if a mobile was sold for Rs.24408 after allowing 10% discount on the marked price and adding 13% VAT.Findthe discount amount.

Answer: the correct answer is D.

Step-by-step explanation:

Since we are given the values of angle B and side(a) we can set up an equation cos43.2=3.2/x

we will get 4.4 so c=4.4

using the paythagorion theorm (4.4)^2=x^2+(3.2)^2

we will get an approximate value of 3 so b=3

and for the finding the third angle x+43.2+90=180

x=46.8 degrees

Answer D

Answer:

370 mm²

Step-by-step explanation:

The area of this figure can be calculated by taking the whole figure as a full rectangle, and consider the part that is cut out from the middle of the shape as another rectangle.

Find the area of the cut-out part and subtract from the area of the full rectangular shape to get the area of the composite figure.

=>Area of full rectangular shape:

Length = 30 mm

Width = 15 mm

Area = L * B = 30*15 = 450 mm²

=>Area of the cut-out Rectangle part:

Length = 10 mm

Width = 8 mm

Area = 10*8 = 80 mm²

=>Area of composite figure = 450 mm² - 80 mm² = 370 mm²

Answer:

Sine angle of <ACB = 38.68°

Step-by-step explanation:

Hello,

To solve this problem, we need a good representation of the sides and the angle.

See attached document for better illustration.

Assuming it's a right angled triangle,

AC = hypothenus

AB = opposite

BC = adjacent

AC = 40

BC = 25

AB = 25

From trigonometric ratios

Sinθ = opposite/ hypothenus

Sinθ = AB / AC

Sinθ = 25 / 40

Sinθ = 0.625

θ = sin⁻¹0.625

θ = 38.68°

Sine angle of <ACB = 38.68°

Answer:

Option (C)

Step-by-step explanation:

Domain of any graph is defined by the x-values or the input values of a function.

Similarly, y-values on the graph of a function define the Range.

In the graph attached, x-values varies from (-∞) to (+∞).

Therefore, Domain of the graphed function will be (-∞, ∞)

Or -∞ < x < ∞

Similarly, y-values of the graph varies from (-∞) to (1)

Therefore, range of the graphed function will be (-∞, 1).

Or -∞ < y < 1

Option (C) will be the answer.

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

2x - 2(-2x + 5) = 2

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

Answer:

(0,-3)

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

It has a 45 45 90 ratio, so if the hypotenuse is 7 root 2, then the two sides have to be 7.

Answer:

x^2 +4x + y^2 -2y +1 =0

Step-by-step explanation:

First we need to find the radius

Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2

A circle can be written in the form

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x--2)^2 + (y-1)^2 = 2^2

(x+2)^2 + (y-1)^2 = 4

FOIL ing

x^2 +4x+4  + y^2 -2y +1 = 4

Combining like terms

x^2 +4x + y^2 -2y +5 -4 =0

x^2 +4x + y^2 -2y +1 =0

Answer and Step-by-step explanation:

Answer:

x^2 +4x + y^2 -2y +1 =0

Step-by-step explanation:

First we need to find the radius

Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2

A circle can be written in the form

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x--2)^2 + (y-1)^2 = 2^2

(x+2)^2 + (y-1)^2 = 4

FOIL ing

x^2 +4x+4  + y^2 -2y +1 = 4

Combining like terms

x^2 +4x + y^2 -2y +5 -4 =0

x^2 +4x + y^2 -2y +1 =0

Answer:

The correct option is;

A.) A dilation by a scale factor of two-fifths and then a translation of 3 units up

Step-by-step explanation:

The given information are;

Square S undergoes transformation into square S'

From the figure, the dimension of S' = 2/5 dimension of S

Therefore, the scale factor of the dilation is two-fifths

The center of dilation = The origin

Therefore, given that the top right edge of S is at the center of dilation, the initial location of the dilated figure will be (0, 0), (2, 0), (2, -2), and (0, -2)

Given that the lowermost coordinates of S' are (0, 1) and (2, 1), and the lowermost coordinates of the initial dilation are (0, -2) and (2, -2), we have that the translation to S' from the initial dilation is T (0 - 0, 1 - (-2)) = T(0, 3) which is 3 units up.

Answer:

A

Step-by-step explanation:

Answer:

the answer is C. 180°clockwise

Answer:

4

Step-by-step explanation:

y=mx+b

b=y-intercept.

In this case...

mx=-5<-- this is the slope of the line.

b=4<-- y intercept.

Hope this helps, any further questions, please feel free to ask.

Answer:

185

Step-by-step explanation:

All you have to do is multiply 200 by 92.5/100 (because it is 92.5%). This gives you 185.

Hope this helps!

Answer:

185

We know 92.5% of 100 is 92.5%, so 92.5 of 200 is just 92.5×2.

Answer:

6 is the best estimate.

Step-by-step explanation:

(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.

Choose 6 as your best approximation.

Answer:

40 m

Step-by-step explanation:

The perimeter of the flat, orange shape is the sum of all the sides that forms a boundary around the shape.

The shape is made up of 4 triangles having 2 equal side lengths each, which surrounds the center square.

Each side length of the triangle, that forms a boundary round the shape = 5 m.

There are 8 of this equal side length.

Perimeter = 8(5m) = 40 m

Answer:

x=70

Step-by-step explanation:

the angles opposite 3.5 equal 55 degrees

180-55-55=70

Answer:

70°

Step-by-step explanation:

since the both size are equal which is 3.5,it is equal length, so the other angle should be 55 also. Just use the triangle =180° ，180-55-55=70°

Answer: 1/5 , 1/2, and 5/6

Step-by-step explanation:

given;

probability that the cube shows a three (3) or five (5).

probability that it stops on yellow.

1. the probability p of the spinner stopping on yello  

= 1/5 times

a cube has 6 sides

2. probability that it shows a 3

this is going to be 3 divided by the total sides on the cube which is 6

P = ( 3 ) = 3/6

Divide both side by 3

= 1/2.

3. probability that it shows a 5,

this is going to be 5 divided by the total sides on the cube which is 6

P = ( 5 )

  = 5/6.

He tells us that the 4 daughters have a brother, so, since they belong to the same family, the sisters are the same because they have only one brother.

Answering our question:

or Mr. Smith has 4 daughters and also 1 son.

Answer:

one son

Step-by-step explanation:

each daughter had a brother, means there is only one son

Mr. smith has 1 son

Answer:

77 bags

Step-by-step explanation:

if he brought 49 bags then he brought 28 more bags49+28=77

Answer:

Multiply every coordinate from the old one by 0.75

Step-by-step explanation:

I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.

The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.

Answer:

x, y ----> 3/4x, 3/4y

Step-by-step explanation:

The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.

Yellow: 3 spaces out of 6, so the probability is 3/6 = 1/2

Red: 2 spaces out of 6, so the probability is 2/6 = 1/3

Blue: 1 space out of 6, so the probability is 1/6

multiplying the probability of each color by 150:

Yellow: 1/2 * 150 = 75 times

Red: 1/3 * 150 = 50 times

Blue: 1/6 * 150 = 25 times

Terefore The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.

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Hey there! I'm happy to help!

To find the volume of a cylinder, you multiply the base by the height and then divide by three. The volume of a cone is the same as the volume of a cylinder with the same dimensions divided by three.

So, since a cone's volume is 1/3 of that of a cylinder, we just divide 72 by 3!

72/3=24

Therefore, the volume of the cone is 24 feet cubed.

Have a wonderful day! :D

Answer: its 24.

Step-by-step explanation:

Answer:

i believe a=105, b=29, and c=45

Answer:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex]

Step-by-step explanation:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex] . First multiply 7*-6=-42.

Then do 16*13=208.

Simplify by dividing both by 2.

You get [tex]\frac{-42}{208}=\frac{-21}{104}[/tex].

Your final simplified answer is [tex]\frac{-21}{104}[/tex]

I hope this helps!

Answer:

We accept H₀, with CI = 90 %, porcentage of O blood type in college students does not differ from the world population porcentage

Step-by-step explanation:

The test is a proportion  two-tail test ( note: differs)

p₀ = 45 %      or  p₀ = 0,45

n = 1000

p =  47 %        or  p  = 0,47

Test Hypothesis

Null hypothesis                                H₀                   p  =  p₀

Alternative hypothesis                    Hₐ                   p  ≠ p₀

CI  we assume 90 %  then  α = 10 %    α  =  0,1    α/2  = 0,05

z score  from z-table   z(c) = 1,64

To calculate z(s) = ( p - p₀ ) / √ p₀q₀/ n

z(s)  = ( 0,47  -  0,45 )/ √( 0,45)*(0,55)/1000

z(s)  =  0,02/√( 0,2475)/1000

z(s)  =  0,02/0,01573

z(s) = 1,2714

Now we compare z(s) and z(c)

z(s) < z(c)      1,2714 < 1,64

Then z(s) is in the acceptance region we accept H₀

Answer:

b. 5 + 17i

Step-by-step explanation:

Answer:

x(x-3) ( x+4)

Step-by-step explanation:

  2               5

---------- + ------------

x^2 -3x     x^2 + x - 12

Factor the denominator

  2               5

---------- + ------------

x(x -3)     (x-3) (x+4)

The common denominator is

x(x-3) ( x+4)

Answer:

z = 8.5

Step-by-step explanation:

Let O be the center of the circle, and A, B, C are three points on the circle.

Draw OA and OC are shown in the figure. To make the central angle.

In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is

[tex]\angle AOC=118^{\circ}[/tex]

Subtended angle on arc AC is  

[tex]\angle ABC=(6z+8)^{\circ}[/tex]

According to central angle theorem of circle, central angle is twice of angle subtended by the arc.

[tex]\angle AOC=2\times \angle ABC[/tex]

[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]

[tex]118=12z+16[/tex]

[tex]118-16=12z[/tex]

[tex]102=12z[/tex]

[tex]\dfrac{102}{12}=z[/tex]

[tex]8.5=z[/tex]

Therefore, the value of z is 8.5.

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 ​minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72​, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is given by = P(X > 82 min)

       P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)

                                                           = 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)

                                                           = 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)

                                                           = 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 ​minutes, then we conclude that the population mean must be more than 72​, since the probability is so low.

Answer:

Step-by-step explanation:

From the given data

mean, u = 72

Standard deviation [tex]\rho[/tex] = 23

A) Probability that a randomly selected time interval between eruptions is longer than 82​minutes

[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]

B)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]

C)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]

D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases

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Answer:

the third graph is correct

Step-by-step explanation:

edge

the second part is x<1

Answer:

the third graph and the send part it is x<1

Step-by-step explanation:

Round this however you need to

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

Explanation:

The reference angle is 56 degrees. The side 26.5 is adjacent to this angle as it is the leg closest to the angle (in contrast to the opposite leg or opposite side that is furthest from the reference angle)

The hypotenuse is d. The hypotenuse is always the longest side. The longest side is always opposite the largest angle of a triangle.

We will use the cosine ratio as it is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

cos(56) = 26.5/d

d*cos(56) = 26.5

d = 26.5/cos(56)

d = 47.3897287242421

You use your calculator for the last step shown above. Make sure your calculator is in degree mode. Round that value however you need to.

Here is the formula of sin cos tan :

sin x = opposite/hypotenuse

cos x = adjacent / hypotenuse

tan x = opposite / adjacent

d = hypotenuse

x = the angle known in your pic

like example if in your picture:

adjacent = 26.5

if want to find the d

cos x = adjacent / hypotenuse

cos 56 = 26.5 / d

d = 26.5 : cos(56)

d = 47.390 (3 significant figures)

and if want to find the opposite

tan x = opposite/adjacent

tan 56 = opposite/ 26.5

opposite = 26.5 × tan(56)

opposite = 39.288

-> Sorry if im wrong