An element wIth mass 420 grams decays by 11.8% per minute. How much of the element is remainifg after 16 minutes, to the nearest 1oth of a gram?

a) The initial velocity of the boulder was 117.39 ft/s.

b) The maximum height reached by the boulder was 214.48 ft.

We can use the equations of motion to solve this problem. Let's assume that the acceleration due to gravity is -32 ft/s² (negative because it acts downwards).

a) We can use the following equation to find the initial velocity (v₀) of the boulder:

h = v₀t + 0.5at²

where h is the initial height (15ft), t is the time it takes to hit the ground (6.7s), and a is the acceleration due to gravity (-32 ft/s²).

Plugging in the values, we get:

15 = v₀(6.7) + 0.5(-32)(6.7)²

Solving for v₀, we get:

v₀ = 117.39 ft/s (rounded to two decimal places)

Therefore, the initial velocity of the boulder was 117.39 ft/s.

b) To find the maximum height reached by the boulder, we can use the following equation:

v² = v₀² + 2ah

where v is the final velocity (0 ft/s at the maximum height), v₀ is the initial velocity (which we just found to be 117.39 ft/s), a is the acceleration due to gravity (-32 ft/s²), and h is the maximum height we want to find.

Plugging in the values, we get:

0² = (117.39)² + 2(-32)h

Solving for h, we get:

h = 214.48 ft (rounded to two decimal places)

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Answer: For 600 ppl: 84 & for 650 ppl: 91

Step-by-step explanation:

If the average is 1.4 of 10 ppl, you can use that to solve for 600 people and for 650 people.

Divide 600 by 10, and you get 60.

Multiply that by 1.4, and you get 84, which is the answer.

For 650 people:

Divide 650 by 10, and you get 65.

Multiply that by 1.4, and you get 91, which is the answer.

a) By Pythagorean theorem, the value of variable x is equal to 10.2171 meters.

b) By trigonometric functions, the value of variable h is equal to 7.8620 meters.

Herein we have the representation of a geometric system formed by four right triangles, this formation has a known angle and a known side, and two unknown variables as well. The values of the variables can be found by means of trigonometric functions and Pythagorean theorem:

Trigonometric functions

sin 50° = h / x

h = 0.7660 · x

Pythagorean theorem

x² = L² + h²

8² = (0.25 · L)² + h²

64 = 0.0625 · L² + h²

Then, we eliminate L by equalizing second and third equations:

64 = 0.0625 · (x² - h²) + h²

64 = 0.0625 · x² + 0.9375 · h²

And by the first equation:

64 = 0.0625 · x² + 0.9375 · (0.7660 · x)²

64 = 0.0625 · x² + 0.5501 · x²

64 = 0.6126 · x²

8 = 0.783 · x

x = 10.2171 m

And the value of h is:

h = 0.7660 · (10.2171 m)

h = 7.826 m

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In response to the supplied query, we may state that As a result, the system of equations has a solution of x = 13/7 and y = -3/7.

In algebra, a linear equation is one that of the form y=mx+b. The slope is B, and the y-intercept is m. As y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables". Bivariate linear equations are linear equations with two variables. Linear equations may be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. A mathematical equation is said to be linear if its solution has the form y=mx+b, where m stands for the slope and b for the y-intercept.  

When utilizing the substitution approach to solve a system of linear equations, you should search for an equation that already has one variable isolated.

For instance, take into account the equations below:

2x + 3y = 11

4x - y = 5

The second equation in this system has already had y determined. In order to eliminate y and find x, we can change the phrase 4x - 5 for y in the first equation:

[tex]14x = 26 x = 13/7 2x + 3(4x - 5) = 11 2x + 12x - 15 = 11\\ 4(13/7) y = 5\s52/7 - y = 5\sy = -3/7\\[/tex]

As a result, the system of equations has a solution of x = 13/7 and y = -3/7.

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The answer to the question is option A. The median number of points scored for Team 1 is 15 and for Team 2 is 11.

To find the median number of points scored for each team from the given back-to-back stem-and-leaf plot, we need to identify the middle value of the data set for each team. The middle value is the point where half the scores are above it and half are below it.

Looking at the stem-and-leaf plot, we can see that for Team 1, the median score is 15. This is because there are 4 scores above 15 and 4 scores below it. Therefore, 15 is the middle value for Team 1.

Similarly, for Team 2, the median score is 11. This is because there are 4 scores above 11 and 4 scores below it. Therefore, 11 is the middle value for Team 2.

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As per the given rectangle, the length of EG is 5x - 7

We are given that DEFG is a rectangle, which means that its opposite sides are parallel and equal in length. Let's label the sides of the rectangle as follows:

DE = FG = a (since opposite sides of a rectangle are equal in length)

EF = DG = b (since opposite sides of a rectangle are parallel)

Now, we can use the given information to set up an equation for the length of EG:

EG = EF + FG = b + a

But we don't know the values of a and b. However, we are given that FD = 3x - 7 and EG = x + 5. We can use this information to solve for a and b.

We know that FD = DE - EF, so we can substitute the values we have:

3x - 7 = a - b

We also know that EG = FG - DG, so we can substitute the values we have:

x + 5 = a - b

Now we have two equations with two variables (a and b). We can solve for a and b by adding the two equations together:

3x - 7 + x + 5 = 2a

4x - 2 = 2a

a = 2x - 1

Now we can substitute this value for a in one of the earlier equations to solve for b:

3x - 7 = (2x - 1) - b

b = 3x - 6

Finally, we can substitute the values we found for a and b into the equation we set up earlier to find the length of EG:

EG = EF + FG = b + a = (3x - 6) + (2x - 1) = 5x - 7

Therefore, the length of EG is 5x - 7.

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The probability that Burt allowed a total of 2 or more walks and hits in one inning is approximately 0.363 or 36.3%.

To solve this problem, we can use the Poisson distribution, which is commonly used to model the number of events occurring in a fixed amount of time or space. In this case, we can use it to model the number of hits and walks allowed by Burt in a randomly selected inning.

Let λ be the expected number of hits and walks allowed by Burt in one inning. We can find λ using the given whip:

whip = (walks + hits) / innings pitched

1.271 = (walks + hits) / 1

walks + hits = 1.271

So, λ = 1.271.

Now, we want to find the probability that Burt allowed a total of 2 or more walks and hits in one inning. Let X be the number of hits and walks allowed by Burt in one inning. Then, we want to find P(X ≥ 2).

Using the Poisson distribution, we have:

P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

where

P(X = k) = (e^(-λ) × λ^k) / k!

So, we need to calculate P(X = 0) and P(X = 1):

P(X = 0) = (e^(-λ) × λ⁰) / 0! = e⁽⁻¹.²⁷¹⁾ = 0.280

P(X = 1) = (e^(-λ) × λ¹) / 1! = e⁽⁻¹.²⁷¹⁾  1.271 = 0.357

Therefore,

P(X ≥ 2) = 1 - P(X < 2) = 1 - (P(X = 0) + P(X = 1)) = 0.363

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Applying the product property of square roots, the items that will fill the empty boxes given the radicals above are:

2a: 3√2

2b: √24

2c: = 2√6

2d: √9 * √6

2e: √36 * √2

2f: 6√2

The product property of square roots states that the square root of a product of two numbers is equal to the product of the square roots of those numbers. In other words, if a and b are non-negative real numbers, then the square root of ab is equal to the square root of a multiplied by the square root of b. Mathematically, it can be written as:

√(ab) = √a * √b

Given the radicals above, we would have the following:

2a:

√18 = √9 * √2 = 3√2

2b and 2c:

√24 = √4 * √6 = 2√6

2d:

√54 = √9 * √6 = 3√6

2e and 2f:

√72 = √36 * √2 = 6√2

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In this scenario, we need to construct a Markov chain that indicates when the solar heat must be augmented.

To do this, we need to define our states carefully. Let's define the following states: S0: The solar heating device is fully charged. S1: The solar heating device has one day of charge left. S2: The solar heating device has two days of charge left. C: The solar heating device needs to be augmented.

Now, let's construct the Markov chain. We will use the probabilities given in the original Markov chain to determine the probabilities of transitioning between states in our new Markov chain.

The new Markov chain will look like this:S0 → S1 (probability = 0.2)S0 → S2 (probability = 0.8)S1 → S2 (probability = 0.8)S1 → C (probability = 0.2)S2 → C (probability = 0.2)S2 → S1 (probability = 0.8)C → S0 (probability = 1).

The new Markov chain will indicate when the solar heat must be augmented by transitioning to the C state. When the Markov chain is in the C state, it means that the solar heating device needs to be augmented by some other heat source.

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Answer:The coordinates of point P in a parabola depend on the specific parabola being considered.

In general, a parabola is a symmetrical U-shaped curve and can be defined by an equation of the form y = ax^2 + bx + c, where a, b, and c are constants.

To find the coordinates of point P on the parabola, we need to know its x-coordinate (let's call it xP), and then we can substitute it into the equation to find the corresponding y-coordinate.

The x-coordinate of point P can be given explicitly, or it can be found by solving an equation involving the parabola and some external information (e.g., the coordinates of another point on the parabola or some geometric property of the parabola).

Step-by-step explanation:

Answer:

Calculation: First, converting R percent to r a decimal r = R/100 = 3.875%/100 = 0.03875 per year, then, solving our equation

Step-by-step explanation:

The money which should be deposited today in an account is found as $11,430.

Compound interest is calculated as follows:

CI = P[tex](1 + \frac{r}{12}) ^{12t}[/tex] - P,

where t is the time, P is the principle sum, and r is indeed the interest rate expressed as a decimal.

A =  P[tex](1 + \frac{r}{12}) ^{12t}[/tex]

Put the values:

12,000 = P[tex](1 + \frac{0.025}{12}) ^{12*2}[/tex]

P = 12,000 / 1.05

P = 11428.57

P = 11430 (approx)

Thus, money which should be deposited today in an account is found as $11,430.

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The correct question is -

How much money should be deposited today in an account that earns 2.5% compounded monthly so that it will accumulate to $12,000 in 2 years?

The value of 25 cm/s = 900 m/h using the dimensional analysis.

Examining the dimensions of the relevant physical variables is a key step in the study and solution of issues in science and engineering using dimensional analysis. Physical quantities have defined dimensions and are stated in terms of units like metres, kilogrammes, seconds, and degrees Celsius. Physical quantities also include length, mass, time, and temperature. Dimensional consistency in physical equations and connections is the fundamental tenet of dimensional analysis.

To convert 25 cm/s to m/h using dimensional analysis, we have:

1 m = 100 cm

1 h = 3600 s

25 cm/s x (1 m/100 cm) x (3600 s/1 h) = 900 m/h

Hence, the value of 25 cm/s = 900 m/h using the dimensional analysis.

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The graph that is an example of a cubic function is the one that approaches x = negative 2 in quadrant 3, increases to a point of inflection at (0, 1), and then increases again and approaches x = 2.

A polynomial function is a mathematical function that may be written as a sum of terms, where each term is made up of a variable raised to a non-negative integer power multiplied by a constant coefficient. The degree of the polynomial is the largest power of the variable in the function.

The graph that is an example of a cubic function is the one that approaches x = negative 2 in quadrant 3, increases to a point of inflection at (0, 1), and then increases again and approaches x = 2. This is because a cubic function is a polynomial function of degree three

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The expression in standard form for the volume V of the box is: [tex]V = 6n^3 + 5n^2 + 2n[/tex]

How do you measure the volume of a box?

You must take measurements of a box's length, breadth, and height in order to determine its size. To get the box's volume in cubic units, multiply all three measurements together.

The volume V of the box can be expressed as:

V = (depth) x (height) x (width)

Substituting the given values, we get:

V = n x (2n+1) x (3n+2)

Expanding the expression, we get:

V =[tex]6n^3 + 5n^2 + 2n[/tex]

Therefore, the expression in standard form for the volume V of the box is: [tex]V = 6n^3 + 5n^2 + 2n[/tex]

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Answer:

H: 1:4

Step-by-step explanation:

Number of blouses that she packed is option (a) 3

Let's start by figuring out how many different outfit combinations Dorian can create with the 4 skirts and 2 belts she packed.

Since Dorian can wear each skirt with any of the 2 belts, she has 4 x 2 = 8 different skirt and belt combinations.

For each of these combinations, she can choose one of the blouses she packed. So, if she has packed x blouses, she can create 8x different outfits.

We know that she can create 24 different outfits in total, so we can set up an equation:

8x = 24

Solving for x:

x = 3

Therefore, correct option is (a) 3

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Answer: A: 3 Blouses

Step-by-step explanation:

Area of a rhombus = ab/2 where a is 12cm and b is 10cm (diagonals)

Area = 12 x 10 /2 =120/2

Area = 60cm

Answer:

In this problem, we have a graph of the PDF (Probability Density Function). To compute probabilities in a certain interval (a, b), we must integrate this function from x = a to x = b.

(1) P(X ≤ 22)

We integrate the function from x = -∞ to x = 22, we get:

We separated the integral to use the data from the graph.

(2) P(X > 21)

We integrate the function from x = 21 to x = ∞, we get:

(3) The Q1 is the value x = a of the interval (-∞, a) that gives a probability equal to 0.25. So we must find x such that:

(4) The median is the value x = a of the interval (-∞, a) that gives a probability equal to 0.5. Proceeding as before, we have:

(5) The Q3 is the value x = a of the interval (-∞, a) that gives a probability equal to 0.75. Proceeding as before, we have:

(6) The IQR is given by the difference between Q3 and Q1. Using the results from above, we get:

Answer

• P(X ≤ 22) = 0.5

,

• P(X > 21) = 0.75

,

• Q1 = 21

,

• median = 22

,

• Q3 = 23

,

• IQR = 2

Step-by-step explanation:

Hope this helps

If James and Apple have AGI of $417,100, file jointly, and claim three dependent children, the total child and other dependent credit for James and Apple is $0.

To calculate the total child and other dependent credit for James and Apple, we need to use the information provided and the IRS guidelines.

The child and dependent care credit allows eligible taxpayers to reduce their tax liability based on qualifying expenses paid for the care of a qualifying individual. For three dependent children, the maximum credit allowed is $6,000.

However, the credit amount is reduced based on the taxpayer's AGI. The credit is reduced by 1% for each $2,000 (or fraction thereof) by which the taxpayer's AGI exceeds $125,000. The credit is reduced to a minimum of 20% of the qualifying expenses.

In this case, James and Apple's AGI of $417,100 exceeds $125,000 by $292,100, which is 146 times $2,000. Therefore, the credit is reduced by 146%, and the maximum credit of $6,000 is reduced to $0.

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Complete question is:

James and apple have a AGI of $417,100,file jointly and claim three dependent children ages 7, 10, and 19

calculate the total child and other dependent credit.

Answer: To determine if a constant rate can be used to describe the relationship between the number of hours and the gallons of paint used, we need to see if the sprayer uses paint at a consistent rate over time.

From the information given, we know that in 4 hours, the sprayer uses 42 gallons of paint. This means that the rate of paint usage is 42/4 = 10.5 gallons per hour.

If the sprayer uses paint at a constant rate, then we would expect it to use the same amount of paint for each hour of use. However, we don't have any information about how the sprayer uses paint beyond the first 4 hours, so we can't determine if the rate of paint usage is constant over time.

Therefore, we cannot definitively say whether a constant rate can be used to describe the relationship between the number of hours and the gallons of paint used. It is possible that the rate of paint usage changes over time, or that other factors (such as the surface area being painted or the type of paint being used) affect the amount of paint used.

Step-by-step explanation:

The level of private saving in the given closed economy is $4 trillion.

Given, Y = $14 trillion C = $8 trillion G = $3 trillion S pub = $1 trillion T = $5 trillion We have to find the level of private saving, spriv, in this economy.

In a closed economy: Y = C + I + G Here, I = investment in the economy Thus, Y = C + S + T When we add G to both sides of the equation we get, Y + G = C + S + T + G Now, from the given data we have, Y + G = $14 + $3 = $17 trillion C = $8 trillion T = $5 trillion

So, we have, Y + G = C + S + T + G Solving for S, we get; S = Y + G - C - TS = $17 trillion - $8 trillion - $5 trillion S = $4 trillion Therefore, the level of private saving in the given closed economy is $4 trillion.

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Answer:

[tex]p = 800 \frac{2}{5} ^{T}[/tex]
Step-by-step explanation:

Let's assume that the initial value of the phone is $800, and that its value decreases by 3/5 each year.

After one year, the phone will be worth 2/5 of its initial value:

$800 x (2/5) = $320

After two years, the phone will be worth 2/5 of its value after one year:

$320 x (2/5)^1 = $128

A factor is a number divided by another without leaving a remainder.

And, Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Factor:

A factor is a number divided by another without leaving a remainder. In other words, if multiplying two integers results in a product, the numbers we multiply are factors of the product because they are divisible by the product. There are two ways to find factors: multiplication and division. Additionally, separability rules can also be used.

According to the Question:

Factors of 24:

We can write 24 as a product of two numbers in multiple ways:

24 = 1 × 24;

24 = 2 × 12;

24 = 3 × 8;

24 = 4 × 6

Therefore, all the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

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The number of mangoes bought by Camila is 5 mangos.

We have given in the question,

Cost of each apple = $0.50

Cost of each mango = $0.75

Total amount Camila have = $7.75

Number of apples bought = 8

We have to find the number of mangoes bought by Camila

The calculation to find,

Assume;

The number of mangoes bought by Camila = a

So,

(0.50)(8) + (0.75)(a) = 7.75

4 + 0.75a = 7.75

0.75a = 3.75

a = 3.75 / 0.75

a = 5

Therefore, The number of mangoes bought by Camila is 5 mangos.

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Answer:

Step-by-step explanation:

To find the probability P(T < -1.05) where T follows a t-distribution with degrees of freedom (df) equal to 30, we can use a statistical software or a calculator that has a built-in t-distribution function.

Using Python and the scipy library, we can find the probability as follows:

from scipy.stats import t

df = 30

t_value = -1.05

p_value = t.cdf(t_value, df)

print(f"P(T < {t_value}) = {p_value:.4f}")

This gives the output:

css

P(T < -1.05) = 0.1518

Therefore, the probability P(T < -1.05) is approximately equal to 0.1518, rounded to four decimal places.

Im more of a coder and i understand this is probably not the anwser u where looking for so im sorry but i hope i helped a little :)

The value of the logarithm expression are

1. ln 35.2 = 3.561046

2. ln (2/3) ≈ -0.405465108

1. ln 35.2:

We can evaluate ln 35.2 using a calculator or by using the identity:

ln x = y if and only if e^y = x

So, we need to find e^y = 35.2, where y is the value we're looking for. Taking the natural logarithm of both sides, we get:

ln e^y = ln 35.2

y ln e = ln 35.2

y = ln 35.2

Therefore, ln 35.2 ≈ 3.561046 (using a calculator).

2. ln (2/3):

We can use the identity:

ln (a/b) = ln a - ln b

to rewrite ln (2/3) as:

ln 2 - ln 3

Therefore, ln (2/3) ≈ -0.405465108 (using a calculator).

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The mean of [tex]X_n[/tex] is 1 and the variance of [tex]X_n[/tex] is [tex](4/7)((7/4)^n - 1).[/tex] The mean and variance of X_n can be found by using the law of total expectation and the law of total variance.

By the law of total expectation, we have : [tex]E[X_n] = E[E[X_n|X_{n-1}]][/tex]
Since each individual in the population dies with probability 1/2 or doubles with probability 1/2:
[tex]E[X_n|X_{n-1}] = (1/2)X_{n-1} + (1/2)(2X_{n-1}) = X_{n-1}[/tex]
Plugging this back into the law of total expectation :
[tex]E[X_n] = E[X_{n-1}] = E[X_{n-2}] = ... = E[X_0] = 1[/tex]

Therefore, the mean of [tex]X_n[/tex] is 1.
Next, let's find the variance of [tex]X_n[/tex] . By the law of total variance, we have:
[tex]Var(X_n) = E[Var(X_n|X_{n-1})] + Var(E[X_n|X_{n-1}])[/tex]
Since each individual in the population dies with probability 1/2 or doubles with probability 1/2, we can write:
[tex]Var(X_n|X_{n-1}) = (1/2)(X_{n-1} - X_{n-1})^2 + (1/2)(2X_{n-1} - X_{n-1})^2 = (3/4)X_{n-1}^2[/tex]


[tex]E[X_n|X_{n-1}] = X_{n-1}[/tex]
Plugging these back into the law of total variance, we get:
[tex]Var(X_n) = E[(3/4)X_{n-1}^2] + Var(X_{n-1}) = (3/4)E[X_{n-1}^2] + Var(X_{n-1})[/tex]
Since [tex]E[X_n] = 1,[/tex] we have:
[tex]E[X_{n-1}^2] = Var(X_{n-1}) + E[X_{n-1}]^2 = Var(X_{n-1}) + 1[/tex]
Plugging this back into the equation for [tex]Var(X_n)[/tex], we get:

[tex]Var(X_n) = (3/4)(Var(X_{n-1}) + 1) + Var(X_{n-1}) = (7/4)Var(X_{n-1}) + (3/4)[/tex]
Using the fact that  [tex]Var(X_0) = 0[/tex], we can write:
[tex]Var(X_n) = (7/4)^nVar(X_0) + (3/4)(1 + (7/4) + ... + (7/4)^{n-1}) = (3/4)((7/4)^n - 1)/(7/4 - 1) = (4/7)((7/4)^n - 1)[/tex]

Therefore, the variance of [tex]X_n[/tex] is [tex](4/7)((7/4)^n - 1).[/tex]
In conclusion, the mean of [tex]X_n[/tex] is 1 and the variance of [tex]X_n is (4/7)((7/4)^n - 1).[/tex]

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The value of x is given as follows:

x = 10.

The geometric mean between 15 and 18 is given as follows:

16.43.

The two triangles for the problem are similar, meaning that the proportional relationship for the side lengths is given as follows:

x/20 = 6/12.

The relationship can be simplified as follows:

x/20 = 0.5.

Applying cross multiplication, the value of x is obtained as follows:

x = 20 x 0.5

x = 10.

The geometric mean between two amounts is given by the square root of the multiplication of these two amounts.

Hence, for the amounts 15 and 18, the geometric mean is given as follows:

sqrt(15 x 18) = 16.43.

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Answer:correct

Step-by-step explanation: