Gaurav bought 500 mangoes for Rs. 1000. He then packed them into small boxes with 25 in each. If each box is sold for Rs. 60, how much profit is made

Answer:

Step-by-step explanation:

You want the value of the variable k and the angle measures around triangle XYZ in the given figure.

The exterior angle at X is equal to the sum of the remote interior angles at Y and Z:

  14k -4 = (5x -3) +(11k -23)

  14k -4 = 16k -26

  7k -2 = 8k -13 . . . . . . divide by 2 (because we can)

  11 = k . . . . . . . . . . add 13-7k

The value of k is 11.

  Y = (5k -3)° = (5·11 -3)°

  Y = 52°

  Z = (11k -23)° = (11·11 -23)°

  Z = 98°

  angle WXZ = Y +Z = 52° +98°

  angle WXZ = 150°

__

Additional comment

The exterior angle at X is the supplement of the adjacent interior angle X. That interior angle is also the supplement of the sum of angles Y and Z. Two angles are equal when their supplements are equal. Hence angle WXZ is the sum of angles Y and Z.

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Answer:

The volume of 65 kg of the substance is 13 liters.

Step-by-step explanation:

If a substance's mass varies directly from its volume, it means that the ratio of mass to volume remains constant. In this case, we can calculate the continuous ratio and then use it to find the volume.

Given:

Mass1 = 30 kg

Volume1 = 6 liters

Let's denote the constant ratio as k.

Mass1 / Volume1 = k

30 kg / 6 liters = k

k = 5 kg/liter

Now, we can find the volume2 for a mass of 65 kg using the constant ratio:

Mass2 = 65 kg

Volume2 = ?

Mass2 / Volume2 = k

65 kg / Volume2 = 5 kg/liter

To find Volume2, we can cross multiply:

65 kg = 5 kg/liter * Volume2

Volume2 = 65 kg / 5 kg/liter

Volume2 = 13 liters

The number of different possible outcomes if you spin a spinner labeled Red, Blue, Yellow five times (excluding outcomes where the same color is spun five times) is 243 x 1/10 = 24.3, which we can round down to 24.

If you spin a spinner labeled Red, Blue, Yellow five times, there are a total of 3^5 (three raised to the power of five) different possible outcomes.

This is because each spin has three possible outcomes and the number of possible outcomes is calculated by multiplying the number of outcomes for each spin together.

Therefore, 3 x 3 x 3 x 3 x 3 = 243. However, this includes outcomes where the same color is spun five times, which we want to exclude.

To calculate this, we can use the formula for combinations: nCr = n! / (r! * (n-r)!). In this case, we want to find the number of combinations of 3 colors taken 5 at a time, which is 3C5 = 3! / (5! * (3-5)!) = 3! / (-2! * 5!) = 1/10.

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Step-by-step explanation:

I believe there is something missing from the description.

I base my solution and explanation on the following assumptions :

in other words, (20, -21) is not just any point on the line, but it is the upper vertex of the triangle.

the baseline of the triangle, which is the radius of the surrounding circle is then the distance from the origin to the point.

Pythagoras (= distance formula) gives us for the distance between 2 points (x1, y1) and (x2, y2) :

distance² = (x1 - x2)² + (y1 - y2)²

in our case

distance² = (20 - 0)² + (-21 - 0)² = 400 + 441 = 841

distance = radius = 29

remember, sine is the up/down leg, cosine is the left/right leg.

so,

sin(theta) = -21/29

FYI : theta ≈ -46.4°

cos(theta) = 20/29

tan(theta) = sin(theta)/cos(theta) = -21/29 / 20/29 =

= -21/20

you were right about tan(theta), not about sin(theta) and cos(theta).

if you mistook theta for a 0, you were still wrong :

sin(0) = 0, cos(0) = 1.

The values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent Inequality in terms of d is d ≥ -24.

To make the inequality 3d ≥ -72 true, we need to find values of d that satisfy the inequality.

Dividing both sides of the inequality by 3, we get:

d ≥ -24

Therefore, any value of d that is greater than or equal to -24 will satisfy the inequality.

An equivalent inequality in terms of d would be:

d + 24 ≥ 0

We can simplify this inequality by subtracting 24 from both sides:

d ≥ -24

This is the same inequality we found earlier, which means that any value of d greater than or equal to -24 will make the inequality true.

the values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent inequality in terms of d is d ≥ -24.

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Answer: Put this in your own words:

Convenience sampling is like staying in a certain area of a mall and giving samples to  people as the come by you stay there at that one place because it is convenient  because you don't want to move from that spot so you stay at that spot and only that spot. Convenience sampling is also like ordering food because it is convenient and you don't want to cook.

Step-by-step explanation:

The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.

