Enlarge the picture below by a scale factor of 3.

The derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).

What is a derivative?

A derivative is a mathematical concept used in calculus to determine the rate at which a function changes with respect to its input variable. It measures the instantaneous rate of change of the function at a specific point, and is calculated as the limit of the rate of change as the input variable approaches zero. The derivative is represented by the notation f'(x) or dy/dx, and can be used to find important information about the function, such as its slope, maxima and minima, and points of inflection.

What are expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are combined in some way using mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

To find the derivative of f(x) = √[9x - sin²(2x)], we can use the chain rule and the power rule of differentiation:

f(x) = √[9x - sin²(2x)]

f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))

Using the chain rule, we first take the derivative of the expression inside the square root, which is 9x - sin²(2x), and then multiply it by the derivative of the expression inside the square root. The derivative of the expression inside the square root is:

(1/2)(9x - sin²(2x))^(-1/2) * (d/dx)(9x - sin²(2x))

Using the chain rule and the power rule of differentiation, we can find the derivative of 9x - sin²(2x) as:

d/dx (9x - sin²(2x)) = 9 - 4sin(2x)cos(2x)

Substituting this into the expression for f'(x), we get:

f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))

So, the derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).

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The derivative of f(x) is: f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))].

Differentiation is a mathematical concept used to calculate the rate at which one quantity changes with respect to another. In calculus, it refers to the process of finding the derivative of a function, which gives the slope of the tangent line at any point on the function.

In the given question,

To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.

f(x) = √[9x - sin²(2x)]

Let's first simplify the expression under the square root:

g(x) = 9x - sin²(2x)

Taking the derivative of g(x) gives:

g'(x) = 9 - 2sin(2x) * cos(2x) * 2

g'(x) = 9 - 4sin(2x)cos(2x)

Now we can use the chain rule to find f'(x):

f'(x) = [1/2(9x - sin²(2x))^(-1/2)] * g'(x)

f'(x) = [1/2√(9x - sin²(2x))] * [9 - 4sin(2x)cos(2x)]

Therefore, the derivative of f(x) is:

f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))]

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If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted. For example, if the numbers he has sorted are 9, 5, and 3, then the next number would be 1.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is a computer algorithm that sorts a list, typically of numbers, words, or other items, into increasing or decreasing order. It is often used to arrange data so that it can be more easily analyzed or used in other applications. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order. Sorting algorithms are used in many areas of computing, including data structures, artificial intelligence, databases, and programming languages.

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The numbers on teddy bears are sorted as 656, 666, 676, 686. The pattern rule is adding 10 so, the next number will be 696.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is often used to arrange data so that it can be more easily analyzed or used in other calculation. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order.

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted.

The numbers on teddy bears are sorted as 656, 666, 676, 686.

Now, observe the pattern.

656 + 10 = 666

666 + 10 = 676

676 + 10 = 686

This indicates that the pattern rule is "adding 10", which means the next number in series is:

686 + 10 = 696

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The complete question is as follows:

The prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.

PrοbabiIity is a measure οf the IikeIihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, with 0 indicating impοssibiIity and 1 indicating certainty. It is used in variοus fieIds such as mathematics, statistics, science, ecοnοmics, and finance.

The prοbabiIity οf getting the true/faIse questiοn cοrrect is 1/2 οr 0.5. The prοbabiIity οf getting the muItipIe-chοice questiοn cοrrect is 1/4 οr 0.25. The prοbabiIity οf getting the Iast questiοn cοrrect is 1/2 οr 0.5.

Tο find the prοbabiIity οf getting aII 3 answers cοrrect, we muItipIy the prοbabiIities οf getting each questiοn cοrrect:

0.5 * 0.25 * 0.5 = 0.0625

Sο the prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.

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Accοrding tο the standard nοrmal distributiοn, the prοbability that z is greater than -0.25 is 0.5987.

Nοrmal distributiοn, alsο knοwn as Gaussian distributiοn οr bell curve, is a prοbability distributiοn that describes the randοm variatiοn οf a cοntinuοus variable in a pοpulatiοn. In a standard nοrmal distributiοn, the mean is 0 and the standard deviatiοn is 1, and the curve is fully described by the parameters οf mean and standard deviatiοn. The nοrmal distributiοn is used in many statistical applicatiοns tο mοdel and analyze cοntinuοus data.

Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the area tο the right οf z=-0.25 is apprοximately 0.5987.

Therefοre,

[tex]$$P(z > -0.25) = 1 - P(z \leq -0.25) = 1 - 0.4013 = 0.5987$$[/tex]

Sο the prοbability that z is greater than -0.25 is 0.5987.

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Complete Question

Find P(Z > 0.25), using the standard normal distribution. The average number of calories in a 1.5-ounce chocolate bar is 250. Suppose that the distribution of calories is approximately normal with standard deviation 10. Find the probability that a randomly selected chocolate bar will have between 230 and 260 calories. A single die is rolled 5 times. Find the probability of getting at least one number which is greater than 4. Given data values: 11, 3, 5, 12, 17, 13, 10, 6, 8, 21, 14, 20, 9, 15, 7. (a) Find the percentile rank for 10. (b) What value corresponds to the 70th percentile? A survey found that the American family rates an average of 25 pounds of glass garbage each year. Assume the standard deviation of the distribution is 7pounds. Find the probability that the mean of a sample of 49 families will be between 19 and 26 pounds.

Hence, 160 mL of oxygen is contained inside a 200 mL air tank using the same ratio as a 500 mL air tank.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were trying to compare one piece of data (A) to some other data point (B). We are multiplying information A by data B, as this suggests. In the event that A and B are both 5, for example, your ratio would've been 5/10.

80% of 500 mL of oxygen if indeed the air tank contains 80% oxygen & 20% nitrogen, which is:

0.80 x 500 mL = 400 mL

This means that the air tank contains 400 mL of oxygen and 100 mL of nitrogen.

To find the amount of oxygen in a 200 mL air tank that contains the same ratio, we need to use proportions:

If 500 mL contains 400 mL of oxygen, then 1 mL contains 400/500 = 0.8 mL of oxygen.

Therefore, if 200 mL contains the same ratio of oxygen, it will contain:

0.8 mL x 200 mL = 160 mL

So, the amount of oxygen in a 200 mL air tank with the same ratio as the 500 mL air tank is 160 mL.

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Answer:

To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:

(a+bx)(c+d) = (c+dx)(a+b)

Expanding the terms on both sides:

ac + adx + bc + bdx^2 = ac + abx + cdx + bd

Simplifying and rearranging the terms:

adx + bdx^2 - abx - cdx = bd - ac

dx(ad - ab - c) = bd - ac

Now, since we know that cb=ad, we can substitute ad=cb into the equation:

dx(cb - ab - c) = bd - ac

dx(cb - ab - c) = b(cd - ac)

x = b(cd - ac)/(d(cb - ab - c))

Therefore, the solution for x is:

x = b(cd - ac)/(d(cb - ab - c))

The fraction that is equivalent to 5/7 is 15/21

It is important to note that fractions are simply described as part of a whole number or element.

Also, equivalent expressions are defined as expressions that have the same solution but differ in the mode of arrangement of the values.

From the information given, we have;

The numerator be x

The denominator is 9 less than twice the numerator

This is represented as;

x/2x - 9 = 5/7

Cross multiply the values, we have;

7(x) = 5(2x - 9)

expand the bracket

7x = 10x - 45

collect the like terms, we have;

7x - 10x = -45

-3x = -45

Make 'x' the subject

x = 15

Then, the fraction = 15/21

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Answer:

[tex]\textsf{1.}\quad \sf \overline{AZ} = 28 \; meters[/tex]

[tex]\textsf{2.}\quad \sf \overline{AM} = 28 \; meters[/tex]

[tex]\textsf{3.}\quad b = \sf 4[/tex]

[tex]\textsf{4.}\quad \sf Perimeter = 112\; meters[/tex]

[tex]\textsf{5.}\quad \sf \overline{MX} = 22\; meters[/tex]

[tex]\textsf{6.}\quad \sf \overline{AX} = 10\sqrt{3}\; meters[/tex]

[tex]\textsf{7.}\quad \sf \overline{EX} = 10\sqrt{3}\; meters[/tex]

[tex]\textsf{8.}\quad \sf \overline{AE} = 20\sqrt{3}\; meters[/tex]

Step-by-step explanation:

All sides of a rhombus are the same length. Therefore, for rhombus MAZE:

[tex]\sf \overline{AZ} = \overline{AM} = \overline{ZE} = \overline{EM}[/tex]

Given:

As the sides of a rhombus are the same length, we can equate the expressions for sides AZ and AM, and solve for b:

[tex]\begin{aligned}\overline{\sf AZ}&=\overline{\sf AM}\\8b-4&=5b+8\\8b-4-5b&=5b+8-5b\\3b-4&=8\\3b-4+4&=8+4\\3b&=12\\3b \div 3&=12 \div 3\\b&=4\end{aligned}[/tex]

Therefore, the value of b is 4.

To find the length of AZ and AM, substitute the found value of b into one of the expressions:

[tex]\begin{aligned}\overline{\sf AZ}&=8b-4\\&=8(4)-4\\&=32-4\\&=28\end{aligned}[/tex]

Therefore, as AZ = AM, then AZ = 28 and AM = 28.

[tex]\hrulefill[/tex]

As the sides of a rhombus are equal in length, each side length is 28 meters (as found previously).

The perimeter of rhombus MAZE is the sum of its side lengths. Therefore:

[tex]\begin{aligned}\sf Perimeter\;MAZE&=\sf \overline{AZ} +\overline{AM} +\overline{ZE}+ \overline{EM}\\&=28+28+28+28\\&=112\; \sf meters\end{aligned}[/tex]

Therefore, the perimeter of rhombus MAZE is 112 meters.

[tex]\hrulefill[/tex]

The point of intersection of the diagonals of rhombus MAZE is point X.

As the diagonals of a rhombus are perpendicular bisectors of each other, then:

[tex]\sf \overline{AX}=\overline{EX}\quad and \quad \overline{AX}+\overline{EX}=\overline{AE}[/tex]

[tex]\sf\overline{MX}=\overline{ZX}\quad and \quad\overline{MX}+\overline{ZX}=\overline{MZ}[/tex]

Given MZ = 44 meters, and MX is half of MZ, then:

[tex]\sf \overline{MX}=\overline{ZX}=22\;meters[/tex]

As the diagonals bisect each other at 90°, m∠MXA= 90°. Therefore, ΔMXA is a right triangle with hypotenuse AM = 28 and leg MX = 22.

As we know the lengths hypotenuse AM and leg MX, we can use Pythagoras Theorem to calculate the length of the other leg, AX:

[tex]\begin{aligned}\sf \overline{AX}^2+\overline{MX}^2&=\sf \overline{AM}^2\\\sf \overline{AX}^2+22^2&=\sf 28^2\\\sf \overline{AX}^2&=\sf 28^2-22^2\\\sf \overline{AX}&=\sqrt{\sf 28^2-22^2}\\\sf \overline{AX}&=\sf 10\sqrt{3}\; meters\end{aligned}[/tex]

As the diagonals bisect each other, AX = EX. Therefore:

[tex]\sf \overline{EX}=\sf 10\sqrt{3}\; meters[/tex]

The length of diagonal AE is the sum of segments AX and EX. Therefore:

[tex]\begin{aligned}\sf \overline{AE}&=\sf \overline{AX}+\overline{EX}\\&=\sf 10\sqrt{3}+10\sqrt{3}\\&=\sf 20\sqrt{3}\; meters\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Note: The attached diagram is drawn to scale.

Okay, just think of dilations as scaling the object bigger or smaller. You are just multiplying all points on the shape by a common scalar.

The only other thing is a negative dilation reflects the shape over the origin (which is quite intuitive cause you negate all the coordinates).

Now for question 1 your just trying to find the scale factor given an original point and a dilated point. Since all points are multiplied by the same factor,

(-3,6)x = (-4,8)

x=4/3

For the second question, just check points to see if all follow the same dilation scale factor. For our purposes it suffices to just check the each vertex.

(1,1) -> (2,2) so the scale factor must be 2

(1,4) -> (2,8) good

(5,1) -> (10,2) good

(5,4) -> (10,8) good

So, this transformation describes a dilation. The scale factor is 2.

The radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC

Since the line AB is tangent to the circle at point B, then the triangle ABC is a right triangle and the Pythagoras rule can be applied as follows:

(50 + r)² = r² + 80²

r² = (50 + r)² - 80²

r² = (50 + r - 80)(50 + r + 80) {difference of two square}

r² = (r - 30)(r + 130)

r² = r² + 130r - 30r - 3900 {expansion of brackets}

r² - r² + 130r - 30r = 3900 {collect like terms}

100r = 3900

r = 3900/100 {divide through by 100}

r = 39

Therefore, the radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC.

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It took Rapunzel approximately 14.58 minutes to clean her room.

Cleaning refers to the process of removing dirt, dust, and other unwanted substances from a surface or an object.  

Let's start by converting the time to minutes.

15 1/2 minutes = 15.5 minutes

Let's now subtract the time she finished cleaning from the time she started cleaning:

15.5 - 0.92 = 14.58 minutes

Therefore, it took Rapunzel approximately 14.58 minutes to clean her room.

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An equation to represent relationship of the weights shown on the scale include the following: 22 + x = 34.

Based on the information provided about the weights on this balanced scale, we can logically deduce the following parameters;

Each small square = 1 unit.

Each larger square = 10 units.

The variable x represent the weight of the triangle.

Since there are four small squares and three large squares each labeled ten on one side of this balanced scale, we have:

Total weight = 4(1) + 3(10)

Total weight = 34 units.

Similarly, there are two small squares, two large squares, and a triangle labeled x on the other side of this balanced scale, we have:

Total weight = 2(1) + 2(10) + x

Total weight = 22 + x

By equating the two equations, we have:

22 + x = 34

x = 34 - 22

x = 12

In conclusion, there are 34 units on each side of this balanced scale.

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The first thing we must do for this case is to find the surface area of the rectangular prism.

We have then:

[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]

Where,

w: width

l: long

h: height

Substituting values we have:

[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]

[tex]A = 448 \ in ^ 2[/tex]

Answer:

the least amount of wrapping paper needed to wrap the gift box answer is:

A = 448 in²

Answer:

3x² -2xy + 4y² at x = -1, y = -2  = 15

Step-by-step explanation:

Given function is

f(x, y) = 3x² -2xy + 4y²

To find At x = - 1 and y - 2 just plug these values for x and y into f(x, y)

f(-1, -2) = 3(-1)² - 2(-1)(-2) + 4(-2)²

(-1)² = 1 ==>   3x²  = 3(-1)² = 3 x 1 = 3

(-1) (-2) = 2   ==>   2xy = 2(-1)(-2) = 2 x 2 = 4

(-2)² = 4  ==> 4y² = 4 (-2)² = 4 x 4 = 16

f(-1 1, - 2) = 3x² -2xy + 4y²
= 3 - 4 + 16

= 15

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Gracie's statement is not necessarily correct about the tens digit in a dividend is less than the divisor and the divisor has one digit. Gracie says the quotient must have a 0 in the tens place.

What is dividend?

In mathematics, a dividend is the number that is being divided in a division problem. For example, in the division problem 18 ÷ 3 = 6, 18 is the dividend.

Gracie's statement is not necessarily correct. Let's look at a couple of examples to see why.

Example 1:

Dividend = 25

Divisor = 4

In this case, the tens digit of the dividend (2) is less than the divisor (4). The quotient is 6 with a remainder of 1. There is no 0 in the quotient, so Gracie's statement is incorrect.

Example 2:

Dividend = 35

Divisor = 4

In this case, the tens digit of the dividend (3) is also less than the divisor (4). The quotient is 8 with a remainder of 3. Again, there is no 0 in the quotient, so Gracie's statement is still incorrect.

From these examples, we can see that Gracie's statement is not always true. It is possible for the tens digit of the dividend to be less than the divisor, and for the quotient to not have a 0 in the tens place.

The only time Gracie's statement would be true is if the remainder is 0 after dividing the dividend by the divisor. In that case, the quotient would indeed have a 0 in the tens place. However, this is not always the case.

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Answer: LN = 15

Make a proportional relationship:

[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]

Insert the values:

[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]

cross multiply:

[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]

Simplify:

The value of x in the rectangle is 36.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.

Therefore, let's find the value of x in the angles.

Hence,

∠2 = x + 30

∠5 = 2x - 48

Therefore,

∠2 + ∠5 = 90°

x + 30 + 2x - 48 = 90

3x - 18 = 90

3x = 90 + 18

3x = 108

divide both sides by 3

x = 108 / 3

x = 36

Therefore,

x = 36

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The volume of the solid is (64/3)√3 cubic units, which is answer choice B.

A circle is a geometric shape in a two-dimensional plane, consisting of all the points that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Circles have many real-world applications, such as in the design of wheels, gears, and other rotating objects. They are also important in mathematics and science, as they provide a simple and elegant way to study and understand the properties of curves and curved surfaces.

We can approach this problem by considering a vertical slice of the solid taken perpendicular to the y-axis. This slice will be an equilateral triangle with a side length that depends on the y-coordinate.

At y = 0, the circle x² + y² = 16 intersects the x-axis at x = ±4. This means that the equilateral triangle at y = 0 has side length 2√3 times the distance from the origin to the x-axis, which is 4√3. Therefore, the area of this triangle is:

A(0) = (√3/4) (4√3)² = 12√3

At a general y-coordinate y > 0, the equilateral triangle will have side length equal to the distance between the points where the circle intersects the line y = k, where k is the y-coordinate. This distance can be found using the Pythagorean theorem:

d = √(16 - k²) - √k² = √(16 - 2k²)

The area of the equilateral triangle at y is then:

A(y) = (√3/4) d² = (√3/4) (16 - 2k²)

To find the volume of the solid, we can integrate the cross-sectional areas with respect to y from 0 to 4, using the formula for the area of an equilateral triangle:

V = ∫(0 to 4) A(y) dy = ∫(0 to 4) (√3/4) (16 - 2k²) dy

= (√3/4) (16y - (2/3) y³)|0 to 4

= (√3/4) [(64 - (2/3)(64)) - (0 - 0)]

= (64/3)√3

Therefore, the volume of the solid is (64/3)√3 cubic units, which is answer choice B.

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Answer:

6 units the answer is C. just see it

Answer:

D) 115.2π cm².

Step-by-step explanation:

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

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:

Surface Area = 2π(4)² + 2π(4)(10.4)

Surface Area = 2π(16) + 2π(41.6)

Surface Area = 32π + 83.2π

Surface Area = 115.2π

Therefore, the exact surface area of the candle is 115.2π cm².

The answer is (D) 115.2π cm².

Answer: The answer is D, 115.2π cm²

Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91

We can divide this by pi to get 115.2π cm²

Hope this helped!

The missing angles in the diagram are: Angle ABD = 60 degrees, Angle BDC = 120 degrees, Angle ACD = 60 degrees, and Angle ADC = 120 degrees.

To find the measure of the missing angles, we can use the fact that the sum of the angles in a triangle is 180 degrees, and the sum of the angles around a point is 360 degrees.

Let x be the measure of angle ABD.

Therefore, angle BDC has measure 180 - x degrees.

Similarly, angle ACD and angle ADC form a straight line, so their measures sum to 180 degrees. Therefore, angle ADC has measure 180 - 60 = 120 degrees.

Finally, since angle BCD and angle ADC form a straight line, their measures sum to 180 degrees. Therefore, angle BCD has measure 180 - 120 = 60 degrees.

Let y be the measure of angle CFE.

Similarly, angle DEF and angle CDF form a straight line, so their measures sum to 180 degrees. Therefore, angle DEF has measure 180 - 75 = 105 degrees.

Finally, since angle CDE and angle DEF form a straight line, their measures sum to 180 degrees. Therefore, angle CDE has measure 180 - 105 = 75 degrees.

Therefore, the missing angles have measures of 60 degrees and 75 degrees for the left and right triangles.

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find the measure of missing angles?

The sentence represented as an algebraic expression is x² - 1

Algebraic expressions can be defined as a mathematical expression that consists of terms, variables, constants, coefficients and fractions.

Also, these algebraic expressions are identified with arithmetic or mathematical operations. These operations are;

From the information given, we have that;

Let the number be x

If 1 is then subtracted from the square of a number.

Fiirst, the square of the number is x²

This is represented as;

x² - 1

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The amount and the compound interest on a sum of Rs. 62500 are Rs. 65625 and Rs. 3125, respectively.

Given:

Principal amount (P) = Rs. 62500

Rate of interest (R) = 5%

Time period (t) = 1 year

Interest is compounded yearly.

Formula for calculating compound interest is given as:

A = P(1 + R/100)ᵗ

where A is the amount.

Using this formula, we can find the amount (A) after one year:

A = 62500(1 + 5/100)¹

A = 65625

Therefore, the amount after one year is Rs. 65625.

To find the compound interest, we can subtract the principal from the amount:

Compound Interest = A - P

= 65625 - 62500

= 3125

Therefore, the compound interest is Rs. 3125.

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Using simple interest his monthly installments are $1243.38

The amount on Simple interest is given by A = P(1 + rt) where

Now, since Justin purchased his dream car worth $18500 on a finance for 4 years. He was offered 6% interest rate. Assuming no other charges and no tax, we want to find his monthly installments.

His installments are his principal. so, making P subject of the formula, we have that

P = A/(1 + rt)

Given that

Substituting the vales of the variables into the equation, we have

P = A/(1 + rt)

P = $ 18500/(1 + 0.06 × 4)

P = $ 18500/(1 + 0.24)

P = $ 18500/1.24

P = $ 14919.35 per year

To find his monthly installments, we divide P by 12.

So, P' = P/12

= $ 14919.35/12

= $1243.38

So, his monthly installments are $1243.38

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The parameter for determining the diameter of an object depends on the specific object being measured. Here are some examples of parameters that can be used to determine diameter  the answer is  5276.7 cm3. Thus, option D is correct.

The formula for the volume of a sphere is  [tex]V = (4/3)πr^3[/tex] , where r is the radius of the sphere.

Since we are given the diameter of the sphere, we can find the radius by dividing the diameter by 2:

[tex]r = 21.6 cm / 2 = 10.8 cm[/tex]

Substituting this value into the formula, we get:

[tex]V = (4/3)\pi(10.8)^3[/tex]

[tex]= 4.18879 \times (10.8)^3[/tex]

[tex]= 5276.794 cm^3[/tex]

Rounding to the nearest tenth, we get:

[tex]V \approx 5276.8 cm^3[/tex]

Therefore, the answer is D) 5276.7 cm3.

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The given question is incomplete. the complete question is given below.

The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary. A) 693.2 cm3 B) 1453.8 cm3 C) 1868.5 cm3 D) 5276.7 cm3

Therefore, the difference between the most common and least common amounts on the line plot is 8.

"Least common" refers to the item or value that appears the fewest number of times in a given set or group. For example, if you have a set of numbers {2, 4, 2, 5, 3, 4, 1}, the least common number in the set is 1 because it appears only once, while the most common number is 2 and 4 because they both appear twice. In a line plot, the least common amount is the one that appears the fewest number of times on the p.

Given by the question.

To find the difference between the most common and least common amounts on a line plot, follow these steps:

Look at the line plot and identify the most common amount. This is the amount that appears the most frequently on the plot.

Look at the line plot and identify the least common amount. This is the amount that appears the least frequently on the plot.

Subtract the least common amount from the most common amount. The result will be the difference between the most common and least common amounts on the line plot.

For example, if the most common amount on the line plot is 10 and the least common amount is 2, then the difference would be:

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Answer:

Adam's thinking is not correct.

When subtracting 10 from 708, we need to borrow 1 from the hundreds digit and add it to the tens digit. This will result in a new hundreds digit of 6 and a new tens digit of 9. The ones digit remains the same. Therefore, the correct answer would be 698.

Adam's answer is also 698, but his reasoning is incorrect. He thinks that both the tens and hundreds digits change, which is not the case. In reality, only the tens digit changes while the hundreds digit decreases by 1 due to the borrowing process.

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