A rectangle is 8m longer than it is wide. If the length is increased by 2m and the width is increased 2m, the area is
increase by 68m 2. Find the original dimensions.

The change in area is 0.8π [tex]m^{2}[/tex] and percentage is 20%.

What is change in area?

Let A denotes the area of the circle when its radius is r, then A=πr2 Now, the rate of change of the area with respect to its radius is given by, dA dr = d dr(πr2) = 2πr When r= 4cm,(dA dr)r=4= 2π(4) = 8π cm2 per cm Hence, the area of the circle is changing at the rate of 8πcm2/cm

Given,

initial radius = 2m

increased radius = 2.02 m

change in radius dr = 2.02 - 2 = 0.02m

Area = π[tex]r^{2}[/tex] = 4π

dA = 2πrdr

=2π(2)(0.02)

=0.08π [tex]m^{2}[/tex]

Estimated percentage = 0.08/4×100

=2%

Hence, the estimated percentage is 2%.

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The diagram for the angle of depression is constructed.

The angle of depression is defined as "an angle made between the horizontal line as well as the line of sight whenever a watcher looks directly down at an object." The term "angle of depression" refers to the following:

For the given question;

The height of the cliff is 300 m.

The distance of the table from the cliff is 600 m.

The angle of depression is 30 degrees.

Thus, the diagram for the angle of depression is made.

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As per the tangent angle, the value of x in the given diagram is 7cm.

Tangent angle

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Given:

Here we have the two right angled triangle, through this we have to identify the value of x.

According to the given question, we have a diagram with two right angled triangles.

Now, in the upper right angled triangle

tan 50° = opposite side / 5

⇒ 1.19 = 0pposite side/ 5

⇒ opposite side = 1.19 × 5

⇒ opposite side = 1.2 × 5

⇒ opposite side = 6cm

Now, the opposite side with respect to the angle 50  degrees in the upper right angle triangle is a adjacent side according to angle 38 degrees in the lower right angle triangle.

So, in the lower right angle triangle.

tan 38° = x / adjacent side

⇒ 0.78 =  x/6

⇒ x = 0.78 × 6

⇒ x = 4.68

⇒ x = 7cm

Hence, the value of x in the given diagram is 7cm.

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The value of subtracting the expressions (4.97n − 3.6) − (3 + 15.6n) is -10.63n − 6.6

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(4.97n − 3.6) − (3 + 15.6n)

Start by opening the brackets

So, we have

(4.97n − 3.6) − (3 + 15.6n) = 4.97n − 3.6 − 3 - 15.6n

Next, we collect the like terms

So, we have

(4.97n − 3.6) − (3 + 15.6n) = 4.97n  - 15.6n − 3.6 − 3

Next, we evaluate the like terms

So, we have

(4.97n − 3.6) − (3 + 15.6n) = -10.63n − 6.6

Hence, the value of the expression is -10.63n − 6.6

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The Grand Answer is....

A!

I got the exam right...

Can I get brainliest?

Answer:

7776

Step-by-step explanation:

you divide 5 by 2 to get 2.5 then put 36 to the power of 2.5 to get 7,776

the expected value of the largest value in the sample is:

np​.​random​.​uniform​(​0,​1,​100)

this question is about random samples from the uniform(0,1) distribution.

recall that for a sample of size mm from a uniform(0,1) distribution

the expected value of the largest value in the sample is:

np​.​random​.​uniform​(​0,​1,​100)

import numpy as np

pass the random uniform generated array into x

x = np random uniform(low, high, size)

here low = 0, high = 1, size = 100

x = no. random uniform(0,1,100)

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For the given inequality 2(b + 2) ≥ 24 solution of the graph represented by number line with closed point at 10 with arrow pointing right.

As given in the question,

Given inequality is :

2(b + 2) ≥ 24

Solution of the given inequality 2(b + 2) ≥ 24 is equal to :

2(b + 2) ≥ 24

Divide both the sides by 2

[2(b  + 2 )] / 2 ≥ 24 /2

Subtract 2 from both the sides

b + 2 -2 ≥ 12 - 2

⇒ b ≥ 10

Interval form is represented by [10, ∞)

Solution of the graph represent 10 is included to arrow moves towards positive infinity.

Therefore, for the given inequality 2(b + 2) ≥ 24 solution of the graph represented by number line with closed point at 10 with arrow pointing right.

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A computer base unit of mass 4.5 kg is dragged along smooth desk, if tension in each arm of the person dragging it is 16 N and acts at 22° above the horizontal, then what is the normal reaction force is 32.12N.

A force is effect that can alter an object's motion according to physics. A force can cause an object with mass to accelerate when it changes its velocity, for as when it moves away from the rest. An obvious way to describe force is as push or a pull. A force is vector quantity since it has both magnitude and direction. It is calculated by using newton SI unit (N). Force is denoted by letter F. (formerly P).

The net force acting on object is equal to the rate at which its momentum varies over time, according to Newton's second law in its original formulation. This law suggests that object's acceleration is directly proportional to the net force acting on it, is in the direction of the net force, and is inversely proportional to mass of the object if the object's mass is constant.

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Answer:

−54v−27y+36

Step-by-step explanation:

hope this helped

have a good day ^^

Answer:-50x+36

Step-by-step explanation:

Answer:

-50+36

Step-by-step explanation:

i hope that helps

a) The expected value is calculated to be 2.273 and b) the standard deviation is 1.499 if a random sample of 200 children is selected.

According to the report 1 in 88 American children has been diagnosed with ASD, therefore the probability can be given as;

p = 1 / 88

a) the expected value can be calculated as follows;

E (X) = n × p

here n = sample size = 200

p = probability = 1 / 88

E (X) = 200 × 1 / 88

E (X) = 2.273

b) To find the standard deviation, first, we have to determine the variance of the random variable;

V (X) = n × q × p

V (X) = 200 × 87/88 × 1/88

V (X) = 2.2468 = 2.247

Now we can calculate the standard deviation as follows;

standard deviation = √V(X)

standard deviation = √2.247

standard deviation = 1.499

Therefore, the expected value and standard deviation are calculated to be 2.273 and 1.499 respectively.

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Answer:

answer is 4

because y is directly proportional to x2

Answer:

y is directly proportional to x

y=kx^2

20=2^2k

20=4k

k=5

y=6k

y=6(5)

y=30

Plssmark as brainliest

Answer: 37/20 1 17/20

Step-by-step explanation:

Hope this helps

Answer:

93/20

Step-by-step explanation:

7/10 + 2/5 + 3/4

= (70+8+15)/20 [.°. L. C. M. of 10, 5 , 4 ]

=93/20

If the steps are shaped like rectangular prism, then the expression that can be used to find the volume is option (B)  (6×16×6)+(14×16×7)

The steps are shaped like rectangular prism

The length of the rectangular prism = l×w×h

Where l is the length

w is the width

h is the height

First we have to separate the given steps in to two rectangular prism and find the volume of each prism

The volume of the top prism = l×w×h

= 6×16×6 cubic inches

The volume of the bottom prism = l×w×h

= 14×16×7 cubic inches

The total volume = (6×16×6)+(14×16×7) cubic inches

Hence, if the steps are shaped like rectangular prism, then the expression that can be used to find the volume is option (B)  (6×16×6)+(14×16×7)

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Answer:

3

Step-by-step explanation:

The temperature outside an airplane that took off and climbed to 5000 m will be -15 degrees Celsius.

We will use Unitary method to solve the iven problem.

The ground temperature at Pearson Airport was 10 degrees Celsius.

The temperature drops 5 degrees for every 1000 m above ground. This can be written as,

5 degrees  Celsius      ---------------->   1000m

1m      ---------------->   (5/1000) degrees  Celsius

5000m      ---------------->   (5/1000)×5000 degrees  Celsius

5000m      ---------------->    25 degrees  Celsius

For 5000m above the ground, the drop in temperature will be 25 degrees  Celsius.

The temperature outside an airplane that took off and climbed to 5000 m will be = 10 - 25 = -15 degrees Celsius.

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The remainder when [tex]5^{400}[/tex] is divided by 19, the remainder is 17.

Remainder

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

We can write,

[tex]5^{400} = (5^4)^{100} = 625^{100}[/tex]

We know that,

19*33 = 627

Hence, we can write 625 as 627 - 2

It will become,

[tex]\frac{(627-2)^{100}}{19}=\frac{(-2)^{100}}{19}[/tex]

We know that, even power of any number and its negative counterpart will be same.

Hence, we can write,

[tex]\frac{(-2)^{100}}{19}=\frac{(2)^{100}}{19} = \frac{2*2^{99}}{19}[/tex]

We know that 99 = 11*9

Hence, we can write,

[tex]\frac{2*({2^9})^{11}}{19} =\frac{2*512^{11}}{19}[/tex]

We know that,

19*27 = 513

Hence, we can write, 512 as 513 - 1

[tex]\frac{2*(513-1)^{11}}{19}=\frac{2(-1)^{11}}{19}[/tex]

2*(-1)/19 = -2/19

It means the remainder will be 19 - 2 = 17.

