Relationship between scale factor,area and volume of enlarged figures ​

The length of the two line segments together is 80 cm

Step 1: Convert 500mm into cm.

We know that the value of 1mm is equal to 0.1 cm.

Then,  500mm will be  500mm*0.1 = 50 cm.

Therefore, the second line segment is  50 cm long.

Step 2: Calculate total length.

Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.

Now, the total length is

L = L1 + L2

Substitute the values L1= 30 cm and  L2= 50 cm in L = L1 + L2.

Hence, the length of the two line segments together is 80 cm

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The number of square feet that the seed cover per pound is given as follows:

168 square feet per pound.

The number of square feet that the seed covers per pound is obtained applying the proportions in the context of this problem.

The term proportion is used because the number of square feet that the seed covers per pound is given by the division of the total area by the number of pounds in the bag.

The parameters for this problem are given as follows:

Hence the  number of square feet that the seed cover per pound is calculated as follows:

56/(1/3) = 56 x 3 = 168 square feet per pound.

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Of all the total units of measurements, the seven base units are given above.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given are the units of measurements.

The seven SI base units, which are comprised of:

Therefore, of all the total units of measurements, the seven base units are given above.

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The estimated amount of paint needed for the grain silo is 103.61 m².

The cylinder and the conical lid are the two components that make up the figure. As a result, we solve for the total surface area of the cylinder and the cone and add.

TSA for cylinder = 2πr (h + r), for h = 6.2 m and r = 1.7 m.

= 2π * 1.7 (6.2 + 1.7)

= 84.38

TSA for cone = πr (l + r), for l = slant height = 1.9 m and r = 1.7,

resulting in a value = π * 1.7 (1.9 + 1.7) = 19.23

TSA for the cone plus TSA for the cylinder equals how much paint is needed.

how much paint needed = 84.38 + 19.23

how much paint needed = 103.61 m²

The volume of paint to be used depends on the thickness of the painting.

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Answer:

3(5/3c+p)

Step-by-step explanation:

5c+3p=3(5/3c+p)

Length of the person's shadow is 3.75 feet.

Consider triangle as shown, segment DE represent the person standing, A represent the location of light, 22 feet away from ground, BC. The shadow's length would be the length of CE.

In triangle ABC and triangle DEC, ∠C is common, and ∠CBA = ∠CED = 90°. So by AA criterion, the triangles are similar. Thus

BC/ CE = AB/ DE

(BE + CE)/CE = AB/ DE

1 + BE/CE = AB/ DE

1 + 10/CE = 22/6

10/CE = 16/6 = 8/3

CE = (10 × 3)/8

CE = 3.75

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Mean is NOT a value in the 5-number summary among the given options..

In descriptive studies or during the first exploration of a big data set, a five-number summary is very helpful. The maximum and lowest values, the median, the lower and upper quartiles, and the most extreme values in the data set make up a summary.

Comparisons may be made between five summaries of numbers. We shall see that two sets with comparable means and standard deviations may have summaries of five numbers that are substantially different. A normal probability plot, often known as a box and whiskers graph, can be used to quickly compare two five-number summaries.

5-number summary consists of : Min, Q₁, Median, Q₃, and Max

Thus, mean is not a value in the 5-number summary

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The complete question is as follows:

both the equation both equations are similar and they may or may not be equivalent.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Given equation (2d) / (d/r1) + (d/r2)

and (r1t1 + r2t2) / (t1 +t2)

Taking LCM: 2d/(dr2) (dr1) / r1r2

The product 2r1r2/ r1+r2

So both the equation equations are similar and they may or may not be equivalent.

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△TAN ≅ △LEF, by the SSS congruence theorem.

The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.

From the triangles given by the image presented at the end of the answer, the congruent sides are given as follows:

(the congruence of each side is represented by the |, || and ||| notations).

As the three sides are congruent, we have that triangles TAN and LEF are congruent by the Side - Side - Side congruence theorem.

The two triangles are given by the image presented at the end of the answer.

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A graph when plotted, we get a straight line and it is called linear graph. Linear graph is a graph of linear function.

Domain refers to all the possible input values, it is the values in the x-axis of the graph. A range means all the output values, when each domain is used in a function. It is the y-axis values.

To determine the domain identify all the X- coordinates in the linear function graph. To determine the range, identify all Y-coordinates in the functions graph. The domain and range are usually represented as a set of values.

If the domain have values from 0-6, it is represented as {0<x<4}

If the range is values between -1 to 10, then it is represented as {-1<x<10}.

Lets consider the linear function y= 3x, the domain is between 0 and 10, and range above are,

Function  y= 3x

Domain  0    1      2    3     4     5       6        7         8        9        10

Range    0     3     6     9    12    15      18     21        24      27      30

So domain is the X-coordinates, and range the Y-coordinates.

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The 4 types of computer system components are Input devices, Output devices, Memory and Central Processing Unit (CPU).

To give input and instructions to the computer for processing, input devices are employed. These items, which also go by the name of peripheral devices, include the mouse, keyboard, microphone, scanner, etc.

Monitors and printers are examples of output devices that are used to display the outcomes of the instructions that the computer has processed.

The main part of a computer that processes data is called a CPU (Central Processing Unit). The mother board, registers, buses, and other subcomponents of the CPU are used to carry out processing operations. Memory, another crucial computer component, is used by the CPU to temporarily or permanently store the instructions.

Then, there are further types of memory, including RAM, ROM, and supplementary storage devices. Together, these parts carry out the numerous instructions provided by the user.

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So, the coach could have participated in at least 14 handshakes.

The total number of handshakes is the sum of the handshakes between gymnasts from different teams and the handshakes between gymnasts from the same team and the coach.

The coach shakes hands with each gymnast from her own team, so the number of handshakes between the coach and gymnasts is equal to the number of gymnasts on the team.

Let's assume the number of gymnasts on a team is x. And the number of teams is y. So the number of handshakes between gymnasts from different teams is x*(x-1)*y/2.

Given the total number of handshakes is 281, we know that:

x*(x-1)*y/2 + x = 281

In order to get the minimum number of handshakes the coach could have participated in, we can assume the maximum number of gymnasts on a team, which is x = 14.

So the equation becomes:

1413y/2 + 14 = 281

So we can find the value of y by solving this equation:

y = (281-14)/(13/2) = 17

Therefore, with x = 14 and y = 17, the minimum number of handshakes the coach could have participated in is 14, which is the number of gymnasts on the team.

So the coach could have participated in at least 14 handshakes.

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The equation of g(x), after the translations, is given as follows:

g(x) = x² + 8x + 14.

There are four translation rules that can be applied to a function, and they are listed as follows:

The parent function for this problem is given as follows:

f(x) = x².

The translations, along with their effects, are given as follows:

Hence the function g(x) is defined as follows:

g(x) = (x + 4)² - 2

g(x) = x² + 8x + 16 - 2

g(x) = x² + 8x + 14.

Which is in the standard form as is desired for this problem.

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The shaded area between three mutually tangent circles of radii 5, 6, and 9 cm is 0.23 cm².

The three circles are mutually tangent which means that the distance between the centers of any two circles is equal to the sum of the radii of those circles.

Let's call the center of the largest circle C1, the center of the middle circle C2, and the center of the smallest circle C3.

Therefore, the distance between C1 and C2 is 9 cm + 6 cm = 15 cm, the distance between C2 and C3 is 6 cm + 5 cm = 11 cm and the distance between C1 and C3 is 9 cm + 5 cm = 14 cm. So semi-perimeter is

s = ( 15+11+14)/ 2 = 40/2 = 20

Area of triangle C1C2C3 is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A = \sqrt{20 (20-15)(20-11)(20-14)}[/tex]

A ≈ 73.48 cm²

Now we can use the area of a sector formula which is

(n/360)πr²

where n is degree subtended by the sector, to find the shaded area.

Area of the sector of C1 = (cos⁻¹(7.5/14)/360)π9² = 40.72 cm²

Area of the sector of C2 = (cos⁻¹(5.5/15)/360)π6² = 21.52 cm²

Area of the sector of C3 = (cos⁻¹(7/11)/360)π5² = 11.01 cm²

The shaded area enclosed between the circles is the sum of the above three area of sector subtracted from the area of triangle C1C2C3:

Shaded area = 73.48 - 40.72 -21.52 - 11.01 = 0.23 cm²

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On solving the provided question, we can say that bye equation, The total cost will be: [tex]= $75 + $60 = $135[/tex]

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

from the data provided

opportunity cost of time will be $144.

opportunity cost oftown will be -

[tex]= 1.5 × 30 = $45.[/tex]

The total cost will be:

= $45 + $86 = $131

[tex]= 2.5 × 30 = $75[/tex]

The total cost will be:

[tex]= $75 + $60 = $135[/tex]

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According to the given information Every 10th product in the line is selected.

Systematic sampling is a probabilistic strategy that includes selecting people from the general population at predetermined intervals, such as each 15th people on a list of the population. If the community is set up in a random order, this can replicate the benefits of simple random sampling.

Biased sample sizes and subpar survey results are reduced by systematic sampling. If there is a low chance that data will be manipulated: Data validity may be compromised if researchers rearrange a data set. The best strategy for surveys when there is little likelihood of data manipulation is systematic sampling.

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If the number of flu patients at the school is modelled by the equation [tex]F=10e^{0. 12d}[/tex] , then the number of days that it will take for the number of patients to reach 50 is 13 days .

The Exponential Growth equation is given as : [tex]F=10e^{0. 12d}[/tex] ;

We have to find How many days will it take for the number of new flu patients to equal 50 .

So , we substitute the value [tex]F=50[/tex] in the model equation ;

we get ;

⇒ [tex]50 = 10e^{0. 12d}[/tex] ;

dividing both side by 10 ,

we have ;

⇒ [tex]5=e^{0. 12d}[/tex] ;

taking [tex]\ln[/tex] on both sides ,

⇒ [tex]\ln 5 = 0.12d(\ln e)[/tex]   ,....we know that [tex]\ln e = 1[/tex] ;

⇒[tex]d= \frac{\ln 5}{0.12}[/tex] ⇒ 13.41198 ;

≈ 13 days .

Therefore , it will take 13 days for the number of patients to reach 50 .

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The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.

z1 = (8181-7676)/55 = 1.89

z2 = (8686-7676)/55 = 3.04

Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.

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If a quadratic equation  ax² + bx + c = 0, has equal roots , then the value of b , is : (a) ± 2√ac

The general form of a quadratic equation is;

ax² + bx + c = 0

The quadratic formula used to solve this quadratic equation is;

x = [-b ± √(b² - 4ac)]/2a

The quadratic equation ax² + bx + c = 0 has equal roots if its discriminant b² - 4ac = 0.

Thus;

b² = 4ac

b =  ±√4ac

b =  ±2√ac

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4 and 2 have only one polynomial, which is [tex]x^2-6x+8[/tex]

If a polynomial has two real zeros, then it will be a Quadratic polynomial. A quadratic polynomial is a polynomial that has a degree of two. Zeros of a Quadratic polynomial can be found by two methods, 1. Splitting the middle term 2. Quadratic formula. In this question, zeros are given for this we will use the reverse of splitting the middle term.

4 and 2 are two zeros of a polynomial. It can be represented as:

[tex]x=4\\x=2[/tex]

therefore,

[tex]x-4=0\\x-2=0[/tex]

The Above Linear polynomials are a simplified form of a quadratic polynomial. When multiplying both equations, we get:

[tex](x-4)(x-2)=0[/tex]

[tex]=x^2-2x-4x+8[/tex]

[tex]=x^2-6x+8[/tex]

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Answer:

20/9 laps

Step-by-step explanation:

convert everything to minutes to make things a little easier

3/10 of an hour = 1/10 of an hour (6 minutes) * 3 = 18 minutes

2/3 of an hour = 1/3 of an hour (20 minutes) * 2 = 40 minutes

18 minutes = 1 lap

40 minutes = ? laps

multiply the first equation by 40/18 to get 40 minutes on the left sides

40 minutes = 40/18 laps = 20/9 laps

The value of x which makes ΔABC congruent to ΔDEF is 12.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

ΔABC is congruent to ΔDEF

This means,

∠A = ∠D ____(1)

∠B = ∠E ____(2)

∠C = ∠F _____(3)

Now,

From (1),

42 = 4x - 6

42 + 6 = 4x

48 = 4x

x = 48/4

x = 12

From (2),

7x + 10 = 94

7x = 94 - 10

7x = 84

x = 12

Thus,

The value of x is 12.

