A rectangle has length x and width y. Select all the statements that must be true.

The slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.

1) Biconditional statement: If two lines are parallel, then the alternate interior angles formed by a transversal are equal.

Formula: m∠1 = m∠3 and m∠2 = m∠4

Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the alternate interior angles formed by the transversal must have the same measure (m∠1 = m∠3 and m∠2 = m∠4).

2) Biconditional statement: If two lines are parallel, then the corresponding angles formed by a transversal are equal.

Formula: m∠1 = m∠4 and m∠2 = m∠3

Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the corresponding angles formed by the transversal must have the same measure (m∠1 = m∠4 and m∠2 = m∠3).

3) Biconditional statement: If two angles are equal, then the lines that form them are parallel.

Formula: m1 = m2

Calculation: If two angles have the same measure, then the slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.

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The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

∠TSR = 5x and ∠UVW = 7x

Angle ∠TSR and angle ∠UVW are the supplementary angles. Then the equation is given as,

5x + 7x = 180

12x = 180

x = 180 / 12

x = 15

The equation will be 5x + 7x = 180. Then the value of the variable 'x' will be 15.

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The total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely fill the entire surface of an enclosed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The shaded sections in the trapezoid are triangles.

The area of the triangle is given by the following formula:

A = 1/2 (b)(h)

For the first triangle, b = 5 and h = 6.3. Substituting the value in the formula we have:

A1 = 1/2 (5)(6.3)

A1 = 15.75

For the second triangle, b = 5.4 and h = 6.3. Substituting the value in the formula we have:

A2 = 1/2 (5.4)(6.3)

A2 = 17.01

The total area of the shaded region of the trapezoid is calculated by adding the area of the individual shaded portion:

A = A1 + A2

A = 15.75 + 17.01

A = 32.76

Hence, the total area of the shaded sections of the trapezoid in square inches is 32.76 square inches.

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According to the empirical rule -

a) About 95% of organs will be in range of weights of organs 230 grams and 430 grams.

b) 68% percentage of organs weighs between 280 grams and 380 grams.

c) 32% percentage of organs weighs less than 280 grams or more than 380 grams.

d) 97.35% percentage of organs weighs between 180 grams and 430 grams.

What is empirical rule?

The empirical rule 68-95-99.7 tells us that:

68% of the data is expected to be within 1 standard deviation from the mean.

95% of the data is expected to be within 2 standard deviation from the mean.

99.7% of the data is expected to be within 3 standard deviation from the mean.

There is a bell shaped distribution ( assume as approximately normal) with mean of 330 g and standard deviation of 50 g.

a) This happens for an interval with ±2 standard deviations from the mean.

That is:

X1 = μ + z1 × σ                  X2 = μ + z2 × σ

X1 = 330 - 2 × 50             X2 = 330 + 2 × 50

X1 = 330 - 100                  X2 = 330 + 100

X1 = 230                           X2 = 430

Therefore, the range of weights of organs is 230 grams and 430 grams.

b) Calculate the z-scores for each value to know how many standard deviations are from the mean.

z1 = (x1 - μ)/σ                   z2 = (x2 - μ)/σ

z1 = (280 - 330)/50        z2 = (380 - 330)/50

z1 = -50/50                     z2 = 50/50

z1 = -1                              z2 = 1  

The values are 1 standard deviations from the mean each.

Therefore, the expected percentage is 68%.

c) This is the complementary of the point b.

Then, it is expected that (100 - 68)% = 32% of the organs weigh less than 280 grams or more than 380 grams.

d) Calculate the z-scores for each value to know how many standard deviations are from the mean.

z1 = (x1 - μ)/σ                   z2 = (x2 - μ)/σ

z1 = (180 - 330)/50        z2 = (430 - 330)/50

z1 = -150/50                     z2 = 100/50

z1 = -3                              z2 = 2  

The values are 1 standard deviations from the mean each.

Therefore, the expected percentage is 68%.

The values are 3 standard deviations from the mean each. Between 180 and 330 there is 99.7%/2 = 49.85% of the data.

The values are 2 standard deviations from the mean each. Between 330 and 430 there is 95%/2 = 47.5% of the data.

Then, between 180 grams and 430 grams there is (49.85% + 47.5)% = 97.35% of the data.

Therefore, the expected percentage is 97.35%.

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The probability of a claim of at least $4000 is 0.35, option(d), the expected value of C is $2770 option (c), and the best interpretation is If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C), option(d).

Given probability distribution

C       $0       $1000      $4000       $10000

P(C)   0.60       0.05        0.13             0.22

The probability that the insurance company will have to pay a claim of at least $4000 for a randomly selected car is

= (1-0.60-0.05) = 0.35

so the expected value of C

= 0x0.60 + 1000x0.05 + 4000x0.13 + 10000x0.22

= 50+520+2200 = $2770

Now, the best interpretation of expected value:

If the company insures a large number of these cars, they can expect the cost per car to average approximately Exp(C).

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Yes, every vector in R^4 can be written as a linear combination of the columns of the matrix B.

This can be proven using the definition of linear combinations, which is as follows: a vector v in R^n can be written as a linear combination of vectors v1, v2, ..., vk if and only if there exist scalars c1, c2, ..., ck such that v = c1*v1 + c2*v2 + ... + ck*vk. With this definition, we can prove that the columns of B span R^4 by showing that for any vector v in R^4, there exist scalars c1, c2, c3, c4 such that v = c1*B1 + c2*B2 + c3*B3 + c4*B4, where B1, B2, B3, B4 are the columns of the matrix B above. To prove this, we can simply solve the system of equations given by c1*B1 + c2*B2 + c3*B3 + c4*B4 = v for c1, c2, c3, c4. This can be done by using Gaussian elimination, which will yield a set of scalars c1, c2, c3, c4 that can be used to express any vector in R^4 as a linear combination of the columns of the matrix B, thus proving that the columns of B span R^4.

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Answer:

see below

Step-by-step explanation:

Step 1

5(x – 3) = x + 13

Step 2

See if x is a solution

5 (6-3) ?= 6+13

5 (3) ?= 19

15 ?= 19

Step 3

This is not true so it is not a solution

Step 4

5(x – 3) = x + 13

Distribute

5x-15 = x+3

Subtract x from each side

5x-x -15 = x+13-x

4x-15 = 13

Add 15 to each side

4x-13+13 = 15+13

4x =28

Divide each side by 4

4x/4 = 28/4

x = 7

7 is a solution

Answer:

First you substitute 6 for x!

5(6 - 3) = 6 + 13

6 - 3 = 3

The equation is now:

5 * 3 = 6 + 13

5 * 3 = 15

6 + 13 = 19

The result is:

15 = 19 which is not a true statement.

x is not equal to 6.

Now lets try 7.

5(7 - 3) = 7 + 13

7 - 3 = 4

7 + 13 = 20

5 * 4 = 20

Thus: x = 7

Step-by-step explanation:

Hope it helps! =D

Answer:

14

Step-by-step explanation:

We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.

Answer:

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

Explanation for problem 1

The center of dilation is point P, which is not located on line AB. This means line A'B' will move further away from P after applying the scale factor. It means segments AB and A'B' are not on the same line.

Side note: Side BC is through line P, so segment B'C' shares the same line with BC.

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

Explanation for problem 2

The scale factor enlarges the side lengths. In this case, the scale factor 2 will double each side. This in turn doubles the perimeter.

perimeter of A'B'C' = 2*(perimeter of ABC)

new perimeter = 2*(old perimeter)

Therefore, the perimeters are not the same.

Answer: The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

What exactly is inequality?

A variation between two values indicates whether one is smaller, larger, or otherwise unrelated to the other.

In other words, inequality is the inverse of equality. For example, if 2 = 2, it is equal; however, if I say 3 = 6, it is incorrect; the correct expression is 3 6.

Step-by-step explanation:As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Answer:

45

Step-by-step explanation:

100-25-30=45

The distance of CD is 5.93.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given a circle.

Radius of circle = 11.5

AB = AD = 11.5

Since the tangent line is perpendicular to the radius of the circle at the point of tangency, ABC is a right angled triangle.

AC² = AB² + BC²

       = 11.5² + 13.1²

       = 303.86

AC = 17.432

CD = AC - AD

     = 17.432 - 11.5

     = 5.93

Hence the distance of CD is 5.93.

