Mrs. Gurung allowed 10% discount on her fancy items to make 25% profit and sold a lady bag for Rs 5,085 with 13% VAT. Due to the excessive demands of her items, she decreased the discount percent by 2%. By how much was her profit percent increased?​

Based on the triangle midsegment theorem, the true statements are:

DE║AC

2DE = AC

If a line segment joins two sides of triangle and divides them at their midpoint, the divided segments will be congruent, and thus, the line segment joining the two sides is a midsegment of the triangle. According to the triangle midsegment theorem, the midsegment will be parallel to the third side that is not divided and also would be 1/2 its length. That is, the third side is twice the midsegment of that triangle.

In the image given, considering triangle ABC, we can make the following conclusions based on the triangle midsegment theorem:

D and E are midpoints of sides AB and BC respectively because they are divided by segment DE equally.

The midsegment is DE.

DE would be parallel to the third side, line segment AC.

Length of AC would be twice the length of DE

In conclusion, the true statements based on the triangle midsegment theorem are:

DE║AC

2DE = AC

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Answer:

A ≈ 75 in²

Step-by-step explanation:

the area (A) of the circle is calculated as

A = πr² ( r is the radius )

here r = 5 and using 3 for π , then

A = 3 × 5² = 3 × 25 = 75 in²

Answer:

75 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

The image gave us the value of the radius right away, so the question will be a lot easier to solve.

--> The reason why the radius is needed is that the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 5.

--> A = 25 [tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 25 x 3

--> A = 75

We can conclude that the area of the circle is 75 in^2.

Answer:

  D.  x ≈ 2.60

Step-by-step explanation:

The equation we have graphed is the one shown in the attachment. It is slightly different from the one in this problem statement.

It is often convenient to find a graphical solution to an equation by writing it in the form ...

  f(x) = 0

Then the solutions are the x-intercepts of the graph, points that most graphing calculators can readily identify.

We have done this here by defining ...

  [tex]y_1=3x^2-6x-4\\\\y_2=-\dfrac{2}{x+3}+1[/tex]

The graph is of y₁ -y₂. X-values where y₁-y₂ = 0 are solutions to the original equation, y₁ = y₂.

This equation is seen to have three solutions, approximately ...

  x = {-3.05, -0.55, 2.60}

Of these, only x ≈ 2.60 is listed among the answer choices.

__

Additional comment

The value of y₁ -y₂ expressed in standard form is ...

  [tex]3x^2-6x-4+\dfrac{2}{x+3}-1=0\\\\\dfrac{(x+3)(3x^2-6x-5)+2}{x+3}=0\\\\\dfrac{3x^3+3x^2-23x-13}{x+3}=0\\\\3x^3+3x^2-23x-13=0\quad(x\ne -3)[/tex]

The irrational solutions to this cubic can be found "exactly" by any of several applicable formulas. Numerical solutions are almost trivial to find with appropriate technology.

  x ≈ {−3.04857564747, −0.547524627423, 2.5961002749}.

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Answer:2,695

Step-by-step explanation: just add.

The conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25

We know that the conditional probability is given by,

P(B | A) = probability of occurrence of event B, given that event A has

               occurred

           = P(A ∩ B) / P(A)

Here, P(A ∩ B)  means the probability of happening two events A and B at the same time.

We also know that  if  P (B | A ) = P(B)   i.e.,   P(A ∩ B) = P(A) × P(B)  the two events A and B are independent of each other.

For this question, let the dice D1 and D2 are rolled once.  

Let the numbers displayed on the dice be d1 and d2 respectively.  

The dice D1 and D2 are independent.

We need to find the conditional probability that the sum is greater than 6, given that neither die is a two.

Let S represents the sum of the numbers displayed on the dice.

S = d1 + d2

The sum is even, if d1 = d2 is odd OR  if d1 = d2 is even

P(d1 = even) = 3/6

                    =1/2

P(d2=even) = 1/2

P(d1 = odd) = 1/2

P(d2 = odd) = 1/2

So, P(S = even) = [P(d1=even) × P(d2 = even)] + [P(d1= odd) × P(d2=odd)]

                          = [1/2 × 1/2] + [1/2 × 1/2]

                          = 1/2

So, we can say that, the sum is either even or odd which are equally likely and hence its probability is 1/2.

First we find the probability for the sum is greater than 6 i.e., P(S > 6)

The possible combination of d1 and d2 for the sum greater than 6 would be,

{(1,6), (2,5), (2, 6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

⇒ n(S > 6) = 21

The number of all possible outcomes = 36

So, P(S > 6) = 21/36

                   = 7/12

Now we find the probability that neither die is a two

⇒ P(neither die is a two) = [P(1) ∪ P(3 ≤ d1 ≤ 6)]  AND  [P(1) ∪ P(3 ≤ d1 ≤ 6)]

⇒ P(neither die is a two) = 5/6 × 5/6

⇒ P(neither die is a two) = 25/36

Now, we find the probability that the sum S > 6 AND  neither die is a two.

The possible combination for  the sum S > 6 AND  neither die is a two would be,

{(1,6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}

⇒ n(S > 6 AND neither die is a two) = 17

So, P(S > 6 AND neither die is a two) = 17/36

Now we find the conditional probability P(S > 6 | neither die is a two)

⇒ P(S > 6 | neither die is a two) = P(S > 6 AND neither die is a two) ÷

                                                           (neither die is a two)

⇒ P(S > 6 | neither die is a two) = (17/36) / (25/36)

⇒ P(S > 6 | neither die is a two) = 17/25

Therefore, the conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25

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Answer:

False

Step-by-step explanation:

If two angles are right angles, then they are congruent.

Answer:

58, 66, 79, 84, 87 (see explanation for the exact answer)

Step-by-step explanation:

{58, 66, 79, 84, 87}

minimum = 58

lower quartile = 66

median = 79

upper quartile = 84

maximum = 87

Answer + Step-by-step explanation:

58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87

The data set is in order then :

the minimum = 58

The maximum = 87

Determining the median :

first ,we notice that the data set has an even number (14) of numbers

Then

The median is the average of the two central values of the data set :

the two central values are the 7th and 8th numbers:

[tex]\text{median} =\frac{79+79}{2} =79[/tex]

Determining the lower quartile  :

The lower quartile is the median of the set :

58, 60, 65,  67 , 68, 72, 79

this set has an odd number (7) of values

Then

The central value is 67

Therefore

The lower quartile is 67

Determining the upper quartile  :

The upper quartile is the median of the set :

79, 80, 81,  82  , 86, 86, 87

this set has an odd number (7) of values

Then

The central value is the 4th number which is 82

Therefore

The upper quartile is 82

Interquartile range :

82 - 67 = 15

The mark on the tape measure that is closest to 3.16228 is 3.1875

The measurement is given as:

Length = 3.16228

The tape measure is marked in sixteenths of an inch i.e 1/16 or 0.0625

So, we have the following range:

0.0625, 0.125, 0.1875, 0.25,.....

Rewrite the range as follows:

3.0625, 3.125, 3.1875, 3.25,.....

The length 3.1622 is between 3.125 and 3.1875.

The difference between the measurement and the range is

3.16228 - 3.125 = 0.03728

3.1875 - 3.16228 = 0.02522

0.02522 is smaller than 0.03728

Hence, the mark on the tape measure that is closest to 3.16228 is 3.1875

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Complete question

The length of tile B 3.16228 is about inches. Which mark on the tape measure is closest to 3.16228 inches? Remember, the tape measure is marked in sixteenths of an inch.

The verbal expression for the mathematical expression 5(x - 4) + 2 is the number 5 times the difference between an unknown x and the number 4 and plus 2.

It is defined as the combination of constants and variables with mathematical operators.

It is given that a mathematical expression as below:

= 5(x - 4) + 2

Here x is the unknown number

The number

Number 5 times the difference between an unknown x and number 4 and plus 2

Thus, the verbal expression for the mathematical expression 5(x - 4) + 2 is number 5 times the difference between an unknown x and number 4 and plus 2.

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the petrol cost for the trip is:

C = 2.125*$2.05 = $4.36

After a search online, I've found that the trip is of 25km.

Here we know that the car uses 8.5L per 100km, then in 25 km, the car will use one-fourth of 8.5L, that is:

8.5L/4 = 2.125L

So the volume of petrol that the car uses for the trio is 2.125 liters of petrol.

And each liter costs $2.05, then the petrol cost for the trip is given by the product between the total volume of petrol consumed and the cost per liter.

C = 2.125*$2.05 = $4.36

Thus, we conclude that the petrol cost for the trip is 4.36 dollars.

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[tex]e-\frac{1}{e} +\frac{4}{3} 0r 3.687[/tex]  is the value when the equation is to integrate with respect to x or y

we integrate with respect to x

Area = [tex]\int\limits^b_a{(f(x)-g(x))} \, dx[/tex]

       = [tex]\int\limits^1_-1{e^{x}-x^{2} +1 } \, dx[/tex]

        =[tex]e^{x} -\frac{x^{3} }{3} +x[/tex]

   substitute 1 and -1 in place of x

  = [tex](e-\frac{1}{3}+1-\frac{1}{e} -\frac{1}{3} +1)[/tex]

  = [tex]e-\frac{1}{e} + \frac{4}{3} or 3.6837[/tex]

The diagram was attached in the given below.

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[tex]a=3x^3\hspace{5em}b=4x^4 \\\\[-0.35em] ~\dotfill\\\\ c=ab^2\implies c=(\underset{a}{3x^3})(\underset{b}{4x^4})^2\implies c=(3x^3)(4^2x^{4\cdot 2}) \\\\\\ c=3x^3\cdot 16x^8\implies c=(3\cdot 16)x^{3+8}\implies c=48x^{11} \\\\[-0.35em] ~\dotfill\\\\ \boxed{bc}\implies (\underset{b}{4x^4})(\underset{c}{48x^{11}})\implies (4\cdot 48)x^{4+11}\implies \boxed{192x^{15}}[/tex]

Answer:

  bc = 192x^15

Step-by-step explanation:

Perform substitution as required, then simplify.

  bc = b(ab^2) = ab^3 = (3x^3)(4x^4)^3 = (3·4^3)(x^3)(x^(4·3))

  = 192x^(3+12)

  bc = 192x^15

__

Additional comment

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

Answer:

Find the interval of convergence of the following series

Possible Answers:

(4,6)

[4,6)

(4,6)

[4,6]

Correct answer:

(4,6)

Explanation:

Step-by-step explanation:

Find the interval of convergence of the following series

Possible Answers:

(4,6)

[4,6)

(4,6)

[4,6]

Correct answer:

(4,6)

Explanation:

The sum of the geometric series is 2199; option E.

S6 = a(rⁿ - 1) / r -1

= 1468(1/3^6 - 1) / (1/3 - 1)

= 1468(0.00137174211248 - 1) / -2/3

= 1468(-0.9986282578875) / -0.66666666666666

= -1,465.98628257885 / -0.66666666666666

= 2198.97942386829

Approximately,

S6 = 2199

Arithmetic series

Sn = n/2{2a + (n -1)d}

= 36/2 {2×27 + (36-1)-5/2}

= 18{54 + (35)-5/2}

= 18(54 + 175/2)

= 18(54 + 87.5)

= 18(141.5)

s36 = 2547

a36 = a + (n - 1) d

= 27 + (36 - 1)-5/2

= 27 + (35)-5/2

=27 + -175/2

= 27 - 87.5

= -60.5

S20 = n/2{2a + (n -1)d}

= 20/2{2×27 + (20-1)-5}

= 10(54 + (19)-5)

= 10{54 + (-95)}

= 10(54-95)

= 10(-41)

s20 = -410

Missing terms of the geometric sequence:

nth term = ar^n-1

448/135 = 63/80×r^(6-1)

448/135 = 63/80×r^5

r^5 = 448/135 ÷ 63/80

= 448/135 × 80/63

= 35,840/8,505

r = 5√35,840/5√8505

= 946.57/461.11

r = 2.05

Second term = a×r

= 63/80×2.05

= 1.614375

Third term = ar²

= 63/80×2.05²

= 63/80×4.2025

= 3.30946875

Fourth term = 63/80 × 2.05³

= 63/80×8.615125

= 6.7844109375

Therefore, none of these are correct

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a. The amount of paper that he is going to need would given as 12 square inches.

b. If it is 11 inches what is needed to cover the wall is given as 396

We have the area of a rhombus to be given as

0.5 *d1 * d2

We have d1 = 6 inches

d2 = 4 inches

then area would be

0.5 * 6 * 4

= 12 inches

b. The amount of paper used as length is 11 feet long

1 ft = 12 inches

then 11 feet = 11 * 12

= 132

Number needed = 4

132/4 = 33

Then the area would be 33 * 12 inches to cover the wall

= 396

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Answer:

12 and 396

Step-by-step explanation:

The angles and lengths of each of the given triangles are;

5) m∠B = 57.52°

6) B = 70.81°

7) AB = 55.43 Km

8) AC = 39.06 ft

The cosine rule is expressed as;

c = √[a² + b² - 2ab(cos C)]

5) Using cosine rule;

BC = √[21² + 13² - 2(21*13)(cos 91)]

BC = 24.89

Using sine rule, we can find angle B as;

21/sin m∠B = 24.89/sin 91

sin m∠B = (21 * sin 91)/24.89

sin m∠B = 0.8436

m∠B = sin⁻¹0.8436

m∠B = 57.52°

6) Using cosine rule;

14² = 11² + 13² - 2(11*13)(cos B)]

196 = 121 + 169 - 286(cos B)

cos B = (121 + 169 - 196)/286

cos B = 0.3287

B = cos⁻¹0.3287

B = 70.81°

7) Using cosine rule;

AB = √[24² + 36² - 2(24*36)(cos 134)]

AB = 55.43 Km

8) Using cosine rule;

AC = √[21² + 26² - 2(21*26)(cos 112)]

AC = 39.06 ft

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Answer: f(12) = 137, f(-7) = 42

Step-by-step explanation: In a function, what you want to do is plug in the value they give you for x. This means you substitute x with the value they are looking for.

In this case, they are looking at 12 and -7. Let's do 12 first.

The equation becomes (12^2) - 7. 12^2 is 144, and 144-7 is 137.

Now we do -7. The equation becomes (-7)^2 - 7. -7^2 is 49, and 49 - 7 is 42.

Hope this helped!

Answer:

8 one-dollar bills

3 five-dollar bills

2 ten-dollar bills

Step-by-step explanation:

Let x = # of one-dollar bills, y = # of five-dollar bills, and z = # of ten-dollar bills. Total amount in the wallet is $43, so the first equation would be 1x + 5y + 10z = 43. Next, there are 4 times as many one-dollar bills as ten-dollar bills, so x = 4z. There are 13 bills in total, so x + y + z = 13

x + 5y + 10z = 43

x = 4z

x + y + z = 13

x + 5y + 10z = 43

x + 0y - 4z = 0

x + y + z = 13

5y + 14z = 43

-y - 5z = -13

5y + 14z = 43

-5y - 25z = -65

-11z = -22

z = 2

x = 4z

x = 4*2 = 8

x + y + z = 13

8 + y + 2 = 13

10 + y = 13

y = 3

I assume that 0.53 with a bar means the decimal fraction in which 3 is repeating.

24/45, 8/15, and 48/90 all result in the same decimal value. Thus, we are simply looking for the one that is fully simplified.

The correct answer is 8/15.

Hope this helps!

Answer:

$700

Step-by-step explanation:

If he made a loss of 15%, then it means that selling price is 85% of the cost price.

If the cost price is x, then we have;

0.85x = 595

x = 595/0.85

x = $700

The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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Answer:

Point A

Step-by-step explanation:

See attached worksheet.

Answer:

Below in bold.

Step-by-step explanation:

This figure is a trapezoid.

We can find the missing side  length by applying the Pythagoras Theorem to the right triangle on the left of the figure.

The dotted line has length 12 cm and the base of the triangle = 25 - 18 = 7 cm

So x^2  = 12^2 + 7^2     (where x = missing length)

            =  144 + 49

            = 189

x = √189

  =  13.75 to nearest hundredth

So the perimeter

  =    18 + 12 + 25 + 13.75

  =    68.75 cm.

Area of a trapezoid = 1/2 (a + b) * h.

Area =  1/2 *(18 + 25) * 12

        =  258 cm^2.

Yoshi should buy 3 flats.

To find how many flats Yoshi should buy:

Therefore, Yoshi should buy 3 flats.

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x + 7 = -8

(x + 7) - (7) = -8 - (7)

x = -8 - 7 = -15

The correct answer is -15

❄ Hi there,

let us first consider this: What should we do to get x all alone, on one side of the equation?

Since

we should

[tex]\ \sf{x=-8-7}[/tex]

[tex]\triangleright \ \sf{x=-15}[/tex]

That's it!

❄

The domain is the water balloon's height increasing will be (0, 2), staying the same will be (2, 4), decreasing the fastest will be (6, 10), and the height of the water balloon at 16 seconds the will be 0.

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

Part A:

As seen from the graphic, increase from 0 to 2 sec.

The domain is (0, 2), where the height of the water balloon increases.

Part B:

The water balloon stays the same from 2 to 4 sec.

The field means that the height of the water balloon remains the same (2, 4).

Part C:

Height decreasing fasted at 4 to 6 sec.

Because the slope is steepest downward from 4 to 6 sec as comfort to 6 to 10 sec.

The domain is where the height of the water balloon decreases rapidly (6, 10).

Part D:

The balloon's height will be almost near the ground as resistance will play its role.

But it will almost touch the ground.

The height of the water balloon will be 0 in 16 seconds.

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Inverse variation is the relationship that occurs between two quantities in which one decreases as the other increases.

The types of variation which exists are;

For instance;

The relationship between John's speed and distance is inversely proportional. If John's speed is 5km/h, his distance is 6km. Find John's distance when his speed increases to 6km/h.

s = k / d

where,

k = constant of proportionality

s = k / d

5 = k/6

30 = k

s = k / d

6 = 30/d

6d = 30

d = 30/6

d = 5 km

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The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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Answer:

91.5 - 5.2 = 86.3

Step-by-step explanation:

The initial weight was 91.5 pounds.

The dog lost 5.2 pounds which means subtraction.

91.5 pounds subtracted by 5.2 pounds that the dog lost equals 86.3 pounds.