The cosine law is writen as question, and 2 more Questions down below. Please solve.

The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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Using the Laplace transform to solve the given integral equation  f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is [tex]\frac{4(1-2e^-5s)/}{s}[/tex]

explanation is given in the image below:

Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.

The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.

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There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

According to the given question.

Total number of items, n = 12

Total numbers of items to be selected, r = 5

Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.

[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]

Where,

[tex]^{n} P_{r}[/tex] is the total number of permutations.

n is the total number of objects.

r is teh total number of objects to be selected.

Therefore,

The number of different groups or permutaions of 5 items that can be selected from 12 distinct group

[tex]^{12} P_{5}[/tex]

[tex]= \frac{12!}{(12-5)!}[/tex]

[tex]= \frac{12!}{7!}[/tex]

[tex]= \frac{12\times11\times10\times9\times8\times7!}{7!}[/tex]

= 12 × 11 × 10 × 9 × 8

= 95040

Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

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Answer:

11.692945103

Step-by-step explanation:

take out a calculator divide 1016 by 86.89

Daniel’s  answer was  wrong because he used  square root instead of the cubed root.

From the expression , which is [tex]t = 5.825 \sqrt[3]{3590/p}[/tex]

Then we can perform some operations to Solve for the value of  p.

Then we can make division on the  both sides of the equation  using 5.825 , then we have

2.304 = [tex]} (3590/p)^{\frac{1}{3}[/tex]

We can cube the both side of the equation to will eliminate the radical and  we will have

12.174 = 3590/p

then ,  p = 294.89  which implies that Natasha’s answer is correct.

Therefore , Daniel’s  answer was  wrong because he used  square root instead of the cubed root.

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The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.

According to the statement

we have to explain about the function in which cryptography takes a string of any length as input and returns a string of any requested variable length.

So, For this purpose,

we know that the

A sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length.

So from definition and its working process it is clear that for this purpose the sponge function is used.

this function returns the string of any variable length.

So, The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.

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Answer: A. 33

Step-by-step explanation:

The amount to be invested​ now, or the present value​ needed, is $22873.75

We solve the problem using the compound interest formula for amount

A = P(1 + r)ⁿ where

Making P subject of the formula, we have

P = A/(1 + r)ⁿ

Given that

Substituting the values of the variables into the equation, we have

P = A/(1 + r)ⁿ

P = 50000/(1 + 0.07)¹⁴

P = 50000/(1.07)¹⁴

P = 50000/1.7317

P = 22873.75

So, the amount to be invested​ now, or the present value​ needed, is $22873.75

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Answer:

87

Explanation:

This is an arithmetic sequence with common difference: 7 and first term: 17

Arithmetic sequence:

a + (n - 1)d                    where n is term position, d is difference, a is first term

17 + (n - 1)7

7n + 10

The eleventh term:

7n + 10

7(11) + 10

77 + 10

87

To Find :-

Solution :-

Given A.P.,

First term (a) is 17.

Common difference (d) = 24 - 17 => 7

We know that :

Here n would be 11.

>> t11 = 17 + (11 - 1) 7

>> t11 = 17 + (10) 7

>> t11 = 17 + (10) × 7

>> t11 = 17 + 70

>> t11 = 87

Therefore, eleventh term in the sequence is 87.

Answer:

227.02

Step-by-step explanation:

[tex]400.00-172.98 \\ \\ =300 - 72.98 \\ \\ =230-2.98 \\ \\ =228-0.98 \\ \\ =227.02[/tex]

Answer:

227.02

Step-by-step explanation:

[tex]400.00\\-172.98[/tex]

To solve: First subtract 172 from 400, resulting in 228, then you may subtract the 0.98, leaving 227.02.

Answer:

Ten thousands place

Step-by-step explanation:

84 530 216

Frm here u can see that the 3 is in the ten thousands place

Answer:

84

Step-by-step explanation:

substitute n = 5 into the expression

16n + 4

= 16(5) + 4

= 80 + 4

= 84

Answer:

The expression will have the value of 84

Step-by-step explanation:

[tex]16n + 4[/tex]

given expression

Thus, plug n=5

[tex]16(5) + 4 \\ 80 + 4 = 84[/tex]

Finally, we get the value 84

Step-by-step explanation:

-3p+6p is 3p

-3 + 6 = 3

So when you simplify the equation you get 3p

The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.