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A rectangle having perimeter 26 m has a length of 8m and breadth of 5m.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

The value for perimeter of a rectangle is - 26 m

Let x be the length of the rectangle and y be the breadth.

The formula for perimeter of rectangle is 2(l + b)

From the given information, it is known that -

Perimeter = 2(x + y) = 26 m...(1)

Difference between the length and breadth = x - y = 3 m....(2)

Use the first equation to solve for one of the variables in terms of the other -

2x + 2y = 26

x + y = 13....(3)

Add equation (2) and (3) -

x + y + x - y = 13 + 3

2x = 16

x = 16/2

x = 8 m

Now substitute the value of x in equation (2) -

x - y = 3

8 - y = 3

y = 8 - 3

y = 5 m

Therefore, the length is 8 m and the breadth is 5 m.

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The copayment amount, given that it is 20 % of the amount is $ 840

The benefit amount is  $ 3, 360

A copayment for health insurance is a defined dollar amount that is determined by the insurance plan and used to divide the cost of covered treatments between the plan and the consumer.

The copayment amount is 20 % of the cost which is $ 4, 200 so the copayment is:

= 20 % x 4, 200

= $ 840

This then means that the benefit amount would be;

= Cost - copayment

= 4, 200 - 840

= $ 3, 360

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The resulting answer is 39000 N/mm, this equation can be used to convert a given measurement from N/cm to N/mm.

39000/1 = ? N/mm

Multiply 39 by 1000 to convert centimeters to millimeters.

39000/1 = ? N/mm

Divide the measurement 39000 N/cm by 1 to convert it to N/mm.

The answer is 39000 N/mm.

To convert a measurement from N/cm to N/mm, the equation that needs to be set up is 39000/1 = ? N/mm. This equation can be broken down into two steps. First, the measurement needs to be multiplied by 1000 to convert centimeters to millimeters. Then, 39000/1 needs to be divided to convert the measurement from N/cm to N/mm. The resulting answer is 39000 N/mm. Therefore, this equation can be used to convert a given measurement from N/cm to N/mm.

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In other words, 3/4 fraction of the bill are for vegetables, while 1 part is for fruit.

Using the data provided in the issue, we can determine what percentage of Marco's bill is made up of veggies. We are aware that fruit and vegetables account for 7/12 of the total bill and make up 1/8 of the total. By deducting the portion of the bill that is for fruit from the portion that is for fruit and vegetables, we can determine the portion of the cost that is for vegetables.

We must identify a common denominator for the two fractions in order to accomplish this. Since 12 and 8 have a denominator of 24, we convert both fractions to have a denominator of 24.

1/8 turns becomes 3/24

7/12 changes to 21/24.

We deduct 3/24 from 21/24 in order to derive the percentage of fruit from the percentage of fruit and vegetables.

21/24 - 3/24 = 18/24

Vegetables make up 18/24, or 3/4, of Marco's bill.

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The answers include the following below:

This is referred to as the discounted price at which goods or services are being sold.

Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.

This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).

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The order in which you shoot the scenes will not matter in terms of the final outcome of the movie.

The mathematical property that one can use to answer this question is scheduling.

From the information, in order to produce the movie, one needs to shoot a scene for a high-speed chase and need to shoot a scene for a bank robbery.

Here, the film production crew will be putting the movie together. However, it may impact the logistics of the production process and the scheduling of the crews. It is not a mathematical property that I used to answer this question. It is simply a matter of logistics and scheduling.

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Answer:

12,000

Step-by-step explanation:

How can we do this?

We can do this by taking the number 11,900,

11,900

looking at the hundredths place,

11,900

and figuring out if it is closer to 10, or 0. 9 is closer to 10, so we round up.

12,000

Therefore, 11,900 rounded to the nearest thousand is 12,000.

