1) Perimeter of a rectangular field is 230m. If the length of that field is 70m, what will be its breadth ?

2) A rectangular field has a length of 175m and a width of 125m. what will be the cost of erecting a fence around the field at a rate of Rs 12/m ?
​

Answer:

$0.001967/gallon

Step-by-step explanation:

John uses alot of water.... and it sure is cheap.

19.67/10000 =

Answer:

im in 6th grade so i have no idea

Step-by-step explanation:

The required domain and the range of the given function are (-2, 3) and (2, -3) respectively.

Given that,
To determine the domain and the range of the function given in the graph.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
From the graph, the domain of the function is defined for x = -2 to x = 3,
While the range of the graph for a given function is defined for y = 2 to y = -3 corresponding to the domain.

Thus, the required domain and the range of the given function are (-2, 3) and (2, -3) respectively.

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Answer:

P = 7

Step-by-step explanation:

We have 21 total cards and out of those 21 cards, 14 of those are birthday cards. So that means that the amount of cards that are not birthday cards is the number of cards subtracted by the number of birthday cards, also shown as 21 - 14. So 21 - 14 = P, so now we solve what 21 - 14 is which is 7, so that means P = 7.

Let me know if you have any questions.

Answer:

-1/4xy+y=0

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

We can simplify this expression by solving it.

\(2-(-5)+1\)

Subtracting a negative is the same as adding a positive:

\(2+5+1\)

And addition here shows that \(2+5+1=8\).

Hope this helped!

Answer:

Step-by-step explanation:

\(2-\left(-5\right)+1\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a\\\\-\left(-5\right)=+5\\\\=2+5+1\\\\2+5=7\\\\= 7+1 \\\\=8\)

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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Answer:

81 men and 108 women

Step-by-step explanation:

3 men +4 women=7

189÷7=27.

for every 3 men,27×3=81

for every 4 women,27×4=108

kya karna hai isme

what we have to do in this

Answer:

\(y=\frac{11}{5}x-35\)

Step-by-step explanation:

The equation of a line is y=mx+b

Plug in the points

35m+b=42 (1)

15m+b=-2 (2)

(1)-(2)

20m = 44

m = 11/5

33+b=-2

b=-35

\(y=\frac{11}{5}x-35\)

Answer: 14,5,15 is correct

Step-by-step explanation:

Answer:

636:1200

Step-by-step explanation:

Answer:

247

Step-by-step explanation:

Answer: If im not wrong it should be 1920

Step-by-step explanation:

Answer:

b. x/8 + x/16 = 3/4

4 miles

Step-by-step explanation:

edge

Answer: -2 and 4

Step-by-step explanation:

\(f(x) = \frac{-2x+2}{2x+4}\)            g(x) = -2x+8

Question asks what the domain is if we had f(x) ÷ g(x)

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4}\)  ÷                  >When dividing fractions, keep the first

                                                      Change the sign, flip the second fraction

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4} * \frac{1}{-2x+8}\)        

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{(2x+4)(-2x+8)}\)          

> you can never get a 0 on the bottom of division so that is where the exception of what x cannot be.

2x+4 = 0

2x= -4

x =  -2

and

-2x+8 = =

-2x = -8

x = 4

So x cannot be -2 and 4

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

\(-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}\)

Step-by-step explanation:

Given the initial value problem \(\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\\) subject to y(π) = 1. To solve this we will use the variable separable method.

Step 1: Separate the variables;

\(\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\\frac{1}{\theta}(\frac{dy}{sin\theta d\theta} ) =\frac{ y}{y^{2}+1 } \\\frac{1}{\theta}(\frac{1}{sin\theta d\theta} ) = \frac{ y}{dy(y^{2}+1 )} \\\\\theta sin\theta d\theta = \frac{ (y^{2}+1)dy}{y} \\integrating\ both \ sides\\\int\limits \theta sin\theta d\theta =\int\limits \frac{ (y^{2}+1)dy}{y} \\-\theta cos\theta - \int\limits (-cos\theta)d\theta = \int\limits ydy + \int\limits \frac{dy}{y}\)

\(-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y +C\\Given \ the\ condition\ y(\pi ) = 1\\-\pi cos\pi +sin\pi = \frac{1^{2} }{2} + ln 1 +C\\\\\pi + 0 = \frac{1}{2}+ C \\C = \pi - \frac{1}{2}\)

The solution to the initial value problem will be;

\(-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}\)

Using separation of variables, it is found that the solution of the initial value problem is:

The differential equation is given by:

\(\frac{1}{\theta}\left(\frac{dy}{d\theta}\right) = \frac{y\sin{\theta}}{y^2 + 1}\)

Applying separation of variables, we have that:

\(\frac{y^2 + 1}{y}dy = \theta\sin{\theta}d\theta\)

\(\int \frac{y^2 + 1}{y}dy = \int \theta\sin{\theta}d\theta\)

The first integral is solved applying the properties, as follows:

\(\int \frac{y^2 + 1}{y}dy = \int y dy + \int \frac{1}{y} dy = \frac{y^2}{2} + \ln{y} + K\)

The second integral is solved using integration by parts, as follows:

\(u = \theta, du = d\theta\)

\(v = \int \sin{\theta}d\theta = -\cos{\theta}\)

Then:

\(\int \theta\sin{\theta}d\theta = uv - \int v du\)

\(\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \int \cos{\theta}d\theta\)

\(\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \sin{\theta}\)

Then:

\(\frac{y^2}{2} + \ln{y} + K = -\theta\cos{\theta} + \sin{\theta}\)

\(y(\pi) = 1\) means that when \(\theta = \pi, y = 1\), which is used to find K.

\(\frac{1}{2} + \ln{1} + K = -\pi\cos{\pi} + \sin{\pi}\)

\(\frac{1}{2} + K = \pi\)

\(K = \pi - \frac{1}{2}\)

Then, the solution is:

\(\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} = -\theta\cos{\theta} + \sin{\theta}\)

\(\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} + \theta\cos{\theta} - \sin{\theta} = 0\)

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Answer:

WOMP WOMP WOMP!!!

Step-by-step explanation:

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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The volume of the cuboid is 58 cubic units.

A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;

volume of cuboid = length x width x height

From the given question, we have;

the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;

volume of cuboid = length x width x height

                             = 2.9 x 5 x 4

                             = 58

The volume of the cuboid with the given dimension is 58 cubic units.

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Answer:

The first option: \(-1 \frac{4}{5}\)

Step-by-step explanation:

Multiply both sides 9.

-2x = 18/5

Divide both sides by -2.

x = -9/5 or -1  4/5

Answer: 31

Step-by-step explanation: if x = 8 it would look like this

3(8) + 7

\/      \/

24 + 7

   \/

  31

STEP - BY - STEP EXPLANATION

What to find?

The initial amount (principal).

Given:

Amount(final) = $40000

time = 18

rate(r)=7.6% =0.076

n=4

Step 1

Recall th compound interest formula.

Step 2

Substitute the values into the formula.

Step 3

Simplify and solve for p.

Divide both-side of the equation by 3.87740573623

ANSWER

The amount to be invested now is 10316.18

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The diagram shows two pairs of angles lying on a straight line. Please remeber that angles on a straight line equals 180. Also you can observe two pairs of vertically opposite angles, and vertically opposite angles are equal. Hence, the angle opposite angle z also equals z. This means angles 9x - 17 and z (to the right) lie on a straight line. Similarly angle 12x - 62 and z (to the left) also lie on a straight line. Therefore;

Therefore, x = 15 and z = 62

Answer:

Step-by-step explanation:

20=total marbles

  7/20 × 6/20=  21/400   or 5.25%

   red     white

Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

5 + 7 = 12 total fruits, which means that \(N = 12\)

7 apples, which means that \(k = 7\)

You receive 2 fruits, which means that \(n = 2\)

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182\)

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.