Answer: Average velocity = 11.1 m/s
Step-by-step explanation:
Given data,
A baseball is tossed up into the air at an initial velocity = 16 m/s.
The height of the baseball at time t in seconds is given by,
h(t) = 16t - 4.9t² (in meters).
So,
The average velocity is,
To calculate the velocity travelled by the ball, differentiate the function.
dh/dt = 16 - 2(4.9t)
dh/dt = 16 - 9.8t (eq-1)
Let us assume, t = [1,1.5]
Substitute t for 1 in the above Differential function
dh/dt = 16 - 9.8 (1)
But ,
dh/dt = velocity
So, dh/dt = V
V = 16 - 9.8
V = 6.2 m/s
Therefore,
Average velocity = ( U + V ) / 2
Average velocity = (16 + 6.2)/2
Average velocity = 22.2/2
Average velocity = 11.1 m/s
Hence, Average velocity = 11.1 m/s.
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14. Kristin is using paper for an art project that
is 0.025 mm thick. If she glues a layer of the
paper onto a construction board with a
thickness of 7 x 10-2 mm, what will the total
thickness of the paper and the construction
board be? Write your answer in scientific
notation.
The thickness of the paper and the construction board will be 9.5 x [tex]10^{-2}[/tex] mm.
What will the thickness be?The thickness of the paper is written in standard form while the thickness of the construction board is written in scientific notation.
Scientific notation is used to compress large numbers into smaller number. In order to write a digit that is less than zero in scientific notation, count the numbers after the decimal point to the first non-zero digit, the numbers counted would be the power of the notation. he power would have a negative number.
Thus, 0.025 becomes 2.5 x [tex]10^{-2}[/tex]
(2.5 x [tex]10^{-2}[/tex]) + (7 x [tex]10^{-2}[/tex]) = 9.5 x [tex]10^{-2}[/tex] mm
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The average American woman self-reports consuming 1.785×103 kcal/day. For a 147.0 lb woman, express this value in joules per second per kilogram of body mass (watts per kilogram).
Energy consumed equals 0.133 W/kg
What is energy?
Energy is described as the "capacity to accomplish work, which is the ability to apply a force that causes an object to move." Despite this perplexing terminology, the meaning is straightforward: energy is just the force that causes objects to move. Potential energy and kinetic energy are the two forms of energy.
Weight = 147 lb = 66.68 kg (since, 1 lb = 0.453 kg)
Energy consumed = 1.785 x 103 kcal/day
In Watts = 1.785 x 103 x 0.0484 = 8.9 W/day
Energy consumed watts per kilogram = 8.9/66.68 = 0.133 W/kg
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2.75 divided by (2.2)
Answer:
1.25
Step-by-step explanation:
=2.75/2.2
=1.25
it is answer .it think answer give some help
Shep Company’s records show the following information for the current year:
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Determine net income (loss) for each of the following separate situations. (For all requirements, losses should be entered with a minus sign.)
a. Additional common stock of $4,600 was issued, and dividends of $8,600 were paid during the current year.
b. Additional common stock of $15,400 was issued, and no dividends were paid during the current year.
c. No additional common stock was issued, and dividends of $13,600 were paid during the current year.
.
The determination of the net income for each of the following separate situations is as follows:
Situation A Situation B Situation C
Net income $21,800 $2,400 $31,400
How is the net income determined?The formula for determining the net income (loss) for the year is:
Net Income (loss) = Ending Equity - Beginning Equity - Additional stock + Dividend Paid).
Data and Calculations:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Situation A:
Common Stock issued = $4,600
Dividend paid = $8,600
Situation A:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 4,600
Dividend paid (8,600)
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$21,800 ($47,400 - $29,600 - 4,600 + 8,600)
Situation B:Common Stock issued = $15,400
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 15,400
Dividend paid
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$2,400 ($47,400 - $29,600 - 15,400)
Situation C:Dividends paid = $13,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued
Dividend paid $13,600
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$31,400 ($47,400 - $29,600 + 13,600)
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100 POINTS!!!!
An airplane travels at 145 km/hr for 2 hours in a direction of 220 degrees. At the end of this time, how far south of the airport is the airplane?
Note: Directions are given in degrees clockwise from north.
Answer:
53.83 km.
Step-by-step explanation:
53.83 km.
give the person above me brainliest
Find the cost of 12¼ m of cloth, if 1 m of cloth costs rupees 17⅓
The cost of 12¼ m of cloth is 212.3 rupees.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
We have been given that 1 m of cloth costs rupees 17⅓.
We have to determine the cost of 12¼ m of cloth.
Let the cost of 12¼ m of cloth would be x rupees
We can write this as a ratio as
1 m : rupees 17⅓ = 12¼ m : x rupees
[17⅓ = 52/3 = 17.3 and 12¼ = 49/4 = 12.25]
1 m : 17.3 rupees = 12.25 m : x rupees
⇒ 1 /17.3 = 12.25 /x
⇒ (1)(x) = (12.25 )×(17.3)
⇒ x = 212.3
Therefore, the cost of 12¼ m of cloth is 212.3 rupees.
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Write an expression that represents the area of the rectangle below.
2x 1
X-6
The expression that represents the area of the given rectangle is: 2x² - 11x - 6.
How to Find the Area of a Rectangle?The area of a rectangle is the product of its width and its length. A rectangle's area is calculated using the formula below:
Area = (length)(width)
Given the following:
Length of the rectangle = 2x + 1
Width of the rectangle = x - 6
Therefore, substituting these into the formula, we have:
Area of the rectangle = (2x + 1)(x - 6)
Area of the rectangle = 2x(x - 6) +1(x - 6)
Area of the rectangle = 2x² - 12x + x - 6
Combine like terms
Area of the rectangle = 2x² - 11x - 6
Therefore, the expression that represents the area of the given rectangle is: 2x² - 11x - 6.
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The first week of January, there are
49 dogs and 28 cats in an animal shelter.
Throughout the month, the ratio of dogs
to cats remains the same. The last week
of January, there are 20 cats in the
shelter. How many dogs are there?
Convert 3.5% to a decimal.
Question 2 options:
0.0035
0.35
0.035
3.5
Answer:
0.035
Step-by-step explanation:
hope this helps :)
Let X be the number of students who show up for a professor's office hour on a particular day, pmf of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15, what is the probability at least 2 students show up? I tried doing P(p(1) u p(2)) = P(p(1)) + P(p(2)) - (P(p(1) n p(2))) what would be the correct formula?
The probability of at least 2 students showing up is .70 or 70%
Let X be the number of students who show up for a professor's office hour on a particular day, probability of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15
If we add the probability of 1 student showing up, 2 students to show up, 3 students to show up, and 4 students showing up
We get 0.10+ 0.20+ 0.25+ 0.15 =1
As the sum of these individual 4 possibilities is 1 that means these are the only possibilities to exit
Now we need to find out the probability of at least 2 students showing up which means the probability of two or more students showing up
Which can be written as
p(≥2) = p(2) + p(3) + p(4)
p(≥ 2) = 0.25+0.30+0.15
p(≥2) = 0.70
Hence, the probability of at least 2 students showing up is .70 or 70%
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Consider the statements in the table shown. Select True or False for
each statement about the sequences of transformations that can
verify that triangle ABC is congruent to triangle A'B'C'.
The sequences of transformations can verify that triangle ABC is congruent to triangle A'B'C'. which is the correct answer would be (D)
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
Triangle ABC has translated 12 units to the right, followed by a reflection across the x-axis. Which is a true statement
Triangle ABC is reflected across the y-axis, followed by a translation 12 units down. Which is a false statement
Triangle ABC is reflected across the x-axis, followed by a translation of 12 units to the right. Which is a true statement
Therefore, the sequences of transformations can verify that triangle ABC is congruent to triangle A'B'C'.
Hence, the correct answer would be (D)
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The rectangular floor of a classroom is 30 feet in length and 21 feet in width. A scale drawing of the floor has a length of 10 inches. What is the area, in square inches, of the floor in the scale drawing? this is for a lot of points and please answer correctly or i will be reporting.
The width of the drawing maintaining the given scale factor will be 70.83 inches².
