Find the volume of the sphere. Leave your answers In terms of pi

The problem can be solved using algebra. Let's say the discount rate is x, then the price after discount is:

60000 (1 - x/100)

The price after VAT is:

60000 (1 - x/100) (1 + y/100) = 58986

Where y is the rate of VAT.

Rearranging the equation we get:

(1 - x/100) (1 + y/100) = 58986/60000

Multiply both sides by 100 to get rid of the fractions:

100 (1 - x/100) (1 + y/100) = 981

Expanding and grouping like terms, we get:

100 - x + 100y - xy = 981

We can see that x is in two terms, so we can move one side of the equation and get:

100 - x + 100y = 981 + x

x = (981 + x - 100 + 100y)/100 = (981 + xy - 100y)/100

Now we have x in only one term and we know the value of x is 10%, so we can substitute it:

10 + 10y = 9.81

Solving for y we can find that y = 0.81 or 81%

So the VAT rate is 81%

Answer:

-3x^2

Step-by-step explanation:

We must do the 'work' inside the parentheses first:

(3x squared)  works out to  3x^2

after which we preface this result with the ' - ' sign:  -3x^2

Note:  if we write ONLY 3x squared the correct interpretation is 3x^2.  But if we write (3x) squared, the correct interpretation is 9x^2.  Double check the original problem, please, or (better yet) share an image of the original problem.

Answer:

12+14i

Step-by-step explanation:

For -(-9-4i), you need to clean up the parentheses so you would distribute. -1 times -9 and -1 times -4i.

You will get 9+4i

Now you have 3+10i+9+4i. You will now add like terms. 10i+4i= 14i. 9+3= 12.

12+14i

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Answer:

7.8cos23 feet

Step-by-step explanation:

Which expression can be used to find AC

From the given diagram;

Hypotenuse = AB = 7.8ft

Adjacent to <A = AC

Using the SOH CAH TOA identity;

cos theta = adjacent/hypotenuse

cos 23 = AC/AB

cos 23 = AC/7.8

AC = 7.8cos23

AC = 7.8(0.9205)

Hence the measure of AC is 7.8cos23 feet

Answer:

4834.91 cubic ft.

Step-by-step explanation:

The volume of a right-cylinder is

[tex]\pi{r}^{2} h[/tex]

we are only concerned with the total amount of water from A.

plug in the respective radius (half the diameter) and height for A into our formula above and solve.

In the case of a 24-pack for $5. 49, the cost of the unit is the lowest.

The cost per item is nothing to the amount of money invested in buying one item.

As we have 3 different scenarios:

Case A. 6- pack for $2. 49

As here. cost of 6 packs is $2.49, so for determining the cost of one pack we will divide $2.49 by 6.

So, the cost of 1 pack will be = 2.49/6 = 0.415 $/pack

B. 12-pack for $3. 99

As here. cost of 12 packs is $3.99, so for determining the cost of one pack we will divide $3.99 by 12.

So, the cost of 1 pack will be = 3.99/12 = 0.3325 $/pack

C. 24-pack for $5. 49

As here. cost of 24 packs is $4.49, so for determining the cost of one pack we will divide $5.49 by 24.

So, the cost of 1 pack will be = 5.49/6 = 0.22875 $/pack

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Answer:

cosS is 33/65

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets get started.

Area is given as 49 square inches.

The formula for area A =  

base is given as x

Height is given as x

Hence area is A

A =  

Multiplying 2 in both sides

Taking square root on both sides

hence the answer is x = 9.9 in   :  Answer

Hope it will help :)

Answer:this is confusing

Step-by-step explanation:

Answer:

M(4,0)

K(0,5)

L(6,5)

go down one

Answer:

The squares would be 2

First one would be 2 × 2 × 2 = 8

The triangles would be 3

Second one would be 2 × 3 × 3 × 3 = 54

Circles would be 1

Third one would be 2 × 3 × 1 × 1 = 6

So that means the last one would be 1 × 2 × 3 = 6

Hope it all made sense and helped :)

Answer:

The volume of the cone is 1526.04 km cubed

Step-by-step explanation:

The equation for a right cone is πr^2 multiplied by h/3. The r equals radius and the h equals 18. So, we get the equation π(9)^2 multiplied by 18/3. When put into a calculator, you get 1526.04. (Remember to use 3.12 NOT π.)

Answer:

(1) 6:45 p.M. - ______18: 45H

(2) 17:15 H - ______ 5: 15 pm

(3) 1:25 a.M. - ______  1:25 Hours

(4) 4:15 p.M. - ______  16: 15H

(5) 00:15 H - ______ 12:15 am .

Step-by-step explanation:

(1) 6:45 p.M. - ______18: 45H

This is ( 6:45 + 12) 18 hours and 45 minutes from the beginning of day .

So the 24 hour time is 18: 45H

(2) 17:15 H - ______

This is 17 hours and 15 minutes from the beginning of day.

Taking 12 hours from the morning gives 5 hours since midday. So it will be in the evening i.e 5: 15 pm

(3) 1:25 a.M. - ______

This is 1 hours and 25 minutes from the beginning of day.

So it will be in the  ( 00:00+ 1:25) 1:25 Hours in the 24 hour clock.

(4) 4:15 p.M. - ______

This is ( 4:15 + 12) 16 hours and 15 minutes from the beginning of day .

So the 24 hour time is 16: 15H

(5) 00:15 H - ______

This is only 15 minutes from the beginning of day.

So it will be in the  ( 12:00+ 0:15) 12:15 am .

The Triangle STP is similar to Triangle SRQ.

We can prove that triangle STP is similar to triangle SRQ using the Angle Bisector Theorem and the ratios of the sides of the triangles.

The Angle Bisector Theorem states that if point P bisects angle RST, then the ratio of the length of the side ST to the length of the side SR is equal to the ratio of the length of the side PT to the length of the side PQ.

In this case, we are given that 2SP = 3SQ and 2ST = 3SR.

Dividing both sides of the equation 2SP = 3SQ by 2 and both sides of the equation 2ST = 3SR by 2, we get:

SP/PQ = 3/2 and ST/SR = 3/2

As the ratio of the length of the side ST to the length of the side SR is equal to the ratio of the length of the side PT to the length of the side PQ.

Therefore, triangle STP is similar to triangle SRQ.

It can also be proven using the fact that PS bisects angle RST which means that the angle PST = PSR. And if two angles of two triangles are equal and the sides are in proportion then the two triangles are similar.

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The surface area of the figure after a cubic hollow runs to the height of the rectangular prism is 364 square feet.

The surface area is 364 square feet.

Find the surface area of the rectangular prism.

To do this, use the formula for the surface area of a rectangular prism:

(2 x length x width) + (2 x width x height) + (2 x length x height)

In this case, the length is 9 feet, the width is 8 feet, and the height is 5 feet. Plugging these values into the formula gives:

= (2 × 9 × 5) + (2 × 8 × 5) + (2 × 9 × 8)

= 314 square feet

When a cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet, 2 cubic faces is removed and 4 cubic faces added to the surface area of the resultant solid. So

surface area = 314 - 2×5² + 4×5²

= 314 + 2×5²

= 314 + 50

= 364 square feet

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Anytime one makes a traffic manoeuvre, such as changing lanes or passing another vehicle, a person put both himself and other drivers on the road in danger.

What are the methods for passing risky situations?

Avoid driving at intersections with railroads, railroad crossings, and entrances to shopping centres.

Only pass to the left if there are two lanes on the road. It is frequently illegal and dangerous to pass on the right. Only when the car in front of you flashes its left turn signal is there an exemption.

When there is a long line of traffic and an oncoming car is right ahead, it is advisable to wait until the incoming vehicle has passed before making a passing motion.

Therefore, it is best to wait until one can see fully ahead because there might be an approaching car right around the bend.

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All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2(3y + 4) − 3 (y − 2) = 2⁢y

Simplify the equation, then we have

2(3y + 4) − 3 (y − 2) = 2⁢y

6y + 8 − 3y + 6 = 2y

3y + 14 = 2y

14 = 2y - 3y

14 = - y

y = - 14

All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.

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Answer:

14 dollars

Step-by-step explanation:

Anjali had 12 dollars after recieving the 5. So in order to find out how much she had before cleaning the gutters, we substract those 5 dollars from the 12. That leaves us with 7 dollars. This is the amount of money she had after spending half at the movies, and before cleaning the gutters. Which mean's it's half of her allowance. 7 x 2 is 14, which is your answer! :)

Answer:

y=7/3x²-13/3x+2

Step-by-step explanation:

Determine the value of c:

y=ax²+bx+c

2=a(0)²+b(0)+c

2=c

Substitute (1,0) into the quadratic and create an equation with a and b:

y=ax²+bx+2

0=a(1)²+b(1)+2

0=a+b+2

-2=a+b

Do the same with (3,10) to get a second equation:

y=ax²+bx+2

10=a(3)²+b(3)+2

10=9a+3b+2

8=9a+3b

Set the two equations equal to each other and solve for a and b:

-2=a+b

8=9a+3b

Multiply first equation by 3 and eliminate b to find a:

 -6=3a+3b

- (8=9a+3b)

_______

-14=-6a

14/6=a

7/3=a

Substitute 7/3=a into the first equation:

-2=7/3+b

-2-(7/3)=b

-13/3=b

Final equation:

y=7/3x²-13/3x+2

See the graph for a visual representation

Step-by-step explanation:

12 holes / 6 minutes = 2 holes / 1 minute

the simplified ratio is 2/1 = 2.

so, for 25 minutes we need to keep the same ratio :

x holes / 25 minutes = x/25 = 2

x = 2×25 = 50

it drills 50 holes in 25 minutes.

So we know that if you multiply a negative number by a positive number, you get a negative number. We also know that if you multiply a negative number by a negative number you get a positive number! (Two negatives cancel each other out!)

So going down the list:

(-3)(-6) = positive (two negatives!)

(-3)(6) = negative (one negative, one positive!)

-(-3)(6) = positive (this is because you multiple left to right. because the negative is technically a -1 multiplying the -3, your -3 turns into a +3!)

(2)(3)(-6) = negative

(-2)(-3)(-6) = negative (remember, you multiply in the order of left to right! So multiplying the -2 and -3 gives you a positive. However, the -6 makes that positive number negative!)

(2)(-3)(-6) = positive

I hope this helps!

Inversely proportional graphs are reciprocal graphs consisting of one smooth curve in the first quadrant only.

When one quantity grows, the other quantity decreases, and vice versa, this is known as an inverse proportion. Indirect proportion is another name for inverse proportion.

Consider a task like painting a fence as an illustration. The amount of time it takes to complete the task lowers as the number of employees rises. The amount of time it takes to complete the task grows as the number of workers reduces.

If y  is inversely proportional to x then we write y = 1/x

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Answer:

the value of x is 61 degree because the base angles of an isosceles triangle are equal.

Step-by-step explanation:

Hope it helps you!!

When working with a normal distribution, you can use the z-score to determine how many standard deviations away from the mean a certain data point is.

Given that the average price for houses in the area is $280,000 and the standard deviation is $12,000, we can use the z-score formula to find the price of a house whose z-score is 2.5:

z = (x - mu) / sigma

where x is the price of the house, mu is the mean price of houses in the area, and sigma is the standard deviation of the price of houses in the area.

In this case, we are looking for the value of x, which is the price of a house whose z-score is 2.5, so we can rearrange the formula to solve for x:

x = (z * sigma) + mu

x = (2.5 * $12,000) + $280,000

x = $350,000

So the price of a house whose z-score is 2.5 is $350,000

It's worth noting that the value of Z-Score 2.5 is considered an outlier, it is usually very rare to find houses that far from the average and standard deviation.

The examples of horizontal symmetry is B, C, H, E.

The term horizontal symmetry is defined as is a line about which the object is symmetric.

Here we know that the symmetry line or horizontal axis of a shape which divides the shape into two identical halves is known as horizontal line of symmetry.

Which defines that  the axis here crosses across the shape to cut it into two equal parts.

Therefore, the English alphabets such as B, C, H, E, are the examples of horizontal symmetry.

In this case, here we have a horizontal line passing through the middle of the image and when the image is folded along this line, then we get the two halves overlapping and coinciding perfectly.

Therefore, this one is also an example for this could be a square or a rectangle or any other object that is symmetric horizontally.

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Answer:

-8 [tex]\leq[/tex] -8

Step-by-step explanation:

-8[tex]\leq[/tex]2-10

-8[tex]\leq[/tex]-8

Answer:

-8

Step-by-step explanation:

-8≤2-10
2-10 = -8
-8≤-8

Answer:

900π

Step-by-step explanation:

surface area of a sphere: 4πr²

=> 4 × π × 15²

=> 900π

Answer:

hexagonal based pyramid

E

7 faces

12 edges

7 vertex

13

15

Hope it helps :)