Experimental and theoretical see pic

The discount rate is 15% and the VAT rate is 13%

The following can be deduced:

MP = 2080

Discount = d%

VAT = (d-2)%

Cost = 1997.84

Apply discount:

2080 - d% = 2080*(1 - 0.01d)

Add VAT:

2080*(1 - 0.01d) + (d - 2)%

2080*(1 - 0.01d) * (1 + (d -2)/100)

2080*(1 - 0.01d) * (0.98 + 0.01d)

= 1997.84

(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080

0.98 + 0.01d - 0.0098d - 0.0001d²

= 0.9605

- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0

0.0001d²- 0.0002d - 0.0195 = 0

d² - 2d + 195 = 0

Solving the quadratic equation we get:

d = 15

Therefore discount is 15%

VAT rate = d - 2 = 15% - 2% = 13%

The concept shown above is the calculation for the discount and the amount of the value added tax.

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Answer:

Step-by-step explanation:

y = 1.416x − 0.76

For (7, 8):

residual value = Measured value - Predicted value

residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)

When x = 7:

value of y from the equation, y1 = 1.416*7 - 0.76

                                                  y1 = 9.912 - 0.76

actual y-coordinate of the point, y2 = 8

From:

residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)

residual value = y2 - y1

residual value = 8 - 9.152

Answer:

A: -1.152

Step-by-step explanation:

I did it and it was right!

Three decimal that sum of 114.056 is 52.2+34.15+28.5.

What is decimal?

decimal is a term that describes the base-10 number system, probably of the most commonly used the  number system. The decimal number system of  consists of ten single-digit numbers.

We will represent this as 1.5 pizzas in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case "1," represents one whole pizza, and the number after the decimal point, or the fractional part, represents the other half of the pizza. You may have seen decimal numbers similar to these while grocery shopping, on a scale, or even during a baseball game.

Sol- we have to add three decimal that have a sum of 114.056 no parts are given here.

Let's take

X+Y+Z = 114.056

We need to add any particular number here

Let's put 52+34+28

Still we need .056 extra

So we have to add points here

52.2+34.15+28.5

So these are 3 decimal point.

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The person must buy 10 gumballs so that she gets 4 gumballs that are the same color.

Given, gumball machine contains 9 red gumballs

7 white gumballs and

8 blue gumballs.

we are asked to determine the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.

If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.

Hence 10 gumballs should be purchased.

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Answer:

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Explanation:

To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.

Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so

r² = 537/1986

r² = 0.2704

r = √0.2704

r = 0.52

Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so

For 1 hour

Amount left = 1986(0.52) = 1032.7 grams

In the same way, the amount left after 3 and 4 hours is

For 3 hours

Amount left = 537(0.52) = 279.2 grams

For 4 hours

Amount left = 279.2(0.52) = 145.2 grams

Therefore, the complete table is

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Answer: 1 dollar per bottle

Step-by-step explanation:

       If they cost $20 and she bought 20 bottles, we can use division.

$20 / 20 bottles = 1 dollar per bottle

[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.

Given:

[tex]f(x) = 1048 - 16x^{2}[/tex]

Since the function f(x) is the height (h), we can write the function as :

[tex]h = 1048 - 16x^{2}[/tex]

We will make x the subject:

[tex]16x^{2} = 1048 - h[/tex]

[tex]x^{2} = \frac{1048 - h}{16}[/tex]

[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]

[tex]x = \sqrt{65.5 - 0.0625h }[/tex]

Since:

[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]

Thus:

[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]

Therefore, the inverse function is  [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.

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Answer:

c = 23

Step-by-step explanation:

To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.

(2c + 51)° = 97°

Next, you want to subtract 51 from both sides.

(2c + 51) - 51 = 97 - 51

2c = 46

Lastly, you isolate c by dividing 46 by 2.

c = 46 ÷ 2

c = 23

SOLUTION:

Step 1:

In this question, we have the following:

Step 2:

Part A:

The function that models the population of Star, ID in years since 2000 is:

Part B :

Use your function to predict the population of Star, ID in 2050

The year 2050 means that t= 50, we have that:

Part C:

The function:

models the population of Eagle, ID in years (x) since 2000.

Which city is growing faster? How do you know?

Answer:

From this equation, we can see that the growth rate is 5.6% annually.

Comparing this, with the initial function:

We can see that the annual growth rate of f(x) is 9.9 %

CONCLUSION:

The population of Star ID, with the function, g (x) has a faster growth rate.



Answer:

(you got it right, not quite sure why it isn't there though!)

Step-by-step explanation:

remember PEMDAS

parentheses first

(8g+5) but we can't add them up since they not like terms

now we go from left to right (since we have Multiplication first and then Addition)

distribute the 4 to the (8g+5)

which makes it 32g +20

now we go back to the equation,

32g +20 + 6

are there any like terms we can combine?

yes, the 20 and the 6

20+6=26

leaving us with

Given that the numbered disks are placed in a box, you need to find the probability of selecting an odd number, given that a green disk is selected.

Therefore, you need to use the Conditional Probability Formula:

In this case, let be "A" the event of selecting an odd number, and "B" the event of selecting a green disk.

You can identify that:

- There are a total of 8 disks.

- There are 4 green disks that have odd numbers.

- There are a total of 7 green disks.

Therefore, you can determine that:

And:

Then, you can substitute values into the formula and evaluate:

Hence, the answer is:

Answer:

BIDMAS is a math term that is used to describe these 6 terms.

Brackets

Indices, which is another word for exponents

Division

Multiplication

Addition

Subtraction

Answer:

It is the order of operation in order to know how to calculate an equation starting from which order.

Step-by-step explanation:

Brackets first

Indices second

Division and multipaction third. From left to right

Addition and subtraction last. From left to right

The coat has a total cost of  $533.644

From the question, the given parameters are:

Cost of a coat = $74.95

Sales tax in the city = 612%

Using the sales tax, the total cost for the coat is calculated using

Total cost of coat = Cost of a coat + Cost of a coat * Sales tax in the city

Substitute the known values in the above equation

So, we have the following equation

Total cost of coat = 74.95 + 74.95 * 612%

Evaluate the products

Total cost of coat = 74.95 + 458.694

Evaluate the sum

Total cost of coat = 533.644

Hence, the total cost of the coat is $533.644

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Answer: x = -4

Step-by-step explanation:

Multiply both sides by 2 to get:

-3x = 12

Then, divide both sides by -3 to get:

x = -4

Hope this helps!

Answer:

x = -4

Step-by-step explanation:

Using the concept of area, we got 165 bags is the smallest number of bags there groundskeeper must buy to cover the circular field.

The branch of mathematics which deals with measuring is known as Mensuration. It was basically first used for land surveys and other civic works in  Egypt. The father of mensuration is known as Archimedes. Mensuration is a discipline of mathematics which studies the measurements of various geometrical forms  possible and their areas, perimeters, and volumes, among other things.

Diameter of the field = 290 feet, radius = 145 feet

Area of the circular field =[tex]\pi r^{2}[/tex]

=>[tex]\pi[/tex]×145×145 =66018.5 square feet.

No of bags to be brought = 66018.5/400=165bags,

Hence, the smallest number of bags is 165 which groundskeeper must buy to cover the circular field.

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Step 1

Given

Required: To arrange them from smallest to largest.

Note: 0.5 = 1/2

Step 2

Find the lowest common multiple of the numbers in the denominator : 3,8,2 and 5

Hence, the lowest common multiple will be

Step 3

Use the LCM to arrange the numbers as seen below

From the numbers gotten from using the LCM, we can now conclude

Step 4

Arrange them from smallest to largest

We can arrange them as follows

The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].

What is probability?

Probability is defined as the possibility of an event to occur.

An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]

Thus probability of success will be [tex]p=0.98[/tex]

So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]

To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.

Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]

Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].

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Answer: Length = 10√2

Step-by-step explanation: You have to use the pythagorean theorem

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional.

Occurrence to determine the conditional probability. P(A and B) = P(A) * P if A and B are two Independent events (B).

How can you calculate the likelihood of two occurrences, A and B, coming together?

The probability of their union, or the event that either A or B occurs, is equal to the total of their probabilities less the sum of their intersection if two occurrences A and B are not disjoint. P(A) + P(B) - P(A and B) (A and B).

The answer is then (0.28 + P(B) - (0.51 = 0.23).

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Answer:

10 1/2 as an improper fraction is [tex]\frac{21}{2}[/tex]

the reciprocal of 10 1/2 is [tex]\frac{2}{21}[/tex]

so [tex]\frac{21}{2} * \frac{2}{21} = 1[/tex]

below is an image of the rest of the answers

Answer

Option D is correct.

Midpoint = (2, 1)

Explanation

The midpoint of two coordinates is obtained by respective x-coordinates together and dividing by 2 and then doing similarly for the y-coordinate.

(-4, -8) and (8, 10)

Midpoint = (x, y)

x = (-4 + 8)/2 = (4/2) = 2

y = (-8 + 10)/2 = (2/2) = 1

Hope this Helps!!!

Answer:

realto, hindi ako sure eh

Step-by-step explanation:

tama yan

The distance between the two cities on the map is 0.45 inches , the correct  option is (A) 0.45inches  .

In the question ,
it is given that

the scale factor of the  map is 25 miles = 0.1 inches

So, 1 mile = 0.1/25 inches

= 0.004 inches

So , on the map 1 mile is represented by 0.004 inches

Given that the real distance between the two cities is 112.5 miles

So , on the map  112.5 miles = 112.5*0.004 inches

= 0.45 inches

Therefore , the distance between the two cities on the map is 0.45 inches , the correct  option is (A)0.45inches  .

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Using proportions, it is found that:

42. x and y are not proportional.

43. The number 21 is 60% of 35.

44. The number 27 is 36% of the number 75.

Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.

From the table, the ratios are given as follows:

Different ratios, hence the variables x and y are not proportional.

To find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.

The decimal equivalent of a percentage of 60% is:

60/100 = 0.6.

Hence the percentage of 35 is calculated as follows:

0.6 x 35 = 21.

The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:

27/75 x 100% = 36%.

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The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].

The given expression is [tex](4^{-2})^3[/tex].

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

The given expression can be simplified as follows

[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]

So, the positive exponent = [tex]\frac{1}{4^6}[/tex]

Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].

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There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.

The equation of a perpendicular line to a line in point-slope form is expressed as:

Determine the slope:

Since there is no slope, hence the equation of the line will be in the form y = b.

Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.

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Correct question:

2) Choose the correct answer.

A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).

(A) y = 5

(B) x = -1

(C) x=5

(D) y= -1/2x + 13/3

(E) y = -1

Answer: It will take just 1 hour & 36 minutes with 4 large pumps & 4 small pumps

Step-by-step explanation:

60 milligrams of medication A should be used this week

Given:

Last week, 130 milligrams of Medication A was mixed with 117 milligrams of Medication B

This week, 54 milligrams of medication B was used

To find:

the milligrams for medication A used this week

To determine the milligrams of medication A used, we will apply the ratio of medication A to B

Last week:

A : B = 130 : 117

This week:

A : B = A : 54

Hence, 60 milligrams of medication A should be used this week

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

i got it right on the exam!