Olivia deposited $2,136.70 into a saving account with an interest rate of 2.7% compounded quarterly. About how long will it take for the account to be worth $4,000?

Answer:

Step-by-step explanation:

a) From the image attached, the area of the small section is 16ft² and the area of the large  section is 50 ft². The area of a square = length × length = length².

For the small section: Area = length²

16 = length²

length = √16 = 4 ft

For the large section: Area = length²

50 = length²

length = √50

The length of entire shed = length of small area + length of large area = 4 + √50

The length of entire shed = 4 + √50

b) All square root of integers other than perfect squares are irrational numbers , hence 4 + √50 is an irrational number. All numbers belongs to the set of real numbers. Therefore  4 + √50 is an irrational number and real number

Answer:

y = 6/5x -2

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b

y = 6/5 x +b

We have a point on a line

4 = 6/5( 5) +b

4 = 6+b

Subtract 6 from each side

4-6 = 6+b-6

-2 = b

The equation is y = 6/5x -2

Answer:

( 9w - 2z)^2

Step-by-step explanation:

81w^2 - 36wz + 4z^2

Rewriting as

(9w)^2 - 2 * 9 w 2z + (2z)^2

We  recognize that this is a perfect square binomial

a^2 -2ab + b^2 is a perfect square binomial because it factors to (a - b)^2

let a = 9w  b = 2z

81w^2 - 36wz + 4z^2 = ( 9w - 2z)^2

Answer:

A)

Important information:

The total cost includes the price of 2 tickets and the price of yogurt.

The total cost: 19.90$

The price of yogurt: 5.5

The price of 2 tickets: unknown

Each of the tickets costs the same amount of money.

Verbal Description:

For the unknown value, the letter x is often selected to represent this unknown value.

Here, we select x that is the price of 1 ticket, then the price of 2 tickets would be 2x.

=> We have the equation: 2x + 5.5 = 19.90

Transfer 5.5 to the right, and then divide both sides by 2, we have:

(2x)/2 = (19.9 - 5.5)/2

Take the simplification, we have:

x = 7.2$ (this is the price of a ticket)

B)

Use the same strategy as shown in A), we have:

Total number of stamps: 100

Mari's number of stamps: x

Carlos's number of stamps: x + 5

Amanda's number of stamps: 3x

=> 3x + x + x + 5 = 100

=> 5x = 100 - 5

=> 5x = 95

=> x = 19

Mari's number of stamps: 19

Carlos's number of stamps: 19 + 5 = 24

Amanda's number of stamps: 3 x  19 = 57

C)

The perimeter of the garden:

perimeter = (width + length) x 2

perimeter = 256

width = w

length = w + 8

=> We have:

256 = (w + w + 8) x 2

<=>256 = (2w + 8) x 2

<=> 256/2 = (2w + 8) x 2/2

<=> 128 = 2w + 8

<=> 128 - 8 = 2w

<=> 120 = 2w

<=> w = 60

=> width of garden: 60

=> length of garden: 60 + 8 = 68

Answer:

68

Step-by-step explanation:

The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first point be A ( x₁ )

The value of A ( x₁ ) = A ( -12 )

Let the second point be B ( x₂ )

The value of B ( x₂ ) = B ( -7 )

Let the distance between the two points on the number line be = D

Now , the equation will be

The distance between the points A and B is calculated by

The distance D = B - A

Substituting the values in the equation , we get

The distance D = -12 - ( -7 )

Distance D = -12 + 7

Distance D = -5

Therefore , the value of D is -5

Hence , The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

x=−1,−7

Step-by-step explanation:

Answer:

The solutions are {-1, 9}

Step-by-step explanation:

x² - 8x + 16 can be re-written as (x - 4)^2, and 9 + 16 as 25.

Taking the square root of both sides of (x - 4)^2 = 25, we get:

x - 4 = ±5, or:

x = 4 + 5 = 9, and

x = 4 - 5 = -1

The solutions are {-1, 9}

Answer:

168 adult tickets were sold

Step-by-step explanation:

$10. 50 per adults

$3. 75 per student

There are 82 students..

.. So...

$3. 75 × 82 = $307. 50

Overall the amount of money made was $2071.50

If you subtract $307.50 from $2071. 50 you will get $1,764

We now need to find out how many adults bought tickets by dividing $1, 764 by the price adults have to pay so..

Amount of adults who bought tickets are

= $1, 764 ÷ $10. 50

= 186 adults

Answer: The answer is 6!

Step-by-step explanation:

Answer:

Strong Negative

Step-by-step explanation:

Took the test and know this is the right answer.

The direction and strength of the association between the variables is  strong negative.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The relationship between the variable X and Y plotted on the graph depicts a strong negative association between the two variables.

The direction of the trend on a linear plot gives an information about the direction of the slope of the graph, the graph slopes downwards as variable X increases, hence we have a negative relationship between X and Y

The trend produced by the graph is straight forward with points close to one another, hence forming a well - defined pattern. These depicts a Strong association between the variables.

When the trend isn't clearly defined and obvious, the relationship is weak.

Hence, the direction and strength of the association between the variables is strong negative.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ2

Answer:

63c^7 + 70c^3.

Step-by-step explanation:

7c^2(9c^5 + 10c)

= 7c^2 * 9c^5 + 7c^2 * 10c

= 63c^7 + 70c^3.

Answer:

The function would be positive in:

(-9, 3]

Step-by-step explanation:

A function is considered positive on the X-axis when the changed values ​​in the function are greater than zero.  f(x) > 0

And is considered negative when f(x) < 0.

In this case, the numbers that make the function positive are the numbers from -9 to 3, but not including -9.

This can be written as (-9, 3]

It means that -9 is not taken but any number greater than -9 is.

Here is the correct question

Gin Rummy and are holding 10 cards in your hand from a standard deck of 52 cards.

a) How many ways can you select three kings and four 6's from the deck, the remaining cards not kings or 6's

b) Find the probability that three kings and four 6's are being held by you from the deck.

Answer:

a) 52976

b) [tex]\mathbf{3.34866744 \times 10^{-6}}[/tex]

Step-by-step explanation:

So from the information above,

no of ways three kings can be selected and four 6's from the deck without the remaining cards being kings or 6's can be expressed as:

no of ways to select 3 kings from 4 kings is [tex](^4_3)[/tex]

no of ways to select 4 6's from (4 6's) is [tex](^4_4)[/tex]

no of ways to select the remaining 3 cards from (52 - 4 - 4) = 44 cards is [tex](^{44}_3)[/tex]

Mathematically, multiplying the three together we have:

[tex]= (^4_3) (^4_4) (^{44}_3)[/tex]

[tex]= \dfrac{4!}{3!(4-3)!} \times \dfrac{4!}{4!(4-4)!} \times \dfrac{44!}{3!(44-3)!}[/tex]

[tex]= 4 \times 1 \times 13244[/tex]

= 52976

To find the probability that you are holding three kings and four 6's from the deck, the remaining cards not kings or 6's can be calculated as follows;

To do this, we need to first know the no of ways we can  select 10 cards out of the pack of 52 cards

i.e

[tex](^{52}_{10})[/tex]

= [tex]\dfrac{52!}{10!(52-10)!}[/tex]

= [tex]\dfrac{52!}{10!(42)!}[/tex]

= 1.58200242 × 10¹⁰

Now, to find the  probability that you are holding three kings and four 6's from the deck, the remaining cards not kings or 6's :

we will need to divide the number of ways we can select three kings and four 6's from the deck by the no of ways we can select 10 cards out of the pack of 52 cards.

Mathematically; we have,

[tex]=\dfrac{52976}{1.58200242 \times 10^{10}}[/tex]

= [tex]\mathbf{3.34866744 \times 10^{-6}}[/tex]

Answer:

y = 1/3x + 4

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find slope m

m = (2 - 3)/(-6 - -3)

m = -1/(-6 + 3)

m = -1/-3

m = 1/3

y = 1/3x + b

Step 2: Find y-intercept b (plug in coordinates)

3 = 1/3(-3) + b

3 = -1 + b

b = 4

Step 3: Rewrite linear equation

y = 1/3x + 4

Multiplying M by any matrix A would return new matrix, B, in which

• the 1st row of B is equal to the 4th row of A,

• the 2nd row of B is equal to the 3rd row of A,

• the 3rd row of B is equal to the 2nd row of A,

• the 4th row of B is equal to the 5th row of A, and

• the 5th row of B is equal to the 1st row of A.

The pattern here is

1 => 4 => 5 => 1

2 => 3 => 2

Let {4, 3, 2, 5, 1} denote the matrix M, where each number refers to the row of the identity matrix, I.

Using this notation, the pattern above gives

M² = {5, 2, 3, 1, 4}

M³ = {1, 3, 2, 4, 5}

M⁴ = {4, 2, 3, 5, 1}

M⁵ = {5, 3, 2, 1, 4}

M⁶ = {1, 2, 3, 4, 5}

so that n = 6.

(Notice that the first cycle has length 3 and the second one has length 2; the minimum n needed here is then LCM(2, 3) = 6.)

Answer:

The slope is 5/4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 5/4x - 7/5

The slope is 5/4 and the y intercept is -7/5

Answer:

D

Step-by-step explanation:

Smaller p values that there is evidence to show that the alternate hypothesis should be accepted. The smaller the p value, the more evidence there is that we are not to accept the null hypothesis. The p value during a hypothesis yet, tells us how significant our result is. It gives a measurement of how strong the evidence is, against the null hypothesis.

Answer:

b. y=sec(x/3) and y=-1

Step-by-step explanation:

sec(x/3) + 4 > 2 − sec(x/3)

2 sec(x/3) > -2

sec(x/3) > -1

Graph y = sec(x/3) and y = -1.

Answer:

  3z^2

Step-by-step explanation:

Factors of the different terms are ...

  12z^3 = 2·2·3·z·z·z

  45z^2 = 3·3·5·z·z

  18z^5 = 2·3·3·z·z·z·z·z

The common factors are 3 and z·z.

The greatest common factor is 3z^2.

Answer:

[tex]-3/13[/tex]

Step-by-step explanation:

So we have the expression:

[tex]\frac{y^3+\sqrt{x-2}}{|4x-y|}[/tex]

And we want to evaluate it for x=6 and y=-2.

Thus, substitute:

[tex]=\frac{(-2)^3+\sqrt{(6)-2}}{|4(6)-(-2)|}[/tex]

Let's do the numerator first:

[tex](-2)^3+\sqrt{6-2}[/tex]

Cube the first term and subtract under the radical:

[tex]=-8+\sqrt4[/tex]

Simplify:

[tex]=-8+2[/tex]

Add:

[tex]=-6[/tex]

Now, do the denominator:

[tex]|4(6)-(-2)|[/tex]

Multiply:

[tex]=|24-(-2)|[/tex]

Simplify and add:

[tex]=|24+2|\\=|26|[/tex]

Remove the absolute value bars:

[tex]=26[/tex]

So, together:

[tex]=\frac{(-2)^3+\sqrt{(6)-2}}{|4(6)-(-2)|}\\=-6/26[/tex]

Reduce:

[tex]=-3/13[/tex]

And that's our answer: :)

Answer:

The coefficient would be 94

Step-by-step explanation:

A coefficient is the number used to multiply the variable! Hope this helps!

Answer:

2x + 6 = 30

hope this helps

Answer:

3, 3.024, 3.04, 10

I'm sorry if I misunderstood.

Good luck mate! :)

Please add Brainliest if you'd like, not that it matters.

Remember to try your best every day!

Answer: f = x^2-7yx+4y^2-6y

Step-by-step explanation:

A vector field is conservative if the work done by that vector field around any loop is 0 or the end points only matter when calculating the work done, not the path in between (think of gravity). The curl(F) must equal 0.

curl(F) = ∇ x F =0

= det( [tex]\left[\begin{array}{ccc}\frac{d}{dx} &\frac{d}{dy} \\(2x-2y)&(-7x+8y-6)\end{array}\right][/tex] ) (***partial derv)

-7 - (-7) = 0

Yes, it is conservative, which means we can find the potentional energy function by turning the vector field into the gradient of scalar function.

[tex]f_x=2x-7y\\f_1=x^2-7yx+C(y)\\f_1y=-7x +C'(y)\\\\C'(y)=8y-6\\C(y)=4y^2-6y\\\\f=x^2-7yx+4y^2-6y\\[/tex]

Answer:

7/2

Step-by-step explanation:

17=4x+3

4x=17-3

4x=14

x=14/4

x=7/2

Answer:

"Subtracting 3 from four times the square of an unknown number gives 13"

Step-by-step explanation:

The expression

[tex]4\,y^2-3 = 13[/tex]

in word form could be:

"subtracting 3 from four times the square of an unknown number gives 13"

Answer:

  1000

Step-by-step explanation:

1000/1 = 1000

Multiplying or dividing any number by 1 does not change its value.

__

In the US, "standard form" is the number written in the usual way: digits to the left and/or right of a decimal point, with zeros as placeholders where required. (If there is no fractional part, the decimal point is optional.*)

In the UK, "standard form" is what is called "scientific notation" in the US. There is one digit to the left of the decimal point, and the remaining significant digits are to the right of the decimal point. The number is multiplied by ten to the power corresponding to the place value of the most significant digit. In this "standard form", 1000 = 1.×10³.

_____

* When you're concerned about significant digits, the presence of a decimal point will indicate any zeros immediately to its left are significant. That is, 20 has 1 significant digit; 20. has 2 significant digits. The zero is indicated as being significant by the presence of the decimal point.

Greetings from Brasil...

First let's define the rational number....

→ Division between two numbers with the detail that the dividend or denominator cannot be zero

A/B or A ÷ B

where B ≠ 0

(just for the sake of knowledge. If B = 0 we would have +∞ as an answer)

A ∈ ℤ

and

B ∈ ℤ*   (B ≠ 0)

In this way, when dividing A by B, we will obtain a whole number or a number with a decimal (finite decimal or periodic tenth)

Let's go to the alternatives

4 ∈ ℤ and 5 ∈ ℤ*, so we have a rational number

B = √27 = 5.1961524227066318805823390245176

(There is no repetition of tithing periods (numbers after the point) - non-periodic tithe). So we have an Irrational Number

C = 4.020020002000002

There is no periodic tenth - Irrational Number

D = √31 = 5.5677643628300219221194712989185

Irrational Number - Non-periodic tithe

Answer:

P=-w/m +s

Step-by-step explanation: