A cone with a diameter of 8 centimeters has volume 143.6 cubic centimeters. Find the height of the cone

A Linear and Quadratic pair of  parent functions are inverses of each other on the domain x > 0.

In mathematics, a parent function is a basic representation of a function type without manipulations such as translation and dilation. For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simply shifting and stretching parallel to the axes. Function is defined as the set of all input values have at least one output value.

According to the question,

a. A pair of linear functions :

let the function be y = x.

Domain : (-∞ , ∞) set of all real numbers

Range : (-∞ , ∞) set of all real numbers

Inverse of linear function is linear domain and range set of all real numbers.

Option A is the correct answer.

b. A cubic function and a cube root function :

Let y = x³

Domain: (-∞ , ∞) set of all real numbers

Range : (-∞ , ∞) set of all real numbers

Inverse function  , x = ∛y ,

Domain: (-∞ , ∞) set of all real numbers

Range : (-∞ , ∞) set of all real numbers

Option B is not a correct answer.

c. a quadratic function and a square root function :

Domain of square root function: y = √x is [ 0, ∞)

Range of square root function: y = √x is [ 0, ∞)

Domain of quadratic function is (-∞ , ∞) set of all real numbers.

Range : all possible values of y.

Option C is not a correct answer.

D. A logarithmic function and an exponential function :

Domain : ( 0, ∞)

Range : set of all real numbers

Exponential function:

Domain : set of all real numbers

Range : ( 0, ∞)

Option D is not a correct answer.

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Answer:

The given equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing this with the given equation:

y = x - 2

We can see that the slope (m) is 1 and the y-intercept (b) is -2.

Answer:

C.

Step-by-step explanation:

The vertex and the point of intersection is just one point identifiied by its x and y vlaues

The probability of drawing a lettered card from a deck of shuffled 52 cards is 50%.

There are 52 cards in a deck, and 26 of them are lettered cards (A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2) while the other 26 cards are suited cards (clubs, spades, hearts, diamonds).

If the deck is well shuffled, each card is equally likely to be drawn.

Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is simply the number of lettered cards divided by the total number of cards:

P(Drawing a lettered card) = Number of lettered cards / Total number of cards

= 26 / 52

= 1/2

= 0.5

Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is 0.5 or 50%.

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Answer: Square

Step-by-step explanation:

A square has 4 parallel sides and has 4 90 degree angles

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:

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?

A recursive sequence is a sequence in which terms are defined using one or more previous terms that are given.

If you know the term n of an arithmetic sequence and you know the common difference, d, you can find the term [tex](n + 1)[/tex] by tossing the recursive formula to [tex]n + 1 = a \ n + d[/tex]

We have then:

[tex]5, 15, 30, 50[/tex]

[tex]an = (\dfrac{5}{2} ) \times (n) \times (n + 1)[/tex]

Answer:

the recursive formula for 5, 15, 30, 50, is:

an = (5/2) x (n) x (n + 1)

Answer:

NO

Step-by-step explanation:

It is a parabola, you can tell cuz of the x^2

:)

When Sarah and Gavyn win money, they divide it in a 5:3 ratio.If  Sarah gets £14 more than Gavyn, Gavyn gets £21.

Let's call the amount of money that Sarah and Gavyn win "x".

According to the problem, they share the money in the ratio 5:3, which means that Sarah gets 5 parts and Gavyn gets 3 parts.

Let's call the amount of money that Gavyn gets "y". Then, we know that:

Sarah gets £14 more than Gavyn, which means that Sarah's share is y + £14.

We can set up an equation to represent the fact that the ratio of their shares is 5:3:

5/3 = (y + £14)/y

To solve for y, we can cross-multiply:

5y = 3(y + £14)

5y = 3y + £42

2y = £42

y = £21

Therefore, Gavyn gets £21.

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Answer:h<13

Because h has to be less than 13, so h<13 is the correct answer

Step-by-step explanation:

Answer:

it could either be h<13 or 13-h depending on what you're studying

In the trapezoid , C) Area = 22.5 [tex]mi^2[/tex] , Perimeter = 22.5 mi.

What is area and perimeter?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape.

Here Base a = 3.5 mi , Base b = 5.5 mi and Height h = 5 mi.

Then Area of the Trapezoid = [tex]\frac{1}{2}[/tex] ( a + b ) h square unit

=> A = [tex]\frac{1}{2}(5.5+3.5)\times5[/tex]

=> A = [tex]\frac{1}{2}\times9\times5[/tex]

=> A = 22.5 [tex]mi^2[/tex]

Now perimeter is sum of all sides of the trapezoid. Then,

=> 3.5+5.5+7.5+6

=> 22.5 mi

Hence the area is 22.5 [tex]mi^2[/tex] and perimeter is 22.5 mi.

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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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Step-by-step explanation:

Using similar triangles:

6ft height is to 5 feet shadow as   tower height is to 40 ft tower shadow

6/5  = h / 40     <====solve for 'h'

40 * 6/5 = h  =  tower height = 48 feet tower height

For the right-angled triangle, the value for x is obtained as √2/4.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right angle triangle is given.

It has angles 90°, 45° and 45°.

The hypotenuse measures 4√2.

The perpendicular measures x.

In a 45°-45°-90° right triangle, the legs are congruent and the hypotenuse is √2 times the length of a leg.

Therefore, in this triangle, each of the legs has length -

(4√2)/√2 = 4

So x is equal to one of the legs, which is 4.

To fill in the blanks -

x : 4√2 = 1 : 4

4x = 4√2

x = (√2)/4

Therefore, the value for x is obtained as √2/4.

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Pythagorean Theorem can be used to find the missing side that is equal to 21.3.

Distance formula states that the distance between two points is equal to the square root of the sum of the squares of the differences of the coordinates.

The missing side can be found by using the Pythagorean Theorem, which states that the square of the length of the hypotenuse (longest side of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.

Therefore, the missing side is equal to the square root of the sum of the squares of the sides we already have:

b² = (16)² + (14)²

= 256 + 196

= 452

b = √452

= 21.3

We can also use the distance formula here.

The distance between (16, 14) and (0, 0) =

√(16² + 14²)

= √(256 + 196)

= √452

= 21.3.

This confirms that the missing side is equal to 21.3.

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Question:

Find the length of the missing side. If necessary, round to the nearest tenth.

21.3

30

15

7.7

(it is a triangle and it has a right angle and you are looking for b and the numbers on the triangle are 16 [this is the longest side and slanted] and 14 [this is straight with no slant)

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:

These angles are complementary and congruent, so x = 15.

Step-by-step explanation:

[tex]3x + 45 = 90[/tex]

[tex]3x = 45[/tex]

[tex]x = 15[/tex]

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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So the acute angle of the rhombus is 90 degrees, and the obtuse angle is twice as large, or 180 degrees.

The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's start by finding the length of one half of the longer diagonal. We can use the shorter diagonal (which we know is 10 cm) and the side length (which we know is 13 cm) to form a right triangle. The hypotenuse of this triangle is half of the longer diagonal, so we can solve for it using the Pythagorean theorem:

[tex]a^2+b^2 = c^2 \\(13/2)^2 + 10^2 = c^2\\169/4+100 =c^2 \\ 269/4= c^2 \\c = \sqrt{(269)}/2\\[/tex]

Therefore, the length of one half of the longer diagonal is sqrt(269)/2 cm. To find the full length of the longer diagonal, we just need to double this value:

longer diagonal = [tex]2 \times \sqrt{(269)}/2 = \sqrt{(269)}cm[/tex]

Now, we can use the fact that the sum of the angles in a rhombus is 360 degrees to solve for x:

2x + 2x = 360

4x = 360

x = 90

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There are 27 students in the class who walk to school.

Word problem refers to problem expressed entirely in words typically used as an educational tool.

Given that:

Total number of students in the class: 80

Number of girls in the class: 44

Number of girls who walk to school: 17

Number of boys who cycle to school: 14

Number of boys who take the bus to school: 12

We have to subtract the students who take the bus or cycle from the total number of students first. The number of boys who walk to school will be:

= Total number of boys - Boys who cycle - Boys who take the bus

= (Total number of boys) - 14 - 12

= (80 - 44) - 14 - 12

= 36 - 14 - 12

= 10

To get total number of students who walk to school, we compute as follow. The number of students who walk to school:

= Number of girls who walk to school + Number of boys who walk to school

= 17 + 10

= 27.

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So, the inverse function of f(x) = -x + 3 is g(x) = 3 - x, and it is in slope-intercept form. The slope of g(x) is -1 and the y-intercept is 3.

An inverse function is a function that reverses the operation of another function. More specifically, if f is a function that maps inputs from a set A to labors in a set B, also an inverse function g is a function that maps labors from B back to inputs in A, similar that for any input x in A, applying f and also g (or g and also f) results in the same value. In other words, if f(a) = b, also g(b) = a

by the question.

To find the inverse function of f(x) = -x + 3 in slope-intercept form, we need to solve for x in terms of y.

Start by replacing f(x) with y:

[tex]y=-x+3[/tex]

Now, isolate x on one side of the equation. To do this, we can add x to both sides:

[tex]y+x=3[/tex]

Finally, solve for x by subtracting y from both sides:

[tex]x=3-x[/tex]

So, the inverse function of f(x) = -x + 3 is given by:

[tex]f^{-1}(x)=3-x[/tex]

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Answer:

40, 60 and 80.

Step-by-step explanation:

Let x = t he size of the smallest angle

x + 2x + x + 20 = 180  The sum of the interior angles of a triangle is 180

4x + 20 = 180  Subtract 20 from both sides

4x = 160  Divide both sides by 4

x = 40

The smallest angle is 40.  The largest angle is 80.  The other angle is 60.  The total is 180

Helping in the name of Jesus.

According to the given figure, the area of the shaded region in the shape is 49.5mm2.

The total area of every one of the shapes which cover an object's surface is known as its surface area. The length and width of this type of rectangle are multiplied to determine its area.

To solve the following question we first need to separate the single shape into two according to the shapes given

Therefore we have two shapes with us, i.e., rectangle and triangle.

First of all, we need to calculate the area of both the shares separately:

Firstly, area of the rectangle, formula is:

Area = length x width

By entering the length and width values,

Area of rectangle= 7 x6

Area of rectangle= 42 mm2

Now, we need to calculate the area of the second shape, that is, triangle,

Triangle area is equal to height x base / 2.

Now, by putting values in the formula:

Area of triangle=3 x 5 / 2

Area of triangle= 15/2

Area of triangle= 7.5 mm2

Therefore, the area of the shaded region:

Area = (rectangular area + triangular area)

Area = 42 + 7.5

Area = 49.5 mm2

Therefore, the area of the shaded region of the shape given is 49.5 mm2.

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The probability of selecting a green marble from a jar containing 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles is 0.1875 or 18.75%.

To find p(g), we need to first determine the total number of marbles in the jar, and then determine the number of green marbles in the jar.

Total number of marbles = 4 blue marbles + 3 green marbles + 7 red marbles + 2 white marbles = 16 marbles.

Number of green marbles = 3.

So p(g) = number of green marbles / total number of marbles = 3 / 16.

Therefore, p(g) = 0.1875 or 18.75%.

Therefore, Choosing a green marble from a container holding 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles has a probability of 0.1875 or 18.75%.

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Answer:

(9x)/(2-2x)

Step-by-step explanation:

let f-1(x) = y

then, f(y) = x

so, (2y)/(9+2y) = x    

 ***remember the thing inside the () in  f(x) can change! y can go in x's place, any number or any other variable can go in x's place! BUT, nothing else can be changed in the function***                

   now just solve for y!

multiply both sides by (9+2y): 2y = 9x + 2xy

bring the y's together (subtract both sides): 2y-2xy =9x

hey! we can factor the left side (where the y's are): 2y(1-x) = 9x

get all the x's together  (divide both sides) : 2y = (9x)/(1-x)

get y alone (divide both sides by 2): (9x)/(1-x) * (1/2)

*finally*  distribute/simplify: (9x)/(2-2x)

you can double-check the answer on desmos!

                          ~ lmk if u got Qs   :>

Using a calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:

y = 6.5x - 279.1.

To find the equation, we need to insert the points (x,y) in the calculator. The same is true for any regression equation such as quadratic or exponential. However, as the problem states, a line of best fit is calculated in this problem.

From the table presented in the problem, the points are given as follows:

(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).

Inserting these points into the calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:

y = 6.5x - 279.1.

Here

x is the daily temperature, in F.

y is the sales, in dollars.

The complete question is-

The table compares the average daily temperature and ice cream sales each day

Temperature ("F) Ice Cream Sales

$112

$135

$138

$146

$166

$180

$188

$199

$220

$280

58.2

642-

64.3

66.8

684

71.6

72.7

76.2

77.8

82.8

Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth

09=38x-1092

09=-38xx-1092

Oý=65x-279.1

O ý= -65x-279.1

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Three lollipops are more expensive than two pencils.

Given that three erasers cost as much as 2 lollipops.

Let e denote the cost of an eraser and l denote the cost of a lollipop.

A pencil costs as much as two erasers, which implies that the cost of a pencil is two times the cost of an eraser. Therefore, the cost of a pencil is 2e.

Likewise, three erasers cost as much as 2 lollipops, which implies that the cost of an eraser is (2/3) l.

Therefore, the cost of a pencil is 4/3 times the cost of a lollipop.

Thus, the cost of two pencils is 4/3 * 2l = 8/3 l.

The cost of three lollipops is 3l.

Now, we must determine whether 8/3 l is greater than 3l or vice versa.

8/3 l = 2.67 l

Since 2.67 l < 3 l, the conclusion is that three lollipops are more expensive than two pencils.

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