Answers
The amount of money Laurie would pay to have the pond cleaned is equal to $3,161.85.
How to calculate the volume of a hemisphere?In Mathematics and Geometry, the volume of a hemisphere can be calculated by using the following mathematical equation (formula):
Volume of a hemisphere = 2/3 × πr³
Where:
r represents the radius.
Note: Radius = diameter/2 = 13/2 = 6.5 feet.
By substituting the given parameters into the formula for the volume of a hemisphere, we have the following;
Volume of a hemisphere = 2/3 × 3.14 × (6.5)³
Volume of a hemisphere = 574.881 ft³
Cost = 5.50 × 574.881 ft³
Cost = $3,161.85
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Related Questions
The following monthly data are taken from Ramirez Company at July 31: Sales salaries, $580,000; Office salaries, $116,000; Federal income taxes withheld, $174,000; State income taxes withheld, $39,000; Social security taxes withheld, $43,152; Medicare taxes withheld, $10,092; Medical insurance premiums, $14,000; Life insurance premiums, $11,000; Union dues deducted, $8,000; and Salaries subject to unemployment taxes, $64,000. The employee pays 40% of medical and life insurance premiums. Assume that FICA taxes are identical to those on employees and that SUTA taxes are 5.4% and FUTA taxes are 0.6%.
1. & 2. Using the above information, complete the below table and prepare the journal entries to record accrued payroll, including employee deductions, and cash payment of the net payroll (salaries payable) for July.
3. Using the above information, complete the below table.
4. Record the accrued employer payroll taxes and other related employment expenses and the cash payment of all liabilities related to the July payroll-assume that FICA taxes are identical to those on employees and that SUTA taxes are 5.4% and FUTA taxes are 0.6%.
Answers
The answers are 1) 360,000, 2) 217,060, 3) 37,140 and 4) 180,080.
1) To calculate the amount of premium paid by the employee and the employer =
Consider employee medical insurance payable, and employee life insurance payable.
The journal entries for accrual payroll, including employee deductions, consider sales salaries expense office salaries expense, social sec taxes payable Medicare tax payable, employee income taxes, life insurance payable, union dues, salaries payable.
2) Journal entry for cash payment of net payroll for month of July consider salaries payable and cash.
3) Calculate the unemployment tax amount, consider state unemployment taxes and federal unemployment taxes,
Journey Entries for accrued employer payroll taxes,
Payroll taxes expenses, social taxes, Medicare taxes, state unemployment taxes, federal unemployment taxes, employee medical and life insurance.
4) Journal entries for cash payment of all libraries, consider, social medical taxes, employee fed, medical, life and state income taxes payable.
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How do you calculate this???
Picture below. Thank you.
Answers
We can see here that the measure of variability using the range will be: 1.
What is measure of variability?A statistical metric known as a measure of variability tells us how widely spaced or dispersed a group of data points are. Measures of variability are used to quantify how significantly different a dataset's individual data points are from one another.
The measure of variability using range will:
Mean (Peak season) - Mean (Off Peak Season) = 6 - 5 = 1.
We see here that the mean of the peak season population is increased compared to that of the off-peak season. The mean of the off-peak season is seen to be lower.
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A researcher started tracking the number of mice in the lab.
Which of the following equations models how many mice there will be in the lab after 10 months?
Select one:
m(10) = 3 + 2(10)
m(10) = 2(3)^10
m(10) - 3(10)^2
m(10) = 3(2)^10
Answers
The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.
We have,
From the given data, we can see that the number of mice is being multiplied by 2 every month.
That means the growth is exponential.
We can use the formula for exponential growth:
[tex]m(t) = a \timesr^t[/tex]
where m(t) is the total number of mice after t months, a is the initial number of mice (when t = 0), and r is the common ratio
From the given data, we can see that when t = 0, there are 3 mice.
So, a = 3.
Also, we can see that the common ratio is 2 (i.e., the number of mice is being multiplied by 2 every month).
