The 45th term of the sequence is 267.
The 45th term of a sequence can be calculated using the formula:
Tn = a + (n – 1)d
Where,
Tn = the nth term
a = the first term
n = the term position
d = the common difference
In this sequence, the first term is 3, the common difference is 6, and the term position is 45.
Therefore, the 45th term of the sequence is:
T45 = 3 + (45 – 1)6
T45 = 3 + (44)6
T45 = 3 + 264
T45 = 267
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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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Find the sum of (8a +2b - 4 ) and ( 3b - 5)
The sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9). We can find it in the following manner.
To find the sum of (8a + 2b - 4) and (3b - 5), we can simply add the corresponding coefficients of the variables a and b, as well as any constant terms.
So we have:
(8a + 2b - 4) + (3b - 5)
= 8a + 2b + 3b - 4 - 5 (grouping like terms)
= 8a + 5b - 9
Therefore, the sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9).
We can also explain this process by using the distributive property of addition over subtraction. This property states that the sum of two numbers with the same sign (positive or negative) can be found by adding their absolute values and keeping the common sign.
In this case, we can think of the expression (8a + 2b - 4) as the sum of three terms: 8a, 2b, and -4. Similarly, we can think of the expression (3b - 5) as the sum of two terms: 3b and -5.
Using the distributive property, we can add the terms with the same variable together:
(8a + 2b - 4) + (3b - 5)
= 8a + (2b + 3b) - (4 + 5)
= 8a + 5b - 9
Thus, we obtain the same result.
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PLS HELP IT IS DUE TODAY
Therefore, the equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point (4, 5) is y = 2x - 3.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. An equation is usually written with an equal sign (=) between the two expressions. Equations are used to represent mathematical relationships between quantities, to solve problems, and to model real-world situations. They can be used to find unknown values, to predict outcomes, and to test hypotheses. There are many types of equations, including linear equations, quadratic equations, polynomial equations, trigonometric equations, and differential equations. Each type of equation has its own rules and methods for solving it.
Here,
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given that the y-intercept is (0, -3), so b = -3. To find the slope, we can use the two given points (0, -3) and (4, 5).
slope = (y2 - y1)/(x2 - x1)
= (5 - (-3))/(4 - 0)
= 8/4
= 2
Now that we know the slope and the y-intercept, we can write the equation in slope-intercept form:
y = 2x - 3
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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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WILL GIVE BRAINLIEST, NEED HELP ASAP.
A fisherman on the atchafalaya basin drops a line that lands in the water 1225 ft below, the equation [tex]\frac{d}{25} =t^{2}[/tex] represents the distand in feet, d, the object falls in t seconds. How long does it take to reach the bottom?
Answer:
7 seconds
Step-by-step explanation:
d is 1225, and we need to find t.
plug in 1225 for d:
1225/25 = t^2
49 = t^2
t = 7
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°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) }
Ms. Ibrahim travelled a total of 150 miles for work in 5 days. She traveled the same distance for work each day. Which 3 points lie on the line that represents the total distance in miles y, she traveled for work in x days. Circle three correct points.
Three pοints οn the line are: (0,0), (1,30), and (2,60)
what is slοpe-intercept fοrm?When yοu knοw the slοpe οf the line tο be investigated and the given pοint is alsο the y intercept, yοu can utilise the slοpe intercept fοrmula, y = mx + b. (0, b). The y value οf the y intercept pοint is denοted by the symbοl b in the fοrmula.
Tο sοlve the prοblem, we can start by using the fοrmula fοr the equatiοn οf a line in slοpe-intercept fοrm:
y = mx + b
We can use the given infοrmatiοn tο find the slοpe:
m = tοtal distance / number οf days = 150 miles / 5 days = 30 miles/day
b = 0 miles
Therefοre, the equatiοn οf the line representing the tοtal distance Ms. Ibrahim travels fοr wοrk in x days is:
y = 30x
When x = 0 (i.e., when Ms. Ibrahim dοes nοt wοrk), y = 0.
When x = 1 (i.e., οn the first day), y = 30 miles.
When x = 2 (i.e., οn the secοnd day), y = 60 miles.
Sο, three pοints οn the line are: (0,0), (1,30), and (2,60)
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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?
A circle with center � ( 5 , 2 ) O(5,2) contains the point � ( 11 , 10 ) A(11,10)
The point (11,10) lies on the circle with center (5,2).
The equation of the circle with center (5,2) and point (11,10) is given by [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2.[/tex]
Substitute the coordinates of the center and point in the equation and simplify, we get
[tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= (x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= x^2 - 10x + 25 + y^2 - 4y + 4 = x^2 - 22x + 121 + y^2 - 20y + 100= -10x + 25 - 4y + 4 = -22x + 121 - 20y + 100= -10x - 22x = 121 - 25 - 20y + 4y=-32x = 96= x = 3[/tex]
Substitute this value of x in [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2[/tex] and simplify, we get
[tex](3-5)^2 + (y-2)^2 = (3-11)^2 + (y-10)^2= (-2)^2 + (y-2)^2 = (-8)^2 + (y-10)^2= 4 + y^2 - 4y + 4 = 64 + y^2 - 20y + 100= -4y + 8 = -20y + 96= 16 = 16[/tex]
Hence, the point (11,10) lies on the circle with center (5,2).
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complete question
Explain with formula and calculation how a circle with center (5,2) contains the point (11,10).
19. A piece of wire 44 cm long is cut into two parts.
Each part is bent to form a square. Given that
the total area of the two squares is 65 cm², find the
perimeter of each square.
Answer:28 and 16 cams
Step-by-step explanation: let the two parts be x cms and 44 -x cms.
So side of squares will be x/4 and (44-x)/4 resp
Area will be (x/4)^2 and ((44-x)/4)^2 resp
Equation is(x/4)^2 + ((44-x)/4)^2 = 65
(X-28)(x-16) = 0
X =28 or x = 16 cms
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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A concrete pillar has the shape of a cylinder. It has a diameter of 4 meters and a height of 5 meters. If concrete costs $107 per cubic meter, how much did the concrete cost for the pillar?
For your calculations, do not round any intermediate steps, and use the pi button on a calculator. Round your answer to the nearest cent.
The cost of the concrete used to make the cylinder was approximately $6,776.89.
The problem is asking us to find the cost of the concrete used to make a cylindrical pillar, given its dimensions and the cost per cubic meter of concrete. We first need to calculate the volume of the cylinder using the formula for the volume of a cylinder:
[tex]V=pir^2h[/tex]
where V is the volume, r is the radius, h is the height, and π is the constant pi (approximately 3.14159).
In the problem, the diameter of the cylinder is given as 4 meters, which means the radius is half of that, or 2 meters. The height of the cylinder is given as 5 meters.
Substituting these values into the formula, we get:
[tex]V = \pi r^2h = \pi (2)^2(5) = 20\pi cubic meters[/tex]
Next, we need to find the cost of the concrete used to make the cylinder, given that the cost per cubic meter of concrete is $107. We can do this by multiplying the volume of the cylinder by the cost per cubic meter of concrete:
20π × $107 = $6,776.89
Rounding to the nearest cent, we get that the cost of the concrete used to make the cylinder was approximately $6,776.89.
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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.
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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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'.
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:
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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Assignment: Waves Math Exploration
What is the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m?
Please answer immediately if able to!
200 m/s is the wave speed of a wave that has a frequency .
What do you name a wave?
There are two different types of waves: longitudinal and transverse. Longitudinal waves are similar to those of sound in that they alternate between compressions and rarefactions in a medium, much like transverse waves in that the surface of the medium rises and falls.
The pattern of disruption brought about by the movement of energy through a medium (such as air, water, or any other liquid or solid matter) as it spreads away from the source of the sound is known as a sound wave.
The wave speed (v) of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Mathematically, we can express this as
v = f x λ
Substituting the given values of frequency and wavelength into this formula, we get:
v = 500 Hz x 0.40 m
Multiplying these values, we get:
v = 200 m/s
Therefore, the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m is 200 m/s.
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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 right-angled triangle, what is the side opposite the right angle called?
Answer:
The hypotenuse.
Step-by-step explanation:
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 7
Blue 6
Green 12
Yellow 19
Purple 19
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.
Explanation
Add up the frequencies:
7+6+12+19+19 = 63
Out of those 63 total spins, 6 of them landed on blue.
The empirical (aka experimental) probability of landing on blue is therefore 6/63 = 2/21
Estimate the length of the hypotenuse. y C. 5.7 7 8.1 410
The hypotenuse's length could therefore be between 9.03 and 10.70 units based on these estimates.
Define a right-angled triangle.The term "right triangle" refers to a triangle with an internal angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two limbs of the right angle.
Based on the information provided, it is reasonable to infer that we have a right-angled triangle with two sides that are y and 7, and we need to determine the length of the hypotenuse.
The hypotenuse's square length is equal to the total of the squares of the lengths of the other two sides, according to the Pythagorean theorem.
The result is:
y² + 7² = hypotenuse²
hypotenuse² = y² + 49
we can determine the length of the hypotenuse by assuming that y is somewhere between 5.7 and 8.1.
If y is 5.7, then:
hypotenuse² = 5.7² + 49
hypotenuse² = 81.49
hypotenuse ≈ 9.03
If y is 8.1, then:
hypotenuse² = 8.1² + 49
hypotenuse² = 114.61
hypotenuse ≈ 10.70
So, based on these estimations, the length of the hypotenuse could be around 9.03 or 10.70 units.
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Complete question
Estimate the length of the hypotenuse, If the length of the two sides is y and 7 respectively
1) If y= 5.7
2) If y= 8.1
Using identities evaluate :78x82
Answer:
6436
Step-by-step explanation:
78 x 82
= (80-2) * (80+2)
= (80^2 - 2^2)
= 6436
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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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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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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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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The attorney does not accept legal cases involving litigation that would result in less than a $45,000 fee. The attorney has the opportunity to represent a client who will pay him $175 per hour plus 25% of the settlement. What is the minimum acceptable settlement on a case on which the attorney spent 110 hours?
Therefore, the minimum acceptable settlement on the case is $103,000.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100 or 50/100, which is equivalent to the fraction 1/2 or the decimal 0.5.
Percentages are commonly used to express proportions, rates, or changes. They are used in many different fields, such as finance, statistics, science, and everyday life. For instance, we might use percentages to describe the rate of interest on a loan, the percentage of people who have received a vaccine, or the percentage increase or decrease in the stock market.
by the question.
First, we need to calculate the total fee the attorney will earn based on the hourly rate and the percentage of the settlement.
The attorney's fee is the sum of the hourly fee and the percentage of the settlement:
hourly fee = 110 hours x $175 per hour = $19,250
percentage of the settlement = 25% of the settlement
total fee = hourly fee + percentage of the settlement
We know that the total fee must be greater than or equal to $45,000, so we can set up an equation to solve for the minimum acceptable settlement:
$19,250 + 0.25S ≥ $45,000
where S is the settlement amount.
Subtracting $19,250 from both sides, we get:
0.25S ≥ $25,750
Dividing both sides by 0.25, we get:
S ≥ $103,000
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