The complete expression of the algebra is;

4a(-2a³ + 4a + 3) + 2a(3a³ - 2a + 7) = -2a⁴ + 12a² + 26a

We are given the expression as;

4a(-2a³ + 4__ + 3) + 2a(__a³ - 2a + _) = -2a* + 12a² + 26a

Expanding the left hand side gives;

-8a⁴ + __(16a) + 12a + __(2a⁴) - 4a² + __(2a)

Grouping like terms gives;

-8a⁴ + __(2a⁴) + 12a + __(2a) + __(16a) - 4a²

Factorizing out exponents gives;

a⁴(-8 + __(2)) + a(12 + __(2)) + a²((16/a) - 4)

Comparing this with the right hand side gives;

a⁴(-8 + __(2)) = -2a*  -----(1)

((16/a) - 4)a² = 12a²    -----(2)

(12 + __(2))a = 26a   ----(3)

From eq 1, we can see that;

* = 4

From eq 2;

((16/a) - 4) = 12

16/a = 12 + 4

a = 16/16

a = 1

From eq 3;

(12 + __(2)) = 26

___ * 2 = 26 - 12

___ = 14/2

___ = 7

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The length of the apothem of a regular hexagon is 4√3

The apothem of a regular hexagon is the distance from the center of the hexagon to the midpoint of one of its sides.

To find the length of the apothem, we can use the formula:

apothem = (side length) / (2 * tan(180/n))

where n is the number of sides of the polygon.

In this case, n = 6 (since the hexagon is regular).

So, to find the apothem of a regular hexagon with a side length of 8 ft, we can plug these values into the formula:

apothem = (8 ft) / (2 * tan(180/6))

This gives

apothem = 8 ft / (2 * tan(30))

Evaluate

apothem = 4√3 ft

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The base distance will be 10.9 feet .

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

The Pythagorean theorem states that, in a right triangle, the length of the hypotenuse squared equals the sum of the squares of the other two sides or legs of the triangle.  Algebraically, a2+b2=c2.  In your example, the length of the ladder would be the hypotenuse and the distance from the wall would be one of the legs.  So substitute these values into the equation to get: 25+b2=144 or 25+b2=144 and then subtract 25 from both sides to get b2=119.  Therefore b=√119≈10.908.  If your problem requires an exact answer in its most simplified form, please note that √119=10.9

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The variance of the four employees' salaries is 5.1, meaning that the difference in their salaries is 5.1 thousand dollars.

Step 1: Find the mean of the four salaries

33 + 31 + 24 + 36 = 124

124 ÷ 4 = 31

Mean = 31

Step 2: Find the difference between each salary and the mean

33 - 31 = 2

31 - 31 = 0

24 - 31 = -7

36 - 31 = 5

Step 3: Square each of the differences

2² = 4

0² = 0

(-7)² = 49

5² = 25

Step 4: Add up the squared differences

4 + 0 + 49 + 25 = 78

Step 5: Divide the sum by the number of salaries (minus 1)

78 ÷ (4 - 1) = 78 ÷ 3 = 26

Step 6: Take the square root of the variance

√26 = 5.1

Variance = 5.1

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Answer:

x-3 =0 or x-8 =0

x= +3 or x = +8

Answer:4.8×105 g  

Step-by-step explanation:

The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them.  The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true.

My student ID is 12345678.

The argument, filled-in with my student ID, is sound. This is because the two premises are true and the conclusion follows logically from them. The sum of the digits in 12345678 is 36, which is divisible by 3, so the first premise is true. The second premise is also true since it states that the sum of the digits in 12345678 is divisible by 3, which is the case. Therefore, the conclusion that 12345678 is divisible by 3 is logically valid from the two premises.

Student ID: 12345678

The argument, filled-in with the student ID 12345678, is sound because the two premises are true and the conclusion follows logically from them.

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A statement which is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals include the following: E. The shortest streak is of length 1.

In this scenario, the distribution of Kobe’s streak lengths from the 2009 NBA finals is plotted on a histogram with the length represented by the x-coordinate (x-axis) while the count is represented by the y-coordinate (y-axis).

By critically observing the histogram, we can reasonably infer and logically deduce the following true statements:

In conclusion, the shortest streak lengths is 0 while the longest streak of baskets is of length 4.

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Complete Question:

Which of the following is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals.

A. The distribution of Kobe’s streaks is unimodal and right skewed.

B. The typical length of a streak is 0 since the median of the distribution is at 0.

C. The IQR of the distribution is 1.

D. The longest streak of baskets is of length 4.

E. The shortest streak is of length 1

Answer:

Step-by-step explanation