We can estimate that about 9 grams of water vapor per kg of air would have to condense out to maintain saturation and a relative humidity of 100%.
When air is saturated, it holds the maximum amount of water vapor it can at a given temperature and pressure. Any decrease in temperature leads to the condensation of water vapor out of the air, which can lead to the formation of dew or frost.
To maintain a relative humidity of 100%, the air must remain saturated. So, if the temperature of the room continues to decrease for one more hour, some of the water vapor in the air will condense out to maintain saturation. The amount of water vapor that condenses out depends on the initial temperature, the final temperature, and the amount of water vapor in the air.
To calculate the amount of water vapor that condenses out, we can use the concept of dew point temperature. The dew point temperature is the temperature at which the air becomes saturated and condensation begins to occur. If the temperature of the room reaches the dew point temperature, the air will be fully saturated, and any further decrease in temperature will lead to the condensation of water vapor.
Assuming that the initial temperature of the room was above the dew point temperature, we can estimate the amount of water vapor that would condense out after one hour of cooling by calculating the difference between the initial temperature and the dew point temperature, and then using a psychrometric chart or an online calculator to determine the corresponding amount of water vapor that would have to condense out.
For example, if the initial temperature of the room was 25°C and the dew point temperature was 20°C, and the room cooled to 19°C after one hour, then we can estimate that about 9 grams of water vapor per kg of air would have to condense out to maintain saturation and a relative humidity of 100%. However, this is just an estimate, and the actual amount of water vapor that condenses out depends on many factors, including the humidity and air circulation in the room.
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The housing market has been very intense since 2020 when the pandemic began. People in Southern California as well as across the USA wanted to buy homes away from cities with a prefence towards the suburbs and rural areas. Southern California homes experienced a 12. 6 % year over year increase in price gains since 2020 and this is still going on. Inventory is too low, that is the supply of homes is low. Home builders aren't able to build fast enough to keep up with demand, or won't. A: If a modest 2 bedroom 2 bathroom house in Santa Barbara county used to cost $567,000 in 2020, give the exponential formula that models the price of this house over time, assuming the percent appreciation sustains currently and into the future. Let P(t) be the "asking price" of the house. Let "r" be the rate of the appreciation value. Let t be time in years. Use decimals only. B: What would be the price of such a house in 2022? ( Round your answer to two places after the decimal, also known as the hundredths place).
A: P(t) [tex]= $567,000 * (1 + 0.126)^t[/tex]
B: [tex]567,000 * (1 + 0.126)^2 = $671,448.14[/tex]
How can we calculate the price of a 2 bedroom 2 bathroom house in Santa Barbara county in 2022, assuming the current rate of appreciation continues?A: To model the price of the house over time, we can use the exponential formula: P(t) = P₀ * (1 + r)^t, where P₀ is the initial price, r is the rate of appreciation, and t is the time in years.
In this case, the initial price (P₀) of the house is $567,000 and the rate of appreciation (r) is 12.6% expressed as a decimal, which is 0.126. Therefore, the exponential formula to model the price of the house over time would be: P(t) = 567,000 * (1 + 0.126)^t.
B: To find the price of the house in 2022, we substitute t = 2022 - 2020 = 2 into the exponential formula.
P(2) = 567,000 * (1 + 0.126)^2
P(2) = 567,000 * (1.126)^2
P(2) ≈ 567,000 * 1.268
P(2) ≈ $719,976.00
Therefore, the price of such a house in 2022 would be approximately $719,976.00
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HELP FAST PLEASEEEEEE I NEED HELPPPPP
The median means that as many as friends have less than A. 1. 5 pets as those that have more than A. 1. 5 pets.
What does the median mean ?The median is a measure of central tendency in statistics that represents the middle value of a dataset when it is ordered from smallest to largest. The median is often used as a more robust measure of central tendency than the mean, because it is less affected by extreme values in the dataset.
From the box plot, the data set of friends with pets would be:
0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, ,2 ,2, 2, 2, 2, 3, 4, 4, 7.
The median here is:
= ( 10 th position + 11 th position ) / 2
= ( 1 + 2 ) / 3
= 1. 5
This therefore means that as many friends have more than 1. 5 pets as those with less than 1. 5 pets because the median shows the number which had the same number above, and the number below.
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Find
(Round your answer to the nearest hundredth)
The missing side length is 5√3 centimeters.
We can use the Pythagorean theorem to find the missing side length. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In equation form, this looks like:
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
To use this formula to solve for the missing side length, we can plug in the values we know:
5² + b² = 10²
We can simplify this equation by squaring 5 and 10:
25 + b² = 100
Next, we can isolate the variable (b) on one side of the equation by subtracting 25 from both sides:
b² = 75
Finally, we can solve for b by taking the square root of both sides:
b = √(75)
This simplifies to:
b = 5*√(3)
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Complete Question:
By using the Pythagoras theorem, Find the value of the Other side when the value of hypotenuse is 10 cm and the value of the side is 5 cm.
A method for determining whether a critical point is a relative minimum or maximum using concavity.
To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.
If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.
On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.
If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.
Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.
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Complete question is:
What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.
Carla, the baker, worked for 5 hours to make cookies..
She ended with 380 cookies altogether. Write an
equation to express how many cookies Carla made
each hour.
Answer:
5x=380
x = 76
Carla made 76 cookies each hours
Step-by-step explanation:
Just make an equation, so the total number of cookies is 380 and she works for 5 hours, so it is just 380/5.
For f(x)=1/x^2 show there is no c such that f(1)-f(-1)=f'(c)(2).
Explain why the mean value theorem doesnt apply over the interval
[-1,1]"
Prerequisites for the MVT are not met due to the discontinuity and non-differentiability of f(x) at x = 0 within the interval [-1, 1].
Let's first understand the Mean Value Theorem (MVT). The MVT states that if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
Now, consider the function f(x) = 1/x^2. This function is continuous and differentiable for all x ≠ 0. However, in the interval [-1, 1], the function is not continuous nor differentiable at x = 0. Therefore, the Mean Value Theorem does not apply to this interval.
Since the MVT does not apply, we cannot say there exists a c in the interval (-1, 1) such that f'(c) = (f(1) - f(-1)) / (1 - (-1)). This is because the prerequisites for the MVT are not met due to the discontinuity and non-differentiability of f(x) at x = 0 within the interval [-1, 1].
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Appreciate if somebody answered this question
Thank you
A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
A probability can be classified as experimental or theoretical, as follows:
Experimental -> calculated after previous trials.Theoretical -> calculate before any trial.Over a small number of trials, these two probabilities can be different, but over a large number of trials, their values get closer.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
(each of the eight sides is equally as likely, and a six is one of these sides).
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%.400 trials: 44/400 = 0.11 = 11%.(given in the problem).
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Tina is selling tickets for a fundraiser.
She wants to sell more than $300 worth
of tickets. The inequality 12t> 300 can
be used to determine the number of
tickets, t, she must sell in order to meet
her goal. Which number line represents
the solution to this inequality? (6. 9B |
6. 1A, 6. 1B, 6. 10, 6. 1F)
10
20
30
B
to
10
20
30
+
С
+o
+
10
20
30
D
+
10
O
20
30
The number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.
To solve the inequality 12t > 300, we need to isolate t on one side of the inequality. We can do this by dividing both sides by 12:
12t/12 > 300/12
t > 25
This means that Tina must sell more than 25 tickets in order to meet her goal of selling more than $300 worth of tickets.
To represent this solution on a number line, we can start by plotting a point at 25. Since the inequality is greater than (>) and not greater than or equal to (≥), we use an open circle at 25.
Then, we need to shade the area to the right of 25 to represent all the possible values of t that satisfy the inequality. This is because any value of t greater than 25 will make 12t greater than 300.
Out of the answer choices given, the number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.
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which of the following groups of numbers is ordered from least to greatest?
A. 1/5, 3/8, 4/10, 0.45, 0.6
B. 1/5, 3/8, 0.45, 4/10, 0.6
C. 0.6, 0.45, 4/10, 3/8, 1/5
D. 0.6, 4/10, 0.45, 1/5, 3/8
ans.(a) is correct
only in option (a) numbers are arranged from least to greatest.
Question 4 of 15
Cryshel is mailing pillows with a total volume of 9. 5 ft3. She needs a mailing
box that has a volume greater than 9. 5 ft.
• Box A: length = 3 ft, width = 2 ft, height = 1. 5 ft
• Box B: length = 2. 5 ft, width = 2 ft, height = 2 ft
Which box is large enough to hold all of her pillows?
O
A. Neither box
B. Both box A and box B
ОО
C. Box B
D. Box A
Answer:
C. Box B
Step-by-step explanation:
You want to know which of these two boxes has a volume greater than 9.5 ft³:
Box A: 3 ft by 2 ft by 1.5 ftBox B: 2.5 ft by 2 ft by 2 ftVolumeThe volume of each box is found by multiplying its dimensions:
Box A: (3 ft)(2 ft)(1.5 ft) = 9 ft³
Box B: (2.5 ft)(2 ft)(2 ft) = 10 ft³
Only box B is large enough, choice C.
<95141404393>
Find the surface area of the composite figure.
3 cm
5 cm
4 cm
8 cm
10 cm
SA =
8 cm
5 cm
7 cm
[?] cm²
If you'd like,
you can use a
calculator.
Enter please help I don’t want to fail!
The surface area of the composite figure is given as follows:
446 cm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The figure is this problem is given by the composition of two rectangular prisms, with dimensions given as follows:
5 cm, 10 cm and 7 cm.8 cm, 4 cm and 3 cm.Hence the surface area is given as follows:
S = 2 x (5 x 10 + 5 x 7 + 10 x 7) + 2 x (8 x 4 + 8 x 3 + 4 x 3)
S = 446 cm².
Missing InformationThe prism is given by the image presented at the end of the answer.
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two cards are drawn from a deck of 52 playing cards. the first card is not replace before the 2nd card is drawn. what is the probabilty of drawing a king and another king?
A. 3/676
B. 1/221
C. 1/169
D. 2/169
Answer:
1/221.
Step-by-step explanation:
Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).
Now there are 51 cards left in the pack, 3 of which are Kings, so:
Probability(second card is a King) = 3/51 = 1/17.
These 2 events are independent so we multiply the probabilities:
Required probability =
1/13 * 1/17
= 1/221.
A tree’s cross sectional area is called its basal area and is measured in square inches. Tree growth can be measured by the growth of the tree’s basal area. The initial base area of tree observed by a biologist is 154 square inches and annual growth rate is 6%. What will be the basal area after 10 years of growth?
The basal area of the tree after 10 years of growth would be approximately 279.7 square inches.
Given the initial basal area of a tree, which is 154 square inches, and the annual growth rate, which is 6%. To find out what the basal area of the tree will be after 10 years of growth.
By using the formula for compound interest, which can be applied to the growth of the basal area over time. The formula is:
A = P(1 + r)ⁿ
where:
A is the final amount
P is the initial amount
r is the annual growth rate
n is the number of years
To find A, the final basal area of the tree after 10 years of growth. We know that P is 154 square inches, r is 6% or 0.06 and n is 10.
By applying these values in the formula, we get:
A = 154(1 + 0.06)¹⁰
A = 154(1.06)¹⁰
A = ≈ 279.7
Therefore, the basal area of the tree after 10 years of growth would be approximately 279.7 square inches.
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Help asap
what is the measure of angle oac if major arc ab measures 220 degrees?
a. 55
b. 70
c. 110
d. 140
pls explain/show work
The measure of angle OAC if major arc AB measures 220 degrees is 110 degrees. Therefore, the correct option is C.
To find the measure of angle OAC, we need to use the central angle theorem which states that the measure of an inscribed angle is equal to half the measure of the intercepted arc.
Here, we are given that the major arc AB measures 220 degrees. So, the measure of angle AOB (the central angle) is 220 degrees.
Since angle OAC is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB.
Therefore, measure of angle OAC = (1/2) * 220 = 110 degrees.
So, the correct answer is option (c) 110.
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Select the expressions that are equivalent to 3v+2v. A. V*5
B. V+5
C. V+5v
D. V+v+v+v+v
The expression that is equivalent to 3v+2v is:
D. v+v+v+v+v
How to write equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
To find the expressions that are equivalent to 3v+2v, we need to find the expression which when simplified will give the same expression as 3v+2v. That is: 3v + 2v = 5v
v*5 = 5v
v+5 = v + 5
v+5v = 6v
v+v+v+v+v = 5v
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Austin spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -1.9°F. Between 9am and noon, the temperature rose 11.3°F. Between noon and 3pm, the temperature dropped 7.9°F. Between 3pm and 6pm, the temperature dropped 12.7°F. What was the temperature at 6pm?
