Find the side of square , if it's perimeter is 18cm .also find its area​

Answer:

96000

Step-by-step explanation:

N=4years

R=4 %

We have S.I.=

100

PNR

=

100

P×4×4

=

100

16P

=0.16P

And on interest being compounded for 3 years and R=5 %, Amount=P(1+

100

R

)

N

=P(1+

100

5

)

3

=P×(1.05

3

)=1.157625P

So, C.I.=A−P=1.157625P−P=0.157625P

Given, S.I.−C.I=Rs228

=>0.16P−0.157625P=Rs228

=>0.002375P=Rs228

=>P=Rs96,000

The value of the interval where each function is continuous is,

⇒ (- ∞ , 1} - {1/2, 3}

We have to given that;

Function is,

⇒ f (x) = √ - (x + 1) / (2x² - 7x + 3)

Now, We know that;

Function is not defined at denominator = 0.

Hence,

2x² - 7x + 3

2x² - 6x - x + 3

2x(x - 3) -1 (x - 3)

(x - 3) (2x - 1)

So, Function is not defined at x = 3,and x = 1/2.

And,

- (x + 1) ≥ 0

x + 1 ≤ 0

x ≤ 1

Thus, The value of the interval where each function is continuous is,

⇒ (- ∞ , 1} - {1/2, 3}

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Answer: 9°

Step-by-step explanation:

(3w + 7)° + 90° + (7w - 7)° = 180°

=> 3w + 7 + 90 + 7w - 7 = 180

=> 10w + 90 = 180

=> 10w = 180 - 90 = 90

=> w = 90 / 10 = 9°

The required proportion of cupcakes that have no creme filling with 98% confidence interval is equal to (0.012, 0.058).

Total number of cupcakes = 346

Number of defective cup cakes = 12

Confidence interval = 98%

To construct a confidence interval for the proportion of all cupcakes that have no creme filling,

Use the following formula,

CI = p ± z√((p(1-p))/n)

where,

p = proportion of defective cupcakes

n = sample size

z = z-value for the desired confidence level (98% in this case)

Plug in the values we have,

p = 12/346

  = 0.0347

n = 346

z = 2.33 (from a standard normal distribution table for a 98% confidence level)

CI = 0.0347 ± 2.33√((0.0347(1-0.0347))/346)

   = 0.0347 ± 0.023

So the 98% confidence interval for the proportion of all cupcakes that have no creme filling is (0.012, 0.058).

Therefore, 98% confidence interval that have true proportion of all cupcakes with no creme filling is between 0.012 and 0.058.

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

Work Shown:

sin(A)*cot(A)

sin(A)*( cos(A)/sin(A) )

cos(A)

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

Basically I replaced cot(A) with cos(A)/sin(A). Then the sin(A) terms canceled out leaving cos(A) behind.

Answer:

cosA

Step-by-step explanation:

Using the identity

cotA = \(\frac{cosA}{sinA}\) , then

sinA × cotA

= sinA × \(\frac{cosA}{sinA}\) ( cancel sinA )

= cosA

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

Triangle WRD's angles are all 60 degrees, angle W and angle R and angle D.

Triangle WRD is an equiangular, equilateral triangle. It is also an acute triangle, as all angles are less than 90 degrees.

Step-by-step explanation:

You are told that WRD has all equal sides, each 3 inches long.

In a triangle, if sides are equal, then the opposite angles are also equal. So if ALL the sides are equal, then ALL the angles are equal.

The sum of the interior angles in a triangle is always 180 degrees. Since the trhee angles are all equal and they must add up to 180 degrees, 180/3 =60, so the angles must all be 60 degrees.

Triangle are classified by sides as

*** scalene = no equal sides

*** isosceles = two equal sides

*** equilateral = all equal sides

Triangles are classified by angles as

*** right triangle = one 90 degree angle

*** obtuse triangle = one angle larger than 90 degrees

*** acute triangle  = all angles less than 90 degrees

*** equiangular = all angles equal

There can be overlap in the categories, like an acute triangle also being equiangular.

The air pressure at the peak of Mount Marcy is approximately 164.17 pascals.

Air pressure, also known as atmospheric pressure, is the force exerted by the weight of the Earth's atmosphere on any given surface. It is the weight of the column of air that extends from the Earth's surface up to the top of the atmosphere.

The Pascal (symbol: Pa) is the SI (International System of Units) unit of pressure, named after the French mathematician and physicist Blaise Pascal. One pascal is defined as the pressure exerted by the force of one Newton on an area of one square meter. In other words, 1 Pa = 1 N/m².

