A 5 m 60 cm high vertical pole cat a hadow 3 m 20 cm long. Find at the ame time
(i) the length of the hadow cat by another pole 10 m 50 cm high,

Answer:

b

Step-by-step explanation:

i think b because it makes more sense than a or c

The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:

side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))

The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:

side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))

This formula is derived from the Law of Cosines, which states that the sum of the squares of any two sides of a triangle is equal to the square of the third side, minus twice the product of those two sides multiplied by the cosine of the angle between them.

In other words, the formula states that:

side_3^2 = side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle)

which is then solved for side_3 by taking the square root of both sides. Thus, the formula for the third side can be written as:

side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))

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The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.

An algebraic equation is formed by comparing two algebraic expressions to one another.

In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8

If G-H-I is a line and GH, HI and GT lies between G to I

To find G to I ⇒ GI = GH + HI = GT

GI = 2x - 9 + 14 = 3x - 8

2x + 5 = 3x - 8

2x - 3x = -8 - 5

-x = -13

x = 13

Substituting x in GT = 3x - 8; GI = GT

GI = 3(13) - 8

GI = 39 - 8

GI = 31

Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31

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The original price of the case of candles before markup was $8.50.

Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:

Original price = Marked up price / (1 + markup percentage)

In this case, the original price would be:

$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50

So the original price of the case of candles before markup was $8.50.

Thus, Original price is $8.5

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i thinj the answer is 2-1

The coefficient of expression 5x^2 in 5x^2 5x is 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.

The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.

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The residue from $0 to $82 is 44 ≡ x(mod83)

17−1≡x(mod83)

17∗17−1≡17x(mod83)      

5∗1≡5∗17=85(mod83)

5≡2x(mod83)

42∗5=210≡2∗42x=84x≡x(mod83)

44 ≡ x(mod83).

A mathematical operations that performs a calculation on two numbers is known as an arithmetic provider. They are used in everyday arithmetic, and most computer languages include a set of such operators that can be used within equations to perform a variety of sequential calculations. The following are examples of basic arithmetic operations are:

(+) Addition

Subtraction (-) (-)

() Multiplication            

() division

In programming, computers use different symbols to represent multiplication (*) and division (/). More complex operators, such as

Let's look at an ice cream multiplication example.              

There are two  groups, each has its own ice cream.

The total number of ice creams is 2x3=6    

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Since, Kim works on commission and her trend of monthly earnings are not constant, Calculate the average from the data and estimate for the whole year , The answer is C) $15,720

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It helps to make sense of large amount of data and use it to draw conclusions and make informed decisions. It provides methods to summarize, describe and analyze data, as well as techniques to infer characteristics of a population from a sample.

The mean is a measure of central tendency and a way to describe the average value of a dataset. It is calculated by adding up all the values in a dataset and then dividing by the number of values. The resulting value is the mean of the dataset, also known as the arithmetic average. Mean is commonly used to describe a large data set, while median is used to describe data with values have outliers.

salary for four months = $1625, $960, $1235, and $1420.

Average = ($1625 + $960+ $1235+$1420) /4 = $1310

for whole year = $1310 * 12 = $15,720

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To find the slope of two points on a graph, use the formula:

[tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]

Substitute the coordinates of the two points into the formula and solve for the slope.

The slope of two points on a graph is a measure of how steep the line connecting the two points is. To find the slope, you can use the slope formula: [tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]

This formula requires the coordinates of the two points, which can be found on the graph. Once you have the coordinates, you can substitute them into the formula and solve for the slope. This will give you the slope of the line connecting the two points.

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The answer is 11, 12, 13

The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P

Let

F = k/ d²

Where k = constant of proportionality

If F = 0.045 Newtons and d = 2.4 metres

F = k/ d²

0.045 = k / 2.4²

cross product

k = 0.045 × 2.4²

k = 0.2592

Find d when F = 0.7 Newton's

F = k/ d²

0.7 = 0.2592 / d²

cross product

0.7 × d² = 0.2592

0.7d² = 0.2592

divide both sides by 0.7

d² = 0.2592 / 0.7

d² = 0.370285714285714

find the square root of both sides

d = √0.370285714285714

d = 0.6085110634045

d = 0.61 to 2 decimal place.

Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.

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Answer:

unidentified

Step-by-step explanation:

could you please send the other polygon or send an attachment of the whole question because this information is not enough

f(x)=1/2x^2+1/2x-10 in intercept form is (1/2)(x+4)(x-3)

The x-intercepts are x=-5 and x=4.

The vertex of symmetry is (-1/2, -81/8).

The axis of symmetry is:  x = -1/2

A vertical intercept is a point where the graph of a function or relation meets the y-axis of the coordinate system in analytical geometry,

f(x) = 1/2x^2+1/2x-10

=  (1/2)(x² + x - 20)

= (1/2) (x² + 5x - 4x - 20)

= (1/2) { x(x+5) -4(x+5)

= (1/2) (x+5)(x-4)

Hence, Intercept form: f(x) =(1/2) (x+5)(x-4)

The x-intercepts will be where the factors = 0

x + 5 = 0 ⇒x = -5

x - 4 = 0  ⇒ x = 4

Therefore, the x-intercepts are x=-5 and x=4

To find the axis of symmetry, take the average of intercepts (to find the center of parabola)

(-5 + 4)/2 = -1/2

Axis of symmetry ⇒ x = -1/2

To find the vertex, put the axis of symmetry into the equation

f(x) = (1/2)(x + 5)(x - 4) = (1/2)(-1/2 + 5)(-1/2 - 4) = (1/2)(9/2)(-9/2) = -81/8

vertex is  (-1/2, -81/8)

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The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

f(x) = (1/2)x² + (1/2)x - 10

2f(x) = x² + x - 20

2f(x) = x² + x + 1/4 - 1/4 - 20

2f(x) = (x + 1/2)² - 81/4

f(x) = 1/2 (x + 0.50)² - 10.125

The x-intercepts are given as,

f(x) = 0

1/2 (x + 0.50)² - 10.125 = 0

(x + 0.50)² = 20.25

x + 0.50 = ± 4.50

x = - 0.50 ± 4.50

x = - 0.50 - 4.50, - 0.50 + 4.50

x = - 5, 4

The equation of the axis of symmetry is given as,

x + 1/2 = 0

x = - 1/2

The graph is attached below.

The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.

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Sixth grade math class can be difficult, even for students who have done well in math previously. In sixth grade you begin to learn more advanced topics such as ratios and rates.

You also work more with fractions. Sixth grade is also when you begin building the foundations of algebra, geometry, and statistics.

example

given problem in maths

- x + 8 > 6 ( isolate the term in x by subtracting 8 from both sides )

- x > - 2 ( multiply both sides by - 1 )

Remembering to reverse the inequality symbol when multiplying/dividing by a negative quantity

x < 2 ← reverse symbol

From the given list the only value less than 2 is 1, hence

x = 1 ← is the only possible solution

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The most probable prediction( according to biogeography theory of islands) for this situation would be continued colonization of large species population( due to balance between immigration and extinction of species) through time on the island.

A species is a unit of biodiversity as well as the fundamental classification and taxonomic rank of an organism in biology.

Given:

Consider a species that occupies a large, but fixed, number of islands.

The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events.

According to island biogeography theory the population of an island is maintained constant through time when the immigration rate of new species to the island and extinction rate of species in the island is constant.

In a model for the relationship between the fraction of islands occupied by species and time, if the number of new species immigrating to the island will be equal to the number of species that become extinct in the island species population and will thrive continuously through time( will never become extinct) as the island species population will be maintained due to the existence of a dynamic equilibrium of species in the island.

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well, let's take a looksie, hmm the sector is really a sector with a central angle of 90°, wait a second!! a circle has a total of 360°, so 90°+90°+90°+90° = 360°, so 90°is really just one quarter that of a circle.

Now, if we just get the whole area of the circle, then grab only one quarter of that, we'll be set, yeahhhh!!

[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies A=\pi (9)^2 \\\\\\ \stackrel{\textit{one quarter of that}}{\cfrac{1}{4}\cdot \pi (9)^2}\implies \cfrac{81\pi }{4}\implies \cfrac{81(3.14)}{4} ~~ \approx ~~ \text{\LARGE 63.6}[/tex]

Answer:

AROC = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

the average rate of change of g(x) in the closed interval [ a, b ] is

[tex]\frac{g(b)-g(a)}{b-a}[/tex]

here [ a, b ] = [ - 4, 5 ] , then

g(b) = g(5) = - 1 ← point (5, 1 ) on graph

g(a) = g(- 4) = 5 ← point (- 4, 5 ) on graph

average rate of change = [tex]\frac{-1-5}{5-(-4)}[/tex] = [tex]\frac{-6}{5+4}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]

There are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.

We know that the company uses the same ratio of different types of nuts in each container. Therefore, we can use the ratio of peanuts to the total weight in the 20-ounce container to find the weight of almonds in the 42-ounce container.

In the 20-ounce container, 11 ounces of the nuts are peanuts. Therefore, 20-11 = 9 ounces of the nuts are not peanuts.

To find the weight of almonds in the 42-ounce container, we can use the same proportion of non-peanut nuts to the total weight. So,

9 ounces / 20 ounces = x / 42 ounces

Cross-multiplying we get:

9 × 42 ounces = 20 × x

x = 37.8 ounces

So, there are 37.8 ounces of almonds in a 42-ounce container of the company's mixed nuts.

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According to the pattern Brett receives points as follows 5,10,15,20,25,30,35 and according to the pattern of Yolanda, Yolanda receives points as 25,60,95,130,165,200,235 .

What is recursion  ?

It is a process in which it calls itself to solve the given problem is called as recursion.

The recursive formula to find the nth term of a geometric sequence is:

an = an-1 * r for n ≥ 2

In Brett's case,

if n=2

a2 = a1 * r  

given a2 = 10 a1 =5

10 = 5 *d

d=2

a4 = a3 * d = 20*2 = 40

a5 = a4*d = 40*2 = 80

a6 = a5*d = 80*2 = 160

a7 = a6 * d = 160*2 = 320

In Yolanda case,

The recursive formula to find the nth term of an arithmetic sequence is:

an = an-1 + d for n ≥ 2

if n=2

a2 = a1 + d

60 = 25 + d

d = 35

a4 = a3+d = 95 + 35 = 130

a5 = a4+d = 130 + 35 = 165

a6 = a5+d = 165 + 35 = 200

a7 = a6 +d = 200 + 35 = 235

Hence the pattern in Brett's case could be 5,10,15,20,25,30,35 and in Yolando's case could be 25,60,95,130,165,200,235 .

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According to the pattern Brett receives points as follows 5,10,15,20,25,30,35 and according to the pattern of Yolanda, Yolanda receives points as 25,60,95,130,165,200,235 .

It is a process in which it calls itself to solve the given problem is called as recursion.

The recursive formula to find the nth term of a geometric sequence is:

an = an-1 * r for n ≥ 2

In Brett's case,

if n=2

a2 = a1 * r  

given a2 = 10 a1 =5

10 = 5 *d

d=2

a4 = a3 * d = 20*2 = 40

a5 = a4*d = 40*2 = 80

a6 = a5*d = 80*2 = 160

a7 = a6 * d = 160*2 = 320

In Yolanda case,

The recursive formula to find the nth term of an arithmetic sequence is:

an = an-1 + d for n ≥ 2

if n=2

a2 = a1 + d

60 = 25 + d

d = 35

a4 = a3+d = 95 + 35 = 130

a5 = a4+d = 130 + 35 = 165

a6 = a5+d = 165 + 35 = 200

a7 = a6 +d = 200 + 35 = 235

Hence the pattern in Brett's case could be 5,10,15,20,25,30,35 and in Yolando's case could be 25,60,95,130,165,200,235 .

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Answer:

7/12

Step-by-step explanation:

y = 12

x = 7

y = Kx

K = y/x

K = 7/12

The equation can be solved by adding 3 to both sides of the equation.

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From the given graph, at Point B a total of 8000 fluffernutters & 500 blank books could be produced.

The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this context, a graph is made up of vertices connected by edges.

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.

Straight line graphs called linear graphs are used to show the relationship between two quantities. This graph makes it easier to show a result as a collection of straight lines. The term "linear" simply means a straight line; curves, dots, bars, etc. are not used.

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ln() is a function in Excel that calculates the natural logarithm of a number. The natural logarithm is the logarithm to the base e, where e is an irrational number approximately equal to 2.718281828.

1. Enter the number for which you want to calculate the natural logarithm in a cell.

2. Click on the cell and enter "=ln()" function (without the quotation marks) in the formula bar.

3. Within the parentheses, enter the cell reference or the number for which you want to calculate the natural logarithm.

4. Press the Enter key and the natural logarithm of the number will be calculated and displayed in the cell.

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83.2 square feet is the area of the figure.

A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given figure is a cone with radius 3 ft and height 5 ft.

We need to find the area of cone=A=πrl+πr²

where l is √r²+h²

A=πr(r+√r²+h²)

=π×3(3+√3²+5²)

=3π(3+√34)

=3×3.14(3+5.83)

=3×3.14(8.83)

=83.2 square feet

Hence, 83.2 square feet is the area of the figure.

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Answer:

Eva spends £35 in a month.

Step-by-step explanation:

We know that Eva gets £42 a month for her allowance and for every £5 she spends, she saves £1.

We are looking to find out how much money does she spend in a month.

To calculate this, we can use the following formula:

Spent money = Allowance - (Allowance / (5 + 1))

Plugging in the known values:

Spent money = 42 - (42 / (5 + 1))

Spent money = 42 - (42 / 6)

Spent money = 42 - 7

Spent money = 35

So, Eva spends £35 in a month.

Answer:

Step-by-step explanation:

A unit rate means a rate for one of something. You should write it as a ratio with a denominator of one.

For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate

IT's  0.80 per serving i think

The volume of the cone is one third the volume of the cylinder.

The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter

Similar to a prism, a cylinder has two bases, but they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a figure in space with equal distances between each of its points and the center.

The cone's volume is one-third that of the cylinder. A sphere's volume is 2/3 that of a cylinder with the same radius, and its height is equal to its diameter.

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The minimal number of employees who did not get their preferred shift that week was 20.

Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.

But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.

We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.

But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.

Thus, 20  is the minimum number of staff members who failed to receive her preference of shift that week.

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Answer for the given problem,

a.  Percentage of 160 in number 40 is, 400%

b. The number for which 40 is 160% of that number is,  25

c.  The number which is 40% of 160 is, 64

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

a.   present quantity = 160

     whole quantity  = 40

    Percentage = 400 %

b.  present quantity = 40

    Percentage = 160

    Whole quantity  = 25

c.   whole quantity  = 160

     Percentage = 40%

     Present quantity = 64

Hence, Answers are respectively,  400%,  25,  64

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