one day jasmine earned 25.20 for earned 6 hours of work another day she earned 16.80 fir 4 hours of work witch function shows how much jasmine earns (c) for working (h) hours
c+ h = -4.20 (hours) + 49.20 shows how much jasmine earns (c) for working (h) hours
Let's assume that Jasmine earns at a constant rate per hour of work. We can use the formula for the equation of a line, y = mₓ + b, where y represents the amount of money earned, x represents the number of hours worked, m represents the rate of earnings per hour, and b represents the y-intercept or the amount of money earned without working. We can use the two points given in the problem to find the slope, m, of the line:
m = (y₂ - y₁) / (x₂ - x₁)
m = (16.80 - 25.20) / (4 - 6)
m = -4.20
Now that we know the slope, we can use either point and the slope to find the y-intercept, b:
y = mₓ + b
25.20 = -4.20 × (6) + b
b = 49.20
Therefore, the equation that represents Jasmine's earnings is:
c + h = -4.20 hours + 49.20
This function shows how much Jasmine earns, c, for working h hours.
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Tina went to the store four gallons of orange juice for a party the store only sold orange juice in pint cartons.How many pint cartons does tine need to buy?
A gallοn cοntains 8 pints, sο fοur gallοns οf οrange juice equals 32 pints. equatiοn Tina wοuld therefοre need tο purchase 32 pint cartοns οf οrange juice fοr the party.
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn "x²+ 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in many different areas οf mathematics, such as algebra, calculus, and geοmetry.
A gallοn cοntains 8 pints, sο fοur gallοns οf οrange juice equals 32 pints. Tina wοuld therefοre need tο purchase 32 pint cartοns οf οrange juice fοr the party.
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4)how to find the value of angle PQR
Answer:
please make me brainalist and keep smiling dude I hope you will be satisfied with my answer is updated
Step-by-step explanation:
now we have QPR = 75°now we have QPR = 75°and also we know.now we have QPR = 75°and also we know.QRP + QPR + PQR = 180°now we have QPR = 75°and also we know.QRP + QPR + PQR = 180°75° + 75° + PQR = 180°now we have QPR = 75°and also we know.QRP + QPR + PQR = 180°75° + 75° + PQR = 180°150° + PQR = 180°now we have QPR = 75°and also we know.QRP + QPR + PQR = 180°75° + 75° + PQR = 180°150° + PQR = 180°PQR = 180° - 150°now we have QPR = 75°and also we know.QRP + QPR + PQR = 180°75° + 75° + PQR = 180°150° + PQR = 180°PQR = 180° - 150°PQR = 30°there are six professors teaching the introductory discrete structure class at fiu. the same fnal exam is given by all six professors. if the lowest possible score on the fnal is 0 and the highest possible score is 100, how many students must there be to guaranteethat there are two students with the same professor who earned the same fnal examination score?
607 students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score
We use Pigenhole principle to solve this problem.
We know the Pigenjole principle states that if y number of items are put into z number of containers, with y > z, then it means that that at least one container must definitely contain more than one item.
Here, the possible scores are from 0 to 100 with both inclusive.
So, the number of possible scores = 101.
Now, there are two students with the same professor who earned the same final examination score.
The number of students would be = 101 + 1
= 102
For each student there are 6 professors.
so the possible combination for a score would be = 6
So, the number of students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score: (6 × 101) + 1 = 607
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What is the value of f?
Answer:
f = 120
Step-by-step explanation:
1. The Entire line in which the angles rest on = 180 degrees.
2. 180-60 = 120
3. 120 Degrees is your answer
according to A1 Jazeera approximately what percentage of deaths were civilians as of September 2015
According to Al-Jaz/eera, approximately, 90% of deaths were civilians as of September 2015 in Syria.
What caused the Civilian death in Syria in 2015?The Syrian conflict, which began in 2011, has resulted in widespread violence and civilian casualties. In 2015, the primary causes of civilian deaths were airstrikes and shelling by the Syrian government and its allies including Russia against rebel-held areas.
