In a '15% off sale, Freya bought a DVD player for £179.99. What was the original price of this

DVD player?

Solution:

Given;

The simple interest, I, is;

Thus, the amount to be repaid is;

The amount that must be repaid is $24,992

Answer:

m∠2 = m∠7 ( ): Alternate Exterior angles theorem

m∠7 + m∠8 = 180° ( ) : linear pair theorem

Step-by-step explanation: I got it right

The missing statements which prove that ∠2 and ∠8 are supplementary angles are Alternate exterior angles theorem and Linear pair theorem.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

Given that,

Lina a is parallel to line b.

Both lines are intersected by transversal t.

Here, ∠2 and ∠7 are alternate exterior angle.

By the "Alternate Exterior Angles Theorem", the alternate exterior angles formed by two parallel lines intersected by a transversal are equal.

So, m∠2 = m∠7 [By Alternate Exterior Angles Theorem]

∠7 and ∠8 are angles formed on a line. That is, they are linear pair of angles.

By "Linear pair theorem", linear pair of angles are supplementary.

So, m∠7 + m∠8 = 180° [Linear pair theorem]

Hence the blanks are Alternate exterior angles theorem and Linear pair theorem.

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Answer:

equation: a/.5b=h

h=9

Step-by-step explanation:

a=1/2bh

divide both sides by 1/2b to get h alone

a/.5b=h

a/.5b=h

54/0.5(12)=h

54/6=h

9=h

Using the simplex method, the maximum value of Z=5A+4B is found to be 19.2 when A=3.6 and B=1.2. The calculations can be confirmed by using any software that solves linear programming problems.

To solve the given linear programming problem using the simplex method, we start by converting the problem into standard form. We introduce slack variables to convert the inequalities into equations.The initial tableau is as follows:

      | A | B | S1 | S2 | S3 | S4 |   RHS

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

 Z    | -5 | -4 | 0  | 0  | 0  | 0  |    0

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

 S1   |  6 |  4 | 1  | 0  | 0  | 0  |   24

 S2   |  1 |  2 | 0  | 1  | 0  | 0  |    6

 S3   | -1 |  1 | 0  | 0  | 1  | 0  |    1

 S4   |  0 |  1 | 0  | 0  | 0  | 1  |    2

We perform the simplex iterations until the optimal solution is reached. After applying the simplex method, the final tableau is obtained as follows:

      |  A  |  B  |  S1  |  S2  |  S3  |  S4  |   RHS

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

 Z    |  0  | 1.8 | 0.2  | -1   | -0.4 |  0.4 | 19.2

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

 S1   |  0  |  0  |  0   | 1.5  | -1   |  1   |  3

 S2   |  1  |  0  | -0.5 |  0.5 |  0.5 | -0.5 | 1.5

 A    |  1  |  0  | 0.5  | -0.5 | -0.5 |  0.5 |  0.5

 S4   |  0  |  0  |  1   | -1   | -1   |  1   |  1

From the final tableau, we can see that the maximum value of Z is 19.2 when A=3.6 and B=1.2. This solution satisfies all the constraints of the problem. The calculations can be verified using any software that solves linear programming problems, which should yield the same optimal solution.

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Answer:

5 classes - 2 bass classes and 3 viola classes.

Step-by-step explanation:

Find the greatest common factor (GCF)

List the factors of 20 and 30:

20: 1, 2, 4, 5, 10, 20

30: 1, 2, 3, 5, 6, 10, 15, 30

The greatest factor that both numbers share is 10.

Therefore, there are 10 students in each class. So, she teaches 2 bass classes and 3 violas classes.

hope this helps! <3

Answer: A. 6n-11

Step-by-step explanation:

First, ignore the parenthesis because it is addition and subtraction so they are commutative. 10n-4n = 6n and -8-3 is the same as -8+-3 which is -11. Combining the answer gives 6n-11.

Answer:

Step-by-step explanation:

A: The denominator doubles every step.

B: 1/16 1/32 1/64

Answer:

20=5+2.5d

Step-by-step explanation:

Answer:

incomplete question friend

Answer:

2x+3y+5=0

a = 2  b = 3  c=5

Step-by-step explanation:

We are asked to express 2x+3y=-5 in the form ax+by+c=0

Add 5 to both sides

2x+3y+5=0

We can now find the values of a, b and c now that the equation is in standard form.

Answer:

-55

Step-by-step explanation:

8+3²-2-6

7-1-2

Answer:9/5

Step-by-step explanation:

x is each friend

3x + 28 > 200

3x > 172

x > $57.33

if right can a i get brainliest pls

Answer:

Step-by-step explanation: $200-$28= $172

                                                $172÷3=$57.33

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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Answer:

90

Step-by-step explanation:

4x+22=-6x+192 since 4x+22 is the same as angle 5 due to parallel lines, and then 5 = -6x+192 as it is straight across.

4x+22=-6x+192

10x+22=192

10x=170

x=17

plug back in to equation

4(17)+22= 90

Answer:

∠3  =  90°

Step-by-step explanation:

∠4 = ( 4x + 22 )°                          [ Vertically opposite angles ]

∠4 = ( -6x + 192)°                         [ Corresponding angles ]

Therefore ,

4x + 22 = - 6x + 192

4x + 6x = 192 - 22

10x = 170

x = 17

∠4 = 4x + 22 = (4 × 17 ) + 22 = 90°

∠4 = 90°

∠3 + ∠4 = 180°                              

∠3 + 90° = 180°                              

∠3  = 180° - 90°                            

∠3  = 90°  

The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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The expected value of the number of times an odd number will be rolled can be calculated using the formula: E(x) = np, where n is the number of trials, and p is the probability of success. In this case, the probability of rolling an odd number on a standard six-sided die is 3/6, or 1/2, since there are three odd numbers (1, 3, 5) and three even numbers (2, 4, 6).

Therefore, the expected value of the number of times an odd number will be rolled in 1515 trials is:

E(x) = np
E(x) = 1515 * (1/2)
E(x) = 757.5

So the expected value of the number of times an odd number will be rolled in 1515 trials is 757.5.

Answer: 757.5.

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Answer:

40 meters

Step-by-step explanation:

x=4

3x-4=12-4

2x-3=8-3

12-4=8

8-3=5

8x5=40

Answer:

x = -7/5

Step-by-step explanation:

3( x - 6 ) - 8x = -2 + 5(2x + 1)

3x - 18 - 8x = -2 + 10x + 5

-5x - 18 = 3 + 10x

-5x - 10x = 3 + 18

-15x = 21

x = \(-\frac{7}{5}\)

Answer:

the slope is Undefined

Step-by-step explanation:

Answer:1/48

Step-by-step explanation: multiply the fraction by 1/2

Answer:

\(x = 56\)

Step-by-step explanation:

Use tangent function.

\( \tan(x) = \frac{18}{12} \)

Take the arctan

\( \tan {}^{ - 1} ( \frac{18}{12} ) \)

which is about

0.98279372.

Convert from radians to degrees in you will get

56 degrees.

Answer:

Step-by-step explanation:

You can solve this by using trigonometry and the formula SOH CAH TOA. You're looking for an angle that is adjacent (next to) 12, and opposite 18. Therefore, you will needed to use TOA, which stands for tangent = opposite/adjacent.

With substitution, this gives you tangent  = 18/12. 18/12 is equal to 1.5. Because we are looking for an angle we need to use the tan^-1 (tan to the power of -1) button on our calculator. Tan(1.5)^-1 equals 56.31 to 2dp.

Hope this helps!

30 km far has the athlete run.

A rectangle may be a geometric shape that is characterized by its four sides, where opposite sides are parallel and break even within the length. It has four sides the longer side is named length and the shorter side is named as breadth.

An Athlete runs around a rectangular field = 10 times

The Length of the rectangle = \(1.08 km\)

The Breadth of the rectangle = \(0.42 km\)

 \(1km = 1000 m\\= 420 /1000 m\\= 0.42 km\)

Therefore, perimeter of the rectangle = 2 (length + breadth)

                                                              =  \(2 ( 1.08 + 0.42)\)

                                                              = \(2 (1. 50)\)

                                                              = \(3 km\)

So, the athlete runs around a rectangular housing 10 times = \(3\)×\(10\)

                                                                                                   = \(30 km\)

Therefore, the athlete runs 30 km far.

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a. The categorical qualitative variables from the ones listed above are:

- MarketSize (small, medium, or large market)

- PromotionType (Promotion 1, 2, or 3)

- WeekNumber (Week 1, 2, 3, 4)

b. The numerical (quantitative) variables from the ones listed above are:

- Sales (in $1000)

- AgeOfStore (in years)

c. The level of measurement for each variable is as follows:

- MarketSize: Nominal level of measurement. The categories (small, medium, large) are mutually exclusive and there is no inherent order or numeric value associated with them.

- PromotionType: Nominal level of measurement. The promotions (Promotion 1, 2, 3) are distinct categories with no inherent order or numeric value.

- WeekNumber: Ordinal level of measurement. The weeks (Week 1, 2, 3, 4) have a natural order but the differences between them are not necessarily equal.

- Sales: Ratio level of measurement. The variable represents the actual sales in dollars, which has a meaningful zero point and allows for meaningful ratios and calculations.

- AgeOfStore: Ratio level of measurement. The variable represents the age of the store in years, which has a meaningful zero point and allows for meaningful ratios and calculations.

Understanding the level of measurement of variables is important for selecting appropriate statistical methods and understanding the nature of the data. In this case, we have identified the categorical qualitative variables (MarketSize, PromotionType, WeekNumber) and the numerical (quantitative) variables (Sales, AgeOfStore) and determined their respective levels of measurement.

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To find the value of x, we need to follow these steps:

1. Calculate the total sum of the ages of the 6 cars.
2. Subtract the sum of the known ages from the total sum.
3. The result will be the value of x.

Step 1: Since the average age of the 6 cars is 7 years, we multiply the average (7) by the number of cars (6) to find the total sum of ages.
Total sum of ages = 7 * 6 = 42 years

Step 2: Subtract the sum of the known ages (6, 14, 5, 1, and 8) from the total sum.
Sum of known ages = 6 + 14 + 5 + 1 + 8 = 34 years
42 (total sum of ages) - 34 (sum of known ages) = 8

Step 3: The result is the value of x.
x = 8

So the value of x is 8.

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The fully factorized form of expression 5r² - 27r - 18 is (r - 6)(5r + 3)

To factorize the quadratic expression 5r² - 27r - 18, we can use a factoring method such as grouping or quadratic factoring.

One possible approach is to use quadratic factoring.

We look for two binomials that, when multiplied together, give us the quadratic expression.

The quadratic expression 5r² - 27r - 18 can be factored as follows:

5r² - 27r - 18

5r² - 30r+3r - 18

5r(r-6)+3(r-6)

= (r - 6)(5r + 3)

So, the fully factorized form of 5r² - 27r - 18 is (r - 6)(5r + 3)

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