The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:

f(x) = 1 / (b - a)

where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:

f(x) = 1 / (3.5 - 2.5) = 1

To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:

Probability = (width of range) / (total width)

= 0.2 / 1

= 0.2

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Answer:

C.  x = -3

Step-by-step explanation:

Given equation:

[tex]10x+57=9-6x[/tex]

Add 6x to both sides of the equation:

[tex]10x+57+6x=9-6x+6x[/tex]

[tex]16x+57=9[/tex]

Subtract 57 from both sides of the equation:

[tex]16x+57-57=9-57[/tex]

[tex]16x=-48[/tex]

Divide both sides by 16:

[tex]\dfrac{16x}{16}=\dfrac{-48}{16}[/tex]

[tex]x=-3[/tex]

Therefore, the solution to the equation is x = -3.

Hello !

Answer:

[tex] \boxed{\sf Option \: C\text{:} \: x= -3} [/tex]

Step-by-step explanation:

Solve the equation by isolating the variable 'x'.

[tex] \\ [/tex]

We are given the following equation:

[tex] \sf 10x + 57 = 9 - 6x [/tex]

[tex] \\ [/tex]

Subtract 57 from both sides and combine like terms:

[tex] \sf 10x + 57 - 57 = 9 - 6x - 57 \\ \sf 10x = -6x - 48 [/tex]

[tex] \\ [/tex]

Add 6x to both sides of the equation and combine like terms:

[tex] \sf 10x + 6x = -6x - 48 + 6x \\ \sf 16x = -48 [/tex]

[tex] \\ [/tex]

Finally, divide both sides by 16, which is the coefficient of the variable.

[tex] \sf \dfrac{16x}{16} = \dfrac{-48}{16} \\ \\ \boxed{\sf x= -3} [/tex]

Have a nice day ;)

To find the surface area of a cylindrical can, we need to calculate the sum of the areas of its curved surface and its two circular bases.

The curved surface area (CSA) of a cylinder can be calculated using the formula:

CSA = 2πrh

In this case, the height (h) of the can is 10 cm and the radius (r) is 4 cm.

Using the formula, we can calculate the curved surface area:

CSA = 2 × 3.14 × 4 cm × 10 cm

CSA = 251.2 cm²

The area of each circular base can be calculated using the formula:

Base Area = πr²

Substituting the radius (r = 4 cm) into the formula, we get:

Base Area = 3.14 × (4 cm)²

Base Area = 50.24 cm²

Since the can has two circular bases, the total area of the bases is 2 times the base area, which is:

2 × 50.24 cm² = 100.48 cm²

To find the total surface area, we add the curved surface area and the area of the bases:

Total Surface Area = CSA + 2 × Base Area

Total Surface Area = 251.2 cm² + 100.48 cm²

Total Surface Area = 351.68 cm²

Therefore, the surface area of the cylindrical can is approximately 351.68 cm².

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Answer:

5

Step-by-step explanation:

im right

Answer:

  (2, 5)

Step-by-step explanation:

You want the ordered pair that is a solution to y ≤ 4x -3 from those on the list:

The attachment shows a graph of the inequality, along with the offered solution points. The only solution among those shown is (2, 5). That solution lies on the boundary line. The "≤" symbol means the boundary line is included in the solution set.

We can use a calculator to check the solutions, too. Rearranging, we have ...

  4x -3 -y ≥ 0

The calculator in the second attachment is able to make this calculation using the list of x-values and the list of y-values. The solution list only has one number that is not less than zero. That corresponds to (x, y) = (2, 5).

__

Additional comment

We like to avoid having to enter the same equation over and over with different data. That is why we have chosen the solution methods here. A spreadsheet can repeat the calculation and comparison for you, too.

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The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.

The table provides information about whether individuals have a brother and a sister.

Based on the options given, let's calculate the relative frequencies to see which association is suggested:

Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)

Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)

By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.

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Answer: Figure C

Step-by-step explanation:

Figure C is a translation of Figure A because it moved down. Figure A moved down 5 units in order to be Figure C. A translation is moving in a direction. Figure B and D have both been altered some other way, but Figure C has just been moved down.

a) To find the area of region R, we need to calculate the area between the curves y = 2√x and y = 6 in the first quadrant. The region is bounded by the y-axis and the horizontal line y = 6.

To find the area, we integrate the difference between the upper and lower curves with respect to x:

Area = ∫[0 to a] (6 - 2√x) dx,

where 'a' is the x-coordinate where the curves intersect.

b) To find the volume of the solid generated when region R is rotated about the horizontal line y = 7, we can use the method of cylindrical shells. Each cylindrical shell has a height of 6 - 7 = -1 (as y = 6 is below y = 7) and a radius equal to x.

