Compute the derivatives at the given value of a

The volume of water in liters the pool holds is 68.4 liters.

Given, we know that 12 buckets of water is needed to fill the swimming pool.

Pool surface area is calculated by multiplying length by breadth. The volume in cubic meters is calculated by multiplying that by the average depth. Due to the fact that there are 7.5 gallons in every cubic foot, you can convert your results to gallons to get the pool volume.

one bucket holds 1.5 gallons .

There are approximately 3.8 liters in 1 gallon.

Therefore, the volume of the swimming pool = ?

12 buckets holding how many gallons of water = each bucket containing 1.5 gallons × total number of buckets

= 1.5 × 12

= 18

Therefore, total volume of water in the swimming pool = total gallons of water × liters in one gallon

= 18  × 3.8

= 68.4 liters

Hence we get the total volume of the swimming pool as 68.4 liters.

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6 hundreds+ 30 ones = 630

630 + 2 tenths+ 4 hundredths + 6 thousandths=

Yes this shape belong in a group of shapes having more than one perpendicular sides.

As listed before, the most common shapes with perpendicular sides are squares and rectangles. Another common shape with perpendicular sides is the right triangle. It is called a right triangle because it has a right angle for one of its three angles, this is where the perpendicular sides meet.

Perpendicular is a very common term used in geometry. It helps to define shapes, understand angles, and calculate missing angles. Perpendicular means two lines, or sides, that meet at a right angle. A right angle is the measurement of 90 degrees. Perpendicular sides are very common in real-life situations like houses and storage. Any box, with rectangles on each side, has perpendicular sides. Most houses have perpendicular walls because they meet at a right angle with each other. Let's discover how important perpendicular sides are in everyday life.

Perpendicular sides are at a 90-degree angle. Since they are so common, there is a special symbol to signify the sides are perpendicular without measuring. This looks like a box in the corner angle. Any angle with this box symbol is exactly 90 degrees, not a degree more or less. Below is an image that shows a rectangle that has four perpendicular sides, labeled with the boxes in each corner, signifying that each angle is a right angle or 90 degrees.

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Answer:

26.5

Step-by-step explanation:

Answer:

9.92

Step-by-step explanation:

Hope this help you!!

The algebraic expression for the verbal phrase, "7 more than a number b" is translated as: b + 7.

A mathematical statement that is made up of operation signs (-, +), any variable (letters representing unknown quantity or number that varies), and numbers is referred to as an algebraic expression.

Algebraic expression are simplified or short form of translated phrases.

Let us represent the unknown number in the phrase as b.

"7 more than" means "+ 7".

Thus, the verbal phrase, "7 more than b" would be translated into an algebraic expression as:

b + 7.

Therefore, the algebraic expression for the verbal phrase, "7 more than a number b" is translated as: b + 7.

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that's, she pays $4.48 for eggs.. that simple means that orange is also the same amount of the egg,,,

$4.48×3=$13.44

i.e X=$13.44

The simplified value of the expression 5/6 - 7/2 - 5/3 is -13/3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

5/6-7/2-5/3

Convert the mixed fractions to improper fractions

So, we have

5/6 - 7/2 - 5/3

Evaluate the product of the numerators and the denominators in the above expression so that the denominators are the same

So, we have

5/6 - 7/2 - 5/3 = 5/6 - 21/6 - 10/6

Take the LCM of the denominators in the above expression

So, we have

5/6 - 7/2 - 5/3 = (5 - 21 - 10)/6

Evaluate the difference of the numerators in the above expression

So, we have

5/6 - 7/2 - 5/3 = -26/6

Simplify the above fraction

So, we have

5/6 - 7/2 - 5/3 = -13/3

Hence, the simplified value of the expression 5/6 - 7/2 - 5/3 is -13/3

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Answer:

(2) 21 years old

Step-by-step explanation:

Answer: 22.8571428571 hours

Step-by-step explanation:

Answer: 6%, .32, 1/2

Step-by-step explanation:

if you put all of them into decimals, you get

1/2=.50

.32=.32

6%=.06

Based on the mapping diagram shown, the function f(g(13)) is equal to 32.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

In Mathematics, there are different types of function and these include the following;

From the mapping diagram shown, g(13) is equal to 16 and f(g(13)) ⇒ f(16) would be equal to 32.

