Make the mathematical expressions. Simplify them and find the correct answers. a) The total cost of 4 pens at Rs 20 each, 5 pencils at Rs 5 each and 2 boxes at Rs 60 each. ​

The area of the window that lets in the most light will be the one that causes the window to transmit the most light overall.

To find the proportions of the window that will admit the lightest, we need to maximize the total area of the window while keeping the perimeter fixed. The total area of the window is the sum of the area of the rectangle and the area of the semicircle. The area of the rectangle is the product of its length and width, and the area of the semicircle is half the product of its radius and the area of a full circle with the same radius.

Since the perimeter is fixed, the length and width of the rectangle are also fixed. The radius of the semicircle can be found using the perimeter and the length and width of the rectangle.

Once we have the radius of the semicircle, we can find the area of the rectangle, the area of the semicircle, and the total area of the window. Since the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does, we will have to multiply the area of the semicircle by 0.5 to find the total amount of light transmitted by it.

Finally, we will have to compare the total amount of light transmitted by the window for different values of the length and width of the rectangle. The proportion of the window that admits the most light will be the one that results in the maximum total amount of light transmitted by the window.

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Definition of Ray:

'A part of a line that has one endpoint and extends indefinitely in one direction'.

The correct statement is A.

A ray is a part of the line having one fixed point and the other point does not have an end. It means that a ray has one terminating end and the other end is extending infinitely.

Given definitions of ray:

A. a part of a line that has one endpoint and extends indefinitely in one direction.

B. the set of all points in a plane that are a given distance away from a given point.

C. lines that lie in the same plane and do not intersect.

D. a part of a line that has two endpoints.

Only statement A satisfies the definition of ray.

Hence, the definition of ray is described by statement A.

A part of a line that has one endpoint and extends indefinitely in one direction.

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Answer:

It would look like that I think

Step-by-step explanation:

All 45-45-90-degree triangles have sides that are in a unique ratio. The two legs are exactly the same length.

This triangle is important because any time we're given one side of a 45-er triangle, we can figure out the other two sides.

The 30-60-90 degree triangle is half of an equilateral triangle, cut straight down the middle along its altitude. This triangle has angles of 30°, 60°, and 90°.

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Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.

Let's first try to understand what is a fraction.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction would be 5/10, for instance.

Here, the numerator is 5 and the denominator is 10.

6/8 is a fraction.

6/8 can be simplified further.

6/8 = 3/4

9/12 is also a fraction.

9/12 can be simplified further.

9/12 = 3/4

To compare 2 fractions first we try to make the same denominator.

we have the same value. so they are equivalent.

Given question is incomplete complete the question here:

Are 6/8 and 9/12 equivalent?

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999.06ft999.06 in feet is the ladder.

Pythagorean Theorem is a mathematical formula used to calculate the length of the sides of a right triangle. It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, which is known as the hypotenuse. The formula is written as a² + b² = c², where a and b are the two shorter sides, and c is the hypotenuse.

To find the length of the ladder, use the Pythagorean Theorem. The length of the ladder is equal to the square root of the sum of the squares of the side lengths of the right triangle formed by the ladder and the wall.

The two side lengths of the right triangle are 999\,\text{ft}999ft999, start text, f, t, end text and 3\,\text{ft}3ft3, start text, f, t, end text.

Therefore, the length of the ladder is equal to the square root of (999^2+3^2), which is equal to 999.06\,\text{ft}999.06ft999.06,

start text, f, t, end text.

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Answer:

5

Step-by-step explanation:

0-6x will be -6x if we divide that six then we will get -30/-6 since minus gets cancelled we will be left with 5

On solving the provided question, we can say that the values of the equation here will be y +1 = 8X 8y = 16 => y = 9.455

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y+1= -4(x - 2) 2x8y = 16​

x = 0

y +1 = 8X 8y = 16

y = 9.455

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Answer:

Step-by-step explanation:

Consider the following:

a) y=0.25x+7

b) $10.75

Explanation:

a)

y=mx+b is the slope-intercept form.

B is our Y intercept meaning any fee or initial charge that adds to total cost. In this situation, the initial fee of $7 is our Y-Intercept. . Our mx is the slope. A slope increases based on the amount (x) of certain things you have. In this situation, you are buying maybe 1, 2 or 3 tickets and each ride costs $0.25.

Our x remains the same, that is where we plugin the amount of tickets we will buy (x). The M value is the price per ticket which as said, is $0.25 per. Our slope therefore will be 0.25x.

Combining our Y-Intercept and our Slope will leave us with y (total cost) = 0.25x + 7

b)

We have found our slope, 0.25x+7

Now, we have to plugin our number of rides (x) which is 15.

If done correctly it should be 0.25(15)+7 and that is equal to $10.75 for 15 rides.

Jackie spends 15 minutes running every day.