To find the temperature at 6pm, we need to start with the temperature at 9am and then add or subtract the changes in temperature that occurred during the day.
We know that the temperature at 9am was -1.9°F. Between 9am and noon, the temperature rose 11.3°F, so at noon the temperature was:
-1.9 + 11.3 = 9.4°F
Between noon and 3pm, the temperature dropped 7.9°F, so at 3pm the temperature was:
9.4 - 7.9 = 1.5°F
Between 3pm and 6pm, the temperature dropped 12.7°F, so at 6pm the temperature was:
1.5 - 12.7 = -11.2°F
Therefore, the temperature at 6pm was -11.2°F.
Find the indicated length
Answer:
y = 32/3 or 10.67 units------------------------------
The two smaller right triangles are similar by AA property.
Use ratios of corresponding sides to get:
8/y = 6/8Simplify and solve for y:
8/y = 3/4y = 8*4/3y = 32/3 ≈ 10.67David is setting up camp with his friend Xavier. David and Xavier want to place their tents equal distance to the ranch where the mess hall is. A model is shown, where points D and X represent the location
tents and point R represents the ranch. DR = (12.3z + 12.4) meters (m) and XR= (10.5z+34) m.
D
X
R
What is the distance Xavier and David are from the ranch?
The distance from Xavier and David to the ranch can be found using the distance formula:
distance = sqrt((change in x)^2 + (change in y)^2 + (change in z)^2)
In this case, we are given the distances DR and XR, which represent the change in x, y, and z coordinates between the tents and the ranch. We know that the tents are located at equal distances from the ranch, so the change in x, y, and z coordinates for both David and Xavier will be the same.
Let's call the distance from each tent to the ranch "d", then we have:
DR = XR = d
Substituting the given values, we get:
12.3z + 12.4 = 10.5z + 34
Solving for z, we get:
z = 6.8
Now we can find the distance from each tent to the ranch using the formula:
distance = sqrt((change in x)^2 + (change in y)^2 + (change in z)^2)
For David's tent:
distance = sqrt((12.3z)^2 + 0^2 + (12.4)^2) = sqrt((12.3*6.8)^2 + (12.4)^2) = 87.9 meters (rounded to one decimal place)
For Xavier's tent:
distance = sqrt((10.5z)^2 + 0^2 + (34)^2) = sqrt((10.5*6.8)^2 + (34)^2) = 95.6 meters (rounded to one decimal place)
Therefore, David and Xavier are 87.9 meters and 95.6 meters away from the ranch, respectively.
Mike has some candies. he gave some to his friend. then, his mom gave him twice as much as he had in the beginning. how much did he have in the beginning if he has a total of 60 candies now?
According to given question Mike has 25 candies in the beginning.
Let's assume that Mike had "x" candies in the beginning.
After giving 15 candies to his friend, he would have had (x - 15) candies left.
His mom then bought him twice as many candies as he had in the beginning, which would be 2x candies.
So, the total number of candies Mike has now is (x - 15) + 2x = 60.
Combining like terms, we get 3x - 15 = 60.
Adding 15 to both sides, we have 3x = 75.
Finally, dividing both sides by 3, we find that x = 25.
Therefore, Mike had 25 candies in the beginning.
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The complete question is Mike had some candies. He gave 15 of them to his friend. After that, his mom bought him twice as many candies as he had in the beginning. How many candies did Mike have in the beginning if he now has a total of 60 candies?
In △def, d = 20, e = 25, and f = 30. find m∠f to the nearest degree.
m∠f to the nearest degree is 83°.
The Law of Cosines is used to find an angle when all triangle sides are known.
f² = d² +e² -2de cos(F)
To find angle ∠F, we need to find the value of cos(∠F), which we can do by rearranging the Law of Cosines as follows:
cos(F) = (d² +e² -f²) / (2de)
cos(F) = (20² + 25² - 30²) / (2 × 20 × 25)
cos(F) = (400 + 625 - 900) / (1000)
cos(F) = 125/1000
∠F = arccos(1/8)
∠F = 82.8°
Rounding to the nearest degree
∠F = 83°
Hence, m∠f to the nearest degree is 83°.
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Evaluate the following indefinite integral si 3x^2 – 3x +1/ x^3 + 2
To evaluate the indefinite integral of 3x^2 – 3x +1/ x^3 + 2, we can use partial fraction decomposition.
