Which number below correctly represents 0.0005682 using scientific notation?

The investment yields a greater return over a 10-year​ period if he invested 7.83​% compounded daily.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Suppose that you have ​$4000 to invest.

The total amount of the investment after 10 years in each case will be given as,

At = r = 7.83% compounded daily, then we have

[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.0783}{365} \right)^{10\times 365}[/tex]

A = $4,000 × (1.000214521)³⁶⁵⁰

A = $4,000 × 2.1878

A = $8,751.37

At = r = 7.9% compounded quarterly, then we have

[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.079}{4} \right)^{10\times 4}[/tex]

A = $4,000 × (1.01975)⁴⁰

A = $4,000 × 2.186

A = $8,745.98

The investment yields a greater return over a 10-year​ period if he invested 7.83​% compounded daily.

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The area of the circle is obtained as 78.50 square feet. The correct option is (A).

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre.

The Centre of the circle does not lie on it.

Given that,

The radius of the circle is 5 feet.

The expression for the area of the circle is given as πr².

Substitute the value of r and take π = 3.14 to obtain,

Area = πr²

        = 3.14 × 5²

        = 3.14 × 25

        = 78.50

Hence, the area of the circle with given radius is obtained as 78.50 square feet.

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Answer:

13 and 15

Step-by-step explanation:

We set up equations.

X=Y-2

2Y=3X-9

We change X=Y-2 into Y=X+2.

Substituting for Y, we get 2Y=2X+4=3X-9

We now solve for x.

2X+4=3X-9  |-2X

4=X-9  |+9

13=X.

X=13

Substituting for Y, we get that Y =15 from the equation Y=X+2.

So, X=13 and Y=15

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.

If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,

P = 3/9

P = 1/3

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

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The evaluation of the table, equations, and graphs in the question are as follows;

First question;

Part A; The table does not represent a function

Part B; The value of f(300) is $123 represents the total cost for driving 300 miles

Second question;

Part A; The equation is; y = -2·x + 8

Part B; The graph can be obtained by finding the ordered pair of values for the first five hours and plotting the result on a graph, to form a straight line graph.

Third question;

Part A; The solution is; (2, -1)

Part B; Two solutions for f(x) are; (1.5, 0) and (0, 3)

Part C; The solution for the equation, g(x) = f(x) is the point (0, 3)

A function is rule, law or expression that maps the elements of one set A unto the elements of another set B such that each element of the set A maps unto exactly one element of the set B.

First question;

Part A: The value of x = 4 has two values of y = 2, and -2

The value of x = 9 has to values of output, y = 3 and -3

The function therefore is; y = f(x) = ±√x

The above function indicates that a value of x returns two values of y, which indicates that a vertical line drawn through the graph of the function f(x) = ±√x intersects the graph twice for values of x > 0, therefore, the equation, f(x) = ±√x, represented by the values in the table is not a function

Part B: The function for the total cost of driving a car is f(x) = 90 + 0.11·x

Where; f(x) = The total cost in dollars

x = The distance the car is driven in miles

Therefore, f(300) is obtained by plugging in x = 300 as follows;

f(300) = 90 + 0.11 × 300 = 123

The value of f(300) = $123

f(300) represents the total cost of driving the car for 300 miles

Second question set;

The velocity of the runner after one hour = 6 km/h

The velocity of the runner after three hours = 2 km/h

Part A:  The ordered pair of points of the function are; (1, 6) and (3, 2)

Making use of a linear model, we get;

Slope of the equation of the model, m = (2 - 6)/(3 - 1) = -2

The equation of the model is therefore; y - 6 = (-2) × (x - 1) = -2·x + 2

y = -2·x + 2 + 6

y = -2·x + 8

Where: y = The speed of the runner

x = The number of hours the runner has been running

Part B:

The graph of the equation can be plotted from the values of y obtained from the corresponding values of x for the first 5 hours as follows;

[tex]\begin{array}{|c|c|}x & y \\1 & 6 \\2 & 4\\3 & 2 \\4 & 0 \\5 & -2\\\end{bmatrix}[/tex]

Please find attached the graph of the velocity of the runner with time created using the above table of values found with MS Excel

Third Question;

Part A; The solution to pair of equation can be found from the point of intersection of their graphs

Therefore, the solution of the pair of equations represented by p(x) and f(x) is the point of intersection of the graph of f(x) and p(x), which is the point (2, -1)

Part B; Two solutions for the function f(x) can be obtained by the point of intersection of the x- and y-axis as follows;

The x-intercept of f(x) = (1.5, 0)

The y-intercept of f(x) = (0, 3)

Part C; The solution for g(x) = f(x), is the point of intersection of g(x) and f(x), which is the point (0, 3)

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Answer:

(4,-10)

Step-by-step explanation:

Graphing calculator

Answer:

Step-by-step explanation:

Yes, the lines are parallel.

so its d. trust me :)

As two angles are Complementary Angles they sum up to 90.