The volume is given by the integral:

Volume = ∫[0 to a] 2πx(6 - 7) dx,

where 'a' is the x-coordinate where the curves intersect.

c) To find the volume of the solid generated when region R is rotated about the y-axis, we can use the method of disks. Each disk has a radius equal to y and a thickness given by dx.

The volume is given by the integral:

Volume = ∫[0 to b] π(y^2) dx,

where 'b' is the y-coordinate where the curves intersect.

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Answer:

Step-by-step explanation:

You can find the hieght from slant height and side edge using this formula:

[tex]\sqrt{s^{2} - \frac{a}{2}^{2} }[/tex]    where s is the slant height and a is the base length of one edge.

[tex]\sqrt{92.5^{2} - (\frac{24.2}{2} )^{2} }[/tex]

[tex]\sqrt{8556.25 - 146.41}[/tex]

[tex]\sqrt{8409.84}[/tex]

91.705 in

can be rounded to 91.71 in

The value of x, which is the radius of this cone is 64 units.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

512π = 1/3 × π × x² × 24

512π = π × x × 8

Radius, x = 512/8

Radius, x = 64 units

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Complete Question:

The volume of the right cone below is 512π units³. Find the value of x.

True. The double integral can be used to compute the area of a region d in a plane by integrating the function f(x,y). In fact, the double integral of f(x,y) over a region D in the xy-plane gives the volume of the solid between the surface z=f(x,y) and the xy-plane over the region D.

However, if we take the function f(x,y) to be the constant function 1, then the double integral of f(x,y) over the region D is simply the area of the region D. Therefore, we can compute the area of a region D in a plane by integrating the constant function 1 over the region D using the double integral. Integrating over two variables requires calculating two separate integrals, so the answer is more than 100 words.
True. A double integral can be used to compute the area of a region D in a plane by integrating the function f(x, y). To find the area, you would integrate the function f(x, y) = 1 over the region D, as the double integral represents the sum of the function values over the entire area. The double integral can be thought of as a generalization of single-variable integration, allowing us to find the area in two dimensions.

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The length of the model when the scale given is used would be = 240 yards.

To calculate the length of the model, the formula for scale factor should be used. That is;

Scale factor = Actual length/Model length

The scale factor = 1/4

Actual length = 60 yards

Model length = ?

That is;

1/4 = 60/?

Model length = 60×4

= 240 yards

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By distributive property to write an expression that is equivalent to 12 + 4x is equal to  4 (x + 3) and 2 ( 2x + 6)

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms which quality can be expressed as the following symbol:

A ( B+ C) = AB + AC

We have given an expression as;

12 + 4x

since 4 and 12 both have a common factor of 4.

4x + 12 = 4 (x + 3)

Additionally, given that 4 and 12 both have a factor of 2

4x + 12 = 2 ( 2x + 6)

Therefore, by the distributive property to write an expression that is equivalent to 12 + 4x ;

4 (x + 3) and 2 ( 2x + 6)

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The surface area of the cylinder, rounded to the nearest square meter, is: D. 142 square meters

The surface area of a cylinder can be calculated by using the formula expressed as:

SA = 2[tex]\pi[/tex]r(h + r), where r is the radius and h is the height.

Given the following:

[tex]\pi[/tex] = 3.14

radius (r) = 2.6 m

height of the cylinder (h) = 6.1 m

Plug in the values:

[tex]\sf SA = 2 \times 3.14 \times 2.6 \times (6.1 + 2.6)[/tex]

[tex]\sf SA \thickapprox 142[/tex] square meters (rounded to the nearest square meter)

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The probability that the sample mean would be greater than 135.7 WPM is 0.1686.

Calculate the standard deviation:

The standard deviation of the WPM typed by a speed typist is √100 = 10.

Calculate the z-score

The z-score is calculated by subtracting the population mean (135) from the sample mean (135.7) and dividing it by the standard deviation (10).

z = (135.7 - 135) / 10 = 0.07

Calculate the probability

The probability of the sample mean being greater than 135.7 WPM can be calculated using the z-score.

P(x > 135.7) = 1 - P(x ≤ 135.7)

P(x > 135.7) = 1 - 0.8314 = 0.1686

Therefore, the probability that the sample mean would be greater than 135.7 WPM if 43 speed typists are randomly selected is 0.1686, rounded to four decimal places.

Complete Question:

The mean number of words per minute WPM typed by a speed typist is 135 with a variance of 100. What is the probability that the sample mean would be greater than 135.7 WPM if 43 speed typist are randomly selected? round your answer to four decimal places.

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The required, age of Trisha is 15 years old.

Let's represent Trisha's age as "T." Then we can use this variable to represent the ages of her brothers and father as well.

According to the problem, Trisha's first brother is three years older than her, so his age would be T + 3. Her second brother is three years younger than her, so his age would be T - 3. Trisha's third brother is one-third of her age, so his age would be T/3. Trisha's father is three times her age, so his age would be 3T.

The sum of all their ages is 95, so we can create the equation:

T + (T + 3) + (T - 3) + (T/3) + 3T = 95

T = 15

Thus, the required age of the Trisha is 15 years.

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Answer:

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

The first explanation comes from the information given in the question.

It says the population decreases.

From the function itself, we look at the base of the exponent. The function is representing a growth if the base is greater than 1 and decay if the base is less than 1.

In our case 0.92 < 1, hence the function represents exponential decay.

Answer:

64 pounds

Step-by-step explanation:

so first what you have to do is find the perimeter of the barn:

2l+2w

2*12)+2*4)= 32 m

Then it costs 2 pounds per meter

So they you multiply

32m * 2 pounds

64 pounds

Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.

The number 1.overline00 represents a repeating decimal. To understand its nature, let's break it down.

The overline above the zeros indicates that the zeros repeat infinitely. Therefore, 1.overline00 can be represented as 1.000000... with the zeros repeating indefinitely.

1.) Whole number: A whole number is a non-negative integer. Since 1.overline00 is greater than 1, it is not a whole number.

2.) Integer: An integer includes both positive and negative whole numbers, including zero. As 1.overline00 is greater than 1, it is not an integer.

3.) Rational: A rational number can be expressed as the ratio of two integers, where the denominator is not zero. To determine if 1.overline00 is rational, we can convert it into a fraction. Let x = 1.overline00. Multiplying both sides by 100, we get 100x = 100.overline00. Subtracting the original equation from this new equation, we get 100x - x = 100.overline00 - 1.overline00, which simplifies to 99x = 99. Therefore, x = 1. Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.

4.) Irrational: An irrational number cannot be expressed as the ratio of two integers. Since we have determined that 1.overline00 is rational, it is not irrational.

Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.

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The work required to pump the sludge is approximately 21449.6 ft-lbs.

To calculate the work required to pump the sludge, we need to determine the volume of the sludge and then multiply it by the weight of the sludge.

First, let's find the volume of the sludge in the tank. Since the tank is formed by rotating the segment between (2, 0) and (4, 4) around the y-axis, it forms a frustum of a cone. The formula for the volume of a frustum of a cone is:

V = (1/3) * π * h * (R^2 + r^2 + R*r),

where h is the height of the frustum, R is the radius of the larger base, and r is the radius of the smaller base.

In this case, the height of the frustum is the difference in y-coordinates between the two points: h = 4 - 0 = 4 ft.

The radius of the larger base, R, is the y-coordinate of the point (4, 4): R = 4 ft.

The radius of the smaller base, r, is the y-coordinate of the point (2, 0): r = 0 ft.

Substituting these values into the volume formula, we have:

V = (1/3) * π * 4 * (16 + 0 + 0) = (4/3) * π * 16 = 67.03 ft^3 (approximately).

Next, we need to calculate the weight of the sludge, which is the volume multiplied by the density:

Weight = Volume * Density = 67.03 ft^3 * 80 lbs/ft^3 = 5362.4 lbs (approximately).

Finally, we can calculate the work required to pump the sludge 4 feet upwards. The work is given by the formula:

Work = Force * Distance,

where Force is the weight of the sludge and Distance is the vertical distance it is pumped.

Work = Weight * Distance = 5362.4 lbs * 4 ft = 21449.6 ft-lbs (approximately).

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a) Marcus' result is likely to be more reliable.

b) Because the sample was bigger.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The higher the total number of outcomes, the more reliable the probability calculated is.

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1) The value of cos θ is,

2) The value of sin θ is,

3) The value of cos θ is,

We have to given that;

The value of sin θ is,

⇒ sin θ = 3/5

Hence,

cos θ = √1 - sin²θ

cos θ = √1 - 9/25

cos θ = √16/9

cos θ = 4/3

Since, It is quadrant II.

Hence,

cos θ = - 4/3

Since, cos θ = - 5/12

Hence,

sin θ = √1 - cos²θ

sin θ = √1 - 25/144

sin θ = √119/144

Since, It is quadrant III,

Hence,

sin θ = - √119/12

The value of sin θ is,

⇒ sin θ = - 15/17

Hence,

cos θ = √1 - sin²θ

cos θ = √1 - 225/289

cos θ = √64/289

cos θ = 8/17

Since, It is quadrant IV.

Hence,

cos θ = 8/17

Since, Value of sine is always positive,

And, Values of cosine is always greater than - 1.

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Answer:

The Mean is 6.

Step-by-step explanation: