A principal of $2000 is placed in a savings account at 3% per annum compounded annually. How much is in the account after one year, two years and three years?

Answer:

[tex](2, 17)[/tex]

Step-by-step explanation:

A parabola has the general function: [tex]f(x)=ax^2+bx+c[/tex]

In this case we have: [tex]f(x) = x^2 - 4x + 21[/tex]

where

[tex]a=1[/tex]

[tex]b=-4[/tex]

[tex]c=21[/tex]

the vertex of a parabola is in the coordinates:

[tex](\frac{-b}{2a}, \frac{-b^2+4ac}{4a} )[/tex]

substituting all of the known values, we get the following:

[tex](\frac{-(-4)}{2(1)} ,\frac{-(-4)^2+4(1)(21)}{4(1)} )\\\\(\frac{4}{2} ,\frac{-16+84}{4} )\\\\\\(2 ,\frac{68}{4} )\\\\\\(2,17)[/tex]

the vertex of  [tex]f(x) = x^2 - 4x + 21[/tex] is at the point (2,17) which is the second option.

Answer:

2,17

Step-by-step explanation:

Answer: she is 215m from her starting point

Step-by-step explanation:

The diagram representing the situation is shown in the attached photo. Triangle ABC is formed with AC representing her distance from her starting point.

Angle B = 28 + 90 = 118°

To determine AC, we would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b(AC). Likening the expression to the given triangle, it becomes

AC² = AB² + BC² - 2(AB × BC)CosAC

AC² = 60² + 180² - 2(60 × 180)Cos118

AC² = 3600 + 32400 - 21600Cos118

AC² = 36000 - 21600(-0.46947156)

AC² = 36000 + 10140.59

AC² = 46140.59

AC = √46140.59

AC = 215 m

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:

11

Step-by-step explanation:

the answer is 11

Answer: Option B.

Step-by-step explanation:

The price per ounce can be calculated as the amount of you paid divided the number of ounces that you get.

A) we have a table:

ounces          price

18                     $1.5

36                    $3.00

54                    $4.5

We can see that here we have a linear relationship. for example, the price for 18 ounces is $1.5

Then the price per ounce is:

p = $1.5/18 = $0.083

B) here we know that 15 oz cost $0.75, the price per ounce is:

p = $0.75/15 = $0.05

C) here we have 11 ounces, and the price is $2.20

then we have:

p = $2.2/11 = $0.2

Then we can conclude that the least expensive is option B.

Answer:b

Step-by-step explanation:

did it on khan

Answer: 1324.12 sq. cm.

Step-by-step explanation:

A=2πrh+2πr2

A = 2π x 8.2 x 17.5 + 2π x 8.2^2

A = 2π x 143.50 + 2π x 67.24

A= 1324.12

Answer:

SA = 1324.1 cm²

Step-by-step explanation:

Surface Area of Cylinder = [tex]2\pi rh+2\pi r^2[/tex]

Where r = 8.2 cm, h = 17.5 cm

=> SA = [tex]2(3.14)(8.2)(17.5)+2(3.14)(8.2)^2[/tex]

=> SA = [tex]901.6+2(3.14)(67.24)[/tex]

=> SA = 901.6 + 422.5

=> SA = 1324.1 cm²

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]

PART B

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

[tex]=\dfrac{15}{64}\\=0.234375[/tex]

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]

Answer:

Do it your self

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the figure attached,

Given : LM ≅ OP

            PQ ≅ MN

            NL ≅ QO

To Prove : ΔLMN ≅ ΔOPQ

In the triangles LMN and OPQ,

             Statements              Reasons

1). LM ≅ OP                       1). Given

2). PQ ≅ MN                     2). Given

3). NL ≅ QO                      3). Given

4). ΔLMN ≅ ΔOPQ            4). By SSS property of congruence

Answer:

believe its 2x cause 1 was wrong

Answer:

x+y=7

y= x+3

Step-by-step explanation:

i just took the test

The system of the equation that represents the given condition will be x + y = 7 and y = x + 3. And the solution is (2, 5).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of x and y is 7. The value of y is three more than the value of x. Then the equation is given as,

x + y = 7                ...1

y = x + 3               ...2

From equations 1 and 2, then we have

x + x + 3 = 7

2x = 4

x = 2

Then the value of the variable 'y' will be given as,

y = 2 + 3

y = 5

The system of the equation that represents the given condition will be x + y = 7 and y = x + 3. And the solution is (2, 5).

More about the solution of the equation link is given below.

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Answer:

x = -1/8

Step-by-step explanation:

The greater than sign can be replaced with an equal sign to solve.

5x + 4 < 3 – 3x =>

5x + 4 = 3 - 3x =>

+3x  -4    +3x - 4

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

8x = -1

x = -1/8

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer:

Step-by-step explanation:

Parallel lines have same slope

19) y = x - 4

m = 1 ;   (2, 3 )

Equation: y - y₁ = m(x- x₁)

             y - 3 = 1(x - 2)

              y - 3 = x -2

                   y = x - 2 + 3

y = x + 1

20) 2x + 3y = 3

We have to write in y = mx + b  form

3y =  - 2x - 3

[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)

[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]

for perpendicular lines, m2 = -1/m1

21) y = 2x+ 5

m1 = 2

[tex]m_{2}=\frac{-1}{2}[/tex];     (-2,8)

[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]

22) x+ 4y = 8

           4y = -x + 8

             [tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]

m2 = 4;  (-2,-11)

y - [-11] = 4(x -[-2])

y + 11 = 4 (x + 2)

y + 11 = 4x + 8

      y = 4x + 8 - 11

      y = 4x - 3

Answer:

x = 12:15=×5

36

060

Step-by-step explanation:

12:15=0

x=0

Answer:

4

Step-by-step explanation:

Divide the left side by 3

12:15

12/3 : 15/3

4:5

x would be 4

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

[tex]h=-16t^2 + 36t + 10[/tex] ......(1)

Part (a) :

The maximum height reached by the ball is given by :

[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]

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Answer:

1,500,000.

Step-by-step explanation:

Convert to standard notation by first deriving the value of 10 to the exponent given:

[tex]10^{6} = 1,000,000[/tex] (6 zeros)

Multiply:

1.5 × 1,000,000 = 1,500,000

Answer: 0.5

Step-by-step explanation:

Total bags (U) = 140

Number of bags with both button and zip:

(48 + 47 + x + 22) = 140

117 + x = 140

x = 140 - 117

x = 23

Therefore, probability that bag has button :

Total Number of bags with button:

(Bags with button alone + bags with both button and zip)

(47 + 23) = 70

Probability = (required outcome / Total possible outcomes)

P(bag has button) = (number of bags with button / total number of bags)

P(bag has button) = 70/140 = 0.5

P(bag has button) = 0.5

Answer:

Height of building is 57.12 m.

Step-by-step explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled [tex]\triangle OBT[/tex])

with [tex]\angle B =90^\circ[/tex]

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

[tex]\angle O = 55^\circ[/tex]

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]

[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]

So, height of building is 57.12 m.

Answer:

-9=-9

8=8

-48=-48 or -8(-6)=-48

-6=-6 or 18/-3=-6

Step-by-step explanation:

Answer:

Simplify each expression involving signed numbers.

-7 – 2 =

✔ –9

12 + (-4) =

✔ 8

-8(-6) =

✔ 48

StartFraction 18 over negative 3 EndFraction =

✔ –6

can I have some brainiest

Step-by-step explanation:

Answer:

0.100

Step-by-step explanation:

0.0995 has 4 decimal places

5>4 so round up

9 turns to 10, the 1 is "added on" to the number ahead

9 turns to 10 again, the 1 is "added on" to the number ahead

0 turns to 1

you are left with 0.100

Answer:

0.100

Step-by-step explanation:

Three decimal places: 0. 0 / 9 / 9 / 5

Rounding number: 0. 0 / 9 / 9 / 5

Since it is 5, add 1 to the second 9. This will result to 0 while adding 1 to the first 9. Again, this would result to 10 which will add 1 to the next number, 0.

0.1000

Since the question wants you to round three places, you were not told to remove the zeros in those decimal places. So only remove the last 0.

0.100 is the answer

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

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Answer:

A. <

Step-by-step explanation:

The symbol "<" means less than.

Comparing 4.589 with 4.958, 4.958 is greater than 4.589 by 0.369 (4.958 - 4.589).

So therefore, if we are to write 1 statement for both, we would say "4.589 is less than 4.958".

This can be written by using just symbols without words, thus, we have:

4.589 < 4.958.

The correct option is A. <

Answer:

x = 1 ± √89

Step-by-step explanation:

Step 1: Expand

x² - 2x - 63 = 25

Step 2: Isolate xs

x² - 2x = 88

Step 3: Complete the square

x² - 2x + 1 = 88 + 1

(x - 1)² = 89

Step 3: Square root both sides

√(x - 1)² = ±√89

x - 1 = ±√89

Step 4: Isolate x

x = 1 ± √89

Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

Answer:

Y=15 when x=5

Step-by-step explanation:

if y= -6 when x= -2

So y=? When x=5

Y=15

Hope this helps

Good Luck

Answer:

t ≤ 4.24

Step-by-step explanation:

P(t) ≥ 40000 implies

500t/(2t²+9) ≥ 40000

Multiplying through by t², we have

500t ≥ 40000(2t²+9)

500t/40000 ≥ 2t²+9

Collecting like terms

0.0125t  ≥ 2t²+9

0  ≥ 2t²+ 9 - 0.0125t

2t²+ 9 - 0.0125t  ≤ 0

2t²- 0.0125t + 9 ≤ 0

Using the quadratic formula,

[tex]t = \frac{-(-0.0125) +/-\sqrt{(-.0125)^{2} - 4 X 2 X 9} }{2 X 2} \\= \frac{0.0125 +/-\sqrt{(0.00015625 - 288} }{4}\\= \frac{0.0125 +/-\sqrt{-287.9998} }{4}\\= \frac{0.0125 +/-16.97i }{4}\\=0.00313 + 4.24i or 0.00313 - 4.24i[/tex]

The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)

So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0

(t - 0.00313)² - 4.24² ≤ 0

(t - 0.00313)² ≤ 4.24²

taking square-root of both sides,

√(t - 0.00313)² ≤ √4.24²  

t - 0.00313 ≤ 4.24

t ≤ 4.24 + 0.00313

t ≤ 4.24313 ≅ 4.24

t ≤ 4.24

Answer: y = 1/2x - 6

Step-by-step explanation:

#4 We are going to use slope intercept form, (y = mx+b)

1. The line crossing the y-intercept at (0,-6)

2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)

3. Make the equation: y= 1/2x - 6

Answer: 3 . y = -1/3 + 4/3   4. y= 1/2x -6

Step-by-step explanation:

3.   In the first graph  they have the coordinates,  (-2,2)  and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.

To find the slope we have to find the change in the y values  and divide it by the difference in the x values.

2-0 = 2

-2 -4 = -6

2/-6 =  -1/3  Now we know that the slope is -1/3  so we need to  find the y-intercept.

2= -1/3(-2) +b   where be is the y intercept.

2= 2/3 + b

-2/3  -2/3

b= 4/3  

Now we could write the equation as  y= -1/3 + 4/3  

4. The same with number 4.  

We will find the slope and the y intercept by using some points on the number line.

(0,-6)  This already have the y-intercept graphed so we will need to just find the slope.

(0,-6)

(4,-4)  

-6 - (-4) = -2

0 - 4 =  -4

-2/-4 = 1/2

Equation: y = 1/2x  -6