Suppose that you invest $6000 into a high yield savings account that earns 2% annual interest and is compounded monthly. If you do not deposit or withdraw any money from the account, how much money will be in the account after 20 years?

Answer:

184.85 square mm

Step-by-step explanation:

The area of a sector of a circle is [tex]\frac{1}{2} r^{2} \theta[/tex], where r is the radius and [tex]\theta[/tex] is the angle in radians subtended by the arc at the centre of the circle.

Since, diameter = 40.6 mm

So, radius(r)=20.3 mm and  [tex]\theta[/tex]=[tex]\frac{2 \pi}{7}[/tex] radians

So, area of sector= [tex]\frac{1}{2} r^{2} \theta[/tex]

=[tex]\frac{1}{2} (20.3)^2 (\frac{2 \times 3.14}{7})[/tex]

=184.85 square mm

The area of the sector using given data is equal to 184.96 mm².

The area of a sector with a central angle of 2π7 radians and a diameter of 40.6 mm.

To solve this, we need to find the radius of the circle, which is half the diameter, and then use the formula for the area of a sector, which is ½ ×r² × θ, where θ is the angle in radians.

First, find the radius: r = ½ × diameter = 0.5 × 40.6 mm = 20.3 mm.

Then, substitute the values into the formula for the area of a sector:

Area = ½ × (20.3 mm)² × (2π7)

        = 1/2 × (20.3)² × (2 × 3.14 /7)

        = 1/2 × 412.09 × 0.89714

        = 184.96 mm²

Rounded to the nearest hundredth, the area of the sector is 184.96 mm².

Answer:

Area of triangle is 25.

Step-by-step explanation:

We have been given an isosceles right triangle

Isosceles triangle is the triangle having two sides equal.

Figure is shown in attachment

By Pythagoras theorem

[tex]BC^2=AC^2+AB^2[/tex]

AD is altitude which divides the triangle into two parts

DC=5 implies BC =10 since D equally divides BC

Let AC=a implies AB=a being Isosceles

On substituting the values in the Pythagoras theorem:

[tex]10^2=a^2+a^2[/tex]

[tex]100=2a^2[/tex]

[tex]\Rightarrow a^2=50[/tex]

[tex]\Rightarrow a=\pm5\sqrt{2}[/tex]

WE can find area of right triangle by considering height AB and AD

Area of triangle ABC is:

[tex]\frac{1}{2}\cdot BC\cdot AD[/tex]     (1)

[tex]\Rightarrow \frac{1}{2}\cdot 10\cdot AD[/tex]

And other method of area of triangle is:

[tex]\frac{1}{2}\cdot AB\cdot BC[/tex]       (2)

Equating (1) and (2) we get:

[tex]\frac{1}{2}\cdot 10\cdot AD=\frac{1}{2}\cdot a\cdot a[/tex]

[tex]\Rightarrow AD=\frac{a^2}{10}[/tex]

[tex]\Rightarrow AD=\frac{50}{10}=5[/tex]

Using area of triangle is: [tex]\frac{1}{2}\cdot BC\cdot AD[/tex]

Now, the area of triangle ABC=[tex]\frac{1}{2}\cdot 5\cdot 10[/tex]

[tex]\Rightarrow 25[/tex]

Answer:

The zoo's daily supply of leaves is 500 kg leaves at most.

Each giraffe eats 24 kg leaves per day.

Step-by-step explanation:

We have been given an inequality: [tex]47E+24G\leq 500[/tex], where E represents the number of elephants and G represents the number of Giraffes. Every day, each giraffe eats the same amount of leaves, and each elephant eats 47 kg of leaves.

We can see that each elephant eats 47 kg of leaves per day, which is represented by 47E in our given inequality. The amount of leaves eaten by a giraffe is 24 kg, which is represented by 24G in our given inequality, therefore, each giraffe eats 24 kg leaves per day.

We can see that total amount of leaves eaten by E elephants and G giraffes is less than or equal to 500, which means that zoo's daily supply of leaves is at most 500 kg.

Answer:

1. Daily supply of leaves is 500 kg;

2. Each giraffe eats 24 kg of leaves per day.

Step-by-step explanation:

Let E represent the number of elephants and G represent the number of giraffes that the zoo can feed with its daily supply of leaves.

If each elephant eats 47 kg of leaves, then E elephants eat 47E kg of leaves.

Consider inequality

[tex]47E+24G \leq 500.[/tex]

The first term of this inequaliy represents the number of kilograms all elephants in zoo eat per day. The second term 24G represents the number of kilograms all giraffes in zoo eat per day. The sum 47E+24G represents the number of kilograms all elephants and giraffes in zoo eat per day (together). This amount of leaves should be less or equal than 500 kg. This means that all elephants and giraffes cannot eat more than 500 kg of leaves per day.

Her Pop music which started at 3 hours increases by 5% which is written as 0.05 as a decimal.

You need to multiply the number of hours of pop music by 5% every month to find the new total and then add that to the 2 hours of classical.

The equation would be: f(x) = 3(1.05)x + 2

Answer:

f(x) = 3(1.05)x + 2

Step-by-step explanation:

i took the test and got it right

Answer:

(1)

Closed circle graph

(2)

Closed circle graph

Step-by-step explanation:

(1)

we are given

[tex]|x|=1[/tex]

we know that absolute value is always positive

so, we can write as

[tex]-x=1[/tex]

[tex]x=-1[/tex]

[tex]x=1[/tex]

So, value of x are

[tex]x=-1,x=1[/tex]

so, graph will be of closed circle

(2)

we are given

[tex]|x|=2[/tex]

we know that absolute value is always positive

so, we can write as

[tex]-x=2[/tex]

[tex]x=-2[/tex]

[tex]x=2[/tex]

So, value of x are

[tex]x=-2,x=2[/tex]

so, graph will be of closed circle

Answer:

|x| = 1

Closed circles on -1 and 1.

|x| = 2

Closed circles on -2 and 2.

(See attachments.)

The number of bags that can be filled completely is 105 and the 3 rocks will be left over.

Division is the process of dividing a number by a given number.

Given that, the number of rocks is 1578 and the number of rocks in each bag is 15.

To find the number of bags, divide the number of total rocks by the number of total rocks in each bag:

1578/15

= 105.2

≈ 105

Now, the number of rocks in 105 bags is:

105 ×15

= 1575

So, the number of rocks left is:
1578 - 1575

= 3

Hence, the number of bags that can be filled completely is 105 and the 3 rocks will be left over.

To learn more about division, click here:

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Answer:

Toy Cars=6 and total spending by Mr.Lee=$156

Step-by-step explanation:

Let us first consider

Number of Airplanes=A Cars=C and Trains=T

Now how to start with the problem ? Just start reading it step by step. First statements says that The number of airplanes is 2/3 of The number of cars.

Now how to convert it into an mathematical expression?

here the word "=" is of most important, The number of airplanes "is" whenever you encountered "is" just place a "="

so the first statement can be converted into mathematical expression as,

A=2/3*C  (The number of airplanes is 2/3 of The number of cars.)

Now as per the second condition we can write it in mathematical form as,

C=3/5*T (The number of cars is 3/5 the number of trains).

and the third condition as,

C=3/5*T (The number of cars is 3/5 the number of trains).

Now , we have expressed the statements in mathematical expressions. we have three expressions.

Now It is also given that total number of Toys=20 so we can write it as,

A+C+T=20. ............(1)

Till now we have expressed everything in the question in mathematical form.

now for solving such type of question we need to express the expression giving total in a single entity, expressed it in terms of Airplanes,Cars or Trains,

here we are expressing it in terms of Cars so we can rewrite it (1) as,

2/3*C+C+5/3*C=20 (A=2/3*C and C=3/5*T so T=5/3*C)

by solving this we will get C=6

Total number of car toys, answer of first part

now put this value of C in expression 1,

2/3*C+C+T=20

so the value of T will be 10. T=10

and the total is toys are 20 so 20-10+6=4

Means Airplanes are 4.

Now the cost for each toy is.

A=$12,C=$8 and T=1/2 A i.e T=$6.

So the total cost would be,

4*12+6*8+10*6=$156

$156 answer of second part

I Hope this will help you to solve such kind of Problems.

Mr. Lee buys 6 toy cars for his store. The total cost for all the toys he purchased is $156. This includes the cost of toy airplanes, cars, and trains, with each toy tailoring a specific price.

The student wants to know how many toy cars Mr. Lee bought and the total cost of all toys he purchased for his store. We start with the relationships provided: the number of airplanes is 2/3 the number of cars, and the number of cars is 3/5 the number of trains. We also know that the total number of toys is 20. Let A be the number of airplanes, C be the number of cars, and T be the number of trains. So, we have A = (2/3)C and C = (3/5)T.

From these ratios, we can express airplanes and trains in terms of cars: A = (2/3)C, T = (5/3)C. The equation A + C + T = 20 becomes (2/3)C + C + (5/3)C = 20. Simplifying this, we get (10/3)C = 20, so C = 6. Thus, Mr. Lee buys 6 cars. The number of airplanes, A = (2/3) * 6 = 4, and the number of trains, T = 20 - A - C = 20 - 4 - 6 = 10.

Now let's calculate the total cost. Each toy airplane costs $12, each toy car costs $8, and each toy train costs half as much as an airplane, which is $6. The total cost is 4 airplanes * $12 + 6 cars * $8 + 10 trains * $6, which equals $48 + $48 + $60, resulting in a total of $156 spent by Mr. Lee.

(x, y) → (x, y + n) - translate the graph n units up

(x, y) → (x, y - n) - translate the graph n units down

(x, y) → (x - n, y) - translate the graph n units left

(x, y) → (x + n, y) - translate the graph n units right

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

Look at the picture.

(x, y) → (x - 5; y + 4)

To scale down Tom's photo with the original dimensions of 20 cm by 30 cm to a width of 5 cm, the new length should be 7.5 cm. This is calculated using a proportion that maintains the original aspect ratio.

To determine the new length that a photo should be when scaling down, we will maintain the ratio of the original width to the original length. Tom's photo has a width of 20 centimeters and a length of 30 centimeters. If he wants to reduce the width to 5 centimeters, we calculate the new length by setting up a proportion and solving for the missing value:

We set up the following proportion:
20/5 = 30/new length

To solve for new length, we cross-multiply:
(20) * (new length) = (5) * (30)

Then,
new length = (5 * 30) / 20

So,
new length = 150 / 20 = 7.5

Therefore, the new length that Tom should have for his wallet-sized photo is 7.5 centimeters when the width is 5 centimeters.

Given:

Tracy invests $5,000 at 4.5% and the simple interest earned on the investment is moved into a separate account at the end of each year.

To Find:

The total simple interest accumulated in the checking account after 2 years.

Answer:

$450 is the total simple interest accumulated in the checking account after 2 years.

Step-by-step explanation:

The principal sum invested by Tracy is $5000.

The rate of simple interest is given to be 4.5% and the time period given is 2 years.

To calculate the total amount of interest accrued we use the formula

[tex]\frac{P.R.T}{100}[/tex]

where P is the pricipal amount of money, R is the rate of interest and T is the time period.

So, putting the given values into the formula, we have

[tex]\frac{(5000)(4.5)(2)}{100}\\\\=\frac{45000}{100}\\\\=450[/tex]

Thus, $450 is the total simple interest accumulated in the checking account after 2 years.

Final answer:

To find the population of Smallville and population density per square mile, divide the total population by the area of the town.

Explanation:

The population of Smallville:

Population of Smallville: 72450

Area of Smallville: 5 miles x 1 mile = 5 square miles

Population density in Smallville:

Population density = Population / Area = 72450 / 5 = 14490 people per square mile

The lines j' and k' are parallel lines.

                Option: B is the correct answer.

We are given Line j ans Line k such that both are parallel to each other.

Now as we know that the translation transformation just change the position of the location but does not changes it shape.

As both the lines were parallel to each other so on translating both of them they just shifted some units to the right but the behavior remains the same.

Also, from the figure attached to the answer we may observe that the two lines are parallel to each other as the distance between the two lines at each point is constant.

            Hence, the correct answer is:

                       Option: B

Answer:

The speed of the car is 42 miles per hour

Step-by-step explanation:

Step 1:

(Blank) x s = (Blank)

Let us evaluate this. Something times s miles per hour is going to gives us? 126 miles. So, our second blank would be 126 since that's our total:

(Blank) x s = 126

Step 2:

On the other hand, our first blank would be 3. Why? Because that's the amount of time it takes us to go 126 multiplied by s miles per hour; Our new equation is:

3 x s = 126

Step 3:

We can simplify this equation to:

3s = 126

Step 4:

We now have a one step equation. Divide each side by 3 to get s by itself.

[tex]\frac{3s}{3} =\frac{126}{3}[/tex]

Step 5:

We end up getting:

s = 42

That means that the car is traveling at 42 miles per hour. If the car continues at that rate for 3 hours, the car would have traveled 126 miles.

Hope this helps!

Answer:

3 X S = 126

Step-by-step explanation:

because the variable (s) is speed then we must know that 126 is tyhe total that it is driving in 3 hours so 3 time S is 126

Answer:

8x(4+z) and 32x+8z, = Not equivalent

9(g+h) and 9g+9h = Equivalent

Step-by-step explanation:

Answer:

336$

Step-by-step explanation:

Given: Each invitation costs a total of 3$.

Given: There were a total of 112 invitations made.

So, the question is asking you to find the total amount spent making the invitations. To do so we need to find the product/sum. Product in mathematical terms is used to describe the answer to a multiplication problem. Sum on the other hand is used to describe the answer to an addition problem. Now you could just add, but multiplication is a better way of simplifying the problem. So instead of saying 3 + 3 + 3 + 3.. or 112 + 112 + 122, we say 122 x 3 = x.

Now that we've created the equation, we can find the answer.

122 x 3 = 336

Answer: Andri spent 336$ on materials for her invitations.

Good luck! c:

Answer:

A, B, C, D

Step-by-step explanation:

A polynomial is 2 or more terms connected by operations where at least one has a variable with a power or exponent. Each has two or more terms with variables with a power. We can rewrite square roots and fractions as an exponent power.

The answer is x = 3, because x = 3 has an undefined slope (m = 0 or is imaginary), and it contains 3, 0 which makes 3, 0 a solution.

Answer: x=3

Step-by-step explanation:

The graph never crosses the y axis.

The point (3,0) is on the graph.

So are all points (3,y) with y any real number.

There can't be a slope because x never changes.

Answer:

Sam picked 27

Step-by-step explanation:

41-8=33

33+27=60

Answer:

27.

Step-by-step explanation:

So there was 41 peaches, and they sold 8 so that's 41 - 8 which is 33 peaches. But now there is 60, so you do 60 - 33 gives you how many were picked and 60 - 33 is 27.

Answer:

21

Step-by-step explanation:

since its a rectangle there are two lengths of six. If you add them together you get 12. subtract the total perimeter of 54 by the 12 and get 42. Since there is 2 sides left divide by 2. You should get 21 for the width of the rectangle

Answer:

thats wrong

Step-by-step explanation:

Answer: Choice B

I'm assuming choice B shows the quantity (1-cos(60)) all over the quantity (1+cos(60)), and that is one big fraction under the square root.

The trig identity we'll use is what I'm showing in the attached images below. All we do is replace theta with 60 and that's all there is to it. An identity like that is either memorized or you will have it handy on a notecard or reference sheet.

Answer:

[tex]\pm \sqrt{\frac{1-\cos 60^{\circ}}{1+\cos 60^{\circ}}}[/tex]

Step-by-step explanation:

Tangent function is one of the trigonometric function such that [tex]\tan \theta =\frac{\sin \theta }{\cos \theta }[/tex]

Basically, we can also say that tangent function is ratio of side opposite to the angle and side adjacent to the angle.

Given: [tex]x=60^{\circ}[/tex]

We need to rewrite [tex]\tan \left ( \frac{x}{2} \right )[/tex].

As [tex]\tan \left (x \right )=\pm \sqrt{\frac{1-\cos 2x}{1+\cos 2x}}[/tex]

As we need to express [tex]\tan \left ( \frac{x}{2} \right )[/tex], divide angle by 2, we get,

[tex]\tan \left ( \frac{x}{2} \right )=\pm \sqrt{\frac{1-\cos x}{1+\cos x}}[/tex]

At [tex]x=60^{\circ}[/tex],

[tex]\tan \left ( \frac{60^{\circ}}{2} \right )=\pm \sqrt{\frac{1-\cos 60^{\circ}}{1+\cos 60^{\circ}}}[/tex]

Answer: (B) 4√2

Step-by-step explanation:

45-45-90 is a special triangle because the side lengths are congruent and the hypotenuse is √2 times the side lengths.

So, m√2 = 8

           [tex]m=\dfrac{8}{\sqrt2}[/tex]

           [tex]m=\dfrac{8}{\sqrt2}(\dfrac{\sqrt2}{\sqrt2})[/tex]

           [tex]m=\dfrac{8\sqrt2}{2}[/tex]

           [tex]m=4\sqrt2[/tex]

Answer:

79

Step-by-step explanation:

91 x 2 is 182. 340-182 is 158 divide by 2 and you get 79

Answer:

The width is 79 yards

Step-by-step explanation

Okay, so the perimeter of a shape is the sum of all the side-lengths of said shape. Because the shape is a rectangle, there are 4 sides (2 sides being the length, 2 sides being the width). This being said, the equation that can be used to find the perimeter is Perimeter = Length + Length + Width + Width or Perimeter = 2Length + 2Width. You would then plug in your given variables and solve for width. I have shown my work in the image below, I hope this is helpful :)

Answer:

[tex]\frac{1}{2} QP = UT[/tex]

Step-by-step explanation:

We are given  a ΔPQR  in which S is the mid point of QP  , T is the mid point of  QR , U is the mid point of PR

i) is true

⇒ [tex]\frac{1}{2} QP = UT[/tex]

Using mid segment theorem which states that In a triangle, the line joining the midpoints of any two sides will be parallel to the third side and that same line joining the midpoints is also half of length of third side .

So, by refering image we can see that UT is the line joining the two mid points . So, by using above theorem    1/2QP=UT and UT is parallel to PQ

Thus, (i) statement is true

⇒[tex]\frac{1}{2} QP = UT[/tex]

Answer:

it's A and D

Step-by-step explanation:

Answer:

B.4.47

Step-by-step explanation:

The equation to calculate the distance between two points is

D=[tex]\sqrt{(x_{1}-y_{1}  )^{2}+(x_{2}-y_{2}  )^{2 }[/tex]

here

[tex](x_{1},y_{1})=(-1,5)\\(x_{2},y_{2})=(3,7)[/tex]

substituting the values

[tex]\sqrt{(-1-3)^{2}+(5-7)^{2}  }[/tex]

[tex]\sqrt{(-4)^{2}+(-2)^{2}  }[/tex]

[tex]\sqrt{20}[/tex]

[tex]\sqrt{20}=4.47[/tex]

To find the sales tax on a $60 bill with a 5% rate, convert the percentage to a decimal (0.05) and multiply by the total amount ($60). The sales tax is $3.

The sales tax on a total bill can be calculated by converting the percentage rate of the sales tax into a decimal and then multiplying it by the total amount of the bill.

In this case, the total cost is $60 and the sales tax rate is 5%. First, convert 5% into a decimal by dividing it by 100, which gives us 0.05. Then, multiply this decimal by the total bill amount to find the amount of sales tax. The calculation would be as follows:

$60 × 0.05 = $3

Therefore, the sales tax for a $60 bill at a 5% rate is $3.

The sum of the first ten terms in the geometric series 4 – 12 + 36 – 108 + ... will be the negative 59048.

The series is given below.

4 – 12 + 36 – 108 + …

The complete series wall be

4 – 12 + 36 – 108 + 324 – 972 + 2916 – 8748 + 26244 – 78732

Then the sum of the first ten terms in the geometric series will be

⇒ 29524 – 88572

⇒ – 59048

More about the sum of the geometric series link is given below.

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Answer:

option:B

Step-by-step explanation:

on saturday the number of ice-cream cones sold are 8x+16

on sunday the number of ice cream cones sold are 7x-9

so the total number of ice cream cones sold are=number of ice cream cones sold on saturday+number of ice cream cones sold on sunday

=8x +16+7x-9

=15x+ 7

hence option B is correct.

Answer:

B. 15x + 7

Step-by-step explanation:

We are given that,

The number of ice-creams sold on Saturday = 8x + 16 and

The number of ice-creams sold on Sunday = 7x - 9

Therefore,

The total number of ice-creams sold = Number of ice-creams sold on Saturday + Number of ice-creams sold on Sunday

i.e. Total number of ice-creams = (8x+16)+(7x-9) = (8x+7x)+(16-9) = 15x + 7

Hence, the total number of ice-creams sold is 15x + 7.

Answer: x = 9 (choice D)

Assuming this is a geometric kite, then this means that triangle ABD is a reflection over the line BD to get triangle BCD. Furthermore, this points to AB and BC being the same length

AB = BC

3x - 5 = 22 .... substitution

3x - 5+5 = 22+5 .... add 5 to both sides

3x = 27

3x/3 = 27/3 ..... divide both sides by 3

x = 9