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio between two dimensions that determines how big or tiny a given figure is.
The length of the floor in actuality = 30 feet
⇒ 30 × 12 = 360 inches
Length of the floor in drawing = 10 inches
Scale factor = 10/360 = 1/36
By maintaining this scale factor
Width of the floor in drawing = (21 × 12)/36
⇒ 7.083 inches
Area = length × width
Area = 10 × 7.083
⇒ 70.83 inches²
Hence "The width of the drawing maintaining the given scale factor will be 70.83 inches²".
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Assume the cards are drawn sequentially and without replacement. In how many ways can 5 spades be drawn from a standard deck of 52 cards?
The number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement = 154440
In this question we have been given a standard deck of 52 cards.
We need to find the number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement.
We use the permutation formula.
We know that the number of ways to choose r elements from a set of n distinct objects where order does matter and replacements are not allowed.
^n(P_r) = n! / (n - r)!
We know that, in a standard deck of 52 cards, there are 13 spade cards.
So, n = 13
5 spades to be drawn
So, r = 5
Using the formula of permutation,
^13(P_5)
= 13! / (13 - 5)!
= 154440
Therefore, the number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement = 154440
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How are translations along the vectors ⟨a,b⟩ and ⟨-a,-b⟩ similar and how are they different ?
The similarity of two vectors ⟨a,b⟩, and ⟨-a,-b⟩ is that they can both be placed on the same graph; the difference is that they belong to different quadrants.
What are vectors?A vector is a two-dimensional object with a magnitude and a direction. A vector can be visualized geometrically as a directed line segment with an arrow indicating the direction and a length equal to the magnitude of the vector. The vector's direction is from its tail to its head.So, the similarity between two vectors ⟨a,b⟩, and ⟨-a,-b⟩ is that they can be placed on the same graph and the difference between the two is that they belong to different quadrants.
⟨a,b⟩ belongs to the 1st quadrant, and ⟨-a,-b⟩ belongs to the 3rd quadrant.Therefore, the similarity of two vectors ⟨a,b⟩, and ⟨-a,-b⟩ is that they can both be placed on the same graph; the difference is that they belong to different quadrants.
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There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=0.33c+38T=0.33c+38, where TT represents the temperature in degrees Fahrenheit and cc represents the number of times the cricket chirps in one minute. What could the number 38 represent in the equation?
The temperature at which the crickets do not chirp is represented by the number 38, which serves as the y-intercept of the linear equation.
The equation is as follows:
T = 38 + 0.3*c
The temperature is denoted by T, while the number of chirps in a minute is denoted by c.
We want to know what the number 38 means.
Take c = 0 to demonstrate this as there are no chirps.
Then:
T = 38 + 0.33*0 = 38
T = 38
This is the temperature where crickets cease to chirp.
The temperature at which the crickets do not chirp is represented by the number 38, which is the y-intercept of the linear equation.
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The given signs denote the following operations/relationships:
A+B means A is greater than B.
A-B means A is less than B.
A-B means A is greater than or equal to B.
A*B means A is not equal to B.
A/B means A is equal to B.
Which of the two conclusions I and II is/are definitely true based on the information
provided?
Statements:
E*F, F/G, G-H
Conclusions:
1. E*G
II. F-H
Based on the given information, the EFG GH Findings.
Refer to the symbols and their associated meanings below.
The symbols shown signify the following.
operations/relationships:
A+B denotes that A is bigger than B.
A-B indicates that A is less than B.
A is more than or equal to 8 when A=B.
A B denotes that A and B are not equal.
A = B is expressed as A/B.
Which of the two conclusions is unquestionably true?based on the details offered?
Statements: EFG GH Findings
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An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.
Because food grows more quickly in the hills when exposed to heat and rain rather than sunlight all day. Then for 1 sheep 1 bushel is required in the hills.
What are statistics?
The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.
Given that a remote agricultural nation is divided into two distinct geographic areas: a lowland plain and an upland of rough hills. A farmer can grow 10 bushels of grain or pasture 10 sheep on one unit of land on the plain. A farmer in the hills can pasture 4 sheep or grow 2 bushels of grain on one unit of land.
As opposed to being exposed to sunlight all day, food develops more quickly in the hills when it is exposed to heat and rain.
For uphill = 10 sheep = 10 bushels
For uphill = 1 sheep = 1 bushels
For down plain = 4 sheep = 2 bushels
For down plain = 1 sheep = (1 / 2 ) bushels
Therefore, then for 1 sheep 1 bushel is required in the hills.
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Sam and Bethan share £54 in the ratio 5:4 how much does each person get
Answer:add 5 and 4, you get 9. divide 54 by 9, and you get 6. this is because for every 5 sam gets bethan will get 4. if you add, that, you will get the total amount for 1 share.
Step-by-step explanation:
Answer:
Sam gets £30
Bethan gets £24
Step-by-step explanation:
Since they split the money in a ratio of 5:4, that means for every 5 parts of the money that Sam gets, Bethan gets 4 parts. The total of 5 parts and 4 parts is 9 parts.
To find how much each part is, we divide £54 by 9.
£54/9 = £6
Each part is £6.
Sam gets 5 parts: 5 × £6 = £30
Bethan gets 4 parts: 4 × £6 = £24
help please i need help
Answer:
100
Step-by-step explanation:
first let's convert 240 mins to hours
240/60 = 4
now let's find approximately how many pages per hour
200/4 = 50
so, in one hour she approximately read 50 pages
let's say she reads 25 pages per hour
25(4)= 100
A bag contains 10 red, 5 yellow, and 6 blue marbles. What is the probability of pulling out one blue marble and then one red marble without replacing the first blue marble?
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
How to determine the probability?The given parameters are
Red = 10
Yellow = 5
Blue = 6
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is
P = P(Blue) * P(Red Having selected Blue)
So, we have
P = 6/21 * 10/20
Evaluate
P = 1/7
Hence, the probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
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PLEASE HELP<33333
(A): describe in words a sequence of transformation that maps ABC to A”B”C (hint, there are two different transformations.
(B): Write an ordered pair rule for each transformation in the sequences.
one negative two and then shifted to the rights, that's the translation to the right two units.
What is the sequence of transformation?
A certain order of transformational occurrences is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.its a 180 Degree Rotation.
And let's see With a 180 degree rotation.
, we can say coordinates is that X. Y. Two negative X. Negative Y.
It goes to one negative two and he goes to two negative five And c goes to 5 -2.
So if one negative two and then shifted to the rights, that's the translation to the right two units.
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The probability density of a random variable X is given in the figure below. The random variable is uniformly distributed between 0 and 2. From this density, find the probability that X is at least 0.48.
The probability that X is at least 0.48 given the information about the density of a random variable X is 0.76.
How to calculate the probability?Given that x is uniformly distributed between 0 and 2.
Therefore, the probability density function:
f(x)= 1 / (b-a) = 1 / (2-0)
= 0.5
This will be illustrated as:
P(X<=x)=(x-a)/(b-a)=(x-0)/(2-0)=x/2
Now, we have to find:
P(x >= 0.48)
= 1 - P(x<=1.68)
= 1-(0.48 / 2)
= 1 -0.24
= 0.76
Therefore, the probability that X is at least 0.48 given the information about the density of a random variable X is 0.76.
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The marching band needs to create rows for its performance. There are 48 instruments and 32 flag bearers. Only one type of performer can be in each row. What is the maximum number of performers in each row so that all the rows are equal in length?
48
32
16
2
The maximum number of performers in each row so that all the rows are equal in length is C. 16.
How to calculate the value?It should be noted that there are 48 instruments and 32 flag bearers and only one type of performer can be in each row.
The maximum number of performers in each row so that all the rows are equal in length will be the highest common factor between both numbers.
It should be noted that the highest common factor between 32 and 48 is 16
Therefore the correct option is C.
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given then functions: f(x)=4x+9 and g(x)=7x-5
Part 1
[tex](f+g)(x)=f(x)+g(x) \\ \\ =4x+9+7x-5 \\ \\ =11x+4[/tex]
Part 2
[tex](f-g)(x)=f(x)-g(x) \\ \\ =(4x+9)-(7x-5) \\ \\ =4x+9-7x+5 \\ \\ =-3x+14[/tex]
Part 3
[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =(4x+9)(7x-5) \\ \\ =28x^2-20x+63x-45 \\ \\ =28x^2+43x-45[/tex]
Part 4
[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ =\frac{4x+9}{7x-5}[/tex]
10. Write an algebraic expression that represents the perimeter of the figure shown below.
Simplify completely. Show your work.
3x
X
8x
4x
10x
2x
The perimeter of the given figure is 56x.
What do we mean by perimeter?A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.So, perimeter: sum of all the sides
Then, according to the given figure:
Algebraic expression: 3x + x + 8x + 4x + 10x + 2x + (10x + 8x + 3x) + (x + 4x + 2x)28x + (10x + 8x + 3x) + (x + 4x + 2x)28x + 21x + 7x49x + 7x56xTherefore, the perimeter of the given figure is 56x.
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A student wants to find out if LMC students prefer eating out or eating in
the cafeteria. She talks to 25 of her friends in the Transfer Academy and
finds that they prefer eating in the cafeteria. She then concludes that LMC
students prefer eating in the cafeteria.
What is the intended population?
What is the actual population?
What is the sample?
The intended population based on the information given is LMC students.
The actual population based on the information illustrated is Transfer Academy.
The sample is the 25 friends that the student talked to.
How to illustrate the information?Using the data, the student decides to interview 25 of her acquaintances from the Transfer Academy to learn whether LMC students prefer eating in or eating outside of the cafeteria.
According to the data shown, Transfer Academy is the actual population in this circumstance. It is important to remember that the sample represents the population.
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Edwin needs to buy a car, a truck, and a motorcycle for his shipping business. He wants the car to be red or yellow; the truck to be black, white, or silver; and the motorcycle to be green, blue, or orange. Help pls
Answer:
The answer is that there are 18 different combinations of vehicles.
Step-by-step explanation:
We are given that the number of vehicles for his business = 3.
The vehicles are a car, truck, and motorcycle.
So we know that there is two possibilities for car: Red and yellow.
Three possibilities for truck: Black, white, and silver.
Three possibilities for motorcycle: Green, blue and orange.
So now we can make an equation of the different combinations of vehicles that Edwin have to chose from.
So 3 x 3 x 2 = 18
Therefore, there are 18 different combinations of vehicles.
I hope this helps, have a good day!! :D
Which of the following values is greater than −2.5?
Answer:
-2,-1.5,-1,-0.5 etc
Step-by-step explanation:
The smaller the negative value the greater the value compared to other negative value carrying a negative sign.
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?
A up to seven digits long
B up to six digits long
C any finite length
D infinitely long
Answer: a
Step-by-step explanation:
Every six powers of ten, the cycle repeats. In other words, a repeating decimal with a denominator of 7 can have a repeating cycle that is up to six digits long.
The repeating cycle of a repeating decimal for the rational number with a denominator of 7 can be determined by considering the factors of the denominator.
In this case, the denominator is 7, which is a prime number. The length of the repeating cycle can be determined by examining the powers of 10 modulo 7.
To find the length of the repeating cycle, we need to find the smallest positive integer "n" for which 10ⁿ - 1 is divisible by 7. In other words, we are looking for the smallest "n" such that 10ⁿ ≡ 1 (mod 7).
Let's calculate the powers of 10 modulo 7:
10¹ ≡ 3 (mod 7)
10² ≡ 2 (mod 7)
10³ ≡ 6 (mod 7)
10⁴ ≡ 4 (mod 7)
10⁵ ≡ 5 (mod 7)
10⁶ ≡ 1 (mod 7)
As you can see, the cycle repeats every 6 powers of 10. This means that the repeating cycle of a repeating decimal with a denominator of 7 can be up to six digits long.
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how are decimal .009 and .09 related
Answer-
-They are related because they are numbers that are less than 1 that can be converted into a fraction.
-They also both contain the number nine.
-They are not repeating decimals.
-They are positive numbers.
Those are just a few examples of how they are related. I hope this helps, good luck!