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Answer:

40m² + 57mn - 27n²

Step-by-step explanation:

(8m - 3n)(5m + 9n)

each term in the second factor is multiplied by each term in the first factor, that is

8m(5m + 9n) - 3n(5m + 9n) ← distribute both parenthesis

= 40m² + 72mn - 15mn - 27n² ← collect like terms

= 40m² + 57mn - 27n²

The correct answer is C. Exponential growth. As the function given f(x) = ½ • (5)ª is in exponential form, its range f(x) will increase for any input x.

The given function is defined as;

f(x) = ½ • (5)ª

As, the function is written in the exponent form or power form , its is said to be exponential function.

Now, for any increasing value of x, the value of function will also increase but with increasing difference.

Thus, the function is termed as the exponential growth function.

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Answer:

x=30 degrees

Step-by-step explanation:

both triangles are congruent therefor x will be the same as angle BAD

Hence , the rock will be 3 meters from ground level in 4.55 seconds.

It is given that  rock is thrown upward with a velocity of 12 meters per second from the top of a 50 meter high cliff, and it misses the cliff on the way back down.

Using newton's equation s = ut + 1 /2 at² + s₀

where v₀ is velocity and s₀ is the height above ground when thrown, then we have

Putting u = 12 , a = -g = - 9.8 m/s² , s = 3 , s₀ = 50

 3 = 12t + 1 / 2 (-9.8)t² + 50

 0 = 12t - 4.9t²+ 47

4.9t² -12t - 47 = 0

Putting a = 4.9 , b = -12 , c = -47 in quadratic formula , we get

    t = -(-12) ± √(-12)²-4(4.9)(-47) / 2(4.9)

      = 12 ± √144 + 921.2 /9.8

       = 12 ± √1065.2 /9.8

        = 12 ± 32.63/9.8

         = 44.63/9.8

          = 4.55 s

We will consider only positive value as time cannot be in negative

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According to the inequality, the number of the cells of the knives the need is a 10 cells.

According to the statement

We have to find that the inequality for the knives which are need to buy.

So, For this purpose, we know that the

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the given information:

Everyone is order some new supplies for the restaurant where he works the restaurant needs at least 587 knives there are currently 387 nice if it set on cell contains 20 knives

Then

Number of the knives they need = 587 knives

Number of the knives present = 387

Number of the knives they need = 587 - 387

Number of the knives they need = 200

Then

The cell contains knives = 20 knives

Then

The number of the cells they need = 200/20

The number of the cells they need = 10 cells.

If s is the number of the cells of the knife needs then inequality become

s > 10.

So, According to the inequality, the number of the cells of the knives the need is a 10 cells.

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Answer:

The total amount of the new coffee mixture would be:

8 + 12 = 20 (pounds)

The price of 20 pounds of coffee mixture would be:

8(9.2) + 12(5.5) = 139.6 (dollars).

Therefore, the average price would be:

139.6/20=6.98 (dollars).

Answer: $6.98 per pound.

The amounts of the three parts of the investment are $6000, $10000, and $18000.

The total amount invested = $34000

We know that the amount was split into three parts, let the parts be x, y, z

then, x + y + z = 34000 //Equation 1

interest of any part after a year = the amount of the part times it's interest

interest of first part after a year = x* 0.08 // 8% = 8 / 100 = 0.08

interest of second part after a year = y * 0.06

interest of third part after a year = z * 0.09

we know that the total interest earned by the total investment = $2700

i.e, 0.08x + 0.06y + 0.09z = 2700 // Equation 2

Guven that interest from the first investment was 4 times the interest from the second.

i.e, 0.08x = 4 * 0.06y

= x = 3y // substituting this relation in the above eauations

x + y + z = 34000 //Equation 1

3y + y + z = 34000

= 4y + z = 34000 //Equation 3

0.08x + 0.06y + 0.09z = 2700 // Equation 2

= 0.08(3y) + 0.06y + 0.09z = 2700

=0.3y + 0.09z = 2700 // simplyfying the equation by multiplying with 100

= 30y + 9z = 270000 // Equation 4

Solving 3 and 4 equations;

36y + 9z = 306000 //Equation 3 multiplied by 9 to make it simple to solve with equation 4

30y + 9z = 270000

6y = 36000

y = 36000 / 6 = 6000// second part of the investment

x = 3y = 3 * 6000 = 18000 // first part of the investment

z = 34000 - (x + y) // from equation 1

z = 34000 - 24000 = 10000 // third part of the investment.

Therefore, the amounts of the three parts of the investment are $6000, $10000, and $18000.

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Based on the cost of 1kg packets of chicken, it will not be possible for Mandy to buy 4 packets of 1 kg chicken.

The cost of a single packet of 1kg chicken is R40.

This means that the cost of 4 packets of 1kg chicken is:

= 40 x 4

= R160

Mandy only has R140 which means that Mandy won't have enough to buy 4 packets of chicken. The amount remaining would be:

= 160 - 140

= R20

In conclusion, it will not be possible for Mandy to buy the chicken packets.

Missing part of question:
The cost of 1kg packets of chicken is R40 per packet.

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Answer:

28.30282671

Step-by-step explanation:

Step 1: Find the mean.

Step 2: For each data point, find the square of its distance to the mean.

Step 3: Sum the values from Step 2.

Step 4: Divide by the number of data points.

Step 5: Take the square root.

Answer:

Step-by-step explanation:

500-250= 250

there for its half off 50% because its split down the middle, so thats an easy one

The area covered by region 1 is 16 units and that by region 2 is 15 units.

Given the area of a square be 1unit.

So. the number of block completely covered = a

number of block that are coverered approximately half = b .

So, total area covered = 1*a + 0.5 * b

for figure 1.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 8.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 8

= 12 + 4

= 16units

for figure 2.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 6.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 6

= 12 + 3

= 15units

Therefore, the area covered in region 1 is 16 unit and the area covered in region 2 is 15 unit.

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The area covered by region 1 is 16 units and that by region 2 is 15 units.

Given the area of a square be 1unit.

So. the number of block completely covered = a

number of block that are coverered approximately half = b .

So, total area covered = 1*a + 0.5 * b

for figure 1.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 8.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 8

= 12 + 4

= 16units

for figure 2.)

the number of block completely covered = a = 12

number of block that are coverered approximately half = b = 6.

Therefore Total area covered = 1*a + 0.5 * b

= 1*12 + 0.5 * 6

= 12 + 3

= 15units

Therefore, the area covered in region 1 is 16 unit and the area covered in region 2 is 15 unit.

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Answer: A

Step by step explanation:

Answer:The answer is the first one multiply both sides of the equation by -1/3

Step-by-step explanation:please give brainliest.

The no. of ounce of  spearmint tea is = 60.50 ounce

the no. of ounce of  peppermint tea is =  32.49 ounce

We have been given that -

Cost of  spearmint tea = $3.15

Cost of  peppermint tea = $5.01

Cost of the mixture =  $3.80

solution-

Let the quantity of spearmint tea =  x ounce

and the quantity of peppermint tea =  y ounce

1 ounce quantity contains  spearmint tea and peppermint tea =

(x+y=1) ......eq (1)

the cost

($3.15)x +($5.01)y =  $3.80

3.15x + 5.01y = 3.80......... eq(2)

multiply equation (1) with 3.15.

∴ 3.15x +3.15y =3.15

using alligation..

Alligation: It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.

substract equation (1) and equation (2)

(3.15x + 5.01y = 3.80) -(3.15x +3.15y =3.15)

After solve the equations we get

1.86y = o.65

   y = 0.65/1.86

  y = 0.349462... per ounce

put the value of y in equation (1)

x +y= 1

x = 1-y

x = 1-0.349462

x = 0.650538 per ounce

So the quantity of spearmint tea =  93 ×x per ounce

                                                    93 ×0.650538

                                                     60.50 ounce

and the quantity of peppermint tea = 93×y per ounce

                                                             93× 0.349462

                                                             32.49 ounce

hence, the no. of ounce of  spearmint tea is = 60.50 ounce

           the no. of ounce of  peppermint tea is =  32.49 ounce

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The required grade resistance of car to the uphill movement is -2.9 degrees.

A 3000Lb Car traveling uphill has a grade resistance of -110 pounds. with the help of a  tangent function to estimate the angle of the grade.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
Weight of car = 3000 Lb
grade of resistance = -110
Now,
Angle of the grade = tan⁻¹(-110 / 3000)
The angle of the grade =  tan⁻¹(-0.05)
The angle of the grade = -2.9

Thus, the required grade resistance of the car to the uphill movement is -2.9 degrees.

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The y values or the range of the function are as follows;

The function is expressed as follows;

y = 1 / 2 x + 3

The domain of a function is the input of a function. They are the independent value of a function

Therefore, the domain of the function is as follows;

Therefore, the range, which is the y values or the output can be found as follows;

when x = 4

y = 1 / 2(4) + 3

y = 5

when x = 6

y = 1 / 2(6) + 3

y = 6

when x = 9

y = 1 / 2(9) + 3

y = 7.5

when x = 11

y = 1 / 2(11) + 3

y = 8.5

Hence, the y values or the range of the function are as follows;

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