The marked price of an article is Rs 4,500. After allowing some percent of discount
and levying 10% VAT it is sold at Rs 4,400, find the discount percent.​

Answer:

24 units2

Step-by-step explanation:

Hope it helps !! :)

The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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Answer:

8x+6

Step-by-step explanation:

Because each pizza is $8 you would have to multiply 8 by the amount of pizzas. Then you add the six because you only pay for the delivery charge once.

Answer:

12=2.5h+4

Step-by-step explanation:

The blanks can be filled as: 1) union, 2) 120, 3) Mutually exclusive, Independent.

1- The union of two events A and B is the event in which either A or B or both occur.

The union of two events A and B includes all outcomes that belong to either A or B or both.

2- Calculate 5! (5 factorial) which is 5 x 4 x 3 x 2 x 1 = 120.

To calculate factorial of a positive integer n, multiply n by all positive integers less than n and greater than 0; alternatively, recursively multiply n by (n-1)!

3. Two events are said to be:

Mutually exclusive if they cannot occur at the same time.

Independent if the occurrence of one does not influence the probability of occurrence for the other..

Mutually exclusive events cannot occur together, while independent events can occur together but their occurrence does not affect each other.

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Answer:

i) c. 1,08,00,000 cm³

ii) c. 1687.5 cm³

iii) b. 6400

Q.3) Suface area of cube is 294 cm².

Step-by-step explanation:

Q.2. 12 men are building a wall which is 8 m long, 6 m high and 22.5 cm thick using bricks. On this basis answer the following.

i. Find the volume of the cuboidal wall.

Substituting all the given values in the formula to find volume of cuboidal wall :

\( \begin{gathered}\qquad{\longrightarrow{\sf{V = LBH}}} \\ \\ \qquad{\longrightarrow{\sf{V = L \times B \times H}}} \\ \\ \qquad{\longrightarrow{\sf{V = 800 \times 600 \times 22.5}}} \\ \\ \qquad{\longrightarrow{\sf{V = 480000 \times 22.5}}} \\ \\ \qquad{\longrightarrow{\sf{\underline{\underline{\red{V = 1,08,00,000 \: {cm}^{3}}}}}}} \end{gathered}\)

Hence, the volume of cuboidal wall is 1,08,00,000 cm³.

———————————————————————

ii. If the dimension of each brick is 25 cm × 11.25 cm × 6 cm, then find the volume of the brick.

Substituting all the given values in the formula to find the volume of cuboidal brick :

\( \begin{gathered}\qquad{\longrightarrow{\sf{V = LBH}}} \\ \\ \qquad{\longrightarrow{\sf{V = L \times B \times H}}} \\ \\ \qquad{\longrightarrow{\sf{V = 25 \times 11.25\times 6}}} \\ \\ \qquad{\longrightarrow{\sf{V = 281.25\times 6}}} \\ \\ \qquad{\longrightarrow{\sf{\underline{\underline{\pink{V = 1687.5 \: {cm}^{3}}}}}}} \end{gathered}\)

Hence, the volume of cuboidal brick is 1687.5 cm³.

————————————————————

iii. How many bricks will be required to construct the cuboidal wall.

Substituting all the given values in the formula to find the number of bricks :

\( \begin{gathered} \quad{\longrightarrow{\sf{No. \: of \: bricks = \dfrac{Volume \:of \: wall}{Volume \: of \: brick}}}}\\ \\ \quad{\longrightarrow\sf{No.\: of \: bricks = \dfrac{10800000}{1687.5}}} \\ \\ \quad{\longrightarrow{\sf{No. \: of \: bricks = \cancel{\dfrac{10800000}{1687.5}}}}} \\ \\ \quad{\longrightarrow{\sf{\underline{\underline{\purple{No. \: of \: bricks = 6400}}}}}}\end{gathered}\)

Hence, 6400 bricks will be required to construct the cuboidal wall.

———————————————————————

Q.3 The volume of a cube is 343 cm³. Fibd its surface area.

For clear understanding please check the given attachment.

\(\rule{300}{2.5}\)

Answer:

Step-by-step explanation:

B

Answer:

shhhhhhhhhsghhhhhhsghhhhhsgshhhhh

Answer: Let us call the centers of the four circles C1, C3, C5, and C7, respectively, where the subscript refers to the radius of the circle. Without loss of generality, we can assume that the tangent point A lies to the right of all the centers, as shown in the diagram below:

                 C7

          o-----------o

       C5 /             \ C3

         /               \

        o-----------------o

                C1

                |

                |

                | l

                |

                A

Let us first find the coordinates of the centers C1, C3, C5, and C7. Since all the circles are tangent to line l at point A, the centers must lie on the perpendicular bisector of the line segment joining A to the centers. Let us denote the distance from A to the center Cn by dn. Then, the coordinates of Cn are given by (an, dn), where an is the x-coordinate of point A.

Using the Pythagorean theorem, we can write the following equations relating the distances dn:

d1 = sqrt((d3 - 2)^2 - 1)

d3 = sqrt((d5 - 4)^2 - 9)

d5 = sqrt((d7 - 6)^2 - 25)

We can solve these equations to obtain:

d1 = sqrt(16 - (d7 - 6)^2)

d3 = sqrt(4 - (d7 - 6)^2)

d5 = sqrt(1 - (d7 - 6)^2)

Now, let us consider the region S that lies inside exactly one of the four circles. This region is bounded by the circle of radius 1 centered at C1, the circle of radius 3 centered at C3, the circle of radius 5 centered at C5, and the circle of radius 7 centered at C7. Since the circles are all tangent to line l at point A, the boundary of region S must pass through point A.

The maximum possible area of region S occurs when the boundary passes through the centers of the two largest circles, C5 and C7. To see why, imagine sliding the circle of radius 1 along line l until it is tangent to the circle of radius 3 at point B. This increases the area of region S, since it adds more points to the interior of the circle of radius 1 without removing any points from the interior of the other circles. Similarly, sliding the circle of radius 5 along line l until it is tangent to the circle of radius 7 at point C also increases the area of region S. Therefore, the boundary of region S must pass through points B and C.

Using the coordinates we obtained earlier, we can find the x-coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (d7 - 6)^2)

x_C = a + 6 + sqrt(9 - (d7 - 6)^2)

To maximize the area of region S, we want to maximize the distance BC. Using the distance formula, we have:

BC^2 = (x_C - x_B)^2 + (d5 - d3)^2

Substituting the expressions we derived earlier for d3 and d5, we get:

BC^2 = 32 - 2(d7 - 6)sqrt(9 - (d7 - 6)^2)

To maximize BC^2, we need to maximize the expression inside the square root. Let y = d7 - 6. Then, we want to maximize:

f(y) = 9y^2 - y^4

Taking the derivative of f(y) with respect to y and setting it equal to zero, we get:

f'(y) = 18y - 4y^3 = 0

This equation has three solutions: y = 0, y = sqrt(6)/2, and y = -sqrt(6)/2. The only solution that gives a maximum value of BC^2 is y = sqrt(6)/2, which corresponds to d7 = 6 + sqrt(6)/2.

Substituting this value of d7 into our expressions for d1, d3, and d5, we obtain:

d1 = sqrt(16 - (sqrt(6)/2)^2) = sqrt(55/2)

d3 = sqrt(4 - (sqrt(6)/2)^2) = sqrt(19/2)

d5 = sqrt(1 - (sqrt(6)/2)^2) = sqrt(5/2)

Using these values, we can compute the coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (sqrt(6)/2)^2) = a - 2 - sqrt(55)/2

x_C = a + 6 + sqrt(9 - (sqrt(6)/2)^2) = a + 6 + sqrt(55)/2

The distance between points B and C is then:

BC = |x_C - x_B| = 8 + sqrt(55)

Finally, the area of region S is given by:

Area(S) = Area(circle of radius 5 centered at C5) - Area(circle of radius 7 centered at C7)

= pi(5^2) - pi(7^2)

= 25pi - 49pi

= -24pi

Since the area of region S cannot be negative, the maximum possible area is zero. This means that there is no point that lies inside exactly one of the four circles. In other words, any point that lies inside one of the circles must also lie inside at least one of the other circles.

Step-by-step explanation:

Answer:

95°

Step-by-step explanation:

Here we have angles of 30° and 55°, so the remaining angle is:

Answer:

Life forms change over time

Step-by-step explanation:

Answer:

1/10

hope this is helpful

According to the question The rate at which the base is changing is 0 cm/min, as it remains constant.

To solve this problem, we can use the relationship between the area, altitude, and base of a triangle. The formula for the area of a triangle is given by:

Area = (1/2) * base * altitude

We are given that the altitude is increasing at a rate of 2.5 centimeters/minute and the area is increasing at a rate of 2.5 square centimeters/minute. We need to find the rate at which the base is changing.

