The line segment joining the points A (5, 3) and B (-3, 11) is divided by the point C (3,5) in the ratio
(a) 1:3 (b) 3:1 (c) 2:3 (d) 3:2​

There are 13 elements of the sample space that will have a green ball.

The various ways in which objects from a set may be selected, generally without replacement, to form subsets.

Since, when a green ball is drawn, three coins are tossed. So, sample points are  OHHH, OHHT, OHTH, and OHTT. OTHH, 0THT, OTTH, OTTT

So, clearly, 9 sample points will have an orange ball.

When a blue ball is drawn, two coins are tossed. So, sample points are BHH, BHT, BTH, and BTT.

So, clearly, 4 sample points will be when a blue ball is drawn.

Total samples points=4+9=13

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The present age of Lia is 35 and the present age of Myra is 5.

The sum of Lia's age and Myra's age is 40.

Let the present age of Myra is x and the present age of Lia is y.

So the equation should be

x + y = 40..................(1)

After 10 year the age of Myra is x + 10 and age of Lia is y + 10.

In 10 year Lia will be three time a older than Myra.

y + 10 = 3(x + 10)

Simplify

y + 10 = 3x + 30

Subtract 10 on both side, we get

y = 3x + 20

Now putting the value of y in the equation 1.

x + 3x + 20 = 40

4x + 20 = 40

Subtract 20 on both side, we get

4x = 20

Divide by 4 on both side, we get

x = 5

The present age of Myra is 5.

Now putting the value of x in equation 1

x + y = 40

5 + y = 40

Subtract 5 on both side, we get

y = 35

The present age of Lia is 35.

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The complete question is:

The sum of Lia's age and Myra's age is 40. In 10 year Lia will be three time a older than Myra. How old is each person?

Number of Excavation                                  Height of Soils(inches)

0                                                                       3 ins

1                                                                        5 ins

5                                                                       13 ins

10                                                                      23 ins

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

It is already noted that when Levi starts digging the hole is already 3 inches dip with soil

In each excavation he digs 2 inches of soil each

So, when number of Excavation is :

Zero :  the inches of soil is 3 inches

One : the inches of soil is 3+2 = 5 inches

Five : the inches of soil is 3+2*5 = 13 inches

Ten :the inches of soil is 3 + 2*10 = 23 inches

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Half a kilogram of mixed nuts costs 36 cents.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Five-sixths of a kilogram costs 60 cents.

That means,

1 kilogram of mixed nuts costs = 60 x 6/5 = 72 cents.

So,

half a kilogram of mixed nuts costs = 72/2 = 36 cents.

Therefore, the required cost is 36 cents.

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Step-by-step explanation:

this means a triangle with one angle 30°, a second angle 60°, and the third angle 90°.

the sides of such a 30-60-90 triangle are always in the ratio of 1 : √3 : 2

that means the Hypotenuse is twice the length of the shorter leg. and the longer leg is square root of 3 times longer than the shorter leg.

30-60-90 Theorem: If a triangle has sides in the ratio x: x 3: 2 x and angles of 30, 60, and, then it is a triangle. The longer leg, the hypotenuse, and the shorter leg are always the same. The Pythagorean Theorem can be used in their place if you ever forget these theorems.

Triangle with sides of 30-60-90

Sides of a triangle with angles of 30–60–90:

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The decimal equivalent of 1101.011 in base 7 is 343.14300.

The decimal system is a base 10 numbering system that is widely used in everyday life.

To convert 1101.011 from base 7 to decimal, we need to start by converting the whole number portion of the value. 1101 in base 7 is equivalent to

=> 1 x 7³ + 1 x 7² + 0 x 7¹ + 1 x 7⁰ = 343

Next, we need to convert the fractional portion of the value. The fraction 0.011 in base 7 is equivalent to

=> 0 x 7⁻¹ + 1 x 7⁻² + 1 x 7⁻³ = 0.143

Finally, we add the decimal equivalent of the whole number portion and the fractional portion to find the decimal equivalent of 1101.011 in base 7.

=> 343 + 0.143 = 343.143,

which is the decimal equivalent of 1101.011 in base 7.

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Josh washed a total of 5 plates if he want to do the dishes after work.

To find the total number of plates washed by Josh:

The scenario describes a person named Josh who had to wash dishes after work.

The method used to find the total number of plates washed by Josh was simple addition. The number of small plates (1) and the number of large plates (4) were added together to find the total number of plates (1 + 4 = 5). This type of problem is usually taught in grade 1 or grade 2, as part of early mathematics education that focuses on basic addition and counting skills.

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the dimensions of rectangle is  l = 23 and w = 14

Given,

A rectangle has perimeter 74 inches, and its area is 322 square-inches

To find the dimensions of this rectangle.

Steps:

With this question it is known that the perimeter of the rectangle is 74 inches and the area is 322 inches. the question is what is the length and width of the rectangle.

The formula for the perimeter of a square is P = l + l + w + w or P= 2(l + w) and the formula for the area of a rectangle is A = l x w.

the formula for the perimeter of a rectangle is P= 2(l + w) that means w=l(p/2-l) and the formula for the area of a rectangle is A = l x w, usually l is longer than w

insert the w equation with the perimeter formula into the area formula A = l (p/2-l) to

solve this equation:    [tex]l\\^{2}[/tex] - ([tex]\frac{P}{2}[/tex]) x l + A=0 to get l

 [tex]l\\^{2}[/tex] - (74/2) l +322=0

 [tex]l\\^{2}[/tex] - 37l + 322=0

(l-23)(l-14)=0 so

l =23 and l=14,

it can be concluded that l = 23 and w = 14

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Answer:

18.84 inches

Step-by-step explanation:

circumference of a circle = diameter x pi

diameter = radius x 2

==> circumference = radius x 2 x pi = 3 in x 2 x 3.14 = 18.84 in

The 6n × 6n board can be tiled with trominoes if n is even.

A tromino is a geometric shape made up of three squares, and a 6n × 6n board is a grid of squares with 6n rows and 6n columns.

The question is whether it is possible to tile a 6n × 6n board with trominoes so that no two overlap and all squares are covered.

In order for a 6n × 6n board to be tiled with trominoes, n must be an even number. This is because each tromino covers three squares and there must be a whole number of trominoes to cover the entire board. If n is even, the board can be tiled with trominoes.

To do so, the board is divided into 2n rows of 3 squares each and 2n columns of 3 squares each. A tromino is placed in each of the resulting 3 × 3 squares, covering all of the squares in the board.

Each tromino covers three squares and the board can be divided into a grid of 3 × 3 squares that can each be filled with a tromino.

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Using fractions subtraction, we know that the original fraction in the given situation is -7/8.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.

So, we have the fraction:
1/8

Now, the original fraction would be:

1/8 - 4/4

1-8/8

-7/8

Therefore, using fractions subtraction, we know that the original fraction in the given situation is -7/8.

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The required simplified solution of the given radical expression is  [tex]\sqrt{15} \times x^{1/6} / \sqrt[3]{10} \times y[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a radical expression,
[tex]= \sqrt{15xy} / \sqrt[3]{10xy^3}[/tex]

Now, [tex]\sqrt{15xy} = [15xy]^{1/2}[/tex] and [tex]\sqrt[3]{10xy^3} = [10xy^3]^{1/3}[/tex]
[tex]= [15xy]^{1/2}/ [10xy^3]^{1/3}\\[/tex]

After simplifying the above expression,
= [tex]\sqrt{15} \times x^{1/6} / \sqrt[3]{10} \times y[/tex]

Thus, the required simplified solution of the given radical expression is  [tex]\sqrt{15} \times x^{1/6} / \sqrt[3]{10} \times y[/tex].

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Logarithm ln3 is approximately 1.682.

Logarithm, the exponent or power to which a base must be raised in order to produce a specific number.

The linear approximation of the natural logarithm function near x=e is given by y ≈ ln(e) + (y'(e))(x-e), where y'(e) is the derivative of the logarithm function at x=e.

Since ln'(x) = 1/x, we have y'(e) = 1/e.

