Rob put some money in an investment account. He uses the function V(t)=480(1.065)t to model the total value of the account, in dollars, after t years. What does the number 480 represent?

Answer:

Step-by-step explanation:

The bucket of fish are the sea otters fed each day is 2 buckets or 3/2 bucket(in fractions).

What is fraction?
A fraction is a mathematical expression that represents a part of a whole. It is written as a number (the numerator) over another number (the denominator), separated by a horizontal line. The denominator indicates the number of equal parts into which the whole is divided, while the numerator indicates how many of those parts are being considered.

Explanation:

The sea otters are fed 1/4 as much fish as the dolphins, which means they are fed:

(1/4) x 6 = 6/4 = 3/2 buckets of fish each day.

However, we cannot have half a bucket of fish, so we need to round this up to the nearest whole number. Therefore, the sea otters are fed:

2 buckets of fish each day.

So the answer is: 2 buckets.

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1) r base number is 3.

2)This is an exponential growth function

3) the Y interception is (0,2)

4)The purple line in the graph is a Horizontal asymptote and it has an equation 1.

5)The domain of the function is all real numbers.

6) The range of the function is all the real numbers >1

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

This is an exponential growth function so

Our base number is 3.

For statement 2 as explained, it is a growth function.

As far we get in X-axis higher is the value.

For statement 3 the Y interception is (0,2) as sowed below.

For statement 4 The purple line in the graph is a Horizontal asymptote and it has an equation 1.

For statement 5 The domain of the function is all real numbers.

For statement 6 The range of the function is all the real numbers >1. Because we do not include the asymptote.

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Answer:

Step-by-step explanation:

To find what the ratio would be, we need to know what to multiply 5 & 3 by so that when we add them, we get 80. Let's assume the number we multiply by is x:

5x + 3x = 80

8x = 80

x = 80 / 8

x = 10

Now, we multiply 5 by 10 and 3 by 10

= 50:30

Your ratio would be 50:30

Double check: 50 + 30 = 80

To become a forensic pathologist, you must first complete an undergraduate degree in medicine, biology, chemistry, or a similar discipline, with electives in forensic science, psychology, or a related field.

what is a forensic pathologist?

The forensic pathologist is a pathologist who specialises in the examination of people who die suddenly, unexpectedly, or brutally. A forensic pathologist specialises in establishing the cause and manner of death.

Autopsies are performed to determine the presence or absence of disease, injury, or poisoning; to evaluate historical and law-enforcement investigative information pertaining to determine the cause of death; to gather medical evidence, such as trace evidence and secretions; to document sexual assault; and to recreate how a person was injured.

Now,

To become a forensic pathologist, you must first complete an undergraduate degree in medicine, biology, chemistry, or a similar discipline, with electives in forensic science, psychology, or a related field.

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45 is 5 times as many as 9 and is 9 times as many as 5.

We have the following statement -

45 is x times as many as 9 and is y times as many as 5

We have to find x and y.

A number 'n' is 'a' times as many as 'b'. Then n equals to ?

n will be equal to -

n = ab

According to the question -

45 is x times as many as 9 and is y times as many as 5. Using the method shown above we can write two equations -

45 =  x 9     ---(1)

and

45 = y x 5     ---(2)

Now -

Solving both, we get -

x = 5 and y = 9

Hence, 45 is 5 times as many as 9 and is 9 times as many as 5.

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The method to convert milimeter to kilometre will be the formula - quantity in milimeter divided by 10⁶.

We know that mm represents milimeter and km represents kilometres. Now, relating the two quantities as follows -

1 kilometre is equal to 10⁶ milimeter

So, converting milimeter to kilometres using the above mentioned relation.

10⁶ milimeter is 1 kilometre

So, 1 milimeter in kilometre will be = 1/10⁶ kilometres

Now, convert the 5000 milimeter to kilometres for practice.

So, the formula will be -

Distance from milimeter to kilometre = 1/10⁶ kilometres

The required distance is = 5000 /10⁶

Performing division on Right Hand Side of the equation

The required distance = 0.005 kilometres

Hence, 5000 milimeter will be 0.005 kilometre.

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Answer: If there are 12 identically matched points on the picture of the sun, then the angle between any two adjacent points is 360/12 = 30 degrees.

When you line up two suns directly on top of each other, all of the matched points on the top sun will line up with the corresponding matched points on the bottom sun.

To find the least number of degrees that you can rotate the top sun so that the two suns are perfectly aligned again, you need to find the smallest angle that is a multiple of 30 degrees.

The smallest angle that is a multiple of 30 degrees is 360 degrees, which is equivalent to rotating the top sun all the way around once. Therefore, the least number of degrees that you can rotate the top sun so that the two suns are perfectly aligned again is 360 degrees.

Step-by-step explanation:

Answer: 18x+24

Step-by-step explanation:

The closure of set a) includes the boundary, unit circle, and origin; the closure of set b) includes the boundary, line segments, origin, and closed disk; the closure of set c) includes the boundary and origin; the closure of set d) includes the boundary, imaginary axis, origin, and closed half-plane to the right of the imaginary axis.

a) The closure of the set {-pi < arg(z) < pi, z ≠ 0} includes all points on the boundary of this region. This boundary consists of the real axis (where arg(z) = 0), the imaginary axis (where arg(z) = ±pi/2), and the unit circle centered at the origin (where |z| = 1). The closure of the set also includes the point at the origin, since this is a limit point of the set.

b) The closure of the set {|Re(z)| < |z| ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the unit circle centered at the origin (where |z| = 1/2) and the line segments connecting this circle to the x-axis (where |z| = |Re(z)|). The closure of the set also includes the origin and the points on the closed disk centered at the origin with radius 1/2.

c) The closure of the set {Re(1/z) ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the line Re(z) = 1/2 (where the imaginary part of z can take on any value) and the point at the origin, since this is a limit point of the set.

d) The closure of the set {Re(z^2) > 0} includes all points on the boundary of this region. This boundary consists of the imaginary axis (where Re(z^2) = 0) and the rays emanating from the origin at angles ±π/4 (where Re(z^2) is positive). The closure of the set also includes the origin and the points on the closed half-plane to the right of the imaginary axis.

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The area of the shaded region that is the segment of the circle is equal to 4.6 ft² to the nearest tenth.

To calculate the area of a segment of a circle, you need to know the radius of the circle, the central angle of the segment (in radians or degrees), and possibly the height of the segment (the distance from the chord of the segment to the center of the circle).

The formula for the area of a segment of a circle is:

A = θ/360° × πr² - 1/2 × r² × sinθ

where A is the area of the segment, r is the radius of the circle, and θ is the central angle of the segment in degrees.

From the question;

the central angle = 90°

radius r = 4ft

Area of the segment = 90°/360° × π4² - 1/2 × 4² × sin90°

Area of the segment = 1/4 × π × 4 × 4 - 1/2 × 4 × 4 × 1 {sin90° = 1}

Area of the segment = 4π × 8

Area of the segment = 4.5714

Therefore, the exact area of the shaded region that is the segment of the circle is equal to 4.6 ft² to the nearest tenth

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The range of the number of miles Maria jogged is 1 to 7.99

C. 1 to 7.99

What is the histogram?

A histogram is a graph used to represent the frequency distribution of a few data Set of one variable.

Let's recall that for calculating the range of a data set, we have to find out the lowest and the highest values of the data set.

As we can see in the graph below, the lowest value in the histogram is 1 and the highest is 7.99, therefore the correct answer is:

Hence, the range of the number of miles Maria jogged is 1 to 7.99

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The approach used to test if the function is even or odd is as follows: if it is an even function, it will be symmetrical around the y-axis: f(x)=f (-x). Odd functions are also symmetric about the x- and y-axes: f(x)=-f (-x).

When its input is changed to its negative, the output of an even function remains intact.

An odd function is one whose output changes sign when its parameter is made negative.

We may plot a function and examine its graph to determine if it is even or odd. The function is an even function if the graph is symmetrical around the origin (x=0, y=0). The function is an odd function if the graph is symmetrical around the y-axis (x=0).

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False. The Six Sigma DMAIC approach is best suited for number of problems and issues that require a systematic approach and have measurable results. It should not be employed for all problems as some may require a different approach.

The Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) approach is a systematic process that is used to identify and eliminate defects in processes, products, or services. This approach is best suited for problems and issues that have a structured approach, measurable results, and an opportunity for improvement. However, it should not be employed for all problems as some may require a different approach such as root-cause analysis or process mapping. Additionally, some number of problems may require creative solutions that cannot be addressed using the DMAIC approach. In these cases, alternative approaches such as brainstorming or design thinking should be employed.

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The length of the shadow casted by the building is 31.06 meters. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is a discipline of mathematics that deals with the study of sides, angles, and relationships in triangles.

We are given that at a certain time of day, the angle of elevation of the sun is 44 degrees. The height of the building is given as 30 meters.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 44° = 30/x

⇒0.9657 = 30/x

⇒x = 31.06

Hence, the length of the shadow casted by the building is 31.06 meters.

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The value of 12.5 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 27.55 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 12.5 x 2.20462262184878

= 27.55 pounds or lbs.

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So the answer is: the first arc should pass through point B (not A). All other elements in the diagram appear to be correct.

The elements or members of a set are the parts that make it up. To divide the components of a set, commas and two curly (idle) braces are typically employed. Capital letters are always used to print the set's name. The set "A" in this context consists of the letters v, w, x, y, and z.

Based on the given diagram and instructions, it appears that the error in the construction is that the first arc is centered at point C instead of point A. The correct procedure for constructing a line parallel to line AB and passing through point P is as follows:

1.Draw a line AB and mark point P not on line AB.

2.From point P, draw an arc that intersects line AB at points D and E.

3.Draw another arc, centered at point D, with the same radius as the first arc. This arc should intersect the first arc at point F.

4.Draw a line through point P and point F. This line is parallel to line AB and passes through point P.

So the answer is: the first arc should pass through point B (not A). All other elements in the diagram appear to be correct.

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The third arc should be drawn centred at F.

What is an arc?

In geometry, an arc is a curved segment of a circle or any curved line. It is a part of a curve that is bounded by two distinct endpoints and is characterized by its length, its curvature, and its central angle.

Constructing a parallel line to line AB and passing through point P.

To find:

The error occurred in the construction.

The procedure is,

The first arc must be drawn centred at C.

The second must be drawn centred at P.

Finally, the third arc must be drawn centred at F.

But here, the third arc is drawn centred at D. This is wrong.

The correct step is that the third arc must be centred at F.

Hence, The third arc should be drawn centred at F.

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1800

200 is the hundreds place value
2000 is the value to its left
2000-200 is 1800

The percentages of executives receiving bonuses are given as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for the percentage of executives receiving bonuses in t years after 1998 is given as follows:

B(t) = 4.816(1.338)^t.

2002 is 2002 - 1998 = 4 years after 1998, hence the percentage is given as follows:

B(4) = 4.816(1.338)^4 = 15.44%.

The percentage for 2003 is then given as follows:

B(5) = 4.816(1.338)^5 = 20.65%.

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In the United States, a bushel is legally defined as 2,150.42 cubic inches or approximately 35.24 liters. The weight of a bushel depends on the density of the item being measured.

For example, a bushel of wheat weighs approximately 60 pounds, a bushel of soybeans weighs approximately 60 pounds, and a bushel of apples weighs approximately 42 pounds.

A bushel is a unit of measurement used to quantify dry goods such as grains, fruits, and vegetables. The exact weight of a bushel can differ depending on the item being measured.

It is worth noting that the bushel is not a universal measurement, and other countries may use various standards for measuring dry goods.

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From the given information provided, the approximate volume of the cone is 94.24777 cubic inches.

The volume of a cone can be calculated using the formula V = (1/3) × π × r² × h, where "r" is the radius of the base of the cone, "h" is the height of the cone, and "π" is the mathematical constant approximately equal to 3.14159.

Radius r= 3 inches

Height h= 10 inches

π = 3.14159

Using the formula for the volume of a cone, V = (1/3) × π × r² × h, we can substitute the given values to calculate the volume of the cone:

V = (1/3) × 3.14159 × 3² × 10

V ≈ 94.24777 cubic inches

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The value of c that makes the function, f(x) = x² , x ≠0 and c , x = 0, continuous at x=0 is equals to 3.

The condition for continuity of a function f(x) at x=a : limf(x) = f(a)

x→a

Before convincing the above condition, we have to examine that the limit is exit or not at x=a. To test the condition for existancy of a limit at x=a of a function

f(x), we have to fulfill the following condition: lim f(x) = lim f(x)

x→a⁻ x→a⁺

Sometimes to evaluate a limit, we get indeterminate forms such as 0/0 or ∞/∞. In those cases, we use L'Hospital's Rule.

Now, we have f(x) = x² , x ≠0 and c , x = 0.

limf(x) = lim x² + 3 = (0)² + 3 = 3

x→0 x→0

So, lim f(x) = 3. For f(x) to be continuous

x→0

lim f(x) = f(0) => c = 3. Thus, c will work as

x→0

we have provide function is continuous.

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Complete question:

Find a value of c that makes the following function continuous at x = 0, explain why the value of c works. f(x) = x² , x ≠0 and c , x = 0

Answer: the answer is C

Step-by-step explanation:

To make the systems equivalent, we need to multiply both sides of each equation in the first system by the same constant in order to get the corresponding equations in the second system.

If we multiply the first equation in the first system by 4, we get:

16x + 20y = -12

If we multiply the second equation in the first system by -4, we get:

-20x + 12y = 52

Comparing this to the second system, we see that the equation -20x + 12y = 52 matches the second equation in the second system. Therefore, the value of C in the second system must be 52.

So, the answer is C.

Therefore, the solutions to the simultaneous equation are (x, y) = ((5 + √(21))/2, (5 - √(21))/2) and (x, y) = ((5 - √(21))/2, (5 + √(21))/2).

To solve the simultaneous equation 1÷x + 1÷y = 5, 1÷y - 1÷x = 1, we can use the substitution method. Here are the steps to solve the equation:
1. Rearrange the first equation to get 1÷y = 5 - 1÷x
2. Substitute this into the second equation to get 1÷(5 - 1÷x) - 1÷x = 1
3. Multiply both sides by x(5 - 1÷x) to get x - (5 - 1÷x) = x(5 - 1÷x)
4. Simplify and rearrange to get x² - 5x + 1 = 0
5. Use the quadratic formula to solve for x: x = (-(-5) ± √((-5)² - 4(1)(1)))÷(2(1)) = (5 ± √(21))/2
6. Substitute the values of x back into the first equation to find the corresponding values of y: y = 1÷(5 - 1÷((5 + √(21))/2)) = (5 - √(21))/2 and y = 1÷(5 - 1÷((5 - √(21))/2)) = (5 + √(21))/2

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Parallel lines are lines that are always the same distance apart and will never intersect. Intersecting lines are lines that cross or meet at a point. Perpendicular lines are lines that intersect at a right angle (90 degrees).

To determine if lines are parallel, you can look at their slopes. If two lines have the same slope, they are parallel. For example, the lines y = 2x + 3 and y = 2x - 5 are parallel because they both have a slope of 2.

To determine if lines are intersecting, you can look at their slopes and y-intercepts. If two lines have different slopes, they will intersect at some point. For example, the lines y = 2x + 3 and y = -x + 7 are intersecting because they have different slopes (2 and -1, respectively).

To determine if lines are perpendicular, you can look at their slopes. If the product of the slopes of two lines is -1, they are perpendicular. For example, the lines y = 2x + 3 and y = -0.5x + 7 are perpendicular because the product of their slopes (2 and -0.5) is -1.

I hope this helps! Let me know if you have any further questions.

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The function that can be graphed is option (d) f(x) = √(x + 1) + 8

Functions are commonly used in mathematics to describe relationships between variables.

To determine which of the four functions could be graphed, we first need to identify the curve's intercepts and asymptotes.

From the graph, we can identify the intercepts as (0,8) and (–3,0). The asymptotes are given by the equations x = 0 and y = 8. We can then use these points to compare the given functions and determine which one could be used to graph the curve.

Of the four functions, only f(x) = √(x + 1) + 8 fits the given description. This function has intercepts at (0,8) and (–3,0) and asymptotes at x = 0 and y = 8. Thus, f(x) = √(x + 1) + 8 is the function that could be graphed

Therefore, option (d) is right choice.

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Answer: D

Step-by-step explanation:

EDGE 2023

Answer:

Step-by-step explanation:

Plug in the functions.

(x^2+3x-5) + (2x+1)

Then, combine like terms.

= x^2 + 5x -4

The number of the ways to seat the jury members around a circular table for deliberations are 5040.

A permutation is a word that describes the number of ways things can be ordered or arranged.

Given that, we need to find that how many ways are there to seat the jury members around a circular table for deliberations,

We know that,

There are (n-1)! ways to seat n people at a circular table,

Since, there are no number of people is given, let us assume that there are 8 members,

Therefore,

The number of ways to seat the jury members around a table =

(8-1)! = 7!

= 5040

Hence, the number of the ways to seat the jury members around a circular table for deliberations are 5040.

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The algebraic expression for the total weight of x bags of fertilizer when each bag weighs 50 pounds is:

50x

In this expression, 50 represents the weight of each bag of fertilizer, and x represents the number of bags. When we multiply the weight of each bag by the number of bags, we get the total weight of all the bags of fertilizer.