After 2 minutes of leaving home, Abby meet Betty.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Abby's distance from home is given with the function :
S{t} = 100t² + 400t, where {t} is time in minutes.
The given function is -
S{t} = 100t² + 400t
dS{t}/dt = 0
200t = 400
t = 2
Therefore, after 2 minutes of leaving home, Abby meet Betty.
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you throw a small rock straight up with initial speed v0 from the edge of the roof of a building that is a distance h above the ground. the rock travels upward to a maximum height in time tmax, misses the edge of the roof on its way down, and reaches the ground in time ttotal after it was thrown. neglect air resistance. if the total time the rock is in the air is three times the time it takes it to reach its maximum height, so ttotal
The initial velocity is related to the maximum height by the relation [tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex]
The initial velocity (v0) is the velocity of an object at the beginning of its motion. In the scenario you described, the initial velocity of the rock is the velocity at which it is thrown upward from the edge of the roof of a building.
Without any information about the velocity at which the rock is thrown, it is not possible to determine the initial velocity.
Using the fact that the velocity at maximum height is zero, we can write the following:
[tex]v_{y}=v_{y_{0,t} }+ a_{y}t[/tex]
at maximum height, the equation becomes
[tex]0=v_{0}-gT_{max}[/tex]
=> [tex]T_{max}=\frac{v_{0} }{g}[/tex]
Now, the displacement is (-H)−H) when the rock hits the ground, so we can use one of the kinematic equations to write the following
[tex]y-y_{0}=v_{0}t+\frac{1}{2}a_{y}t^{2}[/tex]
where [tex]y_{0} =0 and y=-H[/tex]
On substituting the values and rearranging we get:
[tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex]
Therefore, The initial velocity is related to the maximum height by the relation [tex]v_{0}=\sqrt{\frac{2gH}{3} }[/tex].
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Stuart Wilkinson, the engineer of "Chew-Chew" said, "we stole the idea of eating food
from the biological world, but we are marrying that idea to useful robotic capabilities."
Which of the following would not be an application of Stuart Wilkinson's theory?
A. a trash compactor that feeds on garbage
B. a garden cultivator that feeds on soil
C. a lawn mower that feeds on grass clippings
D. a leaf mulcher that feeds on foliage
E. a recycling truck that feeds on petroleum
A recycling truck that feeds on petroleum is would not be an application of Stuart Wilkinson's theory.
What is about Stuart Wilkinson's theory?A recycling truck that runs on petroleum is designated as option E and would not be a practical application of Stuart Wilkinson's thesis in terms of merging the concept of beneficial robotic capabilities in terms of consuming food.This is referred to as a machine that can automatically mimic some human movements and functions with the help of an external control system.A recycling truck that feeds on petroleum is inaccurate since petroleum isn't a form of food because Stuart Wilkinson's thesis aims to combine the concept of beneficial robotic capabilities in terms of consuming food.To learn more about Stuart Wilkinson's theory refer to:
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Randomly selecting 20 cards out of 52 card deck, the probability of each outcome will be basically the same whether it is done with or without replacement 1
TRUE OR FALSE?
Answer:
False
Step-by-step explanation:
If the card is removed after it is picked, the number of cards in the deck decreases. For example, if you pick the first card remove it. The cards available decreases to 51, so the probability becomes 1/51 for the next draw. This is dependant probability.
Which value for x would make the ratios equivalent?
3/8 =x/32
A x=4
B x=6
C x=8
D x=12
Answer:
D. x = 12
Step-by-step explanation:
8 x 4 = 32
3 x 4 = 12
let z be a b digit positive integer such as 247247 whose first three digits are the same as its last 3 digits taken in the same order. which of the following numbers must be a factor of z
The number which must be a factor of 247247 is 11.
Given integer = 247247
To find the factor, we can add and minus signs alternately in front of each digit to determine whether a number is divisible by any of the given options. and then compute the answer. For example: If the integer is divisible by 11 if this result is divisible by 11 (including 0), if not, the number is not divisible by 11.
As per the question, and given integer -
+2 - 4 + 7 -2 + 4 - 7
= 0
Since the outcome is 0, the number 247247 can be divided by 11.
Complete Question:
Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of Z$
a) 11
b) 19
c) 101
d) 111
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helpp pls! find the value of each variable in the parallelogram.
The value of each variable in the parallelogram is h = 9 and g = 59.
What is a parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has neighboring angles that add up to 180 degrees. Angles on either side are equal.
We know that the opposite sides of a parallelogram and the opposite angles of a parallelogram are equal.
Using the above statement, we can write:
16 - h = 7
16 - 7 = h
h = 9
g + 4 = 63
g = 63 - 4
g = 59
Hence, the value of each variable in the parallelogram is h = 9 and g = 59.
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Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Answer:
3 3
Step-by-step explanation:
graph of a line passing through the points 0 comma 3 and 3 comma 1
Need help with this
Answer:
f(6) = -22
g(-2) = -10
Step-by-step explanation:
Plug in 6 into f(x) = -4x + 2
f(6) = -4(6) + 2
f(6) = -24 + 2
f(6) = -22
Plug in -2 into g(x) = 2x^3 + 6
g(-2) = 2(-2)^3 + 6
g(-2) = 2(-8) + 6
g(-2) = -16 + 6
g(-2) = -10
I hope this was able to help you :D
the 10% condition when constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size.
The 10% condition when constructing a confidence interval for a population proportion states that the sample size should be less than 10% of the population size.
This is expressed mathematically as follows:
n/N < 0.10
Where n is the sample size and N is the population size. For example, if the population size is 500, then we must ensure that the sample size is less than 50 (500 x 0.10 = 50). This is because if the sample size is larger than 10% of the population size, then the confidence interval will not be reliable. In other words, the results of the confidence interval may be inaccurate and biased.
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Elena has $10.00 to spend. Which list of items shows what Elena could buy?
The list of items that shows what Elena could buy is the list for which the sum of all prices is at most 10.
How to obtain the list of items?The maximum amount that Elena can spend is given as follows:
$10.
Hence, for each list, the sum is calculated for the prices of all the items, giving the total price.
The list with a sum of at most $10 is the list that shows what Elena can buy.
Missing InformationThe problem is incomplete, hence the general procedure needed to solve it is presented.
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in which row of pascal's triangle do three consecutive entries occur that are in the ratio 3 : 4 : 5
The row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5 is the 62nd row.
To find the row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5, we will use the concept of binomial coefficients.
The binomial coefficient C(n, k) represents the number of ways to choose k items from a set of n items, and is given by the formula -
C(n, k) = n! / (k! (n-k)!).
In Pascal's triangle, the entries are arranged such that the nth row contains n+1 entries, and the kth entry in that row is given by C(n, k).
We can determine the ratio of three consecutive entries in Pascal's triangle by looking at the binomial coefficients C(n, k), C(n, k+1), and C(n, k+2) in a particular row.
In order to find the row where the ratio of these three consecutive entries is 3:4:5, we will set up the following equation:
C(n, k) / C(n, k+1) = 3/4 and C(n, k+1) / C(n, k+2) = 4/5
We will now use the formula for binomial coefficients to simplify these equations as follows -
(n! / (k! (n-k)!) ) / (n! / ((k+1)! (n-(k+1))!)) = 3/4
Similarly,
(n! / ((k+1)! (n-(k+1))!)) / (n! / ((k+2)! (n-(k+2))!)) = 4/5
Solving for n, we can get n = 62
Therefore, the row in Pascal's triangle where three consecutive entries are in the ratio 3:4:5 is the 62nd row.
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which of the following represents z = -6\sqrt(3) + 6i in trigonometric form? a. z = 12(cos 150 + i sin 150) b. z = 12(cos 210 + i sin 210) c. z = 6(cos 150 + i sin 150) d. z = 6(cos 210 + i sin 210)
The trigonometric form of complex number -6√3 + 6i will be option a. 12(cos150 + isin150)
We are given z = -6√3 + 6i
Now the polar form of a complex number is given by r(cosx + isiny)
We first need the modulus which for a complex number a + bi
r = √(a² + b²)
Hence r = √(108+36)
= √(144)
= 12
Now we need to find the angle x such that
tan x' = |b/a|
or, tan x' = |-1/√3|
or, tan x' = 1/√3
or, tan x' = tan(π/6)
or, x' = π/6
Now since a < 0 and b > 0 x will lie in Quadrant 2
Hence x = π - π/6
= 5π/6 =
Hence we get the trigonometric form to be
12(cos5π/6 + isin5π/6)
= 12(cos150 + isin150)
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A waffle recipie uses 6 eggs to make 16 waffles. Jenny has 9 eggs. If she alters the recipe, what is the greatest amount of waffles she can make?
Answer:
24 waffles
Step-by-step explanation:
16÷6=2.66 so she can make that many waffles per egg
9x2.66= 23.94 which would round up to 24 waffles
1) M.H Find the perimeter of 4.1am
Answer:
Step-by-step explanation:
If the water irrigation tank holds 275 gallons, how many minutes before Angel can turn off the tap?
The answer to this question is determined on the volume of water coming from the faucet. When the tap is switched on but no water flows out, the tank can retain 275 gallons eternally. Yet, if water flows out of the tap at a constant pace, the tank will take a given period of time to empty.
What is a gallon?A gallon is a volume unit used mostly in the United States, equivalent to 128 US fluid ounces or 3.785 liters.
To establish how long it will take to empty the tank, we must first know the flow rate of the tap, which is normally measured in gallons per minute (GPM). We may use the following calculation to calculate the time it will take to empty the tank once we have known the GPM:
Time (minutes) = 275 gallons per minute / GPM
For example, if the tap is running at a rate of 10 GPM, the time required to empty the tank is:
Time (minutes) = 275 gallons /10 GPM = 27.5 minutes
As a result, if the tap is set at 10 GPM, it will take 27.5 minutes for the tank to empty before Angel can turn off the water.
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Choose the equation for the graph.
a) y = 2|x - 3| +1
b) y = -2|x - 3| +1
c) y = 2x - 3| − 1
d) y = -2|x + 3| − 1
e) y = 2|x + 3| +1
Answer:
not e
Step-by-step explanation:
a charge nurse is reviewing orthostatic hypotension with a group of newly licensed nurses. what make the statements should the charge nurse make?'
A charge nurse is reviewing orthostatic hypotension with a group of newly licensed nurses. the statements should the charge nurse make is c) a decrease of 20 mm of Hg in the diastolic pressure with a position change indicates orthostatic hypotension.
About Orthostatic hypotensionOrthostatic hypotension — also called postural hypotension — is a form of low blood pressure that happens when standing after sitting or lying down. Orthostatic hypotension can cause dizziness or lightheadedness and possibly fainting.
Orthostatic hypotension can be mild. Episodes might be brief. However, long-lasting orthostatic hypotension can signal more-serious problems. It's important to see a health care provider if you frequently feel lightheaded when standing up.
Occasional orthostatic hypotension is usually caused by something obvious, such as dehydration or lengthy bed rest. The condition is easily treated. Chronic orthostatic hypotension is usually a sign of another health problem, so treatment depends on the cause.
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two socks are drawn from a drawer which contains one red sock, three blue socks, two black socks, and two green socks. once a sock it is not replaced. determine the probability.
1. p(a black sock and then a green sock)
2. p(two blue socks)
3. p(a green sock and then a red sock)
4.p(two green socks)
Answer:
p(a black sock and then a green sock)
The probability of drawing a black sock first is 2/8=1/4, and then the probability of drawing a green sock next is 2/7=2/14 since we have one less sock left. So the overall probability is (1/4) * (2/14) = 1/7
p(two blue socks)
The probability of drawing a blue sock first is 3/8, and then the probability of drawing another blue sock next is 2/7 since we have one less sock left. So the overall probability is (3/8) * (2/7) = 6/56 = 3/28
p(a green sock and then a red sock)
The probability of drawing a green sock first is 2/8, and then the probability of drawing a red sock next is 1/7 since we have one less sock left. So the overall probability is (2/8) * (1/7) = 2/56 = 1/28
4.p(two green socks)
The probability of drawing a green sock first is 2/8, and then the probability of drawing another green sock next is 1/7 since we have one less sock left. So the overall probability is (2/8) * (1/7) = 2/56 = 1/28
Note that these are the theoretical probabilities, and in reality, drawing a sock and not replacing it will change the number of socks left, so the probability of the next draw will change accordingly.
Step-by-step explanation:
last year small manufacturing company netted $540,000 the net profit increased this year by 135% what is the net profit of the company this year
The net profit of the company this year is $729,000
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
Last year small manufacturing company netted $540,000
The net profit increased this year by 135%
Now, to find 135% of $540,000
Let the profit this year be x
x*100/$540,000=135
x=135*5400
x=729000
Therefore, net profit by 135% will be $729,000
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Someone Help me Please.
1) The table below shows a future estimated population and the number of hospitals in
2009 in the United States and the three states - Texas, California, and Florida. Use
the data to answer each question.
Estimated Future Population and Number of Hospitals by State (2009)
Number of
hospitals in
2009
5,008
428
343
210
United States
Texas
California
Florida
Projected
Population
316 million
26.4 million
38.3 million
19.5 million
Patients Admitted in
2009 (in Thousands)
35,527
2,621
3,433
2,453
Assume Florida has the same number of hospitals per million people as Texas.
Estimate the number of hospitals in Florida. Is this estimate close to the actual
number of hospitals in Florida in 2009?
If Florida had the same number of hospitals per million people as Texas, it would have 558 hospitals in 2009. This is slightly higher than the actual number of hospitals in Florida in 2009 (343).
What is proportional reasoning?Proportional reasoning is a mathematical process used to compare the ratios of two or more similar quantities.
This question uses the theory of proportional reasoning.
In this case, we are comparing the ratio of the number of hospitals per million people in Texas to the ratio of the number of hospitals per million people in Florida.
By comparing these two ratios, we can estimate the number of hospitals in Florida given the same ratio as Texas.
1. Calculate the number of hospitals per million people in Texas: 428 hospitals / 26.4 million people = 16.2 hospitals per million people.
2. Calculate the number of hospitals per million people in Florida: 343 hospitals / 19.5 million people = 17.6 hospitals per million people.
3. Multiply the number of people in Florida (19.5 million) by the number of hospitals per million people in Texas (16.2): 19.5 million people x 16.2 hospitals per million people = 315.3 hospitals.
4. Round the result to the nearest whole number: 315.3 hospitals = 315 hospitals.
5. Compare the estimated number of hospitals in Florida (315) to the actual number of hospitals in Florida in 2009 (343).
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Rewrite the following multiplication problem using the associative property and then show that both results will be the same.
3/7 x 5/6 x1/4
The answer is the same i. e., 4.375 in all the cases as shown
What is multiplication problem ?There are two terms which describe the three numbers in a multiplication problem. The factors are the numbers that are being multiplied together. The product is the result or answer of multiplying the multiplicand by the multiplier.
= 3/7 x 5/6 x1/4
= 38/8
= 3/7 x 1/4 x 5/6
= 5/6 x 1/4 x3/7
= 5/6 x 3/7 x 1/4
= 1/4 x 5/6 x 3/7
=1/4 x 3/7 x 56
= 4.375
The answer is the same i. e., 4.375 in all the cases as shown.
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can someone please answer this question
Sarah and Winston buy the same brand of T-shirts from different stores. Sarah pays $8 and Winston pays $4.The simplest way of writing this as a ratio 2:1.
What is Ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The relationship between the amounts of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
We are given;
Sarah pays $8 for t shirt
Winston Pays $4 for t shirt
So, Simplest way of writing this as in ratio is ;
Sarah/Winston = 8/4=2/1
Hence , this is written in ratio as 2:1.
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or
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
A boutique in Belmont specializes in leather goods for men. Last month, the company sold 20 wallets and 14 belts, for a total of $2,202. This month, they sold 20 wallets and 83 belts, for a total of $5,859. How much does the boutique charge for each item?
the boutique charges $
for a wallet, and $
for a belt.
The cost of one belt is $53 and the cost of one wallet is $ 73.
