Which expression shows how to convert 60 hours to days? 60 hours Over 1 times 1 hour Over 24 days 60 hours Over 1 times 1 day Over 24 hours 60 hours Over 1 times 24 hours Over 1 day 60 hours Over 1 times 24 days Over 1 hour

The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)

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Answer:

x=-2

Step-by-step explanation:

log x, log (x+2) , log (x+16) are in A.P.

2log (x+2)=log (x+2) +log (x+16)

log (x+2)²=log [(x+2)(x+16)]

(x+2)²=(x+2)(x+16)

x²+4x+4=x²+2x+16x+32

4x-18x=32-4

-14x=28

x=28/(-14)=-2

Answer:

Y= -8

Step-by-step explanation:

i think so......

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Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

Answer:

n = +1

Step-by-step explanation:

Hope this helps

Answer:

im pretty sure -9 is the answer

There is no maximum and minimum values.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=∛(x+1)

Find where the first derivative is equal to 0 to find the local maxima and minima.

By differentiating the given function we get

\(f(x)=(x+1)^{\frac{1}{3} }\)

\(f'(x)=\frac{1}{3(x+1)^{\frac{2}{3} }}\)

For maxima f'(x)=0

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

No local maxima or minima

Therefore, there is no maximum and minimum values.

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Answer:

22

Step-by-step explanation:

Say angle 1 is x and angle 2 is y and the overall angle is m

m=x+y

x=2y

replace x with it’s equivalent

m=2y+y

m=3y

replace m with it’s equivalent

 66=3y

—————

      3

22=y

22 = Angle 2

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Answer:

Answer is A

Step-by-step explanation:

Thats all And do i need to explain ?

Option (b) is the correct answer: Perpendicular segments.

Perpendicular rays, perpendicular segments, perpendicular lines, and parallel lines are important concepts in geometry that describe the relationship between lines and line segments.

1. Perpendicular Rays: Perpendicular rays are two rays that intersect at point and form a right angle (90 degrees) at the point of intersection. The rays extend indefinitely in opposite directions from the point of intersection.

2. Perpendicular Segments: Perpendicular segments are line segments that intersect at a right angle. They share a common endpoint but do not extend indefinitely like rays. The right angle is formed at the point of intersection.

3. Perpendicular Lines: Perpendicular lines are lines that intersect at a right angle. They continue indefinitely in opposite directions and form four right angles at the point of intersection. Perpendicular lines are often denoted by a symbol ⊥.

4. Parallel Lines: Parallel lines are lines that never intersect. They remain equidistant from each other at all points. Parallel lines have the same slope and do not converge or diverge. In Euclidean geometry, parallel lines are denoted by a double vertical line symbol (||).

Understanding these concepts is fundamental in geometry as they help define angles, shapes, and spatial relationships. The properties of perpendicular and parallel lines play a crucial role in various geometric theorems and applications.

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Answer:

Step-by-step explanation:

5 and 5

Answer:

the decimal point should be moved 5 places to the right because there are five zeros in 10 with the power of 5

Step-by-step explanation:

The length of the rectangle is 96 m, the width of the rectangle is 77 cm , the length of the rectangle is 1/8 mile, the length and width of the rectangle is 7 m and 42 m respectively, VW is  11 units.

According to the question,

1) Perimeter of rectangle = 344 M

Width = 76 M

Perimeter of rectangle = 2(length + width)

2(length+76) = 344

length+76 = 172

length = 172-76

Length of the rectangle = 96 M

2) Area of a rectangular window = 7315 \(cm^{2}\)

Length of the window is 95 cm.

Area of rectangle = length*width

95*width = 7315

width = 7315/95

Width of the rectangle = 77 cm

3) The perimeter of a rectangular garden is 5/8 mile.

The width of the garden is 3/16 mile.

Perimeter of rectangle = 2(length+width)

2(length+3/16) = 5/8

length+3/16 = 5/(2*8)

length = 5/16-3/16

Length of the rectangle = 2/16 or 1/8 mile

4) The area of a rectangular window is 8256 \(m^{2}\).

The length of the window is 86 m.

Area of rectangle = length*width

86*width = 8256

width = 8256/86

Width of the rectangle = 96 m

5)  The length of a rectangle is six times its width. The perimeter of the rectangle is 98 m.

Let's take width of the rectangle to be x m.

Length of rectangle = 6x m

2(length+width) = 98

2(6x+x) = 98

2*7x = 98

14x = 98

x = 98/14

x = 7 m

Width = 7 m

Length = 7*6 m or 42 m

6) The perimeter of the pentagon is 58 units.

3z+10+z+3+2z-1+10 = 58

6z+10+3-1+10 = 58

6z+22 = 58

6z = 58-22

6z = 36

z = 36/6

z = 6 units

VW = 2z-1

VW = 2*6-1

VW = 12-1

VW = 11 units

Hence, the answer to 1 is 96 m , 2 is 77 cm, 3 is 1/8 mile , 4 is 96 m , 5 is 7 m and 42 m and 6 is 11 units.

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Answer:

62°

Step-by-step explanation:

If it is a right triangle, subtract 90, from 180 and then subtract 28 to get D.  D should = 62°

D must be equal to 28° in order for triangle ABC to be similar to triangle DEF.

The correct answer is option B.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We know that if two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar.

Since angle A is congruent to angle D, we need to find the value of D that makes this true.

Therefore,

D must be equal to 28° in order for triangle ABC to be similar to triangle DEF.

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Answer:

A dashed line

Step-by-step explanation:

Because it is just a less than sign but if it was a less than or equal to it would be a solid line.

Hope That Helped :)    

the counting number just before C5F16 is 3,072.

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

exact form : 2√3

decimal form : 3.46410161… or 3.46

hope this helps you!

Answer:

The value of the function is \(\sqrt{12}\). Rounded to the nearest hundredth, the answer is 3.46

Step-by-step explanation:

We are given the value of x, so we simply have to evaluate the function:

\(f(x)=\sqrt{x+4}\)

Substitute 8

\(f(8)=\sqrt{8+4}\)

Add in the radical

\(\sqrt{12}\)

The value of the function is sqrt(12).

Rounded to the nearest hundredth: \(3.46\)

Answer:

\(\frac{13}{145}\)

The two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

The unit circle is rotationally symmetric, meaning that any angle of rotation on the unit circle will take a point to another point on the unit circle with the same distance from the origin. This means that if we rotate point A by 7π/6 radians, we can also rotate it by 19π/6 or 31π/6 radians and end up at the same point B.

The point A has polar coordinates (1, 0). This means that it is located at a distance of 1 unit from the origin and has an angle of 0 radians with the positive x-axis.

The point B has polar coordinates (√3/2, 1/2). This means that it is located at a distance of √3/2 units from the origin and has an angle of 7π/6 radians with the positive x-axis.

If we rotate point A by 19π/6 radians, we get a point with polar coordinates (√3/2, -1/2). This point is located at the same distance from the origin as point B and has the same angle with the positive x-axis.

Therefore, the two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

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The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Answer:

b 500

Step-by-step explanation:

the middle number wich is 500