Now,
The equation that models how many mice there will be in the lab after 10 months is:
m(10) = 3 × 2^10
Simplifying this equation gives:
m(10) = 3 × 1024
m(10) = 3072
Therefore,
The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.
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A bag has 6 blue cubes, 3 red cubes, and 3 green cubes. If you draw a cube and replace it in the bag 120 times, which of the following amounts would you expect to pull?
Answers
The expected values are 60 blues, 30 reds and 30 greens
Which amount would you expect to pull?From the question, we have the following parameters that can be used in our computation:
6 blue cubes, 3 red cubes, and 3 green cubes
This means that we have the following proportions
Blue = 6/(6 + 3 + 3) = 1/2
Red = 3/(6 + 3 + 3) = 1/4
Green = 3/(6 + 3 + 3) = 1/4
If you draw a cube and replace it in the bag 120 times, we have
Blue = 1/2 * 120 = 60
Red = 1/4 * 120 = 30
Green = 1/4 * 120 = 30
Hence, the expected values are 60 blues, 30 reds and 30 greens
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A soda can has a radius of 1 inch and a height of 5 inches and a density of 3.2 g/mL. What is the mass?
Answers
The mass of the soda can is given by the formula M = V*d, where d is the density of the soda can. Substituting the given values, we get M = 15.708 cubic inches * 3.2 g/mL = 50.226 g.
Therefore, the mass of the soda can is approximately 50.226 grams.
Claire tried to subtract two polynomials which step did Claire make an error or are there no errors
Answers
Use powers to rewrite these problems: Example: 5 x 5 = 52
a. 5 * 5 * x*x*x
b. 8*8*8 = 8^3
c. 4*4*4*x*x*x*x
Answers
b. 8 * 8 * 8 = 8^3
c. 4 * 4 * 4 * x * x * x * x = 4^3 * x^4
solve this equation
4(x-1)=2(6-2x)
Answers
Answer:
4(x-1)=2(6-2x)
4x-4=12-4x
4x+4xd=12+4
8x=16
x=2
Answer:
x=2
Step-by-step explanation:
Step 1: Distribute
To solve this problem, the first step is distributing the four and the 2.
[tex]4(x-1)=2(6-2x)\\\\4x-4=12-4x[/tex]
So this is our simplified problem.
Step 2: Solve for x
Step 2a: Add 4x to both sides:
(This is because we do not have two variables in the equation, making it easier to solve.
[tex]4x+4x-4=12-4x+4x\\\\8x-4=12+0\\\\8x-4=12[/tex]
Step 2b: Add 4 to both sides:
(We do this to leave the variable on one side and the constant on the other. )
[tex]8x-4+4=12+4\\\\8x+0=16\\\\8x=16[/tex]
Step 2c: Divide both sides by 8:
(The reason why we do this is to isolate the variable without any coefficient in front.)
[tex]\frac{8x}{8} =\frac{16}{8} \\\\x=2[/tex]
The 5-lb collar slides on the smooth rod, so that when it is at A it has a speed of 10 ft/s. A) if the spring to which it is at- tached has an unstretched length of 3 ft and a stiffness of k-= 10 lb/ etermine the normal force on the collar at this instant. B)Determine the acceleration of the collar at this instant.
Answers
The acceleration of the collar at point A is 5 ft/s^2.
A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:
N - 5 = 0
where N is the normal force. Solving for N, we get:
N = 5 lb
B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:
x = L - y = 3 - 0 = 3 ft
where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:
F = kx = 10 lb/ft × 3 ft = 30 lb
The weight of the collar is:
W = mg = 5 lb
where g is the acceleration due to gravity. The net force on the collar is therefore:
Fnet = F - W = 30 - 5 = 25 lb
Using Newton's second law, we can write:
Fnet = ma
where a is the acceleration of the collar. Solving for a, we get:
a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2
Therefore, the acceleration of the collar at point A is 5 ft/s^2.
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Helppppp
I really neeed this answer
Answers
s√3 is the distance from point A to point B. Therefore, the correct option is option D among all the given options.
While distance and displacement appear to have the same meaning, they actually have very different definitions and meanings. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "the amount of ground the object has travelled over during its motion."
Distance² = s² + s² + s²
Distance² = 3 s²
Distance = s√3
Therefore, the correct option is option D among all the given options.
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I need help fast I’ll rate
Answers
The polynomial equation of the smallest degree is f(u) = (u + 2)³(u - 1)²(u - 3)
The minimal degree of the graphGiven that we have the graph of a polynomial
The degree of the graph is the number of times the graph intersect and/or crosses the x-axis
In this case, we have the following points at which the graph intersect and/or crosses the x-axis
Lies on the x-axis at u = -2; so the multiplicity is 3Intersects with the x-axis at u = 1; so the multiplicity is 1Touches the x-axis at u = 3; so the multiplicity is 2When the multiplicities are added, we have
Degree = 3 + 1 + 2
Degree = 6
So, the degree is 6
The zero at u = 1In (a), we have
Intersects with the u-axis at x = 1; so the multiplicity is 1This means that
The zero at u = 1 has a multiplicity of 1
The equation of the smallest degreeThe equation is represented as
f(u) = (u - zero)^multiplicity
So, we have
f(u) = (u + 2)³(u - 1)²(u - 3)
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Which equation describes a vertical translation of the square root parent function?
A. y = x − 4−−−−−−√
x
−
4
B. y = x−−√−6
x
-
6
C. y = x−−√
x
D. y = −x−−√
Answers
Answer:
The equation that describes a vertical translation of the square root parent function is A. y = x − 4−−√ + k where k is the vertical shift.
The square root parent function is f(x) = √x. To perform a vertical translation of this function, we add or subtract a constant value to the function. In this case, the function y = x − 4−−√ represents a vertical translation of the square root parent function by 4 units downwards.
Option B, y = x−−√−6 represents a vertical translation of the square root parent function by 6 units downwards. Option C, y = x−−√, represents the square root parent function without any vertical shift. Option D, y = −x−−√, represents a reflection of the square root parent function about the y-axis.
15.Marla and Kelly purchased flowers. Marla
purchased 7 roses for x dollars each and 10
daisies for y dollars each. She spent $40.50 on
the flowers. Kelly bought 3 roses and 15
daisies at the same cost as Marla. She spent
$30.75 on her flowers. The system of
equations below represents this situation.
7x+10y = 40.5
3x + 15y = 30.75
Which statement below is correct?
Answers
A statement which is correct include the following: A. Roses cost $2.75 more than daisies.
How to write an equation to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the cost of roses and cost of daisies, and then translate the word problem into a linear equation as follows:
Let the variable x represent the cost of roses.Let the variable y represent the cost of daisies.Based on the information provided about the flowers purchased by Marla and Kelly. we have the following system of linear equations;
7x + 10y = 40.5
3x + 15y = 30.75
By solving the system of linear equations simultaneously, we have:
x = 4 and y = 1.25
Difference = 4 - 1.25
Difference = $2.75
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which ordered pair is a solution to the Equation? 3y = -2x - 4
(1, -2)
(-1, 3)
(3, 4)
(-2, 4)
Answers
The ordered pair that is a solution to the equation 3y = -2x - 4 is given as follows:
(1, -2).
How to obtain the ordered pair?The equation for this problem is defined as follows:
3y = -2x - 4
To verify whether an ordered pair is a solution to the equation, it must make the equation true.
When x = 1 and y = -2, we have that:
3y = 3(-2) = -6.-2x - 4 = -2(1) -4 = -6.Hence the ordered pair (1,-2) is a solution to the equation for this problem.
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Solve the equation 4m = 28 for m.
A. 3
B. 4
C. 5
D. 7
Answers
Answer:
Dividing both sides by 4, we get:
4m/4 = 28/4
Simplifying, we get:
m = 7
Therefore, the answer is D. 7.
Julia saved 1 cent ($0.01) on the first day of the month, 2 cents ($0.02) on the second day, 4 cents ($0.04) on the third day, and double the previous day's amount on each successive day. Julia's savings for the first five days are shown in the table below.
On what day will Julia first save an amount greater than $1.00?
Select one:
day 7
day 50
day 8
day 20
Answers
Answer:
Step-by-step explanation:
Because we're told the amount doubles on each successive day, we know we're dealing with an exponential function.
The general form for an exponential function is
[tex]f(x)=ab^x[/tex], where a is the initial value, b is the base, and x is the exponent.
We know that Julia saved $0.01 on the first day so our a value is 0.01.
Because the amount doubles each time, our base is 2.
Furthermore, since we're want to find when Julia's savings exceed $1.00, we can turn the general exponential formula into an inequality where the formula is greater than 1 and solve for x (time in days):
[tex]1.00 < 0.01(2)^x\\100 < 2^x\\log(100) < log(2)^x\\log(100) < x*log(2)\\log(100)/log(2) < x\\6.64 < x\\7 < x[/tex]
We had to round the 6 to the nearest whole number (7) to get the answer.
We can check our work by plugging in both 6.64 for x and 7 for x to see how at 7 days, Julia's savings exceed 1.00
Plugging in 6.64 for x:
[tex]f(6.64)=0.01(2)^6^.^6^4\\f(6.64)=0.01*99.7\\f(6.64)=0.997\\f(6.64)=1.00[/tex]
Using 6.64 for x makes Julia's savings equal 1, but they don't exceed 1
Plugging in 7 for x:
[tex]f(7)=0.01(2)^7\\f(7)=0.01*128\\f(7)=1.28[/tex]
1/2,1,2/3,2 pattern arithmetic sequence
Answers
Answer:
The given pattern does not form an arithmetic sequence as there is no common difference between each term. An arithmetic sequence is a sequence in which there is a fixed difference between each consecutive term. For example, 1, 3, 5, 7 is an arithmetic sequence with a common difference of 2 (adding 2 to each term gives the next term). However, the given pattern of 1/2, 1, 2/3, 2 does not follow this pattern as the difference between each term varies. Therefore, this pattern does not fit the definition of an arithmetic sequence.
Step-by-step explanation:
Using any example of a 2 by 2 matrix;
Show that (A inverse) inverse = A; where A is a 2 by 2 matrix
Answers
The inverse of A is A^-1 (see picture), where A^-1 = (1/(determinant of A))*(adjoint of A). Note that the inverse of A only exists if ad - bc ≠ 0.
So, if ANY example of a 2 by 2 matrix is allowed… we use an example where a = 1, b = 2, c = -3, d = -5. The inverse matrix will have the terms -5, -2, 3, 1. (See photo)
To show that the inverse OF the inverse equals A, follow the same process. And.. yes, (A^-1)^-1 = A. We want to see the identity matrix 1, 0, 0, 1 since A*A^-1 = I (this is an uppercase i).
I’m on my phone so it’s harder to type. Refer to the picture to see my work:
I hope this helps!
Accounting 125000 loan for 5 years to start business
Owner paid 250 to the county for a business license
Answers
Answer:
p
Step-by-step explanation:
ok so first u take away the underlined letter and give and carry sorry the first one
A fair die is rolled 4 times. What is the probability of having no 1 and no 4 among the rolls? Round your answer to three decimal places.
Answers
The probability of rolling a number that is not 1 or 4 on all four rolls is (2/3)^4, since the rolls are independent events and the probability of each roll is 2/3.
(2/3)^4 = 0.197
Rounding to three decimal places, the probability of having no 1 and no 4 among the rolls is approximately 0.197.
Need help I have 20 min! x=In^20 Write in exponential form.
Answers
The given equation in exponential form will be [tex]20 = x^e[/tex]
Given is an equation, x = ㏑ 20,
So, we know that,
㏑(x) = [tex]log_e(x)[/tex]
And,
logₐ (x) = b
x = bᵃ
Therefore,
x = ㏑ 20
will be converted into,
[tex]20 = x^e[/tex]
Hence, the given equation in exponential form will be [tex]20 = x^e[/tex]
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The dimensions of square A are three times the dimensions of square B. The area of square B is 64 cm what is the area of square A
Answers
Then the area is 9 times bigger because you are working in squared dimensions for area. You must square the given scale factor 3.
If B is 64. Then A is 64x9=576
Need help with his page 20 points
Answers
Answer:
m/2 -6= m/4+2 can be solved as follows:
Multiply both sides of the equation by the least common multiple of the denominators, which is 4:
4(m/2 - 6) = 4(m/4 + 2)
2m - 24 = m + 8
Subtract m from both sides:
m - 24 = 8
Add 24 to both sides:
m = 32
Therefore, the value of m is C) 32.
k/12 = 25/100 can be solved as follows:
Multiply both sides of the equation by 12:
k = 12 * (25/100)
k = 3
Therefore, the value of k is A) 3.
9/5 = 3x/100 can be solved as follows:
Multiply both sides of the equation by 100:
100 * (9/5) = 3x
Simplify:
180/5 = 3x
36 = 3x
Divide both sides by 3:
x = 12
Therefore, the value of x is not one of the options provided.
Step-by-step explanation:
Answer:
Question 18:-[tex] \sf \longrightarrow \: \frac{m}{2} - 6 = \frac{m}{4} + 2 \\ [/tex]
[tex] \sf \longrightarrow \: \frac{m - 12}{2} = \frac{m + 8}{4}\\ [/tex]
[tex] \sf \longrightarrow \: 4(m - 12) =2(m + 8)\\ [/tex]
[tex] \sf \longrightarrow \: 4m \: - 48 =2m + 16\\ [/tex]
[tex] \sf \longrightarrow \: 4m \: - 2m = 16 + 48\\ [/tex]
[tex] \sf \longrightarrow \:2m = 64\\ [/tex]
[tex] \sf \longrightarrow \:m = \frac{64}{2} \: \\ [/tex]
[tex] \sf \longrightarrow \:m = 32 \: \\ [/tex]
[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: C) \: \: \: 32 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]
__________________________________________
Question 19:-[tex] \sf \leadsto \: \frac{k}{12} = \frac{25}{100} \\ [/tex]
[tex] \sf \leadsto \: 100(k)= 12(25) \\ [/tex]
[tex] \sf \leadsto \: 100 \times k= 12 \times 25 \\ [/tex]
[tex] \sf \leadsto \: 100 k= 300 \\ [/tex]
[tex] \sf \leadsto \: k= \frac{300}{100} \\ [/tex]
[tex] \sf \leadsto \: k= 3 \\ [/tex]
[tex] \qquad{ \underline{\overline{ \boxed{ \sf{ \: \: a) \: \: \: 3 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]
__________________________________________
Question 20:-[tex] \sf \longrightarrow \: \frac{9}{5} = \frac{3x}{100} \\ [/tex]
[tex] \sf \longrightarrow \: 100(9)= 5(3x) \\ [/tex]
[tex] \sf \longrightarrow \: 100 \times 9= 5 \times 3x \\ [/tex]
[tex] \sf \longrightarrow \: 900= 15x \\ [/tex]
[tex] \sf \longrightarrow \: x= \frac{900}{15} \\ [/tex]
[tex] \sf \longrightarrow \: k= 60 \\ [/tex]
[tex]\qquad{\underline{\overline {\boxed{ \sf{ \: \: a) \: \: \: 60 \: \: \: \: \: \checkmark }}}}} \: \: \bigstar[/tex]
__________________________________________
A straw is placed inside a rectangular box that is 1 inches by 3 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
The length of the straw is 4.26 inches.
