Arun wants to make a model of a cone with paper whose diameter is 6cm and slant height
is 7cm. Then he covered the cone with a lid (circular shape). How much paper is required to
make the model.

[tex]72x^{2}+3x+3[/tex]Answer:

Step-by-step explanation:

[tex]1. (4x^{2}+34x^{2} +34x^{2} )+(x+x+x)+3\\ 2. 72x^{2} +3x+3[/tex]

On solving the given question, we got Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2

A prism is a polyhedron in geometry that has an n-sided polygonal basis, a second base that is a shifted version of the first base, and n additional faces—necessarily all parallelograms. Connect the matching sides of the two bases.

h = 51 cm

a = 2cm

therefore,

volume of a Triangular Prism = (½) abh cubic cm

245.8 = [tex]\frac{1}{2}[/tex] X 2 X b X 51

[tex]= > b = \frac{245.8 X 2}{2 X 51}[/tex]

[tex]= > b = \frac{491.6}{102}[/tex]

[tex]= > b = 4.819[/tex]

Now Area of base of prism

Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2

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A method for deriving facts is to multiply by 10 or to add using 10. This means that before using the make-ten strategy, kids need to know some facts by hear. Use of a make 10 strategy requires knowing that 8+2=10 and 9+1=10. In order to use the make 10 strategy, add 8 and 5, then decompose 5 into 2 and 3.

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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a. The motion of the bus in each part is given as follows:

b. The graph is classified as follows:

c. The graph is non-linear.

The relation graphed is defined as follows:

Distance x time -> distance as a function of time.

The origin on the graph is the point that the Bus starts and then returns, at the end of the part 5.

Then the graph is also non-linear, as the position changes without linearity, meaning that the acceleration is not uniform.

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The circumcenter and Incenter of a triangle can be found this way :

Finding the incenter

The junction of a triangle's three angle bisectors is where you may locate its incenter. The incenter has an intriguing attribute as a result of its position: it is equally removed from each of the triangle's three sides. This feature is unique to this point. Like centroids, incenters are always contained within their triangles.

Two triangles are depicted in the above image along with their incenters and incircles (circles drawn inside the triangles so the circles barely touch the sides of each triangle). The incircles' centers are known as the incenters. (If you want to fit in with the in-crowd, don't talk about this "in" stuff too much.)

Finding the circumcenter

The point where the perpendicular bisectors of the triangle's sides meet is the triangle's circumcenter. Due to its position, the circumcenter has an intriguing property: it is equally removed from each of the triangle's three vertices.

In the illustration above, two triangles are shown along with their circumcenters and circumcircles (circles drawn around the triangles so that they pass through the vertices of each triangle). The centers of the circumcircles are known as the circumcenters.

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Answer: Equivalent fractions are two or more fractions that are all equal even though they have different numerators and denominators. For example, the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000.

*(This is not my work)*

Step-by-step explanation:

Answer: ([tex]\frac{-3}{5}[/tex], 1) and ([tex]\frac{-3}{5}[/tex], 3) are two you could use, but there are countless possibilities.

Step-by-step explanation:

   To solve this question, we will first isolate the variable x.

       -5x = 3

       [tex]\displaystyle \frac{-5x}{-5} =\frac{3}{-5}[/tex]

       x = [tex]\frac{-3}{5}[/tex]

   Next, we will find points that satisfy the equation. Any value in the y-coordinate will work as long as x = [tex]\frac{-3}{5}[/tex]. Some examples:

([tex]\frac{-3}{5}[/tex], 1)

([tex]\frac{-3}{5}[/tex], 6)

([tex]\frac{-3}{5}[/tex], -4)

([tex]\frac{-3}{5}[/tex], [tex]\frac{1}{2}[/tex])

([tex]\frac{-3}{5}[/tex], 0)

     Etcetera.

   I have attached a graph with two of the examples to further show. This graph uses ([tex]\frac{-3}{5}[/tex], 1) and ([tex]\frac{-3}{5}[/tex], 6). Negative three-fifths is equal to -0.6.

The number of boats needed for 1491 people are 20.

What is the cross-product?

The cross product, also known as the vector product in mathematics, is a binary operation on two vectors in a Euclidean vector space that is oriented in three dimensions. It is represented by the symbol times.

We have,
134 people decided to go scuba diving,
523 people decided to neither scuba dive nor go on a boat tour,

So, people go to boat tour = 2148 -(134 + 523)
= 2148 - 657
= 1491
now, since each boat holds 78 people.

[tex]\frac{1491}{78} = 19\frac{3}{26}[/tex]

= 20 boats.
Hence, the number of boats needed for 1491 people are 20.

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Complete Question
The 2148 guests at a hotel have the. the choice to either go on a boat tour or go scuba diving.  134 people decided to go scuba diving.  523 people decided to neither scuba dive nor go on a boat tour. Each boat holds 78 people. How many boats are needed? Explain your reasoning.

yes

Step-by-step explanation:

5

Answer: A

Step-by-step explanation:

The quotient is the result of the division between two numbers.

Answer:

n/3

Step-by-step explanation:

When you divide you get a quotient.

n divided by 3 will equal a quotient.

The amount of lavender oil y is proportional to the amount of jojoba oil x

Two quantities are said to be linearly proportionate if change in one quantity produce proportionate amount of change in the other quantity, or the ratio of the two quantities is fixed.

Given,

In the first case, 20 drops of lavender oil and 8 teaspoons of jojoba oil.

In second case, 50 drops of lavender and 20 teaspoons of jojoba oil.

Ratio in first case:

x:y  =  20:8

      = 5:2

Ratio in second case:

x:y  =  50:20

      = 5:2

Since ratio is fixed in both the cases, the amount of lavender oil y is proportional to the amount of jojoba oil x.

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Answer:

Step-by-step explanation:

1) Subtract 5 from both sides.

[tex]m-5=-0.5d[/tex]

2) Divide both sides by -0.5.

[tex]-\frac{m-5}{0.5} =d[/tex]

3) Switch sides.

[tex]d=-\frac{m-5}{0.5}[/tex]

Thank you,

Eddie

1) The estimated probability of patrick flipping a head with his coin is; 0.45

2) The margin of error for Patrick's estimated probability is; 0.218

3) The confidence interval for the chance of flipping a head with his coin is; CI = (0.232, 0.668)

No, the 95% confidence interval does not contain 50% as a probability, so it will be illogical to think that Patrick's lucky coin has a probability different from 0.5

We are given;

Number of trials; n = 20

Number of successful outcomes; x = 9

Thus; Proportion; p^ = x/n = 0.45

Now, the formula for the confidence interval of proportions is;

CI = p^ ± z√(p^(1 - p^)/n)

where;

z√(p^(1 - p^)/n) is margin of error

1) Probability of Patrick flipping a head with his lucky coin is;

p^ = x/n = 9/20 = 0.45

2) The margin of error is from the formula;

z√(p^(1 - p^)/n)

z for 95% confidence level is 1.96. Thus'

E = 1.96√(0.45(1 - 0.45)/20)

E = 0.218

3) Confidence interval is;

CI = 0.45 ± 0.218

CI = (0.232, 0.668)

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The amount of radioactive lead remaining after 4 years, 8 years, and 20 years will be 527.91, 464.48, and 435.69, respectively. And the half-life is 21.66 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

An example of 600 g of radioactive lead-210 rots to polonium-210 as per the capability [tex]\rm A(t) = 600 \times e ^{-0.032t}[/tex], where t is time in years.

The amount of radioactive lead remaining after 4 years is given as,

[tex]\rm A(4) = 600 \times e ^{-0.032\times 4}[/tex]

A(4) = 527.91

The amount of radioactive lead remaining after 8 years is given as,

[tex]\rm A(8) = 600 \times e ^{-0.032\times 8}[/tex]

A(8) = 464.48

The amount of radioactive lead remaining after 10 years is given as,

[tex]\rm A(10) = 600 \times e ^{-0.032\times 10}[/tex]

A(10) = 435.69

The half-life is calculated as,

[tex]\rm 300 = 600 \times e ^{-0.032\times t}[/tex]

-0.032t = ln (1/2)

0.032t = -0.693

t = 21.66 years

The amount of radioactive lead remaining after 4 years, 8 years, and 20 years will be 527.91, 464.48, and 435.69, respectively. And the half-life is 21.66 years.

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Answer:

According to the SAS ( Side Angle Side ) rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the equivalent two sides and angle between the sides of the other triangle.  

Step-by-step explanation:

Two figures are said to be "congruent" if they can be placed exactly over one another.

According to the SAS ( Side Angle Side ) rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the equivalent two sides and angle between the sides of the other triangle.  

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The rate of change of the table is -500

The average rate of change of a function, graph, table or ordered pair is simply the slope of the relation

The function is represented by the table of values

The interval of the function are the x values

So, we make use of  x values

x = 0 and x = 2

Start by calculating f(0) and f(2)

From the table, we have

f(0) = 30000

f(2) = 29000

So, the average rate over these intervals is calculated as:

Average rate = [f(2) - f(0)]/[2 - 0]

Substitute known values

Average rate = [30000 - 29000]/[0 - 2]

Simplify

Average rate = -500

Hence, the rate of change is -500

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Exponential decay graph looks like see the given image attached.

The process of diminishing an amount by a constant percentage rate over time is known in mathematics as exponential decay. The quantity drops gradually, followed by a dramatic decline in the rate of change and growth over time.

A linear function reduces the original number by the same amount each time, but exponential decay reduces the original amount by a constant percentage over time. Exponential decay differs from linear decay in this way: the decay factor depends on a percentage of the original quantity.

The exponential decay formula is used to determine this decline in growth.

Formula of exponential decay is given by

Its graph is given by

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[tex] \frac{1}{2} x - 4 < 3 \\ [/tex]

Add both sides 4

[tex] \frac{1}{2} x - 4 + 4 < 3 + 4 \\ [/tex]

[tex] \frac{1}{2} x < 7 \\ [/tex]

Multiply both sides by 2

[tex]2 \times \frac{1}{2} x < 2 \times 7 \\ [/tex]

[tex]x < 14[/tex]

_____________________________________________

[tex]7 \leqslant 3x + 5[/tex]

[tex]3x + 5 \geqslant 7[/tex]

Subtract both sides minus 5

[tex]3x + 5 - 5 \geqslant 7 - 5[/tex]

[tex]3x \geqslant 2[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} \geqslant \frac{2}{3} \\ [/tex]

[tex]x \geqslant \frac{2}{3} \\ [/tex]

The probabilities are given as follows:

a) Hardware product given that it is from company B: (50 - y)/50.

b) Hardware product given that it is from company A: 3/7.

c) The probability in part a is greater than in part B for y < 8.57.

A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes in the context of the experiment.

For item a, the outcomes are given as follows:

Hence the probability is of:

p = (50 - y)/50.

For item b, the outcomes are given as follows:

Hence the probability is of:

30/70 = 3/7.

The inequality for item c is given as follows:

(50 - y)/50 > 3/7

Applying cross multiplication, the solution is obtained as follows:

7(50 - y) > 3(50)

210 - 7y > 150

-7y > -60

7y < 60

y < 60/7

y < 8.57.

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The number that should be multiplied by 2/3 to get a product 1 is 3/2

What is the Reciprocal of two numbers?

One of two numbers that, when multiplied together, equals to 1 is known as a reciprocal or multiplicative inverse.

Transposing the numerator and denominator will allow you to get the reciprocal if you can reduce the number to a fraction.

Let the number that would result in product 1 be "x"

So, According to the question:

=> x × 2/3 = 1

Solving for x,

Dividing by 3/2 both sides

⇒x = 3/2 which is the reciprocal of 2/3

Hence,

The number that should be multiplied is 3/2

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All the inequalities that model the given situation are;

x + y ≥ 25

x > 10

y > 0

We are told that;

x represents the number of apples.

y represent the number of oranges.

Now, Mia needs to bring at least 25 pieces of fruit to the school picnic. Thus, the inequality is expressed as;

x + y ≥ 25

She is bringing both apples and oranges, and was told to be sure to bring more than 10 apples. Thus, the inequality is expressed as;

x > 10

Since we are not told the maximum number of oranges, then we can say it must be more than zero and as such we have the third inequality as; y > 0

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Each side of quadrilateral A changed by a factor of 1/4

When quadrilateral A was reduced the size of each angle remain unchanged

The dimensions of quadrilateral A are 16, 10, 6, 20

The dimensions of quadrilateral B are  4, 2.5, 1.5, 5

comparing the two dimensions

Let the factor be r

4r = 16

r = 16/4

r = 4

2.5r = 10

r = 10/2.5

r = 4

1.5r = 6

r = 6/1.5

r = 4

5r = 20

r = 20/5

r = 4

Therefore we can conclude that quadrilateral B was increased by 4, similarly, quadrilateral A was reduced by a factor of 1/4

16 * 1/4 = 4

10 * 1/4 = 2.5

6 * 1/4 = 1.5

20 * 1/4 = 5

since the reduction are similar quadrilateral A is similar to quadrilateral B

and the size of each angle were not affected

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Answer:

Step-by-step explanation: How much is 1 t shirt

Answer:

[tex]\textsf{D.} \quad 5^9=x[/tex]

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_5x-\log_525=7[/tex]

[tex]\textsf{Apply the quotient log law}: \quad log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]

[tex]\implies \log_5\left(\dfrac{x}{25}\right)=7[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 5^7=\dfrac{x}{25}[/tex]

Multiply both sides by 25:

[tex]\implies 25 \cdot 5^7=x[/tex]

Rewrite 5 as 5²:

[tex]\implies 5^2 \cdot 5^7=x[/tex]

[tex]\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 5^{2+7}=x[/tex]

[tex]\implies 5^9=x[/tex]

The function of piecewise graph shown in the figure is,

f(x) = {y = 6   for x < -5

        { [tex]y = -\frac{19}{9}x-\frac{5}{9}[/tex]    for -5 ≤x < 5

        { y = 8/5x -14   for x ≥ 5

What is piecewise function?

A piecewise-defined function in mathematics is a function with several sub functions, each of which has a certain interval in the domain for which it is applicable. Piecewise definition is a method of expressing the function, not a property of the function.

From graph we can see that the first function is a line y = 6

Hence, f(x) = {y = 6    for x < -5}

Now to find the equation of second function.

From graph we get two points (-5, 10) and (4, -9).

First to find the slope

[tex]m = \frac{-9-10}{4+5} = \frac{-19}{9}[/tex]

Now to find the equation of line, using slope point form

[tex]y - 10 = \frac{-19}{9} (x-(-5))\\y-10=-\frac{19}{9}x-\frac{95}{9} \\ y=-\frac{19}{9}x-\frac{95}{9} + 10\\y = -\frac{19}{9}x -\frac{5}{9}[/tex]

So, f(x) = { [tex]y= -\frac{19}{9}x-\frac{9}{5}[/tex],    for -5 ≤ x < 5}

Now to find the equation of third line.

From graph we get two points (5, -6) and (10, 2).

First to find the slope of the line

[tex]m = \frac{2-(-6)}{10-5} = \frac{8}{5}[/tex]

Now to find the  equation of line, using slope point form

[tex]y-(-6)=\frac{8}{5}(x-5)\\ y+6=\frac{8}{5}x-8\\ y = \frac{8}{5}x - 14[/tex]

So, f(x) = {[tex]y = \frac{8}{5}x-14[/tex],   for x ≥ 5}.

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The degree of a polynomial in factored form is the number of zeros or roots of that polynomial.

Given:

Degree of a polynomial:

Degree is the highest or the greatest power of a variable in a polynomial equation.

ex : 2x^2 + 2xy^2

Degree = 3

Degree of a polynomial in factored form:

Degree of a polynomial in factored form is the number of zeros or roots of that polynomial.

Example:

= (x-1) (x-2) (x-3)

number of roots = 3

Degree = 3

= (y-5)(y+3/2)(y-4)(y+1)

number of roots = 4

Degree = 4

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