Let's denote the altitude as h, the base as b, and the area as A. We have the following equations:

dA/dt = (1/2) * b * dh/dt   (differentiating the area equation with respect to time)

dh/dt = 2.5 cm/min   (given)

dA/dt = 2.5 cm^2/min   (given)

Now we can substitute the given values into the equations and solve for db/dt, the rate at which the base is changing:

2.5 = (1/2) * b * 2.5

2.5 = 1.25b

b = 2 cm

So, when the altitude is 8 centimeters and the area is 81 square centimeters, the base is 2 centimeters. Therefore, the rate at which the base is changing is 0 cm/min, as it remains constant.

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The length of the arc with a central angle of 45 degrees and radius 6 cm is 4.71 cm

From the question, we have the following parameters that can be used in our computation:

Central angle = 45 degrees

Radius = 6 cm

Using the above as a guide, we have the following:

Length of arc = central angle/360 * 2 * 3.14 * Radius

Substitute the known values in the above equation, so, we have the following representation

Length of arc = 45/360 * 2 * 3.14 * 6

Evaluate

Length of arc = 4.71

Hence, the length of the arc is 4.71 cm

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Answer:

Yes

Step-by-step explanation:

1 ton = 2000 pounds

6 tons = 12000 pounds

13000>12000

The truck is 1000 pounds overweight so yes it is too heavy to cross the bridge.

The main difference between the reciprocal and inverse of a function is their definition and properties. The reciprocal of a function f(x) is defined as 1/f(x), while the inverse of a function f(x) is a function f^(-1)(x) such that \(f(f^(-1)(x))=x and f^(-1)(f(x))=x\) for all x in their respective domains.

The domains of sine, cosine, and tangent functions need to be restricted to define their inverse functions because they are not one-to-one functions. In order to have an inverse, a function must be both one-to-one (each output has only one input) and onto (each output value is mapped by at least one input value).

For example:
- sine: restricted domain to [-π/2, π/2] to define its inverse, arcsin (sin^(-1))
- cosine: restricted domain to [0, π] to define its inverse, arccos (cos^(-1))
- tangent: restricted domain to (-π/2, π/2) to define its inverse, arctan (tan^(-1))

These restrictions ensure that the functions become one-to-one and onto, making it possible to define their inverses uniquely.

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The estimated cost if they use a contractor to complete the house would be $435,000.

The cost of the house is based on what home builders typically charge for a house similar to the one Mrs. Pavlinski and her husband Zander have in mind.

In this case, the contractor's price is $150 per square foot of her home while the area of the house is given as 2,900 square feet.

Total cost = Cost per square feet x Area of house

Solving for the estimated cost gives:

= 150 x 2,900

= $435,000

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The given question is incomplete and the complete question is as follows.

"Mrs. Publinsky and her husband, Xander are planning their dream house. The lot for the house sits high on a hill with a beautiful view of the White Mountains. The plans show the size of the house to be 2,900 sq ft. The average price for a lot and house similar to this one has been 150 per sq ft. Fortunately, Xander is a retired plumber and feels he can save money by installing the plumbing himself. Mrs Publinsky feels she can take care of the interior decorating. They both feel they can complete the exterior painting with the help of their two sons."

Answer:

one solution

Step-by-step explanation:

3x + 9 = 25x + 14

-3x         -3x

9 = 22x + 14

-14         - 14

-5 = 22x

Answer:Thanks!

Step-by-step explanation:

Answer: thx

Step-by-step explanation:

The probability that the amount dispensed per box will have to be increased is 0.

To answer this question, we need to know the target amount that should be distributed per carton.

Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.

hence the probability of having to increase the amount is 0.

z = (target volume - mean) / standard deviation

z = (1 - 1) / 0.2

z = 0

A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.

However, the target amount is equal to the mean value,

In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.

If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.

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Answer:

D.

About 9.4 units!

Step-by-step explanation:

\( \sqrt{(9 - 4)^{2} + (10 - 2)^{2} } \)

\( = 9.4444..\)

Answer:

Step-by-step explanation:

\(V(n)=4(1.3)^n\)

Answer:

V(n)=4(1.3)^n

Step-by-step explanation:

4 is the original value

1.3x is how much the value multiplies every year

n is the amount of years

It's not the 1st or 3rd since that would be depreciating value

It's not the 2nd because that's adding a value instead of multiplying the original

Answer:

100 degrees

Step-by-step explanation:

They have to add up to 180 because they're on a straight line together.

180 - 80 = 100 degrees

The expression is f(x) = $0.95x+$9.50

From the question, we have

A cell phone company charges $9.50 per month to rent a cell phone and $0.95 per minute.

f(x) = $0.95x+$9.50

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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Answer:

B) Each friend gets 3, there are 4 left over

Step-by-step explanation:

Caden starts with 40 chips.

He takes 12 chips for himself.

40 - 12 = 28

He now has 28 chips left to divide evenly by 8.

28/8 = 3 remainder 4

Check: 3 × 8 = 24, and 24 + 4 = 28

Answer: B) Each friend gets 3, there are 4 left over

Answer:

We can determine the roots of the quadratic equation f(x) = x^2 + 4x + 7 by using the quadratic formula, which states that for a quadratic equation of the form ax^2 + bx + c = 0, the roots are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 4, and c = 7. Substituting these values into the quadratic formula, we get:

x = (-4 ± sqrt(4^2 - 4(1)(7))) / 2(1)

Simplifying this expression, we get:

x = (-4 ± sqrt(16 - 28)) / 2

x = (-4 ± sqrt(-12)) / 2

Since the square root of a negative number is not a real number, the roots of the equation f(x) = x^2 + 4x + 7 are complex conjugates. Therefore, the equation has no real roots.

the distributor should use 120 gallons of $10.00 water, 60 gallons of $1.00 water, and 120 gallons of $4.50 water to make up 300 gallons of sparkling water.

Let'sLet's denote the number of gallons of the $10.00 water as x, the number of gallons of the $1.00 water as y, and the number of gallons of the $4.50 water as z.

According to the given information, the distributor wants to make 300 gallons of sparkling water.

We have the following equations:

Equation 1: x + y + z = 300    (total gallons equation)

Equation 2: z = 2y       (twice as much $4.50 water as $1.00 water)

We also know the price per gallon for the sparkling water:

Equation 3: (10x + 1y + 4.50z) / 300 = 6.00     (price per gallon equation)

Now, we can solve this system of equations:

Substitute z = 2y from Equation 2 into Equation 1:
x + y + 2y = 300
x + 3y = 300

Rearrange Equation 3 to eliminate the fraction:
10x + y + 4.50z = 6.00 * 300
10x + y + 4.50z = 1800

Substitute z = 2y from Equation 2 into Equation 3:
10x + y + 4.50(2y) = 1800
10x + y + 9y = 1800
10x + 10y = 1800
x + y = 180

Now we have the following system of equations:
x + 3y = 300
x + y = 180

Solve this system of equations to find the values of x and y.

Subtract the second equation from the first equation:
(x + 3y) - (x + y) = 300 - 180
2y = 120
y = 60

Substitute y = 60 into the second equation to find x:
x + 60 = 180
x = 120

We have found that x = 120 and y = 60.

Now, substitute the values of x and y into Equation 2 to find z:
z = 2y
z = 2(60)
z = 120

Therefore, the distributor should use 120 gallons of $10.00 water, 60 gallons of $1.00 water, and 120 gallons of $4.50 water to make up 300 gallons of sparkling water.

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Answer:

13.9 miles

Step-by-step explanation:

We know

A group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream. How far did they walk altogether

8 7/10 = 87/10

5 1/5 = 26/5

87/10 + 26/5 = 87/10 + 52/10 = 139/10 = 13.9 miles

So, they walked 13.9 miles.

Answer:

x+5≥13

Step-by-step explanation:

The values in the missing observation are:

X1    X2

76 22  

82 25

91 32

101    41

88 28

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x1 x2

76 22  

82 __

91 32

__    41

88 28

The difference between each row are:

76 - 22 = 54

82 - 25 = 57

91 - 32 = 59

101 - 41 = 60

88 - 28 = 60

We see that,

57 - 54 = 3

59 - 57 = 2

60 - 59 = 1

60 - 60 = 0

So,

The difference between the numbers is consecutive as 3, 2, 1, 0.

Thus,

The missing values of X1 and X2 are 101 and 25.

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Answer:

x = 41°

Step-by-step explanation:

Complementary angles are angles that add up to 90°

y = x + 8

x + y = 90°

Plug in x+8° for y:

-Chetan K