For a uniform distribution, the probability of any given value is the same across the entire range of the distribution. Therefore, for the given random variable Y, the probability of Y being less than or equal to 0.4 (P(Y <= 0.4)) is 0.4. The probability of Y being less than 0.4 (P(Y < 0.4)) is also 0.4.
For the third probability, P(0.1 < Y <= 0.15 or 0.77 ≤ Y < 0.88), the probability is the sum of the probabilities of the two ranges. The probability of Y being between 0.1 and 0.15 is 0.05, and the probability of Y being between 0.77 and 0.88 is 0.11. Therefore, the total probability is 0.05 + 0.11 = 0.16.
In conclusion, the probabilities of the given random variable Y are P(Y <= 0.4) = 0.4, P(Y < 0.4) = 0.4, and P(0.1 < Y <= 0.15 or 0.77 ≤ Y < 0.88) = 0.16.
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Do females have testis
Answer + Explanation:
First of all, odd question but okay. Anyways, no, females do not have testes. Testes are male reproductive organs that produce sperm and hormones such as testosterone. Females have ovaries, which produce eggs and hormones such as estrogen.
Answer:
some have like 2out of 100
Speed Seed Company mixes bluegrass seed that costs $7.60 per kilogram with ryegrass seed that costs $6.25 a kg. How many kiolgrams of bluegrass seed should be mixed with 200 kg of
150 kg of bluegrass seed should be mixed with 200 kg of ryegrass seed to make a blend that costs of amount $7.00 per kg.
To calculate, use the following formula:
7.60x + 6.25(200 - x) = 7.00(200)
7.60x + 1,250 - 6.25x = 1,400
1.35x = 1,400
x = 1,040/1.35
x = 770/1
x = 770
Therefore, 770 kg of bluegrass seed should be mixed with 200 kg of ryegrass seed to make a blend that costs of amount $7.00 per kg.
The complete question is :
Speed Seed Company mixes bluegrass seed that costs $7.60 per kilogram with ryegrass seed that costs $6.25 a kg. How many kiolgrams of bluegrass seed should be mixed with 200 kg of ryegrass seed to make a blend that costs $7.00 per kg?
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Determine the time intervals (in seconds) in which the particle moves in the positive direction and the negative direction. (Enter your answers using interval notation.) positive direction ______. negative direction______.
Given that, the function s(t) describes the motion of a particle along a line. s(t) = t³ − 13t² + 35t − 220
We need to find the time intervals in which the particle moves in the positive direction and the negative direction.
The given equation is s(t) = t³ − 13t² + 35t − 220
Taking the derivative,
v(t) = s'(t) = 3t² -26t + 35 = velocity at time t
s'(t) = 3t² -26t + 35 = 0
(3t -5)(t-7) = 0
t = 5/3 and 7 seconds
Therefore, the velocity > 0 when s'(t) > 0, when t>7 or t < 5/3 seconds
velocity <0 when 5/3 < t < 7 seconds
When moving in a positive direction, the intervals :-
(-∞, 5/3) ∪ (7, ∞)
When moving in a negative direction, the interval :-
(5/3, 7)
Hence, the time intervals are; positive direction (-∞, 5/3) ∪ (7, ∞) and negative direction (5/3, 7)
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The question was incomplete, so I solved for the question;
The function s(t) describes the motion of a particle along a line.
s(t) = t³ − 13t² + 35t − 220
(a) Find the velocity function v(t) of the particle at any time t ≥ 0.
(b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.)
(c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.)
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 83 people in the 18-21 age bracket and finds that 70 of them respond and 13 refuse to respond. When 268 people in the 22-29 age bracket are contacted, 238 respond and 30 refuse to respond. Assume that 1 of the 351 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond
Two different age brackets (18-21 and 22-29) were surveyed and the number of people who responded and refused to respond was recorded.
We can use the formula for probability:
Probability = Number of favorable outcomes by Total number of outcomes, P(A) = f / N
First, let's find the number of people in the 22-29 age bracket who agreed to respond:
238 out of 268 people in this age bracket agreed to respond.
Next, let's find the number of people in the 18-21 age bracket who agreed to respond:
70 out of 83 people in this age bracket agreed to respond.
So, the total number of people who agreed to respond is 238 + 70 = 308 out of 351 people.
Therefore, the probability of getting someone in the 22-29 age bracket or someone who agreed to respond is 308/351.
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what are the units of a z - score? does a z-score have any units? Please help, and bear in mind that spam will be reported
Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
What is a confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.
Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
When assessed in terms of standard deviation units, a raw score's location in relation to its distance from the mean is indicated by a z-score.
If a value is above the mean, the z-score is positive; if it is below the mean, it is negative.
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I need help solving these questions.
£13,000 was deposited in a savings account that pays simple interest.
After 17 years, the account contains £18,525.
Work out the annual interest rate of the account.
Give your answer as a percentage (%) to 1 d.p.
Look at the image, can I get help with this work sheet?
Answer:
For 2:The y intercept is whatever the y coordinate is when x = 0. Basically, where does the line hit the line going up and down? For number two, the y intercept is negative 3.
Slope intercept form y = mx + b
m = slope
b is y intercept
so far its
y = mx - 3
the slope is how many time you have to go up and over to get to the next number. Rise/run. For 2, the slope is negative! It is - 1/1 so
y = -1x - 3 is the first equation
For 3, the y inttercept is 0! so
y = mx + 0
or just y =mx
The slope is going to be negative
1/2
so - 1 / 2
y = -1/2x +0 or just y = -1/2x
Next one 4 is a positive slope. y intercept is 4
slope is 3 /1 or just 3
y = 3x + 4
5 is negative slope as well :)
The y intercept is 3
The slope is - 1/3
y = - 1/3x + 3
for 6, it is going to be a positive slope
y intercept is -3
Sloep is 2/1 so
y = 2x - 3
Step-by-step explanation:
a segment that connects a vertex to the opposite side so that it creates a 90° angle
A segment that connects the vertex of a triangle with the opposite side so it makes a 90-degree angle is called Altitude.
In geometry, Altitude is used to describe the height of a polygon, triangle, or other two-dimensional shapes. The altitude of a figure is a line segment perpendicular to the base and passes through the vertex of the constitution. It is used to calculate the area of the figure and to determine the lengths of the sides and angles.
In three-dimensional figures, the altitude can also refer to the distance between the highest and lowest points of the constitution. The concept of altitude is widely used in mathematics, particularly in geometry, trigonometry, and related fields.
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Complete Question:
A line that connects the vertex of a triangle with the opposite side so it makes a 90 degree angle_____.
What is the solution to the equation −6x−11=19 − 6 x − 11 = 19 ?
Answer:
This equation has no solution.
Step-by-step explanation:
A constant zero never equals zero..
50 POINTS
Which of the following tables represents a linear relationship that is also proportional?
1.
x −3 0 3
y 0 2 4
----------------------------------
2.
x −4 −2 0
y −2 0 2
----------------------------------
3.
x −4 0 4
y 1 0 −1
----------------------------------
4.
x −1 0 1
y −5 −3 −1
Answer:
3.
x −4 0 4
y 1 0 −1
-----------------------
5. Function f is defined by the equation f(x) = x².
a. What is (2)?
b. What is (3)?
c. Explain why f(2) + f(3) ‡ f(5).
f (2) = 2^2 = 2 * 2 = 4
f (3) = 3^2 = 3 * 3 = 9
f(2) + f(3) = 4 + 9 = 13
f (5) = 5^2 = 5 * 5 = 25
13 does not equal 25
a. 4
b. 9
c. f(2) + f(3) ‡ f(5) can be stated as 13 does not equal 25
It’s not really that hard but I am just busy so please do this for me.
The Surface area are shown below.
What is Surface Area?The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.
Given:
1. The height of the cone shape, h = 84 inches
radius = 8 inches
The cost per cubic inch is $2.25.
The cost of nickel for the sculpture is given by
= 2.25 x 1/3πr²h
= 2.25 x 1/3 x 3.14 x 8 x 8 x 84
= $12660.48.
2. The measure of sides are
A = 12
B = 10
C= 5
D= 13
So, the Lateral Surface Area
= ( 12 + 13 + 5) x 10
= 30 x 10
= 300 cm²
and, the total surface Area
= Area of two triangles + Area of rectangle
= 2 x 1/2 x 5 x 12 + 300
= 60+ 300
= 360 cm²
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Three softball players discussed their batting averages after a game.
Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
The statement Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2) is correct.
What is probability?The probability that an event will occur is equal to the ratio of positive outcomes to all outcomes, according to the probability formula. The proportion of positive outcomes to overall outcomes, or P(E), determines the likelihood that an event will occur.
Given three softball players discussed their batting averages after a game.
Probability
Player 1 is seven elevenths = 7/11
P(Player 1) = 0.636
Player 2 is six ninths = 6/9
P(Player 2) = 0.666
Player 3 is = five sevenths = 5/7
P(Player 3) = 0.714
so the probability of P(Player 3) > P(Player 2) > P(Player 1).
so Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).
Hence option D is correct.
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Can someone help me with this one rq
The expression that represents the volume of the rectangular prism is given as follows:
8 x 3 x 2 units ³.
How to obtain the volume of the rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
8 units.3 units.2 units.Hence the volume is given by the multiplication of these dimensions as follows:
8 x 3 x 2 units ³.
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a pair of dice are thrown one time. what is the probability that the sum will be equal to seven if we know at least one of the dice is a 4?
If we know that at least one of the dice is a 4, the probability that the sum of the two dice will be equal to 7 is 1/3.
The probability that the sum of two dice will be equal to seven if we know that at least one of the dice is a 4 can be calculated as follows:
There are two cases to consider:
The first die is a 4 and the second dice can be any value from 1 to 6. The probability of this event is 1/6.The second die is a 4 and the first dice can be any value from 1 to 6. The probability of this event is also 1/6.Since the two events are mutually exclusive, the total probability that the sum of the dice will be equal to 7 is the sum of the individual probabilities, which is
1/6 + 1/6 = 2/6 = 1/3.
In conclusion, if we know that at least one of the dice is a 4, the probability that the sum of the two dice will be equal to 7 is 1/3. This means that there is a 1 in 3 chance of getting a sum of 7 when rolling two dice and knowing that at least one of the dice is a 4.
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PLEASEE HELP ASAP!! 50 POINTS!
Select the correct answer. The graph of function f is shown. If g(x) = -2f(x), which graph is the graph of function g?
The graph of function f is shown. If g(x) = -2f(x), which graph is the graph of function g is show on the attachment
What is a graph?Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x). That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).
See the attached image. The table shows how the values of y change for each value of x used in the respective function. Plot those new values to produce the graph.
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find the function whose derivative is f ' ( x ) = x 1 x and that passes through the point ( 1 , 3 ) .
The function whose derivative is f'(x) = x^(-1) is f(x) = ln(x) + C, where C is the constant that needs to be found.
To find C, we can use the point (1, 3). Plugging x = 1 and y = 3 into the equation f(x) = ln(x) + C, we get 3 = ln(1) + C, so C = 3 - ln(1). Therefore, the function is f(x) = ln(x) + 3 - ln(1). This can also be written as f(x) = ln(x) + 2.
The function whose derivative is f'(x) = x1/x is given by f(x) = ln|x| + c, where c is a constant. To find the constant c, we can use the point (1, 3). We know that if a function passes through the point (1, 3), then f(1) = 3. Therefore, we can substitute x = 1 into f(x) to find c.
This gives us ln|1| + c = 3, or c = 3. Therefore, the function that satisfies the given conditions is f(x) = ln|x| + 3. We can check this by taking the derivative of f(x):
To calculate the value of f(x), we can substitute the value of x into th equation. For example, to find the value o f(4), we would calculate f(4) = ln(4) + 2 = 1.38629 + 2 = 3.38629.
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The resistance y (in ohms) of 1000 feet of solid copper wire at 68 degrees Fahrenheit can be approximated by the modely=10, 770/x²-0.37 , 5<=x<=100where x is the diameter of the wire in mils (0.001 inches).(a) Complete the table.x5102030405060708090100y(b) Use the table of values in part (a) to sketch a graph of the model. Then use the graph to estimate the resistance when x=85.5�=85.5.(c) Use the model to confirm algebraically the estimate you found in part (b).
The graph of the model is illustrated below and the resistance when x = 85 is 1.12
The resistance of a conductor (such as a wire) is a measure of the opposition it presents to the flow of electric current. The resistance of a wire is dependent on various factors such as its length, cross-sectional area, and material. In this case, we are looking at the resistance of 1000 feet of solid copper wire, where the diameter of the wire is given in mils (0.001 inches).
The resistance of the wire can be approximated using the mathematical model:
=> y = 10,770/x² - 0.375,
where x is the diameter of the wire in mils and y is the resistance in ohms. The model is valid for values of x ranging from 5 to 100.
To complete the table, you need to plug in different values of x into the model and solve for y. For example, when x = 10,
=> y = 10,770/(10²) - 0.375 = 106.975 ohms.
The graph of the model can then be plotted by plotting the points (x,y) from the table and connecting them with a smooth curve. The graph can be used to estimate the resistance of the wire when x = 85.5 mils by finding the y-coordinate of the corresponding point on the graph.
Finally, you can use the model to algebraically confirm the estimate you found from the graph by plugging in the value x = 85.5 into the model and solving for y then we get the value as 1.12. This should give you the same answer as you found from the graph.
In conclusion, the resistance of a wire can be estimated using the mathematical model and can be used to make predictions about the resistance for different wire diameters.
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convert the following decimal numbers to binary: 187,891,2014, and 20486.
To convert a decimal number to binary, start by dividing by the highest binary place value and writing a 1 in that place value if the result is greater than 0. the converted values is 10111011, 10111011 , 10110101 , 11011101.
187:
Start with the binary place values equal to or less than the number: 128, 64, 32, 16, 8, 4, 2, 1.
Begin with the highest place value of 128 and subtract from 187. 187 - 128 = 59.
Since 59 is greater than 0, a 1 is placed in the 128 place value.
Next, subtract the next binary place value, 64, from 59. 59 - 64 = -5.
Since -5 is less than 0, a 0 is placed in the 64 place value.
Continue this process until all of the place values are filled.
The binary number for 187 is 10111011.
891:
Start with the binary place values equal to or less than the number: 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.
Begin with the highest place value of 512 and subtract from 891. 891 - 512 = 379.
Since 379 is greater than 0, a 1 is placed in the 512 place value.
Next, subtract the next binary place value, 256, from 379. 379 - 256 = 123.
Since 123 is greater than 0, a 1 is placed in the 256 place value.
Continue this process until all of the place values are filled.
The binary number for 891 is 1110100011.
2014:
Start with the binary place values equal to or less than the number: 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.
Begin with the highest place value of 1024 and subtract from 2014. 2014 - 1024 = 990.
Since 990 is greater than 0, a 1 is placed in the 1024 place value.
Next, subtract the next binary place value, 512, from 990. 990 - 512 = 478.
Since 478 is greater than 0, a 1 is placed in the 512 place value.
Continue this process until all of the place values are filled.
The binary number for 2014 is 10111011.
20486:
Start with the binary place values equal to or less than the number: 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.
Begin with the highest place value of 16384 and subtract from 20486. 20486 - 16384 = 4102.
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henry walks to and from school each day after 100 daqys of school he has walked 125 miles how many miles does henry walk to and from school each day
Answer: 0.8 miles
Step-by-step explanation:
which situation abiut samfs money could be described of using the sum of 2,5
Sam owes his dad $12.50 represents the correct situation.
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 are the situations about Sam's money that could be described using the sum of -2.5 and -10.
The sum of - 2.5 and -10 is :
{x} = - 2.5 + (- 10) = - 12.5
{x} = - 12.5
Sam owes his dad $12.50 represents the correct situation.
Therefore, Sam owes his dad $12.50 represents the correct situation.
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{Complete question -
Which situation about Sam's money could be described using the sum of -2.5 and -10?
A. Sam owes his dad $12.50
B. Sam earned $12.50
C. Sam owes his dad $7.50
D. Sam earned $7.50}
what is the value of X in the equation x + 5 = 4z - 1?
Answer:
150000
Step-by-step explanation:
Slope=0.500/2.000=0.250
-6/1 = 6.00000
6/4 = 3/2 = 150000
DJ Ralph charges a $60 event fee plus $20 per hour. DJ Felicia charges an $80 event fee plus $15 per hour.
Which equation can be used to determine the number of hours for both DJ's charges to be equal to each other.
A
60h+20=80h+15
B
20h+60=15h+80
C
60h=20h+80
D
20h=15h+80
An equation which can be used to determine the number of hours for both DJ's charges to be equal to each other is: B. 20h + 60 = 15h + 80.
How to write the required equations?In order to write an equation that model this situation, we would assign variables to the cost charged by DJ Ralph and DJ Felicia, and the number of hours respectively, and then translate the word problem into algebraic equation as follows:
Let the variable T represent the cost charged by DJ Ralph and DJ Felicia.Let the variable h represent the number of hours.Since DJ Ralph charged a $60 event fee plus $20 per hour while DJ Felicia charges an $80 event fee plus $15 per hour, a system of equations that models their charges is given by:
T = 20h + 60 ..............equation 1.
T = 15h + 80 ..............equation 2.
By equating the system of equations, we have:
20h + 60 = 15h + 80
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Penelope is playing a number game with her sister June. Penelope is
thinking of a number and wants June to guess it. Five more than three
times her number is between -1 and 35. Write a compound inequality
that shows the range of numbers that Penelope might be thinking of.
This compound inequality is the range of numbers that Penelope might be thinking of;
Compound inequalities are inequalities that have been joined by the words “and” or “or.” For example: − 2 < x ≤ 5 Read, “ is greater than -2 and less than or equal to 5.” x ≥ 3 or Read, “ is greater than or equal to 3 or less than -4.” Notice that both of these inequalities have two inequality signs.
3x + 5 > -1 and 3x + 5 < 35
This compound inequality is the range of numbers that Penelope might be thinking of; the first inequality shows that the number must be greater than -1, and the second inequality shows that the number must be less than 35.
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PLEASE HELP
When rotated about it’s center, a regular heptagon has _ rotational symmetries. In addition to rotational symmetry, a regular heptagon has _ lines of reflectional symmetry.
When rotated about it’s center, a regular heptagon has 5 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 7 lines of reflectional symmetry.
What is rotational symmetry?The number of times an object is precisely the same as the original object during a full 360° revolution is known as rotational symmetry, a sort of symmetry. It can be found in various geometrical objects as rhombuses, squares,
A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.
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How many 2in x 2in quare tile will fit along the edge of a quare moaic that ha an area of 196in2
The number of tiles that will fit along the edge of the square mosaic is 28 tiles.
The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.
To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:
sqrt(196) = 14
So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.
Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.
Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.
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The number of tiles that will fit along the edge of the square mosaic is 28 tiles.
The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.
To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:
sqrt(196) = 14
So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.
Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.
Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.
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A bottle of juice initially has a temperature of 85degreeF. It is left to cool in a refrigerator that has a temperature of 36 degreeF. After 10 minutes the temperature of the juice is 56degreeF. a. Use Newton's Law of Cooling, T-C + (T_0 - C)e^kt, to find a model for the temperature of the juice, T, after t minutes. T = C + (T_1 - C)e^kt T = 36 + (49)e t leftarrow Solve for k and enter the answer (Round to four decimal places.) b. What is the temperature of the juice after 15 minutes? T= degreeF (Type an integer. Round to nearest degree.) c. When will the temperature of the juice be 51 degreeF? f= minutes (Type an integer. Round to nearest minute.)
A: The model for the temperature of the juice is:
T = 36 + (85 - 36)e^(-0.2659t)
B: Rounding to the nearest degree, we have:
T = 51 degreeF
C: The temperature of the juice will be 51 degreeF after 20 minutes.
What is temperature ?
Temperature is a measure of the average thermal energy of the particles in a substance or system. It is an intensive property, meaning that it does not depend on the amount of matter in the system. The unit of temperature in the International System of Units (SI) is the kelvin (K).
a. To find the value of k in the model, we can use the initial temperature and time given in the problem: T = 56 degreeF, t = 10 minutes. Plugging these values into the equation, we get:
56 = 36 + (85 - 36)e^(10k)
20 = 49e^(10k)
ln(20/49) = 10k
Solving for k, we get:
k = ln(20/49) / 10
Rounding to four decimal places, we have:
k = -0.2659
Hence, the model for the temperature of the juice is:
T = 36 + (85 - 36)e^(-0.2659t)
b. To find the temperature of the juice after 15 minutes, we plug in t = 15 into the model:
T = 36 + (85 - 36)e^(-0.2659 * 15)
Rounding to the nearest degree, we have:
T = 51 degreeF
c. To find when the temperature of the juice will be 51 degreeF, we solve for t in the model:
51 = 36 + (85 - 36)e^(-0.2659t)
15 = 49e^(-0.2659t)
ln(15/49) = -0.2659t
Solving for t, we get:
t = ln(15/49) / -0.2659
Rounding to the nearest minute, we have:
t = 20 minutes
Hence, the temperature of the juice will be 51 degreeF after 20 minutes.
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In the graph, ADEF = AD'E'F'
What is the coordinate rule that maps ADEF
onto AD'E'F"?
(x,y) → (
The ΔDEF is mapped onto ΔD'E'F' by translation and rotation rules of triangle.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
As the figure is rotated by 90 degree and translated by moving from 2nd and 3rd quadrant to 1st and end quadrant.
Hence,
The ΔDEF is mapped onto ΔD'E'F' by translation and rotation rules of triangle.
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determine whether ⃗b is in the column space of a, and state whether the system ax=b is consistent
The system Ax = b is consistent, we use matrix multiplication and the Gauss Jordan Elimination method.
Given a matrix A, and a vector b, we can determine whether b is in the column space of A by performing a matrix multiplication. The column space of A is the set of all linear combinations of the columns of A. We can represent this set by multiplying A by a vector x, such that Ax = b. If the result of the matrix multiplication yields b, then b is in the column space of A.
We can determine whether the system Ax = b is consistent by evaluating the rank of A and the rank of the augmented matrix, [A|b]. If the rank of A is equal to the rank of [A|b], then the system is consistent. To determine the rank of A, we can use the Gauss Jordan Elimination method to find the reduced row echelon form of A and then count the number of non-zero rows.
In summary, to determine whether b is in the column space of A, and whether the system Ax = b is consistent, we use matrix multiplication and the Gauss Jordan Elimination method.
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