First, we factor the denominator: x^3 + 2 = (x + ∛2)(x^2 – ∛2x + 2).
Next, we can write the fraction as:
3x^2 – 3x +1/ x^3 + 2 = A/x + B(x^2 – ∛2x + 2) + C(x + ∛2)
Multiplying both sides by the denominator, we get:
3x^2 – 3x + 1 = A(x^2 – ∛2x + 2)(x + ∛2) + Bx(x + ∛2) + C(x^2 – ∛2x + 2)
To solve for A, B, and C, we can plug in specific values of x. For example, if we plug in x = -∛2, we get:
-2√2 + 1 = A(4√2) + C(0)
Therefore, A = (2 – √2)/8.
If we plug in x = 0, we get:
1 = A(2√2) + B(0) + C(√2)
Therefore, C = 1/√2.
Finally, if we plug in x = 1, we get:
1 = A(3√2) + B(1 – √2) + C(1 + √2)
Therefore, B = (-1 + √2)/4.
Now that we have A, B, and C, we can write the original fraction as:
3x^2 – 3x +1/ x^3 + 2 = (2 – √2)/8 * 1/x + (-1 + √2)/4 * (x^2 – ∛2x + 2) + 1/√2 * (x + ∛2)
Using this partial fraction decomposition, we can now integrate each term separately.
Integrating the first term, we get:
∫(2 – √2)/8 * 1/x dx = (1/8)(2ln|x| – √2 ln|x^2 + 2|) + C
Integrating the second term, we can complete the square to get:
∫(-1 + √2)/4 * (x^2 – ∛2x + 2) dx = (-1 + √2)/4 * ∫(x – ∛1/2)^2 + 3/2 dx = (-1 + √2)/4 * ((x – ∛1/2)^2 + 3/2) + C
Integrating the third term, we get:
∫1/√2 * (x + ∛2) dx = (1/2√2) * (x^2/2 + ∛2x) + C
Putting it all together, we have:
∫(3x^2 – 3x +1)/ (x^3 + 2) dx = (1/8)(2ln|x| – √2 ln|x^2 + 2|) + (-1 + √2)/4 * ((x – ∛1/2)^2 + 3/2) + (1/2√2) * (x^2/2 + ∛2x) + C
where C is the constant of integration.
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Evaluate JJ ) Ry0 +52, 15y52. (y + xy-2) dA; R= {(x,y): 0 < x
the evaluated double integral is approximately 14.25.
To evaluate the given double integral, we need to first understand the problem properly. We have the function f(x, y) = y + xy, and the region R is described by the inequalities: 0 < x < y^2, and 1 < y < 2.
Now we can set up the double integral:
∬(y + xy) dA over the region R.
Since we are given that 0 < x < y^2 and 1 < y < 2, we can set up the integral using the given limits of integration:
∫(from y = 1 to 2) ∫(from x = 0 to y^2) (y + xy) dx dy.
Now, we can start by integrating the inner integral with respect to x:
∫(from y = 1 to 2) [(yx + (1/2)x^2*y) evaluated from x = 0 to x = y^2] dy.
After evaluating the inner integral, we have:
∫(from y = 1 to 2) (y^3 + (1/2)(y^2)^2*y) dy.
Now, we can integrate the outer integral with respect to y:
[((1/4)y^4 + (1/6)y^6) evaluated from y = 1 to y = 2].
After evaluating the outer integral, we get:
[(1/4)(2^4) + (1/6)(2^6)] - [(1/4)(1^4) + (1/6)(1^6)].
Calculating the final result:
(4 + 10.6667) - (0.25 + 0.1667) = 14.6667 - 0.4167 ≈ 14.25.
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plunk and ms. q run a $100$-meter race. plunk runs at $8$ meters per second, and ms. q runs at $5$ meters per second. because ms. q runs slower, she is given a $3$-second head start. plunk wins the race. how much time, in seconds, is it between the time plunk passes ms. q and the time that plunk finishes the race?
The seconds, is it between the time plunk passes Ms. q and the time that plunk finishes the race is 7.5 seconds..
Flow Distance In the Mathematics or Quants part of any competitive test, time is one of the most well-liked and significant topics. For inquiries about a variety of subjects, including motion in a straight line, circular motion, boats and streams, races, clocks, etc.
The notion of Speed, Time, and Distance is frequently employed. Candidates should make an effort to comprehend how the variables of speed, distance, and time interact.
Ms. q being slow will get a head start for the race so,
3 second head start = 3 x 5 = 15 meters
There difference in speed is 8- 5 = 3 m/s
Time required for the Plunk to catch up to Ms. q is:
15 / 3 = 5 seconds when P catches Q
(this is 8 seconds after Q starts the race)
In 5 seconds Plunk runs 5 x 8 = 40 meters this is when they are at the same point that is at time 8 seconds.
60 meters left in the race will take Plunk :
60 m / 8 m/s = 7.5 seconds to finish the race.
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Identify the line of symmetry for the function below:
g(x) = |x +9|- 11
Answer:
x = -9
Step-by-step explanation:
As this is an absolute value function, the line of symmetry is the x-value of the maximum/minimum point. An absolute value function can be denoted as y = |x - h| + k, where (h, k) is the maximum/minimum point. We only need the x-value of the maximum/minimum point, so we only have to look at "h". Now, we can use y = |x - h| + k and turn it into g(x):
y = |x - h| + k
g(x) = |x - -9| + -11 --> this means h = -9, and the line of symmetry is at x = -9
g(x) = |x + 9| - 11
Answer:
I think x equals --9
1. Jason draws a rectangle in the coordinate plane at the right to represent his yard. To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Draw arrows on the coordinate plane to show Jason’s path. Write the coordinates for his start and end points.
START:___ END:___
2. Use the coordinate plane in problem 1. What is the perimeter of rectangle YARD?
units
3. Mary models her rectangular room in the coordinate plane at the right. She plans to hang strings of lights on two perpendicular walls. What are the lengths of and ?
units units
4. Use the coordinate plane in problem 3. What is the area of Mary’s room?
square units
5. The coordinate plane at the right models the streets
of a city. The points A(3, 8), B(6, 3), and C(3, 3) are connected to form a park in the shape of a triangle. Connect the points to form the triangle. Which two sides of the park form a right angle?
and
6. Use the coordinate plane in problem 5. Tyler walks along the two sides of the park that form the right angle. How many blocks does he walk in all?
blocks
7. How can you find distances between points in a coordinate plane?
1. The coordinates are: START: (0,0) END: (6,-4), 2. The perimeter of rectangle YARD is 20 units,3. The lengths of YX and YZ are 4 units and 6 units, respectively, 4. The area of Mary's room is 24 square units,
1-To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Starting from the origin, his starting point is (0,0). From there, he moves 4 units down to the point (0,-4), and then 6 units right to reach his endpoint, which is at (6,-4).
2-The rectangle has two sides of length 4 and two sides of length 6. The perimeter is the sum of the lengths of all sides, so it is equal to 2(4) + 2(6) = 8 + 12 = 20 units.
3-The coordinates of points Y, X, and Z are not given, so we cannot calculate the lengths directly. However, we know that the sides of a rectangle are perpendicular, so we can use the Pythagorean theorem to find the lengths. Let Y be the origin (0,0), and let X be the point (0, -4). Then YX has length 4 units. Similarly, let Z be the point (6, 0), so YZ has length 6 units.
4.To find the area of a rectangle, we can multiply the lengths of its sides. From problem 3, we know that the lengths of the sides are 4 and 6 units, so the area is 4 x 6 = 24 square units.
5. The sides AB and AC form a right angle.
To determine which sides of the triangle form a right angle, we need to find the slope of each side. The slope of AB is (3-8)/(6-3) = -5/3, and the slope of AC is (3-3)/(6-3) = 0. Since the product of the slopes of two perpendicular lines is -1, we can see that AB is perpendicular to AC. Therefore, sides AB and AC form a right angle.
6. Tyler walks 9 blocks in all.
To find the distance Tyler walks, we need to calculate the length of sides AB and AC. Using the distance formula, we can find that the length of AB is sqrt[(6-3)² + (3-8)²] =√[(34) units, and the length of AC is 3 units. Therefore, Tyler walks 3 + √[34 units along the two sides that form the right angle. This is approximately 9.4 blocks, so he walks 9 blocks in all.
7. The distance between two points in a coordinate plane can be found using the distance formula:
d = √[(x₂-x₁)² + (y₂-y₁)²]
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them. The formula is derived from the Pythagorean theorem, which relates the sides of a right triangle.
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Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5 meters high. the maximum kinetic energy she can reach when she skis to the bottom of the slope is joules. use pe = m × g × h and g = 9.8 m/s2. ignore air resistance and friction.
Dina can reach a maximum kinetic energy of 2450 Joules when she skis to the bottom of the slope.
How much kinetic energy can Dina reach?Potential energy (PE) = m x g x h
where m = mass, g = acceleration due to gravity, and h = height
Here, Dina's mass (m) = 50 kg, height (h) = 5 m, and acceleration due to gravity (g) = 9.8 m/s².
So, PE = 50 x 9.8 x 5
PE = 2450 Joules
When Dina skis down the slope, all of her potential energy will be converted into kinetic energy (KE) at the bottom of the slope, neglecting any losses due to friction and air resistance.
Thus, the maximum kinetic energy (KE) Dina can reach at the bottom of the slope is also 2450 Joules.
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The maximum kinetic energy she can reach when she skis to the bottom of the slope is 2452 joules
To find the maximum kinetic energy that Dina can reach when she skis to the bottom of the slope, we need to use the principle of conservation of energy, which states that the total energy of a system remains constant.
At the top of the slope, Dina has potential energy due to her position relative to the ground. This potential energy is given by:
PE = m × g × h
where m is Dina's mass (50 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slope (5 m).
PE = 50 kg × 9.8 m/s^2 × 5 m = 2450 J
When Dina skis to the bottom of the slope, all of her potential energy is converted into kinetic energy, which is given by:
KE = 1/2 × m × v^2
where v is her velocity at the bottom of the slope.
To find the maximum velocity, we can use the fact that the total energy of the system remains constant:
PE = KE
2450 J = 1/2 × 50 kg × v^2
v^2 = 98 m^2/s^2
v = sqrt(98) = 9.90 m/s
Finally, we can substitute this velocity into the kinetic energy equation to find the maximum kinetic energy that Dina can reach:
KE = 1/2 × 50 kg × (9.90 m/s)^2 = 2452 J
Therefore, Dina can reach a maximum kinetic energy of 2452 Joules when she skis to the bottom of the slope.
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The diagram below shows the radius of the circular opening of a Ice cream cone.
Which of the following Is closest to the circumference of the opening in inches.
Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?
The price of one apple is $0.70, obtained by solving the system of equations 4x + 9y = 12.70 and 8x + 11y = 17.70 using elimination.
How much would Patricia pay for each apples?Let's use a system of equations caculation the problem.
Let x be the price of one apple and y be the price of one banana.
From the first sentence, we know that:
4x + 9y = 12.70
From the second sentence, we know that:
8x + 11y = 17.70
Now we can solve for x by using either substitution or elimination.
Let's use elimination.
We can multiply the first equation by 11 and the second equation by -9, then add them together:
44x + 99y = 139.70
-72x - 99y = -159.30
-28x = -19.60
Dividing both sides by -28, we get:
x = 0.70
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what’s the inverse of f(x) for f(x)=4x-3/7
Answer:
x/4 + 3/28 = y
Step-by-step explanation:
To find the inverse, switch the x's and y's (note that f(x) is y) and solve for y:
x = 4y - 3/7
x + 3/7 = 4y
x/4 + 3/28 = y
Answer:
−1(x) = 3√2(x+7) 2 f - 1 (x) = 2 (x + 7) 3 2 is the inverse of f (x) = 4x3 − 7 f (x) = 4 x 3 - 7.
The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection. 4 8 12 16 20 24 28 32 36 40 44 48 speed of cars (miles per hour) a. What is the smallest value in the data set? 4 b. What is the largest value in the data set? 48 c. What is the median?â
a. The smallest value in the data set is 4 miles per hour. b. The largest value in the data set is 48 miles per hour. c. The median is 26 miles per hour.
a. The smallest value in the data set is 4 miles per hour.
b. The largest value in the data set is 48 miles per hour.
c. To find the median, we need to arrange the values in order from smallest to largest:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
The median is the middle value in this list. Since there are an even number of values, we take the average of the two middle values:
Median = (24 + 28) / 2 = 26
Therefore, the median speed of the 100 cars as they passed through the busy intersection is 26 miles per hour.
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