Each year a certain amount of money is deposited in an account which pays an
annual interest rate of r so that at the end of each year the balance in the account is
multiplied by a growth factor of x = 1 + r. $500 is deposited at the start of the first
year, an additional $200 is deposited at the start of the next year, and $600 at the
start of the following year.

Answer:

-0.595

Step-by-step explanation:

..

A geometric series exist as the totality of an infinite number of terms that contain a constant ratio between consecutive terms.

The infinite geometric series 1/64 + 1/32 +1/16 + . . . . diverges.

The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.

The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the sequence be 1/64 + 1/32 + 1/16 + . . . .

a(first  term) = 1/6

r(common ratio) = a2/a1 = (1/32) / (1/64)

= (64/32) = 2

Since, | r | > 1, the infinite geometric series diverges.

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B

Step-by-step explanation:

just did this one and got a 100%

Answer:

20

Step-by-step explanation:

We know that two vertical angles are equal to each other.

Then

First, We have to solve the equation 5y + 10 = 2y + 16  for y.

After that ,we can easily find the measure of the angles by substituting y by its value in their expression.

SOLVING THE EQUATION :

5y + 10 = 2y + 16

⇔ 5y - 2y = 16 - 10

⇔ 3y = 6

⇔ y = 2

Determining the measure of the angles :

angle 1 → 5(2) + 10 = 20

angle 2 → 2(2) + 16 = 20

Athlete swam at a constant rate, his speed in m/s is 2.343 m/s

The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.

The formula for speed is as straightforward as dividing a distance by a time. We may define speed as the rate of change of position of an item in any direction by taking the distance traveled and dividing it by the time.

Given,

the distance covered = 50m

total time taken = 21.34s

Speed = distance / Time

speed = 50/ 21.34

speed = 2.343 m/s

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The required wood needed to build four vertical sides is 60 inch.

According to the question, the given parameters for the box-shaped drum is as follows:

Length = 18 inch; Breadth = 12 inch; Height = 11 inch

To know the quantity of the wood need to build four vertical sides, calculation of perimeter is required.

Therefore, perimeter of the box = 12 + 18 + 12 + 18 = 60 inch

Hence, the required wood needed to build four vertical sides is 60 inch.

What is perimeter of a shaped box?

Perimeter of a shaped box is the addition of all the sides of a box. It is used for the closed shaped boxes. And it is measured in the linear units like meter, centimeter, etc.

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Answer: 6,7,8

Step-by-step explanation:

Answer:

The price of a ticket after the team loses 22 games is $26.93

Step-by-step explanation:

Original value = $31.55

value decrease per game lost = $0.21

equation uses C and L

C = 31.55 - 0.21L

22 games lost

C = 31.55 - 0.21(22)

C = 31.55 - 4.62

C = 26.93

C = $26.93

The value of a for the given equation is a=(r-q)/g.

The given equation is ga+q=r.

We need to find the value of a from the given equation.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, ga+q=r can be solved for a as follows:

⇒ga=r-q

⇒a=(r-q)/g

Therefore, the value of a for the given equation is a=(r-q)/g.

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The components of the two vectors are added and subtracted to produce the addition and subtraction vector PQ. i.e. →PQ = →Q + →P and →PQ = →Q - →P

A vector, which denotes the mathematical and geometrical direction of the provided quantity, is a quantity with both magnitude and direction.

For example : Velocity, Displacement etc.  

Let's start by assuming that,

P(x,y,z) and Q(u,v,w)

Now, we need to find the vector addition and subtraction

Addition of vectors to give →PQ

→PQ = →Q + →P

= (ui + vj + wk ) + (xi + yj + zk)

= (ui + xi ) +(vj  + yj) + (wk +zk)

= (u+x) i + (v + y) j + (w + z)k

= →PQ

Similarly, Subtraction of vectors to give →PQ

→PQ = →Q - →P

= (ui + vj + wk ) - (xi + yj + zk)

= (ui + vj + wk  - xi - yj - zk)

= (ui - xi ) +(vj  - yj) + (wk -zk)

= (u-x) i + (v - y) j + (w - z)k

= →PQ

For example : Let P(1,2,1) and Q ( -1, -2,4)

Then, Addition →PQ = →Q + →P

= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)

=  (1-1) i + (2 -2) j + (1 + 4)k

= oi+0j +5j

= 5j

Subtraction →PQ = →Q - →P

= (1i + 2j + 1k ) - (-1i + (-2)j + 4k)

=  (1+1) i + (2 +2) j + (1 - 4)k

= 2i+4j -3j

Hence, the vector PQ addition and subtraction is given by the addition & subtraction of the components of the two vectors.

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By the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA

From the question, we are to prove that ΔBXA ≅ ΔBYA

From the Hypotenuse Leg theorem which states that "two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side".

From the given information,

BX ⊥ XA.

ΔBXA is right triangle with hypotenuse AB

Also,

BY ⊥ YA.

ΔBYA is right triangle with hypotenuse AB

∴ The hypotenuses of the triangles are congruent

Also, from the given information,

XA is congruent to YA

XA and YA are the legs of the right triangles.

Hence, by the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA

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The solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is a = -1

In this question, we have been given an equation.

[tex]\frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}[/tex]

We need to find the solution of given equation.

[tex]\Rightarrow \frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}\\\\\Rightarrow \frac{2(2a+1)+6a}{12}=\frac{a-1}{3}\\\\\Rightarrow \frac{4a+2+6a}{12}=\frac{a-1}{3}\\\\ \Rightarrow \frac{10a+2}{4}=a-1\\\\\Rightarrow 10a+2=4a-4\\\\\Rightarrow 6a=-6\\\\\Rightarrow a=-1[/tex]

We need to check above solution.

Substitute a = -1 in LHS of given equation.

2a + 1 / 6 + a/2

= [2(-1) + 1 / 6] + [-1/2]

= (-1/6 - 1/2)

= -(4/6)

= -2/3

Substitute a = -1 in RHS of given equation.

a-1/3

= (-1 - 1)/3

= - 2/3

So, LHS = RHS

Therefore, the solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is      a = -1

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Answer:  the distance is (4,2)

Step-by-step explanation: it takes from 3 to seven 4 1s. and 6 -4 will be 2

hope this helps

By using distributive property 15(3 + 8) 15 11 = 165 both approaches yield the same conclusion.

Distrubutive Property Formula : a(b+c)=a b+a c

The distributive property is also known as the distributive law of multiplication over addition and subtraction. By its very name, the procedure implies that something will be divided or distributed.  According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC. Subtraction also belongs to the scope of this distributive law, which is expressed as A (B - C) = AB - AC. The distribution of operand A among the other two operands is seen from this.

A (B + C) = AB + AC represents the distributive property of multiplication over addition.

15(3+8) = (15.3) + (15.8)

15.11 = 45 + 120

165 = 165

Using the law of BODMAS, we can now attempt to solve the expression. The solution is as follows. We will first add the figures in brackets, and then we will multiply this total by the figure outside of the brackets.

Hence, using distributive property, it follows that 15(3 + 8) x 15 = 165. As a result, both approaches yield the same conclusion.

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Based on the linear pair postulate, the statements and the reasons for the proof are explained below.

The linear pair postulate states that if two angles form a linear pair, then both angles are supplementary, and therefore have a sum of 180 degrees.

The proof that states that angle 1 and angle 3 are congruent angles is shown below:

Statement 1. ∠1 and ∠2 are a linear pair

Reason: Given

Statement 2: ∠1 and ∠2 are supplementary      

Reason: Linear Pair Postulate  

Statement 3: m∠1 + m∠2 = 180°  

Reason: Definition of Supplementary Angles  

Statement 4: ∠2 = ∠4      

Reason: Given  

Statement 5: ∠3 = ∠4

Reason: Vertical Angles Theorem

Statement 6: ∠2 = ∠3

Reason: Corresponding angles theorem  

Statement 7: m∠2 = m∠3

Reason: Corresponding angles are congruent  

Statement 8: m∠1 + m∠3 = 180

Reason: Supplementary angle theorem

Statement 9: <1 and <3 are supplementary

Reason: Definition of supplementary angles

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Answer:

73

Step-by-step explanation:

97 - 2 × (16 - 4) ← evaluate parenthesis

= 97 - 2 × 12 ← evaluate multiplication

= 97 - 24 ← evaluate subtraction

= 73

Answer:

73

Step-by-step explanation:

97 - 2 x (16-4) =

97 - 2 x (12) =

97 - 24 =

73

Answer:

[tex]4x\left(x-3\right)[/tex]

Step-by-step explanation:

[tex]x^{y+z}=x^yx^z\\x^2=xx\\=4xx-12x\\=4xx-4\cdot \:3x\\=4x\left(x-3\right)[/tex]

Answer: quadrant 4 (IV)

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Should be C because the other choices seem false

The quadrilateral is a parallelogram because the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

Given:- A quadrilateral ABCD in which AB=CD and AD=BC.

To prove:- AB∥CD and AD∥BC

Construction:- Joi A and C.

Proof:-

In △ABC and △CDA,

AB=CD(Given)

AD=BC(Given)

AC=AC(Common)

∴△ABC≅△CDA(By SSS)

Therefore, by CPCTC,

∠ACD=∠BAC

∠DAC=∠ACB

Since alternate angles are equal, thus the lines are parallel.

Therefore,

AB∥CD and AD∥BC

Since both the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

Hence proved.

A quadrilateral in geometry may be a four-sided polygon with four sides and four corners (vertices). The Latin words Quadri, a variation of 4, and latus, meaning "side," are the source of the name. In regard to other polygons, it's also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon). Since "gon" is an anagram for "angle," it's also known as a quadrilaterals or 4-angle.

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According to the given data  the property justifies statement is: Multiplication Property of Equality.

According to the Multiplication Property for Equations, an equation can be multiplied as well as divided by the exact number upon every of the equation's sides without changing the solution.

If a = b, then a/c = b/c where c is greater than zero. In other words, if two expressions are equal and subsequently multiply or divide (except for 0) the same constant by both, the two sides will remain equal.

x/2=7

x = 14

Multiplication Property of Equality is :

If a = b,

Multiply constant on both sides.

a * c = b * c

so ,

in the given sum x/2 = 7

multiplying this equation by 2 * x/2 = 7 * 2

                                                                                       = x = 14

According to the given data  the property justifies statement is: Multiplication Property of Equality.

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Graph for the function f(x)=(3.1)⁴ is parallel to the x-axis and passing through coordinate (0, 92.3521 ).

As given in the question,

Function: f(x)=(3.1)⁴

Here x  is independent variable and f(x) is dependent variable on x.

f(x)=(3.1)⁴ is a constant value and does not have any x variable.

It is shown in the drawn graph.

x =0 , f(x)=(3.1)⁴

x =1 , f(x)=(3.1)⁴

x = 2 , f(x)=(3.1)⁴

x = -1 , f(x)=(3.1)⁴

x = -2 , f(x)=(3.1)⁴ and so on.

Therefore, graph for the function f(x)=(3.1)⁴ is parallel to the x-axis and passing through coordinate (0, 92.3521 ).

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The probabilities from the binomial probability mass function P(x ≤ 2) will be 0.9298.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

q = 1 - p = 1 - 0.10 = 0.90

Let x be a binomial random variable with p = 0.1 and n = 10.

The probabilities from the binomial probability mass function P(x ≤ 2) will be

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x ≤ 2) = ¹⁰C₀ × (0.1)⁰ × (0.9)¹⁰ + ¹⁰C₁ × (0.1) × (0.9)⁹ + ¹⁰C₂ × (0.1)² × (0.9)⁸

P(x ≤ 2) = 0.3487 + 0.3874 + 0.1937

P(x ≤ 2) = 0.9298

Your question was incomplete but the complete question is given below.

Let x be a binomial random variable with p = 0.1 and n = 10. Calculate the probability from the binomial probability mass function less than or equal to 2.

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The function g(3)'s expression is 8, which is

The supplied function is defined by a single expression, as per the query. Calculate the value of the other function using the provided expression.

In light of this, g(r) = -5 + 13 = 8

Additionally, the computed value can also be used as the value of the function expression g(3).

Consequently, the value of the function provided is 8.

The relationship between the dependent and independent variables is explained by the function. For the functions, it has a collection of values that may be connected using the domain technique.

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Answer:

Step-by-step explanation:

Differences are 3 less then 2 less.

So, the next term would be 4-1 = 3.

The number according to the given statement is x<-0.55.

Given the statement is five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​.

A mathematical statement is a meaningful component of words that can be true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Five and three-tenths of a number means 5.3x.

And two and seven-tenths means 2.7.

So, five and three-tenths times a number plus two and seven-tenths means 5.3x+2.7.                ......(1)

It is also given that three and three-tenths times a number means is 3.3x.      

And one and six-tenths means 1.6.

So, three and three-tenths times a number plus one and six-tenths​ means 3.3x+1.6         .......(2)

Now, we will substitute equation (1) less than equation (2) according to the given statement is

5.3x+2.7<3.3x+1.6

Further, we will subtract 2.7 from both sides, we get

5.3x+2.7-2.7<3.3x+1.6-2.7

5.3x<3.3x-1.1

Now, we will subtract 3.3x from both sides, we get

5.3x-3.3x<3.3x-1.1-3.3x

2x<-1.1

Now, we will divide both sides by 2, we get

2x/2<-1.1/2

x<-0.55

Hence, the number for the given statement "five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​" is -0.55.

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If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

In the given triangle below;

Line segment BC is intersecting at the midpoint of AD and AE.

Now,

Since ΔABC ≈ ΔADE by similarity property.

So,

AB/AD = BC/DE

AB/(AB + BD) = BC/DE

Since AB = BD = AB lets say,

AB/2AB = BC/DE

BC/DE = 1/2

Hence "If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved".

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Answer:

1. x < 4

2. x > 1

3. x < 5

Step-by-step explanation: