Prove the following?

The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

To compare between 0.67 and 0.670

Now, We know that;

The value of zero after any number in decimal expression has neglect.

So, By definition of decimal numbers, we get;

The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

Hence, The correct comparison symbol from the drop-down box is,

⇒ 0.67 = 0.670

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The probability P(G|N) value is 0.585 when P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41.

To find P(G|N), which represents the probability of event G given event N, we can use the formula:

P(G|N) = P(G∩N) / P(N)

Given that P(G∩N) = 0.24 and P(N) = 0.41

we can substitute these values into the formula:

P(G|N) = 0.24 / 0.41

Calculating the division:

P(G|N) = 0.585

Therefore, the value of P(G|N) is 0.585.

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Based on the information, it should be noted that the value of tan(A-B) is 234/583.

Given:

tanA = 60/11

sinB = 45/53

A and B are in Quadrant I

We can use the following identity to find tan(A-B):

tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)

Substituting the given values, we get:

tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))

= (15/53)/(295/583)

= 234/583

Therefore, the value of tan(A-B) is 234/583.

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Answer:

V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet

Work Shown:

d = diameter = 28

r = radius = d/2 = 28/2 = 14

V = volume of a sphere

V = (4/3)*pi*r^3

V = (4/3)*3.14*(14)^3

V = 11,488.2133 cubic feet approximately

The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.

Answer:

Step-by-step explanation:

The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side of the square.

Let y be the length of the side of the small square.

Then, the area of the small square is y^2 cm^2.

According to the question, the area of the small square is 1/25 of the area of the large square.

Thus, the area of the large square is (25)(y^2) cm^2.

The length of a side of the large square is given by the formula s = √A.

Therefore, the length of a side of the large square is √(25y^2) = 5y cm.

Since the length of a side of a cube is equal to its height, width, and length, the dimensions of the cube are 5y cm x 5y cm x 5y cm = (5y)^3 cm^3.

Therefore, y = 40/5 = 8.

Thus, the dimensions of the cube are 40 cm x 40 cm x 40 cm.

x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations.

To simplify this expression, we need to use the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). We can simplify the expression step-by-step, following the rules of PEMDAS.
First, we need to simplify the parentheses, which contain an addition operation. We have:
x - 3(9 + 7)x - (-3x)
= x - 3(16)x + 3x   (remember that -(-3x) is the same as +3x)
= x - 48x + 3x     (multiplying 3 by 16 gives us 48)
= -44x + x
= -43x

Therefore, the expression x - 3(9+7)x-(-3x) simplifies to -43x.
In summary, x - 3(9+7)x-(-3x) equals -43x, which is the answer we get after applying the order of operations. Remember to follow the rules of PEMDAS carefully, and take your time simplifying each part of the expression.

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Answer:

Solution in attached photo.

Step-by-step explanation:

This question tests on the properties of angles, such as corresponding angles and sum of angles in a straight line.

The relation C is the relation that does not represent a function.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

In the context of this problem, we look at option C, where there are two arrows departing from the input of 1, meaning that:

As the input of 1 is mapped to multiple outputs, the relation does not represent a function.

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DC and DE are tangents to the circle at C and E respectively A is the centre of the circle B lies on the circle and BAE is a straight line L N

7.2.1: AABC is parallel to ADEC (AABC|||ADEC).

7.2.2: This completes the proof of both statements:

AABC|||ADEC and AE · EC = BC · DE.

To prove that AABC is parallel to ADEC, we can make use of the properties of tangents and alternate angles.

Proof:

AABC|||ADEC

DC and DE are tangents to the circle at C and E, respectively.

BAE is a straight line.

To prove AABC|||ADEC, we need to show that the alternate interior angles are congruent.

First, let's consider angle AED and angle ABC.

These angles are alternate interior angles formed by transversal AE intersecting the lines DE and BC.

Since DE is a tangent to the circle at E, angle AED is a right angle (90 degrees).

We know that a tangent to a circle is perpendicular to the radius at the point of tangency.

angle AED = 90 degrees.

Let's consider angle ABC. Since DC is a tangent to the circle at C, angle ABC is also a right angle (90 degrees).

Again, this follows from the property that a tangent is perpendicular to the radius at the point of tangency.

Since both angle AED and angle ABC are right angles, they are congruent:

angle AED = angle ABC.

By the alternate interior angle if two lines are intersected by transversal and the alternate interior angles are congruent, then the lines are parallel.

AABC is parallel to ADEC (AABC|||ADEC).

7.2.2 Showing that AE · EC = BC · DE

To prove that AE · EC = BC · DE, we can use the fact that AABC is parallel to ADEC.

Since AABC is parallel to ADEC, we can apply the intercept theorem or the proportionality theorem.

According to the intercept two parallel lines intersect a set of parallel lines, then the segments formed on one transversal are proportional to the corresponding segments formed on any other transversal.

Using the intercept theorem, we can write the following proportion:

AE/BC = DE/EC

To find AE · EC, we can cross-multiply the proportion:

AE · EC = BC · DE

We have shown that AE · EC is equal to BC · DE.

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Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

Pam will use 27/50 cups of apple juice.

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

To get how many cups of apple juice Pam will use, we must calculate 3/5 of 9/10 cups.

The 3/5 of 9/10 is:

= (3/5) * (9/10)

= (3 * 9) / (5 * 10)

= 27/50

Therefore, Pam will use 27/50 cups of apple juice.

Translated question:

A recipe calls for 9/10 cups of apple juice. Pam is preparing 3/5 of the recipe. How many cups of apple juice will Pam use?​

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The length of the variable are as follows;

x = 27.4 units

y = 12.7 units

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

5(x + 5) = 6(21 + 6)

5x + 25 = 126 + 36

5x + 25 = 162

5x = 162 - 25

5x = 137

x = 137 / 5

x = 27.4 units

Let's find variable y as follows;

If a secant and a tangent are drawn to a circle from the same external point, the product of the length of the secant and its external segment equals the square of the tangent segment.

Therefore,

y² = (21 + 6)6

y² = 27 × 6

y² = 162

y = √162

y = 12.7279220614

y = 12.7 units

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The length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.

Given is a triangle with angles 64° and 32°, and side 21.1 and 30, we need to find the third side,

So, according to the angle sum property of triangle,

Third angle = 180° - (64° + 32°)

Third angle = 84°

To find the length of the third side, which is opposite the angle of 84°, we can use the Law of Sines.

The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.

Let's label the triangle with angles A, B, and C, and sides a, b, and c, respectively.

In this case, angle A is 84°, angle B is 64°, and angle C is 32°. Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.

Using the Law of Sines, we have the following equation:

sin(A) / a = sin(B) / b = sin(C) / c

We want to find the length of side a, so we can rearrange the equation as follows:

sin(A) / a = sin(B) / b

Now we can substitute the given values:

sin(84°) / a = sin(64°) / 30

To find side a, we can solve for it algebraically:

a = (sin(84°) × 30) / sin(64°)

Calculating this expression, we get:

a ≈ 30.1

Therefore, the length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.

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The required sample size for a margin of error of less than 0.04 is given as follows:

n = 601.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence the proportion is used as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of 0.04, the sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 0.5}{0.04}\right)^2[/tex]

n = 601.

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Answer:

Step-by-step explanation:

The areas of the triangles are listed below:

Triangle A: A = 30 cm²

Triangle B: A = 14 cm²

Triangle C: A = 15 cm²

Triangle D: A = 40.997 cm²

In this problem we have a composite figure in the form of a square and formed by three right triangles (A, B, C) and a non-right triangle (D). The area of each triangle must be found, the areas of the each right triangle can be determined by this formula:

A = 0.5 · b · h

Where:

And the area of the non-right triangle can be found by Heron's formula:

A = √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

First, determine the areas of the right triangles:

Triangle A

A = 0.5 · (10 cm) · (6 cm)

A = 30 cm²

Triangle B

A = 0.5 · (7 cm) · (4 cm)

A = 14 cm²

Triangle C

A = 0.5 · (3 cm) · (10 cm)

A = 15 cm²

Second, find the side lengths of the non-right triangle by Pythagorean theorem:

a = √[(10 cm)² + (6 cm)²]

a = 2√34 cm

b = √[(7 cm)² + (4 cm)²]

b = √65 cm

c = √[(3 cm)² + (10 cm)²]

c = √109 cm

Third, calculate the semiparameter of the non-right triangle:

s = 0.5 · (2√34 cm + √65 cm + √109 cm)

s = 15.082 cm

Fourth, calculate the area of the non-right triangle:

A = √[(15.082 cm) · (15.082 cm - 2√34 cm) · (15.082 cm - √65 cm) · (15.082 cm - √109 cm)]

A = 40.997 cm²

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Answer: 2(x+3)(x+2)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

Answer:

The answer is number 2

(1) The triangles ABC and DEF are not similar

(2) The triangles JKL and JMN are similar by the SAS similarity statement

(3) The triangles ABC and XYZ are similar

(4) The triangles PQR and TSR are similar

(1) Triangle ABC and DEF

The triangles in this figure are

ABC and DEF

These triangles are not similar is because:

The triangles do not have similar corresponding sides i.e. Ratio = 30/24 ≠ Ratio = 24/18

Evaluate

Ratio = 1.25 ≠ Ratio = 1.33

(2) Triangle JKL and JMN

The triangles in this figure are

JKL and JMN

"If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar"

This means that they are similar by the SAS similarity statement

(3) Triangle ABC and XYZ

The triangles in this figure are

ABC and XYZ

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 33/22 = 45/30 = 42/28

Evaluate

Ratio = 1.5

(4) Triangle PQR and TSR

The triangles in this figure are

PQR and TSR

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 10/5 = 9/4.5

Evaluate

Ratio = 2

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The length f the diagonal of the square is

The marked points represents the diagonal hence we find the distance between the points

The distance between them is calculated using the following formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the points (3, 5) and (12, 14), we can substitute the values into the formula and calculate the length of the line segment:

d = √((12 - 3)² + (14 - 5)²)

= √(9² + 9²)

= √(81 + 81)

= √162

≈ 12.73

Therefore, the length of the line segment between (3, 5) and (12, 14) is approximately 12.73 units.

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The possible trigonometric ratios for the angle θ are given as follows:

A. [tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

B. [tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

The sine for the angle θ is given as follows:

sin(θ) = 2/3.

The identity relating the sine and the cosine is given as follows:

sin²(θ) + cos²(θ) = 1.

Hence the cosine of the angle is given as follows:

cos²(θ) = 1 - 4/9

cos²(θ) = 5/9

[tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex]

The tangent is given by the division of the sine by the cosine, hence it is calculated as follows:

[tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

(if the cosine is negative, the tangent is then negative, as the sine is positive).

The secant is the division of one by the cosine, that is, it is the inverse fraction of the cosine, hence:

[tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex]

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Answer:

$132.54

Step-by-step explanation:

$1060.32 / 8 families = $132.54 / family

Answer:

x = 8, m2 = 78, m4 = 102, m6 = 78, m7 = 78,

Step-by-step explanation:

The period of the function is 4π, and the amplitude is 2.

Given data ,

Let the function be represented as f ( x ) = y

Now , the value of f ( x ) is

y = 2sin ( 1/2 )x

To find the period and amplitude of the function y = 2sin((1/2)x), we can use the standard form of a sine function: y = Asin(Bx).

In this case, the amplitude (A) is 2.

The amplitude represents the maximum displacement from the midpoint of the sinusoidal function.

To find the period, we can use the formula:

Period = (2π) / |B|.

B = 1/2.

Period = (2π) / |1/2|

P = (2π) / (1/2) = 2π * 2/1 = 4π

Hence , the period of the function is 4π, and the amplitude is 2.

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Answer:

Step-by-step explanation:

The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3

The Phase shift is 45 and the vertical shift is 2

From the question, we have the following parameters that can be used in our computation:

f(x) = 2cos[3(θ + 45)] + 2

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

Phase shift = C

vertical shift = D

Using the above as a guide, we have the following:

Amplitude = 2

Period = 2π/2

Next, we have

Phase shift = 45

vertical shift = 2

Hence, the amplitude is 2 and the period is 2π/3

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75,582 different groups of 8 can be formed from the 19 volunteers.

In this case, we want to calculate C(19, 8), which represents the number of ways to choose 8 volunteers from a set of 19 volunteers.

The formula for combinations is given by:

C(n, r) = n! / (r!(n-r)!)

Using this formula,

C(19, 8) = 19! / (8!(19-8)!)

C(19, 8) = 19! / (8!11!)

C( 19, 8) = 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 / 8 x7 x6 x 5x 4 x 3 x 2

C( 19, 8) = 75,582

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Answer:

The fraction of cupcakes they ate is:

5 / 8

The fraction of cupcakes left is:

3 / 8

The statement you provided refers to a concept known as Russell's paradox in set theory.

The paradox arises when we consider the set of all sets that do not contain themselves as elements. If we assume such a set exists, we can define a paradoxical set, often denoted as R, which contains all sets that do not contain themselves.

The statement you provided is suggesting that the paradox arises from the concept of the set of all sets, rather than from the concept of comprehension itself.

The , in set theory, refers to the idea of defining a set by specifying a property or condition that its elements must satisfy. The paradox does not arise from the idea of defining sets in this way but rather from the specific concept of the set of all sets.

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