Find a principal which will amount to Rs.2000 in 6 years 8 months at the rate of interest 5% per annum.

Answer:

  381 feet

Step-by-step explanation:

You are 220 ft from a tree whose top you see at a 60° angle of elevation. You want to know the height of the tree.

The tangent relation between sides of a right triangle is ...

  Tan = Opposite/Adjacent

where "opposite" and "adjacent" refer to the sides opposite and adjacent to the acute angle of interest.

Here, the 60° angle of elevation is adjacent to the 220 ft distance from the tree, and opposite the height of the tree. This means ...

  tan(60°) = height/(220 ft)

Multiplying by 220 ft, we find the height to be ...

  height = (220 ft)tan(60°) = 220√3 ft ≈ 381 ft

The tree is 381 feet tall.

__

Additional comment

The triangle that models this geometry is a 30°-60°-90° right triangle, one of the "special" right triangles that often shows up in geometry and trigonometry problems. Its side lengths have the ratio 1 : √3 : 2. Knowing this, you know the tree height is √3 times the distance from the tree:

  220√3 ft

Your calculator can tell you this is about 381 feet.

To find the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the distance from the tree) and the angle. The formula is:

Why is it referred to as a tangent function?

Tangent is derived from the Latin verb tangere, which means "to touch." A circle has one point where a line that is tangent to it intersects.

tangent(angle) = opposite / adjacent

In this case, the angle is 60 degrees, the opposite side is the height of the tree, and the adjacent side is the distance from the tree, which is 220 feet. So we can write:

tan(60) = height / 220

To find the height, we can divide both sides by the tangent of 60 degrees:

height = 220 * tan(60)

The exact value of the height of the tree is not possible to be obtained with the given information, the height of the tree is a number in the infinite set of real numbers.

We can use a calculator or a table of tangents to find an approximate value of the height.

It could be around 379.3 ft.

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The size of the angle marked y correct to three significant figures is 26.6°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given is a right angled triangle.

By the definition of trigonometric functions,

Sin y = Opposite side / Hypotenuse

sin y = 31.4 / 70.2

sin y = 0.447

y = 26.57

  = 26.6

Hence the value of y is 26.6.

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Answer:yes

Step-by-step explanation:

Answer:

correct

Step-by-step explanation:

The cost of plan A is represented by the equation:

Cost A = 40 + 0.02x

where x is the number of minutes of calls.

The cost of plan B is represented by the equation:

Cost B = 0.18x

To find the point where the two plans cost the same, we can set the two equations equal to each other and solve for x:

40 + 0.02x = 0.18x

40 = 0.16x

x = 250

So when the customer makes 250 minutes of calls, the cost of the two plans will be the same.

The cost of plan A will be 40 + 0.02250 = $50 and the cost of plan B will be 0.18250 = $45

So when the customer makes 250 minutes of calls, Plan A and Plan B cost the same amount of money.

Answer:

ans is= Rs.2925. . . . . . .

Answer:

1.77865216

Step-by-step explanation:

Spinning a spinner with three equal sections colored white, red, and blue yield the probability of having yellow color is B: '0%', i.e p (yellow) = 0%.

As in the given scenario where a spinner with white, red, and blue colors is rolled and is asked about determining the p(yellow). That is the probability of getting yellow at which the spinner stops. It is clearly written that the spinner has three sections of equal colors which are red, blue and white. And there is no section on the spinner with yellow color, so it is not possible to get yellow color over rolling of the spinner.

It means that 0% probability exists for yellow color.

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The correct option is 'The domain of both functions is all real numbers'.Option A

Generally, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, the set of all real numbers constitutes the domain of f(x).

Due to the fact that f(x) and g(x) both return the same result,

Therefore, the set of real numbers is likewise included in the domain of g(x).

Now, the range of f(x) is , R=  { 5x : x belongs to all real numbers.}

As a result, the set of possible values for f(x) includes only real numbers.

In addition, the range of g(x) includes all real values.

Given what has been said so far, it is clear that only choice (1) should be considered accurate.

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CQ

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

Answer:

x = 3

Step-by-step explanation:

18/2 = 27/x

9/1 = 27/x

9x = 27 × 1

x = 3

Answer:

x = 3 because 18 divided by 2 equals nine, also meaning that 2 x 9 = 18. Now since we figured out that 9 is how many times more/less the number is between the polygons. (I'm so sorry if I can't explain clearly) Now we just get 27 and divide it by 9 which leaves us with our answer 3.

Divide the population standard deviation () by the square root of the sample size (n) to obtain the standard deviation of the sample mean (X).

The sample mean is normally distributed, with mean X= and standard deviation X=/n, where n is the sample size, for samples of any size taken from a population that is normally distributed.

The standard deviation of the population divided by the square root of the sample size is equal to the standard deviation of the sampling distribution of means.