We are given the formula that relates the altitude (a) and the atmospheric air pressure (P):

a = 15,500 (5 - log₁0 P)

We are also given that the altitude at the peak of Mount Marcy is 1629 meters. We can use this information to find the atmospheric air pressure at the peak of Mount Marcy by plugging in a = 1629 and solving for P:

1629 = 15,500 (5 - log₁0 P)

Dividing both sides by 15,500, we get:

(5 - log₁0 P) = 1629 / 15,500

Subtracting 5 from both sides, we get:

-log₁0 P = (1629 / 15,500) - 5

Simplifying the right-hand side, we get:

-log₁0 P = -1.5454

Taking the inverse logarithm (base 10) of both sides, we get:

P = 10⁻¹.⁵⁴⁵⁴

Using a calculator, we can evaluate this expression to get:

P ≈ 164.17 pascals

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The predicted value of y when x = 3, based on the least-squares regression line equation y = 50 - 15x, is y = 50 - 15(3) = 5.

The given least-squares regression line equation y = 50 - 15x represents a linear relationship between the variables x and y. In this equation, the coefficient of x (-15) represents the slope of the line, and the constant term (50) represents the y-intercept.

To find the predicted value of y when x = 3, we substitute x = 3 into the equation and solve for y. Plugging in x = 3, we have y = 50 - 15(3). Simplifying this expression, we get y = 50 - 45 = 5.

Therefore, when x = 3, the predicted value of y based on the least-squares regression line is 5. This means that according to the regression line, when x is 3, the expected or estimated value of y is 5.

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The height in feet of its replica at this park, rounded to the nearest whole number is 14 feet.

Distance is the measurement of an object's horizontal distance from a specific location, whereas height is the measurement of an object's height in the vertical direction.

Since the heights of real buildings are 1:10 times higher than those of model buildings, this is evident. We also know that the actual height of the US Capitol is 289 feet, so we divide that figure by 20 to determine the model's height. That amounts to 14.45, rounding to 14. Thus, the duplicate is 14 feet, rounded up to the nearest whole number.

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the answer must be t equal to Q over MC

Answer:

T= Q over MC

Step-by-step explanation:

I did the test

Answer: $3.96 per quart

Step-by-step explanation:

2 gallons = 8 quarts

Price per quart = 31.68/8 = $3.96

Therefore, price per quart = $3.96

Answer:

$3.36 per gallon

Step-by-step explanation:

So 2 gallons is equal to 8 quarts, so then you do $31.68 divided by 8 which gives you the answer of $3.36 per gallon

Answer:

Step-by-step explanation:

4x - 3y = 8

5x - 2y = -11

8x - 6y = 16

-15x + 6y = 33

-7x = 49

x = -7

4(-7) - 3y = 8

-28 - 3y = 8

-3y = 36

y = -12

Answer:

1, 8, 27, 64, 125, 216, 343, 512,

Answer:

  x = 20

Step-by-step explanation:

The marked angles are vertical angles, hence congruent.

  6x -10 = 3x +50

  3x = 60 . . . . . . . . . add 10-3x to both sides

  x = 20

Step-by-step explanation:

Vertically Opposite Angles: The two intersecting lines with a common point so formed angles Vertically opposite angles and they are equal.

Given: (3x+ 50)° and (6x - 10)°

Asked: find the value of x = ?

Solution:

Angle (3x+ 50)° = Angle (6x - 10)°

Remove to brackets both sides on LHS and RHS.

⇛3x + 50° = 6x - 10°

Shift variables on LHS and Constants on RHS, changing it's sign.

⇛3x - 6x = -10° - 50°

Subtract the and add the values on LHS and RHS.

⇛-3x = -60°

Shift the number 3 from LHS to RHS.

⇛x = -60/-3

Simplify the fraction on RHS to get the final value of x.

⇛x = {(60÷3)/(3÷3)}

⇛x = 20°/1°

Therefore, x = 20°

Answer: Hence, the value of x is 20°

Explore More:

Now, finding the the measure of each angles by putting the value of "x" in their places.

•Angle (3x+ 50)° = (3*20 + 50)° = (60 + 50)° = (100)° = 110.

Next

Angle (6x - 10)° = (6*20 -10)° = (120 - 10)° = (110)° = 110.

Verification:

Check whether the value of x is true or false.

Angle (3x+ 50)° = Angle (6x - 10)°

Substitute the value of x in equation then

⇛Angle (3*20 + 50)° = Angle (6*20 - 10)°

⇛Angle (60 + 50)° = Angel (112 - 10)°

⇛Angle (110)° = Angle (110)°

Angle 110° = Angle 110°

LHS = RHS is true for x = 20°

Hence, verified.

Answer:

Step-by-step explanation:

This will result in cylinder with radius of 4 and height of 3.

Total surface area:

Answer:

\(y=25x\)

Step-by-step explanation:

If Bella types 50 words in 2 minutes, we can divide 50 by 2 to see how many words she types in 1 minute.

\(50/2=25\)

So, Bella types 25 words per minute. When she first began writing her essay, she did not have words to start with, so there is no y-intercept (\(b\)).

Therefore, the equation that represents this relation is \(y=25x\).

Solving the equation

We can divide 400 by 25 to determine how many minutes it would take her to finish her essay.

\(\frac{400}{25} =16\)

Therefore, it will take her 16 minutes to complete her essay.

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Answer:

Step-by-step explanation:

w  = -3 and 21/25

The value of w in 7/60=5/24w+11/12 is 6/5.

Given,

7/60 = 5/24 w + 11/12

We need to solve for w.

It depends on the type of equation given.

We need to keep the variable that we are solving for in one side and simplify the other terms.

Find the value of w.

We have,

7/60 = 5/24 w + 11/12

Subtract 11/12 on both sides.

7/60 - 11/12 = 5/24 w + 11/12 - 11/12

7/6 - 11/12 = 5/24 w

Simplify the left-hand side into a fraction.

(14 - 11 ) / 12 = 5 / 24 w

3 / 12 = 5 / 24 w

Multiply 24 / 5 on both sides.

24/5 x 3/12 = 24/5 x 5/24 w

6 / 5 = w

w = 6 / 5

Thus the value of w in 7/60=5/24w+11/12  is 6/5.

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Answer:

x ≥ - 7

Step-by-step explanation:

3(x - 4) ≥ 5x + 2

3x - 12 ≥ 5x + 2

3x - 12 + 12 ≥ 5x + 2 + 12

3x - 5x ≥ 5x - 5x + 14

- 2x ≥ 14

- 2x ÷ - 2 ≥ 14 ÷ - 2

x ≥ - 7

The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.

First, we need to calculate the standard error of the mean (SEM) using the formula

SEM = standard deviation / sqrt(sample size)

SEM = 29.5 / sqrt(45) = 4.4

Next, we can standardize the sample mean using the formula

z = (x - μ) / SEM

where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

For the lower limit, we have

z = (185.7 - 193.2) / 4.4 = -1.70

For the upper limit, we have

z = (206.5 - 193.2) / 4.4 = 3.02

We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

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To find the rate of change of y with respect to time t, we need to take the derivative of the function y = 500(1-0.2)^t with respect to t:

dy/dt = 500*(-0.2)*(1-0.2)^(t-1)

Simplifying this expression, we get:

dy/dt = -100(0.8)^t

Therefore, the rate of change of y with respect to t is given by -100(0.8)^t. This means that the rate of change of y decreases exponentially over time, and approaches zero as t becomes large.

Both (a) and (b) have the same answer, which is 61.81.

Let u = (1 − 1, 91), v = (81, 8 + 1), w = (1 + i, 0), and k = −i. We need to evaluate the expressions in parts (a) and (b) to verify that they are equal.

The dot product (u · v) and (v · u) are equal, whereu = (1 - 1,91) and v = (81,8 + 1)(a) u · v.

We will begin by calculating the dot product of u and v.

Here's how to do it:u · v = (1 − 1, 91) · (81, 8 + 1) = (1)(81) + (-1.91)(8 + 1)u · v = 81 - 19.19u · v = 61.81(b) v · u.

Similarly, we will calculate the dot product of v and u. Here's how to do it:v · u = (81, 8 + 1) · (1 − 1,91) = (81)(1) + (8 + 1)(-1.91)v · u = 81 - 19.19v · u = 61.81Both (a) and (b) have the same answer, which is 61.81. Thus, we have verified that the expressions are equal.

Both (a) and (b) have the same answer, which is 61.81. Hence we can conclude that the expressions are equal.

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Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

Answer:

6%

Step-by-step explanation:

30/ 500  =   x/100

30*100= 3,000

3,000 /  500 = 6

it would be 6% hope this helps

The root of f(x) = x² - 3 obtained using both methods with the given initial values is approximately 2.3333.

To find the root of the function f(x) = x² - 3 using the Secant Method and Regula Falsi Method, we start with the initial values x₁ = 1 and x₂ = 2.

Using the Secant Method:
1. Calculate f(x₁) and f(x₂):
  f(x₁) = (1)² - 3 = -2
  f(x₂) = (2)² - 3 = 1

2. Find the next approximation x₃ using the formula:
  x₃ = x₂ - f(x₂) * (x₂ - x₁) / (f(x₂) - f(x₁))
  x₃ = 2 - 1 * (2 - 1) / (1 - (-2)) = 7/3 ≈ 2.3333

3. Repeat step 2 until reaching the desired level of accuracy or convergence.

Using the Regula Falsi Method:
1. Calculate f(x₁) and f(x₂) (same as above).

2. Determine the value of x₃ using the formula:
  x₃ = x₂ - f(x₂) * (x₂ - x₁) / (f(x₂) - f(x₁))
  x₃ = 2 - 1 * (2 - 1) / (1 - (-2)) = 7/3 ≈ 2.3333

3. Evaluate f(x₃):
  f(x₃) = (7/3)² - 3 ≈ -0.0370

4. Update the intervals [x₁, x₃] or [x₂, x₃] based on the sign of f(x₃) and repeat steps 2-3 until convergence.

The root of f(x) = x² - 3 obtained using both methods with the given initial values is approximately 2.3333.

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Answer:

A. 8

Step-by-step explanation:

Since ∠A and ∠B are vertical, we can create the equation: 40 = 5x.

40 = 5x

There is only one other thing we need to do, and that's divide by 5.

40/5 = x

x = 8

The value of x in this case is 8, which is A.