Grade 11 Math:

Application

3. When Jennifer turned 12 years old, her grandmother gave her $100. Jennifer deposited

the money into a savings account that paid 3.5%/a compounded annually. Since then,

Jennifer’s grandmother has made an automatic deposit of $100 into her account every

year.

a) What is the total amount of the annuity on Jennifer’s 18th birthday? [3 marks]

b) How much of the annuity is interest earned? [1 mark]

Answer:

2 × 10³

Step-by-step explanation:

a number expressed in standard form is

a × [tex]10^{n}[/tex]

where 1 ≤ a < 10 and n is an integer

4 ×[tex]10^{8}[/tex] × 5 × [tex]10^{-6}[/tex]

= 4 × 5 × [tex]10^{8}[/tex] × [tex]10^{-6}[/tex]

= 20 × [tex]10^{(8-6)}[/tex]

= 20 × 10²

= 2 × [tex]10^{1}[/tex] × [tex]10^{2}[/tex]

= 2 × [tex]10^{(1+2)}[/tex]

= 2 × 10³

Answer:

[tex]2.0 \times {10}^{3} [/tex]

is correct ans

Answer:

x = 9

Step-by-step explanation:

When 1 is divided by 9, we understand it is a non-terminating decimal number because the denominator consists of other number other than 2 and 5.

Now, let's get into how to solve for x :

Divide both sides by .111... :

1/.111... x .111... = 1/.111 x 1/x

1 = 1/(x)(.111....)

Multiply both sides by x :

1(x) = (x)/(x)(.111...)

x = 1/.111...

x = 9 (nearest whole number)

Answer:

[tex]\sf 0.\dot{1}=\dfrac{1}{9}[/tex]

Therefore, x = 9

Step-by-step explanation:

To convert 0.11111... to a fraction:

Equation 1

Let:   y = 0.11111...

Equation 2

Multiply both sides by 10:

⇒ y · 10 = 0.11111... · 10

⇒ 10y = 1.11111...

Subtract Equation 1 from Equation 2 to eliminate the recurring digits after the decimal:

⇒ 10y - y = 1.1111... - 0.11111...

⇒ 9y = 1

Divide both sides by 9

[tex]\implies \sf y=\dfrac{1}{9}[/tex]

Therefore,

[tex]\sf 0.\dot{1}=\dfrac{1}{9}[/tex]

So if:

[tex]\sf 0.\dot{1}=\dfrac{1}{x}[/tex]

Then x = 9

The answer could be c

Because the title of the table says the  dollar sales and how much it's increasing so my answer is c

Hope I helped!

TheOneAndOnlyLara~

Answer:

C.

Step-by-step explanation:

Hope it helped!

Answer:

747

Step-by-step explanation:

Have a great day!!

Step-by-step explanation:

the answer for this is 747

Answer:

see picture for the coordinates

A’ = -2,-4

B’ = -3,-7

C’ = -1,-8

D’ = 1,-6

Step-by-step explanation:

add the translation coordinates to the original to get new coordinates

Answer:

Given translation:

Therefore,

⇒ (x, y)  →  (x - 4, y - 3)

Calculations

A (2, -1) ⇒ (2 - 4, -1 - 3) = A' (-2, -4)

B (1, -4) ⇒ (1 - 4, -4 - 3) = B' (-3, -7)

C (3, -5) ⇒ (3 - 4, -5 - 3) = C' (-1, -8)

D (5, -3) ⇒ (5 - 4, -3 - 3) = D' (1, -6)

Therefore, the new coordinates using prime notation are:

Answer:

I belive c angle bisector

Answer:

  ∠TRV and ∠WRS  or  ∠TRS and ∠WRV

Step-by-step explanation:

Vertical angles are angles that share a vertex and have sides that are opposite rays. That is, the opposites of the rays that form one of the angles are the rays that form the other angle.

__

Where lines cross, two pairs of vertical angles are formed. In your diagram, those pairs are ...

  ∠TRV and ∠WRS . . . . one vertical angle pair

  ∠TRS and ∠WRV . . . . another vertical angle pair

_____

Additional comment

In this diagram, the ray RU is of no consequence with respect to any vertical angles. It can be ignored.

The vertical angles will each have one red ray and one blue ray as sides. These rays have end point R. No sides are shared.

Answer:

second option, x + 2y = 3

Step-by-step explanation:

The slope intercept form is y = mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The y - intercept is when x = 0

In the table its shown that (0, 3), y = 3 so b = 3

The slope (gradient) is a number that describes both the direction and the steepness of the line.

slope = rise / run = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

(x_1, y_1)   = coordinates of first point in the line

(x_2, y_2)  = coordinates of second point in the line

x is increasing by 1 (run)

y is decreasing by 2 (rise)

rise / run = -2 / 1 = -2

so the slope is -2

our slope intercept equation is, y = -2x + 3

Choice:

Some choice are in standard form so we need to convert to slope intercept

subtract 2x from both sides, 2x - 2x + y = 3 - 2x

subtract x from both sides, x - x + 2y = 3 - x becomes 2y = 3 - x

divided both sides by 2, 2y / 2 = (3 - x) / 2

subtract x from both sides, x - x - y = 0 - x than switch signs

which option matches?!

THE SECOND ONE

Answer:

hmm try multiplying every number at the top and then put them all together

then divide the answer u got and u have ur answer :)

Step-by-step explanation:

From the graph, the domain of the function will be {x| x = −2,1}. Then the correct option is D.

An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.

From the graph, the domain of the function will be

The function is not defined for x = 2 and x = -1.

Then the domain will be

{x| x = −2,1}

Then the correct option is D.

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The linear factors of the function are the x-intercepts which are (x + 5), (x + 2), (x - 1) and (x - 6)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the graph of the function. The linear factors of the function are the x-intercepts which are (x + 5), (x + 2), (x - 1) and (x - 6)

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Answer:

Parent function

[tex]f(x)=\log_2(x)[/tex]

Since we cannot take logs of zero or negative numbers, the domain is [tex](0, \infty)[/tex] and there is a vertical asymptote at [tex]x=0[/tex].

There are no horizontal asymptotes and the range is [tex](- \infty,\infty)[/tex].

The end behaviors of the parent function are:

[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow - \infty[/tex]

[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]

To determine the attributes of the given function, compare the given function with the parent function.

Given function

[tex]f(x)=- \log_2(x)+5[/tex]

The given function is reflected in the x-axis.  Therefore, the end behaviors are a reflection of those of the parent function:

[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow \infty[/tex]

[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow - \infty[/tex]

As the given function is translated vertically (5 units up) only, the domain, range and asymptote will not change, since the function has not been translated horizontally.

[tex]\textsf{Domain}: \quad (0, \infty)[/tex]

[tex]\textsf{Range}: \quad (- \infty, \infty)[/tex]

[tex]\textsf{Asymptote}: \quad x=0[/tex]

Conclusion

The function f(x) is a [tex]\boxed{\sf logarithmic}}[/tex] function with a [tex]\boxed{\sf vertical}}[/tex] asymptote of [tex]\boxed{x = 0}[/tex].  

The range of the function is [tex]\boxed{(- \infty, \infty)}[/tex], and it is [tex]\boxed{\sf decreasing}[/tex] on its domain of [tex]\boxed{(0, \infty)}[/tex].  

The end behavior on the LEFT side is as [tex]\boxed{x \rightarrow 0^+}[/tex], [tex]\boxed{f(x) \rightarrow \infty}[/tex], and the end behavior of the RIGHT side is [tex]\boxed{x \rightarrow \infty}[/tex], [tex]\boxed{f(x) \rightarrow -\infty}[/tex].

The number of socks for Hailey will be 163.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The number of Haley's socks will be calculated as=

Socks = 777 x 21/100

Socks = 777 x 0.21

Socks = 163

Therefore the number of socks for Hailey will be 163.

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Answer:

10%

Step-by-step explanation:

(26-23.40)/26x100%

Answer:

10%

Step-by-step explanation:

Answer: LN = 15

Make a proportional relationship:

[tex]\sf \dfrac{LN}{JL} = \dfrac{LM}{KL}[/tex]

Insert the values:

[tex]\rightarrow \sf \dfrac{LN}{30} = \dfrac{6}{30-18}[/tex]

cross multiply:

[tex]\rightarrow \sf LN = \dfrac{30(6)}{12}[/tex]

Simplify:

Answer:

LN = 15

Step-by-step explanation:

The arrows on the line segments indicate they are parallel.

[tex]\implies \overline{KM} \parallel \overline{JN}[/tex]

Triangle Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then it divides these two sides proportionally.

[tex]\textsf{If }\overline{KM} \parallel \overline{JN}, \textsf{ then }\dfrac{LK}{LJ}=\dfrac{LM}{LN}[/tex]

Given:

⇒ LK = JL - JK = 30 - 18 = 12

Substituting the values into the equation and solving for LN:

[tex]\begin{aligned}\implies \dfrac{LK}{LJ} & = \dfrac{LM}{LN}\\\\\dfrac{12}{30} & = \dfrac{6}{LN}\\\\12LN & = 30 \cdot 6\\\\LN & = \dfrac{180}{12}\\\\LN & = 15\end{aligned}[/tex]

The equivalent expression of the given expressions is 2x + 5.

Expressions are statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is,

3 + 2x - 9 - 4x + 11 + 5x - x

There are like terms in the expression, which can be operated together.

Write terms with variables together and the constants together.

3 + 2x - 9 - 4x + 11 + 5x - x

= (2x - 4x + 5x - x) + (3 - 9 + 11)

= 2x + 5

Hence the given expression can be simplified to 2x + 5.

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Answer:

Unless im being completely braindead right now there isn't a whole number that works with this. When simplified its 5/2 or 2.5 but because it isn't an actual whole number (like 2, 4 and 6) they don't count.

Answer:

between two whole numbers 2 and 3 or just 3.

Step-by-step explanation:

The answer to 250/100 would be 2.5 but that is a decimal and not a whole number. You couod round 2.5 to 3 to make it a whole nunber or you say that it is in between two whole nunbers which are 2 and 3 if you are allowed to. (since 2.5 alone is not a whole number)

From the given choices, the answer is option A: It is symmetric and has no gaps.

A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark.

The horizontal axis label is Dollar per hour.

There are 2 dots above 4 dollars, 3 dots above 5 dollars, 3 dots above 6 dollars, and 2 dots above 7 dollars.

The title of the line plot is Babysitting Rates.

A dot plot is the same as a histogram but it uses dots instead of bars.

The dot plot as described by the problem is shown in the picture.

A bell shape is drawn for symmetrical data.

From the given choices, the answer is option A: It is symmetric and has no gaps.

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The amount the money will be worth in 4 years is $4072.41

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

Given the following

P = $3700

rate r = 2.4% = 0.024

n =12

t = 4 years

Substitute

A = 3700(1+0.024/12)^12(4)
A = 3700(10.024/12)^48

A =  3700(1.10065)

A= 4072.41

Hence the amount the money will be worth in 4 years is $4072.41

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The missing length in triangle A given the similarity between the two triangles is 18.67

Triangle A is similar to triangle B

Triangle A:

Triangle B:

Ratio of side 1 to side 2 of the triangles respectively

(x + 2) : 8 = 14 : 6

(x + 2) / 8 = 14/6

(x + 2) × 6 = 8 × 14

6x + 12 = 112

6x = 112 - 12

6x = 100

x = 100/6

x = 16.67

Therefore, Triangle A:

Side 1 = (x + 2)

= 16.67 + 2

= 18.67

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Answer:

7

Step-by-step explanation:

4*(x-2)^2 - 9

replace x with 4;     4*(4-2)^2-9

solve inside parenthesis;    4*(2)^2-9

order of operations;     4*4 - 9 becomes 16-9=7

Operations that can be applied to a matrix in the process of Gauss-Jordan elimination are options 1,2 and 4.

Gauss-Jordan Elimination is a matrix-based technique for solving linear equations or determining a matrix's inverse.

When using Gauss Jordan elimination, the following operations may be carried out on a matrix:

1. Replacing a row with twice that row

2. Replacing a row with the sum of that row and another row

3. Swapping row

The optional row(or column) procedures that can be employed are:

1. Alternate any two rows (or columns)

2. Scalar multiples of one row (column) are added or subtracted from another row (column) occurs when a row is substituted with the sum of another row and that row.

3. Multiply any row (or column) fully by a nonzero scalar, as seen below by substituting a row with two rows.

Hence, Gauss-Jordan elimination includes options 1,2, and 4.

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Answer:15

Step-by-step explanation:

A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.

Let the distance of the ladder from the wall be x

The length of the ladder = x+3

The ladder touches the wall at a vertical height of 9 feet.

(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem

x^2 + 6x+ 9 = x^2 + 81

x^2- x^2 +6x = 81-9

6x= 72

x= 12

Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.

Answer:

A) y < 1/3x - 2

Step-by-step explanation:

Answer:

155 Degrees

Step-by-step :

(Time x Rate of Temp) + Initial Temp = Final Temperature

Ex. (6 * 15) + 65 = 155 Degrees

Answer:

The temperature of the oven 6 minutes after being turned on is 155°

The temperature of the oven t minutes after being turned on is 15t + 65

Step-by-step explanation:

y=mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The y intercept is when x = 0, so the initial temperature

b = 65°

The slope is increase at a rate of per minute after being turned on.

m = 15°

The y coordinate will represent the temperature of the oven after a certain amount of minutes after being turned on

y

The x coordinate will represent the amount of minutes after the oven being turn on

x = t

combine:

What is the temperature of the oven tt minutes after being turned on?

y = 15t + 65

What is the temperature of the oven 6 minutes after being turned on?

t = 6 minutes

y = 15t + 65

y = 15(6) + 65

y = 90 + 65

y = 155

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Answer:

Step-by-step explanation:

Quadratic trinomial

In order to determine what kind of roots it has, we need to find the value of the discriminant:

Since the discriminant is negative, its square root is an imaginary number, hence there is no real solution.

Correct answer choice is D.

Answer:

y=0.30x

Step-by-step explanation:

because the amount of money (the fee) will keep increasing with the multiplication of the amount of days

Answer:

the visible number of cubes is 7

Step-by-step explanation:

Assuming that there are no hidden cubes, the # of visible cubes is 7

Answer:

  250

Step-by-step explanation:

The sum of the terms of a geometric series is given by the formula ...

  Sn = a1×(1 -r^n)/(1 -r)

sum of n terms for first term a1 and common ratio r.

__

The given series has first term a1 = 150, and common ratio r = 60/150 = 2/5. Putting these values into the formula gives a sum of 7 terms that is ...

  S7 = 150×(1 -(2/5)^7)/(1 -2/5) = 150((77997/78125)/(3/5))

  S7 = 150×(25999/15625) = 249.5904

Rounded to the nearest integer, the sum of the first 7 terms is 250.

Answer:

5000 lbs

Step-by-step explanation:

if there ae 8 boxes and each one has the weight of 625 you will need to ultiply 8 by 625 and that will be 5000 pounds