So value of d is 10.

Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

60° + 30° in the figure below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,

The opposite of 30° is 60°.

The opposite of 60° is 30°.

Given;

24,(7d-4) are complementary angles

So, 24°+7d-4 =90°;

⇒7d-4=90-24;

⇒7d-4=66;

⇒7d=70;

⇒d=10.

As two angles are Complementary Angles they sum up to 90.

So value of d is 10.

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Answer:

  0.63 or 5.37 seconds

Step-by-step explanation:

You want to know how long a ball was in the air when its height is 54 feet, and its height is described by -16s^2 +96s, for time (s) in seconds.

A graph shows the value of the height function is 54 when s = 0.63 or 5.37.

These solutions mean the ball was in the air 0.63 seconds when it passed 54 feet going up, and it was in the air 5.37 seconds when it was 54 feet in the air on the way down.

if you solve the equation you get k=-1

Answer:yes

Step-by-step explanation:

Answer:

P/mh

Step-by-step explanation:

P = mgh  to solve for g  Divide both sides by mh

[tex]\frac{P}{mh}[/tex] = [tex]\frac{mgh}{mh}[/tex]    On the right side of the equation the m and h cancel out and you are left with

[tex]\frac{P}{mh }[/tex] = g

The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity. Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.

Given

A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.

Velocity,

v = √(1.65)² + (10.7)²

v = √2.722 + 114.49

v = √117.212

v = 10.82

The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.

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Answer:

I think your answer is  [tex]\frac{2}{5} x-3[/tex]

Step-by-step explanation:

1. For the given line segment if PQ = RS then it is proved that PR = QS .

2. From the given angles  if ∠1 is complement to ∠2 (∠1 + ∠2 = 90° )  then angle 1 is complement to angle 3.

As given in the question,

1. Given : PQ = RS

To prove : PR = QS

Proof:

PQ = RS ( given )

Add both the side QR we get,

PQ + QR = QR + RS

From the diagram, it is given P - Q - R - S are collinear points

PR = QS  ( PQ + QR = PR and QR + RS = QS)

Hence, PQ = RS implies that PR = QS.

2. Given: ∠1 is a complement of ∠2

∠2 ≅ ∠3

To prove : ∠1 is a complement of ∠3

proof: ∠1 is a complement of ∠2

⇒∠1 + ∠2 = 90°

⇒∠1 + ∠3 = 90° ( given ∠2 = ∠3 )

⇒∠1 is a complement of ∠3.

Hence, it is proved that ∠1 is a complement of ∠2 implies that ∠1 is a complement of ∠3.

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Elyse has the option of combination of 960 cities, or another to choose from. If Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

Given,

Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.

To determine how many options Elyse will have, we use permutations and combinations.

We can say that she has a choice of any of the eight cities in Asia for every ten cities in Europe. Similar to how she can select any of the 4 cities in Africa for every 8 cities in Asia. The same is true for Australia and Africa.

Elyse has a choice of a total:

10×8×4×3

960

Elyse has the option of combination of 960 cities, or another.

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Answer:10x+2y=38, where x is the dollar cost of cinnamon and y the dollar cost of the spice.1

6x+8y=80multiply the top by -4-40x-8y=-15216x+8y=80.

Add them and y is eliminated.-24x=-72

Step-by-step explanation:

Answer:

0 muffins and 8 cookies

6 muffins and 4 cookies

Explain:

These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.

You have points R(2, 10) and S(6, - 8).

There two ways to construct a right triangle with RS being a hypotenuse.

Please see both ways reflected in the attached.

One triangle is RST and another one is RSU with red or blue legs.

n represents the number of friends, there must have been 2 friends with Matthew at the concert.

What is the arithmetic operation?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Let's call the number of friends n. The cost of the car service for the friends is 75 - 25 = 50 dollars. Since this cost is divided equally among the friends, each friend pays 50/n dollars.

The total cost for each friend, including the cost of the car service and the cost of dinner, is 25 dollars. Therefore, the cost of dinner for each friend is 25 - 50/n dollars.

Since the cost of dinner was divided equally among the friends, each friend paid 60/n dollars for dinner. Therefore, 25 - 50/n = 60/n.

Solving this equation for n, we get:

25 - 50/n = 60/n

50/n - 60/n = -25

10/n = 25

n = 2.5

Hence, n represents the number of friends, there must have been 2 friends with Matthew at the concert.

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Answer:

true 6=hepti

Step-by-step explanation:

Answer:

$162

Step-by-step explanation:

8% of 150 = 12 + 150

solving for m

distribute into parentheses

3m + 15 + 18 -2m = 29

simplify

m + 33 = 29

subtract

m = -4

verify

3(-4+5) -2(-9-4) = 29

3 + 26 = 29

29 = 29

true

m = -4

hope this helps :)

jeron

Answer:

20.69 m

Step-by-step explanation:

36/360 * 2πr = 13

r = 130/2π = 20.69 m

The values of x and are 28° and 58° respectively

It is important to note the properties of a trapezium;

We then have that;

2y + (y + 6) = 180

4x + 2x + 12 = 180

From equation (1), we have;

3y + 6 = 180

collect like terms

3y = 180 -6

3y = 174

y = 58°

From equation (2), we have;

6x = 180 -12

6x = 168

x = 28°

Hence, the values are 28° and 58°

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The approximate measures of the angles of ΔABC and the images formed by translation, reflection, and rotation of ΔABC, which are rigid transformations are;

   ΔABC [tex]{}[/tex]                 ΔA'B'C'                 ΔA''B''C''                     ΔA'''B'''C'''

∠A    =  [tex]{}[/tex]  22°           ∠A'  =  22°              ∠A'' = 22°                  ∠A'''  = 22°

∠B    = [tex]{}[/tex]   120°          ∠B'  =  120°            ∠B   = 120°                 ∠B'''  = 120°

∠C [tex]{}[/tex]   =    38°            ∠C'  = 38°              ∠C  =  38°                   ∠C'''  = 38°

A rigid transformation, also known as congruence transformation, in geometry, is one in which the length of the pre-image is preserved, such that the image and the pre-image have the same side lengths, and are therefore congruent.

The coordinates of the vertices of triangle ΔABC, obtained from a similar question online are;

A(-6, -1), B(-3, -3), C(-1, -2)

The lengths of the sides of triangle ΔABC are;

AB = √((-3 - (-6))² + (-3 - (-1))²) = √(13)

BC = √((-1 - (-3))² + (-2 - (-3))²) = √5

AC = √((-1 - (-6))² + (-2 - (-1))²) = √(26)

The law of cosines can be used to fined the measure of an angle of the triangle as follows;

Let a represent the side BC, let b represent the side AC, and let c represent the side AB, the formula for the law of cosines is presented as follows;

a² = b² + c² - 2·b·c·cos(A)

Where;

∠A = The angle at the vertex A

Therefore;

(√5)² = (√(26))² + (√(13))² - 2 × √(26) × √(13) × cos(A)

5 = 26 + 13 - 2 × √(26) × √(13) × cos(A)

cos(A) = (5 - (26 + 13))÷ (-2 × √(26) × √(13))

∠A = arccos((5 - (26 + 13))÷ (-2 × √(26) × √(13))) ≈ 22°

Similarly, we get:

cos(B) = (26 - (5 + 13))÷ (-2 × √(5) × √(13))

∠B = arccos((26 - (5 + 13))÷ (-2 × √(5) × √(13))) ≈ 120°

cos(C) = (13 - (26 + 5))÷ (-2 × √(5) × √(26))

∠C = arccos((13 - (26 + 5))÷ (-2 × √(5) × √(26))) ≈ 38°

The transformation from  ΔABC to ΔA'B'C', obtained from a similar question online, is a translation 5 units to the right and 2 units up

The transformation from ΔA'B'C' to ΔA''B''C'' is a reflection across the line y = -x

The transformation from ΔA''B''C'' to ΔA'''B'''C''' is a counterclockwise rotation by 270° about the origin

The translation, reflection, and rotation transformations are rigid transformations, such that the shape and sizes of the pre-images are preserved, and we get;

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle ABC & 120^{\circ} & \angle A'B'C' & 120^{\circ} &\angle A''B''C'' &120^{\circ} &\angle A'''B'''C''' &120^{\circ} \\\angle ACB &38^{\circ} & \angle A'C'B' & 38^{\circ} &\angle A''C''B'' &38^{\circ} &\angle A'''C'''B''' &38^{\circ} \\\\end{bmatrix}[/tex]

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle CAB & 22^{\circ} &\angle C'A'B' & 22^{\circ} &\angle C''A''B'' &22^{\circ} &\angle C'''A'''B''' &22^{\circ} \end{bmatrix}[/tex]

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