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b= (2,-1);

(3,1) - left 1, down 2

The number of traditional viewing theater is 14 , number of 3D movie viewing theaters is 2 , and number of luxury movie viewing theater is 5 .

In the question ,

it is given that

The 21-screen movie complex has  three types of movie theaters,

let the number of traditional movie viewing theater be  "a" ,

let the number of 3D movie viewing theater be  "b" ,

let the number of luxury movie viewing theater be  "c" ,

So , a+b+c=21      ...(i)

given that ,

Traditional viewing theaters are twice of the combined number of 3D and luxury theaters ,

So the equation is

a=2(b+c)         ...(ii)

also , the number of luxury theaters exceeds the number of 3D theaters by 3 ,

So , the equation is

c=b+3     ....(iii)

Substituting value of c from (iii) in (ii) and (i) we get ,

a-4b=6 and a+2b=18

Solving , we get a=14 and b=2 .

Substituting a=14 and b=2 in (iii) , we get

c=5 ,

So , a =14 , b=2 and c=5

Therefore , the number of traditional viewing theater is 14 , number of 3D movie viewing theaters is 2 , and number of luxury movie viewing theater is 5.

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By using the fact that the two angles are vertical angles, we will write and solve a linear equation to fine that the value of x is 20.

Here we assume that both of the horizontal lines are parallel. Then the two marked angles (the ones that depend of x) are vertical angles.

This means that the measure of these angles is the same one, then we can write:

(5x - 8)° = (3x + 32)°

So we can solve that linear equation to find the value of x, we will get:

5x - 8 = 3x  + 32

Grouping like terms we get:

5x - 3x = 32+ 8

2x = 40

x = 40/2

x = 20

The value of x is 20.

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Answer:

Any number raised to 0 is equal to 1

hence: 2^0 = 1

The equation of the new function g(x) is g(x) = 2 - |x+2|

Transformation is. way of changing the position of an object on an xy-plane.

Given the parent function  f(x) = |x+3|.

If the function is translated 2 units down and 1 unit right, then the resulting function will be |x+3 - 1| - 2 which is equivalent to  |x+2| - 2

The reflection of the resulting function across the x-axis is given as:

g(x) = -(|x+2|-2)

g(x) = 2 - |x+2|

Hence the new function g(x) if the parent function undergo the transformation is g(x) = 2 - |x+2|

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Answer: x = 70

Step-by-step explanation: the sum of the angle 2x-5  and 45 deg should equal 180 deg, so 2x-5 should be equal to 135 because 180 - 45 = 135

So 2x -5 = 135. Add 5 to both sides to cancel it out. 2x = 140. divide both sides by 2 to cancel 2 on x. Answer is X=70

I think this is how you do it lol but I don't know for sure.

Answer:

24

Step-by-step explanation:

Answer: y = -4.4

              y = -3.8

              y = -3.2

Step-by-step explanation:

There is a 70.6% chance that none of the 4 randomly picked people share your zodiac sign.

Probability is a branch of mathematics in which we determine how likely an event is to happen. It is used when we are not sure about the result or outcome of an event so we consider the probabilities of certain outcomes.

In this case, there are 12 zodiac signs, out of which one is yours. So the probability or chance that the 4 randomly picked people do not share your zodiac sign can be determined as follows;

Probability of one person not having your zodiac sign: 11/12

Probability of 4 people not having your zodiac sign;

11/12 × 11/12 × 11/12 × 11/12 = 0.706

Converting it into percentage:

0.706 × 100 = 70.6%

Hence, the probability that none of the 4 people share your zodiac sign is calculated to be 70.6%.

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The complete statement is: 'When the denominator of a fraction is equal to -1, and the numerator is nonzero, the value of the fraction is equal to the opposite of the numerator of the fraction.'

In this question, we need to fill in the blanks for the statement 'When the _______  of a fraction is equal to -1, and the numerator is nonzero, the value of the fraction is equal to ______'

We know that, a fraction is represented as:

x/y

Where, x represents the numerator,

y represents the denominator

Assume that y = -1

Then the fraction becomes x/(-1) = -x

This means, if the numerator is nonzero, and the denominator is -1, then the fraction has a value opposite of the numerator

Therefore, the complete statement is: 'When the denominator of a fraction is equal to -1, and the numerator is nonzero, the value of the fraction is equal to the opposite of the numerator of the fraction.'

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