According to the statement

we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.

So, for this purpose,

we know that the best method show the relationship is a slope intercept form.

So,

The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

And

Using the coordinate points on the plane (0, 6) and (10, 28)

now we Determine the slope

Slope = 28-6/10-0

Slope = 22/10

Slope = 2.2

And then Determine the y-intercept

6 = 2.2(0) + b

b = 6

And now we have to put in the general form of the slope intercept form which is y = mx + b

Then the equation become

y = 2.2x + 6

So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.

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Answer:

8%

Step-by-step explanation:

The approximate difference between the theoretical and experimental probabilities for rolling an even number is 8%

Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes. As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

Theoretical probability of rolling a cube and getting a even number is 1/2 or 50% as number of odd numbers and number of even numbers are equal.

Experimental probability = Favorable outcomes/Total outcomes

Experimental probability = 10/24 = 5/12 ≅ 42%

Thus approximate difference between these two equals 50% - 42% = 8%

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Answer:

D

Step-by-step explanation:

the figure is composed of a rectangle and a right triangle ( top )

calculate the hypotenuse h of the right triangle using Pythagoras' identity

h² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

h = [tex]\sqrt{100}[/tex] = 10

the base of the rectangle is equal to h , then perimeter (P) of pentagon is

P = 10 + 4 + 6 + 8 + 4 = 32 cm

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the problem want:

 ⇒ the dimensions or the perimeter of the pentagon

What information do we need to find the perimeter:

 ⇒ the unknown side length

Let's find the unknown side length:    

[tex]\hookrightarrow \text{split the pentagon into two shapes as shown in the image below}\\\hookrightarrow \text{the hypotenuse of the right triangle is equal to the length of the unknown side}\\\hookrightarrow\text{hypotenuse}=\sqrt{6^2+8^2}= \sqrt{36+64}=\sqrt{100}=10\\[/tex][tex]\hookrightarrow \text{the unknown side length is 10}[/tex]

Perimeter = 6 + 8 + 4 + 4 + 10 = 32

Answer: 32 or (D)

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Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

Answer:

[tex]\frac{15x^{4}y^{3}}{5x^{3}} \ \ \text{and }\ -10x^{5}\div 2x^{3}y[/tex]

Step-by-step explanation:

the Quotient of Powers Property :

let a be a number where  a ≠ 0

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

……………………

[tex]\frac{15x^{4}y^{3}}{5x^{3}}[/tex]

[tex]= \frac{3 \times 5x^{3}\times x \times y^{3}}{5x^{3}}[/tex]

[tex]= \frac{3 \times x \times y^{3}}{1}[/tex]

[tex]= 3 x y^{3}[/tex]

=============

[tex]-10x^{5}\div 2x^{3}y[/tex]

[tex]= [-5 \times (2x^{3}) \times x^2] \div [(2x^{3}) \times y][/tex]

[tex]= -5 \times x^2 \div y[/tex]

[tex]= -5 x^2 \div y[/tex]

Answer:

length = 235 yd

width = 58 yd

Step-by-step explanation:

Let the width be W.

L = 4W + 3

perimeter = 2(L + W)

perimeter = 2(4W + 3 + W)

perimeter = 2(5W + 3) = 10W + 6

We are told the perimeter = 586 yd

10W + 6 = 586

10W = 580

W = 58

L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235

length = 235 yd

width = 58 yd

Step-by-step explanation:

i)I=PRT/100

I=1800*12*1/100

I=$216

ii) amount to be paid =1800+216

=$2016

iii) monthly installments=2016/12

=$168

b)I=PRT/100

I=

If a trader took a loan of 1,800.00 at an interest of 12 percent per annum

a.  Interest on the loan is $216.

Amount to be paid at the end of the year is $2016

Monthly Installment is $168

b. She took  $2184 to the nearest dollar.

a) i) Interest on the loan:

Interest = Principal × Rate × Time

Interest = $1800 × 0.12 × 1

Interest = $216

ii) Amount to be paid at the end of the year:

Amount = Principal + Interest

Amount = $1800 + $216

Amount = $2016

iii) Monthly installment:

Number of monthly installments = 12

Monthly Installment = Total Amount / Number of Installments

Monthly Installment = $2016 / 12

Monthly Installment ≈ $168

b) Let's X represent the amount she took

Total Payment = Monthly Installment × Number of Months

Total Payment = $200 × 12

Total Payment = $2400

So

Total Payment = X + $216

$2400 = X + $216

Subtract $216 from both sides:

$2400 - $216 = X

$2184 = X

Therefore she took approximately $2184 to the nearest dollar.

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Answer:

D 0.0353

Step-by-step explanation:

a= 0.05. p= 0.65. n=700

S N P = 700 × 065 = 45575

1 n ( 1 - p ) = 700× ( 1 - 0.65 ) = 24575

get the sample is big ,. p~ N ( π. √ π ( 1-π ) p - π

-----------. ------- ~ ( o. 1

n Ñ 1 ~ñ

the margin of error ∆ = Z a

-----. =. √ π ( 1 - π )

2 --------

n

according to the standard normal distribution,

Z d

---. = zo.o25 = 1.96

2

∆=1.96×√p ( 1 - p ). =. 1.96 × √ 0.65× ( 1 - 65)

---------. ---------

π. 700

= 0.0353

By using properties of right triangles and trigonometric functions, we conclude that the length of the side BC is 19 units.

In this problem we can use trigonometric functions to determine the length of the side BC in three steps:

Step 1

BE = AB/tan 60°

BE = 19√2 /4

Step 2

BD = BE/cos 45°

BD = 19/2

Step 3

BC = BD/sin 30°

BC = 19

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Based on the calculations, the coordinates of the mid-point of BC are (1, 4).

First of all, we would determine the initial y-coordinate by substituting the value of x into the equation of line that is given:

At the origin x₁ = 0, we have:

y = 2x + 1

y₁ = 2(0) + 1

y₁ = 2 + 1

y₁ = 3.

When x₂ = 2, we have:

y = 2x + 1

y₂ = 2(2) + 1

y₂ = 4 + 1

y₂ = 5.

In order to determine the midpoint of a line segment with two (2) coordinates or endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate is given by:

Midpoint = (x₁ + x₂)/2

Midpoint = (0 + 2)/2

Midpoint = 2/2

Midpoint = 1.

Midpoint on y-coordinate is given by:

Midpoint = (y₁ + y₂)/2

Midpoint = (3 + 5)/2

Midpoint = 8/2

Midpoint = 4.

Therefore, the coordinates of the mid-point of BC are (1, 4).

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The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.

Quadrilateral FGHJ is dilated according to the rule Do,Two-thirds(x,y) to create the image quadrilateral F'G'H'J', which is not shown. Quadrilateral FGHJ has points F(-5, -4), G(-3, -2), H(-1, -4) and J(-3, -6).

The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)

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Answer:

(-2,-4)

Step-by-step explanation:

Geometry B E2020!! :3

The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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Answer:

[tex]\Large\boxed{a)~4\sqrt{3} }[/tex]

[tex]\Large\boxed{b)~10\sqrt{10} }[/tex]

Step-by-step explanation:

Given term

[tex]\sqrt{48}[/tex]

Factorize 48 inside the radical sign

[tex]\sqrt{2\times2\times2\times2\times3}[/tex]

Combine terms to form squares

[tex]\sqrt{2^2\times2^2\times3}[/tex]

Simplify the radical sign

[tex](2\times2)\sqrt{3}[/tex]

[tex]\Large\boxed{4\sqrt{3} }[/tex]

Given term

[tex]\sqrt{1000}[/tex]

Factorize 1000 inside the radical sign

[tex]\sqrt{2\times2\times2\times5\times5\times5}[/tex]

Combine terms to form squares

[tex]\sqrt{2^2\times5^2\times2\times5 }[/tex]

Simplify the radical sign

[tex](2\times5)\sqrt{2\times5}[/tex]

[tex]\Large\boxed{10\sqrt{10} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The slope of the line would be y=x-1

Step-by-step explanation:

y=x-1

Subsite

3=4-1

3=3  True,

Thus y=x-1

Answer:

3 tiels are in the factor 2: 2 are labeled x and 1 is labeled negative

Answer: B

Step-by-step explanation: