A rectangular parcel of land is 150 ft wide. The length of a diagonal between opposite corners is 50 ft more than the length of the parcel. What is the length of the parcel

The volume of the cone is,

V = 28.1 millimeters

We have to give that,

An oblique cone with a height of 10.5 millimeters and a radius of 1.6 millimeters.

Since the Volume of the cone is,

V = πr²h/3

Here, r = 1.6 millimeters

h = 10.5 millimeters

Substitute all the values,

V = 3.14 × 1.6² × 10.5 / 3

V = 80.4/3

V = 28.1 millimeters

Therefore, The volume is,

V = 28.1 millimeters

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Answer:

x = 9

y = 6

Step-by-step explanation:

3x+6i=27+yi

The real components have to be equal and the imaginary components have to be equal

3x = 27

divide by 3

3x/3 = 27/3

x=9

6i = yi

Divide by i

6 = y

Answer:

x=9, y=6

Step-by-step explanation:

Step-by-step explanation:

we have

3x+6i=27+yi

Equate the Real Numbers

3x=27

solve for x

Divide by 3 both sides

x=27/3=9

Equate the  Imaginary Numbers

6i=yi

Simplify

6=y

Rewrite

y=6

therefore

x=9, y=6

Answer:

14.7 times bigger is (1.176 x 10¹) than (8 × 10-¹) if the numbers are  (1.176 x 10¹) than (8 × 10-¹).

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

To compare numbers this way, we divide.

(1.76 × 10^1) / (8 × 10^-1) =

= 1.76/8 × 10^1 / 10^-1

= 0.22 × 10^(1 - (-1))

= 0.22 × 10^2

= 22

Answer:

  124/999

Step-by-step explanation:

A recurring decimal fraction can be expressed as a rational number by using the recurring digits in the numerator and an equal number of 9s in the denominator:

  \(0.\overline{124}=\dfrac{124}{999}\)

This fraction cannot be reduced.

_____

Additional comment

If the recurring digits don't start at the decimal point, then you can determine the fraction by ...

In this case, you would get ...

  \(1000x = 124.\overline{124}\\\\1000x-x=124.\overline{124}-0.\overline{124}=124\\\\x=\dfrac{124}{999}\)

Compute u * v if u and v are unit vectors and the angle between them is Pie. U * v =  is u.v = -1

that u and v are unit vectors and the angle between them is π.To find u*v, we use the dot product of vectors. Dot product of two vectors a and b is given bya.

b = |a| |b| cosθ

Where |a| is the magnitude of vector a, |b| is the magnitude of vector b, and θ is the angle between the two vectors.Let's find u*v using this formula.

u.v = |u| |v| cos π(u.v) = 1 × 1 × (-1))= -1

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Answer:

98

Step-by-step explanation:

Solution 1, (quick)

When enlarging by a scale factor, the shape's area is multiplied by the scale factor squared.

3.5*7*2^2=98

This works because for a rectangle width x and length y, width 2x and length is 2y, area is 4xy compared to area xy originally.

Solution 2, (technical)

Scale factor of 2 means multiplying by 2

3.5^2=7

7*2=14

7*14=98

Answered By Benjemin ☺️.

Please check the attached answers of image.

The coefficients a, b, and c depend on the values of k1, k2, and k3, and both Joel and Eve's quadratics yield the same values for these ki when evaluated for x=1, x=2, and x=3, their quadratics are necessarily the same.

Joel and Eve are thinking of quadratics using x as their variable.

When they evaluate their quadratics for x=1, x=2, and x=3, they both get the same results (k1, k2, and k3, respectively).

To determine if their quadratics are necessarily the same, we can set up three equations using ax^2 + bx + c = ki:
1. a + b + c = k1
2. 4a + 2b + c = k2
3. 9a + 3b + c = k3

We can then solve for the quadratic coefficients (a, b, and c) in terms of ki:
a = (k1 - 2k2 + k3) / 2
b = (-5k1 + 8k2 - 3k3) / 2
c = (3k1 - 3k2 + k3)

Since the coefficients a, b, and c depend on the values of k1, k2, and k3, and both Joel and Eve's quadratics yield the same values for this ki when evaluated for x=1, x=2, and x=3, their quadratics are necessarily the same.

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The value of SS for the following set of scores [ 0, 1,4,5] is 42.

So, option b is correct

The formula for measuring the deviation from the measured values is the Sum of Squares. The mean value of the complete collection of observed values is used to measure this distance.

When referring to a statistical method for calculating the dispersion of data points in regression analysis, the term "sum of squares" is employed. When determining which function best matches the data by deviating the least from it, the sum of squares can be utilized. Determine how well a data series can be fitted to a function that could aid in explaining how the data series was formed.

Given,

The dats is 0, 1, 4, 5

S0, the value of n is 4

SS=Sum of squares

SS=0²+1²+4²+5²

SS=0+1+16+25

SS=42

Therefore, the value of SS for the following set of scores [ 0, 1,4,5] is 42.

So, option b is correct.

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The arc length of the polar curve r = e^4θ where 0 ≤ θ ≤ 2π is approximately 32.59 units.

To find the arc length of a polar curve, we use the formula:

L = ∫[a,b] √[r² + (dr/dθ)²] dθ

In this case, we have:

r = e^4θ

dr/dθ = 4e^4θ

0 ≤ θ ≤ 2π

So, the arc length is:

L = ∫[0,2π] √[e^8θ + 16e^8θ] dθ

L = ∫[0,2π] e^4θ √(17) dθ

Using integration by substitution with u = e^4θ, we get:

L = (1/4√(17)) [u√(u² + 1)]|[u=e^4θ]^[u=1]

L = (1/4√(17)) [(e^4θ)√(e^8θ + 1) - √2]

L = (1/4√(17)) [(e^(4π)√(e^(8π) + 1) - √2) - (√(e^8 + 1) - √2)]

L ≈ 32.59

So the arc length of the polar curve r = e^4θ where 0 ≤ θ ≤ 2π is approximately 32.59 units.

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The outer perimeter of the no-slip surface is equal to 78 feet.

Perimeter is a term used to describe the sum of the outside edge lengths or it can also be described as the whole of the outer edge or boundary.

The outer perimeter of this swimming pool can be determined by adding 3 feet twice to all the sides of the rectangular swimming pool and then adding these sides together.

Since it is a 12-ft-by-15-ft rectangular swimming pool, this means that two sides of this swimming pool are 12 feet and two sides of this pool are 15 feet, therefore;

12 + 6 = 18

15 + 6 = 21

Now the perimeter can be determined by adding all the sides as follows;

18 + 21 + 18 + 21 = 78 feet

Hence, the outer perimeter of the no-slip surface is calculated to be 78 feet.

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\(~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan \theta = \dfrac{LN}{LM}\\\\\\\implies \theta = \tan^{-1} \left( \dfrac{LN}{LM} \right)\\\\\\\implies \theta = \tan^{-1} \left(\dfrac{12.81}{7.72} \right)\\\\\\\implies \theta =58.92^{\circ}\)

Answer:

She can make 2 2/5 of a necklace. Which is 2.4 to the nearest tenth.

Step-by-step explanation:

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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Answer: r= 1.22

Step-by-step explanation:

Formula for amount with simple interest = \(P(1+rt)\)

, where

P= principal value , r= rate of interest , t = time.

