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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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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:

Answer:

See below.

Step-by-step explanation:

We are given the value of an angle, and the hypotenuse.

x will equal 7.0

Using Trigonometry Functions, we can identify x.

[tex]\textsf{Trigonometry Functions:}[/tex]

[tex]Sin = \frac{Opposite}{Hypotenuse}[/tex]

[tex]Cosine = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]Tan = \frac{Opposite}{Adjacent}[/tex]

[tex]\fbox{We should use Sin.}[/tex]

Let's begin by solving for x.

[tex]\textsf{\underline{We should use;}}[/tex]

[tex]{Sin(23^{\circ})}[/tex]

[tex]\textsf{\underline{Solve for x:}}[/tex]

[tex]Sin(23^{\circ})=\frac{x}{18}[/tex]

[tex]\textsf{\underline{Multiply by 18:}}[/tex]

[tex]18 \times Sin(23^{\circ})={x}[/tex]

[tex]x \approx 7.0[/tex]

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:

Step-by-step explanation:

In this problem, we have to use the formula in finding the volume of a cylinder

[tex]V=\pi r^{2} h[/tex]

r is half of diameter
r= 16ft / 2 = 8ft

The height of the cylinder is 4ft. We have to know the height of the water to know the volume of the water.

h (water) = 4ft - 1/2ft  = 3.5ft

[tex]V=\pi (8)^{2} (3.5)[/tex]

[tex]V = 703.72 ft^{3}[/tex]

[tex]V = 703.72 ft^{3} * \frac{7.48 gallons}{1ft^{3} }[/tex]

[tex]V = 5263.8 gallons[/tex]

[tex]V = 5264 gallons[/tex]

The pool is filled with 5264 gallons of water.

Answer:correct

Step-by-step explanation:

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:

f(4)=14

Step-by-step explanation:

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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Coach Jill put 4,000 mL of sports drink in each cooler to stay hydrated.

Coach Jill brought a total of 28,000 milliliters (mL) of sports drink to the soccer game. She divided the sports drink equally among 7 coolers, so she needed to determine how many milliliters each cooler would receive.

Coach Jill brought a total of 28 L = 28,000 mL of sports drink.

She divided this equally among 7 coolers, so each cooler would receive:

28,000 mL / 7 coolers = 4,000 mL/cooler

Therefore, Coach Jill put 4,000 mL of sports drink in each cooler.

This ensured that each cooler received the same amount of sports drink, which was important to keep all the players equally hydrated during the game. By dividing the sports drink equally, Coach Jill was able to efficiently manage the resources and ensure that each player had access to enough fluids during the game.

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It takes 0.55 secοnds fοr a ball traveling at 80 mph tο reach a batter that is pοsitiοned at the back οf the batter's bοx.

Speed is defined as the distance traveled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

Tο determine hοw lοng it takes fοr the ball tο reach the batter, we need tο use the fοrmula fοr time:

time = distance/speed

First, we need tο determine the distance frοm the pitcher's mοund tο the batter's bοx. Accοrding tο Majοr League Baseball rules, the distance frοm the pitcher's mοund tο hοme plate is 60 feet, 6 inches (18.44 meters). The batter's bοx is typically 4 feet (1.22 meters) behind hοme plate, sο the distance frοm the pitcher's mοund tο the back οf the batter's bοx is:

distance = 60 ft 6 in + 4 ft = 64 ft 6 in = 19.66 meters

Next, we cοnvert the speed οf the ball frοm miles per hοur (mph) tο meters per secοnd (m/s). One mile is equal tο 1,609.34 meters, and οne hοur is equal tο 3,600 secοnds, sο we can cοnvert mph tο m/s using the fοllοwing fοrmula:

speed in m/s = (speed in mph * 0.44704)

Therefοre, the speed οf the ball in m/s is:

speed = 80 mph * 0.44704 = 35.76 m/s

Nοw we can calculate the time it takes fοr the ball tο reach the batter:

time = distance/speed

time = 19.66 meters / 35.76 m/s

time = 0.55 secοnds

Therefοre, it takes apprοximately 0.55 secοnds fοr a ball traveling at 80 mph tο reach a batter that is pοsitiοned at the back οf the batter's bοx.

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Answer:  f(g(-1)) = -16

Step-by-step explanation:

First, we need to find g(−1), which means we substitute -1 in place of x in the function g(x):

g(-1) = 3(-1) = -3

Next, we substitute g(-1) into f(x):

f(g(-1)) = f(-3) = 3(-3) - 7 = -16

Therefore, f(g(-1)) = -16.

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 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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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:

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:

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 :)

Answer:

H: 1:4

Step-by-step explanation:

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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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.

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

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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The cost of a new Honda Accord in terms of the number of years t since 2000 can be represented by the function f(t).

The cost of a new Honda Accord in terms of the number of years t since 2000 is represented by the We can use this function to answer the questions given.

a. The cost (in dollars) of a new Accord in 2005 can be represented by f(5), since 2005 is 5 years after 2000.

b. The difference in cost between a new Accord in 2015 and 2010 can be represented by f(15) - f(10), since 2015 is 15 years after 2000 and 2010 is 10 years after 2000.

c. The ratio of the cost of a new Accord in 2015 to the cost of a new Accord in 2010 can be represented by f(15)/f(10).

d. $520 more than the cost of a new Accord in 2018 can be represented by f(18) + $520, since 2018 is 18 years after 2000.

In conclusion, the cost of a new Honda Accord in terms of the number of years t since 2000 can be represented by the function f(t), and we can use this function to answer the given questions.

The cost of a new Accord in 2005 is represented by f(5), the difference in cost between a new Accord in 2015 and 2010 is represented by f(15) - f(10), the ratio of the cost of a new Accord in 2015 to the cost of a new Accord in 2010 is represented by f(15)/f(10), and $520 more than the cost of a new Accord in 2018 is represented by f(18) + $520.

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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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Neither X nor Y can be well-approximated by a normal random variable, the proportion of exams with passing scores is .7734, the exam score for an exam whose z-score is 1.25 is 85 and if the top 4% of the exams will be given an A+, in order to be given an A+, an exam must earn at least 89 score.

Question 1: Neither X nor Y can be well-approximated by a normal random variable. This is because both X and Y are discrete random variables, meaning they can only take on integer values. Normal random variables, on the other hand, are continuous and can take on any value within a certain range.

Therefore, neither X nor Y can be well-approximated by a normal random variable.

Question 2: The proportion of exams with passing scores is .7734. This can be found by calculating the z-score for a score of 69 and using a z-table to find the corresponding proportion. The z-score is (69-75)/8 = -0.75. Using a z-table, we find that the proportion of exams with scores less than 69 is .2266.

Therefore, the proportion of exams with passing scores is 1-.2266 = .7734.

Question 3: The exam score for an exam whose z-score is 1.25 is 85. This can be found by using the formula for z-scores: z = (x-µ)/σ. Plugging in the values for z, µ, and σ, we get 1.25 = (x-75)/8.

Solving for x, we get x = 85.

Question 4: In order to be given an A+, an exam must earn at least a score of 89. This can be found by using the formula for z-scores and a z-table. We know that the top 4% of exams will be given an A+, so we need to find the z-score that corresponds to the top 4%. Using a z-table, we find that this z-score is 1.75.

Plugging this into the formula for z-scores, we get 1.75 = (x-75)/8. Solving for x, we get x = 89.

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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?

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:

[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