Pythagoras and trigonometry​

Answer:

16 cups

Step-by-step explanation:

1 quart = 4 cups

The mass of platinum cone is more than the mass of the gold cylinder which is 7529.76 grams.

It is defined as the ratio of mass and volume. The density gives an idea of how dense the object is, and it is denoted by the symbol ρ. The unit of the density is kilogram per cubic meter.

The volume for the cylinder = π(6/2)²(5) = 141.37 cubic cm

The density for gold = 19.3 gram/cm³

Mass of gold cylinder = 19.3×141.37 = 2728.44 grams

The volume of the cone = (π(8/2)²×21)/3 = 351.85 cubic cm

The density for platinum = 21.4 gram/cm³

Mass of platinum cone = 21.4×351.85 = 7529.76 grams

Thus, the mass of platinum cone is more than the mass of the gold cylinder which is 7529.76 grams.

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Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.

Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.

Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour.

Here, Thus, Florida Avenue is hypotenuse triangular path and the other two sides are Capitol Street and H Street. The distance of  Florida Avenue is,

[tex]1^2+1.75^2=d^2\\1+3.0625=d^2\\4.0625=d^2\\d=\sqrt{4.0625}\\d=2.0156[/tex]

Thus, Jesse walks 2.0156 with 5 miles per hour. Thus, the time taken by him is

[tex]t_J=\dfrac{2.0}{5}\\t_j=0.4\rm\;hr[/tex]

Mark plans to jog back the way they came which is 2.75 miles (1+1.75) long with speed of 12 miles per hour. Thus, the time taken  by him is

[tex]t_M=\dfrac{2.75}{12}\\t_M=0.23\rm\;hr[/tex]

Thus, Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.

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The probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given that a box of trading cards contains 24-packs of cards in it. And Only two of those packs contain limited edition cards. Therefore, the probability of finding a limited edition card will be,

[tex]P = \dfrac2{24} = \dfrac{1}{12}[/tex]

The probability of not getting a limited edition card will be,

[tex]q = \dfrac{24-2}{24} = \dfrac{22}{24} = \dfrac{11}{12}[/tex]

Now, using the binomial distribution, the probability can be found.

A.)  The probability that a collector will find both limited edition cards if he buys only 2 packs is

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=2) = ^2C_2 \cdot(\dfrac1{12})^2 \cdot (\dfrac{11}{12})^{(0)}\\\\P(x = 2) = 0.0069 \approx 0.007[/tex]

B.) The probability that he gets at least one limited edition card if he buys 3 packs can be written as,

The probability of at least a limited edition card

= 1 - Probability of not getting any limited edition card

The probability of getting no special edition card will be,

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=0) = ^3C_0 \cdot(\dfrac1{12})^0 \cdot (\dfrac{11}{12})^{(3)}\\\\P(x = 0) = 0.77[/tex]

Now,

The probability of at least a limited edition card

= 1 - Probability of not getting any limited edition card

The probability of at least a limited edition card = 1 - P(x=0) = 1-0.77 = 0.23

Hence,  the probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.

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The correct answer is Choice A

Answer:

87.92ft^3

Step-by-step explanation:

Formula:

       V= π*r^2 *h

Answer:

38.7

Step-by-step explanation:

Use cosine

cos = adj / hyp

adj = cos x hyp

adj = cos(49) x 59

adj = 38.7

Answer: the second choice: (0, - 2) and (1, 0).

Explanation:

1) The solution of a graphed system of equations is the points of intersection of the equations.

2) Hence, this method requires to graph each function in one Cartesian coordinate system.

3) To graph the function y = x² + x  - 2, you can follow these steps

      y = (x² + x)  - 2

      y + 1/4 =  (x² + x + 1/4)  - 2

       y + 1/4 = (x + 1/2)²  - 2

       y = (x + 1/2)²  - 2 - 1/4

       y = (x + 1/2)² - 9/4

       Compare with the vertex form y = (x + h)² + k, where the coordinates of the vertex are (h,k). Therefore, the vertex is (1/2, - 9/4).

4) To graph the function y = 2x - 2, you can follow these steps:

The tables show that these points are common to the two functions: (0, - 2) and (1,0).

The graphs are shown in the figure attached.

You can see that the parabola (blue curve) and the line (purple line) intercept each other at those two points ( 0, - 2) and (1,0).

Answer:

[tex]p = (2.33 \times {10}^{4})( {1.07}^{6} )[/tex]

The area of the composite figure composed of two rectangles is 217 centimetres squared

The area of the composite figure can be found as follows:

The area of the composite figure can be found by adding up the individual area of each shape in the figure.

Therefore,

area of the figure = area of rectangle + area of rectangle

area of a rectangle = lw

where

Therefore,

area of the figure =  (14 × 11) + (7 × 9)

area of the figure = 154 + 63

area of the figure = 217 cm²

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Hey ! there

Answer:

Step-by-step explanation:

In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .

And we're asked to find the length of each side of triangle.

So ,

We know that ,

[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]

Solution : -

[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]

Step 1 : Removing parenthesis and cancelling 7 with -7 :

[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]

Step 2 : Adding like terms on left side :

[tex] \longmapsto \qquad 4x = 84[/tex]

Step 3 : Dividing with 4 on both sides :

[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]

On calculating further, We get :

[tex] \longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar[/tex]

According to question ,

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Verifying : -

Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .

Therefore , our answer is correct.

Answer:

about 11,948.05 cubic cm

Step-by-step explanation:

[tex]12 \times \pi( {4.9}^{2} )(13.2) = 11948.05[/tex]

Answer:

The answer to this one is 0.25

Answer:

see the attachment!

i hope this can help you.

Answer:

cylinder = 27π

cone =  9π

sphere = 36π

Step-by-step explanation:

volume of a cylinder = πr²h where r = radius and h = height

height of cylinder (h) = 3 and radius (r) = 3

so volume = π(3)²3

==> simplify exponent

volume = π9(3)

==> multiply 9 and 3

volume of cylinder = 27π

Volume of a cone = πr²(h/3) where r = radius and h = height

height of cone (h) = 3 and radius (r) = 3

so volume = π(3)²(3/3)

==> simplify exponent

volume = π9(3/3)

==> divide 3 by 3

volume = π9(1)

==> multiply 9 and 1

volume of cone = 9π

volume of a sphere = 4/3πr³ where r = radius

radius = 3

so volume = 4/3π(3)³

==> simplify exponent

volume = 4/3π27

==> multiply 4/3 and 27

volume of sphere = 36π

Answer: The smallest number is 118.

Step-by-step explanation:

Let's say that the consecutive numbers are x-1, x, x+1

The sum of the three consecutive numbers is 357

(x-1) + x + (x+1) = 357

So, 3x = 357

x =  357 ÷ 3

x = 119  

The 3 consecutive numbers are: 118, 119 and 120  

The smallest out of the 3 is clearly 118.

Hope this helps!

Answer:

(4,0)

Step-by-step explanation:

standard equation for a circle is (x−h)^2 +(y−k)^2 =r^2

circle center: h, k with radius: r

(x-(+4)^2 + (y-0)^2 = 5

the center is (4, 0)

Answer:

the final option

Step-by-step explanation:

the negative sign causes a reflection, the +6 in the parentheses cases a 6 unit shift left and the +3 causes a 3 unit shift up

The net pay of Simmons will be $494 after the deductions.

The net pay is defined as the actual amount earned after the deductions of taxes and loan emi etc.

here simmon's total earning is $694

After the deductions the simmon will left with:

694x0.92x0.96x0.88=539.38

Now the insurance premiums are of $45

So the final amount will be

=539.38-45=494.38

Hence net pay of Simmons will be $494 after the deductions.

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Answer:

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

Step-by-step explanation:

1. You need the same denominator to subtract

2. You can do this by picking the least common multiple of both denominators or multiplying the denominators by each other. In this case, the LCM (least common multiple) and multiply 4*3 or 3*4 is the same thing: 12.

3. But, what you do to the denominator, you do to the numerator:

[tex]\frac{2*4=8}{3*4=12} \\\\\frac{2*3=6}{4*3=12}[/tex]      This leaves the fractions as [tex]\frac{8}{12} -\frac{6}{12} =\frac{2}{12}[/tex].

4. When you subtract fractions, you don't subtract the denominator.

5. You can simplify this fraction by dividing the numerator and denominator by 6: [tex]\frac{2/2}{12/2} =\frac{1}{6}[/tex]

Answer:

58 more

Step-by-step explanation:

Answer:

Answer: 4/9 of the class are boys and 5/9 of the class are girls.

Step-by-step explanation:

There are 9 nine students in total in the class since 4 + 5 = 9.

Input the amount of boys and girls there are in the class in the numerator  and have 9 as the denominator. 4/9 of the class are boys and 5/9 of the class are girls.

--~Hope this helped~--

Answer:

In math, number blocks are commonly used as models, where a small square equals 1, a long rectangle equals 10, and a large square equals 100. As models, blocks can be used for addition, subtraction, multiplication, and division. You can represent a problem given by using the correct models.

Answer:

a

Step-by-step explanation:

3 feet 11 inches

hope this helps

so let's notice that, the equation is f(x) in x-terms, meaning the variable "x" is the independent and thus the parabola is a vertical parabola.  Also let's notice that the equation is already in vertex form, keeping in mind that the  axis of symmetry occurs for a vertical parabola at the x-coordinate.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(x-\stackrel{h}{5})^2+\stackrel{k}{8}~\hfill \stackrel{vertex}{(5,8)}~\hfill \stackrel{\textit{equation for axis of symmetry}}{x=5}[/tex]