Given: P=  $2000, t= 5 years, r= 1.25% = 0.0125

\(A=2000(1+0.0125\times5)\\\\=2000(1.0625)=2125\)

Formula to compute compound amount : \(P(1+r)^t\)

\(=2000(1+r)^5\)

When both have same worth then

\(2000(1+r)^5=2125\\\\\\ (1+r)^5=\dfrac{2125}{2000}\\\\\\ (1+r)^5=1.0625\)

taking log on both sides , we get

\(5\ln (1+r)=\ln 1.0625\\\\\\ 5\ln (1+r)=0.0606246\\\\\\ \ln (1+r)=0.012125\\\\\\ 1+r=e^{0.005266}\\\\\\ 1+r=1.0122\\\\ r=0.0122\\\\ \\ r=1.22\%\)

Hence, Value of r= 1.22

Answer:

adsefrthgfdsfgd

Step-by-step explanation:

Answer:

x = 14/3

y = 52/3

Step-by-step explanation:

Take the 1st equation plus with the 2nd equation

we got,

3x = 14

x = 14/3

take the value of x and insert in the 2nd equation

-2(14/3) + y = 8

y = 52/3

We have found two quadratic functions with x-intercepts (-5,0) and (5,0): f(x) =\(x^2 - 25\), which opens upward, and g(x) = \(-x^2 + 25\), which opens downward.

For the quadratic function that opens upward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

f(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens upward, then a must be positive. Expanding the equation, we get:

f(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open upward, we need the coefficient of x^2 to be positive, so we can set a = 1:

f(x) = x^2 - 25

For the quadratic function that opens downward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

g(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens downward, then a must be negative. Expanding the equation, we get:

g(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open downward, we need the coefficient of x^2 to be negative, so we can set a = -1:

g(x) = -x^2 + 25

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9514 1404 393

Explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  1/a^b = a^-b

__

  \(5\times2^{n-1}=5\times(2^n)(2^{-1})=5\times2^n\times\dfrac{1}{2}=\boxed{\dfrac{5}{2}\times2^n}\)

Answer: the answe is not at all close to the actual Nobel rate.

Step-by-step explanation:

The dimly lit area is 58 square units in size. The area of a two - dimensional figure is the area that its perimeter encloses.

The area is the space occupied by any two-dimensional figure on a plane. A rectangle's area is how much space it occupies in a the double plane.

The shaded area's size will be determined using the formula

10 units multiplied by 7 units gives a total area of 70 units.

Gap size equals 2 units multiplied by 6 units, or 12 units.

The shaded figure's area is 70 units divided by 12 units, or 58 units.

As a result, 58 square units make up the area of shaded zone.

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(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the non-homogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the no non-homogeneous part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

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The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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Answer: A. 81/625

Step-by-step explanation:

From the question, we are informed that there are 4 traffic signals on ones way to work, and there's a 60% chance of making each one, independent of whether or not the previous one is made.

The probability that one will make it to work on time will be to multiply 60% for the 4 period. This will be:

= 60% × 60% × 60% × 60%

= 60/100 × 60/100 × 60/100 × 60/100

= 3/5 × 3/5 × 3/5 × 3/5

= 81/625

\(\text{Hi there! :)}\)

\(\large\boxed{= 12^{18} }\)

\(12^{3} * 12^{9} * 12^{4}* 12^{2}\)

\(\text{ Use the exponent multiplication rule.}\\\)

\(\text{When multiplying, add the exponents:}\)

\(12^{3 + 9 + 4 + 2}\)

\(\text{Simplify:}\)

\(= 12^{18}\)

The systems of inequalities given is,

Since he can't sell more than 8 items per day, then from the graph given the best region that should be shaded is region 4.

Answer:

x = 2 , y = 11

Step-by-step explanation:

the diagonals of a parallelogram bisect each other , then

PT = TR , that is

y = 5x + 1 → (1)

QT = TS , that is

2y = 6x + 10 → (2)

substitute y = 5x + 1 into (2)

2(5x + 1) = 6x + 10

10x + 2 = 6x + 10 ( subtract 6x from both sides )

4x + 2 = 10 ( subtract 2 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

substitute x = 2 into either of the 2 equations for corresponding value of y

substituting into (1)

y = 5(2) + 1 = 10 + 1 = 11

TR=PT as diagonals bisect each other in parallelogram

Similarly

QT=TS

Equate both equations in (2)

Now

Answer:

Step-by-step explanation: