Evaluate the definite integral. 1 9 cos(πt/2) dt 0

Bianca will earn interest of $382.5 for a period of 3years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same.

Simple interest is calculated with the following formula:

S.I. = P × R × T,

where P = Principal, R = Rate of Interest in % per annum, and T = Time

Given,

Principal P = $3000

Rate of interest R = 4.25% = 4.25/100 = 0.0425

Time T = 3 years

Simple interest S.I. = P × R × T

                               = 3000 × 0.0425 × 3

                               = 127.5 × 3

                       S.I.   = $382.5

Hence, Interest Bianca will earn in 3 years = $382.5

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Answer:

-4d - 6

Step-by-step explanation:

-1/3(12d+18)

-4d - 6

That is the simplest we can simple the function

So, the answer is -4d - 6

Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation: Same thing as 8 / 0.5

The rule for the transformation, which is a dilation, is given as follows:

(x,y) -> (3x/4, 3y/4).

Hence the coordinates of B' are given as follows:

B'(3, -12).

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The general rule is:

(x,y) -> (kx, ky).

In which k is the scale factor.

The scale factor for this problem is given as follows:

k = 3/4.

Hence the rule is:

(x,y) -> (3x/4, 3y/4).

The coordinates of B' are obtained multiplying each of the coordinates of B by the scale factor k = 3/4.

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Answer:

A) 2^4 x 2^7 = 2^(4 + 7) = 2^11

Exponent Law(s): Product Law

B) (-3)^9 divided (-3)^5 = (-3)^(9 - 5) = (-3)^4

Exponent Law(s): Quotient Law

C) (5^2)^-3 x 5^0 = 5^(-6) × 1 = 5^(-6)

Exponent Law(s): Power of a power rule; zero exponent rule

Answer:

The fraction 7/3 cannot be expressed as a whole number. The fraction 7/3 can be expressed as a decimal, which is 2.3333.... and goes on forever, or as a mixed number, which would be 2 and 1/3.

It's important to note that when dividing two integers, the result is not guaranteed to be a whole number.

Step-by-step explanation:

The functions that are represented by WHO are 9/-5 and SEEM are -28, respectively.

The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

as the function which is represented as WHO

= 9/ 7- 12

= 9 / -5

as  the function which is represented as SEEM

= -4(-1 + 8)

= -4 ( 7)

= - 28

The functions that are represented by WHO are 9/-5 and SEEM are -28, respectively.

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The correct question is :- Transfer the word from the top box to the corresponding bottom box by function .

To find the mirror image of a point with respect to a line in 3D, you can use the projection of the point on the line, multiply it with the normal vector of the line, and then subtract the obtained vector from the position vector of the point twice.

To find the mirror image of a point with respect to a line in 3D, you can use the following method:

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Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

9(x - y) = 30,

or (x-y) =30/9

To find :  

a) 18(x - y) = ?

=> 2(9(x - y))

=> 2(30)

=> 60

b)6x - 6y = ?

=> 6(x-y) = 6(30/9)

=> 2*30/3

=> 20

c) 9(x-y)-9

=> 30 -9

=>21

Therefore , the solution of the given problem of  equation comes out to be a.60 , b.20 and c.21.

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On solving the provided question, we can say that the inequality provided is  -s < 6  he values that stratifies will be = 0-6

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality provided is

-s < 6

the values that stratifies will be = 0-6

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[tex]\begin{array}{llll} 3+10(1)\\ 3+10(2)\\ 3+10(3)\\ 3+10(4)\\ \end{array}\hspace{5em}\displaystyle\sum_{n=1}^{4}3+10n[/tex]

So on solving the provided question we can say  that coefficient of expression 5xyz2 is 5  and 3zy is 3

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression Numbers, variables, and functions make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.

here,

coefficient of 5xyz2 is 5

and 3zy is 3

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Let's call the first number in the series "x", and the last number in the series "y".

We know that the series is a consecutive series of odd numbers, and we also know that y is 6 less than the last number in the series.

Since the series is a consecutive series of odd numbers, we can say that the difference between any two consecutive numbers in the series is 2.

So, we can write an equation to represent this information:

y = x + (n-1) * 2

where n is the number of numbers in the series.

We also know that y is 6 less than the last number in the series, so we can add this information to our equation:

y = x + (n-1) * 2 - 6

To solve for n, we can rearrange the equation:

n = (y - x + 6) / 2 + 1

Now, if we know the value of x and y we can substitute them in the equation and find the number of terms in the series.

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There is not sufficient data provided to answer the question. So it cannot be answered.

To find the length of the part of the ramp that is on the ground, we need to know the angle of the ramp and the height of the ramp. If the height of the ramp is 6 inches, and we know the angle of the ramp, we can use the Pythagorean theorem to find the length of the ramp.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides. If we call the length of the ramp "x", and the height of the ramp "h", we can write the equation as:

x^2 = h^2 + (6 inches)^2

We don't have the angle of the ramp, so we can't use the Pythagorean theorem. Therefore, we can't find the length of the part of the ramp that is on the ground with the information given. To find the length, we would need additional information, such as the angle of the ramp or the length of the ramp.

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The loan that offers the best effective annual rate is loan N (option c)

The effective annual rate is the actual  interest rate that is earned on an investment after accounting for the number of compounding.

Effective annual rate = (1 + APR / m ) ^m - 1

Where M = number of compounding

Effective annual rate for loan L = (1 + 0.08254/365)^365 - 1=0.08603 = 8.603%

Effective annual rate for loan M = (1 + 0.08474/52)^52 - 1=  0.08836 = 8.836%

Effective annual rate for loan N = (1 + 0.08533/12)^12 - 1=  0.08875 = 8.875%

Effective annual rate for loan O=8.604%

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Answer:

1a) x+11=x+11 becomes 0=0. What this means is that at all x values the y values are the same, in other words, they are the same line.

Please split up your questions as it is difficult to answer.

$ 286 is the percent.

What in mathematics is a percentage?

When the denominator is 100, percentages are really just fractions. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

 30% * 120  = X

   30/100  * 120 = X

    36 = X

the $250 raised goes to the 7th graders.

            250 + 36

           =  $ 286

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Yes, number 8 is a multiple of 2 is a true statement.

As given in the question,

Given number is equal to :

2

Given multiple is equal to :

8

Multiple is the number which represents when we multiply the given number by any integers.

In standard form multiples of number 'n' is given by :

n × 1 = n

n × 2 = 2n

n × 3 = 3n

n × 4 = 4n

n × 5 = 5n

......... so on.

Multiple of 2 are as follow :

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

2 × 5 = 10

......... so on.

When we multiply 2 by 4 we get 8.

8 is the multiple of 2.

Therefore, yes the given statement 8 is a multiple of 2 is a true statement.

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The solution to the quadratic equations are

a) The number of seconds for the ball to reach the ground is t = 5 seconds

b) The number of seconds to reach the maximum height T = 2 seconds

c) The maximum height of the ball is h ( 2 ) = 144 feet

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as h ( t )

Now , the equation will be

h ( t ) = -16t² + 64t + 80   be equation (1)

a)

The number of seconds for the baseball to reach the ground be t

The height when the ball reaches the ground will be h = 0

Substituting the value of h ( t ) = 0 , we get

0 = -16t² + 64t + 80

On simplifying the equation , we get

16t² - 64t - 80 = 0

Divide by 16 on both sides of the equation , we get

t² - 4t - 5 = 0

On factorizing the equation , we get

t² + t -5t - 5 = 0

t ( t + 1 ) - 5 ( t + 1 ) = 0

( t - 5 ) ( t + 1 ) = 0

The value of t is time and it is not negative

So , when ( t - 5 ) = 0

Adding 5 on both sides of the equation , we get

t = 5 seconds

b)

The number of seconds the baseball to reach the maximum height be T

And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola

T = ( -b / 2a )

On simplifying the equation , we get

T = ( -64 / ( 2 ( 16 )

T = -64 / 32

T = 2 seconds

c)

The maximum height of the baseball is when T = 2

Substituting the value of t = 2 in the equation , we get

h ( t ) = -16t² + 64t + 80

h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80

On simplifying the equation , we get

h ( 2 ) = -64 + 128 + 80

h ( 2 ) = 64 + 80

h ( 2 ) = 144 feet

Hence , the equation is solved

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Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.

The maximum number of rotations that a geometry may accommodate is the order of rotational symmetry. The degree of rotational symmetry is denoted as 360°A°, where A° is the lowest angle that may be used to rotate a figure from its rotated shape back to its original shape. (170 degrees) How many times a perfect circle may be rotated while still preserving its appearance is a measure of a shape's rotational symmetry. The appearance of a full 360° revolution will be the same only when a triangle is placed back in its initial starting position.

given

Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.

A-stable time-stepping approach, is the recommended method for solving evolutive conservative systems of PDEs.

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As of 2021, the largest prime number ever found is a number with 24,862,048 digits, known as M77232917. It was found in December 2018 using a program called GIMPS (Great Internet Mersenne Prime Search).

Prime numbers are numbers that are divisible by only 1 and themselves. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.

Mersenne prime is a specific type of prime numbers that can be represented in the form Mp = 2^p -1 where p is a prime number. Mersenne primes are named after the French mathematician Marin Mersenne who studied them in the early 17th century.

The discovery of large prime numbers is a significant event in the world of mathematics, and it is an ongoing effort by many mathematicians and computer scientists. The Great Internet Mersenne Prime Search (GIMPS) is one such effort, it is a distributed computing project which allows anyone to participate in the search for large Mersenne primes by downloading a free program that runs in the background on a computer, searching for primes while the computer is idle.

The discovery of the largest prime number to date was a huge achievement in the field of mathematics and it was found using the GIMPS project, which is the most successful distributed computing project in the history of mathematics. The discovery of large primes has many implications in number theory, cryptography and computer science.

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The pair of triangles are congruent. using the angle side angle (ASA) congruency theorem

Two triangles are said to be congruent if all the three sides are equal to each other and all the three angles are equal to each other.

The angle side angle (ASA) congruency theorem states that two triangles are congruent if two angles and an included side of one triangle is equal to two angles and an included side of another triangle.

From the diagram, for both triangles, two angles and an included side is equal to that of the other triangle.

The pair of triangles are congruent.

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The minimum of the periodic sine function is - 4 and it's amplitude is |4|.

If there is a positive real number P such that f(x + P) = f(x), for all x being real numbers, then the function y= f(x) is said to be periodic. The fundamental period of a function is the least value of the positive real number P. The period during which a function repeats itself is also known as the fundamental period of the function.

f(x + P) = f(x).

From the graph, we conclude it is a sine function.

The amplitude of the graph is 4 units.

So, The graph reaches it's maximum and minimum at ± 4.

Therefore, The minimum of the function is - 4.

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Answer: 9.8 feet!

Step-by-step explanation:

If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Suppose you know that ∠S and ∠Y are complementary and that ∠S = 5(∠Y) − 150°.

Then the other equation is given as,

∠S + ∠Y = 90°

5(∠Y) − 150° + ∠Y = 90°

6 (∠Y) = 240°

∠Y = 40°

If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.

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The Best Lawn covers the most area per pound is better choice to buy.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Xtra Green covers 1/20 of an acre with 1/2 of a pound of fertilizer granules.

So, area per pound covered by Xtra Green

= (1/20)  /(1/2)

= 1/20 x 2/1

= 1/10

= 0.1

Best Lawn covers 1/15 of an acre with 1/5 of a pound of fertilizer granules.

So, area per pound covered by Best Lawn

= (1/15)  /(1/5)

= 1/15 x 5/1

= 1/3

= 0.333

Hence, Best cover larger Area is better choice.

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a) The amount of money that Tony invested is; £1350

b) The rate of compound interest is; 4%

c) The graph that represents the growth in Toni's account is; Graph C

The formula for the total value of her investment  after t years is given by the formula; v = 1350 * 1.04^t

The general formula used to calculate the interest rate is given by,

a = p * (1 + r)^t

where;

a is amount

p is principal

r is rate of interest

t is time period

Comparing the given equation with standard equation, we have;

a = v  

p = 1350

t = t    

Now, 1 + r = 1.04

1 + r = 1 + 0.04

Thus;

r = 0.04  = 4%

Therefore, the money invested by tony P = £1350

The rate of compound interest is 4%

The graph that represents Toni's account is an exponential equation and since the initial amount is not zero, then the correct graph is graph C

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2x-1+5x-12

question says sum, so i know we are adding. 2 times a number means 2x (or other variable). i simplified plus negative one to minus one. add five times the number (x). and subtract 12.

The sixth term is [tex]\frac{3}{1024}[/tex] .

Given series : 3, [tex]\frac{3}{4}[/tex] , [tex]\frac{3}{16}[/tex] and so on.

We need to find the sixth term, so n = 6.

The given series is in Geometric Progression.

To find the [tex]n^{th}[/tex] term of a Geometric Progression,

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

a is the first term of any series. Here, a = 3

r is common ratio. Here, r = [tex]\frac{1}{4}[/tex]

According to the question,

[tex]a_{6}[/tex] = 3[tex](\frac{1}{4} )^{6-1}[/tex]

⇒   [tex]a_{6}[/tex] = 3 × [tex](\frac{1}{4} )^{5}[/tex]

⇒ [tex]a_{6}[/tex] = 3 × [tex]\frac{1}{1024}[/tex]

⇒ [tex]a_{6}[/tex] = [tex]\frac{3}{1024}[/tex]

So, the sixth term is  [tex]\frac{3}{1024}[/tex].

The first statement is true and the second statement is false.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given that initial population of bacteria = 80

Bacteria triple in population every 5 hours.

Number of bacteria after the time 'x' hours is modeled as,

f(x) = [tex](80)(3)^\frac{x}{5}[/tex] which is given in the first statement.

So the first statement is true.

After 13 hours,

f(13) =  [tex](80)(3)^\frac{13}{5}[/tex]

      = 1391.89 ≈ 1392

But the second statement says the population is 1592 bacteria, which is false.

Hence the statement given first is true and the second one is false.

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