:

Proportion carried away = 16 of the total muffins

Proportion carried away = 4/7 of the total muffins

The above parameters implies that

4/7 of the total muffins = 16

Represent the amount you started with x

So, we have the following representation

4/7 of x = 16

Express as products

4/7x = 16

Make x the subject

x = 7 * 16/4

Evaluate

x = 28

Hence, the total number of muffins is 28

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Answer:

The answer should be -5/2

Step-by-step explanation:

To find the slope take two plots from the table:

(-2,6) and (0,1)

M= y2-y1 / x2-x1

M= 1-6 / 0--2=-5/2

Answer:

67.5 (rounded down to 67, usually)

45/2 is 22.5 so that is for one hour

22.5 x 3 = 67.5

Answer:

add me on brainliest please

Step-by-step explanation:

65 is the answer

The altitude of the original pyramid is about 75.11 units

Given that,

Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :

Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.

(Height ratio)^2 = 1/2

((h -22)/h) ^ 2 = 1/2

(h-22) / h = 1/[tex]\sqrt{2}[/tex]

h-22 = h /[tex]\sqrt{2}[/tex]

h = 75.11 units

Consequently, the original pyramid's altitude is around 75.11 units.

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Answer:

14

Step-by-step explanation:

[tex]\frac{4 \text{ miles}}{1 \text{ hour}} \times 3.5 \text{ hours}=14 \text{ miles}[/tex]

The statement ""what goes up must come down. the ball went up. it will come down." can be reached through a deductive reasoning.

The mental process of forming deductive deductions is known as deductive reasoning. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if the premises cannot be true while the conclusion is false.

The primary distinction between inductive and deductive thinking is that inductive reasoning seeks to develop a hypothesis, whereas deductive reasoning seeks to test an existing theory. Inductive thinking proceeds from individual observations to broad generalizations, whereas deductive reasoning proceeds in the other direction.

In conclusion, the correct option based on the information is a deductive reasoning.

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Answer:

  Barlow School has 178 more boys

Step-by-step explanation:

At Barlow School, 4/9 of 873 students are boys. At Willow School, 2/3 of 630 students are girls. You want to know which school has more boys, and by how many.

The number of boys is ...

  4/9 × 873 = 388

The 1/3 of students that are not girls are presumed to be boys. That number is ...

  1/3 × 630 = 210

The difference in the number of boys is ...

  388 -210 = 178

Barlow School has 178 more boys.

For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years.

As given in the question,

The formula given to us is A = P[tex]e^{rt}[/tex] where

A = accumulation value

P = principal money

t = time period

r = interest rate compounded

P = 9500

A = 2*9500

r = 0.12

By applying it in the given formula we get

19000 = 9500 * [tex]e^{0.12t}[/tex]

2 =    [tex]e^{0.12t}[/tex]

Take natural log on both sides

㏑(2) = 0.12t

0.6931 = 0.12t

t = 5.775

Therefore , For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years after rounding it off to one place after decimal.

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0.3814 is the probability that the sample contains two white balls and two red ones .

What is probability in math?

Total number of balls = 8 + 12 = 20

Total number of elementary cases

           = ( 20 4 )

Total number of favourable cases

           = ( 8 2 ) * ( 12 2 )

Required probability

   = ( 8 2 )  *  ( 12 2 )/( 20  4 )

 = 0.3814

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The width is 5 units.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

length = width + 1

let the width be x

length= x+ 1

So, area of rectangle= l x w

30 = x( x+ 1)

x² + x - 30=0

x² + 6x - 5x - 30=0

x( x+ 6) - 5(x +6)= 0

(x+ 6)( x- 5)= 0

x= -6 or 5

Hence, the width is 5 units.

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A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

0.40(85) + 0.12(34)

34 + 4.08

38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

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Answer:

2. 25

max = 88 feet

See the attachment photo!

The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.

Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.

The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.

Perimeter = x+2y

100 = x+2y

100 = 50+2y

2y = 50

y = 25

Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.

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Assuming it is a standard deck of 52 cards and a standard dice of 6 faces.

There are 13 heart cards in a standard deck, therefore the odd of getting a heart is 13 : 52 = 1/4.

There is only 1 six in a standard dice, therefore the odd of getting a six is 1/6.

For these events to happen simultaneously, we multiply the chances.

Therefore, the chance of getting a heart in a deck of cards and a six on a dice is 1/4 x 1/6 = 1/24.

Answer:

heart from a deck of cards= 13/52 = 1/4

getting a six on a dice= 1/6 = 1/6

Step-by-step explanation:

heart from a deck of cards :

In the context of ordinary maths questions the answer is so obvious as to almost not be worth mentioning. There are 52 cards in an ordinary deck and 13 of them have heart pips, so 13/52 = 1/4.

six from a dice :

There is a 1/6 chance of rolling a 6. There are only 6 sides on a die, and only 1 of them is 6, so there is a 1/6 chance of rolling a 6.

at the same time is:

13/15 + 1/6 = 31/30 = 1/30

Answer:

It would be the last graph (c). It would look like the image below.

Explanation:

Since 3 is negative the answer would have a graph with a line going like this \.

The dimensions that maximize the area are 150ft × 300ft.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

The rectangular pen's surface area is:

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

The value of y is: for x=150

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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The sample size that should be used is 43.

Given that;

The weight of a cereal box is measured as part of a statistical quality control process for the manufacture of cereal. It is understood that the population standard deviation is 0.06 ounces. To attain a margin of error of and a confidence level of 97% 0.02 ounces.

By considering the confidence level scenario, we get to solve how large a sample should be utilized.

The significance level is (α) = 0.03 ( 97% confidence level )

The critical value is (z*) = 2.17 ( From z-table )

The population standard deviation (σ) = 0.06

The margin of error (E) = 0.02

Therefore, the required sample size is;

n = [(z* × σ)/E ]²

n = 42.383

n ≅ 43

Finally, the sample size that should be used is 43.

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The value of x in the given isosceles triangle is x = 15

From the question, we are to determine the value of x.

From the given information,

The length of the base of the isosceles triangle is x

Also,

The length of a leg is 4x - 3

Since, the length of the legs of an isosceles triangle are equal,

Then,

The length of the other leg is 4x - 3

Also, form the given information,

The perimeter of the triangle is 129

Thus,

x + 4x - 3 + 4x - 3 = 129

Now, solve for x

x + 4x - 3 + 4x - 3 = 129

Collect like terms

x + 4x + 4x = 129 + 3 + 3

9x = 135

Divide both sides by 9

9x/9 = 135/9

x = 15

Hence, the value of x is 15

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If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.

D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

A horizontal line now has zero slopes.

The new road has a zero slope as a result.

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