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Answer:

Volume= 62.8 cubic inch

Step-by-step explanation:

V=B×h

B=

[tex]\pi {r}^{2} [/tex]

= 3.14×2^2=12.56

V=12.56×5= 62.8 cubic inch

Answer:

41

Step-by-step explanation:

The maximum height which the rocket attains is 80 m and the time taken by the rocket is 8 sec.

Given,

the following formula yields the height h,

h= -5t² + 40t +45

45m is the height of the launch pad.

We take the first derivative of the function h and then set it to zero to determine the height the rocket reaches.

h' = 0

-10t + 40 =0

-10t = -40

 t = 4

Therefore, height reached by the rocket in time t = 4 is,

h= -5t² + 40t +45

  = -5(4)²  + 40(4) + 45

  =125 m

As a result, the rocket can reach:

125- 45

= 80 m

(To determine the real height the rocket travels, we have subtracted the height of the launch pad.)

The rocket takes twice as long to launch as it does to reach the peak.

t = 2*4 = 8 sec

Therefore,

the rocket goes 80 meters in height

the rocket's flight time is 8 seconds.

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Considering the information, the minimum and maximum size of the concrete walkway is is -900 and -450 units respectively

Minimum and maximum values of the area of the square garden is the area the square garden can occupy.

The given parameters are

A=S²

S= a side of the square= A(x) = (15+2x)

Now, hence A=S²

This implies that

(15+2x)(15+2x)

Expand the brackets to get

225+60x+4x=0

Solving the equation using the quadratic formula

x=± (√b²-4ac)÷2a

This implies that  

x= -60±(√60²-4*4*225)÷2*4

Simplifying the equation we have

(-60±0)÷8

x=-30

Now if x= -3

Therefore (15+2*-30) = -45 and (15*x)

= 15*-30=-450 units

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Answer:

Z< 3

Step-by-step explanation:

Hope this helps :)

The values of y when x is 0 1 2  is 0,3,6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

To get the values of y, we substitute for the values of x  in the equation 3x=y

When x = 0

3(0)=y; y = 0

When x = 1

3(1)=y; y = 3

When x = 2

3(2)=y; y = 6

x   |     3x     |    y    |    (x, y)

----------------------------------------

0   |     3(0)  |   0    |   (0, 0)

----------------------------------------

 1   |     3(1)    |    3   |   (1, 3)

----------------------------------------

 2   |     3(2)  |    6   |    (2, 6)

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Answer:

The three consecutive even integers are 40, 42 and 44.

Step-by-step explanation:

Let the consecutive even integers be

The sum of the first and second of three consecutive even integers is 126.

So,

x + (x + 2) + (x + 4) = 126

Open the brackets

x + x + 2 + x + 4 = 126

Combine like terms we get,

3x + 6 = 126

Subtract 6 from both sides we get,

3x + 6 - 6 = 126 - 6

3x = 120

Divide 3 from both sides we get,

3x/3 = 120/3

x = 40

The value of x is 40 and the the consecutive even integers are

x = 40

x + 2 = 40 + 2 = 42

x + 4 = 40 + 4 = 44

Thus, The three consecutive even integers are 40, 42 and 44.

The probability of having the first head at the k-th trial is 1/2.

The formula for the binomial distribution of probability is shown below. It can be used to determine the likelihood of getting K heads out of N coin tosses.

[nC k]* [pk]* [qn-k]

p= probability of receiving a head and

q= probability of having a tail.

Both p and q are 1/2.

As a result, the equation is [f12n! * f! r! * (n-r)!]

If you obtain exactly r successes, you also get (n - r) failures at the same time.

qn - rpr = P(getting r successes and n - r failures) (since the n trials are independent) Using the product theorem

There is no mention of the challenges from which the results were attained. There are nCr methods for selecting successful trials among r trials. The remaining (n - r) trials should be failures once the r trials that were picked for successes have been chosen. These nCr methods are incompatible. P(obtaining exactly r successes) in each of these nCr methods equals qn - rpr.

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The price that that club members pay for the computer is $465.92.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

Since the selling price was first at 728, but then the store advertised a 20% markdown on the system and members of the store's loyalty club get an additional 20% off their computer purchases.

The cost will be calculated thus:

582.40 - (20% × $582.40)

= $582.40 - $116.48

= $465.92

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Answer: A y<3 and y>2/3x+1

Step-by-step explanation: y<3 shades everything under the line because 3 is greater than all the possible values.

y>2/3x+1 shades everything over the line because 2/3x+1 is less than all the possible values.

Answer: D

Step-by-step explanation:

For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.

What is Trapezoid?

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.

Given:

In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.

Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.

We have to find BC:BN

ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.

Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD

But, BC= BN+NC

Therefore, BC:BN = (BN + NC): BN

⇒ BC:BN = (3 + 5): 3

⇒ BC:BN = 8:3

Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.

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The value of ordered pair of   (x,y) is (-2, -3)

x - 5y = 13

4x - 3y = 1

Solve the equation for x

x - 5y = 13

Move '5y' to R.H.S and change it's sign

x=13+5y

Substitute the given value of X into the equation

4x - 3y = 1

4(13+5y)-3y = 1

Solve the equation for y

distribute 4 through the parentheses

52+20y -3y =1

Collect like terms

52+17y = 1

Move constant to R.H.S and change it's sign

17y = 1 - 52

Calculate

17y =  - 51

Divide both sides of the equation by 17

17y/17 = -51/17

Calculate

y = -3

Now, substitute the given value of y into the equation

x = 13 + 5y

x= =13+5x(-3)

Solve the equation for x

Multiply the numbers

= 13 - 15

Calculate the difference

= -2

The possible solution of the system is the ordered pair

( x , y )

( x , y ) = ( - 2 , - 3 )

-----------------------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

-2-5×(-3)=15

4×(-2)-3×(-3)=1

Simplify the equalities

13 = 13

1=1

Since all of the equalities are true, the ordered pair is the solution of the system

( x , y ) = ( - 2 , - 3 )

Therefore the value of ordered pair of   (x,y) is (-2, -3)

The complete question is : Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).

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The probability that both choose Black Panther as their favourite character is 189/3875.

KHS students' list of their favourite Marvel comic character:

Spiderman - 45

Hulk - 30

Black panther - 28

Black widow - 17

Rocket raccoon - 5

Total = 125

             [tex]125C_{2}=\frac{125*124}{1*2} \\\\125C_{2}=\frac{15500}{2}\\\\125C_{2}= 7750[/tex]

              [tex]28C_{2}=\frac{28* 27}{1*2} \\\\28C_{2}=\frac{756}{2}\\\\28C_{2}= 378[/tex]

               [tex]P(BP) = \frac{28 C _{2}}{125C_{2}} \\\\P(BP) = \frac{378}{7750} \\\\P(BP) = \frac{189}{3875}[/tex] or  0.04877

          So, option c is correct.

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Answer:

Step-by-step explanation:

The measure of indicated angle in the given triangle is 71.035°.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given right angled triangle, hypotenuse side is 74 units and the two legs of triangle are 70 units and 24 units.

Let the unknown angle be x.

We know that, tanθ =Perpendicular/Base

Now, tan x= 70/24

tan x= 2.91

x =71.035°

So, one of the angle in the triangle is 71.035°.

Therefore, the measure of unknown angle is 71.035° in the given triangle.

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7.702 is the proper decision.

What exactly is a p-value?

Mr. Ramli's investment in the small entrepreneurship will be doubled in 8 year.

For the stated equation-

rate of increase is given as-

dy/dx = 2(x + 121) < - rate of the change

dy = 2(x + 121)dx

Integrating;

∫dy = ∫2(x + 121)dx

y = x² + 242x + C

At x = 0, y(0) = 0 Thus,

(0)² + 242(0) + C = 2000

C = 2000

Now, y = x² + 242x + 2000

Calculate 't' to get the y(t) = 40,000 (double the amount)

4000 = x² + 242x + 2000

x² + 242x - 2000 = 0

Find the factor;

x = 8 and x = -250

As, x is time in year. So, x = 8 years.

Therefore, it takes eight years for his investment capital to double from what he initially put up.

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Answer: (C) or (44in^2 )

Step-by-step explanation:

Answer:

A = 40 in²

Step-by-step explanation:

the figure is composed of a rectangle and a triangle.

then area (A) is calculated as

A = area of rectangle + area of triangle

  = (16 × 2) + ( [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 6 - 2 = 4 and h = 20 - 16 = 4 , then

A = 32 + ( [tex]\frac{1}{2}[/tex] × 4 × 4)

  = 32 + 8

  = 40 in²

No, the estimate should be higher

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

As, Maximum miles driven=highest consumption per gallon × Maximum  

                                                                                                         gallons

where;

Maximum miles driven per person=64 mile

Maximum miles driven = 64×4

                                     =256 miles

So, highest consumption =24.56 miles per gallon

let the Maximum gallons needed be x

256=24.56 x

24.56 x=256

x ≥ 256/24.56

x ≥10.42 gallons

Hence, No, the estimate should be higher

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The distance between the two points is 2√10

Distance between two points:

The formula for the distance between two points (x₁, y₁) and (x₂, y₂) is given by Distance = √ [(x₂-x₁)² + (y₁ - y₁)²]

This formula can be used to find the length of a line whose endpoints are (x₁, y₁) and (x₂, y₂)

Here we have

The endpoints of the line are (1, 2) and (7, 4)

As we know d =√ [(x₂-x₁)² + (y₁ - y₁)²]

Take (x₁, y₁) = (1, 2) and (x₂, y₂) = (7, 4)

By the given formula,

Distance of line = √ [(7 - 1)² + (4 - 2)²]

=  √[(6)² + (2)²]  

=  √(36 + 4)

=  √40  

= 2√10

Therefore,

The distance between the two points is 2√10

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Answer:  55.7 inches and 60.3 inches

Step-by-step explanation:

I saw this question before in math class, so I know the answer! Hope you find this helpful!

Answer:

3.6

Step-by-step explanation:

The resulting triangle is 9/5 the original triangle.

The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).

Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 9/5,

Then changed triangle is  A'B'C'

So, relation between them is A'B'C' = 9/5(ABC)

Thus, the resulting triangle is 9/5 multiple of triangle ABC.

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Step-by-step explanation:

[tex] {x}^{2} - 12x + 36 = - 36[/tex]

[tex](x - 6) {}^{2} = - 36[/tex]

[tex](x - 6) {}^{} = 6i[/tex]

[tex]x = 6 + 6i[/tex]

[tex]x = 6 - 6i[/tex]