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While some College Board math sections permit all students to use a calculator, other math portion do not. Students can prayer the use of a four-function calculator for use on Non calculator sections.

Four-function calculators are basic calculators that have functions limited to subtraction, addition, multiplication, square roots, division, and percentage.

Four-function calculators can only be used on test portion that need math calculations.

They must be put away during non-mathematical part.

Board policy on use of a calculator may vary by exam. Check by reading calculator rules for the PSAT/NMSQT and PSAT 10 and the SAT or visiting AP Students to read calculator policies for specific AP exams.

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1 is the only number that is neither prime nor composite number. 1 is the only factor of 1. One is the only number that has only 1 factor.

Explore factors using illustrations and interactive example

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When four coins are flipped at once, there is probability a 1/4 chance that the penny and nickel will both come up heads.

As per the data given in the above question are as bellow,

The data provided are as ,

As stated in the query,

Four coins are flipped simultaneously.

Flipping a coin might result in either a head or a tail.

Total results equal 2

For each coin, there is a one-in-two chance of obtaining a head.

likelihood of finding heads on both penny and nickel coins

= ( 1 / 2 ) × ( 1 / 2 )

= ( 1 / 4 )

As a result, 1 / 4 represents the likelihood of finding heads on both the penny and nickel.

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Answer:

The value of b in the equation x^2+bx+c=0 can be found using the quadratic formula. The quadratic formula states that the roots of the equation are given by:

x = (-b ± √(b^2 - 4ac))/2a

Where a = 1, since the coefficient of x^2 is 1, b = b and c = c.

Step-by-step explanation:

Given that the roots of the equation are -4 and 2, we can substitute these values for x into the equation and solve for b.

For the first root of -4, we get:

1x^2 + bx + c = (1)(-4)^2 + b(-4) + c = 0

This simplifies to:

16 - 4b + c = 0

For the second root of 2, we get:

1x^2 + bx + c = (1)(2)^2 + b(2) + c = 0

This simplifies to:

4 + 2b + c = 0

Now we have two equations with two unknowns, we can use the substitution method to find the value of b.

By equating the two equation we get:

16 - 4b + c = 4 + 2b + c

We can simplify it as:

12 - 2b = 0

therefore b = 6

In summary, the value of b in the equation x^2+bx+c=0 is 6 when the roots of the equation are -4 and 2.

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Answer:

x = 19.425

Step-by-step explanation:

x = (asin(B)) / (sin(B))

x = (21sin(61∘)) / (sin(71∘))

x = 19.425 cm

The approximate arc length is 56.52mm.

The central angle that creates the intercepted arc's central angle, or the arc measure, is expressed in degrees. Arc length can be estimated as a percentage of the circle's circumference by multiplying the circle's diameter by the arc length, divided by 360.

The distance between two places along a segment of a curve is known as the arc length.

Given that, the bicycle wheel has a radius (r) = 225 mm

And number of equally spaced spokes (n) = 25

π = 3.14

Perimeter of the bicycle wheel (P) = 2*π*r

Perimeter of the bicycle wheel = 2 * 3.14 * 225 mm

Perimeter of the bicycle wheel = 1413 mm

The arc length = Perimeter of the bicycle wheel (P) / number of spokes (n)

The arc length = 1413 / 25 mm

The arc length = 56.52 mm

The approximate arc length is 56.52mm.

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23 minutes she will be devoting to weightlifting in week 10.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Formula represent the sequential increase in weight lifting time is :

f (n) = 2n + 5

f (n) = 2n + 5

f (10-1) = 2(10-1) + 5

f(9) = 2(9)

f(9) = 18

f(9) = 23

Therefore,23 minutes she will be devoting to weightlifting in week 10.

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