Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation Vh=500(1.025)^t , where Vh is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
B) Va=500(1.025)^t+3 and Va=538.45(1.025)^t
C)Va=500(1.025)^t-3 and Va=538.45(1.025)^t
D)Va=500(1.025)^t+3 and Va=464.30(1.025)^t

The number of users on new social media site increase as 21, 25, 30, 36,
The average rate of change is given by 5.

The function f (t) = 12 (1.2) ^t show how the rate of users increases in weeks.

Average of the values is the ratio of total sum of values to the number of values.

Here,  f (t) = 12 (1.2) ^t is defined in the range of (3, 6)
So the value of the function in its range is given by
1)  f (3) = 12 (1.2) ^3
          = 21
2)  f (4) = 12 (1.2) ^4
   =  25
3)   f (5) = 12 (1.2) ^5
    = 30
4)   f (6) = 12 (1.2) ^6
     = 36
Now the average rate of change = sum of all difference in values at every week / max. Difference in interval of range(3,6)

= f(6)-f(3)/6-3
= 15/3
= 5

Thus required average change of rate is 5.

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The solution of the first graph is 1, 2 while the second graph is a straight line.

We have y > 2x

y< x

First you have to replace the inequality by a mathematical operator

y - 2x = 0

y - 3 = 0

equation 1 is of the form

y = mx

The slope here is 2,

to make a graph we need to have x = 1 then the line would pass through

(1,2).

The second equation is simply a second line that would pass through the x axis.

The correct graph is below:

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Number of physics textbooks sold was 261 & number of maths textbooks sold was 199.

Let, the number of physics textbooks sold = x

According to the question,

The number of math textbooks sold was 62 less than the number of physics textbooks sold.

So, Number of maths textbooks sold = x-62

The textbook store sold a combined total of 460 physics and math textbooks in a week.

So, the equation becomes,

(x-62)+x = 460

⇒ x-62+x = 460

⇒ 2x-62 = 460

⇒ 2x = 460+62

⇒ 2x = 522

⇒ x = 522/2

⇒ x = 261

So, 261 physics textbooks were sold

(261-62) = 199 maths textbooks were sold.

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Answer:

A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

A ∩ B = {3, 1, 2, 4, 5}

Step-by-step explanation:

Given that A = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

B = the set of all Natural numbers

C= the set of all Rational numbers

So set C contains numbers that can be expressed as the ratio of two integers. Since numbers in A can be expressed as follows:

0 = 0/1,  3 = 3/1,  1 = 1/1, 1.3 = 13/10, 2 = 2/1,  4 = 4/1, 5 = 5/1

Then, A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}.

A ∩ B = {3, 1, 2, 4, 5}, since B contains only Natural numbers = {1, 2, 3, ...}.

Answer: the one on the right on the top

Step-by-step explanation:

as x increases by 1, y decreases by 2. this makes a linear function

Answer: the answer is the first option

Step-by-step explanation:

Question : Draw a triangle ABC. Next, create a line through point C that is perpendicular to . Label the intersection between the perpendicular line and as point E. Take a screenshot of the triangle with CE, save it, and insert the image in the space below.

We know that having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional shape. A polygon also includes a triangle.

A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.

The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). The Latin word "perpendicularis," which denotes a plumb line, is where the word "perpendicular" first appeared. Two lines, AB and CD, can be written as AB⊥CD if they are perpendicular to one another. The perpendicular nature of the lines is denoted by the symbol.

Here, we have to draw a triangle. Then we have to draw a line CE which intersects AB at point E.

Image is attached below.

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The value of the expression is 188

Given the expression

= [tex]\frac{7 + (2 + 6)^2}{4 * \frac{1}{2}^4}[/tex]

Expand the bracket

= [tex]\frac{7 + 4 + 36}{ 4 * 1/16}[/tex]

We have

= [tex]\frac{47}{1/4}[/tex]

The denominator becomes the multiplier, we have

= 47 × 4

= 188

Thus, the value of the expression is 188

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Answer:

The G.C.F of (8,24) is 8

Step-by-step explanation:

look at the attachment above ☝️

The end behaviour of the function is When x ---> ∞ , f(x) ---> -∞  , when x ---> -∞ f(x) ----> ∞  , Option D is the correct answer.

A function is a mathematical statement that related the independent and the dependent variable.

The function given is

f(x) = [tex]\rm -2 \sqrt[3]{x}[/tex]

To understand the end behaviour the graph is plotted

When x ---> ∞ , f(x) ---> -∞

when x ---> -∞ f(x) ----> ∞

Therefore Option D is the correct answer.

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The equations for the lines tangent to and normal to the curve at the point (2, 4) are y = 4 · x - 4 and y = (-1/4) · x + 9/2, respectively.

In this question we must use the definitions of linear function, tangent and normal lines and differential calculus to determine the equations needed. The slope of the tangent line (m) is found by implicit differentiation:

2 · x + 2 · y · y' - 3 · (y + x · y') = 0

2 · x + (2 · y - 3 · x) · y' - 3 · y = 0

(2 · y - 3 · x) · y' = 3 · y - 2 · x

y' = (3 · y - 2 · x)/(2 · y - 3 · x)

By (x, y) = (2, 4)

m = (3 · 4 - 2 · 2)/(2 · 4 - 3 · 2)

m = 4

And the slope of the normal line is:

m' = -1/m = -1/4

Lastly, we obtain the intercept for each line:

Tangent line

b = 4 - 4 · 2

b = 4 - 8

b = - 4

The equation of the line tangent to the curve at the point (2, 4) is y = 4 · x - 4.

Normal line

b = 4 - (-1/4) · 2

b = 4 + 1/2

b = 9/2

The equation of the line normal to the curve at the point (2, 4) is y = (-1/4) · x + 9/2.

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Answer:

Graph Number 2

Step-by-step explanation:

Use the horizontal line test: If you can draw a horizontal line at any point and it only intersects the line once, then it's a one-to-one function.

four less than three times that number is:3x-4

is:=

three more than two times the number: 2x+3

Problem to solve:

3x-4=2x+3

3x-2x-4=2x-2x+3

x-4=3

x-4+4=3+4

x=7

Calculated:

3(7)-4=2(7)+3

21-4=14+3

17=17

The sum of the next 5 consecutive positive integers is w + 25

Let the first five numbers be A - E

So, we have:

A + B + C + D + E = W

The next five numbers would be

A + 5, B + 5...... E + 5

So, we have:

Sum = A + 5 + B + 5 + C + 5 + D + 5 + E + 5

Evaluate the like terms

Sum = A + B + C + D + E + 25

Substitute A + B + C + D + E = W

Sum = W + 25

Hence, the sum of the next 5 consecutive positive integers is w + 25

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The value of y in the code segment is 444

The code segment is given as:

y = int(3 * '4')

Evaluate the expression in the bracket

y =int('444')

Remove the bracket

y = 444

Hence, the value of y in the code segment is 444

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Answer:

AC Factor: 420

Factors that add up to 41: 20 and 21

Rewritten equation: [tex](35x^2+21x)+(20x+12)[/tex]

Step-by-step explanation:

so a quadratic equation is generally expressed as [tex]ax^2+bx+c[/tex]. So in this polynomial 35=a and c=12. The ac product would thus be (35)(12) which is 420

The factors of the AC product include: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20 , 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Since we're looking for a bigger number which is 41 you would generally want to look near the middle. and you can disregard any factors equal to or above 42. since they wouldn't add to 41. So I'll start at 30. 420/30 = 14 and 30 + 14 = 44 which is pretty close. Alright I'll try 28 instead. 420/28 = 15 and 15+28 = 43 which is also pretty close so I'll try the next factor 420/21 = 20 and 20+21 = 41! so the two factors are 20 and 21

Now using these two factors you can rewrite the equation as

[tex](35x^2+21x)+(20x+12)[/tex] which simplifies to the same quadratic equation

y=35x²+41x+12

Here

So

Now

Factors that add up to 41 are 21 and 20

Now solve

The coordinates of B' are 3 and -12. so option D is correct (3, -12)

The point P(x, y) may undergo translation to form P' by using a defined translation rule :

If given the rule T(a, b) synch that P undergoes translation on T; then we will have P'(x+a; y+b)

Therefore,

The point B has its coordinates as B(1, - 5)

Translation rule, T(2, - 7) then the coordination of B after undergoing transformation according to T2;

B(1, - 5) - - - > T(2, - 7) - - - - > B'(1+2 ; - 5+-7)

= B'(3, -12)

Hence, the coordinates of B' are 3 and -12. so option D is correct.

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Answer:

(D)   (3, –12)  

Step-by-step explanation:

If a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'? The answer is (3, –12).

The solution to the given expression is 2

Given the equation 48 ÷ ((2 + 6) × 2) − 1

Using PEMDAS

48 ÷ ((8) × 2) − 1

48÷(16) - 1

3 - 1

2

Hence the solution to the given expression is 2

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The bolt of length more than 7.2 cm will be destroyed.

Mean refers to the central tendency of a data set. It is calculated by taking average of the data.

It is given that

any bolts that are more than 2 standard deviations from the mean will be destroyed

Mean = 7 cm

Standard Deviation is = 0.10 cm

The length of the bolt which is not acceptable is = Mean + 2 Standard Deviation.

Length = 7 + 2 * 0.10

Length = 7.2 cm

Therefore if the bolt of length more than 7.2 cm will be destroyed.

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Answer:

96 sq. inch

Step-by-step explanation:

rectangle has 24 inches × 8 inches dimensions

Hence, Area of Rectangle,

A1=24×8

=192 sq. inch

We, know triangle with base 24 inches and height 8 inches has area exactly half of the rectangle's.

ie. A2=½(24×8)

=96 sq. inch

This was for unshaded region. Then remaining half area is for shaded region.

A1-A2=A

ie. 192-96=96 sq. inch

The area of the shaded region is 96 square inches.

To find the area of the shaded region, we need to subtract the area of the triangle from the area of the rectangle.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the rectangle has a length of 24 inches and a width of 8 inches, so its area is 24 inches * 8 inches = 192 square inches.

The area of a triangle is calculated by multiplying its base by its height and dividing the result by 2. In this case, the triangle has a base of 24 inches and a height of 8 inches, so its area is (24 inches * 8 inches) / 2 = 96 square inches.

Now, to find the area of the shaded region, we subtract the area of the triangle from the area of the rectangle:

Shaded Area = Area of Rectangle - Area of Triangle

= 192 square inches - 96 square inches

= 96 square inches

Therefore, the area of the shaded region is 96 square inches.

..

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Answer:

4x+6

Step-by-step explanation:

x/x^2+3x+2 + 3/x+1

x/(x+1)(x+2) + 3/x+1

make the denominator the same

x/(x+1)(x+2) + 3 (x+2)/(x+1)(x+2)

x/(x+1)(x+2) + 3x+6/(x+1)(x+2)

4x+6/(x+1)(x+2)

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The requried, numerator of the simplified sum is 4x + 6. The option is correct.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property

The given expression is x/(x²+3x+2) + 3/(x+1). To make the denominators the same, we need to factor the denominator of the first fraction:

x/(x+1)(x+2) + 3/(x+1)

Now we can add the two fractions by finding a common denominator, which is (x+1)(x+2):

x/(x+1)(x+2) + 3(x+2)/(x+1)(x+2)

Simplifying the numerators, we get:

x + 3x + 6 / (x+1)(x+2)

Combining like terms in the numerator, we get:

4x + 6 / (x+1)(x+2)

Therefore, the simplified expression is (4x+6)/(x+1)(x+2).

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Considering that there are only two possible outcomes for each number, and a fixed number of numbers, the distribution is:

C. binomial.

We have that:

Hence the binomial distribution should be used and option B is correct.

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For the coordinate (5,6), the 90 degree rotation will be equivalent to (-6, 5)

Rotation is a technique used to change the position of an object on an xy-plane.

If the coordinate point (x, y) is rotated 90degrees, the rule will be:

(x, y) -> (-y, x)

For the coordinate (5,6), the 90 degree rotation will be equivalent to (-6, 5)

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Answer:

1 2/3

Step-by-step explanation:

12 inches = 1 foot

So, 20/12 is equal to 1 8/12 foot

remeber to simplify though, so 8/12 simplified is 2/3, so the solution to the problem is 1 2/3 foot

The triangle KLM is rotated about origin by 90 degrees to form the triangle K'L'M'.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Rotation does not change the size and shape of the geometry.

The triangle KLM is rotated about origin by 90 degrees to create the triangle K'L'M'.

The diagram is given below.

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Aimee is shipping a care package to her friend in college, the max volume of the box is mathematically given as

V=1539.6007

Generally, the equation for the height is mathematically given as

V=(20-2x)(40-2x)x

Where x is the height

V=4x^3-120x^2+800x

differentiate v and solve

dv/dx=3x^2-60+200

3x^2-60+200=0

Therefore

x=[tex]\frac{60\pm \sqrt{60^2-4x3x200}}{2*3}[/tex]

x=[tex]\frac{60-34.64}{6}[/tex]

x=4.2265

In conclusion, the second differentiation of v and solve we have

d^2v/dx^2=24-240

Hence

d^2v/dx^2< 0

V=(20-2x(40-2x)x

subsitute x

V=(20-2(4.2265))(40-2(4.2265))(4.2265)

V=1539.6007

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Answer:

2nd Option

Step-by-step explanation:

Hello!

First, let's solve the inequality for x.

Since the symbol is less than or equal to, it will be a closed circle on Point -8 going in the left direction (all values less than -8).

The answer is the Second Number Line.

Answer:

Solve for x

One exterior angle (x) equals to sum of two remote interior angles 50°, 75°

x = 50° + 75

x = 125°

Solve for y

Enclosed by parallel lines, the angles equals to 180°

55° + 50° + y = 180°

105° + y = 180°

y = 180° - 105°

y = 75°

In accordance with propositional logic, quantifier theory and definitions of simple and composite propositions, the negation of a implication has the following equivalence:

[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex] (Correct choice: iii)

Herein we have a composite proposition, that is, the union of monary and binary operators and simple propositions. According to propositional logic and quantifier theory, the negation of an implication is equivalent to:

[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex]

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Using it's concept, an even function is given by:

B. [tex]F(x) = 2\cos{\frac{1}{2}x}[/tex]

Even functions are functions for which the following statement is true for all values of x.

f(x) = f(-x).

The cosine function, without a phase shift, is an example of an even function, hence option B is correct.

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Answer:

K=4a-1

Step-by-step explanation:

K = 4a- 1 (shifting -4a to right side from left)