The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?
A) The initial height, in feet, of the object
B) The maximum height, in feet, of the object
C) The initial speed, in feet per second, of the object
D) The maximum speed, in feet per second, of the object

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

The total amount of spiders needed to have the same mass as spider man would be 84,571.

Step-by-step explanation:

16 ounces = 1 pound

1. divide 16 by 0.035 to get the total number of spiders that weigh 1 pound together (which is 457.142857143 or rounded up to 457)

2. multiply 457.142857143 by 185 to get the total number of spiders that together weigh 185 pounds (which gets you 84571.4285714 or rounded up to 84,571)

3. Check your work

(only trust me if it's a multiple choice question)

a) The sequence {cos(nπ)/3} does not converge.

b) {Sn = ((-1)^n) n} does not converge.

2.b) The limit of [√(n² + n) - n] as n approaches infinity is equal to 1/2.

a) The sequence {cos(nπ)/3} does not converge because the cosine function oscillates between -1 and 1 as the input, nπ, varies. Since n takes on different values for each term in the sequence, the cosine function will have different values for each term. Therefore, the sequence does not approach a specific value and does not converge.

b)  To show that the sequence {Sn = ((-1)^n) n} does not converge, we can demonstrate that there is no single real number towards which the terms of the sequence get arbitrarily close as n approaches infinity.

Let's examine the even terms of the sequence, where n takes on even values. In this case, the sequence becomes {2, 4, 6, ...}. It is clear that the even terms of the sequence are strictly increasing.

Now, let's consider the odd terms of the sequence, where n takes on odd values. In this case, the sequence becomes {-1, -3, -5, ...}. The odd terms of the sequence are strictly decreasing.

Since the even terms of the sequence are increasing and the odd terms are decreasing, the terms of the sequence do not approach a single limiting value. Instead, the sequence oscillates between positive and negative values as n increases.Therefore, we can conclude that the sequence {Sn = ((-1)^n) n} does not converge.

2.b) To prove that the limit of [√(n²+ n) - n] as n approaches infinity is 1/2, we can simplify the expression. Taking the square root and subtracting n, we have:

[√(n² + n) - n] = [√(n²+ n) - n] * [√(n² + n) + n] / [√(n² + n) + n]

                 = (n² + n - n²) / [√(n² + n) + n]

                 = n / [√(n²+ n) + n]

As n approaches infinity, the denominator [√(n² + n) + n] also approaches infinity. Therefore, the fraction n / [√(n² + n) + n] approaches 0. Since the numerator approaches infinity and the denominator approaches infinity, the limit of the expression is 0. Hence, we can conclude that:

lim [√(n² + n) - n] = 0.

However, the original question states that the limit is 1/2. Therefore, there seems to be an error or misunderstanding in the question statement, as the expression does not converge to 1/2.

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Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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Answer:

(10, -2)

Step-by-step explanation:

x = 10 (its given in the problem)

then plug in 10 for x in the second equation and solve for y

3(10) + 5y = 20

30 + 5y = 20

5y = -10

y = -2

so the solution is (10, -2)

The volume of the cylinder can be obtained from the calculation as  1356 \(cm^3\)

We know that the volume of the cylinder is;

π (pi) is a mathematical constant approximately equal to 3.14159

r is the radius of the cylinder's base (the distance from the center to the edge of the circular base)

h is the height of the cylinder (the distance between the bases)

By substituting the appropriate values for the radius and height into the formula, you can calculate the volume of the cylinder.

V = π\(r^2\)h

V = 3.14 *\((12/2)^2\) * 12

h = 1356 \(cm^3\)

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The x is a specific value that the variable can take on.

A random variable is a variable that has a numerical value, which is determined by the result of a random experiment. The numerical value is determined by a set of probabilities, which are associated with each possible outcome of the experiment. Random variables can be classified as discrete or continuous, depending on the type of outcomes that they can have. Examples of random variables include the number of heads in a series of coin tosses, the time until a traffic light changes from red to green, and the height of a randomly selected person.The randomness of a random variable comes from the fact that the outcome of the experiment that it represents is uncertain. The uncertainty arises because the experiment is subject to the effects of chance, rather than being completely determined by fixed physical laws or other deterministic factors. Because of this, it is not possible to predict with certainty what the value of a random variable will be, even if we know the probabilities associated with each possible outcome.There are many different notations that can be used to represent random variables, depending on the context and the preferences of the person using the notation. Some of the most common notations include X, Y, and Z, as well as Greek letters such as µ, σ, and ρ. When a random variable is discrete, it is often represented using a probability mass function, which is denoted by P(X=x), where x is a specific value that the variable can take on. When a random variable is continuous, it is often represented using a probability density function, which is denoted by f(x), where x is a specific value that the variable can take on.

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(a) The NPV at a discount rate of 0 percent is $6,820.00.

(b) The NPV at a discount rate of 10 percent is $3,428.00.

(c) The NPV at a discount rate of 20 percent is -$2,042.80.

(d) The NPV at a discount rate of 30 percent is -$6,073.08.

To calculate the NPV (Net Present Value) at different discount rates, we discount each cash flow to its present value and sum them up.

(a) At a discount rate of 0 percent, the NPV is calculated by simply summing the cash flows:

NPV = -$19,400 + $10,400 + $9,320 + $6,900 = $6,820.00

(b) At a discount rate of 10 percent, we discount each cash flow to its present value using the formula:

PV = Cash Flow / (1 + Discount Rate)^Year

PV1 = $10,400 / (1 + 0.10)^1 = $9,454.55

PV2 = $9,320 / (1 + 0.10)^2 = $7,562.19

PV3 = $6,900 / (1 + 0.10)^3 = $5,264.46

NPV = -$19,400 + $9,454.55 + $7,562.19 + $5,264.46 = $3,428.00

(c) At a discount rate of 20 percent, we calculate the present value of each cash flow:

PV1 = $10,400 / (1 + 0.20)^1 = $8,666.67

PV2 = $9,320 / (1 + 0.20)^2 = $6,859.26

PV3 = $6,900 / (1 + 0.20)^3 = $4,363.64

NPV = -$19,400 + $8,666.67 + $6,859.26 + $4,363.64 = -$2,042.80

(d) At a discount rate of 30 percent, we calculate the present value of each cash flow:

PV1 = $10,400 / (1 + 0.30)^1 = $8,000.00

PV2 = $9,320 / (1 + 0.30)^2 = $5,526.88

PV3 = $6,900 / (1 + 0.30)^3 = $3,246.13

NPV = -$19,400 + $8,000.00 + $5,526.88 + $3,246.13 = -$6,073.08

Note: A negative NPV indicates that the investment may not be financially viable.

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The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

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We can conclude that the series [∞] 1 n 8 − 1 n 9 n = 1 diverges.

To test for convergence or divergence of the given series, we can use the Comparison Test.
The Comparison Test states that if the terms of a series are non-negative and can be compared to the terms of a series that is known to converge or diverge, then the original series will behave in the same way.
In this case, we can compare the given series to the harmonic series, which is known to diverge.
The harmonic series is given by: 1 + 1/2 + 1/3 + 1/4 + ...
Notice that all the terms of the harmonic series are larger than the terms of the given series since 1/n is larger than 1/(n+1) for all positive integers n.
Therefore, by the Comparison Test, since the harmonic series diverges, the given series also diverges.
Therefore, we can conclude that the series [infinity] 1 n 8 − 1 n 9 n = 1 diverges.

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Answer:

[see below]

Step-by-step explanation:

3 * (-5) = -15

Locate the '-15' line and plot a closed circle on it.

-2 * -3 = 6

Locate the '6' line and plot a closed circle on it.

Hope this helps.

