The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes

if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)​ IS 1

P(n) :

1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)​

P(1) :

[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]

[tex]1=\frac{6}{6}=1[/tex]

∴ LHS = RHS

Assume P(k) is true

P(k):

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Answer: 9 2/3

Step-by-step explanation:

you take 29 and divide by 13 to get 2.23076923077 and you then take that times the 4 1/3 to get 9 2/3

Answer:

Step-by-step explanation:

13(X-4 1/3)=29

13X-56.3=29

     +56.3 = +56.3

13X=85.3

X=6.56

a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).

b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.

c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.

d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.

The quadratic function for this problem is defined as follows:

f(x) = 4x² + 8x - 5.

Hence the coefficients are given as follows:

a = 4, b = 8, c = -5.

The discriminant is given as follows:

D = 8² - 4 x 4 x (-5)

D = 144.

Hence the x-intercepts are given as follows:

Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:

f(x) = 4(x - 0.5)(x + 2.5).

As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.

The y-intercept is given as follows:

f(0) = 4(0)² + 8(0) - 5

f(0) = -5.

The coordinates of the vertex are given as follows:

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After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.

Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.

Let, assume miles be m.

and, Let the total cost be x.

According to the question,

0.25m + 50 = x ........(i)

0.41m + 25 = x ........ (ii)

By solving equation (ii) by (i) we get -

0.16 m - 25 = 0

or, 0.16m = 25

or, m = 25 /0.16

or, m = 156.25

Thus, number of miles = 156.25 miles.

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The measure of the central tendency is 67 as the data in the set are integers.

A single number that seeks to characterize a set of data by pinpointing the center position within that set of data is referred to as a measure of central tendency.

As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

Given, A data set 70, 67, 75, 60, 67, 65.

Arranging the data set in ascending order,

60, 65, 67, 67, 70, 75.

Now, The mean of the set is (60 + 65 + 67 + 67 + 70 + 75)/6.

= 67.33.

Mode of the data set 67.

So, The central tendency of the data set is 67 as the data in the set are all integers.

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The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of the line as -

y = 14x - 4

The given equation of line is -

y = 14x - 4

Slope of the line perpendicular to the given line is -

m{p} = -1/14

The equation of this line will be -

y = -(1/14)x + c

For the point (28, 16), we can write -

16 = -(1/14) x 28 + c

c = 16 + 2

c = 18

So, the equation will be -

y = - (1/14)x + 18

Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

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When Python constructs a function, it also generates a temporary variable with the same name, and only the function can access the value of that variable.

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The real world situation that can be modelled with the given  expression can be modelled as shown below.

Given is the expression as -

D/3

A real world situation that can be modelled with this expression can be written as follows -

Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.

Therefore, the real world situation that can be modelled with the given  expression can be modelled as shown above.

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Answer:

the percentage is 62%

Step-by-step explanation:

In the spring of 2012, 2300 student athletes participated in a sport.

The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

In 2014, there were 2277 student athletes participating in spring sports.

Suppose there were x contestants in 2013.

The answer was 2277, which was 110 percent more pupils competing in 2014 than in 2013. So,

[tex]$110 \%$ of $\mathrm{x}=2277$$\frac{110}{100} \times \mathrm{x}=2277$$\mathrm{x}=\frac{2277 \times 100}{110}$$\mathrm{x}=2070$[/tex]

2070 pupils therefore competed in 2013.

Let y be the student who will be vying in 2012.

Now, the number of pupils competing in 2070 was 90% that of the year 2012's.

So,

[tex]$90 \%$ of $y=2070$$$\begin{aligned}& \frac{90}{100} \times y=2070 \\& y=\frac{2070 \times 100}{90} \\& y=2300\end{aligned}$$[/tex]

As a result, 2300 students competed in the 2012 competition.

Therefore, the answer is 2300.

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An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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Answer:

Tamicca made 12 monthly payments of $115, for a total payment of 12*$115 = $<<12*115=1380>>1380.

She bought a computer for $1200, so the finance charge that she paid is $1380-$1200 = $<<1380-1200=180>>180.

Therefore, the finance charge that Tamicca paid was $180, rounded to the nearest cent.

Step-by-step explanation:

According to the probability, there are 540 arrangements that can the cars stack up so that all three lanes are occupied.

Mathematicians use addition and division as well as counting to calculate probability.

There are three partitions of six using digits 1-3.

(4,1,1), (3,2,1), (2,2,2) (2,2,2)

These could be dispersed between the lanes in order that

(3) Possible solutions to (4,1,1)

There are six possible ways to solve the equation (3,2,1).

There is only one possible solution to the equation (2,2,2).

Cars must now move in the lanes in proper order.

The arrangements for (4,1,1) will be 6C4 * 2C1 = 30. Six cars are chosen, sorted, and placed in the appropriate lanes. then decide on 1 of the 2 surviving vehicles.

then place it in a lane.

The arrangements for (3,2,1) will be 6C3 * 3C2 = 60.

There will be 6C2 * 4C2 = 90 arrangements for (2,2,2).

Consequently, there will be 540 arrangements (3*30 + 6*60 + 1*90 = 90+360 + 90).

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Using sine and cosine rule, the length of d in the triangle is equal to 4.5cm

The sine rule is a mathematical formula used to calculate the lengths of the sides and angles of any triangle when given two angles and one side or two sides and one angle. It is also known as the law of sines.

To find the length of d, we have to find the length of E.

Using sine rule;

f / sin F = e / sin E

5 / sin 75 = e / sin 79

e = 5sin79 / sin 75

e = 5.7cm

To find the length of d, we have to find the angle D by using the sum of angle theorem.

m∠ E + m∠ F + m∠ D = 180°

79 + 75 + m∠ D = 180

m∠ D = 180 - 154

m∠ D = 26°

Using cosine rule

d² = e² + f² - 2efCosD

d² = 5.7² + 5² - 2(5.7)(5)cos26

d² = 20.615598

d = √20.615598

d = 4.5cm

The length of side d is 4.5cm

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Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

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Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24

A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.

To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.

So to find out the fraction of a whole pizza  that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,

3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24

Now to equally divide this into 5 person, we need to divide this fraction by 5,

i.e 55/(24*5) = 11/24

Therefore, each person gets 11/24 of the whole pizza.

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a) The minimum number of dogs that could have a mass of more than 27 kg is 6.

b) The maximum number of dogs that could have a mass of more than 27 kg is 18.

We have a table which shows information about the masses of some dogs.

Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.

But we wants minimum of 12 and 6 is 6 .

so, the minimum number of dogs with mass more than 27 kg is 6.

b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.

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Complete question:

The above table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than 27 kg

b) Work out the maximum number of dogs that could have a mass of more than 27 kg

Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

The equations are n + s = 76 and 2n + 1.50 s = 125.

let n = number of Nachos sold

let s = number of sodas sold

Two equations are presented to us, and we can use them together to solve one variable at a time.

Eq. 1: n + s = 76

Eq. 2: 2n + 1.50 s = 125

So, s = 76 - n

Put (76 - n) for s in the second equation

2n + 1.50 (76 - n) = 125

2n + 114 - 1.50 n = 125

2n - 1.50 n + 114 = 125

0.5n + 114 = 125

0.5n = 125 - 114

0.5n = 11

n = 22

s = 76 - 22

s = 54

22 nachos sold and 54 sodas sold.

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Answer:

by using sine rule and cosine rule.

Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation

1. Foil (x+2)(x+1)

X^2 +2x + x + 2

2. Simplify

X^2 + 3x + 2

3. Distribute x^2 + 3x +2 (y-3)

X^2y + 3xy + 2y -3x^2 -9x -6

Answer:

AC = PF

Step-by-step explanation:

Answer:

( - 7, - 1, 1, 4 )

Step-by-step explanation:

( x, y )

where,

x is Domain

y is Range

Hence,

Domain is ( - 7, - 1, 1, 4 )

With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

We have given,

Mean weight of Eskimo dogs is μ = 30 pound

Standard deviation of Eskimo dogs is σ = 2 pound

The range of weights would 99.7% of the dogs have,

R =  μ ± 3σ

R = 30 ± 3*2

R = 30 ± 6

R = (30 - 6) , (30 + 6 )

R = 24, 36

With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

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It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.

Triangles must have equal corresponding sides and equal corresponding angles in order to be congruent.

According to the RHS congruence theorem, two right-angled triangles are congruent if their respective hypotenuses and sides are the same as those of another right-angled triangle.

Here we have

AOC and BOD are diameters of a circle and have a center O.

It is given that AOC and BOD are diameters of a circle.

From the triangles Δ AOC and ΔBOD

⇒ BD = CA  [ Diameters of the circle i.e Hypotenuse of triangles ]    

⇒ ∠BAD = ∠CDA [ Right angles in a semicircle is 90°]

⇒ AD = AD [ Common in both triangles i.e sides of triangles ]

Thus, Using RHS congruence criteria

⇒ ΔABD ≅ ΔDCA

Hence,

It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.

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Answer:

They are parallel line.

AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.

Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.

Now we have

Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.

In ΔAED and ΔCED

ED=ED              (∵Common side are equal)

∠AED=∠CED       (∵Alternate angles)

∠A=∠C        (∵Alternate angles)

By ASA rule, ΔAED≅ΔCED

By Corresponding Parts of Congruent triangles

AE=EC

Hence, AE is conruent to CE.

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Answer:

x = - 1 or x = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

3x² + 5x + 2 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × 2 = 6 and sum = + 5

the factors are 3 and 2

use these factors to split the x- term

3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(3x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]

Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(4)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{20})}}\implies 80+50\implies \text{\LARGE 130}~m^2[/tex]