Simplify each

2. 2
— - —
5 3


3 3
— + —
4 8
With explanation please

When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.

The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I

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Answer: a) i) The width of the floor can be expressed in terms of c as: w = c - 2 cm.

ii) The area of the floor can be expressed in terms of c as: A = c * (c - 2) cm^2.

b) If the area of the room is 15 cm^2, then we can write the equation as:

c * (c - 2) = 15.

c) Solving for c, we get:

c^2 - 2c - 15 = 0.

Using the quadratic formula, we find that:

c = 5 or c = -3.

Since the length of the room cannot be negative, we choose c = 5.

Therefore, the length of the room is 5 cm and the width of the room is 3 cm.

Step-by-step explanation:

Answer:

Explanation:

In the diagram, the angles labeled 4 and 1 are on a straight line, thus, they add up to 180 degrees.

First, solve for x:

Next, angles 3 and 4 are vertical angles, thus, they are equal.

Answer:

y=3/2x +2

Step-by-step explanation:

Rise/run + y-intercept

Answer:

y=3/2x+2

Step-by-step explanation:

By using slope intercept format, which is y=mx+b, you can get the answer.

Answer:

The slope.

Explanation:

No need...

Answer:

M represents the slope of the line

Step-by-step explanation:

Answer:

it could be 1/8

Answer:

b ≥ 8

Step-by-step explanation:

b + 4 + 2(-2b + 4) ≤ -12

b + 4 - 4b + 8 ≤ -12

-3b + 12 ≤ -12

-3b ≤ -24

b ≥ 8

The probability that the person selected drives a truck exercises four or more times per week is 0.633.

The probability of an event occurring is known as probability. This might range from an occurrence being impossible to have a chance to happen to be certain for sure. Probability is measured mathematically on a scale from 0 to 1.

Given,

The person selected who drives a truck exercises four or more times per week.

P(The person selected drives a truck and exercises four or more times per week)

= 36/120 + 52/120 - 12/120

= 76/120

Simplifying,

= 19/30

= 0.633(approximately)

The probability that the person selected drives a truck exercises four or more times per week is 0.633.

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slope formula:

(y2-y1)/(x2-x1)

(-6-6)/(4-(-2))

-12/6=

-2

SLOPE: -2

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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The 95% tolerance limits that contain 95% of the diameters is 2.262

Diameter:

In math, the straight line passing through the center of a circle or sphere and meeting the circumference or surface at each end is known as diameter.

Given,

Here we need to find the 95% tolerance limits that contain 95% of the diameters estimation of the mean diameter, while important, is not nearly as important as trying to pin down the location of the majority of the distribution of diameters.

According to the given question we have identified the following values,

Tolerance percentage = 95%

Diameter percentage = 95%

x = 61,492

n = 10

s = 3035

c = 95% = 0.95

Now, the value of t is determine by looking in the row starting with degrees of freedom 

=> df = n−1 = 10−1 = 9 and in the column with 

=> α/2 = (1−c)/2

=>0.025 

Then as per the table of the Student’s T distribution:

=> tα​=2.262

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Answer:

12

Step-by-step explanation:

36 divided by 3 = 12

Hope This Helps

Answer:

39 or 12

Step-by-step explanation:

i got 39 by 36+3=39

i got 12 by 3 divided by 36= 12

Answer:

Angle 1 = 75°

Angle 2 = 55°

Angle 3 = 55°

Angle 4 = 40°

Angle 5 = 140°

Angle 6 = 40°

Angle 7 = 75°

Angle 8 = 65°

Angle 9 = 115°

Step-by-step explanation:

1) We start with angle 2

Angle 2

Angles on a straight line = 180°

Hence,

b + 125° = 180°

b = 180° - 125°

b = 55°

Angle 2 = 55°

2)Angle 1

The sum of angles in a triangle = 180°

Hence

Let Angle 1 = a

50° + 55° + a = 180°

a = 180° - (50° + 55°)

a = 180° - 105°

a = 75°

3)Angle 3

Angle 2 and Angle 3 are vertical angles

So we use the Vertical angle theorem

This means

Angle 2 = Angle 3

Angle 2 = 55°

Hence, Angle 3 = 55°

4) Angle 4

Sum of Angles in a triangle = 180°

Let Angle 4 = d

Hence:

85° + Angle 3 + d = 180°

85° + 55° + d = 180°

d= 180° - (85° + 55°)

d = 180°- 140°

d = 40°

5)Angle 5

Angle 4 and Angle 5 are angles on a straight line

Sum of angles on a straight line = 180°

Angle 4 = 40°

Let Angle 5 = e

Hence:

40° + e = 180°

Collect like terms

e = 180° - 40°

e = 140°

6) Angle 6

Angle 4 and Angle 6 are vertical angles

Using Vertical angle theorem,

Angle 4 = Angle 6

Angle 4 = 40°

Hence, Angle 6 = 40°

7)Angle 9

Solving for Angle 9,

Sum of angles on a straight line = 180°

Angle 9 = i

i + 65° = 180°

i = 180° - 65°

i = 115°

8) Angle 8

= Angle 9 and Angle 8 are angles in a straight line

= Angle 8 = h

h + 115° = 180°

h = 180° - 115°

h = 65°

9)Angle 7

Sum of angles in a triangle = 180°

Angle 7 = g

g = 180° - (65° + Angle 6)

= 180° - (65 + 40

= 180° - 105°

= 75°

A combined function that gives the surface area of the side of the cylinder is: C. g - f.

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

In this scenario and exercise, we would determine the combined function that gives the surface area of the side of the cylinder by subtracting function f(r) from the function g(r);

Surface area of the side of the cylinder = g(r) - f(r)

Surface area of the side of the cylinder = 2π​r² + 6πr - (2π​r²)

Surface area of the side of the cylinder = f - g

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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A square has 4 congruent side lengths. This means that each side will be the same length. Therefore, we can set the two lengths equal to each other.

\(S=S\)

\(7x-15=2x\)

Isolating a variable: rearranging an equation so that the variable is by itself

3 Step Solving process:

1. Collect like terms

2. Perform inverse operations

3. Simplify if necessary

\(7x-2x-15=0\)

\(5x=15\)

\(\frac{5x}{5}=\frac{15}{5}\)

\(x=3\)

The value of x =  3

The perimeter can be found by adding all of the side lengths. A square has 4 sides.

a + a + a + a = P

However, we know that a square has congruent sides so we can manipulate this formula:

4a = P - where a is equal to the side length

Using a previous equation we know that a side length is equal to 2x and we know the value of x, to be 3. Therefore, a side length must be 6.

we can now input the value of the side length into the formula.

\(4(6)=P\)

\(24=P\)

The perimeter of the square is 24.

If DC = 10, the measure of DB is 20 units.

An equation to solve for x is 5x + 12 = 8x.

The measure of x is 4.

The measure of ∠BAC is 60°.

The measure of ∠B is 30°.

In Mathematics and Geometry, a perpendicular bisector is a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Therefore, the measure of DB can be calculated as follows;

DB = 2DC

DB = 2(10)

DB = 20 units.

Since the perpendicular bisector of DB is AC, an equation to solve for x is as follows;

5x + 12 = 8x

3x = 12

x = 12/3 = 4.

Since ∠D is congruent to ∠ABC, the measure of ∠BAC can be calculated as follows;

∠ABC + ∠BAC = 90° (complementary angles).

30° + ∠BAC = 90°

∠BAC = 90° - 30°

∠BAC = 60°

Similarly, ∠D is congruent to ∠B;

∠D ≅ ∠B = 30°.

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The classification of the given polynomials is as follows: a) Composite, b) Primitive, c) Composite.

a) The polynomial \(x^4 + x^1 + 1\) is composite. To determine this, we need to check if any nonzero seed state gives an LFSR with the same period. In this case, when we set the seed state to 0001 and perform the LFSR operation, we obtain the sequence 0001, 0011, 0110, 1101, 1011, 0111, 1110, 1100, 1001, 0010, 0100, 1000, 0001. As we can see, the period is not the maximum possible length \((2^4 - 1 = 15)\), so the polynomial is composite.

b) The polynomial \(x^4 + x^3 + x^2 + x^1 + 1\) is primitive. This means that every nonzero seed state will produce an LFSR with the maximum possible period. It can be verified that all nonzero seed states for this polynomial generate a sequence with a period of 15, which is the maximum length.

c) The polynomial \(x^4 + x^3\) is composite. Setting the seed state to 0001 and performing the LFSR operation yields the sequence 0001, 0011, 0110, 1101, 1011, 0111, 1110, 1100, 1001, 0010, 0100, 1000, 0001. Again, the period is not the maximum length, indicating that the polynomial is composite.

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- Short-run market equilibrium price: 42.5

- Long-run market equilibrium price: 40

- Number of firms in long-run equilibrium: 40

To find the short-run market equilibrium price, we need to equate the market demand and market supply. The market demand is given by Q = 2000 - 25p, and since there are 50 firms producing the watches, the market supply is 50q, where q is the quantity produced by each firm. Setting the market demand equal to the market supply, we have 2000 - 25p = 50q.

To find the short-run equilibrium price, we need to solve for p when q is determined by the cost curve C = 100 + 20q + \(q^{2}\). By substituting the market supply equation into the cost curve, we get C = 100 + 20\((2000 - 25p) + (2000 - 25p)^{2}\). Simplifying and rearranging, we obtain a quadratic equation: 625\(p^{2}\) - 40000p + 798500 = 0. Solving this equation, we find p ≈ 42.5.

To find the long-run market equilibrium price, we need to consider the condition of zero economic profit in the long run. In a perfectly competitive market, firms will enter or exit the industry until economic profit is driven to zero. Since the cost curve C = 100 + 20q + \(q^{2}\) represents both the short-run and long-run cost curve, we can find the long-run equilibrium price by setting C equal to the market price p. Setting p = 100 + 20q + \(q^{2}\), we can solve for q and find that q ≈ 20. Substituting q back into the market demand equation, we find the long-run equilibrium price p ≈ 40.

The number of firms in long-run equilibrium can be determined by dividing the total market supply by the quantity produced by each firm. Since the market supply is 50q and q ≈ 20, we have 50q / q ≈ 50 firms in long-run equilibrium. Therefore, the number of firms in long-run equilibrium is approximately 40.

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Answer:

x = 6\(\sqrt{5}\)

Step-by-step explanation:

Here we need to use the Pythagorean Theorem

Pythagorean Theorem: a^2 + b^2 = c^2

STEP 1: Define your variables

The legs of the triangle are a and b, and the hypotenuse is c.

a = x

b = 4

c = 14

STEP 2: Plug your variables into the equation and solve

x^2 + 4^2 = 14^2

x^2 + 16 = 196

x^2 + 16 - 16 = 196 - 16

x^2 = 180

\(\sqrt{x^2}\) = \(\sqrt{180}\)

STEP 3: Simplify

Since the question asks you to put the equation in simplified radical form, you do not have to approximate the answer, but you do have to simplify the radical.

\(\sqrt{x^2}\) = \(\sqrt{180}\)

x = \(\sqrt{36}\) * \(\sqrt{5}\)

x = 6\(\sqrt{5}\)

The converted value of the units 3000 meters to the required miles is given by 1. 8641 miles ( round up to four decimal places ) .

Standard form to Convert meters and miles is equal to :

1 meter = 0.000621371 miles

Now,  the value of 3000 meters in miles we get by multiplying it by 0.000621371 we get,

3000 meters = ( 3000 ) × ( 0.000621371 ) miles

                      = ( 1.864113 ) miles

                      = ( 1.8641 ) miles ( round up to four decimals places )

Therefore, the value of 3000 meters to miles is equal to ( 1.8641 ) miles ( round up to four decimals places ) .

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Answer:

D 75 and 125

Step-by-step explanation:

cünkü en büyük ortak böleni 25 dir

prove me wrong

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer:

you would make something like this:

Step-by-step explanation:

Adding a derivational suffix to a word often changes the part of speech is true.

What is derivational suffix ?

A derivational suffix is a type of affix that is added to the end of a base word to create a new word with a different meaning, often a different part of speech.

For example, adding the derivational suffix "-ness" to the base word "kind" creates the new word "kindness," which is a noun that refers to the quality or state of being kind. Similarly, adding the derivational suffix "-able" to the base word "value" creates the new word "valuable," which is an adjective that describes something that is worth a lot.

Derivational suffixes can change the meaning and function of a word, and they are often used to create new words in English. Some common derivational suffixes include "-er," "-able," "-ness," "-ful," "-ish," and "-ize."

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Complete question is: Adding a derivational suffix to a word often changes the part of speech is true.

The angle formed by the triangle is

67.38 degrees

The angle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The direction of movements describes a triangle which is bisected to form a right triangle of

opposite = 3 feet

adjacent = 2 feet

Half of the angle is calculated using tan, TOA

tan (1/2 given angle) = Opposite / Adjacent

tan (1/2 given angle) = 2 / 3

1/2 given angle = arc tan 2/3

1/2 given angle = 33.69

given angle = 67.38 degrees

where given angle is the angle formed by the triangle

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Answer:

A prime number always hacen TWO factors

The estimator 4/3x(3) is more effective than 4x(1) for estimating the parameter θ in the uniform distribution U(0, θ).

Let x1, X2, X3 obey uniform distribution U (0, θ), where θ is the upper limit. The task is to test whether 4/3x(3) or 4x(1) is more effective. The two tests can be defined as follows:

Test 1: 4/3x(3)Test 2: 4x(1)Let t1 be the test statistic for Test 1, and t2 be the test statistic for

Test 2. To determine which test is more effective, we need to calculate the power of each test. The power of a test is defined as the probability of rejecting the null hypothesis when it is false. In other words, it is the probability of correctly detecting a deviation from the null hypothesis. Suppose that the true value of θ is θ0, where θ0 > 0. Then, the distribution of the test statistics under the null hypothesis (i.e., when θ = θ0) is known. Using the formula for the mean and variance of the uniform distribution, we get: E[X] = θ/2, Var[X] = θ^2/12.

For Test 1, the test statistic is t1 = (4/3)*max(X1,X2,X3).Under the null hypothesis, the distribution of t1 is known to be the distribution of the maximum of three independent uniform random variables. Therefore, P(t1 > k) can be calculated as follows :P(t1 > k) = P(max(X1,X2,X3) > k*(3/4)) = 1 - (k*(3/4)/θ0)^3

For Test 2, the test statistic is t2 = 4*X1.Under the null hypothesis, the distribution of t2 is known to be a scaled chi-squared distribution with one degree of freedom. Therefore, P(t2 > k) can be calculated as follows: P(t2 > k) = P(4*X1 > k) = P(X1 > k/4) = 1 - (k/4θ0)For a given level of significance α, we can calculate the critical value of each test statistic as follows:

Test 1: k1 = (4/3)*c1Test 2: k2 = 4c2, where c1 and c2 are the critical values of the maximum of three independent uniform random variables and a scaled chi-squared distribution with one degree of freedom, respectively. The power of each test can then be calculated as follows:

Test 1: Power1 = P(t1 > k1 | θ = θ0 + δ), where δ is the deviation from the null hypothesis.

Test 2: Power2 = P(t2 > k2 | θ = θ0 + δ), where δ is the deviation from the null hypothesis. To determine which test is more effective, we need to compare the powers of the two tests for a given level of significance α and a given deviation δ from the null hypothesis.

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