use differentials to estimate the amount of metal in a closed cylindrical can with diameter 10 cm and height 15 cm if the metal is 0.1 cm thick.

[tex]a = 7[/tex]

[tex]d = 12 - 7 = 5[/tex]

[tex]L = 102[/tex]

[tex]\implies a + (n-1)d = 102[/tex]

[tex]\implies 7 + (n-1)(5) = 102[/tex]

[tex]\implies (n-1)(5) = 95[/tex]

[tex]\implies n - 1 = 19[/tex]

[tex]\implies n = 20[/tex]

[tex]\text{Required sum = n/2} \ (a + L)[/tex]

[tex]= 20 \div2 \ ( 7 + 102)[/tex]

[tex]= 10 \times 109[/tex]

[tex]\bold{= 1090}[/tex]

Answer:

The sum is 1090

Step-by-step explanation:

S=7+12+17+22+...+102 ---> reason=5

We define the values, before starting:

Ratio = r , Term n = Tn , Term number = n , Term one = T1

To do this we first find the term number of 102, with the following formula:

Tn = t1 + (n - 1) r

102 = 7 + (n - 1) 5

102 = 7 + 5n - 5

102 = 5n + 2

100 = 5n

20 = n

Then we realize that 102 is the term N°20, now what we have to do is find the sum of the arithmetic series, with the following values and the following formula:

t1 = 7   ,   tn = 102   ,   n = 20

S = ( [tex]\frac{t1+tn}{2}[/tex]) . n

S = ( [tex]\frac{7+102}{2}[/tex]) . 20

S = 109 . 10

S = 1090

Answer: 5

Step-by-step explanation:

tan(32) = x/8

8 x tan(32) = x

x = 4.998 ≈ 5

The most appropriate way to report the distance driven using the car’s odometer is  181.7.

An odometer  is an instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car. The device may be electronic, mechanical, or a combination of the two.

According to the question

A car’s odometer measures distance to the nearest 0.1 miles.

i.e it measures only 1 digit after decimal

Therefore,

the most appropriate way to report the distance driven using the car’s odometer is  181.7 miles as it has only 1 digit after decimal.

Hence, the most appropriate way to report the distance driven using the car’s odometer is 181.7 .

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Using equations, we can find that there are a total of 45,000 seats available at the baseball game.

An equation is a mathematical statement that has two expressions with equal values, each separated by the symbol "equal to."

Let x be the total number of seats available.

According to the problem, 18% of the seats are bleachers, and 42% of the seats are grandstands.

That means the remaining 40% of the seats are box and club seats combined since 100% - 18% - 42% = 40%.

The problem states that there are 12,600 box seats and 5,400 club seats available, which makes a total of

12,600 + 5,400 = 18,000 box and club seats.

Now, we can set up an equation to find the total number of seats:

0.40x = 18,000

To solve for x, divide both sides of the equation by 0.40:

x = 18,000 ÷ 0.40

x = 45,000

There are a total of 45,000 seats available at the baseball game.

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Based οn the theοretical prοbability, we shοuld expect tο rοll a number 3 20 times οut οf 120 rοlls.

Theοretical prοbability is a type οf prοbability that is based οn mathematical reasοning and analysis. It is the prοbability οf an event οccurring based οn the assumptiοn that all οutcοmes are equally likely.

Fοr example, if yοu rοll a fair six-sided dice, each οutcοme (1, 2, 3, 4, 5, οr 6) is equally likely tο οccur.

Therefοre, the theοretical prοbability οf rοlling a 1 is 1/6, the theοretical prοbability οf rοlling a 2 is 1/6, and sο οn.

Here we have

The faces οf a fair 6-sided cube are numbered 1 thrοugh 6.

The cube is rοlled 120 times,  

Since the cube is fair, each οf the six faces has an equal prοbability οf appearing οn any given rοll.

Hence, the theοretical prοbability οf rοlling a 3 οn a single rοll is 1/6.

Here we can use the fοrmula fοr expected value tο find the number οf times we shοuld expect tο rοll a 3:

Expected value = (number οf trials) x (prοbability οf success)

Expected value = 120 x (1/6) = 20

Therefοre,

Based οn the theοretical prοbability, we shοuld expect tο rοll a number 3 20 times οut οf 120 rοlls.

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Answer:

C=15.7cm

A=78.54cm^2

Step-by-step explanation:

C=πr = π(5cm) = 15.7cm

A=πr^2 =π (5cm)^2 =78.54cm^2

The maximum revenue can be obtained when x = 100 dollars. Thus, the store should offer a rebate of 100 to maximize its revenue.

Given information:

A store has been selling 200 DVD burners a week at 350 each. A market survey indicates that for each 10 rebate offered to buyers, the number of units sold will increase by 20 a week.

Let's assume x is the number of 10 rebate and y is the number of units sold. It is given that a store has been selling 200 DVD burners a week at 350 each. So the initial price is 350 for 200 DVD burners.

Therefore, the demand function y(x) can be given as:

y(x) = 200 + 20x...(i)It is also known that for each 10 rebate offered to buyers, the number of units sold will increase by 20 a week. So the price of DVD burners will be (350 - 10x) for the additional units sold.

Therefore, the revenue function R(x) can be given as:

R(x) = (350)(200 + 20x) + [(350 - 10x)(20x)]...(ii)

The above equation (ii) is the revenue function.

Now we will find the value of x that maximizes R(x).

For the above revenue function, we need to find the value of x that maximizes R(x).

So differentiate R(x) w.r.t x to get the value of x that maximizes R(x).

dR(x)/dx = 350(20) - 10(200 + 20x) + 20(350 - 10x) = 0

Simplifying the above expression:

7x - 700 = 0x = 100

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Answer:

7.654 ft

Step-by-step explanation:

The volume of a hemisphere is [tex]V=\frac{2}{3}\pi r^3[/tex]. Rearranging this equation gives [tex]r=\sqrt[3]{\frac{3V}{2\pi} }[/tex]. Plug in V=939 to find the value of r.

Answer:

a) x = 2

b) x = 10

c) x = 10/3

d) x = 11/2

e) x = 24

Step-by-step explanation:

a) x = 8-6

x=2

b) x=20/2

     x=10

c) 3x = 9+1

3x=10

x=10/3

d) 2x=11

x=11/2

e) x = 6*4

x=24

The measure of angle D is 98°

We know that a quadrilateral is cyclic if and only if its opposite angles are supplementary.

Here, quadrilateral ABCD is inscribed in a circle.

From the attached figure, we can observe that angles A and C are opposite angles, so they are supplementary angles

∠A +  ∠C = 180°

(9x - 1) + 64 = 180

9x + 63 = 180

x = 13

So, the angle B would be:

m∠B = 6x+4

        = 6(13)+4

        = 82°

We can observe that angles B and D are opposite angles, so they are supplementary.

⇒ m∠B + m ∠D = 180°

⇒ 82° + m ∠D = 180°

⇒ m∠D = 98°

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The complete question is:

Quadrilateral ABCD is inscribed in a circle. m∠A is 64°, m∠B is (6x + 4)°, and m∠C is (9x - 1)° What is m∠D?

Answer: The divisors of 20 are 1, 2, 4, 5, 10, and 20. Out of these, only the numbers 1, 2, 4, and 5 are possible outcomes when rolling a standard 6-sided dice.

The probability of rolling any of these four numbers is the total number of favorable outcomes (4) divided by the total number of possible outcomes (6), which gives:

Probability = Favorable outcomes / Total outcomes = 4/6 = 2/3

Therefore, the probability of rolling a 6-sided dice and getting a number that is a divisor of 20 is 2/3 or approximately 0.667.

Step-by-step explanation:

The probability of rolling a six-sided die and getting a result that divides by 20 is 2/6, or around one-third of the time.

There is a 1/3 chance that you will roll a number that divides by 20 when using a six-sided die. There are 6 possible outcomes when a 6-sided die is rolled, however only the numbers 4 and 5 may divide by 20. There are hence 2 positive events and a total of 6 occurrences that could take place. When the number of successful outcomes is divided by the total number of possible outcomes, the probability is 2/6, or 1/3

Because just one-third of results are likely to meet the criteria, the likelihood of rolling a number on a 6-sided die that is a divisor of Twenty is minimal.

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Answer:

x=3

Step-by-step explanation:

Number of remaining rods can she choose as the fourth rod is 10

For the rods to form a quadrilateral with positive area, the fourth rod must satisfy the triangle inequality. That is, the sum of the lengths of any two sides of the quadrilateral must be greater than the length of the remaining side.

Let's start by looking at the rod with length 3 cm. The only other rod that can be paired with it to form a triangle is the rod with length 7 cm, since all the other rods are either shorter or longer than 4 cm. Similarly, the only other rod that can be paired with the rod with length 15 cm is the rod with length 7 cm.

Therefore, to form a quadrilateral with positive area, Joy must choose a rod that is longer than 7 cm but shorter than 18 cm (since the sum of 7 cm and 15 cm is 22 cm). There are 10 rods that satisfy this condition: 8 cm, 9 cm, 10 cm, 11 cm, 12 cm, 13 cm, 14 cm, 16 cm, 17 cm, and 18 cm.

So Joy can choose 10 rods as the fourth rod to form a quadrilateral with positive area.

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The given question is incomplete, the complete question is:

Joy has 30 thin rods, one each of every integer length from 1 cm through 30 cm. She places the rods with lengths 3 cm, 7 cm, and 15 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?

Answer: The volume of the metal cube 1x1x1 m is:

V_cube = l × w × h = 1 m × 1 m × 1 m = 1 m^3

The volume of the metal block that is to be cut from the cube is:

V_block = l × w × h = 3 cm × 3 cm × 4 cm = 36 cm^3

We need to convert the volume of the block to cubic meters, as the volume of the cube is given in cubic meters. We can use the conversion factor 1 m = 100 cm to convert cubic centimeters to cubic meters.

V_block = 36 cm^3 ÷ (100 cm/m)^3 = 0.000036 m^3

The number of blocks that can be cut from the cube is:

N_blocks = V_cube ÷ V_block = 1 m^3 ÷ 0.000036 m^3 = 27,777.78

Since we can only have a whole number of blocks, the maximum number of blocks that can be cut from the cube is 27,777.

The remaining volume of the cube after cutting the metal block is:

V_remain = V_cube - V_block × N_blocks = 1 m^3 - 0.000036 m^3 × 27,777 = 0.999 m^3

The surface area of the remaining cube can be calculated as follows:

S_remain = 6 × (l × w) = 6 × (h^2) = 6 × (0.999 m)^2 = 5.994 m^2

Therefore, the complete number of blocks that can be cut from the metal cube is 27,777. The volume of each block is 36 cm^3 or 0.000036 m^3. The remaining cube has a volume of 0.999 m^3 and a surface area of 5.994 m^2.

Step-by-step explanation:

Answer:

Proved that tan45° × sec40° + tan60° × cosec40° =4 by using the trigonometric ratio formulas.

Given that,

We have to prove that tan45° × sec40° + tan60° × cosec40° =4

We know that,

What is trigonometry ratio?

Trigonometric ratios are ratios of triangle side lengths. These ratios in trigonometry demonstrate the relationship between the sides and angles of a right triangle. The three basic ratios in trigonometry are sine, cosine, and tangent.

Take the left hand side

tan45° × sec40° + tan60° × cosec40°

We know that tan45°=1 and tan60°=√3

1×sec40°+√3×cosec40°

sec40°+√3cosec40°

We know that from formula,

sec40° = \frac{1}{cos40\textdegree}

cos40\textdegree

1

and cosec40° = \frac{1}{sin40\textdegree}

sin40\textdegree

1

\frac{1}{cos40\textdegree}

cos40\textdegree

1

+√3× \frac{1}{sin40\textdegree}

sin40\textdegree

1

1+3

4 (Approximately)

Therefore, Proved that tan45° × sec40° + tan60° × cosec40° =4 by using the trigonometric ratio formulas.

Answer:

104

Step-by-step explanation:

9^2+3(9)-4 = 104

Length of rectangular plot is 144ft

A rectangle is a geometric shape that is characterized by having four straight sides and four right angles. It is a type of quadrilateral, which means that it has four sides. The opposite sides of a rectangle are parallel and of equal length, which makes it a type of parallelogram.

Given;

From the image attached below;

Diagonal length, AB=306 ft

Base length, BC=270ft

As triangluar plot is right angled triangle.

According to pythagoras' theorem

AB²=BC²+CA²

Putting the values, we get

Length side of rectangle, BC=√306²-270²

BC=√20736

BC=144ft

Hence, Length of rectangular plot is 144ft

The right angle is inscribed in rectangular plot. The base and height of right angle is one base and height of the rectangular plot. Hence, the lengths of the legs of a right triangle related to the lengths of the sides of a​ rectangle.

Image is attached below

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Answer:

Step-by-step explanation:

i think i is -1

Answer:

4802 rounded to the nearest 1000 is 5000

Answer:

5,000

Step-by-step explanation:

We are rounding all of the elements in the equation, 2 rounds to 0, 0 rounds to 0, 8 rounds to 9, 9 rounds to 5,000.

Standard deviation of the following data is 0.655.

The standard deviation is equal to the variance's positive square root. It is a fundamental statistical analysis method. The amount by which data values deviate from the mean is referred to as "standard deviation," or "SD."

Whereas a big standard deviation implies that the values are much outside the mean, a low standard deviation shows that the values are frequently only a few standard deviations from the mean.

Here in the question,

Total kids = 20.

Mean = 9+9.5+9.5+10+10+10+10+10.5+10.5+10.5+10.5+11+11+11+11+11+11+11.5+11.5+11.5/20

= 10.52

Now square of distance between mean and ages.

(9-10.52) ² = 2.31

(9.5-10.52) ² = 1.04

(10-10.52) ² = 0.27

(10.5-10.52) ² = 0.0004

(11-10.52) ² = 0.23

(11.5-10.52) ² = 0.96

Now sum of all the differences = 2.31 + 1.04 + 1.04 + 4×0.27 + 4× 0.0004 + 6× 0.23+ 3×0.96

= 8.73

Now standard deviation = √8.73/20

= √0.43

= 0.655

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Let x be Mary’s age

Let x-3 be Ned’s age

Let x+2 be Carla’s age

(x+2)-10=(x-10)+[(x-3)-10]

x+2-10=x-10+x-3-10

x-x-x=-10-3-10-2+10

-x=-15

x=15

Mary is 15, Ned is 12, and Carla is 17.

Hence, the present age of the father is 30 years, and the present age of the son is 4 years.

To find someone's age, you need to know their date of birth and the current date. Then, you can calculate the difference between the two dates to determine their age. Here are the steps you can follow:

Ask the person for their date of birth.

Use a calendar or an online tool to determine the current date.

Calculate the difference between the two dates in years.

If the person has not had their birthday yet this year, subtract one year from the result.

Let's assume the present age of the son is "x" years.

According to the problem statement, the present age of the father is 10 years more than 5 times the age of the son, which can be mathematically represented as:

[tex]Father's present age = 5x + 10[/tex]

Also, it is given that the father was 28 years old two years ago. So, his present age would be 28 + 2 = 30 years.

Now, equating the two expressions for the father's age, we get:

[tex]5x + 10 = 30[/tex]

Solving for x, we get:

[tex]5x = 20\\x = 4[/tex]

Therefore, the present age of the son is 4 years.

And the present age of the father is:

[tex]5x + 10 = 5(4) + 10 = 30 years.[/tex]

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Option B. It defines the joint probability as the probability of the intersection of two events.

A joint probability refers to the probability of two or more events occurring simultaneously. In other words, it is the probability that two or more events will occur together.

The joint probability of two events A and B is denoted as P(A ∩ B), which represents the probability of the intersection of events A and B. This is the probability that both A and B occur at the same time.

For example, if we toss a coin and roll a dice, the probability of getting heads on the coin and a 4 on the dice would be the joint probability of these two events occurring together. This joint probability can be calculated by multiplying the probability of getting heads (1/2) and the probability of rolling a 4 (1/6), giving a joint probability of 1/12.

Therefore, option (b) is the correct answer, as it defines the joint probability as the probability of the intersection of two events.

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The sphere has a volume of around [tex]221.83[/tex] cubic inches.

All of the points on a circle are equally spaced apart from the center along a line, whereas all of the points on a sphere are equally spaced apart from the center along any of the axis. In the case of a ring, we can only calculate the area, however for a sphere, we can compute both the surface area and the volume.

The volume of a cuboid generated by stretching the dimensions of rectangles in place is equal to: Volumes = length [tex]*[/tex] width [tex]*[/tex] height, for instance, if the area of a rectangles is length [tex]*[/tex] breadth.

[tex]V = (4/3)[/tex]π[tex]r^{3}[/tex]

where [tex]r[/tex]  is the radius of the sphere.

In this problem, the radius of the sphere is half the diameter, which is [tex]11[/tex]inches. Therefore, the radius is:

[tex]r = d/2 = 11/2 = 5.5[/tex] inches

Substituting this value into the formula for the volume of a sphere, and using the approximation π [tex]=3[/tex], we get:

[tex]V = (4/3)[/tex]π[tex]r^{3}[/tex] [tex]= (4/3)(3)(5.5^{3} ) = (4/3)(3)(166.375) = 221.83 in^{3}[/tex]

Therefore, the volume of the sphere is approximately [tex]221.83[/tex] cubic inches.

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The size of the angle PRQ is approximately 26.565 degrees.

Since PQ and QR are two sides of a regular 12-sided polygon, they are congruent, and the polygon can be divided into 12 congruent isosceles triangles with base PQ and QR.

Let's call the center of the polygon O. Since the polygon is regular, the angle POQ is 360/12 = 30 degrees. Also, since PR is a diagonal of the polygon, it divides angle POQ into two congruent angles, each measuring 15 degrees.

Now, let's consider the triangle PQR. We know that angle PQR is 180 - (15 + 15) = 150 degrees (since the sum of angles in a triangle is 180 degrees).

Using the Law of Cosines, we can find the length of PR:

PR² = PQ² + QR² - 2(PQ)(QR)cos(angle PQR)

PR² = PQ² + QR² - 2(PQ)(QR)cos(150)

PR² = PQ² + QR² + (PQ)(QR)

Since PQ = QR, we can simplify this to:

PR² = 2(PQ²) + PQ²

PR² = 3(PQ²)

Therefore,

PQ² = (1/3)(PR²)

Now, let's consider the triangle PRQ. We know that PQ is a side of the polygon, so it has length 1 (we can choose any unit of length we like). Also, we know that QR is a side of a regular 12-sided polygon, so we can use the formula for the side length of a regular polygon:

QR = 2PQsin(180/12) = PQ√(6 + 2sqrt(3))

Substituting PQ = 1, we get:

QR = √(6 + 2√(3))

Finally, we can use the Law of Cosines again to find the angle PRQ:

cos(angle PRQ) = (PQ² + QR² - PR²) / (2PQQR)

cos(angle PRQ) = (1 + 6 + 2√3) - PR^2) / (2√(6 + 2√(3)))

Substituting PR² = 3(PQ²) = 3, we get:

cos(angle PRQ) = (7 + 2√(3)) / (2√(6 + 2√(3)))

Taking the inverse cosine, we get:

angle PRQ = 26.565 degrees (to 3 decimal places)

Therefore,  the size of the angle PRQ is approximately 26.565 degrees.

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Answer:

6.6km

Step-by-step explanation:

Area of trapezium = 0.5(a+b)h

201 = 0.5(17+b)17

201 = 8.5(17+b)

201 = 144.5 + 8.5b

201 - 144.5 = 8.5b

56.5 = 8.5b

b = 6.65km

Rounded to the nearest hundredth, the volume of empty space is approximately 6651.72 cm³

Diameter is a straight line passing through the center of a circle or a sphere, and connecting two points on the circumference or surface respectively.

The diameter of each ball is 14 centimeters, so the height of the cylindrical container must be at least 42 centimeters in order to stack three balls inside. Let's assume that the height of the container is exactly 42 centimeters.

The three tennis balls weigh a combined amount of:

3 × (4/3)πr³ = 3 × (4/3)π(7 cm)³ ≈ 1436.76 cm³

The volume of the cylindrical container is:

πr²h = π(7 cm)²(42 cm) ≈ 8088.48 cm³

So the volume of the empty space left inside the container is:

8088.48 cm³ - 1436.76 cm³ ≈ 6651.72 cm³

Rounded to the nearest hundredth, the volume of empty space is approximately 6651.72 cm³.

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The net growth of of population of butterflies led to 560 butterflies.

We know that the population of butterflies is 500.

The population experiences a net growth of 12%.

The net growth can be defined as increase in number of individuals in a population .

So, the gain in the population of butterflies = 12% of 500= (12/100) × 500= 60 Butterflies

So, the new population of butterflies after the gain is 500 + 60 = 560 Butterflies.

This can be calculated by another method which is

112% of 500= (112/100)*500 = 560 butterflies

Hence, the required answer is 560 butterflies.

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Step-by-step explanation:

It is a triangle.....all of the interior angles of ANY triangle su to 180 degrees.

soooo

  x  +   65 + 50   =   180

   x   =   180 - 65 - 50 = _________ degrees