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Slope of the line that contains the points (13, -2) and (3,-2) is 0.

What is Slope of line?

The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

m = y2 - y1/x2 - x1

Given ;

x1 =13, x2 = 3, y1 = -2, y2 = -2

ΔX = x2-x1

ΔX = 3 - 13

ΔX = -10

Now, calculating ΔY ;

ΔY = y2 - y1

ΔY =-2 - (-2)

ΔY = 0

Hence, Slope of the line is ;

Slope(m) = ΔY/ΔX

Slope(m)= 0/-10

Slope (m) = 0

Therefore , Slope of the line that contains the points (13, -2) and (3,-2) is 0.

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Answer: 3:5

Step-by-step explanation:

total students: 12+18=30

ratio: 18 girls :30 students total

simplify: 18/6 : 30/6= 3:5

Answer:

15 boys

Step-by-step explanation:

We know

A group has 20 children

25% girls

25% = 0.25

20 times 0.25 = 5 girls

20 - 5 = 15 boys

So, there are 15 boys

The exact probability that would make the three marbles to be blue is  6/273,

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that exactly three marbles drawn would be blue = (number of blue marbles / total number of marbles) x [(number of blue marbles / total number of marbles) - 1] x [((number of blue marbles / total number of marbles) - 1]

Total number of marbles = 6 + 5 + 4 = 15

= (5/15) x (4/14) x (3/13) = 6/273

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Answer: In an equilateral triangle, the hypotenuse and its opposite side are equal

By the way, I am human. There is too many bot answers.

The values for sine and cosine are equal at 45 degrees because they are related to the right triangle formed by the angle.

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.

When the angle is 45 degrees, the triangle formed is a 45-45-90 triangle, this is a special triangle in which all the angles are 45 degrees and all the sides are in the ratio of 1:1:√2.

In this triangle, the hypotenuse is √2 times the length of either leg. So, the sine of 45 degrees is opposite/hypotenuse = (1/√2) and the cosine of 45 degrees is adjacent/hypotenuse = (1/√2). Since the opposite and adjacent sides are of the same length in the 45-45-90 triangle, the sine and cosine of 45 degrees are equal.

So, sine 45 = cosine 45 = 1/√2.

The point (-4, 2) be located in second quadrant. Due to the fact that x is negative and y is positive.

The coordinate system's two axes, the x-axis and the y-axis, define a region is called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle.

These areas include coordinates, or positive and negative values of the x- and y-axes. The position of a point in a quadrant is indicated by the coordinates.

The first quadrant is located in the graph's upper right-hand corner. Both the x and y values in this quadrant are positive.

The second quadrant is located in the graph's upper left corner. The value of y is positive in this quadrant while the value of x is negative.

The third quadrant is located in the graph's lower left-hand corner. It includes both the negative values of x and y.

Fourth Quadrant, the final quadrant has a positive x value and a negative y value, and it is located in the lower right corner.

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The complete question is:

What quadrant will the point (-4, 2) be located in?

The weight of the cashews plus the weight of the peanuts cannot be more than 192 ounces and the weight of the cashews must be at least one-fourth of the total weight of the mixture.

Step 1: Let c = weight of cashews

Step 2: Let p = weight of peanuts

Step 3: 0.25c + p ≤ 48

Step 4: Multiply both sides by 4

Step 5: 4(0.25c + p) ≤ 4(48)

Step 6: c + p ≤ 192

This system of inequalities models the situation of combining cashews and peanuts to make a nut mixture. The first inequality states that the weight of the cashews plus the weight of the peanuts cannot exceed 48 ounces, and the second inequality states that the weight of the cashews must be at least one-fourth of the total weight of the mixture. To model this situation, we let c equal the weight of the cashews and p equal the weight of the peanuts. We then multiplied both sides of the first inequality by four to get the second inequality, which states that the weight of the cashews plus the weight of the peanuts cannot exceed 192 ounces. This system of inequalities accurately models the situation of combining cashews and peanuts to make a nut mixture, and it ensures that the weight of the cashews is at least one-fourth of the total weight of the mixture.

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The vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is the leading coefficient.

The vertex form can be converted from the standard form (y = ax^2 + bx + c) by completing the square and shifting the parabola horizontally and vertically.

The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola, which is the lowest point for a parabola that opens upwards, and highest point for a parabola that opens downwards. The "a" coefficient is the leading coefficient which represents the direction of the parabola, whether it opens upwards or downwards. The vertex form is useful in identifying the vertex of the parabola and its symmetry axis, as well as its direction.

So, the vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is the leading coefficient.

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To find the number of solutions to given equation by comparing the coefficients of the variables of the equations.

We know that a solution of an equation is a value that satisfies given equation.

We can find the number of solutions to given equation by comparing the coefficients of the variables of the equations.

