What is the area of a rectangular picture frame with twenty inches in length, and a width of fifteen inches?​

Answer:

Step-by-step explanation:

when h=0

0=-1125d²+d

1125d²-d=0

d(1125d-1)=0

d=0

or 1125d-1=0

d=1/1125 meters

The inflection occurs at x = n*pi, while the absolute extreme points, while the critical points can be found with the expression 5 + 5cos(x) = 0.

To find local extreme points, absolute extreme points, and inflection points, we will first take the first and second derivatives of the function.

y = 5x + 5sin(x)

y' = 5 + 5cos(x)

y'' = -5sin(x)

To find critical points, we set the first derivative equal to zero.

5 + 5cos(x) = 0

cos(x) = -1

x = pi

This is the only critical point, so we only need to evaluate the function at x = pi to find any extreme points.

y(pi) = 5pi - 5

So the absolute minimum occurs at (pi, -5).

To find inflection points, we set the second derivative equal to zero.

-5sin(x) = 0

sin(x) = 0

x = k*pi, where k is an integer.

So the inflection points occur at x = n*pi, where n is an integer.

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Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.

Given that-

Volume of cylinder = πr²h

Volume of cylinder = 3.14 *5²*18

Volume of cylinder = 3.14*25*18

Volume of cylinder = 1413 ft³

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

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Answer:

630

Step-by-step explanation:

v= pi×radius squared×hight so its 3.14×5 sqared×8 628 and 628 rounded to the nearest tenth is 630 hope this help

Answer:

153.94 cm2

Step-by-step explanation:

Circle area = π * r² = π * 49 [cm²] ≈ 153.94 [cm²]

π ≈ 3.14159265 ≈ 3.14

d = r * 2 = 7 [cm] * 2 = 14 [cm]

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The area of the shaded region is 88π square inches.

To find the area of the shaded region, we need to subtract the area of the inner circle (with a radius of 9 inches) from the area of the outer circle (with a radius of 13 inches).

The area of a circle is given by the formula A = πr^2, where r is the radius.

Area of outer circle = π * (13²) = 169π square inches

Area of inner circle = π * (9²) = 81π square inches

Area of shaded region = Area of outer circle - Area of inner circle

= 169π - 81π

= 88π square inches

So, the area of the shaded region is 88π square inches.

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See text below



A ring-shaped region is shown below. Its inner radius is 9 in, and its outer radius is 13 in.

9 in

13 in

Find the area of the shaded region.

Use 3.14 for π. Do not round your answer.

2

in2

X

G

Answer:

Step-by-step explanation:

The Unit Circle is a circle with a radius of 1 unit that is centered at the origin of a coordinate plane. It is often used in trigonometry to understand the relationships between angles, coordinates, and trigonometric functions such as sine, cosine, and tangent.

Special angles in trigonometry are angles that have commonly used values for their trigonometric functions. These special angles are 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees, and their corresponding angles in radians (which are the preferred units for angles in the Unit Circle). These angles have well-defined coordinates on the Unit Circle, and their sine, cosine, and tangent values can be easily determined.

To find the coordinates of points on the Unit Circle for special angles, we can use the following steps:

Start with the angle in radians. For example, if we are finding the coordinates for the angle of 30 degrees, we convert it to radians by multiplying by the conversion factor pi/180 (since there are pi radians in 180 degrees): 30 degrees * (pi/180) = pi/6 radians.

Identify the coordinates on the Unit Circle that correspond to the angle in radians. For example, for an angle of pi/6 radians, we know that it is located in the first quadrant of the Unit Circle, and the coordinates of the point where the angle intersects the Unit Circle are (cos(pi/6), sin(pi/6)).

Use the values of cosine and sine for the special angle from trigonometric tables or from memory. For example, the cosine of pi/6 radians is sqrt(3)/2, and the sine of pi/6 radians is 1/2.

Substitute the cosine and sine values into the coordinates of the Unit Circle. For example, for the angle of 30 degrees or pi/6 radians, the coordinates on the Unit Circle are (cos(pi/6), sin(pi/6)) = (sqrt(3)/2, 1/2).

Use the tangent function to find the tangent value of the special angle. The tangent function is defined as the ratio of sine to cosine: tan(theta) = sin(theta) / cos(theta). For example, for the angle of pi/6 radians, the tangent value is (sin(pi/6)) / (cos(pi/6)) = (1/2) / (sqrt(3)/2) = 1/sqrt(3).

In summary, special angles in trigonometry are used to determine the coordinates of points on the Unit Circle, and the sine, cosine, and tangent values of these special angles can be found using trigonometric tables or from memory, and then applied to the Unit Circle to determine the coordinates and trigonometric function values for these angles.

The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.

To find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:

P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024

P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680

Therefore,

P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296

Rounding this to four decimal places, we get: 0.9130

Therefore, the answer is option E: 0.9130.

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Boat is 4.195 miles or  6.749755 km far from the lighthouse B.

The boat has moved 4 kilometers from point A to point x. The distance between B and x is what we're looking for.

Trigonometry can be used to overcome this issue. Let's abbreviate the distance "d" from A to x. Then, we can apply the following formula:

tan(65°) = (9 / d)

We can rearrange this formula to solve for d:

d = 9 / tan(65°)

We find that:

tan(65°) = 2.1445

So, d = 9 / 2.1445

= 4.195 miles (rounded to the nearest tenth)

or  6.749755 km.

Hence, Boat is 4.195 miles or  6.749755 km far from the lighthouse B.

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The probability of picking a prime number is 2/3 or approximately 0.667.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Out of the given options of 2, 3, and 4, only 2 and 3 are prime numbers. Therefore, the probability of picking a prime number is:

P(prime) = number of prime options / total number of options

P(prime) = 2/3

So the probability of picking a prime number is 2/3 or approximately 0.667.

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The zero product property's assistance.  The RP measures 14 cm in length.

The length of a thing refers to its size or length measured from end to end. Or, to put it a different way, it is the larger of a geometrical shape's upper two or three dimensions.

(x+x+2) * (x+2) = (4+6)*4

Conjoin similar terms

(2x+2)(x+2)=10*4

2(x+1)(x+2) = 40

Divide by 2

(x+1)(x+2) = 20

FOIL

x²+2x+x+2=20

x²+3x+2=0

Subtract 20

x²+3x-18=0

Factor

(x +9) (x-6) = 0

Utilising the zero sum property

x+9=0   x-6 =0

x= -9    x=6

The length cannot be negative, hence

x=6

RP = x+2+x

= 6+2+6

= 14

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The function (5) is 10 given that f(x) = x + 5  if x ≥ 0

To solve for f(5), we have to look at the function rule that says f(x) = x + 5 if x ≥ 0. Following this rule we say f(x) = 5 + 5 = 10. The number 10 is greater than 0 which make it valid.

All other rule does not apply to finding f(5).

The above answer is in response to the full question below

if  f(x) = { 2x−3 if x ≤ -4

            {   x²  If -4 < x < 0

             {  x + 5  if x ≥ 0

What is f(5)?

A. 25

B. 7

C. -4

D. 10

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Answer:

the answer is D. 9e³x.

Step-by-step explanation:

If f(x) = e³x, then we can find its derivative using the chain rule of differentiation as follows:

d/dx(e³x) = 3e³x * d/dx(3x) = 3e³x * 3 = 9e³x

= D. 9e³x.

Answer:

A

Step-by-step explanation:

An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Answer:

a) 3/4

b) 21/4  

Step-by-step explanation:

To find the scale factor from A to B take any side of B and divide it by the corresponding side of A

The ratio will be the same for all sides

We have
scale factor = 3/4

We see that the sides 9 and 12 are also in this ratio: 9/12 = 3/4

a) So scale factor from A to B is 3/4

b) w of shape B corresponds to the side with length 7 in shape A

The ratio of w to 7 must be equal to the scale factor

So w/7 = 3/4

w = 7 x 3/4

w = 21/4

Answer:t = 9.6.

Step-by-step explanation:

The value after solving mixed fraction is 32/10=3.2

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.

according to question,

=51/10 - 19/10

=32/10

=3.2

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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.

To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.

5 1/10 can be converted to an improper fraction as follows:

5 1/10 = (5 x 10 + 1)/10 = 51/10

1 9/10 can be converted to an improper fraction as follows:

1 9/10 = (1 x 10 + 9)/10 = 19/10

Now we can subtract the two fractions:

51/10 - 19/10 = (51 - 19)/10 = 32/10

32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.

So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

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Answer: 40

Step-by-step explanation:

math

Answer:i think it is c

Step-by-step explanation:

Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.

Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The total number of pizzas made yesterday can be determined using the information provided as follows:

2121 cheese pizzas total.

Pizzas with vegetables: 1414

2323 pepperoni pizzas total.

1414 sausage pizzas were consumed.

Total pizzas produced were

=>2121 + 1414 + 2323 + 1414 = 7272.

Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.

The likelihood that the following pizza will be a cheese pizza is calculated as follows:

=> 2121 / 7272

The likelihood that the next pizza prepared won't be a cheese pizza is thus:

=> 1 - (2121 / 7272) = 5151 / 7272

Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.

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The value of 'x' in the given figure is 14.73.

The given figure is a Right-angled triangle.

According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.

In the given figure,

Hypotenuse is 19.

The adjacent side is 12.

The opposite side is x.

Now, we have to find the value of x.

According to the theorem,

19² = 12²+x²

361 = 144+x²

x² = 361 - 144

x² = 217

x = √217

x = 14.73

Therefore, the value of 'x' in the given figure is 14.73.

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The function is defined piecewise, and 4 does not fall under any of the conditions where the function is defined. Therefore, the function is not defined for x=4.

So the answer is C, "function is not defined for this value."

Answer:

9

Step-by-step explanation:

Answer: 1.8

Let's put our whole number and fraction side by side so we can visualize the problem we're trying to solve:

3 ÷

5

3

The trick to working out 3 divided by 5/3 is similar to the method we use to work out dividing a fraction by a whole number.

All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator. Let's write this down visually:

3 x 3

5

=

9

5

So, the answer to the question "what is 3 divided by 5/3?" is:

9

5

Sometimes, after calculating the answer we can simplify the resulting fraction down to lower terms. In this example though 9/5 is already in it's lowest possible form.

If you made it this far you must really love your fractions and dividing whole numbers by them. Hopefully this simple guide was easy for you to follow along and you can now go forth and divide more whole numbers by as many fractions as your heart desires.

Convert 3 divided by 5/3 to Decimal

One last little calculation before you go. It's common to want to express your result as a decimal and, to do that, all you need to do is divide your numerator by your denominator:

9

5

= 1.8

Answer: 20a +5,600 < 21,000

move the content to the right

20a < 21,000 -5600

calculate

20a<15400

20a <15400
divide both sides of the inequality by 20

a<770

The answer for the given expression is =1/128[35-56cos2x+28cos4x-8cos6x+cos8x]

What is trignomatric functions?

All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

What is multiple angles?

If angle A is taken as a given, then many angles are 2A, 3A, 4A, etc. The many angle formulas employ the double and triple angles formulas. Sine, cosine, and tangent are the often utilised trigonometric functions for the multiple angle formula.

Answer is attached as a image must check:

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We can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Trigonometric functions raised to powers can be rewritten using double-angle, half-angle, and Pythagorean identities in power lowering formulas. Equations can be made simpler using them, and trigonometric expressions can be precisely determined.

We can use the power-reducing formulas to rewrite sin⁸x in terms of cosines of multiple angles as follows:

sin²x = 1 - cos²x   (first power-reducing formula)

sin⁴x = (sin²x)² = (1 - cos²x)²

      = 1 - 2cos²x + cos⁴x   (second power-reducing formula)

sin⁶x = (sin⁴x)(sin²x)

      = (1 - 2cos²x + cos⁴x)(1 - cos²x)

      = 1 - 3cos²x + 3cos⁴x - cos⁶x   (third power-reducing formula)

sin⁸x = (sin⁶x)(sin²x)

      = (1 - 3cos²x + 3cos⁴x - cos⁶x)(1 - cos²x)

      = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

Now we can substitute the expression for sin⁸x into the given expression and simplify it:

1/128 (35 - 56 cos2x + 28 cos4x - 8 cos6x + cos8x)

= 1/128 (35 - 56(2cos²x-1) + 28(4cos⁴x-3cos²x) - 8(8cos⁶x-8cos⁴x+cos²x) + cos⁸x)

= 1/128 (35 - 112cos²x + 56 + 112cos⁴x - 84cos²x - 64cos⁶x + 64cos⁴x - 8cos²x + cos⁸x)

= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Therefore, we can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

     = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

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

Work Shown:

[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]

The other diagonal is 4 miles long.

La probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de 0.

Este es un problema de distribución binomial con una probabilidad de éxito del evento (obtener un 6 en un lanzamiento de un dado de 6 caras) de 1/6.

Podemos utilizar una aproximación normal para la distribución binomial si el número de ensayos es grande y la probabilidad de éxito es moderada.

La aproximación normal para una distribución binomial se define como:

Z = (X - μ) / σ

El valor esperado de X es:

μ = n * p = 1000 * 1/6 = 166.67

La desviación estándar de X es:

σ = √(n * p * (1-p)) = √(1000 * 1/6 * 5/6) = 11.79

x = 400: z = (X - μ) / σ = (400 - 166.67) / 11.79 = 19.79

x = 500: z = (X - μ) / σ = (500 - 166.67) / 11.79 = 28.27

La probabilidad de obtener entre 400 y 500 éxitos se puede calcular utilizando la tabla de distribución normal estándar o una calculadora de probabilidad normal.

P(400 ≤ X ≤ 500) = P(19.79 ≤ z ≤ 28.27) = 0

Por lo tanto, la probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de aproximadamente 0.

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The value of CE is 14.7 units.

The diameter of a given circle is a straight line which passes through the center of the circle and divides it into two equal semi-circles.

So that in the given circle with center A, we have;

CE = BD  (diameter of a given circle)

BA = EA = CA = DA    (radius of a given circle)

CE is the diameter of the circle, and BA is the radius, so that;

CE = 2*BA

     = 2*7.35

     = 14.7

CE = 14.7

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