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The summation that represents the money in the account 10 years after the initial deposit is  P(10) = 300(1.055)^10

Exponential equations are equations that increase geometrically

The formula for calculating the compound. interest is expressed as:

P(t) = P0(1+r)^t

Given the following

P0 =. $300
r = 5.5% = 0.055

t = 10years

Substitute

P(10) = 300(1+0.055)^10

P(10) = 300(1.055)^10

Hence the summation that represents the money in the account 10 years after the initial deposit is  P(10) = 300(1.055)^10

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Answer: D

Step-by-step explanation:

Answer:

cosΘ = [tex]\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

sin²Θ + cos²Θ = 1 ( subtract sin²Θ from both sides )

cos²Θ = 1 - sin²Θ ( take square root of both sides )

cosΘ = ± [tex]\sqrt{1-sin^20}[/tex]

       = ± [tex]\sqrt{1-(\frac{1}{2})^2 }[/tex]

       = ± [tex]\sqrt{1-\frac{1}{4} }[/tex]

      = ± [tex]\sqrt{\frac{3}{4} }[/tex]

     = ± [tex]\frac{\sqrt{3} }{2}[/tex]

since 0° < Θ < 90° , then

cosΘ = [tex]\frac{\sqrt{3} }{2}[/tex]

Answer:

Jamal will have to borrow 31,800.

Step-by-step explanation:

Total tuition for the full four years = 11,800 + 11,900 + 12,000 + 12,100 = 47,800

Total money from scholarship = 1,500 × 4 = 6,000

Total income received = 2,500 × 4 = 10,000

Total money to borrow = 47,800 - 6,000 - 10,000 = 31,800

Answer:

D. 60 ft²

Step-by-step explanation:

Area formula :

Solving :

Answer:

D. 60 ft2

Step-by-step explanation:

Area of a parrelleogram:

bxh

base x hieght

The base is 10ft, the height is 6 ft

(it cannot be 8ft because that line is slanted)

10x6=60ft2

Answers:

[tex](f \circ g)\;(x) = 4x^2 - 12x + 6\\\\(g \circ f)\;(x) = 2x^2-9\\\\[/tex]

The domain for both is "all real numbers".

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

Explanation:

The work is shown below in the attached image.

The domain for each composite function is the set of all real numbers because we don't have to worry about things like dividing by zero, or taking the square root of a negative number. Any x value is allowed.

The value of arc ST in the circle with center at point V is 125 degrees.

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

mSU = 2 * ∠STU (angle at center is twice angle at circumference)

21x + 8 = 2(13x - 6)

x = 4

mSU = 21(4) + 8 = 92°

mSU + mUT + mST = 360° (angle in a circle)

92 + 143 + mST = 360

mST = 125°

The value of arc ST in the circle with center at point V is 125 degrees.

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Answer:

(5,2)

Step-by-step explanation:

if it’s (x,y) and 4 to the y to get 2

For addition   1.)  28  /  5 2.) 27  / 4  3.)  45  /  8 4.)  4  /  3 5.)  23  /  18

For Subtraction 1.)  27  /  5 2.) 20 /  3 3.) 23  /  6 4.) 6 / 5 5.) 16 / 3

The method of summing up the given data is called addition. A method of removing certain data from the given data is called subtraction.

Addition

1.)  28  /  5

2.) 27  / 4

3.)  45  /  8

4.)  4  /  3

5.)  23  /  18

Subtraction

1.)  27  /  5

2.) 20 /  3

3.) 23  /  6

4.) 6 / 5

5.) 16 / 3

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Using function concepts, it is found that since the savings account receives no interest, the quantity is changing in a linear fashion.

In this problem, the rate of change is a constant of $723 each month, hence the quantity is changing in a linear fashion.

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Dilation centred at origin

So new coordinates are same like previous

Now scale factor is 3

So P':-

Option D

Answer:

D)   (−6, −12)

Step-by-step explanation:

Dilation:  A type of transformation that makes the pre-image larger or smaller without changing its shape.

Center of a dilation:  a fixed point about which all points are dilated.

When the center of dilation is the origin (0, 0), simply multiply the coordinates of the points of the pre-image by the scale factor to determine the points of the image after dilation.

Given:

Therefore:

⇒ P' = (-2 × 3, -4 × 3)

⇒ P' = (-6, -12)

Answer:

5 given as -1 and 8 positive 8 cross by axis

Answer:

Dependent Event

Step-by-step explanation:

Dependent Events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.

Answer:

x < - 3

Step-by-step explanation:

4x + 2 > 6x + 8

=> 4x - 6x > 8 - 2

=> -2x > 6

Divide by -2 (Since dividing by -ve, operator sign changes)

=> x < - 3

Answer: x >-3

Step-by-step explanation: 4x + 2 > 6x + 8

4x - 6x = -2x

6x - 6x = 0

-2x + 2 >8

8 -2 = 6

2-2 = 0

-2x > 6

-2x/-2x = 0

6/-2x = -3

therefore x >-3

Answer:

Step-by-step explanation:

Answer:

[tex]2x^2+x-3=(2x+3)(x-1)[/tex]

Step-by-step explanation:

Rewrite the middle term as a sum of two terms so that the coefficients add up to the coefficient of the middle term, and group the entire polynomial into two binomials in which they have the same factor:

[tex]2x^2+x-3\\2x^2-2x+3x-3\\(2x^2-2x)+(3x-3)\\2x(x-1)+3(x-1)\\(2x+3)(x-1)[/tex]

Hope this helps! Let me know if you are still confused.

Answer:

1. False

2. True

3. true

Step-by-step explanation:

The first answer is false, the second one is true and the third is true

Answer:

the answer is b

Step-by-step explanation:

you multiply 0.1% or 0.001 to 4200

the reason I am not multiplying 1.2% is because that is for yearly and 0.1% is for monthly

Answer:

A

Step-by-step explanation:

find 1.2% of £4,200 then multiply it

Answer:

B)  35.4 ft²

Step-by-step explanation:

Area of a sector

[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Area} & =\left(\dfrac{110^{\circ}}{360^{\circ}}\right) \cdot3.14 \cdot 6^2\\\\& =\left(\dfrac{11}{36}}\right) \cdot3.14 \cdot 36\\\\& =34.54\\\\ & = 35.4\: \sf ft^2 \: (nearest\:tenth)\end{aligned}[/tex]

Hi Student!

Looking at the problem, we first need to determine the important information that is given to us.  We can see that we are given a radius of 6 feet and a central angle of 110 degrees.  We will need to use both of these given values in our problem.

The second step that we need to take, after gathering our information, is to convert our degrees to radians.  The purpose of this is because in our formula we must use radians instead of degrees.  To convert degrees to radians, we multiply it by π/180.

[tex]110\ degrees\ *\ \frac{3.14}{180\ degrees}[/tex]

[tex]1.919[/tex]

Now that we have our angle converted to radians, we can plug our information into the formula and solve.

[tex]Sector\ Area = r^2\ *\ \frac{angle}{2}[/tex]

[tex]Sector\ Area = (6\ ft)^2\ *\ \frac{1.919}{2}[/tex]

[tex]Sector\ Area = 36\ ft^2\ *\ 0.9595[/tex]

[tex]Sector\ Area = 34.542\ ft^2[/tex]

Therefore, after solving the entire equation down to the end, we can see that our answer is 34.542 feet squared.  This matches option B which would be our answer.

Answer:

0.0037

Step-by-step explanation:

In scientific notation, if the exponent is negative, you shift the decimal to the left to find the number in standard form.

Answer:

Step-by-step explanation:

One

If the number was 1000, you just count the numbers starting at the right until you get a number that is between 1 and 10

So starting at the right, you get to go 3 places towards the left. You get the number one, so 1000 would be written as 1 * 10^3.

The the given number is a fraction the rule is Add a minus sign

Answer: 1/1000 = 1 * 10^-3

Two

10 is 10^1 in scientific notation

1/10 = 10^-1

Answer: 1/10

Answer:

i think its D but i'm not very sure. try it

Step-by-step explanation:

Answer:

Second choice

Step-by-step explanation:

This is a circle with center at   0,0

 radius = sqrt 100 = 10

Answer:

1.  smaller value of t = 5

   larger value of t = 9

2.  (7, 4)

Step-by-step explanation:

Given function:  [tex]h(t)=-(t-7)^2+4[/tex]

To find the zeros, set the function to zero and solve for t:

[tex]\begin{aligned}h(t) & =0\\\implies -(t-7)^2+4 & =0\\-(t-7)^2 & =-4\\(t-7)^2 & =4\\t-7 & =\sqrt{4}\\t-7 & =\pm 2\\t & =7\pm 2\\t & = 5,9\end{aligned}[/tex]

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

Therefore, the vertex of the given function is (7, 4)

Answer:

False

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

  = (x + 5)(x - 5) ← expand factors using FOIL

  = x² - 5x + 5x - 25

 = x² - 25 ≠ x² - x - 15

A percentage is a way to describe a part of a whole. The percentage increase in the number of tigers is 21.56%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The percentage change is given by the formula,

Percentage change = |(Intial Value - Final value)|/Initial Value × 100%

Percentage Change = |3200-3890|/3200 × 100% = 21.56%

Hence, the percentage increase in the number of tigers is 21.56%.

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Answer:

205.03125.

Step-by-step explanation:

18/12 = 1.5

27/18 = 1.5

This is geometric with nth term = ar^(n-1)

Here first term a = 12 and common ratio r = 1.5, so

The 8th term = 12(1.5)^(8-1)

= 205.03125

Answer:

160 times X

Step-by-step explanation:

160 is the number of pencils in each box.

And

X is how many boxes there are.

If 1 box contains 160 pencils then the equation which represents the total number of pencils is y=160x.

An equation is a relationship between two or more variables where variables represent some quantity . It is mostly found in equal to form. It is equated to find the value of variables.

Equation form :y=a+bx

There are 160 pencils in one box and x represents the number of boxes. So the equation that represents the total number of pencils can be found by product of x and 160.

Equation will be x*160=160x.

Hence the equation which represents the total number of pencils is y=160x.

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#1

The line should start just over origin

#2

Line should step downwards to contain moSt dots

#3

Quite above origin and half steadier (angle about 30-45)

#4

Almost staright line and almost parallel to x axis