8 months is – percent of 2 years​

The average balance in the bank account is $1,125.64.

So, the average balance of the account will be:

Fill in the values and solve as follows:

Therefore, the average balance in the bank account is $1,125.64.

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Answer:

first collect the like terms so that you have -4x is equals to -2 - 26 then negative 4x is equals to -28 divided by -4x is equals to 7

Answer:

a = 2, b = -2

P is at a minimum

Step-by-step explanation:

For any polynomial function, the turning point is either a maximum or a minimum

It can be determined by taking the first derivative of the function and setting it equal to 0 and solving for x and y

In this case we are given the turning point as x=1, y = 3 and we have to calculate a and b in the equation y = ax² + (ab)x + 5

The first derivative of y, y' = 2ax + ab

If we set this equal to 0 we get 2ax + ab = 0 ==> 2ax = -ab ==> b = -2

So the equation is of the form y = ax² -2ax + 5  (subbing for b)

Since we know that at x = 1, y =3 substitute y and x values in the above equation and solve for a

y = 3 = a(1²) - 2a(1) + 5

a - 2a + 5 = 3

-a + 5 = 3

a = 2

So the equation is of the form y = 2x² -4x + 5

If we plot this we will find that P is a minimum point

However, we can always determine mathematically if P is a max or min by taking the second derivative of the original function and noting the sign.  If it is positive, the point is a minimum, and if it is negative, the point is a maximum.

Taking derivatives,

y' = 4x  - 4

y'' = (4x-4)' = 4

The sign is positive so P is a minimum

Graph attached for reference

The  required answer is the angle between vectors a and b is 44.8 degrees.

To find the angle θ between two vectors a and b, we use the dot product formula:
a · b = |a| |b| cos θ

where |a| and |b| are the magnitudes of vectors a and b, respectively.
First, let's calculate the dot product of a and b:
a · b = (9)(2) + (-1)(0) + (-5)(-8) = 18 + 40 = 58
Variable  were explicit numbers solve a range of problems in a single computation. The quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. A variable is either a symbol representing an unspecified term of the theory , or a basic object of the theory that is manipulated ,without referring to its possible intuitive interpretation.
Next, let's calculate the magnitudes of vectors a and b:
|a| = sqrt(9^2 + (-1)^2 + (-5)^2) = sqrt(107)
|b| = sqrt(2^2 + 1^2 + (-8)^2) = sqrt(69)
the angle θ by taking the inverse cosine of the cosine value: θ = (57 / (√107 * √69)
Now we can substitute these values into the dot product formula to solve for θ:
58 = sqrt(107) sqrt(69) cos θ
cos θ = 58 / (sqrt(107) sqrt(69))
θ = cos^-1(58 / (sqrt(107) sqrt(69)))
Now you have the angle θ between the two vectors a and b.
Using a calculator, we find that θ is approximately 44.8 degrees.

Therefore, the angle between vectors a and b is 44.8 degrees.

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The given series is convergent. It is a p-series with p = 2 because each term is in the form of 1/n².

The p-series with p > 1 always converge, so this series converges. This means that the sum of the terms in the series approaches a finite value as the number of terms approaches infinity.

In other words, the series does not diverge to infinity or oscillate between positive and negative values. The convergence of this series can be proven using the integral test or by comparing it to another convergent series.

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The rational expression (x² + 10x + 25) / (x² + 9x + 20) simplifies to (x + 5) / (x + 4), with the restriction that x cannot be equal to -4.

To simplify the rational expression (x² + 10x + 25) / (x² + 9x + 20), we can factorize the numerator and denominator and then cancel out any common factors.

Factorizing the numerator:

x² + 10x + 25 = (x + 5)(x + 5) = (x + 5)²

Factorizing the denominator:

x² + 9x + 20 = (x + 4)(x + 5)

Now, we can simplify the expression:

(x² + 10x + 25) / (x² + 9x + 20) = (x + 5)² / (x + 4)(x + 5)

After canceling out the common factor (x + 5) from the numerator and denominator, we are left with:

= (x + 5) / (x + 4)

Therefore, the simplified rational expression is (x + 5) / (x + 4). However, we need to note the restriction on the variable. In this case, x cannot be equal to -4 since it would result in division by zero, which is undefined. So, the restriction is x ≠ -4.

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To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.

Inherited amount: RM300,000

Interest rate: 7% per year

Number of years: 20

Using the present value of an annuity formula:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value (inherited amount)

P = Annuity payment (constant amount to be withdrawn each year)

r = Interest rate per period (7% or 0.07)

n = Number of periods (20 years)

Plugging in the values:

300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]

Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.

Therefore, the correct answer is A. RM15,000.

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Answer:

C.) they both got two more questions correctly than Chris did.

Step-by-step explanation:

brian got 14 more right than chris

Chris got 2 less than damien

brian and damien both got 18/20 correct, chris got 16 right

Answer:

1/333 is answer........

Answer:

3/1000

Step-by-step explanation:

3 millimeters = 0.003 meters

So to get to 1 meter from 3 millimeters, you will have to divide by 0.003 or 3/1000 therefore the scale factor is 3/1000

Answer:

C

Step-by-step explanation:

Its a reflection then its dilation, however its not congruent because congruent means that its the same size and shape in this case its only the same shape not size.

First of all the quadrilateral ABCD is reflected, which means sides are changed and then it is dilated. A dilated image is always similar but never congruent. The meaning of congruency is that both size and shape is equal but here only shape is equal not the size so it is not congruent to the original...

Jorge is a recent college graduate who is eagerly seeking new job opportunities after completing his degree.

Currently, he is working part-time to cover his expenses, but his true ambition lies in finding a job that aligns with his long-term career plans. In order to achieve this, Jorge has been actively applying to various positions that match his professional aspirations and utilize the knowledge and skills he acquired during his college education.

Jorge's qualifications can be measured by various factors such as his college degree, GPA, relevant coursework, internships, and any additional certifications he may have obtained. These factors contribute to his overall level of qualification, denoted as x.

Mathematically, we can express this as:

C(x) ≥ D(x)

This inequality indicates that Jorge's qualifications need to meet or surpass the demands of the job market for him to be considered a strong candidate for the career opportunities he desires.

In summary, Jorge's current situation involves a pursuit of a fulfilling career that matches his aspirations.

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Answer:

4 tens, 3 twenties

Step-by-step explanation:

4 tens  ($40) and 3 ($60)  twenties work. I’m sorry I don’t have a formula for it though.

In the fourth stanza, William Blake proposes the course of action of not ceasing from the mental fight and not letting his sword sleep in his hand until they have built Jerusalem in England’s green and pleasant land.

The stanza from the poem "Jerusalem" by William Blake is given below:"Bring me my bow of burning gold!Bring me my arrows of desire!Bring me my spear!O clouds, unfold!Bring me my chariot fire.I will not cease from mental fight,Nor shall my sword sleep in my hand‘Til we have built Jerusalem In England’s green and pleasant land."Explanation:The poem "Jerusalem" is a poem by William Blake that was published in his book Milton: a Poem in 1804. It is the preface poem of the work, which is a long poem consisting of 12 books. The poem is inspired by the legend of the young Jesus Christ who is said to have visited England during his early life. It is a hymn of English nationalism and uses the image of Jerusalem as a metaphor for a new and better society.Blake's Jerusalem is not just a physical place but a metaphorical one as well. The poem urges people to strive for a better, more just society. He uses his imagery of building Jerusalem to convey his message. Blake's use of the phrase "mental fight" suggests that this is not a physical battle but a battle of the mind. Blake believes that people must not give up the fight and must continue to fight for a better society. Therefore, in the fourth stanza of the poem "Jerusalem," Blake proposes the course of action of not ceasing from the mental fight and not letting his sword sleep in his hand until they have built Jerusalem in England’s green and pleasant land.

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A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².

The Area of one triangular face can be calculated as;

A = area of triangle = ½ x b x h

Where,

b = 32 ft

h = 20 ft

A = ½ x 32 x 20 = 16 x 20

A = 320 ft²

Area of 1 triangular face = 320 ft²

B.

Total surface area = area of the 4 triangular faces + area of the base of the square pyramid

T.S.A = 4(320) + (s²)

Where,

s = 32 ft

T.S.A = 4(320) + (32²)

T.S.A = 1,280 + 1,024

= 2,304 ft²

A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².

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The value of the given function `limit as x approaches infinity is the square root of (x^2+1)` is √(x^2 + 1).

We have to find the value of the limit as x approaches infinity for the given function f(x) = sqrt(x^2 + 1).

Let's use the method of substitution.

Replace x with a very large value of positive integer 'n'.

Now, let's solve for f(n) and f(n+1) to check the behavior of the function.f(n) = sqrt(n^2 + 1)f(n+1) = sqrt((n+1)^2 + 1)f(n+1) - f(n) = sqrt((n+1)^2 + 1) - sqrt(n^2 + 1)

Let's multiply the numerator and denominator by the conjugate and simplify:

f(n+1) - f(n) = ((n+1)^2 + 1) - (n^2 + 1))/ [sqrt((n+1)^2 + 1) + sqrt(n^2 + 1)]f(n+1) - f(n) = (n^2 + 2n + 2 - n^2 - 1)/ [sqrt((n+1)^2 + 1) + sqrt(n^2 + 1)]f(n+1) - f(n) = (2n+1)/ [sqrt((n+1)^2 + 1) + sqrt(n^2 + 1)]

Thus, we can see that as n increases, f(n+1) - f(n) approaches to 0. Therefore, the limit of f(x) as x approaches infinity is √(x^2 + 1).

Therefore, the value of the given function `limit as x approaches infinity is the square root of (x^2+1)` is √(x^2 + 1).

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The mean of the difference in sample means is 30 and the variance of the difference in sample means is 533.33. The probability that the average amount of dissolved metals at Jack Creek is at least 50 more than the average amount of dissolved metals at Cataract Creek is approximately 8.5%.

A) To find the mean and variance of the difference in sample means, we can use the following formula:

Mean of the difference in sample means = mean of Jack Creek sample - mean of Cataract Creek sample

= 1000 - 970

= 30

The variance of the difference in sample means = (variance of Jack Creek sample/sample size of Jack Creek) + (variance of Cataract Creek sample/sample size of Cataract Creek)

\(\frac{40^2}{30} + \frac{20^2}{15}\)

= 533.33

Therefore, the mean of the difference in sample means is 30 and the variance of the difference in sample means is 533.33.

B) To find the probability that the average amount of dissolved metals at Jack Creek is at least 50 more than the average amount of dissolved metals at Cataract Creek, we need to find the probability that the difference in sample means is at least 50.

We can standardize the difference in sample means using the formula:

\(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

Where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Using the given values, we can calculate the standard error of the difference in sample means:

\(SE = \sqrt{\frac{40^2}{30} + \frac{20^2}{15}}\)

= 14.55

Then, we can calculate the Z-score:

Z = (50 - 30) / 14.55

= 1.38

Using a standard normal table, we find that the probability of a Z-score being greater than 1.38 is 0.0847. Therefore, the probability that the average amount of dissolved metals at Jack Creek is at least 50 more than the average amount of dissolved metals at Cataract Creek is 0.0847, or approximately 8.5%.

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Answer:

y = 2x + 16

Step-by-step explanation:

slope is parallel and equal to y = 2x + 6

y intercept = 16

Answer:

b - y=2x+16

Step-by-step explanation:

y=y1+m(x+x1)

(-4,8)

y=8+2(x-4)

y=8+2x-8

add 8 on both sides

y=2x+16

Answer:

c. 40.32%

Step-by-step explanation:

8.77-6.25 = 2.52

2.52/6.25 x 100 = 40.32%

Hope this helps!

Answer:

c. 40.32%

Step-by-step explanation:

ΔTRP~ΔTSG by AA~

============================================

Further Explanation:

Triangles TRP and TSG share an overlapping angle at point T. This is one pair of congruent angles.

Due to the parallel lines (PR and GS), we can get two more pairs of congruent angles:

These congruences are valid because of the corresponding angle theorem.

You could use all three, but at minimum, you only need 2 pairs of congruent angles. Once we have two pairs of congruent angles, we can use the AA (angle angle) similarity theorem. Your teacher has abbreviated this as AA~

We cannot use SAS and SSS because we don't have any information about the sides.

Let "c" represent the amount of cashews they each bought.

Let "p" represent the amount of peanuts they each bought.

Mike: 2c + 1.5p = 26

Jim: 2.5c + 1 p = 29

That's the system you need to solve.  We can do this with substitution.

Start with Jim:

    2.5c + p = 29

               p = 29 - 2.5c

Substitute that into Mike and solve for c:

                  2c + 1.5p = 26    

   2c + 1.5(29 - 2.5c) = 26    

    2c + 43.5 - 3.75c = 26

           -1.75c + 43.5 = 26

                      -1.75c  = - 17.5

                             c  = 10

Now substitute that back into Jim's last equation:

               p = 29 - 2.5c

               p = 29 - 2.5(10)

               p = 29 - 25

               p = 4

So they each bought 10 pounds of cashews and 4 pounds of peanuts.

Answer:

d) 94°

Step-by-step explanation:

supplementary means 'adds up to 180°

86 + m∡3 = 180

m∡3 = 180 - 86

The probability that Jill and Ramona will be paired together is given as follows:

1/4.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of pairs for this problem is given as follows:

2² = 4.

Jill and Ramona form one pair, hence the probability is given as follows:

p = 1/4.

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Answer:

see explanation

Step-by-step explanation:

x² - 8x - 9 = 0 ← in standard form

(x - 9)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 1 = 0 ⇒ x = - 1

-------------------------------------------------

100x² - 20x = 0 ( divide through by 20 )

5x² - x = 0 ( factor out x from each term )

x(5x - 1) = 0

x = 0

5x - 1 = 0 ⇒ 5x = 1 ⇒ x = \(\frac{1}{5}\)

------------------------------------------------

2x² - 7x - 15 = 0 ← in standard form

(2x + 3)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - \(\frac{3}{2}\)

x - 5 = 0 ⇒ x = 5

---------------------------------------------------------

x² + 9x + 13 = - 5x - 20 (add 5x + 20 to both sides )

x² + 14x + 33 = 0 ← in standard form

(x + 11)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 11 = 0 ⇒ x = - 11

x + 3 = 0 ⇒ x = - 3

-----------------------------------------------------------

3x² - 12x + 5 = 9 - 4x² ( subtract 9 - 4x² from both sides )

7x² - 12x - 4 = 0 ← in standard form

(7x + 2)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

7x + 2 = 0 ⇒ 7x = - 2 ⇒ x = - \(\frac{2}{7}\)

x - 2 = 0 ⇒ x = 2

Solution set of the given quadratic equations are

1. x = 9 or x = -1

2. x=0 or x = 1 / 5

3. x= 5 or x = -3/2

4. x= -11 or x= -3

5. x= 2 or x= -2/7

" Quadratic equation is an algebraic expression in which highest degree of the given variable is 2."

Formula used

x² +ax + b = (x + c)(x + d)

Where 'a' is the sum 'c' and 'd'

and 'b' is the product of 'c' and 'd'

According to the question,

Factorize all the given quadratic equations we get,

1. x² - 8x - 9 =0

Split middle term of quadratic equation using formula we get,

  x² - 9x + x -9 =0

⇒ x(x-9) +1(x - 9) =0

⇒(x -9)(x +1) =0

⇒ x- 9 =0 or x + 1 =0

⇒ x= 9 or x =-1

2. 100x² -20x =0

⇒20x( 5x -1) =0

⇒ 20 ≠ 0, x=0 or 5x - 1=0

⇒ x =0 or x = 1/5

3. 2x² -7x -15 =0

Split middle term of quadratic equation using formula we get,

2x² -10x + 3x -15 =0

⇒ 2x(x-5) +3(x-5)=0

⇒(2x+3)(x-5)=0

⇒2x+3 =0 or x-5 =0

⇒ x= -3/2 or x=5

4. x² +9x +13 = -5x -20

⇒x² +9x + 5x+13 + 20 = 0

⇒x² +14x +33 =0

Split middle term of quadratic equation using formula we get,

  x² +11x +3x+33 =0

⇒x(x+11) +3(x+11) =0

⇒(x+3)(x+11) =0

⇒ x= -3 or x=-11

5. 3x² -12x +5 = 9- 4x²

⇒3x²+4x² -12x +5 -9 =0

⇒7x² -12x -4=0

Split middle term of quadratic equation using formula we get,

⇒7x² -14x +2x -4 =0

⇒7x(x-2) +2(x-2)=0

⇒(7x+2)(x-2)=0

⇒7x+2 =0 or x-2 =0

⇒x = -2/7 or x=2

Hence, the solution set of the given quadratic equations are

1. x = 9 or x = -1

2. x=0 or x = 1 / 5

3. x= 5 or x = -3/2

4. x= -11 or x= -3

5. x= 2 or x= -2/7

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Answer:

i think your answer would be 35

Step-by-step explanation:

oh sorry it's answer is 42.

calculate by adding all the individuals less than 40

Answer:

Positive discriminant = 2 real solution

x= -5,-40

Step-by-step explanation:

The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.

The discriminant is the part of the quadratic formula inside the square root:

\(b^{2}-4ac\)

Every quadratic formula has the structure:

\(ax^{2} +bx+c=0\)

So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:

\(x^{2} +45x+200=0\)

Our a=1, b=45 and c=200

Now we can substitute these values into the discriminant:

\((45)^{2} -4(1)(200)\)

Solve:

\(2025-800=1225\)

The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:

\(x=\frac{-+/-\sqrt{b^{2}-4ac} }{2a} \\x=\frac{-45+/-\sqrt{1225} }{2}\)

(Same discriminant value)

\(x=\frac{-45+/-35}{2}\)

Now to find the two solutions, we use both signs in the equation. Solution 1:

\(x=\frac{-45+35}{2}\)

\(x=\frac{-10}{2}=-5\)

Our first solution is -5, now for the second:

\(x=\frac{-45-35}{2}\\\\ x=\frac{-80}{2}=-40\)

The two solution to this equation are -5 and -40.

Hope this helped!

Answer:

Tall = 32.9 in

Step-by-step explanation:

Pythagorean theorem:

diagonal² = width² + tall²

59² = 49² + tall²

3481 = 2401 + tall²

3481 - 2401 = tall²

1080 = tall²

√1080 = √tall²

tall = 32.863 in

The nearest thent is:

32.9 in

the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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