a area of a rectangle is 32m squared. what is the length and the width

The principal that would need to be invested to have an accrued amount of 1 million dollars after 30 years is $90,717.95.

The formula compound interest where interest is compounded continuously is expressed as;

A = P × e^(rt)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for P.

A = P × e^(rt)

P = A / e^(rt)

P = $1,000,000 / e^( 0.08 × 30 )

P = $1,000,000 / e^( 2.4 )

P = $90,717.95

Therefore, the amount of principal is $90,717.95.

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Answer:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Step-by-step explanation:

The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.

According to the associative property, grouping symbols can be altered during addition or multiplication without affecting the outcome.

A + (b + c) = A + (b + c) is how this is expressed. In order to multiply a number by all of the distinct addends of another number, one must use the distributive property of multiplication.

A mathematical principle known as the associative property states that the product of a multiplication problem is unaffected by the way the factors are organized.

You can arrange the addends in multiple ways without changing the result, according to the associative property of addition. You can reorder the addends and the result won't change, according to the commutative property of addition.

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For the given matrix, Cartesian products to elements is verified,

(a) (1,2)

A X A: This set contains all possible ordered pairs where x is a member of set A and y is also a member of set A. The element (1,2) does not belong to this set because 1 is a member of set A, but 2 is not.

B X A: This set contains all possible ordered pairs where x is a member of set B and y is a member of set A. The element (1,2) does not belong to this set because 2 is a member of set B, but 1 is not.

A X B: This set contains all possible ordered pairs where x is a member of set A and y is a member of set B. The element (1,2) belongs to this set because 1 is a member of set A and 2 is a member of set B.

B X B: This set contains all possible ordered pairs where x is a member of set B and y is also a member of set B. The element (1,2) does not belong to this set because 1 is not a member of set B.

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Sample average: To calculate the sample average, add up all the measurements and divide by the number of measurements.

42.4 + 65.7 + 29.8 + 58.7 + 52.1 + 55.8 + 57.0 + 68.7 + 67.3 + 67.3 + 54.3 + 54.0 = 751.4

Sample average = 751.4 / 12 = 62.62

Sample standard deviation steps:

Subtract the sample average from each measurement to find the deviations.

Square each deviation.

Add up the squared deviations.

Divide the sum by the number of measurements minus one (n-1).

Take the square root of the result.

Sample standard deviation = sqrt(sum of squared deviations / (n-1))

Dot diagram: A dot diagram, also known as a dot plot, is a simple graphical representation of a set of data where each data point is represented by a dot on a number line. To create a dot diagram, plot each measurement as a dot on a number line with the corresponding value.

This is a useful tool to visualize the distribution of the data and to see the general pattern, such as the presence of outliers, skewness, or clusters.

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Answer:

3570

Step-by-step explanation:

Find the prime factorization of 105

105 = 3 × 5 × 7

Find the prime factorization of 170

170 = 2 × 5 × 17

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:

LCM = 2 × 3 × 5 × 7 × 17

LCM = 3570

The rectangular block has a perimeter of 10 units. The triangle's perimeter is 7.5 units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area.

Here,

area=6 units

length on scale=5-2

=3 units

3*w=6

w=2 units

perimeter=2*(3+2)

=10 units

length of side of triangle=2.5 units

perimeter=2.5+2.5+2.5

=7.5 units

The perimeter of rectangle block is 10 units. The perimeter of triangle is 7.5 units.

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Three fifth of the vegetable in Alia garden are tomatoes so number of tomatoes are 3/5x in Alias garden.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

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If [tex]\overline{x}$[/tex] represents the mean of n observations x₁, x₂, ……xₙ, then the value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is 0.

Mean is the average value of the group of values. It shows the equal distribution of values for a given data set.

To calculate the arithmetic mean of a group of data, first, add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed, we obtain the following formula for the mean ([tex]\overline{x}[/tex]):

[tex]\overline{x}= $\sum {\frac{x}{n} $[/tex]

The formula of the mean ([tex]\overline{x}$[/tex]) is:

[tex]\overline{x} = $\sum_{i=0}^{n} {x_{i}$/n[/tex]

[tex]$\sum_{i=0}^{n} {x_{i} = \overline{x}n[/tex]           Eqn(1)

Here, n is total number of observations.

The value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is calculated as follows:

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = \sum_{i=0}^{n} x_{i} - \sum_{i=0}^{n}\overline{x}[/tex]

Now, from equation (1), we get

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \sum_{i=0}^{n}\overline{x}[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}\sum_{i=0}^{n}1[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}n[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = 0[/tex]

Hence, the correct answer is B.

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The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

AP to PB is in the ratio of 4 to 1. Then the coordinate of the point P is given as,

x = (4 × 8 + 1 × 1) / (4 + 1)

x = (32 + 1) / 5

x = 33 / 5

x = 6.6

y = (4 × 4 + 1 × 3) / (4 + 1)

y = (16 + 3) / 5

y = 19 / 5

y = 3.8

The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).

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By using the Angle Sum Property, we can find that m angle a = 180 - (3(x - 5) + x 25) = 180 - 4x + 25

We can use the Angle Sum Property to solve this problem. The Angle Sum Property states that the sum of the measures of the angles in a triangle is equal to 180°. We can use this to write the equation 180 = m angle bdc + m arc bc + m angle a. Since we have the values for m angle bdc and m arc bc, we can plug them in and rearrange the equation so that m angle a is the only unknown. We get 180 = 3(x - 5) + x 25 + m angle a. Subtracting 3(x - 5) + x 25 from both sides, we get m angle a = 180 - (3(x - 5) + x 25). Simplifying, we get m angle a = 180 - 4x + 25, which is the final answer.

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The expression that represents the area of the playground is 45x² - 13x - 2 square feet.

The area of a rectangle is found by multiplying its length by its width. Here the length is given as 5x - 2 feet and width is given as 9x + 1 feet. So, the expression that represents the area of the playground is:

Area = Length * Width

= (5x - 2) * (9x + 1)

= 5x × 9x + 5x -2 × 9x - 2

= 45x² + 5x - 18x - 2

= 45x² - 13x - 2

Therefore, the expression that represents the area of the playground is 45x² - 13x - 2 square feet.

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(x,y)⇒(x+5,y+10) is the translation rule for A'B, which is a translation of AB.

A translation is a geometric transformation in Euclidean geometry that moves every point in a figure, shape, or space by the same distance in the same direction. A translation may alternatively be thought of as adding a constant vector to each point or changing the coordinate system's origin. A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. A translation in mathematics moves a form left, right, up, or down but does not turn it. The translated (or picture) shapes appear to have the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.

Here,

A translation is a sort of transformation in which every point in a figure moves the same distance in the same direction. Slides are another term for translations. A translation can be described with words like "moved up 3 and over 5 to the left" or using notation.

The translation rule for A'B is a translation of AB is (x,y)⇒(x+5,y+10).

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The difference in area is of about 1445.1 square miles.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius is the distance of the center of the circle to any point on the circumference of the circle.

For the circle with a radius of 18 miles, the area is given as follows:

A = π x 18² = 1017.9 square miles.

For the circle with a radius of 28 miles, the area is given as follows:

A = π x 28² = 2463 square miles.

Hence the difference is of:

2463 - 1017.9 = 1445.1 square miles.

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Answer:

below

Step-by-step explanation:

Use right triangle Pythagorean theorem

L^2 = 8^2 + 4^2

L^2 = 80

L = sqrt (80)   units      <====exact

             approx is sqrt(80) =~8.94 units

Answer:

24x+96

Step-by-step explanation:

so we could use Distributive property

which means -12time -2x+-12times-8

                                   =24x+96

i hope is helpful

Answer:

"In

In a 30-60-90 triangle, the sides are in a ratio of 1:√3:2.

So, the hypotenuse of the triangle is 62 = 12 ft long.

The longer leg of the triangle is 6√3 = 10.8 ft long (to the nearest tenth of a foot)

Answer:

In the given triangle △ABC, AB is equal to 4 and m∠F is equal to 30°. In the triangle △DEF, AB is equal to 6 and m∠F is equal to 50°.

Answer: 45,60

Step-by-step explanation:

OK

The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (1, -7), the value of a and b is 2 and -9 respectively.

The equation of line:

y = 2x - 6

We firstly find the slope of the equation by comparing the equation by y = mx + c.

On comparing m = 2

The point is (1, -7).

So x(1) = 1 and y(1) = -7

The formula of slope intercept form is:

y - y(1) = m(x - x(1))

Now putting the value:

y - (-7) = 2(x - 1)

y + 7 = 2x - 2

Subtract 7 on both side, we get

y = 2x - 9

On comparing the equation from y = ax + b, we get

a = 2 and b = -9

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The complete question is:

The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (1, -7). Find the value of a and b.

(a) the root of the equation is =4.4.(b) x=31pi for x=100 approx.

the root of an equation is said to be that value where the equation gets zero. And the intersection point of two equations is the same value of equations.

The roots of x =tan(x), graph y = x and y = tan(x), and look at the intersection points of the two curves.

a) Find the smallest nonzero positive root of x = tan(x),

after seeing the graph the root of the equation is =4.4.

(The desired root is greater than pi/2).

b) Solve x =tan(x) for the root that is closest to x = 100.

after examining the graph of the function we can see that 31pi for x=100 approximately.

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Answer:

see explanation

Step-by-step explanation:

solving the inequality

n + 6 < 13 ( subtract 6 from both sides )

n < 7

this means that any value less than, but not including, 7 is a solution

listing the values that are a solution from - 10 through to 10 , then list of solutions is

- 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6

Answer:

142

Step-by-step explanation:

6 day av 144 / day so total =144*6

first 3 day av 132 so total =132*3

next 2 days av 163 so total =163*2

144*6= 132*3+163*2+final day

so final day = 142

The results for systems under rotational motion are listed below:

First section:

Part A - The angular speed of the large gear is 90π radians per minute.

Part B - The linear velocity of the large gear is 27π centimeters per minute.

Part C - The linear velocity of the smaller gear is 27π centimeters per minutes.

Part D - The angular speed of the smaller gear is 27π / 8 radians per minute.

Part E - The angular speed of the smaller gear is 27 / 16 revolutions per minute.

Second section:

Part A - The angular speed of the LP is 200π / 3 radians per minute.

Part B - The angular velocity of the LP is 200π / 3 radians per minute.

In the first part of this question we find the case of rigid transmission system under rotational motion, two gears that transmits power and whose angular speed ratio is shown below:

ωL / ωS = rS / rL

Where:

And the linear velocity (v), in centimeters per minute, is calculated by this formula:

v = rL · ωL = rS · ωS

Part A - How many radians per minute is the large gear turning?

R/ The angular speed is:

ωL = 45 rev / min × 2π rad / rev

ωL = 90π rad / min

Part B - What is the linear velocity of the teeth on the large gear?

v = (0.3 cm) · (90π rad / min)

v = 27π cm / min

Part C - What is the linear velocity of the teeth on the smaller gear?

v = 27π cm / min

Part D - How many radians per minute is the smaller gear turning?

ωS = v / rS

ωS = (27π cm / min) / (8 cm)

ωS = 27π / 8 rad / min

Part E - How many revolutions per minute is the smaller gear turning?

nS = 27π / 8 rad / min × (1 / 2π rev / rad)

nS = 27 / 16 rev / min

The second part uses the same kinematic equation used in the previous part:

Part A - How many radians per minute is this:

ω = (33 + 1 / 3 rev / min) × (2π rad / rev)

ω = 200π / 3 rad / min

Part B - Find the angular velocity:

The angular velocity is independent from radius of rotation, thus:

ω = 200π / 3 rad / min

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Three edges and three vertices make up the three-sided polygon known as a triangle. The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Each side is different, and each angle is less than 90 degrees. Obtuse isosceles: two identical sides and identical angles, with one angle more than 90 degrees.

Shapes with three sides are called triangles. The various triangle varieties go under various names. The dimensions of a triangle's sides and angles determine its type (corners).

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Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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The solution to the differential equation y'' + 4y' + 2y = 4 with zero initial conditions is y(t) = 2e^-2t.

CORRECTION: Given the differential equation: y'' + 4y' + 2y = 4

To solve this differential equation using Laplace transforms, we first need to take the Laplace transform of both sides. The Laplace transform of the derivative of y is given by:

L{y'} = sY(s) - y(0) = sY(s) (assuming zero initial conditions)

L{y''} = s^2Y(s) - sy(0) - y'(0) = s^2Y(s) (assuming zero initial conditions)

Now, substituting these Laplace transforms in the given differential equation, we have:

s^2Y(s) + 4sY(s) + 2Y(s) = 4/s

Solving for Y(s), we get:

Y(s) = (4/s) / (s^2 + 4s + 2) = 2 / (s + 2)^2

Finally, taking the inverse Laplace transform of Y(s), we get:

y(t) = L^-1{Y(s)} = 2e^-2t

Therefore, the solution to the differential equation y'' + 4y' + 2y = 4 with zero initial conditions is y(t) = 2e^-2t.

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There about 24 hockey tickets were bought by Bryant. Out of which 14 tickets were child tickets.

A mathematical claim containing two equal algebraic expressions is known as an algebraic equation.

Given that the cost of an adult ticket is $5.50, and a child ticket is $2.00. The total spent is $83, and the total number of tickets bought is 24.

Let us consider the number of adult tickets bought is x and the number of children tickets bought is y.

Then x+y=24. From this, x=24-y.

Also, the given situation is written in an expression as,

[tex]\begin{aligned}5.50x+2.00y&=83\\5.50(24-y)+2.00y&=83\\132-5.50y+2.00y&=83\\-3.5y&=-49\\y&=14\end{aligned}[/tex]

The required answer is 14.

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The process of converting a decimal number to its base 7 equivalent is explained below.

The radix point is the point that separates the whole number part of a number from its fractional part in a numerical system.

The process of converting a decimal number to its base 7 equivalent starts by dividing the decimal number by 7. The remainder from this division will be the first digit after the radix point in the base 7 equivalent.

We continue this process by dividing the quotient obtained in the previous step by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits after the radix point in the base 7 equivalent, in the reverse order.

To get the integer part, we keep dividing the decimal number by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits in the integer part of the base 7 equivalent, in the reverse order.

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Sample 3's mercaptoethanol and urea mixture breaks sulphide bonds, resulting in the loss of tertiary structure and activity, whereas in sample 2, urea is introduced. This chemical denaturing agent aims to break up peptide connections, which would then affect the structure and function of the protein.

An experiment data is given below:

This experiment describes how protein denaturing chemicals affect a protein's ability to function.

Sample 1 preserves protein structure and function because it just contains buffer and no denaturing agent.

Enzymatic activity then results in high fluorescence as a result of this.

In sample 2, urea is added, a chemical denaturing agent that seeks to dismantle peptide bonds, disrupting protein structure and activity.

As a result, there are now less fluorescence products and less active enzyme products overall.

In sample 3, when mercaptoethanol and urea are mixed, sulphide bonds are broken and tertiary structure and activity are lost.

After dialysis, sample 4 had both urea and mercaptoethanol eliminated from it.

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Answer: The one in the middle

Step-by-step explanation:

The one in the middle because of the huge downhill