A person places $748 in an investment account earning an annual rate of 8%,
compounded continuously. Using the formula V = Pert, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 4 years.

8 is the correct answer. By the way, Thank you for the few extra points.. It is very appreciated.

Answer:

y= 5x+13

Step-by-step explanation:

Slope- intercept form

y= mx +b, where m is the gradient and b is the y-intercept.

Parallel lines have the same gradient.

y= 5x +4

Gradient of given line= 5

Thus, gradient of line= 5

Subst. m=5 into the equation.

y= 5x +b

To find the value of b, substitute a coordinate

When x= -2, y=3,

3= 5(-2) +b

3= -10 +b

b= 3 +10 (+10 on both sides)

b= 13

Thus, the equation of the line is y= 5x +13.

Answer:

To me it means that challenges are meant to show your strengths and weaknesses, and that things will challenge your weakness but it ends up making them into strengths.

Step-by-step explanation:

the factor is the division between feet and yards

so

so, the option is C

When it comes to the range covered by the decision given that `x<7  Range covered: x<21`, it means that `x` is a non-negative integer, and its range covered is `x<21`.The decision given can be expressed as:x < 7 To indicate the range covered by this decision, it's important to find the largest possible value of x.

Since x is a non-negative integer, the largest possible value would be 6.When x = 6, the inequality becomes:6 < 7, which is true.This means that any value of x that is less than 6 would also make the inequality true.Therefore, the range covered by `x < 7` is:`0 ≤ x < 7`Now, let's consider the second part of the statement: Range covered: x<21`.This means that the range covered by the inequality `x < 7` is also contained within the larger inequality `x < 21`.Since the range of `x<7` is `0 ≤ x < 7`, which is less than 21, then it's true to say that the range covered by `x < 7

Range covered: x<21` is:`0 ≤ x < 21 Therefore, the range covered by the decision `x < 7 // Range covered: x<21` is `0 ≤ x < 21`.

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The time the ball stays in the air is approximately 2.29 seconds and the ball can be seen 2.1 seconds after its thrown.

c)To find the amount of time the ball stays in the air, we need to find when it hits the ground, i.e., when its height is equal to 0. So, we need to solve the equation:

-16t^2 + 801 + 30 = 0

By using the quadratic formula or factoring, we can find that:

t = sqrt((801+30)/(-16)) = sqrt(831/-16) = sqrt(52.0625) = 2.29 seconds

So, the ball stays in the air for approximately 2.29 seconds.

d) To find the interval of time the ball can be seen from the ground, we need to find when its height is greater than or equal to 100 feet. This can be determined by solving the inequality:

-16t^2 + 801 + 30 >= 100

Solving for t:

t >= sqrt((100-801-30)/(-16)) = sqrt((-701)/(-16)) = sqrt(44.0625) = 2.1 seconds

So, the ball can be seen from the ground for approximately 2.1 seconds after it's thrown.

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Using the interquartile range (IQR) method, the value 2 is considered an outlier in the given data.

To determine if there is an outlier in the given data, we need to calculate the lower and upper bounds using the interquartile range (IQR) method.

First, we need to calculate the first quartile (Q1), second quartile (Q2 or median), and third quartile (Q3) of the data.

Arranging the data in ascending order

2, 9, 13, 17, 18, 20, 23, 24, 33, 34, 43, 45, 53, 53

Q1 = 17

Q2 = 24

Q3 = 43

Next, we can calculate the IQR by subtracting Q1 from Q3

IQR = Q3 - Q1 = 43 - 17 = 26

Now we can calculate the lower and upper bounds

Lower bound = Q1 - 1.5 × IQR = 17 - 1.5 × 26 = -8

Upper bound = Q3 + 1.5 × IQR = 43 + 1.5 × 26 = 79

Any values outside the lower and upper bounds are considered outliers.

In this case, we have a value of 2 that is outside the lower bound of -8. Therefore, 2 is considered an outlier in the given data.

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Answer:

Step-by-step explanation:

Hey! I also asked this question before lol! Someone solved it so this is not my work:

"N+ 1 = 3+2/2

The answer is 3

This is a odd number"

Hope this helps ∞<3

The statement "Exactly 50% of the area under the normal curve lies to the left of the mean" is a true statement.

In a normal distribution, the mean, median, and mode all coincide, and the distribution is symmetrical.

The mean is the balance point of the distribution, with 50% of the area to the left and 50% to the right of it. Exactly 50% of the area under the normal curve lies to the left of the mean.

This implies that the distribution is symmetrical, and the mean, mode, and median are the same.

Therefore, the statement "Exactly 50% of the area under the normal curve lies to the left of the mean" is a true statement.

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Answer:

A) 6 x² - 7x - 20

Step-by-step explanation:

Explanation:-

Given p(x) = 2 x-5 and r (x) = 3 x +4

(pr)(x) = p(x) r(x)

         = (2x -5)( 3 x +4)

        = 2x(3x +4) -5( 3x +4)

       = 6 x² + 8x - 15 x - 20

       =  6 x² - 7x - 20

(pr)(x) = 6 x² - 7x - 20

The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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Answer:

The largest African elephant weighed 13.5 tons (27,000 pounds) The world record holder weighed this much and stood 13ft/4m tall at the shoulder. There are other species of elephants, namely the Asian and the Indian, but they are much smaller than the African. The African elephant is the king among the giants on land. No other land animal comes close to the size of these creatures. It would take 165 full-grown men to make up the same weight as the world's record African elephant. The noise of an elephant digesting its food (when its tummy's growling) can be heard up to 600ft/183m away. Elephants actually have control over their digestive processes because they are able to stop the sounds of digestion when they sense danger. Here are some other cool elephant factoids:

Answer:

Miss Meod lost $88 from Adams' first week of services.

Step-by-step explanation:

Assuming the first sentence stand

As Adams received $125 of wages the break-point is at $250 dollars

which is double of Adams' wage. Below this point the employe cannot realize a gain.

The services performed were $162  we subtract the break even point:

162 - 250 = -88

Durign the first week Miss Adams services generate a variable loss for $88

Answer:

b

Step-by-step explanation:

because

3×(-5)-5×(-6)=15

2×(-5)-(-6)=-4

The given statement "The last indented line of a conditional proof sequence should always be the consequent of the conditional you are trying to prove" is True because this approach confirms that the consequent logically follows the antecedent and validates the conditional statement as true.

A conditional proof is a logical reasoning method used to establish the truth of a conditional statement (if P, then Q) by assuming the antecedent (P) and demonstrating that the consequent (Q) logically follows.

In conditional proof, you start by assuming the antecedent as a temporary hypothesis. Then, using valid inference rules and previously established premises, you deduce the consequent. If you can successfully derive the consequent, this shows that if the antecedent were true, the consequent would also be true. Thus, the conditional statement is proven to be true.

In summary, the last indented line of a conditional proof sequence should indeed be the consequent of the conditional you are trying to prove. This approach confirms that the consequent logically follows the antecedent and validates the conditional statement as true.

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The ratio of technicians to all the helpers is 11:18.


Given, there are 7 ushers and 11 technicians. To find the ratio of technicians to all the helpers, we need to calculate the total number of helpers, which is the sum of ushers and technicians.7 ushers + 11 technicians = 18 helpers.

Now, the ratio of technicians to all helpers can be written as 11:18. This means that out of every 18 helpers, 11 are technicians. It is important to note that the ratio can be simplified by dividing both sides by their greatest common factor, which in this case is 1. Therefore, the simplified ratio is also 11:18. Therefore, the ratio of technicians to all the helpers is 11:18.

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a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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Answer:

-4

Step-by-step explanation:

9-8=1

1x-2=-2

-2x2=-4

Answer:

9.31

Step-by-step explanation:

Distance = 3 ⅘ x 2.45

3 ⅘ = 3.8

3.8 x 2.45 = 9.31

Answer:

C!

Step-by-step explanation:

the sides all have the same ratio

8/12 = 10/15 = 14/21 = 2/3

The values of a, b, and c that satisfy the given conditions are a = 9, b = 143, and c = 52.

A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two.

The given quadratic inequality can be written as:

ax² - bx - c < 0     -----(1)

We are given that this inequality is satisfied only when -1/2 < x < 5.

Therefore, the quadratic expression must be equal to 0 at x = -1/2 and x = 5, and it must be negative in the interval (-1/2, 5). This means that the quadratic expression must have two real roots, one of which is between -1/2 and 5, and the other is outside this interval. Furthermore, since a, b, and c are positive integers, the parabola must open upwards.

The x-coordinate of the vertex of the parabola is given by:

x = -b / 2a

Since the parabola opens upwards, the vertex is the minimum point of the parabola, and the y-coordinate of the vertex is the minimum value of the quadratic expression. Therefore, we can use the given interval to find the value of a, b, and c:

-1/2 < x < 5

-1/2 + 5 > x - 5 > -5/2

23/4 > x - 5 > -5/2

Multiply both sides by a:

23a/4 > ax - 5a > -5a/2

Add c to both sides:

23a/4 + c > ax - 5a + c > -5a/2 + c

We want the left-hand side of this inequality to be equal to 0 when x = -1/2, and we want the right-hand side to be equal to 0 when x = 5. This gives us two equations:

(1) 23a/4 + c = 0.       (Substituting x=-1/2 in above equation)

(2) -5a/2 + c = 0.       (Substituting x=5 in above equation)

Solving for c in equation (1) and substituting into equation (2), we get:

c = -23a/4

-5a/2 - 23a/4 = 0

a = 46/5

Since a is a positive integer, we must have a = 9. Substituting a = 9 into the equations for c, we get:

c = -207/4

Since c is a positive integer, we must have c = 52. Substituting a = 9 and c = 52 into the equation for b, we get:

b = 143

Therefore, a = 9, b = 143, and c = 52.

We can now verify that the quadratic expression ax² - bx - c < 0 is satisfied only when -1/2 < x < 5:

When x = -1/2:

9(-1/2)² - 143(-1/2) - 52 = -83/4 < 0

When x = 5:

9(5)² - 143(5) - 52 = -157 < 0

And the quadratic expression is positive for x outside the interval (-1/2, 5). Therefore, the values of a, b, and c that satisfy the given conditions are a = 9, b = 143, and c = 52.

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The minimum number of dots that could lie on the whole surface of four standard dice glued together is 56.

This can be achieved by placing the faces with 1 dot opposite the faces with 6 dots, the faces with 2 dots opposite the faces with 5 dots, and the faces with 3 dots opposite the faces with 4 dots on all four dice. Since the sum of the numbers on opposite faces of each individual die is always 7, the sum of the numbers on opposite faces of the four glued-together dice is also always 7. Therefore, the minimum number of dots on the whole surface is 7 times the number of faces, which is 7 x 8 = 56.

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Answer:

24

Step-by-step explanation:

The solution to the inequality -2x + 4 < 16 is x > -6.

To solve the inequality -2x + 4 < 16, you can follow these steps:

Start by isolating the variable term. In this case, the variable term is -2x. Move the constant term, which is +4, to the other side of the inequality by subtracting 4 from both sides:

-2x + 4 - 4 < 16 - 4

-2x < 12

Next, divide both sides of the inequality by the coefficient of x, which is -2. It's important to note that when you divide or multiply an inequality by a negative number, you need to reverse the direction of the inequality sign:

(-2x) / -2 > 12 / -2

x > -6

The solution to the inequality is x > -6. This means that any value of x greater than -6 would satisfy the original inequality. Graphically, this represents all the numbers to the right of -6 on the number line.

So, the solution to the inequality -2x + 4 < 16 is x > -6.

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The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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Answer:

The octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 =135 degrees.

The name of the polygon is, ''Octagon.''

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Formula for sum S of n interior angles of n sided polygon is,

S = (n - 2) × 180°

Since, polygon is regular all its interior angles is same, sum of them is 135 degree times n

So, we have S = 135°n

As per formula,

S = (n - 2) × 180°

135n = (n - 2) × 180°

180n - 360 = 135n

180n = 135n + 360

180n - 135n = 360

45n = 360

n = 8

Hence, The name of the polygon is, ''Octagon.''

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