The human heart beats approximately 4.1975 x 10⁸ times in one year and it expressed in scientific notation.
According to the question, the average human heart beats 1.15 x 10⁵ times a day. We need to find out how many times the heart beats in one year, which is 3.65 x 10² days.
To calculate the total number of heartbeats in one year, we can multiply the number of heartbeats in a day by the number of days in a year. Therefore, we have:
Total number of heartbeats in one year = 1.15 x 10⁵ beats/day x 3.65 x 10² days/year
= (1.15 x 3.65) x (10⁵ x 10²) beats/year
= 4.1975 x 10⁸ beats/year
This number may seem large, but it is necessary for the heart to pump blood throughout the body to keep us alive and healthy.
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As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions shown. Abigail sloshes 2/3 of the water out of her cup before she gets a chance to drink any. What is the volume of water remaining in Abigail’s cup?
The volume of water remaining in Abigail’s cup can be found to be 25. 14 cm³ .
How to find the volume left ?First, find the volume of water in the cup when it is full. This would be the volume of the cup which is the formula of the volume of a cone :
Volume = ( 1 / 3 ) × π × r² × h
Volume = ( 1 / 3 ) × π × ( 3 cm )² × ( 8 cm )
Volume = 24π cm³
If Abigail too 2 / 3 to slosh on her face, the amount of water left would be :
= 24π cm³ - ( 1 - 2 / 3 )
= 24π cm³ - 1 / 3
= 8π cm³
= 25. 14 cm³
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The mean of six values is 7. There is one outlier that
pulls the mean higher than the center. What could the
data set be? What is the mean without the outlier?
The data set is 2, 7, 7, 8, 9, and 9, with a mean of 7. The outlier is 2, and the mean without the outlier is 6.6. The outlier pulls the mean lower than the center, but once removed, the mean becomes more representative of the data set.
To find the mean of a set of values, we add up all the values and divide by the total number of values.
In this case, we know that the mean of six values is 7, so we can set up the following equation
(2 + 7 + 7 + 8 + 9 + 9) / 6 = 7
Simplifying the equation, we get
42 / 6 = 7
So, the sum of the six values is 42.
Now, we know that there is one outlier that pulls the mean higher than the center. In other words, one of the values is much larger than the others. Let's assume that the outlier is 20.
So, the new sum of the six values would be
2 + 7 + 7 + 8 + 9 + 20 = 53
To find the mean without the outlier, we need to subtract the outlier from the sum and divide by the remaining number of values. In this case, there are five values remaining. So, we get
(2 + 7 + 7 + 8 + 9) / 5 = 33 / 5 = 6.6
Therefore, the possible data set is 2, 7, 7, 8, 9, and 9, and the mean without the outlier is 6.6.
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--The given question is incomplete, the complete question is given
" The mean of six values is 7. There is one outlier that
pulls the mean higher than the center. What could the
data set be? What is the mean without the outlier?
The possible data set is 2, 7, 7, 8, 9, and 9. "--
In the preceding question you found that tan(3/4). To the nearest degree, measure angle B
The measure of angle B, rounded to the nearest degree, is 37 degrees.
How to find the measure of angle B when tan(B) is equal to 3/4?In trigonometry, the tangent function (tan) relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle.
To find the measure of angle B, we use the inverse tangent function (arctan) with the given tangent value of 3/4:
B = arctan(3/4)
Using a calculator or a trigonometric table, we find that arctan(3/4) is approximately 36.87 degrees. Round the result to the nearest degree to obtain the final measure of angle B.
Therefore, the measure of angle B, rounded to the nearest degree, is 37 degrees.
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An agent claims that there is no difference between the pay of safeties and linebackers in the NFL. A survey of 15 safeties found an average salary of $501,580 and a survey of 15 linebackers found on average salary of $513,360. If the standard deviation in the first sample was $20,00 and the standard deviation in the second sample is $18,000 is the agent correct? Use a=0. 5
The standard deviation in the first sample was $20,00 and the standard deviation in the second sample is $18,000 so the agent's claim cannot be rejected at the 0.05 level of significance.
To test the agent's claim, we can perform a two-sample t-test with a significance level of 0.05. The null hypothesis is that there is no difference in the mean salaries of safeties and linebackers, while the alternative hypothesis is that there is a difference.
We can calculate the t-statistic using the formula:
t = (x1 - x2) / sqrt(s1²/n1 + s2²/n2)
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Plugging in the given values, we get:
t = (501580 - 513360) / sqrt((20000²/15) + (18000²/15))
t = -1.2605
Using a t-distribution table with 28 degrees of freedom (15 + 15 - 2), we find that the critical value for a two-tailed test at a significance level of 0.05 is approximately ±2.048.
Since the absolute value of the calculated t-statistic (1.2605) is less than the critical value (2.048), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that there is a difference in the mean salaries of safeties and linebackers in the NFL.
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The cost of product is birr 92 & the company is having a policy of 15% mark-up on cost,then what tha sale price will be?
The sale price of the product would be Birr 105.80.
If the cost of the product is Birr 92 and the company has a policy of 15% mark-up on the cost, then the sale price can be found by adding 15% of the cost to the cost itself.
To calculate this, we can use the formula:
Sale price = Cost + Mark-up
where the mark-up is 15% of the cost.
Mark-up = 15% of Cost = 0.15 * 92 = Birr 13.80
So, the sale price = Cost + Mark-up = 92 + 13.80 = Birr 105.80.
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Whats the volume of the rectangular prism 9in 3in 2in
Answer:
54
Step-by-step explanation:
9x 3 x2 =54
bacteria in a dirty glass triple every day. if there are 25 bacteria to start, how many are in the glass after 15 days
Answer:
Step-by-step explanation:
25x3x15
a cylinder and a cone have the same diameter: 8 inches. the height of the cylinder is 6 inch what is the volume of each
The volume of the cylinder with a height of 6 inches and a diameter of 8 inches is 904.78 cubic inches.
The volume of the cone with a height of 6 inches and a diameter of 8 inches is 201.06 cubic inches.
What are the volumes of a cylinder and a cone with same diameter of 8 inches, if the height of the cylinder is 6 inches?The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is 8 inches, the radius is half of that, which is 4 inches. So, the volume of the cylinder is:
V = π(4)²(6)
V = π(16)(6)
V = 96π
V ≈ 301.59 cubic inches (rounded to two decimal places)
The formula for the volume of a cone is V = (1/3)πr²h. Again, since the diameter is 8 inches, the radius is 4 inches. So, the volume of the cone is:
V = (1/3)π(4)²(6)
V = (1/3)π(16)(6)
V = (1/3)(96π)
V ≈ 100.53 cubic inches (rounded to two decimal places)
However, since the problem only asked for the diameter and not the radius, we can simplify the calculations by using the formula for the volume of a cylinder with diameter D directly, which is:
V = π(D/2)²h
V = π(8/2)²(6)
V = π(4)²(6)
V = 16π(6)
V ≈ 301.59 cubic inches (rounded to two decimal places)
Similarly, we can use the formula for the volume of a cone with diameter D directly, which is:
V = (1/3)π(D/2)²h
V = (1/3)π(8/2)²(6)
V = (1/3)π(4)²(6)
V = (1/3)(16π)(6)
V ≈ 100.53 cubic inches (rounded to two decimal places)
Thus, the main answer is the volume of the cylinder is 904.78 cubic inches and the volume of the cone is 201.06 cubic inches, both rounded to two decimal places.
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GEOMETRY PLEASE HELP ‼️
The probabilities are given as follows:
a) Square: 1/6.
b) Not the triangle: 43/48.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total area of the figure is given as follows:
12 x 8 = 96 units². (rectangle).
The area of the square is given as follows:
4² = 16 units² (square of the side lengths).
Hence the probability of the square is given as follows:
p = 16/96
p = 1/6.
The area of the triangle is given as follows:
A = 0.5 x 4 x 5 = 10 units². (half the multiplication of the side lengths).
Hence the complement of the area of the triangle is of:
96 - 10 = 86 units².
And the probability of the complement is of:
86/96 = 43/48.
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NEED HELP FAST!!!! Please answer both questions
Therefore, the molarity of the sugar solution is 0.3704 M at 25°C. Therefore, the molality of the NaCl solution is 1.8994 mol/kg.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=). The expressions on either side of the equal sign may contain variables, constants, coefficients, and mathematical operations.
Here,
1. To calculate the molarity of a sugar solution, we need to first determine the number of moles of solute (glucose, C6H12O6) present in the solution. We can then divide this number of moles by the volume of the solution in liters to obtain the molarity. The number of moles of glucose in the solution can be calculated as follows:
Number of moles = mass of solute / molar mass of solute
Number of moles = 100.0 g / 180 g/mol
Number of moles = 0.5556 mol
Next, we can calculate the molarity of the solution using the following formula:
Molarity = number of moles / volume of solution (in L)
Molarity = 0.5556 mol / 1.50 L
Molarity = 0.3704 M
2. To calculate the molality of a solution, we need to know the number of moles of solute (NaCl) per kilogram of solvent (water).
First, let's calculate the number of moles of NaCl:
Number of moles = mass of NaCl / molar mass of NaCl
Number of moles = 200.0 g / 58.5 g/mol
Number of moles = 3.4188 mol
Next, we need to calculate the mass of the solvent (water) in kilograms:
Mass of solvent = 2.00 kg - 0.200 kg
Mass of solvent = 1.80 kg
Note that we subtracted the mass of the NaCl from the total mass of the solution to obtain the mass of the solvent.
Finally, we can calculate the molality of the solution using the following formula:
Molality = number of moles of solute / mass of solvent (in kg)
Molality = 3.4188 mol / 1.80 kg
Molality = 1.8994 mol/kg
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Math please help
An insurance company sells a 20-year term life insurance policy with a face value of $200,000 to a 45-year -old woman. Her annual premium is $990. If the woman dies after paying premiums for 6 years, what is the insurance company’s gain or loss?
Loss of $200,990
Loss of $194,060
Gain of $205,940
Gain of $199,010
The company will have a Loss of $194,060
The lady paid premiums for 6 years, which amounts to a total premium of$ 5,940($ 990 * 6).
Still, the insurance company will pay the face value of the policy, which is $ 00, If she dies.
Thus, the company's total payout would be $200,000, while their total income would be $ 5,940 in premiums.
The loss for the company would be the difference between the payout and the income
200,000-$ 5,940 = $ 194,060
Thus, the insurance company's loss in this scenario would be $194,060.
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a barber has scheduled two appointments, one at 5 pm and the other at 5:30 pm. the amount of time that appointments last are independent exponential random variables with mean 45 minutes. assuming that both customers are on time, find the expected amount of time that the 5:30 appointment spends at the barber shop.
The expected amount of time that the 5:30 appointment spends at the barber shop is, E[W] = 45 + 45/e.
Given that, the barber has scheduled two appointments, one at
5 pm and the other at 5:30 pm.
Since the amount of time that appointments last are independent exponential random variables with mean 45 minutes.
Let W be the time the 2nd person has to wait in chamber Let X be the time the barber takes checking 1st person X-exp(45)
The distribution is,
W= X-45 if X >45
otherwise.
Expected time 2nd person spends in barber chamber
= E (W)+45
[ 45 is the mean time barber takes checking 2nd person]
[tex]E(W) = \int\limits^{\infinity }_0 {WP(X=45+W)} \, dw\\ \\\\=\int {W.1/45e^{\frac{-45+w}{45} } \, dw\\\\[/tex]
[tex]=e^{-1} \int\frac{W}{45} e^{\frac{-w}{45} } dw\\=\frac{45}{e}[/tex]
The expected amount of time that the 5:30 appointment spends at the barber's office is,
[tex]E[W]=45+\frac{45}{e}[/tex].
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the process standard deviation is ounces, and the process control is set at plus or minus standard deviations. units with weights less than or greater than ounces will be classified as defects. what is the probability of a defect (to 4 decimals)?
The probability of a defect in the manufacturing process, assuming that the weight of the products follows a normal distribution, is 0.1587 to four decimal places.
To calculate the probability of a defect, we first need to calculate the z-score of the weight that would classify the product as a defect. The z-score is a measure of how many standard deviations a value is from the mean. In this case, the z-score is -1 or 1, depending on whether the weight is less than one standard deviation below the mean or greater than one standard deviation above the mean.
Once we have calculated the z-score, we can use a standard normal distribution table or a calculator to find the probability of a product being classified as a defect. If the z-score is -1, the probability of a product being classified as a defect is 0.1587. If the z-score is 1, the probability of a product being classified as a defect is also 0.1587.
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8. A square has a side length of 11 V2 meters. What is the length of the diagonal
of the square?
The length of the diagonal of the square is 22 meters.
Define squareA square is a four-sided two-dimensional geometric shape in which all sides are equal in length and all angles are right angles (90 degrees).It is a unique instance of a rectangle with equal sides. The opposite sides of a square are parallel to each other and the diagonals bisect each other at right angles.
A square is divided into two 45-45-90 triangles by its diagonal.
In a 45-45-90 triangle, the hypotenuse (the side opposite the right angle) is √2 times as long as each leg.
