x and y are both differentiable functions of t and find the required values of [tex]dy/dt[/tex] and Given that [tex]x2+y2=100[/tex] and that [tex]dx/dt = 4[/tex] and [tex]dy/dt = -2[/tex], So the required values of [tex]dy/dt[/tex] and [tex]dx/dt.[/tex] are y = 8 and x = 8.
We can explain that x and y are both differentiable functions of t is,
a) To find [tex]dy/dt[/tex]when x=6 and y=8, we first solve the equation for y:
[tex]y2 = 100-x2[/tex]
[tex]y2 = 100-62[/tex]
[tex]y2 = 100-36[/tex]
y = √(100-36)
y = √64
y = 8
Therefore, [tex]dy/dt = 4.[/tex]
Now, for,
b) To find [tex]dx/dt[/tex] when x=8 and y=6, we again solve the equation for x:
[tex]x2 = 100-y2[/tex]
[tex]x2 = 100-62[/tex]
[tex]x2 = 100-36[/tex]
x = √(100-36)
x = √64
x = 8
Therefore, [tex]dx/dt=-2.[/tex]
the required values of [tex]dy/dt[/tex] and [tex]dx/dt[/tex]. with given conditions are y = 8 and x = 8.
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A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3000. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?
The approximate number of miles for a warranty is 41,748.57 miles.
What is Standard Deviation?Standard deviation refers to the distribution's extent of variability or dispersion. It is a measure of how much the data varies from the mean. It is represented by the Greek letter sigma (σ) and is used to calculate the data variability. It is the square root of the variance of a random variable that describes how widely the data points differ from the average value.
What should be the approximate number of miles for a warranty?We have, Mean (μ) = 47,500 miles
Standard deviation (σ) = 3,000 miles
Manufacturer replacement threshold = 10% = 0.1
The number of miles for a warranty would have to be determined if the tire company wanted to replace no more than 10% of the tires.
Suppose x is the number of miles for which a warranty can be offered.
Using the standard normal distribution, we may compute the z-score as follows:
z = (x - μ) / σ
At the 10th percentile of the standard normal distribution, we'll find the z-score. This z-score can be found using the standard normal distribution table or software.
At the 10th percentile, the z-score is -1.28 (from the table).
Now, substitute the given values.
z = (x - μ) / σ
-1.28 = (x - 47,500) / 3,000
Cross-multiplying and solving for x gives us:
x = -1.28 × 3,000 + 47,500x ⇒ 43,660 miles
Therefore, the tire company should offer a warranty for around 43,660 miles (approximated).
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A bank statement is shown. Fill in the gaps to complete the sentence below. This bank statement shows a profit/ loss of £ Description Sales - Monday Staff wages Sales - Tuesday Supplies - office equipment Sales - Wednesday Rent for office space Customer refund Money in £360.00 £295.00 £415.00 Money out £520.00 £70.00 £400.00 £150.00 Please help
The bank statement shows a loss of 70 euros, considering the profit concept.
How to calculate the profit?From the table presented in this problem, the parameters are given as follows:
Money in.Money out.To calculate profit considering money in and money out, you need to subtract the total money out from the total money in.
Hence the formula for calculating profit is given as follows:
Profit = Money In - Money Out
The total money in is given as follows:
Money In = 360 + 295 + 415 = 1070.
The total money out is given as follows:
Money Out = 520 + 70 + 400 + 150 = 1140.
Hence the profit is given as follows:
Profit = Money In - Money Out
Profit = 1070 - 1140
Profit = -70 (negative profit means that it is a loss).
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Jessie is considering a purchase of a $135,000 home at 5. 5%. Under this rate,
her mortgage payment would be $766. 51. If she purchases a point, her new
mortgage payment is $755. 96. How many months would it take her to break-
even on the points purchase?
As per unitary method, the number of months would take her to break - even on the points purchase is 128
To break even on the points purchase, Jessie needs to recoup the cost of the point through the savings in her monthly mortgage payments. In this case, the cost of the point is 1% of the loan amount, which is $1,350.
To calculate the break-even point, we can use the following formula:
Break-even point = Cost of point / Monthly savings
In this case, the monthly savings is the difference between the original mortgage payment ($766.51) and the new mortgage payment with the point ($755.96), which is $10.55 per month.
Substituting the values, we get:
Break-even point = $1,350 / $10.55
Break-even point = 128 months
Therefore, it would take Jessie 128 months, or just over 10 years, to break even on the points purchase.
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A satellite TV company offers two plans. One plan costs $115 plus $30 per month. The other plan costs $60 per month. How many months must Alfia have the plan in order for the first plan to be the better buy?
Please help me answer!
As a result, the percentage of adults who selected math is different from the percentage of kids who did.
what is percentage ?As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.
given
120 80
Total 200
Women Overall Party A Party B
70 60
Overall 130
Therefore, there are 130 ladies in the group.
b) The chart indicates that 70 women plan to support Party A.
Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.
b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.
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The complete question is:- complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?
Men
Party A Party B 120
Total 200
Women 130
Total 380
b How many women intend to vote for Party A?
2 A group of 48 adults are asked what their favourite subject was at school. They can choose from
maths, English and science.
A group of 32 school children are asked the
same question.
with k being all the numbers from one to 100, whats x3+y3+z3=k?
X = -80538738812075974, Y = 80435758145817515,
and Z = 12602123297335631 are the values of x,y,z of whole numbers.
What in mathematics is a whole number?
Complete numbers the sum of all natural numbers plus zero. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.
Natural numbers with a starting value of 1 and higher are considered whole numbers. Let's examine a few instances of entire numbers. The alphabet "W" stands for the collection of whole numbers. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}
x3+y3+z3=k, with k being all the numbers from one to 100
X = -80538738812075974,
Y = 80435758145817515,
and Z = 12602123297335631
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Is [tex]a^2(a-0.4)^3[/tex] completely factored?
The original question was to completely factor this:
[tex]a^5-0.064a^2[/tex]
Answer:
[tex]\bf a^2* (a - 0.4)(a^2 + 0.4a + 0.16)[/tex]
Step-by-step explanation:
Factorize:
First take out the common term a².
[tex]a^5 - 0.064a^2= a^2*(a^3 - 0.064)\\\\[/tex]
Now, factorize using the identity a³ - b³
a³ - b³ = (a - b) (a² + ab + b²)
[tex]a^2 * (a^2 - 0.064) = a^2 * (a^3 - 0.4^3)[/tex]
[tex]= a^2 * (a - 0.4) * (a^2 + a*0.4 + 0.4^2)\\\\=a^2 * (a - 0.4)(a^2 + 0.4a + 0.16)[/tex]
The steps for drawing a bearing of 065° from a point, X, are shown below. Put the steps in the correct order.
Answer:
The correct order to draw 65 agle would be:
C
A
B
D
twenty percent of americans ages 25 to 74 have high blood pressure. if 16 randomly selected americans ages 25 to 74 are selected, find each probability. a. none will have high blood pressure. b. one-half will have high blood pressure. c. exactly 4 will have high blood pressure.
Then we will get the following odds
a. None will have high blood pressure. Let the probability of having high blood pressure be denoted by P(A) and the probability of not having high blood pressure be denoted by P(A'). Since none will have high blood pressure, it means all the sixteen Americans selected are healthy, and therefore P(A') = 1. Therefore
P(A) = 1 - P(A')= 1 - 1= 0
b. One-half will have high blood pressure. The probability that one-half of the sixteen Americans will have high blood pressure can be found using the binomial distribution formula that is given by the expression
[tex]P(X = r) = (nCr) * p^r * q^{(n-r)}[/tex]
Where
r = 8n = 16 p = 0.2 q = 1 - p = 0.8Therefore
[tex]P(X = 8) = (16C8) * 0.2^8 * 0.8^8= 0.202[/tex]
c. Exactly 4 will have high blood pressure Similarly, the probability that exactly four of the sixteen Americans will have high blood pressure can be found using the binomial distribution formula as follows:
[tex]P(X = r) = (nCr) * p^r * q^{(n-r})[/tex]
Where
r = 4n = 16p = 0.2q = 1 - p = 0.8Therefore
[tex]P(X = 4) = (16C4) * 0.2^4 * 0.8^{12}= 0.236[/tex]
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88 books cost \$19. 60$19. 60dollar sign, 19, point, 60. Which equation would help determine the cost of 101010 books?
Choose 1 answer:
The calculation for the price of 10 books is as follows: 10 × (19.60/88) = 2.21
We can use a proportion to determine the cost of 10 books based on the cost of 88 books:
88 books cost $19.60
1 book costs 19.60/88 dollars
Now we can use this information to find the cost of 10 books:
10 books cost 10 × (19.60/88) dollars
Simplifying the expression on the right side, we get:
10 books cost $2.21
Therefore, the equation that would help determine the cost of 10 books is: 10 × (19.60/88) = 2.21 The cost of books is often calculated based on the number of books purchased and the price per book. In this problem, we are given the cost of 88 books, and we need to find the cost of 10 books. Using a proportion, we can find the cost of 1 book and then multiply it by 10 to find the cost of 10 books. This method is useful for determining the cost of any number of books, given the cost of a different number of books. Book prices can vary widely depending on factors such as the format, edition, and publisher, so it is important to carefully consider book prices when making purchases.
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Show using the value x=2 that
5x³ are not equivalent.
20x^6/4x²
and 5x^3 are not equivalent
Answer:
5x³ = 40
20x^6/4x² = 80
100 is not equal to 80
Step-by-step explanation:
5x³ = 5*2^3
= 40
20x^6/4x² = 20*2^6/4*2^2
= 20*64/16
= 80
Smart mugs are the next generations of hot drinks dispensers tha om with built in technology to keep drinks at the perfect temperature for hours on end initial cost of a smart mug was aed 896, because of high demand in market the cost increased by 12% find the new price of the mug
Pls quick its due 30 mins! And also explain with steps pls! it will help alot, also will make brainliest!
prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other
We need to use mathematical logic to prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.
Let's take an example of two sets A and B.
Let's say, A={a, b} and B={1, 2, 3}
To find the cardinality of the cross-product of A and B, we need to make all possible ordered pairs with A and B.
{(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
Counting the number of ordered pairs, we get six.
So, the cardinality of the cross-product of two sets A and B equals the cardinality of each set multiplied by the other. Here,
|A| = 2 and |B| = 3,
so |A x B| = 2 x 3
= 6.
Therefore, it is proved that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.
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Graph the solution to this inequality on the number line.
−5+x≥−3
Answer: 2
Step-by-step explanation:
To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.
Adding 5 to both sides of the inequality, we get:
x ≥ 2
This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.
The resulting graph looks like this:
------•-------------------------------->
2
The shaded region on the right of 2 represents all the values of x that make the inequality true.
14. a) What are the indicated properties in the following figure? b) What is the nature of GENA? c) Suppose MG=2GO. Prove that L is the midpoint of [EM]. d) What does G represent with respect to triangle MEA?
Helllllppppp due tomorrow
Answer: Area = 47.5m(2)
Step-by-step explanation:
Area = Pie X r(2) / 2
Area = 3.14 X 5.5(2)/2
Area = 47.4925
Find the missing side of each triangle.
Answer:
5) 12.2 6) 2
Step-by-step explanation:
Use Pythagoras for both
Rearrange for x in question 6
This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is modeled by y = –0.04088x2 + 0.4485x + 1.862. In what month did Phoenix receive the lowest amount of precipitation? Month (x) Precipitation January 2.27 inches February ? March ? April ? May ? June ? July ? August ? September 2.59 inches October ? November ? December ? Sketch a graph or fill in the table to answer the question. January February November December
the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
Why it is and how to form a graph?
To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.
Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:
y' = -0.08176x + 0.4485
0 = -0.08176x + 0.4485
x = 5.484
This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).
To verify this, we can plug in x = 2 into the quadratic equation:
y = –0.04088(2)²2 + 0.4485(2) + 1.862
y = 2.31752
Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:
Month (x) Precipitation
January 1 2.27 inches
February 2 2.32 inches
March 3 2.57 inches
April 4 2.94 inches
May 5 3.43 inches
June 6 3.94 inches
July 7 2.72 inches
August 8 2.86 inches
September 9 2.59 inches
October 10 2.03 inches
November 11 1.46 inches
December 12 1.03 inches
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Answer:
D: December
The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:
| Month (x) | Precipitation |
|-----------|---------------|
| January | 2.27 inches |
| February | 2.27 inches |
| March | 2.24 inches |
| April | 2.18 inches |
| May | 2.09 inches |
| June | 1.98 inches |
| July | 1.84 inches |
| August | 1.68 inches |
| September | 2.59 inches |
| October | 1.50 inches |
| November | 1.30 inches |
| December | 1.08 inches |
According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.
in part i, you will evaluate an aircraft altimeter data sample from different companies to determine if there are any differences in error. you have the following three options for running the appropriate t-test. option 1 - compare one brand against a hypothesized mean to determine if the brand is statistically different than the assumed norm. in this case, you would have to cite where the hypothesized population mean came from. option 2 - compare one brand against another to see if there are significant differences between them. option 3 - compare either altimeter error of acme or brand x before adjustment and calibration and after adjustment and calibration to see if there are any differences in the means (performance). based on the type of dependent variable data (ratio) and the type of question in the scenario, you will use a t-test. as you know, there are three different types of t-tests you can use: one sample t-test (test for one population mean using excel) two sample t-test (hypothesis test for two population means using excel) paired t-test (compare before and after values for one type using excel)
From the following three options for running the appropriate t-test, Both Options (2) and (3) could be applicable depending on the specific research question being investigated.
The appropriate t-test to use in this scenario is paired t-test. This test compares before and after values for one type using excel. In this scenario, you would be comparing either the altimeter error of ACME or brand x before adjustment and calibration and after adjustment and calibration to see if there are any differences in the means (performance).
Based on the scenario described, Option 1 is not appropriate because there is no hypothesized population mean to compare against. Therefore, we can exclude this option.
Option 2, comparing one brand against another, could be appropriate if we want to investigate if there are any significant differences in altimeter error between brands. This would be a two-sample t-test.
Option 3, comparing the altimeter error of one brand before and after calibration, could also be appropriate to see if the adjustment and calibration had a significant impact on the altimeter's performance. This would be a paired t-test.
This test is the appropriate test to use because the dependent variable data in this scenario is the ratio and the type of question requires a paired t-test. In this scenario, you are comparing the performance of the two brands before and after adjustment and calibration, which requires paired t-test to answer the research question.
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
The number of toy soldiers that Leo has is 48.
How many toy soldiers does Leo have?The first step is to determine the multiples of 4 that lie between 27 and 54. A multiple of a number is the product of an integer and that number.
Multiplies of 4 that lie between 27 and 54 = 28, 32, 36, 40, 44, 48, 52
Now divide each of the multiples by 7 :
28 / 7 = 4
32 / 7 = 4 remainder 4
36 / 7 = 5 remainder 1
40 / 7 = 5 remainder 5
44 / 7 = 6 remainder 2
48 / 7 = 6 remainder 6
52 / 7 = 7 remainder 3
It only 48 that meets this criteria. This means that the number is 48.
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For what value of x do 2x+3 and 3x-6 have the same value
Answer:
x = 9
Step-by-step explanation:
[tex]2x + 3 = 3x - 6[/tex]
[tex]3 = x - 6[/tex]
[tex]x = 9[/tex]
5 to the power of -4
I need help, what does this mean
Answer:
2125 ft/min
33,000 ft
y = -2125x + 33,000
Step-by-step explanation:
A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).
B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.
C. Plug in the values you got for A and B into the slope formula y = mx + b
y = -2125x + 33,000
list and describe the four scales of measurement. please provide an example of each one. which measures of central tendency apply to each scale of measurement?
Measurement scales refer to the various methods of assigning scores to measurements according to their precision and accuracy. There are four primary scales of measurement; nominal, ordinal, interval, and ratio.
The four measurement scales and their definitions are listed below:
Nominal scale: This is the lowest level of measurement. It is used to name, classify, or identify objects, events, or groups. It has no logical order, and its units cannot be compared or arranged in a sequence.
Examples of the nominal scale include; gender (male or female), marital status (single or married), color (black or white), and so on.
Ordinal scale: This scale includes a more elaborate classification than nominal measurement. It distinguishes between levels of preference or priority, but it does not have a constant distance between the levels.
Examples of the ordinal scale include; rankings (first, second, third, and so on), level of satisfaction (very happy, happy, neutral, unhappy, very unhappy), and so on.
Interval scale: This scale has a constant distance between its units, and its elements can be compared or arranged in a sequence. It does not have a true zero.
Examples of the interval scale include; temperature (measured in Fahrenheit or Celsius), time (measured in seconds, minutes, or hours), and so on.
Ratio scale: This is the highest level of measurement, where it has a constant distance between its units, its elements can be compared or arranged in a sequence, and it has a true zero.
Examples of the ratio scale include; weight, length, height, and so on. Measures of central tendency include; mean, median, and mode. The mean is the average of all the data points in a set, the median is the middle value in a set of data, and the mode is the value that occurs most often. The table below provides an example of each measurement scale and the appropriate measures of central tendency for each. Scales of Measurement Examples Measures of Central Tendency Nominal Scale Gender Mean Ordinal Scale Ranking Median Interval Scale Temperature Mean Ratio Scale Height Mode.
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What is the linear equation of a line that goes through (-4, 3) and (0,6)?
Answer:
y=(3/4)x+6
Step-by-step explanation:
Point 1 (-4,3)
Point 2 (0,6)
To obtain the slope, we apply the formula:
m= (6-3) / (0- (-4))
m= 3 / 4
We replace in the equation y=mx+b.
We take any point.
=> (0,6)
y=mx+b
6=(3/4)(0)+b
b=6
Joining all the terms:
y=(3/4)x+6
suppose point p divides the directed line segment xy so that the ratio of xp to py is 3 to 5 . describe point r that divides the directed line segment yx so that the ratio of yr to rx is 5 to 3 .a. R and P are the same pointb. Point R is halfway between point P and point Xc. The distance from point X is the same as the distance prom point P to point Yd. Point R is three fifths of the way from point P to point Y along PY
For point, p divides the directed line segment xy so that the ratio of xp to py is 3 to 5 correct option is d. Point R is three-fifths of the way from point P to point Y along PY.
The directed line segments divide a line into ratios, and each ratio has different properties. The properties of ratios of points on a line are dependent on the way the line is divided. For instance, suppose point p divides the directed line segment xy so that the ratio of xp to py is 3 to 5. We can describe point r that divides the directed line segment yx so that the ratio of yr to rx is 5 to 3 as follows:
We can solve this problem using the concept of directed line segments and the properties of ratios of points on a line.
Since P divides the directed line segment XY in the ratio 3:5, we can write:
XP = (3/8)XY and PY = (5/8)XY
Now, let's consider the directed line segment YX. We want to find a point R on this segment such that YR:RX = 5:3.
We can express YR and RX in terms of XY using the fact that YX = -XY:
YR = (5/8)YX and RX = (3/8)YX
Substituting -XY for YX, we get:
YR = (-5/8)XY and RX = (-3/8)XY
To find the location of point R, we need to find the distance from Y to R along the directed line segment YX. We can do this by adding the distances from Y to P and from P to R:
YR = YP + PR
Using the ratios we derived earlier, we can express YP and PR in terms of XY:
YP = PY = (5/8)XY
PR = R - P = (3/8)XY - (3/8)XY = 0
Therefore, YR = (5/8)XY + 0 = (5/8)XY
This means that point R is located at a distance of 5/8 of the length of YX from Y. So, the correct answer is (d) Point R is three-fifths of the way from point P to point Y along PY.
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An online retailer receives 5% off of all the sales made into here website
After answering the prοvided questiοn, we can cοnclude that the 5% expressiοn discοunt is mοst likely intended tο encοurage custοmers tο purchase.
What is expressiοn ?A cοllectiοn οf symbοls, digits, and cοnglοmerates in mathematics that resemble a pattern οr statistical cοrrelatiοn is knοwn as an expressiοn. Real numbers, mutables, and cοmbinatiοns οf the twο are all acceptable types οf expressiοns. A few examples οf mathematical οperatοrs are additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn. Expressiοns are frequently used in mathematics, geοmetry, and shape. They are used fοr equatiοn sοlving, representing mathematical fοrmulas, and simplifying mathematical relatiοnships.
All purchases made thrοugh the οnline stοre's website appear tο be eligible fοr a 5% discοunt. The custοmer will thus save 5% οff the tοtal cοst οf the purchase with each sale. Fοr instance, if a custοmer spends $100 οn gοοds, they will get a $5 discοunt, lοwering the final cοst tο $95.
It's wοrth nοting that the retailer may chοοse tο sacrifice prοfits in οrder tο οffer this discοunt. Alternatively, they may have negοtiated lοwer prices with their suppliers οr implemented οther cοst-cutting measures tο cοmpensate fοr the cοst οf the discοunt. In any case, the 5% discοunt is mοst likely intended tο encοurage custοmers tο purchase.
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Complete question:
A dart is thrown horizontally at a speed of 10 m/ s at the bull’s-eye of a dartboard 2.4 m away, as in the following figure. (a) How far below the intended target does the dart hit? (b) What does your answer tell you about how proficient dart players throw their darts?
(a) The horizontal velocity of the dart remains constant throughout its motion, so it will take 0.24 seconds to reach the target (since distance = speed × time) and the dart will fall a distance of 0.28 m
During this time, the dart will also be accelerating downwards due to gravity at a rate of 9.81 m/s². The vertical distance fallen can be calculated using the formula: distance = ½ × acceleration × time². Thus, the dart will fall a distance of:
distance = ½ × 9.81 m/s² × (0.24 s)² ≈ 0.28 m
Therefore, the dart will hit the board 0.28 meters below the intended target.
(b) This calculation suggests that even highly skilled dart players may not hit the bull's-eye every time, due to the influence of gravity on the dart's trajectory.
However, skilled players can adjust their aim and release the dart with the correct velocity and angle to hit their target consistently. They may also use techniques such as "aiming high" to compensate for the effect of gravity. Overall, this calculation highlights the importance of understanding the physics of projectile motion in the sport of darts.
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a bowl contains 12 balls, of which 6 are blue, 2 are white, and 4 are red. we draw 4 balls at random, without replacement. what is the probability that the 4 balls include each of the three colors?
The probability of drawing 4 balls at random, without replacement, that include each of the three colors is 0.0061.
What is the probability?The bowl contains 12 balls6 of the balls are blue2 of the balls are white 4 of the balls are red
Sample space = [tex]n(S) = ^{12}C_4=\frac{12!}{4! (12 - 4)!} = 495[/tex]
The formula for conditional probability is:
P(A ∩ B) = P(A) × [tex]P(\frac{B}{A})[/tex]
P(A ∩ B) is the probability that both A and B occur
P(A) is the probability of event A occurring
[tex]P(\frac{B}{A})[/tex] is the probability of event B occurring given that A has occurred
The probability of drawing 4 balls at random that include each of the three colors can be calculated as follows:
First, we calculate the probability of drawing one ball of each color
P (Drawing one ball of each color) = [tex]\frac{(^6C_1^2C_1^4C_1)}{^{12}C_3} = \frac{(6X2X4)}{220} = 0.0545[/tex]
Next, we calculate the probability of drawing a fourth ball of any color
P (Drawing a fourth ball of any color) = [tex]\frac{^9C_1}{^9C_1} = 1[/tex]
Finally, we use the formula for conditional probability to find the probability of drawing 4 balls at random that include each of the three colors
P (Drawing 4 balls at random that include each of the three colors) = P (Drawing one ball of each color) × P (Drawing a fourth ball of any color | Drawing one ball of each color) = [tex](0.0545)\frac{1}{9}= 0.0061[/tex]
The probability of drawing 4 balls at random, without replacement, that include each of the three colors is 0.0061.
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i do not understand how to answer this question
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
What is square root?Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.
Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.
Here,
a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
Using (a + b)(a - b) = a² - b²
⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]
⇒ [tex]$ -1+2}$[/tex]
⇒ 1
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
B. This will be done with the same process,
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]
There, will be same roots of every number until - 8
So,
⇒ [tex]$ -1+8}$[/tex]
= 7
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
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