Substituting x=3 and e=2.71828... into the approximation, we get:

ln(3) ≈ ln(e) + (1/e)(3-e) = ln(e) + (3-e)/e

ln(e) = 1, so the result is:

ln(3) ≈ 1 + (3-e)/e ≈ 1 + 0.682 ≈ 1.682.

Hence, ln3 = 1.682.

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As per the initial-value problem, the formula for the solution is dy/dt = y³

An initial-value problem, which involves finding a formula for a solution based on an initial value and a differential equation.

In this specific problem, the differential equation is

=> dy/dt = y³

and the initial value is

=> y(0) = 1.

To solve for the formula, we will use mathematical techniques to find the solution for y based on the given conditions.

The domain of the definition of the solution refers to the set of all possible values for the independent variable (t in this case) for which the solution is valid. In this problem, the domain of the solution is determined by the conditions that ensure the solution is well-defined.

As the solution approaches the limits of its domain, certain properties of the solution may change.

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The Department of Energy was also eager to sign on, in part because it wanted to learn about how radiation causes genetic mutations.

An modification in the nucleic acid sequence of an organism's, virus's, or extrachromosomal DNA is referred to as a mutation. DNA or RNA can be found in the viral genome.

Any alteration to a cell's DNA sequence. Mistakes in cell division can result in mutations, as can exposure to environmental DNA-damaging substances.

Ionizing radiation may harm genetic material (mutations) in gonads or germ cells, which can result in disorders with a genetic component (hereditary defects). Malformations, metabolic issues, immune system deficits, etc. might occur from them.

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The possible additional amount he will spend more than 15.

An inequality is a relationship that denotes a non-equal comparison between two numbers or mathematical expressions.

According to  the question,

Let Amy, will spend $c additional amount.

Amy will spend more than $32 on gifts.

He spent $17.

We solved this question by using inequality.

The inequality equation is:

  c + 1 7 > 32

    c > 32 -17  ( by changing the sign)

     C > 15

So, the possible additional amount he will spend more than 15.

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Answer:

If angle B is 60 and angle C is 70, We can make an equation by:

180 - (60+70)

The answer for this equation will be 50.

According to the upper equation, angle A is 50, angle B is 60, and angle C is 70.

Answer:

c.

the length of WZ is

[tex] \sqrt[3]{13} [/tex]

The linear equation of line will be y=4/7x-6/7.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

From graph take two point on line

(x1,y1),(x2,y2)=(5,2)(-2,-2)

As standard equation of a line is y=mx+c

where m=slope and c=constant

m=(y2-y1)/(x2-x1)

m=(-2-2)/(-2-5)=4/7

then equation of line will be

y-y1=4/7(x-x1)

y-2=4/7(x-5)

y=4/7x-20/7

Hence,

           The linear equation of line will be y=4/7x-6/7 in form of y=mx+c.

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A soccer ball in the air for time 4.929 seconds.

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory

The vertical position of a projectile launched from the ground with velocity  v and angle  θ  is:

y(t)=−4.9t^2+(vsinθ)t

We can factor this as:

y(t)=t(−4.9t+vsinθ)

Now we know that  t=0  is one root, when you first kick it, so we only need to solve for the other root

−4.9t+vsinθ=0

t=vsinθ/4.9

Plugging in what we have:

t=25sin61/4.9

t = 25 *0.96611777 /4.9

t≈4.929 sec

So about  4.929 seconds.

A soccer ball in the air for time 4.929 seconds.

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Answer:

True

Step-by-step explanation:

the function is y = x/5

The Transformation of the function f(x) = log₅(x) to g(x) = 3 - log₅(x) is a vertical reflection followed by a vertical translation.

(i) The original function f(x) = log₅(x) is first reflected over the x-axis, which changes the sign of the function. The result is a graph that is upside-down compared to the original. the function becomes -log₅(x)  .

(ii) Next, the transformed function g(x) is shifted up by 3 units, which results in the vertical translation of the graph. This transformation changes the range of the original function, but the shape of the graph remains unchanged.

So , the function becomes g(x) = 3 - log₅(x).

Therefore , The transformation of f(x) to g(x) changes the orientation of the graph and shifts it vertically, but does not affect its shape.

The given question is incomplete , the complete question is

The function f(x) = log₅(x) , is transformed to g(x) = 3 - log₅(x).

Describe the transformation.

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Answer:

1 and 1/6

Step-by-step explanation:

You have to add together the growth of the 2 weeks. So, 1/3 + 5/6 but to add these you need to find the common denominator. I would change 1/3 to have a denominator of 6. To turn 3 into 6 you have to multiply by 2 and whatever you do to the bottom you do to the top so 1 x 2. Now that your fraction of 1/3 is 2/6, you can add the 2 weeks together. 2/6 + 5/6 = 7/6, which can also be written as 1 and 1/6.

By taking a quotient we will see that he has saved $450.

On the first month Lance earnesd $546, and on the second month he earned $354.

Adding these we get:

$546 + $354 = $900

So he earned a total of 900 dollars between April and June. And we know that he saves half of that, then the amount saved is equal to that divided by 2:

$90/2 = $450

He has saved 450 dollars.

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If the two-dimensional shape produced by a horizontal slice through the solid is a trapezium, the solid is likely to be a trapezium prism. The correct answer would be an option (D).

When you make a horizontal slice through a solid, it cuts through the object along a plane and the shape that is produced is the cross-section of that plane.

A rectangular prism will produce a rectangle.

A pentagonal prism will produce a pentagon.

A square prism will produce a square.

A trapezium prism will produce a trapezium.

A hexagonal prism will produce a hexagon.

Therefore, if the two-dimensional shape produced by a horizontal slice through the solid is a trapezium, the solid is likely to be a trapezium prism.

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The box should have inches for its length, width, and height. 2. Divide the result of multiplying the length, breadth, and height by 1,728. In cubic feet, this represents the container's volume.

As such, it is listed here for documents that can simply be destroyed.

The instructions below can be used to calculate a container's cubic foot volume.

In cubic feet, this represents the container's volume.

A case in point

18"L x 11.5"W x 9"H = 1,863 cubic inches

1,863/1,728 equals 1.078 cubic feet.

The aforementioned container has a volume of 1.1 cubic feet (round to the nearest tenth).

The Complete Question.

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The linear equation for this scenario could be: y = 5x + 77, where y represents the total amount of money Finn has after cooking x number of meals and 77 is the initial amount owed to his mom.

A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

Ax+By=C is the typical form for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to get both intercepts when an equation is stated in this way (x and y).

As per the data given,

The total amount Finn has = $ 77.

Amount spent on meal = $5 per meal.

Total number of meal = x

So, the amount spent on taking x meal will be = 5*x = 5x

Hence, the required linear equation will be: y = 5x + 77

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∠AGH = ∠GHD = 60° (alternating angles)

∠EGB = ∠AGH = 60° (Vertically Opposite Angles)

Coplanar infinite straight lines that are parallel have no points of intersection. In the same three-dimensional space, parallel planes are any planes that never cross. Curves that are parallel to one another and maintain a predetermined minimum distance do not touch or intersect.

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.

According to the alternative angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent. To demonstrate: If a transversal cuts two parallel lines, then the opposing interior angles are equal.

It is given that AB and CD are parallel to each other

EF is the transversal

∠GHD = 60°

∠AGH = ∠GHD = 60°(alternating angles)

∠EGB = ∠AGH = 60° (Vertically Opposite Angles)

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are  –6x + 15 < 10 – 5x  and an open circle is at 5 and a bold line that starts at 5 and is pointing to the right which is denoted as option C and D.

This is referred to as a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Workings:

-3(2x-5)<5(2-x)

-3(2x-5)<5(2-x)

-6x+15<10-5x --- C

Subtract 15 from both the sides of the inequality

-6x + 15 -15 < 10 -5x -15

-6x < -5 -5x

-6x +5x < -5

-x < -5

Multiply both sides by (-1) ,

x > 5 .

x> 5 on the number line depicts an open circle is at 5 and a bold line starts at 5 and is pointing to the right .

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The full question is:

Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.

(a) x < 5

(b) –6x – 5 < 10 – x

(c) –6x + 15 < 10 – 5x

(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.

(e) A number line from negative 7 to 3 in increments of 1,  An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.