Answer: The answer is 20

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(Equation:\)

\(\rm{3^2 + 1\times 2}\)

\(Simplifying:\)

\(\rm{3^2 + 1\times 2}\)

\(\rm{= 3\times 3+ 1\times 2}\)

\(\rm{= 9 + 1\times2}\)

\(\rm{= 9 + 2}\)

\(\rm{= 11}\)

\(Therefore, your\ answer\ should\ be:\)

\(\huge\boxed{\frak{11}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

2x1-5y=17

2-5y=17

-5y=17-2

-5y=15

y=-3

Step-by-step explanation:

Answer:

x =11

Step-by-step explanation:

2x-5y=17

Let y=1

2x-5(1) = 17

2x-5=17

Add 5 to each side

2x-5+5 = 17+5

2x = 22

Divide each side by 2

2x/2 = 22/2

x =11

Answer:

Step-by-step explanation:

your right there wrong

Answer:

Pretty sure it's "only i"

Step-by-step explanation:

A constant rate of change means that something changes by the same amount during equal intervals.

$30 is the same amount whereas 10% could vary.

Hope this helps.

Answer:

4/3

Step-by-step explanation:

so in y=mx+b form.

m=slope b=y-int

Subtract 5 from both sides to isolate y on a side.

4x-6=3y

Divide both sides by 3 to isolate y on one side.

(4/3)x-2=y

y=(4/3)x-2

m=4/3

b=-2

So the slope is 4/3

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

A = 2

D = 1

B = 4

C = 3

Step-by-step explanation:

Height of water in bathtub is a function of water in bathtub.

P(t) = w ; t = time ; w = height of water.

A: P (0)=0 ; At time, t = 0 ; height of water = 0, there is no water on bathtub

2: The bathtub starts out with no water.

D: P (20) = 0 ; At time, t = 20 ; w = 0 ;the tub is empty.

1: After 20 minutes, the bathtub is empty.

B:P (4)= 10 `; At t = 4, w = 10 ; height of water in bath tub is 10

4: The height of the water is 10 inches after 4 minutes

C:P (10) = 4 ; At t = 10, w =4, height of water in bathtub = 4 inches

3: After 10 minutes, the height of the water is 4 inches.

.

In a primitive Pythagorean triple, the sides a, b, and c are all integers, and they satisfy the equation a^2 + b^2 = c^2.

Now, let's assume that neither x nor y is divisible by 3. This means that x and y can only be 1, 2, 4, 5, 7, or 8 modulo 3. Therefore, x^2 and y^2 can only be 1 or 4 modulo 3. Now, let's consider the equation a^2 + b^2 = c^2 mod 3. If a and b are both 1 or both 2 modulo 3, then their squares will add up to 2 modulo 3, which is not a quadratic residue. Therefore, one of a and b must be 0 modulo 3, and hence, c must also be divisible by 3. We assumed that neither x nor y is divisible by 3. We then looked at the possible residues of x and y modulo 3 and saw that they can only be 1, 2, 4, 5, 7, or 8 modulo 3. We then used the fact that the sum of two quadratic residues is not a quadratic residue modulo 3, and concluded that one of a and b in the Pythagorean triple must be divisible by 3.

In conclusion, either x or y in a primitive Pythagorean triple must be divisible by 3. This is a result of the fact that the sum of two quadratic residues is not a quadratic residue modulo 3.

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The estimated money collected in concession sales is 39000000.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount made in sales:

$10, 486, 525 = hot dog sales

$23, 451,492 = large drink sales

$4,765, 300 = soft pretzel sale

$1,342,653 = nacho sales

Now,

Rounding to the nearest million.

$10, 486, 525 = hot dog sales = $10,000,000

$23, 451,492 = large drink sales = $23,000,000

$4,765, 300 = soft pretzel sale = $5,000,000

$1,342,653 = nacho sales = $1,000,000

Now,

The estimated money collected in concession sales.

= 10,000,000 + 23,000,000 + 5,000,000 + 1,000,000

= 39000000

Thus,

The estimated money collected is 39000000.

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The quotient of the given expression is (X - 4) / 2X(X + 4).

What is quotient ?

In mathematics, the quotient refers to the result of dividing one number by another. It represents the answer to a division problem, and is commonly expressed in the form of a fraction or decimal. For example, the quotient of 10 divided by 2 is 5, and can be expressed as the fraction 5/1 or the decimal 5.0.

Where as, the remainder is the amount left over after one number is divided by another. When one integer is divided by another integer, the remainder is the integer that is left over and does not divide evenly into the quotient.

To simplify the expression, we can start by factoring the denominator of the second fraction:

2X / (X² - 16) = 2X / (X + 4)(X - 4)

Then, we can rewrite the entire expression using the division by fraction rule, which states that division by a fraction is the same as multiplication by its reciprocal:

X / (X + 4) ÷ 2X / (X + 4)(X - 4)

= X / (X + 4) x (X - 4) / 2X

Next, we can simplify by canceling out common factors:

X / (X + 4) x (X - 4) / 2X

= (X / X) x (X - 4) / (X + 4) x (2 x X)

= (X - 4) / (2X² + 8X)

= (X - 4) / 2X(X + 4)

Therefore, the quotient of the given expression is (X - 4) / 2X(X + 4).

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If someone works 48.5 hours in a week and their regular work week is 40 hours, then they would have worked 8.5 hours of overtime.

What is meant by a week?

A week is a unit of time equal to seven days, usually beginning on Monday and ending on Sunday. It is commonly used to measure and organize time.

What is meant by hours?

Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.

According to the given information

In most cases, overtime pay is calculated as 1.5 times the employee’s regular hourly rate.

If someone works 48.5 hours in a week and their regular workweek is 40 hours, then they would have worked 8.5 hours of overtime.

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Answer:

5 : 6

Step-by-step explanation:

100 : 120

= 100 / 120

= 10 / 12

= 5 / 6

= 5 : 6

Therefore, the ratio 100 : 120 in it's simplest form is 5 : 6.

Hope it helps :)

Please mark my answer as the brainliest

the radius of the circle is 30 cm when the circumference is 188.4 . The length of the boundary is its circumference.

A boy has traveled a certain distance if, after sprinting around the park once, he arrives at point "A" from point "A" in the first place. The park's circumference, which has the shape of a circle, is the length or border that it encompasses. The length of the boundary is its circumference.

calculation

Circumference=2πr

188.4=2×3.14×r

188.4=6.28×r

r= 188.4/6.28

radius=30cm

the radius of circle is 30 cm when the circumference is 188.4 .

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The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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To calculate SAM and SOM, you need to follow the following steps:

1. SAM (Simple Arithmetic Mean): SAM is calculated by adding up all the values in a set of data and then dividing that sum by the number of values in the dataset.

Formula: SAM = (x1 + x2 + ... + xn)/n

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SAM would be (2+4+6+8+10)/5 = 30/5 = 6

2. SOM (Simple Geometric Mean): SOM is calculated by multiplying all the values in a set of data and then taking the nth root of that product, where n is the number of values in the dataset.

Formula: SOM = (x1 * x2 * ... * xn)^(1/n)

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SOM would be (2*4*6*8*10)^(1/5) = 3840^(1/5) = 5.16

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Answer: 1/36 ==> c

Step-by-step explanation:

\(6 ^{-2}\)=

\(6 ^{-1*2}\)=

\((6^{-1}) ^{2}\)=

\((\frac{1}{6} ) ^{2}\)=

\(\frac{1^{2}}{6^2}\)=1/36 ==> c

Step-by-step explanation:

well well from your question the value of g wasn't given and we are asked to solve for f

I will have to assume g=g

make f subject of formula

first we open the brackets

-3g+6f=5g

collect like terms

6f=5g+3g

6f=8g

f=8g/6

f=(4/3)g