The principal represents an amount of money deposited in a
savings account subject to compound interest at the given
rate.
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
Click the icon to view some finance formulas.
Principal Rate
$10,000
2%
***
B. The amount of interest earned is $612.08
(Round to the nearest hundredth as needed.)
A. The amount of money in the account after 3 years is $10,612.08.
(Round to the nearest hundredth as needed.)
Compounded
annually
Time
3 years

Answer:

162.4

Step-by-step explanation:

A= 8 * side length * apothem/2

A = 8* 5.8 * 3.5

A = 162.4

Answer:

162.428 m2

=162.4

Step-by-step explanation:

hope this helps

Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Scale factor back to original size = 1/7

        7x and 7 years.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

Hence, the scale factor will be 1/7 back to the original size.

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Answer:

\(\frac{4x^2z^4}{9y^2}\)

Step-by-step explanation:

Answer:

16x4y(-3)z4/36x(-2)yz0

Final result :

 4x2z4

 —————

  9y2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)". 1 more similar replacement(s)

Step by step solution :

Step  1  :

           z4

Simplify   ——

           36

Equation at the end of step  1  :

                      z4

 (((((16•(x4))•(y-3))•——)•x(-2))•y)•1

                      36

Step  2  :

Equation at the end of step  2  :

                     z4

 ((((24x4 • y(-3)) • ——) • x(-2)) • y) • 1

                     36

Step  3  :

Dividing exponents :

3.1    24   divided by   22   = 2(4 - 2) = 22

Equation at the end of step  3  :

   4x4z4

 ((————— • x(-2)) • y) • 1

    9y3

Step  4  :

Multiplying exponential expressions :

4.1    x4 multiplied by x(-2) = x(4 + (-2)) = x2

Equation at the end of step  4  :

  4x2z4

 (————— • y) • 1

   9y3

Step  5  :

Final result :

 4x2z4

 —————

  9y2

Step-by-step explanation:

brainliess plsss

Answer:

it is 6

Step-by-step explanation:

its a reverse diamond

Answer:

1.65

Step-by-step explanation:

I did 1.35/9

The answer I got after dividing the two is 0.15.

Then I multiplied 0.15 by 11 and I got 1.65.

Answer:

Step-by-step explanation:

The perimeter is obtained by taking the sun of the fence :

Outer fencing :

Let's obtain b :

From Pythagoras :

b² = 15² - 12²

b = sqrt(225 - 144)

b = 9

Outer fencing = 2(12+6) + 2(8+9)

= 2(18) + 2(17)

= 36 + 34

= 70

Inner fencing :

(8 + 9 + 12 + 6 + 15 + 10) = 60

(70 + 60) = 130 yards

Answer:

that makes no sense.

Step-by-step explanation:

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

$1

Step-by-step explanation:

i hope i read it right

Answer:

1

Step-by-step explanation:

cuz half of 2 is 1

The equations are solved

a) A = 5/8

b) C = ∛64 + √25 = 13

c) D = 1/2 + 2 3/4 - 3/8 = 30.8 x 10⁵

d) D = 1/2 + 2 3/4 - 3/8 = 23/8

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 equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

a)

A = 1 2/3 : 2 2/3

On simplifying , we get

A = ( 1 2/3 ) / ( 2 2/3 )

A = ( 5/3 ) / ( 8/3 )

A = 5/8

Therefore , the value of the expression is A = 5/8

b)

B = ∛64 + √25

On simplifying , we get

B = 8 + 5

B = 13

Therefore , the value of the expression is B = 13

c)

C = 3.6 x 10⁶ - 5.2 x 10⁵

C = 10⁵ ( 3.6 x 10 - 5.2 )

C = 10⁵ ( 36 - 5.2 )

C = 30.8 x 10⁵

Therefore , the value of the expression is C = 30.8 x 10⁵

d)

D = 1/2 + 2 3/4 - 3/8

D = ( 1/2 ) + ( 11/4 ) - ( 3/8 )

D = ( 13/4 ) - ( 3/8 )

D = ( 26 - 3 ) / 8

D = 23/8

Therefore , the value of the expression is D = 23/8

Hence , the equations are solved

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Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

9514 1404 393

Answer:

  9 : 49

Step-by-step explanation:

Assuming the rectangles are similar, the ratio of their areas is the square of the ratio of their side lengths.

  sides ratio = 3 : 7

  areas ratio = 3² : 7² = 9 : 49

The graph of this proportional relationship would look like this: A line passes through the point (0, 0) and continues through the point (14, 7).

In Mathematics, a graph simply refers a type of chart that is typically used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) increases or decreases, the values on the y-coordinate (y-axis) increases or decreases simultaneously.

By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it passes through both points (0, 0) and (14, 7).

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Answer:

b

Step-by-step explanation:

b b b b b b b b b b b b b b b b b b b b  bb b b b b b b b b b b b b b b b b b

yes

To determine if a linear transformation is onto, we need to check if every vector in the range has at least one pre-image in the domain.

Let T be a linear transformation from R^3 to R^2 given by:

T (x, y, z) = (2x - y, x + 3y - 4z)

(a) To check if T is one-to-one, we need to check if for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3, we have T (x1, y1, z1) ≠ T (x2, y2, z2). Equivalently, we can check if T (x1, y1, z1) - T (x2, y2, z2) ≠ 0 for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3.

So, let (x1, y1, z1) and (x2, y2, z2) be two distinct vectors in R^3. Then:

T (x1, y1, z1) - T (x2, y2, z2) = (2x1 - y1, x1 + 3y1 - 4z1) - (2x2 - y2, x2 + 3y2 - 4z2)

= (2x1 - y1 - 2x2 + y2, x1 + 3y1 - 4z1 - x2 - 3y2 + 4z2)

= (2(x1 - x2) - (y1 - y2), x1 - x2 + 3(y1 - y2) - 4(z1 - z2))

For T to be one-to-one, the only solution to T (x1, y1, z1) - T (x2, y2, z2) = 0 must be (x1, y1, z1) = (x2, y2, z2). So, we need to solve the equation above and check if the only solution is (x1, y1, z1) = (x2, y2, z2).

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Answer:

24

Step-by-step explanation:

Answer:

y + 3= -7(x + 2)

Step-by-step explanation:

...........

Answer:

C. The mean daily salary is greater than $350 per day

Step-by-step explanation:

The computation is shown below:

Y = a + bX

where,

Y = money made by a random selected

a = $150

b = $50

X = number of loan

Now

E(x) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)

= 3.94

Now

E(y) = $150 + ($50 × 3.94)

= $347

hence, the option C is not correct

The mean daily salary is greater than $350 per day and this can be determined by using the given data.

Given :

At a certain company, loan agents are paid based on the number of loans they close in a day.

The computation is given by:

Y = a + bX

where Y is the money made by randomly selected, a is $150, b is $50, and X is the number of loans.

Now, the value of E(x) is given by:

\(\rm E(x) = (1\times 0.5)+(2\times 0.1)+(3\times 0.22)+(4\times 0.3)+(5\times 0.18)+(6\times 0.12)+(7\times 0.03)\)

\(\rm E(x) = 3.94\)

Now, the value of E(y) is given by:

\(\rm E(y) = 150+(50\times 3394)\)

E(y) = $347

So, the correct option is given by C) The mean daily salary is greater than $350 per day.

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Answer:

d is great than -3

Step-by-step explanation:

because negative numbers are less than whole numbers

The given function does not have an end behavior because it is not a polynomial function.

The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The end behavior of this function does not exist because this is not a polynomial.

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Answer:

The best option is to buy Japanese Car.

Step-by-step explanation:

Fuel usage per year is 150000/ 8 = 18750 miles per year

Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5

Japanese Car:

Fuel usage 18750 / 23 = 815 * $3 = $2446  

Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372

Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860

Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804

Present value of cost at 5% = 24674.07

Cost of car is $30,000

Total cost = $54674.07

Amercian Car:

Cost $35,000

Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.

Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208

Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301

Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934

Present value of cost at 5% = 25302.18

Cost of car is $35,000

Total cost = $60302.

German Car:

Cost = $45,000

Fuel usage 18750 / 21 = 892 * $3 = $2678  

Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171

Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316

Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976

Present value of cost at 5% = 27105.73

Cost of car is $45,000

Total cost = $72105.

Answer:

bro there shld be a picture because you said in the figure. Without figure we can't know how will we do

Step-by-step explanation:

i think the ans is 57°

The translation "If you see a penny, pick it up, all day long you'll have good luck" is represented as (SAP) ➡ G in formal logic.

In formal logic, we often use symbolic notation to represent statements and their logical relationships.

In this case, the natural language sentence is being translated into formal logic using symbolic variables and logical connectives.

The translation provided uses three variables:

S represents the statement "You see a penny."

P represents the statement "You pick the penny up."

G represents the statement "All day long you'll have good luck."

The arrow (➡) is a logical connective that represents implication.

It signifies that the statement on the left side of the arrow (SAP) implies the statement on the right side (G).

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Answer:

  a. x = 15

  b. scalene

Step-by-step explanation:

You want to know the value of x and the classification of the triangle whose circumscribing arcs are (8x-10)°, (6x)°, and (10x +10)°.

The sum of arcs around the circle is 360°.

  (8x -10)° +(6x)° +(10x +10)° = 360°

  24x = 360 . . . . . . . . . . . divide by °, simplify

  x = 15 . . . . . . . . . . . . divide by 24

The arc measures around the circle are ...

  (8x -10)° = 110°

  (6x)° = 90°

  (10x +10)° = 160°

Each arc is double the measure of the inscribed angle that intercepts it. The different arc measures mean the angle measures are different, so the triangle is scalene.

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Answer:

Step-by-step explanation:

Let numbers be x and y

Then we have equations:

Comparing

Then, the larger number is

Answer:

E

Step-by-step explanation:

\sqrt 6 is an irrational number, as it cannot be written as the ratio of 2 numbers.

It is also a real number, as it does not include the square root of a negative number.

Therefore, E is the correct option.

The set in intercal notation is:

Answer:

B, C, D

Step-by-step explanation:

-2 is 8 spaces away from 6 so do the math for each possible answer and u get B,C,D.

B.

6 - (-2)

6 + 2 = 8

C.

| -2| = 2

6+2 = 8

D.

|-2+6|

2+6 = 8