Answer:
-[tex]\sqrt{3}[/tex]/2
Step-by-step explanation:
cos is negative in quad II
cos(210)= -cos(30) = -[tex]\sqrt{3}[/tex]/2
2
A farmer places beehives containing bees in her orchard to pollinate the plants. The table
below shows the ratio of the number of beehives to the number of acres in the orchard.
BEEHIVES PER ACRE
A 38
B 40
C 44
Number of
Beehives
48
Number of
Acres
3 9
12
If the bees pollinate the plants at a constant rate, how many acres will be pollinated by the
bees in 18 beehives?
8 24 32
18
?
The number of acres pollinated by the bees in 18 beehives is 48 acres.
A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
x: number of beehives.
y: number of acres.
From the table, the constant is obtained as follows:
3k = 8
k = 8/3
Hence the equation is of:
y = 8x/3.
The number of acres that will be pollinated by 18 beehives is then given as follows:
y = 8(18)/3
y = 48 acres.
Therefore, the number of acres pollinated by the bees in 18 beehives is 48 acres.
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write a situation that matches this inequality 8x+14<100
Suppose you are a small business owner who sells handmade crafts. You have a budget of $100 to purchase materials for your next batch of products. You know that each craft requires some amount of materials, which costs $8 per unit. Additionally, you will need to pay a fixed cost of $14 for other expenses related to production and shipping.
How the situation matches inequality 8x+14<100 ?To make a profit, you must ensure that the cost of materials and fixed expenses does not exceed the $100 budget. Therefore, you can write an inequality to represent this situation:
8x + 14 < 100
Here, x represents the number of units of materials needed for each craft. The inequality states that the total cost of materials (8x) plus fixed expenses ($14) must be less than $100.
To solve this inequality, you can subtract 14 from both sides:
8x < 86
Finally, you can divide both sides by 8:
x < 10.75
This means that for each craft, you can use no more than 10.75 units of materials in order to stay within budget and make a profit.
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pleaseeeee i need helppp in this
The resulting matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:
[tex]M = \left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]M = \left[\begin{array}{ccc}-4&3&1\\-2&-3&r\end{array}\right][/tex]
The rows of the matrix are given as follows:
R1: -4, 3 and 1.R2: -2, -3 and 4.Hence the row 2 of the resulting matrix has the elements given as follows:
Column 1: 4 x -4 - 2 = -18.Column 2: 4 x 3 - 3 = 9.Column 3: 4 x 1 + 4 = 8.More can be learned about operations with matrices at brainly.com/question/16901354
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
The factor of 2xy + 30x^2 - xy - 16y^4 - yx - 5x^2 is 25x2−16y4=(5x+4y2)(5x−4y2)
We are given that;
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
Now,
Combine like terms by adding or subtracting the coefficients of the same variables. For example, 2xy - xy - yx = 0xy, and 30x^2 - 5x^2 = 25x^2. The polynomial becomes:
25x2−16y4
Check if there is a common factor for all the terms. In this case, there is no common factor other than 1, so we cannot use the greatest common factor method.
Check if the polynomial is a difference of two squares, which means it has the form a2−b2. In this case, we can see that both terms are perfect squares: 25x2=(5x)2 and 16y4=(4y2)2. Therefore, we can use the difference of two squares formula:
a2−b2=(a+b)(a−b)
Substituting a=5x and b=4y2, we get:
25x2−16y4=(5x+4y2)(5x−4y2)
Check if each factor can be further factored using any of the methods. In this case, neither factor can be further factored, so we are done.
Therefore, by factorization the answer will be 25x2−16y4=(5x+4y2)(5x−4y2)
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Bandar Industries manufactures sporting equipment. One of the company’s products is a football helmet that requires special plastic. During the quarter ending June 30, the company manufactured 3,500 helmets, using 2,485 kilograms of plastic. The plastic cost the company $16,401.
According to the standard cost card, each helmet should require 0.66 kilograms of plastic, at a cost of $7.00 per kilogram.
Required:
1. What is the standard quantity of kilograms of plastic (SQ) that is allowed to make 3,500 helmets?
2. What is the standard materials cost allowed (SQ × SP) to make 3,500 helmets?
3. What is the materials spending variance?
4. What is the materials price variance and the materials quantity variance
1. The standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.
2. The standard materials cost allowed to make 3,500 helmets is $16,170.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
1. The standard quantity of kilograms of plastic (SQ) allowed to make 3,500 helmets can be calculated as:
SQ = Standard quantity per unit × Actual output
= 0.66 kg/helmet × 3,500 helmets
= 2,310 kg
Therefore, the standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.
2. The standard materials cost allowed (SQ × SP) to make 3,500 helmets can be calculated as:
Standard materials cost allowed = Standard price × Standard quantity allowed
= $7.00/kg × 2,310 kg
= $16,170
Therefore, the standard materials cost allowed to make 3,500 helmets is $16,170.
3. The materials spending variance can be calculated as the difference between the actual cost incurred and the standard cost allowed:
Materials spending variance = Actual materials cost - Standard materials cost allowed
= $16,401 - $16,170
= $231 (Favorable)
Therefore, the materials spending variance is $231 (Favorable).
4. The materials price variance and the materials quantity variance can be calculated as follows:
Materials price variance = (Actual price - Standard price) × Actual quantity
= ($16,401/2,485 kg - $7.00/kg) × 2,485 kg
= $9,141.77 (Unfavorable)
Materials quantity variance = (Actual quantity - Standard quantity allowed) × Standard price
= (2,485 kg - 2,310 kg) × $7.00/kg
= $1,225 (Unfavorable)
Therefore, the materials price variance is $9,141.77 (Unfavorable) and the materials quantity variance is $1,225 (Unfavorable).
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Find the missing side lengths. Leave your answers as radicals in simplest form.
The value of m and n are 2√3 and 4√3/3 respectively.
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
There are special angles in trigonometry, examples are; 60° , 30° and 90°. This angles have exact values and can be calculated without using calculator.
Tan 60 = n/2
√3 = n/2
n = 2√3
cos 60 = 2/m
√3/2 = 2/m
m√3 = 4
m = 4/√3
= 4√3/3
Therefore the value of m and n are 2√3 and 4√3/3 respectively.
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The Morning Gazette offers employees 1.65% of the average of their last 3 years of annual compensation for each year of service. Rita began working for the Morning Gazette in 1994. She retired in 2016. In 2014, she made $76,000 per year. Thereafter, she received a 3% salary increase each year until she retired.
a) How much did she earn for each year from 2014 through 2016?
b) What is the average of her last five years of working?
c) How much was his annual retirement benefit?
She earn fοr each year frοm 2014 thrοugh 2016 is 80628.40. The average οf her last five years οf wοrking $78,302.80. His annual retirement benefit was $28,423.92.
a) Salary οf 2014 : $76000
Salary in 2014 is the salary in 2015 increased by 3% οf the salary
= $76,000+3%
Salary οf 2015 = $78,280
Salary in 2015 is the salary in 2016 increased by 3% οf the salary
=$78,280+3%
Salary οf 2016 = $80,628.40
Hence, she earn fοr each year frοm 2014 thrοugh 2016 is 80628.40
b) The average οf the last three years is the sum οf the salaries divided by the number οf salaries.
= $76,000+$78,280+$80,628.40 / 3
= $78,302.80
Hence, the average οf her last five years οf wοrking $78,302.80
c ) The annual retirement benefit is the prοduct οf the rate and the average and the number οf years οf service.
= 1.65%×$78,302.80×22
=$28,423.92
Hence, his annual retirement benefit was $28,423.92.
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A typewriter says that he can write 50 pages under 60 minutes. You selected 24 cases for these 50 pages, and found that it takes 63.2 (in minutes) and its standard deviation is 7.7 (in minutes). The test statistic for this test is equal to
a.
t = 2.04
b.
Z = 1.79
c.
t = 1.79
d.
t = 2.04
Answer: To determine the correct answer, we need to calculate the t-test statistic using the given information.
The formula for the t-test statistic for a one-sample t-test is:
t = (x - μ) / (s / sqrt(n))
where x is the sample mean, μ is the hypothesized population mean (which is not given in this question), s is the sample standard deviation, and n is the sample size.
Here, x = 63.2 minutes, s = 7.7 minutes, and n = 24 cases. We are not given a hypothesized population mean, so we cannot calculate the exact t-test statistic. However, we can use the sample mean as an estimate of the population mean for the purposes of this question.
Plugging in the values, we get:
t = (63.2 - 60) / (7.7 / sqrt(24))
t = 2.04
Therefore, the correct answer is (a) t = 2.04.
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.42cm
7.42cm and a standard deviation of 0.36cm. Using the empirical rule, what percentage of the apples have diameters that are between 6.34cm and 8.5cm
The percentage of percentage of the apples have diameters that are between 6.34cm and 8.5cm is given as follows:
99.7%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The measures of 6.34 cm and 8.50 cm are the bounds exactly within three standard deviations of the mean, hence the percentage is given as follows:
99.7%.
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what is the interquartile range of this data set? enter answer in box
Answer:
do it by yourself what you do while teacher is teaching
What is the answer to this question pls
51°
4
109°
The length of unknown side is,
⇒ 4.92
We have to given that;
A triangle is shown in image.
Let the length of unknown side = x
Now, From trigonometry formula we get;
⇒ tan 51° = x / 4
⇒ 1.23 = x / 4
⇒ x = 1.23 × 4
⇒ x = 4.92
Thus, the length of unknown side is,
⇒ x = 4.92
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S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B = the number is Between 12 and 25
O = number is Odd
L = number is a Less than 25
Which events are independent.
After considering all the given options we conclude that the number is atleast 21 and the less than 25, which is Option C.
It is given to us that two events are independent if they take place then one event does not trigger the probability of the other event.
Now if the taking place of a certain event triggers the other event then it is referred as dependent
For the given case, we have four events A, B, Q and L.
A = the state when the given number is At least 21
B = is the sate when the given number is Between 12 and 25
Q = is the sate when the given number is Odd
L = is the state when the given number is a Less than 25
It is clearly visible that events A and L are independent due to the number being at least 21, it doesn't affect whether it's less than 25 or not. So, events B and Q are independent because if we know that a number is between 12 and 25, it doesn't affect whether it's odd or not.
Hence, option C) A and L is correct.
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The complete question is
S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B= the number is Between 12 and 25
Q = number is Odd
L= number is a Less than 25
Which events are independent.
Question options:
A) A and B
B) A and O
C) A and L
D) Band O
E) Land B
F) Land O
G) None of the 2 events are independent
Find the circumference and area of the circle.
Answer:
9.38
Step-by-step explanation:
I did the math
The length of circumference of this circle is 21.9911 inches.
The area of this circle is, approximately, 38.4845 (in²).
Step-by-step explanation:For the circumference.1. Formula.The circumference of the circle can be easily found by utilizing the "π" (pi) number.This number is one of the most recognizible and emblematic numbers in math because it's the value of the ratio between any circle's length of circumference to it's diameter. Therefore, another way to express π is:
[tex]\sf \pi =\dfrac{s}{d}[/tex], where "s" is the length of the circumference of a circle, and "d" is the diameter of that same circle.
The value of π is not a variable, it is a constant for all circles, and it's, approximately, 3.141592653589793238... But don't worry, majority of calculator, if not all of them, have a button with the π so you can just click on it and have that value written automatically.
Fun fact: This number doesn't really have an end for its decimal figures because it's irrational.
2. Rewrite the formula.So now, taking the equation of π presented previously, we can rewrite the equation by solving it for "s", which is our variable of interest for this first parth. This is the process of that rewritting:
[tex]\sf \pi(d) =\dfrac{s}{d}(d)\\ \\\\\pi(d) =s\\ \\ \\s=\pi(d)[/tex]
3. Calculate.We're given the diameter of this circle, which is 7 inches. Now, substitute letter "d" on the formula by "7 inches" and calculate:
[tex]\sf s=\pi(7(in))=\boxed{\sf 21.9911(in)}.[/tex].
Remember that π is an irrational number, so any calculation involving it will result in an irrational answer aswell, unless the π is cancelled by another π.
The length of circumference of this circle is 21.9911 inches.
-------------------------------------------------------------------------------------------------------
For the area.1. Formula.These are the most commonly used formulas for the area of circles:
[tex]\sf1) A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
[tex]\sf2) A=\dfrac{\pi d^{2}}{4}[/tex]; where "d" si the diameter of the circle.
Remember that the difference between the radius and diameter is just that the radius is half of the diamaterer. So, technically, everytime you have either the diameter of the radius, you can get both of the parameters.
2. Calculate.Let's use the area formula that directly involves diameter to avoid any conversions.
Substitute letter "d" by the length of the diameter (7 inches).
[tex]\sf A=\dfrac{\pi d^{2}}{4}=\dfrac{\pi (7(in))^{2}}{4}=\pi \dfrac{49}{4} (in^{2} )=\boxed{\sf 38.4845(in^{2} )}.[/tex]
Therefore, the area of this circle is, approximately, 38.4845 (in²).
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Principle amount is 22,000. Interest rate is 4.5%.
1. Determine interest earned each year.
2. Write a recurrence relation to model the value of investment from year to year. Let Sn be the value after n years.
3. Determine value of interest after 5 years.
Answer:
1. $990
2. Sn = Sn-1 + (r/100) * Sn-1
3. $27,037.44
Step-by-step explanation:
1. The interest earned each year can be calculated using the simple interest formula:
Simple Interest = (Principal * Rate * Time) / 100
Here, Principal = $22,000, Rate = 4.5%, and Time = 1 year
So, the interest earned each year would be:
= (22,000 * 4.5 * 1) / 100
= $990
Therefore, the interest earned each year would be $990.
2. The recurrence relation to model the value of investment from year to year is:
Sn = Sn-1 + (r/100) * Sn-1
where Sn represents the value of the investment after n years, Sn-1 represents the value after n-1 years, and r represents the annual interest rate.
Using this recurrence relation, we can calculate the value of the investment for different years:
- S1 = 22,000 + 990 = 22,990
- S2 = 22,990 + (4.5/100) * 22,990 = 24,026.55
- S3 = 24,026.55 + (4.5/100) * 24,026.55 = 25,103.46
And so on...
3. To determine the value of the investment after 5 years, we can simply substitute n = 5 in the recurrence relation:
S5 = S4 + (r/100) * S4
= S3 + (r/100) * S3 + (r/100) * S3
= S2 + (r/100) * S2 + (r/100) * S2 + (r/100) * S2
= S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1
Substituting values from previous calculations:
S1 = 22,000 + 990 = 22,990
So,
S5 = 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990
= $27,037.44
Therefore, the value of the investment after 5 years would be $27,037.44.
please help me for 50 points!!
simplify: -3 √84x^3
A. -6x√21x
B. -6√21
C. 6x√21x
Answer:
C
Step-by-step explanation:
the prime factorization of 84 is 2 x2 x 3 x 7
I can rewrite the problem
-3[tex]\sqrt{84x^{3} }[/tex]
-3[tex]\sqrt{(2)(2)(3)(7)xxx}[/tex] pull out the pairs
-3(2)x[tex]\sqrt{(3)(7)x}[/tex]
-6x[tex]\sqrt{21x}[/tex]
Helping in the name of Jesus.
Correct answer gets brainliest!!!!
Answer:
To find the product of matrices AB, we need to multiply the elements of the rows of matrix A with the corresponding elements of the columns of matrix B, and then sum these products.
Since matrix A is a 2x2 matrix and matrix B is a 2x3 matrix, we can perform the multiplication as follows:
AB = | 1 2 | | 1 2 3 | | (1*1)+(2*4) (1*2)+(2*5) (1*3)+(2*6) |
| 3 4 | x | 4 5 6 | = | (3*1)+(4*4) (3*2)+(4*5) (3*3)+(4*6) |
| | | |
| 9 12 15 | | 9 12 15 |
Therefore, the product of matrices AB is a 2x3 matrix, and the answer is C) 2x3.
Line n is perpendicular to the x-axis and passes through the point (–3,–7).
Write the equation for line n.
What is the slope of line n?
The equation for line n that is perpendicular to the x-axis and passes through the point (–3,–7) is x = -3, and its slope is undefined.
Since line n is perpendicular to the x-axis, it is parallel to the y-axis. Therefore, its slope is undefined since the y-axis is a vertical line with no defined slope.
To write the equation for line n, we know that the y-coordinate of every point on the line will be constant since the line is parallel to the y-axis. We also know that the line passes through the point (-3,-7), so we can write the equation as:
x = -3
This means that for any value of y, the x-coordinate will always be -3. Graphically, this represents a vertical line passing through the point (-3,-7) and parallel to the y-axis.
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what is y= -2/9x +2 in standard form?
Answer:
2x+9y=18
Step-by-step explanation:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
Step-by-step explanation:
C (Wait for another defendant, check with him and write this answer)
If Duane's income tax bill was $1000, what was his taxable income?
To determine Duane's taxable income, we need to know his tax rate. Let's assume that his tax rate is a flat 20%.
We can use the formula:
taxable income = tax bill / tax rate
Plugging in the values given, we get:
taxable income = $1000 / 0.20
taxable income = $5000
Therefore, Duane's taxable income was $5000.
Answer:
Without more information, it is not possible to determine Duane's taxable income.
solve the area of the shaded region
The area of the shaded region is 117.8 m².
Given is a semicircle and a triangle in it, we need to find the area that is shaded,
So, we know that a triangle in a semicircle is always a right triangle whose hypotenuse is the diameter of the semicircle,
So, let us find the hypotenuse of the triangle (diameter of the semicircle) using the Pythagorean theorem,
diameter / hypotenuse = √21.6²+9²
= 23.4m
So the radius = 23.4/2 = 11.7 m
To find the area of the shaded region we will subtract the area of triangle from the semicircle,
So,
Area of the shaded region = π×r²/2 - 1/2×base×height
= 3.14×11.×7²/2 - 1/2×21.6×9
= 215 - 97.2
= 117.8 m²
Hence the area of the shaded region is 117.8 m².
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The table below gives data from a linear function. Find a formula for the function.
Price per shirt, p($) 15 20 25
Number of shirts sold, q = f(p) 1000 750 500
a. f( p) = 1750p − 50 b. f( p) = 1000 − 50p c. f( p) = 1000 + 50 p
d. f( p) = 1750 + 50 p e. f( p) = 1750 − 50p
The formula for the linear function is f(p) = -50p + 1750. So, correct option is E.
To find the formula for the linear function from the given table, we need to determine the equation of a straight line that passes through the three given points. We can use the point-slope form of the equation of a straight line to solve for the slope and y-intercept.
Let's choose two of the given points, say (15, 1000) and (25, 500), to calculate the slope:
slope = (change in y)/(change in x)
= (500 - 1000)/(25 - 15)
= -50
Now, we can use the slope and one of the given points, say (15, 1000), to solve for the y-intercept using the point-slope form:
y - y₁ = m(x - x₁)
y - 1000 = -50(x - 15)
y - 1000 = -50x + 750
y = -50x + 1750
Therefore, the formula for the linear function is f(p) = -50p + 1750, which means that for each additional dollar increase in price per shirt, the number of shirts sold decreases by 50. Option (e) is the correct answer.
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express 7 min 30 sec. as a percentage of 1 hour
Answer:
12.5 is the answer
Step-by-step explanation:
7 × 60 ( 7 being the minutes, 60 being the hour )
= 420
+ 30
= 450
450 ÷ 3600 × 100
45000 ÷ 3600
450 ÷ 30
= 12.5
12.5 being the answer
the price of a shirt was $25, but it is now on sale for $20. what is the percent decrease in price?
Find the Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1
The Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1 is
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]
In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.
The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
In the scenario above, we are given the function f(x) = e and a = 1.
The first derivative of e^x is e^x,
the second derivative is e^x,
and the third derivative is also eˣ.
We then evaluate these derivatives at a = 1, we get:
f(1) = e¹ = e
f'(1) = e¹ = e
f''(1) = e¹ = e
f'''(1) = e¹ = e
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
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The Problem Rodeos have long been a part of the culture in the southernmost part of the country and the growing popularity of the annual Easter event across South America prompted the Rupununi Development Corporation to construct a luxury resort with 60 two-bedroom suites for the visiting cultural troupes (troupe leaders and artistes). Capacity is ten troupe leaders and fifty artistes. Each suite is equipped with a small kitchenette, which contains a 7.3 cu ft. refrigerator, a microwave, and a coffee maker. A Drystan 6-piece bedroom set and the Ashley stationary sofa and love seat (all imported from Manaus at considerable cost) are also part of the furnishings. Each accommodation also has an excellent view if the Kanuku Mountains and nearby savannahs. The facility cost the Corporation $1,920,000 to build and equip and depreciation $160,000 per year (a fixed cost). Other operating costs include: Labor $320,000 per year plus $5 per suite per day Utilities $158,000 per year plus $1 per suite per day Miscellaneous $100,000 per year plus $6 per suite per day In addition to these costs, costs are also incurred on food and beverage for each guest. These costs are strictly variable, and (on average), are $40 per day for troupe leaders and $15 per day for artistes. Required Part A Assuming that the facility can maintain an average annual occupancy of 80% in both troupe leader and artistes suites (based on a 360 -day year), calculate the following: i. the annual fixed costs ii. the variable cost per guest by type of guest iii. the annual number of guest days by type of guest
Malden go company has a balance and its accounts payable control count of $10,500 on January 1, 2021. The subsidiary ledger contains three accounts Smith Company balance of $3000 white company balance of tMalden go company has a balance and it’s accounts payable control count of $10,500 on January 1, 2021. The subsidiary ledger contains three accounts Smith Company balance of $3000 white company balance of $2500 and Marina company during the January the following payable related transactions occurred
Answer:
6
Step-by-step explanation:
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The components of v = 210i + 300i represent the respective number of gallons of regular and premium gas sold at a station. The components of w = 2.8i + 2.99i represent the respective prices per gallon for each kind of gas. Find Vw and describe what the answer means in practical terms.
The station earned $1485 in revenue from selling the gas.
In this problem, we are given two vectors, v and w, representing the number of gallons of gas sold at a station and the corresponding prices per gallon, respectively. We are asked to find the dot product of these two vectors, which is a scalar quantity known as the "Vw". We will then interpret the meaning of this dot product in practical terms.
To find the dot product of v and w, we will use the formula:
Vw = v . w = (210)(2.8) + (300)(2.99)
Vw = 588 + 897 = 1485
Therefore, the value of Vw is 1485.
Practical terms: The dot product of two vectors is a scalar quantity that represents the "projection" of one vector onto the other. In this case, the dot product Vw represents the total revenue earned by selling regular and premium gasoline at the given station.
The components of v represent the number of gallons of regular and premium gas sold, while the components of w represent the respective prices per gallon for each kind of gas. Multiplying the number of gallons sold by the price per gallon gives the total revenue earned for each type of gas. Adding these two values together gives the total revenue earned for both types of gas.
Therefore, the dot product Vw represents the total revenue earned by selling all the gas at the given station. In practical terms, this means that the station earned $1485 in revenue from selling the gas.
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The cost of a pen is $15. Find the cost of 162 pens
Answer: 15 x 162 = 2430$
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µg =0. Compute the value of the t test statistics. Round intermediate
calculations to four decimal places as needed and final answers to three decimal places as needed.
x 9 6 7 5 12
y 6 8 3 6 7
A.t= 2.890
B.t= 1.292
C. t=0.578
D. t=0.415
Answer: To compute the t-test statistic for the paired sample data, we need to first calculate the sample mean difference and the sample standard deviation of the differences. Then we can use the formula:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the standard error of the mean difference is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Let's first calculate the sample mean difference:
x 9 6 7 5 12
y 6 8 3 6 7
The differences between each pair of x and y values are:
(9-6), (6-8), (7-3), (5-6), (12-7) = 3, -2, 4, -1, 5
The sample mean difference is the average of these differences:
sample mean difference = (3 - 2 + 4 - 1 + 5) / 5 = 1.8
Next, we need to calculate the sample standard deviation of the differences. To do this, we first calculate the deviations of each difference from the sample mean difference:
(3 - 1.8), (-2 - 1.8), (4 - 1.8), (-1 - 1.8), (5 - 1.8) = 1.2, -3.8, 2.2, -2.8, 3.2
The sample standard deviation of the differences is the square root of the sum of the squared deviations divided by (n-1):
sample standard deviation = sqrt[(1.2^2 + (-3.8)^2 + 2.2^2 + (-2.8)^2 + 3.2^2) / 4] = 3.153
Finally, we can calculate the t-test statistic:
t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)
where the hypothesized mean difference is 0, and the standard error of the mean difference is:
standard error = sample standard deviation / sqrt(sample size) = 3.153 / sqrt(5) = 1.410
Substituting the values, we get:
t = (1.8 - 0) / 1.410 = 1.277
Rounding the final answer to three decimal places, we get:
t = 1.277
Therefore, the correct option is B. t = 1.292.