These attacks often targeted hospitals, schools, and residential areas, causing significant collateral damage and loss of life. In addition, various rebel groups also carried out attacks on civilians, including sui/cide bombings and shelling of government-controlled areas. The conflict has also led to displacement, with millions of Syrians forced to flee their homes and seek refuge in neighboring countries.
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A survey showed that 45% of a travel company's customers were planning an overseas vacation
the following year. Predict how many of the travel company's 13,400 travelers will vacation overseas
the following year.
Answer: 6030 travelers
Step-by-step explanation:
= .45(13,400)
= 6030
what is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%
We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:
standard error of the mean = standard deviation / √(sample size)
In this case, the standard error of the mean is:
standard error of the mean = 10 / √(6) = 4.08
To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.
The z-score is given by:
z-score = (sample mean - population mean) / standard error of the mean
In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:
z-score = (51 - 42) / 4.08 = 2.21
Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.
This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.
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Complete Question:
A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.
What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
Suppose you are working with a data set that is normally distributed, with a mean of 250 and a standard deviation of 44. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places, e. G. 1. 25. ) (a) 70% of the values are greater than x. (b) x is less than 14% of the values. (c) 22% of the values are less than x. (d) x is greater than 57% of the values
(a) 70% of the values are greater than x: x = 233.43
(b) x is less than 14% of the values: x = 313.32
(c) 22% of the values are less than x: x = 287.09
(d) x is greater than 57% of the values: x = 259.26
(a) To calculate x, we need to find the z-score of the 70th percentile. This can be done using the z-score formula: z = (x-mean)/standard deviation. Plugging in our values, this gives us z = (x-250)/44. Solving for x, we get x = 250 + 44z. We can find z by using a z-score table and looking up the 70th percentile, which is 0.84. Plugging this into our equation yields x = 233.43.
(b) Similarly, for x to be less than 14% of the values, we need to find the z-score of the 14th percentile. Looking up the corresponding z-score in a z-score table, we find it to be -0.91. Plugging this into our equation gives us x = 313.32.
(c) To calculate x given that 22% of the values are less than x, we can again use the z-score formula. This time, we need to look up the z-score corresponding to the 22nd percentile, which is -0.52. Plugging this into our equation yields x = 287.09.
(d) Lastly, to calculate x given that it is greater than 57% of the values, we need to find the z-score of the 57th percentile. Looking up the corresponding z-score in a z-score table, we find it to be 0.41. Plugging this into our equation gives us x = 259.26.
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0.81 x 9.4 work sown
Suppose there is a 70% chance that Reagan will make a field goal at any given time. A computer was used to generate 10 sets of random numbers from 1 to 10, 1-7 represent a successful field goal and numbers 8-10 represent a missed field goal. The results are shown. Trial 1 2 3 4 5 6 7 8 9 10 Numbers Generated 1, 9, 1, 2, 10, 6, 5, 2, 7,2 8, 10, 4, 10, 2, 2, 3, 6, 7, 10 6, 9, 9, 10, 4, 10, 10, 2, 6, 6 8 & 2, 3, 4, 6, 5, 6, 5, 3 1, 10, 1, 2, 5, 6, 9, 4, 10, 3 7, 1, 9, 1, 6, 3, 3, 7, 5, 6 2, 5, 2, 7, 5, 5, 10, 5, 6, 3 9, 6, 10, 4, 9, 6, 8, 9, 9,9 5, 1, 4, 5, 2, 8, 5, 7, 5, 6 7, 6, 5, 5, 1, 10, 9, 3, 9, 2 Find the experimental probability that Reagan will miss the first two field goals and make the third one.
The experimental probability that Reagan will miss the first two field goals and make the third one is 20%
What is experimental probability?Experimental is the probability is the probability of an event occurring based on the performance of actual experiment.
The probability of making or missing a field goal is 0.7 and 0.3 respectively. The probability that Reagan will miss the first two field goals and make the third one, can be obtained from the result by counting the number of times the specific sequence of results occurs in the 10 sets of random numbers and divide by the total number of trials.
The analysis of the sets of numbers indicates that the specific sequence of missing the first two field goals and making the third one occurs twice in 2nd and 4th trials
2; 8, 10, 4, 10, 2, 2, 3, 6, 7, 10
4; 8, 8, 2, 3, 4, 6, 5, 6, 5, 3
Therefore, the experimental probability of the specific sequence occurring is 2/10 = 1/5 (since there are 10 sets of numbers in total)
Theoretically, the probability of making and missing field goals for the three kicks in the sequence are;
0.3 × 0.3 × 0.7 = 0.063
Therefore, the experimental probability of Reagan missing the first two field goals and making the third one is approximately 0.2 (or 20%), while the theoretical probability is 0.063 (or 6.3%)
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Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a 98% confidence level. What does the confidence interval tell about the population of all college students in the state?
3.9, 2.9, 3.9, 4.8, 3.0, 4.2, 3.4, 4.5, 4.5, 4.2, 4.3, 3.9, 3.3, 3.9, 3.7
Answer:
The 98% confidence interval for this data is (3.5, 4.4). This confidence interval tells us that 98% of the time, the average rating of all college students in the state for the course will fall between 3.5 and 4.4.
a wheel whose diameter is 3 feet rolls a distance of 45 feet without slipping. through what radian angle did the wheel rotate?
The wheel having 3feet diameter and travelling a distance of 45 feet is rotated about 30.00 radians.
A circle's circumference is equivalent to π times its diameter.
We can use the circumference formula to determine the circumference of the wheel
C = πd= π(3) = 9.42 feet where d is the diameter.
The wheel has traveled a distance of 45 feet.
We can determine the number of full rotations made by dividing the distance traveled by the circumference of the wheel.
Number of full rotations = distance traveled / circumference of the wheel= 45 / 9.42 = 4.77 full rotations
It is said that the wheel rolled without slipping, therefore the wheel must have turned 4.77 full rotations. The angle in radians through which it rotated is therefore
Angle in radians = number of full rotations x 2π= 4.77 x 2π= 30.00 radians
Therefore, the wheel rotated through a radian angle of 30.00.
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I need help because this is due in 2 hours and 21 minutes
Answer:
Step-by-step explanation:
Sorry it is a bit rushed
'Number of Boards Purchased' is the independant variable quantity. It can be chosen to be any number you want and does not depend on anything else.
The 'number of reward points' is the dependant variable quantity because it is determined based on the 'Number of Boards Purchased'. That is, it depends on the 'Number of Boards Purchased'.
Which can be use to show a decrease in the amount of yogurt in a container?
A. 1/6 B. 1/5 C. Negative 1/3 D. 1/8
The correct answer is option C, Negative 1/3, which means that the container has lost 1/3 of its original yogurt.
When it comes to representing a decrease in the amount of something, the easiest way is to use negative values.
In this case, option C, Negative 1/3 is the correct choice.
The fraction 1/6 means that the container has 1 part of the original 6 parts of the yogurt left.
However, this shows the remaining amount of yogurt in the container, not the decrease.
Therefore, we can say that the fraction 1/6 is not the correct choice in this context.
Similarly, options B and D are not correct choices for the same reason.
The correct answer is option C, Negative 1/3, which means that the container has lost 1/3 of its original yogurt.
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Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
one over 26
four over 25
one fourth
8 over 13
The experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.
What is the prοbability?The study οf prοbability examines the likelihοοds οf results οccurring and is based οn the ratiο οf likely and imprοbable scenariοs.