What is the cost of each item?The first step is to set up a system of equation using the information in the question:
20w + 14b = 2202 equation 1
20w + 83b = 5859 equation 2
Where:
b= number of belts sold
w = number of wallets sold
In order to determine the value of b, take the following steps:
Subtract equation 2 from equation 1 :
69b = 3657
Divide both sides of the equation by 69
b = 3657 / 69
b = 53
Substitute for b in equation 1:
20w + 14(53) = 2202
20w + 742 = 2202
20w = 2202 - 742
20w = 1460
w = 1460 / 20
w = 73
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a cylindrical sample of saturated sandy clay has a diameter of 2.8 inches and a height of 6 inches. the total mass of the sample alone is 1,192.0 g. representative portions of the sample have been used to determine the water content w (%). the mass of these portions was 182 g before oven-drying and 151.7 g after oven-drying.
The water content of the cylindrical sample of saturated sandy clay is 2.54%.
To determine the water content of the sample, we have to calculate the mass of water present in the sample before oven-drying, next divide that value by the total mass of the sample.
Firstly, we have to calculate the mass of water present in the sample before oven-drying. We already know that the mass of the sample before oven-drying is 182g and the mass after oven-drying is 151.7g.
So the mass of water present in the sample is:
mass of water = mass before oven-drying - mass after oven-drying
mass of water = 182g - 151.7g = 30.3g
Next, divide the mass of water by the total mass of the sample and multiply by 100 to get the water content as a percentage:
water content (w%) = (mass of water / total mass of sample) * 100
water content (w%) = (30.3g / 1192.0g) * 100 = 2.54%
So, the water content of the cylindrical sample of saturated sandy clay is 2.54%.
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QUIZ:
Composite Figures
What is the best approximation for the area of this figure?
The best approximation for the area of this figure is A = 12+9.125π units²in the given figure.
What is the diameter of triangle?
In a triangle, the diameter is a line segment that passes through the midpoint of one side of the triangle and is perpendicular to that side. It is also the longest chord of the triangle. The length of the diameter is called the diameter of the triangle.
Draw the diameter from point (-1, -5) to point (2, 3).
The triangle has base 3 and height 8.
The diameter of the semicircle is the hypotenuse of the triangle.
d = root(3² + 8²)
d = 8.544
The radius is half the diameter.
r = d/2 = 8.544/2 = 4.272
The total area is the area of the triangle plus the area of the semicircle.
A = 3*8/2 + π*4.272²/2
A = 12+9.125pi units²
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In the expression n +23, 23 is a
Hey there!
Answer:
In the expression, 23 is the constant.
Hope this helps!
A rectangle is divided into equal parts. Which statement is true? The lines dividing the shape must be drawn from left to right. All the equal parts must be square in shape. The lines dividing the shape must be drawn from top to bottom. All the equal parts must have the same area.
Answer:
The statement that is true is:
All the equal parts must have the same area.
This is true because when a rectangle is divided into equal parts, it means that the area of each part is the same. The lines dividing the shape can be drawn in any direction (top to bottom, left to right, diagonal, etc.) and the shape of the parts can also be different( rectangles, squares or any shape).
What are the last three digits of 5’201?
Answer: The last three digits are 201.
Step-by-step explanation: Hope this helps
p1 - connecting computing a certain computer game is played between a human player and a computer-controlled player. every time the computer-controlled player has a turn, the game runs slowly because the computer evaluates all potential moves and selects the best one. which of the following best describes the possibility of improving the running speed of the game?
The best way to improve the running speed of the game is to use an algorithm which can quickly evaluate potential moves and select the best one.
For example, alpha-beta pruning is an algorithm which is used for game tree search. It prunes the search tree and eliminates the branches which are not likely to contain the optimal solution. Alpha-beta pruning uses the following formula to evaluate positions:
Max(α, Min(β, v))
Where α is the best value that the maximizing player can guarantee at the current branch of the tree, β is the best value that the minimizing player can guarantee at the current branch of the tree and v is the value of the current position. The evaluation of the position helps to quickly identify the best move. This reduces the time taken to evaluate the potential moves and thus improves the running speed of the game.
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