Therefore, in this square, the length of the diagonal (d) can be found by multiplying the length of one side (s) by √2:
d = s√2
In this case, the side length of the square is 11√2 meters, so:
d = 11√2 × √2 = 11 × 2 = 22 meters
Therefore, the length of the diagonal of the square is 22 meters.
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Amal's sister is half as old as Amal. Amal's mother is 3 times amals age. Amals father is 4 times older than amals motherThe sum of all 4 ages si 94. How old was Amal's mother when amal was born
Answer:
Amal's mother was 11.4 years old when Amal was born.
Step-by-step explanation:
Let's start by using variables to represent the ages of each person:
Let A be Amal's ageLet S be Amal's sister's ageLet M be Amal's mother's ageLet F be Amal's father's ageFrom the problem, we know:
S = 0.5AM = 3AF = 4MA + S + M + F = 94Substituting the first three equations into the fourth, we get:
[tex]\sf:\implies A + 0.5A + 3A + 4(3A) = 94[/tex]
Simplifying:
[tex]\sf:\implies A + 0.5A + 3A + 12A = 94[/tex]
[tex]\sf:\implies 16.5A = 94[/tex]
[tex]\sf:\implies A = 5.7[/tex]
So Amal is 5.7 years old. To find the age of Amal's mother when Amal was born, we need to subtract Amal's age from his mother's age:
[tex]\sf:\implies M - A = 3A - A = 2A[/tex]
So Amal's mother was 2A = 2(5.7) = 11.4 years old when Amal was born.
need help on this problem
Answer:
a. n < 14
b. n ≥ 14
Step-by-step explanation:
a.
We see the line to the left of 14, meaning it will be smaller than 14. So, the inequality is n < 14
b.
The line goes to the right of 14, meaning it will be bigger than 14. This has a close circle meaning there will be an equal sign. So, the inequality is n ≥ 14
multiply 5/12 by the reciprocal of 17/-6
Answer:
[tex]\frac{-5}{34}[/tex]
Step-by-step explanation:
[tex]\frac{5}{12} * \frac{-6}{17}[/tex] = [tex]\frac{-30}{204}[/tex]
We can simplify.
[tex]\frac{-15}{102}[/tex] ⇒ Divided both by 2
[tex]\frac{-5}{34}[/tex] ⇒ Divided both by 3
[tex]\frac{-5}{34}[/tex] is the final answer
67. 8 x 9. 7 pls someone answer within the next 20 Minutes with work I'm in school lol
The radius of a circle is 11 kilometers.what is the circle area
Answer:
380.1 square kilometers
Step-by-step explanation:
When he was 30, Kearney began investing $200 per month in various securities for his retirement savings. His investments averaged a 5. 5% annual rate of return until he retired at age 68. What was the value of Kearney's retirement savings when he retired? Assume monthly compounding of interest
Kearney's retirement savings when he retired at age 68, assuming monthly compounding of interest, was $429,336.69.
How much did Kearney save for retirement?To calculate Kearney's retirement savings at age 68, we need to use the formula for the future value of an annuity due, which is:
FV = PMT x [((1 + r/n[tex])^(n*t)[/tex] - 1) / (r/n)] x (1 + r/n)
Where:
FV is the future value of the annuityPMT is the monthly payment (in this case, $200)r is the annual interest rate (5.5%)n is the number of compounding periods per year (12, for monthly compounding)t is the number of years (38, from age 30 to age 68)Plugging in the numbers, we get:
FV = 200 x [((1 + 0.055/12[tex])^(12*38)[/tex] - 1) / (0.055/12)] x (1 + 0.055/12)
FV = $429,336.69
Therefore, Kearney's retirement savings at age 68 would be approximately $429,336.69, assuming he invested $200 per month in securities with an average annual return of 5.5% and monthly compounding of interest. It's important to note that this calculation assumes that Kearney did not withdraw any money from his retirement savings during the 38-year period. Additionally, the actual value of his retirement savings could be different based on fluctuations in the market and any fees or taxes associated with his investments.
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Solve each system by substitution
-5x-6y=2
Y=3
Answer:
x = -4, y = 3.
Step-by-step explanation:
Substitute y = 3 into the first equation:
-5x - 6(3) = 2
-5x = 2 + 18
-5x = 20
x = -4
Use ≈ 0.4307 and ≈ 0.6826 to approximate the value of each expression. 11. log5 5/3
The value of logarithm log5 5/3 is approximately equal to 0.3174.