Part A: The relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day can be represented by the following pair of linear equations:

Equation 1: x + y = 55 (This equation represents the total amount of time Jackie spends running and dancing every day, which is 55 minutes)

Equation 2: y = x + 25 (This equation represents the relationship between the number of minutes Jackie runs and the number of minutes she dances, which is that she dances 25 minutes longer than she runs)

Part B: To find out how much time Jackie spends running every day, we can substitute the second equation into the first equation:

x + (x + 25) = 55

2x + 25 = 55

2x = 30

x = 15

Therefore, Jackie spends 15 minutes running every day.

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Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

Answer:

13

Step-by-step explanation:

mean= (10+19+20+13+13+2+10+8+25+10)/10=130/10=13

The mean number of first cousins for the given sample is 13. Thus, Option C is correct.

Mean is the arithmetic average of the given set of observations.

Mean for ungrouped or raw data is obtained by adding all the observations and dividing it by the number of observations.

Mean = Sum of all the observations/ Total number of observations.

Mean = ∑( x1 + x2 + x3 .... xn /n)

Where X bar represents mean, n is no. of observations and ∑ denotes sigma i.e. sum of all the values.

No. of observations (n) =10

Mean = ∑ (10 + 19 + 20 + 13 + 13 + 2 + 10 + 8 + 25 + 10) / 10

Mean = 130 / 10

= 13

Therefore, Option C is the correct answer.

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The exponential function y = a · 2ⁿ ⁻ ¹, where a is any real number, is generates the geometric series.

Geometric series are sets of elements generated by exponential functions of the form:

y = a · bⁿ ⁻ ¹, where a and b are real numbers and n is a natural number.

Where:

According to the statement, we derive the following expression between the two sums:

9 · a · (1 + b + b²) = a · (1 + b + b² + b³ + b⁴ + b⁵)

Now we proceed to simplify and find the value of b:

8 · a · (1 + b + b²) = a · (b³ + b⁴ + b⁵)

8 · (1 + b + b²) = b³ + b⁴ + b⁵

b⁵ + b⁴ + b³ - 8 · b² - 8 · b - 8 = 0

Then, the value of b by numerical methods is equal to 2.

The geometric series is generated by the exponential function y = a · 2ⁿ ⁻ ¹, where a is any real number.

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Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : (X-5)-1

Thus,

after substituting the value of x with 9

We get,

=> (X-5) -1

=>(9-5)-1

=> 4 -1

=> 3

Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

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Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:

$60.

Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.

The amounts of each item are given as follows:

36, 48 and 24.

Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:

36 - 48 - 24|2

18 - 24 - 12|2

9 - 12 - 6|3

3 - 4 - 2

Hence:

gcf(36, 48, 24) = 2² x 3 = 12.

Which is the number of packages. As each package sells for $5, the amount earned is given as follows:

12 x 5 = $60.

Each package is composed by:

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Answer:

16

Step-by-step explanation:

16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.

Answer:

[tex]$x=\boxed{16}$[/tex]

Step-by-step explanation:

Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.

To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.

Therefore, $x=\boxed{16}$.

Answer:

3

Step-by-step explanation:

Given,

v = 54

l = 6

w = 3

To find : Value of h = ?

Formula : -

v = lwh

h = v/lw

h = 54/( 6 × 3 )

= 54/18

h = 3

Hence, the value of h is 3.

Answer: c=23

Step-by-step explanation: Honest guess

Answer:

10 students are wearing shirts other than blue or white.

Step-by-step explanation:

1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.

2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.

Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.

There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

Answer:

288

Step-by-step explanation:

32 x 9=288

By using formula and solving, Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t

A collision is an event in which two or more objects come into contact with each other. In physics, a collision is defined as a rapid and forceful interaction between two or more objects that causes a transfer of energy. Collisions can be elastic or inelastic, depending on whether or not the total kinetic energy of the objects is conserved.

Force is a physical quantity that describes the interaction between two or more objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, change its shape, or change its direction of motion. Forces can be categorized into different types, such as contact forces, which act when two objects are in contact, and non-contact forces, which act at a distance. Some examples of non-contact forces are gravitational force, electric force, and magnetic force.

To calculate the force of impact on the bowling ball and bowling pin during the collision, you can use the formula:

Force of Impact = Change in momentum / Time of collision

The change in momentum is given by the formula:

Change in momentum = Final momentum - Initial momentum

The initial momentum of the 6 kg bowling ball traveling at 2 m/s is:

Initial momentum (ball) = 6 kg * 2 m/s = 12 kg*m/s

The final momentum of the bowling ball can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision. In this case, since the bowling pin is moving after the collision and the bowling ball is not, the final momentum of the bowling ball is zero.

Final momentum (ball) = 0

Change in momentum (ball) = Final momentum (ball) - Initial momentum (ball) = 0 - 12 kgm/s = -12 kgm/s

The force of impact on the bowling ball is:Force of impact (ball) = Change in momentum (ball) / Time of collision = -12 kg*m/s / t (t is the time of collision, assuming it's a short time)

Similarly, the initial momentum of the 1.5 kg bowling pin at rest is:

Initial momentum (pin) = 1.5 kg * 0 m/s = 0 kg*m/s

The final momentum of the bowling pin can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision.

Final momentum (pin) = Initial momentum (ball) = 12 kg*m/s

Change in momentum (pin) = Final momentum (pin) - Initial momentum (pin) = 12 kgm/s - 0 kgm/s = 12 kg*m/s

The force of impact on the bowling pin is:

Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t

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The measure of angle MAC is 90°.

What is means of isosceles triangle?

An isosceles triangle is a type of triangle where two of its sides are congruent, or have the same length. This means that if you draw a line down the center of an isosceles triangle, it will split the triangle in half and both halves will have the same side lengths.

In an isosceles triangle, the angles opposite the congruent sides are congruent. Therefore, in triangle ABC, m∠BAM = m∠CAB = m∠NAC.

Since angle BAM and angle NAC are congruent, and they are both supplementary to angle MAC, it follows that angle MAC is congruent to itself.

Therefore, m∠MAC = m∠MAC = 180 - m∠BAM = 180 - m∠NAC.

Since m∠BAM = m∠NAC, we can conclude that

m∠MAC = 180 - m∠NAC = 90°

Hence, the measure of angle MAC is 90°.

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The simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].

What is simplified form of the expression?

If a fraction's top and bottom have only the number one in common, then it is expressed in its simplest form. The top and bottom cannot be divided further and remain whole numbers, in other words. The phrase "lowest terms" is another term for the simplest form.

Consider, the given expression

[tex]\frac{(\frac{1}{x^2}-\frac{2}{y} )}{y-2x^2}[/tex]

We have to find the simplified form of the given expression.

Taking cross multiplication of numerator of the above fraction.

[tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2}[/tex]

Using: [tex]\frac{(\frac{a}{b} )}{c} = \frac{a}{b}*\frac{1}{c}[/tex]

⇒  [tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2} = \frac{y-2x^2}{x^2y} *\frac{1}{y-2x^2} = \frac{1}{x^2y}[/tex]

Hence, the simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].

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Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)

Step-by-step explanation:

CDEF is a square so all sides of CDEF are 6cm.

This tells us the area of CDEF which is 36cm squared

This tells us the radius of AE which is the side FE which we know is 6cm.

Area of a half circle= pi x r squared/2

Area of AE= pi x 36/2= 18pi

Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)

Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.

So the area of ABCF is 36-4.5pi.

CD would also have an area of 4.5pi as it is the exact same half circle.

Area of AE=18pi cm squared

Area of CDEF= 36cm squared

Area of ABCF= 36-4.5pi

Area of CD= 4.5pi

18pi+36+(36-4.5pi)+4.5pi

simplified to:

22.5pi + 36 + (36-4.5pi)

The angle of elevation of the coconut palm tree from me is [tex]38\x^{o}[/tex].

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

the angle of elevation is defined as "the angle created between the horizontal line and the line of sight when an observer looks upwards." It is always higher than the observer and at a larger angle. When a person stares downward, they create an angle of depression, which is the opposite of an elevation angle. When studying heights and distances in trigonometry, it is crucial to understand the angle of elevation and depression. Angles, horizontal lines, and line of sight are the three main terms related to the angle of elevation.

Height of the palm tree is 58 ft

Distance at which I am standing from the tree is 74 ft

As per sum

[tex]tan \theta = \frac{58}{74}[/tex]

[tex]\theta = tan\x^{-1} (\frac{58}{74})[/tex]

[tex]\theta\\[/tex] = [tex]38\x^{o}[/tex]

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Answer:

B) -9 + 4 2/3

Explanation:

The answer is B because -9 - (-4 1/3) is -4 2/3 which is equal to -14/3, so that means B also has the same sum.

I hope this helps you! :)

The trigonometric ratio as a fraction for sinC is  , and the decimal is 0.80.

The trigonometric functions are actual functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

The widely used trigonometric functions are sine, cosine and tangent. The trigonometric functions also operate the inverse of the functions.

For the given triangle the trigonometric values are as follows:

For angle A the opposite side is CB, the adjacent side is AB and the hypotenuse is AC.

For angle C the opposite side is AB, the adjacent side is CB and the hypotenuse is AC.

[tex]sinC = \frac{\text{Opposite side }}{Hypotenuse} = \frac{4}{5} =0.80\\ \\ cosC = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{3}{5} = 0.60\\\\tanA =\frac{\text{Opposite side }}{Adjacent side} = \frac{3}{4} = 0.75\\\\tanC= \frac{\text{Opposite side }}{Adjacent side} =\frac{4}{3} = 1.33\\\\cosA = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{4}{5} = 0.80\\\\sinA= \frac{\text{Opposite side }}{Hypotenuse}=\frac{3}{5} =0.60[/tex]

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Answer:

20x²

-5xy

14y²

Step-by-step explanation:

17x² + 3x² = 20x²

-3xy - 2xy = -5xy

14y²