Tο find the experimental prοbability οf drawing a K οr 6, we need tο add the frequencies οf card K and card 6 and divide by the tοtal number οf draws:
Frequency οf K οr 6 = 7 + 6 = 13
Tοtal number οf draws = 4 + 7 + 5 + 6 + 7 + 6 + 8 + 10 + 7 + 10 + 8 + 12 + 10 = 100
Experimental prοbability οf drawing a K οr 6 = Frequency οf K οr 6 / Tοtal number οf draws = 13 / 100
Hence, the experimental prοbability that the card selected was a K οr 6 is 13/100, which is equivalent tο 0.13 οr 13%.
Answer: 8 οver 13 is the clοsest οptiοn tο 13/100, sο the answer is 8 οver 13.
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!! URGENT !! The following data points represent the number of points the Hawaii Eagles football team scored each game.
17
,
33
,
28
,
23
,
10
,
42
,
3
17,33,28,23,10,42,317, comma, 33, comma, 28, comma, 23, comma, 10, comma, 42, comma, 3
Using the data, create a histogram.
Answer:
See image.
Step-by-step explanation:
Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.
3 and 10 fall in 0-15, so thats 2 values
17, 23, and 28 fall in 15-30, so thats 3 values,
33 and 42 fall in 30-45, so thats 2 values.
The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible. The U.S. Naval Observatory lists the following dates for phases of the Moon in the year 2008. Date Moon Phase x: Days since Jan. 8 y: The Amount of Moon Visible Jan 8 New 0 0 Jan 15 1st quarter 7 0.5 Jan 22 Full 13 1 Jan 30 Last quarter 22 0.5 Feb 7 New 30 0 Feb 14 1st quarter 37 0.5 Feb 21 Full 44 1 Feb 29 Last quarter 52 0.5 Mar 7 New 59 0 Mar 14 1st quarter 66 0.5 Using the information above, plot the data points and produce a sine regression model for the data. Round a, b, c, and d to the nearest 0.001. a. y = 0.508 sine (0.212 x + 1.529) minus 0.512 b. y = 0.508 sine (0.212 x minus 1.529) + 0.512 c. y = 0.508 sine (0.212 x minus 1.529 + 0.512) d. y = 0.512 sine (1.529 x minus 0.212) + 0.508
The correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.
What is regression?Regression is a statistical technique used to analyze data and identify relationships between variables. It is used to predict the value of a dependent variable based on one or more independent variables. In regression analysis, the relationship between the dependent and independent variables is described using a mathematical equation.
This sine regression model is based on the data given in the question. The model is in the form y = a* sin(bx + c) + d.
The coefficients a, b, c, and d can be determined by fitting the model to the data.
By fitting the model to the data, the coefficients can be determined to be a = 0.508, b = 0.212, c = 1.529, and d = -0.512.
Therefore, the correct sine regression model for the data is y = 0.508 sine (0.212 x + 1.529) minus 0.512.
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Solve for c. law of cosines
Answer:
5.06
Step-by-step explanation:
Math I guess
:)
pls helpp WITCH TYPES OF ANGLES ARE IN EACH OF THEESE QUADRILLETARLIS
Answer:
Acute and Obtuse
Step-by-step explanation:
Can someone please help me with this question
The line of best fits that predicts the maximum temperature at this resort is the line that cuts across 2, 3, 5, 6, and 8 hours at 22°C.
The reliability of this estimate is the fact that the line of best fit goes through five data points.
What describes a line of best fits?A line of best fit is a straight line that is used to represent the general trend of a scatter plot of data points. It is also called a regression line. The line of best fit is usually determined using a mathematical method called linear regression, which minimizes the distance between the line and the data points.
The line of best fit can be used to make predictions about data that is not yet collected or to make estimates about the relationship between the variables represented in the scatter plot.
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Image transcribed:
This scatter graph shows the daily hours of sunshine and the daily maximum temperature at 10 seaside resorts in England one day last summer.
(a) Another resort had 10 hours of sunshine each day. Use a line of best fit to predict the maximum temperature at this resort.
(2 marks)
(b) Comment on the reliability of your estimate.
(1 mark)
((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 = Answer
On simplifying the given equation ((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 by PEMDAS, we get 6.087 as the answer.
The order of operations that must be followed in order to solve this statement is known as the PEMDAS acronym (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79
(11.5776) + (23.6928 ) ÷ 5. 79
35.2704 ÷ 5.79
≈ 6.087
Therefore, the answer for ((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 ≈ 6.087
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
Step-by-step explanation:
Patel could use the Quadratic Formula to solve it
or
he could 'complete the square' to solve it after dividing thru by 8 or he could solve it graphically
{ or he could use factoring to solve it (difficult) }
thirty-two percent of adults did not visit their physicians' offices last year. the probability, rounded to four decimal places, that in a random sample of 8 adults, exactly 3 will say they did not visit their physicians' offices last year is:
The probability that in a random sample of 7 adults, exactly 2 will say they did not visit their physicians' offices last year is 0.287
This problem can be solved using the binomial distribution, which models the number of successes in a fixed number of independent trials with the same probability of success.
Let's define the following
n = 7 (the number of trials, i.e. the number of adults in the random sample)
p = 0.32 (the probability of success, i.e. the proportion of adults who did not visit their physicians' offices last year)
x = 2 (the number of successes we want to calculate the probability for)
The probability of exactly 2 successes in a binomial distribution is given by the formula
P(X = x) = nCx × p^x × (1-p)^(n-x)
where nCx is the number of ways to choose x items from a set of n items, and is given by the formula
nCx = n! / (x! × (n-x)!)
Plugging in the values, we get
nCx = 7! / (2! × 5!) = 21
P(X = 2) = 21 × 0.32^2 × (1-0.32)^(7-2) = 0.287
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The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
the vertex of the quadratic function is (7.5, 3.675).
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
Mrs. Latham ordered 200 SCVCS business cards and paid $23. She ordered 500 business cards a few moths later and paid $35. Write and solve a linear equation to find out how much Mrs. Latham will spend if she orders 700 business cards.
Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.
Define about the linear equation?In a linear equation, a first-degree polynomial is defined as the sum of a group of terms, where each term is the product of a constant as well as the initial power of a variable.
The linear equation using the slope intercept form is -
Y = mX + b,
where, Y - number of cards
X is the cost. m - slope of the line b = the y-intercept (0, b).Slope = (y2 - y1)/(x2 - x1),
y2=500 cards, y1=200 cards, x2=$35, and x1=$23.
m = (500-200)/(35-23) = 300/12
m = 25.
Now, slope m = 25, apply slope-intercept formula to find y when x=0.
Y = mX + b,
25 = (200 - y)/(23-x),
At, x=0,
25 = (200-y)/23
200 - y = 25*23
575 = 200 - y
y = -375 (y - intercept)
The linear equation :
Y = 25X -375.
Y = 700. Find X
700 = 25X - 375
25X = 325
X = $43
Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.
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How do I solve this problem?
QR has a length of 2√3. According to the given question
HOW TO CALCULATE THE SIDE OF THE SQUARE ?
In order to solve for QR, we need to use the information given to us in the problem and apply some basic geometry concepts.
First, we know that the diagonals of a square are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other in half. This tells us that the length of the diagonal is equal to the square root of two times the length of one of the sides of the square, or d = s√2.
Next, we are given that the midpoint of one of the diagonals is point U, and that US has a length of 3. Because U is the midpoint of the diagonal, we know that SU and UR are equal in length. Let's call this length x.
Now we can use the Pythagorean theorem to solve for x:
(US)²+ (UR)² = (SR)²
3²+ x= (s√2)²
9 + x² = 2s²
We also know that SU and UR are each equal to x, so:
2x² = s²
We can substitute 2x² for s² in the previous equation:
9 + x² = 2(2x²)
9 + x²= 4x²
3x² = 9
x² = 3
x = √3
Now we can use x to solve for the length of QR:
QR = 2x = 2√3
Therefore, QR has a length of 2√3.
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M is the midpoint of line AB and N divides the line BC in the ratio 1:3 ,given that vector AM=a and vector AC=C
(a) express vector AN in terms of a and c
(b) Show that vector NM=¼(2a-3c)
Vector AN = a + ¾ c and we have shown that vector NM = ¼(2a – 3c) where M is the midpoint of line AB and N divides the line BC in the ratio 1:3 .
(a) To express vector AN in terms of a and c, we need to find the vector from A to N. Since N divides BC in the ratio 1:3, we can write:
BN = 3NC
Since M is the midpoint of AB, we have:
AM = MB
Adding these two equations, we get:
AM + BN = MB + 3NC
Substituting the vectors, we get:
a + BN = ½ (a + b + 2c) + 3c
Simplifying, we get:
BN = ½ (b – a) + 2c
But b = 2a – c (since M is the midpoint of AB)
So, we can write:
BN = ½ (2a – 2a + c) + 2c = ¾ c
Therefore, vector AN = vector AB + vector BN = (b – a) + ¾ c
Substituting b = 2a – c, we get:
Vector AN = a + ¾ c
(b) To show that vector NM = ¼(2a – 3c), we need to find vector NM and simplify it. Since M is the midpoint of AB, we have:
Vector NM = vector NC – vector MC
We know that N divides BC in the ratio 1:3, so we can write:
Vector NC = 3/4 vector BC = 3/4 (vector AB + vector AC)
Since M is the midpoint of AB, we have:
Vector MC = 1/2 vector AB
Substituting these vectors, we get:
Vector NM = 3/4 (vector AB + vector AC) – 1/2 vector AB
Simplifying, we get:
Vector NM = 1/4 vector AB + 3/4 vector AC
But AB = 2a – c (since M is the midpoint of AB)
Substituting, we get:
Vector NM = 1/4 (2a – c) + 3/4 c
Simplifying, we get:
Vector NM = ½ a – 3/4 c
Multiplying by 2, we get:
Vector NM = 2/2 (½ a) – 3/4 c
Simplifying, we get:
Vector NM = ¼ (2a – 3c)
Therefore, we have shown that vector NM = ¼(2a – 3c).
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Cameron wants to buy a coat that costs $220. He has to pay 10% taxes on it.How much will he pay for the coat, including taxes
Cameron will have to pay amount $242 for the coat, including taxes.
If the coat costs amount $220 and there is a 10% tax on it, Cameron will have to pay an additional:
10% of $220 = 0.1 x $220 = $22
So the total cost of the coat including taxes will be:
$220 + $22 = $242
Therefore, Cameron will have to pay $242 for the coat, including taxes.
When purchasing goods or services, it's important to be aware of any additional costs such as taxes. In this scenario, Cameron wants to buy a coat that costs $220. However, there is a 10% tax on it, which means he will have to pay an extra $22 in taxes. The total cost of the coat, including taxes, will be $242. It's important to note that tax rates may vary depending on the location and type of item being purchased. Being aware of these additional costs can help individuals better budget and make informed purchasing decisions.
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in a different experiment,a liquid must be cooled 6 times as fast as the liquid in the example but it must still start at 0.c degrees
Answer:
Assuming that the previous example involved cooling the liquid from a certain temperature to 0°C, one way to cool the liquid 6 times as fast while starting at 0°C is to reduce the temperature of the cooling medium by a factor of 6.
For example, if the previous example involved cooling the liquid from 20°C to 0°C using a cooling medium at -10°C, and the cooling rate was not limited by the heat transfer coefficient or other factors, then one way to cool the liquid 6 times as fast while starting at 0°C is to use a cooling medium at -60°C. This would increase the temperature difference between the liquid and the cooling medium by a factor of 6, and hence increase the rate of heat transfer by the same factor.
However, it is important to note that the cooling rate of a liquid depends on many factors, such as the thermal conductivity of the liquid and the container, the surface area of the container, the volume of the liquid, and the cooling mechanism used. Therefore, other factors may need to be taken into account to achieve the desired cooling rate while maintaining the starting temperature of 0°C.