Using the approximation of ≈ 0.4307 for log5 2 and ≈ 0.6826 for log5 3, we can approximate the value of log5 5/3 by subtracting the two approximations.
log5 5/3 = log5 5 - log5 3 ≈ 1 - 0.6826 ≈ 0.3174
To explain further, logarithms are a way to express the relationship between exponential growth or decay and the input values. In this case, we are using the base of 5 to represent the exponent and trying to find the logarithm of 5/3.
By using the approximation values of log5 2 and log5 3, we can estimate the value of log5 5/3 by subtracting the two approximations. This approximation is useful in situations where we need a quick estimate of a logarithmic function without having to do complex calculations.
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Find the following. f'(2) if f(x) = -8x^-1 + 5x$-2 O 13/14
O -3/4
O -13/4
O ¾
The problem involves finding the derivative of a given function at a specified point.
Specifically, we are given the function f(x) = -8x^(-1) + 5x^(-2), and we need to find the value of the derivative f'(2) at x = 2. To find the derivative of f(x), we need to apply the rules of differentiation, which involve taking the derivative of each term separately and applying the power rule and chain rule as needed.
Once we have the derivative function f'(x), we can evaluate it at x = 2 to find the value of f'(2). Differentiation is a fundamental concept in calculus, and is used extensively in many areas of mathematics, science, and engineering. The ability to find derivatives allows us to analyze the behavior of functions and solve a wide variety of problems, from optimization to modeling physical systems.
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Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?
the value of b to –3
the value of m to –3
the value of b to 2
the value of m to 2
The change to move the graph down 3 units is given as follows:
the value of b to 2.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The function in this problem is given as follows:
y = -x + 5.
Moving the graph down 3 units, we subtract by three, hence:
y = -x + 5 - 3
y = -x + 2.
Meaning that the value of b is of b = 2.
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There are 80 boxes and each box weighs 22. 5 how many boxes does the truck have to deliver to cross a bridge that has to have a mass less than 4700
Answer:
The truck can deliver up to 209 boxes without exceeding a mass of 4700.
Step-by-step explanation:
To solve this problem, we need to use the formula:
[tex]\sf:\implies Total_{(Mass)} = Number_{(Boxes)} \times Weight_{(Per\: Box)}[/tex]
We know that each box weighs 22.5, so the formula becomes:
[tex]\sf:\implies Total_{(Mass)} = 22.5 \times Number_{(Boxes)}[/tex]
We want to find the maximum number of boxes that the truck can deliver without exceeding a mass of 4700. So we set up an inequality:
[tex]\sf:\implies 22.5 \times Number_{(Boxes)} \leqslant 4700[/tex]
To solve for number of boxes, we isolate it by dividing both sides by 22.5:
[tex]\sf:\implies Number_{(Boxes)} \leqslant 4700 \div 22.5[/tex]
[tex]\sf:\implies Number_{(Boxes)} \leqslant 209.33[/tex]
Since we can't have a fraction of a box, we round down to the nearest integer:
[tex]\sf:\implies \boxed{\bold{\:\:Number_{(Boxes)} \leqslant 209\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, the truck can deliver up to 209 boxes without exceeding a mass of 4700.
A manager notices that the employees in his division seem under heightened stress. he reviews their results on the osi and notices that the distribution of 25
employees in his division has a mean of 53. he notices that the mean of entire department is 49 (n=150). sd for both = 10.
what are the 95% confidence limits for the division?
The 95% confidence interval for the population mean of the division is (49.08, 56.92).
We can use the formula for the confidence interval for a population mean:
CI = [tex]\bar{X}[/tex] ± z*(σ/√n)
where [tex]\bar{X}[/tex] is the sample mean, z is the z-score for the desired confidence level (95% in this case), σ is the population standard deviation (which we assume to be equal to the sample standard deviation), and n is the sample size.
In this problem, [tex]\bar{X}[/tex] = 53, σ = 10, n = 25, and the z-score for a 95% confidence level is 1.96 (from a standard normal distribution table).
Plugging in these values, we get:
CI = 53 ± 1.96*(10/√25) = 53 ± 3.92
Therefore, the 95% confidence interval for the population mean of the division is (49.08, 56.92).
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Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, `x` kilometres, between Hong Kong and the different destinations and the corresponding airfare, `y`, in Hong Kong dollars (HKD)
The cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.
We start by calculating the Porson's product-moment correlation coefficient between the distance and airfare data. The value of the correlation coefficient ranges from -1 to +1. A value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.
In this case, the correlation coefficient between distance and airfare for Galois Airways flights is 0.948, indicates a strong positive correlation between the distance and airfare.
The regression line is expressed as:
y = a + bx
where y is the dependent variable (airfare), x is the independent variable (distance), a is the intercept (the value of y when x is zero), and b is the slope (the change in y for a one-unit change in x).
The regression equation for Galois Airways flights is:
y = 553.51 + 0.292x
Now, we can use the regression equation to estimate the cost of a flight from Hong Kong to Tokyo, which is 2900 km away.
y = 553.51 + 0.292(2900) = 1429.99 HKD
Therefore, we estimate that the cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.
Finally, we need to explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo. We can do this by examining the assumptions of linear regression. The two main assumptions are that there is a linear relationship between the variables, and that the residuals (the differences between the actual and predicted values) are normally distributed with constant variance.
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Complete question is Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, x kilometres, between Hong Kong and the different destinations and the corresponding airfare, y, in Hong Kong dollars (HKD) Destination Bali, Sydney, Bengaluru. Auckland, Bangkok, Indonesia Australia India Singapore New Thailand Zealand 3400 7400 4000 2600 9200 1700 Distance x, (km Airfare y, (HKD) 1550 3600 2800 1300 4000 1400 The Porson's product-moment correlation coefficient for this data is 0.948, correct to three significant figures. Use your prophio display calculator to find the equation of the regression line y on x. b. The distance from Hong Kong to Tokyo is 2900 km. Use your regression equation to estimate the cost of a flight from Hong Kong to Tokyo with Calois Airways. c. Explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo.
Given that : f(x) = 2 sec x + tan x 0 ≤ x ≤ 2π
a) Find the derivative.
b) Find the critical numbers.
The derivative of the given function is f'(x) = 2(sec x * tan x) + sec^2 x. b) The critical numbers for the function are x = 0 and x = π.of the given function is f'(x) = 2(sec x * tan x) + sec^2 x.
The critical numbers for the function are x = 0 and x = π.
Derivative and critical numbers,
a) Find the derivative: We're given the function f(x) = 2 sec x + tan x.
To find its derivative, we need to find the derivatives of the individual terms (sec x and tan x) and then add them together.
The derivative of sec x is sec x * tan x. So, for the term 2 sec x, the derivative is 2 * (sec x * tan x).
The derivative of tan x is sec^2 x.
Now, we add both derivatives to find the derivative of f(x): f'(x) = 2(sec x * tan x) + sec^2 x
b) Find the critical numbers: Critical numbers are the points where the derivative of the function is either 0 or undefined.
To find the critical numbers, we'll set f'(x) equal to 0 and solve for x, as well as identify where the derivative is undefined.
First, let's set f'(x) to 0: 0 = 2(sec x * tan x) + sec^2 x
We need to solve this equation for x. It's a bit tricky, so let's rewrite the equation in terms of sin and cos: 0 = 2((1/cos x) * (sin x/cos x)) + (1/cos x)^2
Now let's simplify the equation: 0 = 2(sin x/cos^2 x) + 1/cos^2 x
To eliminate the denominators, we'll multiply through by cos^2 x: 0 = 2(sin x) + cos x
Now, we can use the unit circle to find the values of x in the interval 0 ≤ x ≤ 2π that satisfy this equation: For sin x = 0, x = 0, π For cos x = -2, there's no solution in the given interval because the range of cosine is -1 ≤ cos x ≤ 1.
Therefore, the critical numbers are x = 0 and x = π. Your answer:
a) The derivative of the given function is f'(x) = 2(sec x * tan x) + sec^2 x.
b) The critical numbers for the function are x = 0 and x = π.
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Wholesale price: $17
retail price: $25
markup on retail: ?
a. 8%
b. 32%
c. 47%
d. 14%
The markup on retail is 47%. The correct option is c.
he markup on retail price is calculated to determine the percentage increase from the wholesale price to the retail price. In this case, the wholesale price is $17 and the retail price is $25. By subtracting the wholesale price from the retail price ($25 - $17),
we find that the markup is $8. Dividing this markup by the wholesale price ($8 / $17) gives us a ratio. Multiplying this ratio by 100 converts it to a percentage, which is approximately 47.06%.
This means that the retail price is approximately 47% higher than the wholesale price. Option c, 47%, correctly represents the calculated markup on the retail price.
Therefore, the markup on retail is 47%, so the answer is (c).
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help meee 5774 + 252 - 2586 ×35
Answer:
The answer is -84,484
Step-by-step explanation:
using Bodmas
multiplication first
5774+252-(2586×35)
5774+252-90510
6026-90510
-84,484