There are three types of solutions to the set of linear equations:    Unique Solution: The linear equation in one variable (equation of the form ax + b = 0) always has a unique solution.    

No Solution: When the graphs of the linear equations represents parallel lines, then the system of linear equations has no solution.

Infinitely Many Solution: if the system of equations represent coincident lines, and they have the same y-intercept, then the system of equations has infinitely many solutions.

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Its slope is 0, which indicates that it is a horizontal line, and its

y-intercept is −3.

When an equation of a line has only one variable, the resulting graph is a horizontal or a vertical line.

The graph of the line  x=a

, where  a is a constant, is a vertical line that passes through the point  (a,0) . Every point on this line has the x-coordinate equal to a, regardless of the y-coordinate.

The graph of the line  y=b , where  b  is a constant, is a horizontal line that passes through the point  (0,b) . Every point on this line has the y-coordinate equal to b, regardless of the x-coordinate.

We can write

y=−3

as

y=0x−3

So, its slope is 0, which indicates that it is a horizontal line, and its

y-intercept is −3. Hence, its graph looks like

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The area of a triangle with a base of 4.8 cm and height of 3.6 cm is 8.64 cm².

Area of triangle = ½ × base × height

= ½ × 4.8 × 3.6

= 8.64 cm²

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Answer:

Randy

Step-by-step explanation:

Randy:  2 runs / 3 innings = 0.67

Felix:  4 runs / 5 innings = 0.80

Johan:  5 runs / 7 innings = 0.71

The total reports during the year is 15.

percentage, a relative value indicating hundredth parts of any quantity.

Given that tanik turns in his third report. his teacher says 20% of his reports for the year are done.

We have to find the number of research reports will Tanik complete during the school year.

Let the number of reports be = x

As mentioned, when Tanik submitted his 3rd report, he had completed 20% of the reports so

20/100×x=3

0.2x=3

Divide both sides by 0.2

x=15

Hence,  the total reports during the year is 15.

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The substitution method is a powerful tool used to solve systems of linear equations with three variables. Beginning with one of the equations for one of the variables, utilise the substitution method.

This will give you an expression for that variable in terms of the other two. Then, substitute this expression into the other equations and solve for the remaining variables.

Consider, for example, a set of linear equations involving the variables x, y, and z:

x + y + z = 13

2x + 4y - z = 6

3x - 2y + 3z = 11

Start by solving the first equation for x in order to apply the substitution method here:

x = 13 - y - z

Now solve for y and z by substituting this expression into the previous two equations:

2(13 - y - z) + 4y - z = 6

39 - 2y + 3z = 6

3(13 - y - z) - 2y + 3z = 11

39 - 5y + 6z = 11

Subtract 39 from both sides of each equation, then solve for y and z using elimination or another method. Once you have found values for both variables, plug them into the original expression for x to find its value.

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The form of function is a logarithmic function. either "y equals the log of x, base b" or "y equals the log, base b, of x."

What is logarithmic function?

An exponential function's inverse is a logarithmic function. An exponential function's basis is the same as that of a log function. Exponents include logarithms. f(x) = bx is the formula for the exponential function. f(x) = log base b of x is how the logarithmic function is expressed.

The expression "y equals the log of x, base b" or "y equals the log, base b, of x" is the definition of a logarithmic function. In both cases, b > 0, b 1, and x > 0. There are no limitations on y. logarithm, the exponent or power that a base must be increased to in order to get a specific number. If bx = n, then mathematically, x is the base-b logarithm of n.

Determine the logarithmic function of the provided graph by using the provided points in the following manner:

[tex]f(x) = log_a(x-h)[/tex]

Create two equations by substituting the provided points (3/2, 1) and (3, -1) into the formula:

[tex]log_a(\frac{3}{2}-h) = 1[/tex]

[tex]log_a({3}-h) = -1[/tex]

To isolate a, use the log law and rearrange each equation:

[tex]log_a(\frac{3}{2}-h) = 1[/tex]

⇒ [tex]a^1 = (\frac{3}{2}-h)[/tex]

⇒1/a = 3 - h

⇒ a = 1/ [tex]\frac{3}{2}[/tex] - h  ....................................(1)

[tex]log_a({3}-h) = -1[/tex]

⇒[tex]a^{-1} = ({3}-h)[/tex]

⇒ 1/a = 3-h

⇒ a = 1/3-h ..............................................(2)

Solve for h:

⇒ 3/2 - h = 1/3-h

⇒ 3-2h/2 = 1/3-h

⇒ 9 - 9h + 2h^2 = 2

⇒(2h-7)(h-1) = 0

⇒ h = 7/2, 1

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Answer:

Coordinates of C are (22, 20)

Step-by-step explanation:

We can see the squares are identical

The x-distance between A and B is 38 - 6 = 32

This covers 4 squares so each square side length = 32/4 = 8

Since point C is two squares away, the x-coordinate of C is 8 x 2 = 16 units away from the A x coordinate

x-coordinate of C = x-coordinate of A + 16 = 6 + 16 = 22

So x-coordinate of C is 22

To find the y-coordinate of C, because it is a square each vertical side of the square is also 8 units

If the third square were aligned with the top right of the second square, the y-coordinate of that square should be :
y-coordinate of A + 2 x 8 = 7 + 16 = 23

In this case, the y-coordinate of B should have been 23 + 2 x 8 = 23 + 16 = 39

However, because of the downward shift of the third square, the y-coordinate of B is only 36

39-36 = 3

So the third square has been shifted down by 3

Therefore y coordinate of C = 23 - 3 = 20

Coordinates of point C: (22, 20) which will result in the figure shown.

Just to verify

Since point B is 16 units to the right of C, its x-coordinate = 22 + 16 = 38
Point B

Point B y-coordinate is 16 units vertically up from y-coordinate of C.

So y-coordinate of B = 20 + 16 = 36

Hence verified

I hope that makes sense.

The attached figure shows exactly the figure in the question but with the coordinates marked. You can independently verify this

The slope of the given graph is m = -1, and the y-intercept is y = 1.

A line's slope reveals its inclination and direction. Without actually using a compass, determining the slope of lines in a coordinate plane can aid in determining whether the lines are parallel, perpendicular, or have no relation at all.

Any two different points on a line may be used to derive the slope of that line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line equation.

Consider each box of the graph as 1 unit.

So, from the graph, at x = 0

y = 1

So, this is the y-intercept of the line.

Consider any two points

(x₁, y₁) = (0, 1)

(x₂, y₂) = (1, 0)

The slope is given by the slope formula as

m = (y₂ - y₁)/(x₂ - x₁)

= (0 - 1)/(1 - 0)

= -1

The slope of the graph is m = -1.

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We would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.

What is probability ?

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Probability can be expressed as a fraction, decimal, or percentage. For example, a probability of 0.5 is the same as a probability of 1/2 or 50%.

The probability of an event can be calculated by counting the number of favorable outcomes and dividing by the total number of possible outcomes.

If 2% of the population has red hair, we can expect 2 out of every 100 people in the population to be redheads. To find out how many redheads we would expect in a sample of 800 people, we can use this proportion and multiply it by the number of people in the sample.

2/100 * 800 = 16

So, we would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.

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Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of an occurrence and 1 denotes its certainty. It is possible to represent probability as an integer, decimal, or percentage. A probability of 0.5, for instance, is equivalent to a possibility of 1/2 or 50%.

By counting the favorable outcomes and dividing by the total number of potential outcomes, one can determine the probability of an occurrence.

We can anticipate that 2 out of every 100 people in the community will have red hair if red hair makes up 2% of the population. We can calculate the proportion of redheads we would anticipate in an 800-person group by

A BAR graph would be most suitable for displaying the given data.

The visual representation of numerical data is a graph. Graphs offer a visual means of presenting complicated data and demonstrating the link between various variables or data sets. Graphs are a fantastic tool for highlighting patterns and connections in data.

Given data, The number of pets in each student's household.

Stem-and-leaf plot:

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. As data are gathered, they are organised using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf.

Thus it is not suitable for given data.

Line graph:

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time. Line graphs are frequently used in finance to show the historical price movement of an asset or instrument.

Since, we have similar but Discrete with three variables in our data thus this graph is also not suitable.

Bar graph:

A bar graph (also known as a bar chart or bar diagram) is a visual tool that uses bars to compare data among categories. A bar graph may run horizontally or vertically.

Since we need to compare the data thus, bar graph is most suitable for the giving condition.

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A perimeter is the length of a two-dimensional shape's boundary. It is sometimes described as the total length of the object's sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides.

The term "two-dimensional shape" refers to any shape that is flat and has only two dimensions, i.e. length and breadth. Each polygon is a flat, 2-D figure that rests on a plane. Polygons, such as triangles, rectangles, and squares, are closed figures that are enclosed by a series of lines. The length or linear measure of these confined line segments is known as the polygon's perimeter (peri: around; metre: measure). Or to put it another way, it is the length of its borders. The centimetre (cm) or metre is its unit (m).

The whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides. Since a rectangle's perimeter is a linear measurement, the unit will be in metres, centimetres, inches, feet, etc.

Perimeter of a rectangle = sum of four sides

= AB     +     BC        + CD       +   AD

= length + breadth + length + breadth

= 2 length + 2 breadth

Perimeter of a rectangle =   2 × (length + breadth)

The radius of the circle serves as one of the three variables in the perimeter of a circle formula, along with two constants. The formula for calculating a circle's circumference or perimeter is as follows:

Circumference of a circle is equal to 2πr.

where,

r = radius of the circle

D = diameter of the circle

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