We have,
On the bottom face,
Applying the Pythagorean theorem,
x² = 1² + 3²
x² = 1 + 9
x² = 10
Now,
Applying the Pythagorean theorem with the diagonal side.
d² = x² + 3²
d² = 10 + 9
d² = 19
d = √19
d = 4.36 in
Thus,
The length of the straw is 4.26 inches.
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Please help I need this will give 100 points please help
Answers
The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:
-∞ < x < 1 or 1 < x < 6 or 6 < x < 2
Solving Inequality in a given domainGiven the inequality,
f(x²-2) < f(7x-8) over D₁ = (-∞, 2)
We need to find the values of x that satisfy this inequality.
Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.
First, we can find the values of x that make the expressions inside the function equal:
x² - 2 = 7x - 8
Simplifying, we get:
x² - 7x + 6 = 0
Factoring, we get:
(x - 6)(x - 1) = 0
So the values of x that make the expressions inside the function equal are x = 6 and x = 1.
We can use these values to divide the domain (-∞, 2) into three intervals:
-∞ < x < 1, 1 < x < 6, and 6 < x < 2.
We can choose a test point in each interval and evaluate
f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.
Let's choose -1, 3, and 7 as our test points.
When x = -1, we have:
f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)
Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.
When x = 3, we have:
f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)
Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.
When x = 7, we have:
f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)
Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.
Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:
-∞ < x < 1 or 1 < x < 6 or 6 < x < 2
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If diameter EF bisects BC, what is the angle of intersection?
Answers
Answer:
The angle of the intersection is 90 degrees
Step-by-step explanation:
How I know this is because EF is the diameter, which means that arc EF is equal to 180 degrees. Because we know this that means when it is spilt into two parts, the arc and angle measure has to be 90 degrees.
Another way to do this is to remember that a circle is 360 degrees and the circle is split into 4 parts. So all you have to do is divide 360/4 to get 90. Your answer.
What is two ten thousandths in decimal form
Answers
Two ten thousandths are 0.0002.
The number 2 will be in ten thousand place
TENS ONES . TENTHS HUNDREDTHS THOUSANDTHS
. 0 0 0
TEN THOUSANDTHS
2
Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 10 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 8602 dollars. How much did she invest at each rate?
Answers
The amount she invested at each rate of interest for the simple interest are $39,100 and $78,200.
Given that,
Jolene invests her savings in two bank accounts.
Rate of interest for one account = 6% per year
Rate of interest for the other account = 10% per year
Let x be the principal amount invested in the account yielding 10% interest.
Interest amount = 0.1x
Principal amount in the account of 6% interest = 2x
Interest amount = 0.06 × 2x = 0.12x
Annual interest = $8602
0.1x + 0.12x = 8602
0.22x = 8602
x = $39,100
Amount invested for 10% interest account = $39,100
Amount invested for 6% interest account = 2 × $39,100 = $78,200
Hence the amount invested are $39,100 and $78,200.
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Suppose X~N(12,2). The empirical rule stated that about 68% of the x values lie within one stands deviation of the mean. Between what x Values does 68% of the data lie?
Answers
Answer:
Suppose X ~ N(12,2) represents a normal distribution with mean 12 and standard deviation 2. According to the empirical rule, about 68% of the x values lie within one standard deviation of the mean .
We can calculate the endpoints of the interval that represents one standard deviation from the mean as follows:
Lower endpoint: 12 - 2 = 10
Upper endpoint: 12 + 2 = 14
Therefore, about 68% of the x values lie between 10 and 14 1.
Step-by-step explanation:
Which expression is equivalent to
1/sin(2x)-cos(2x)/sin(2x)?
Answers
The trigonometric expression 1/sin(2x) - cos(2x)/sin(2x) = tanx
What is a trigonometric expression?A trigonometric expression is an equation that contains trigonometric ratios.
Given the expression 1/sin(2x) - cos(2x)/sin(2x), we need to find the expression that is equivalent to it.
So, we proceed as follows.
1/sin(2x) - cos(2x)/sin(2x) = [1 - cos(2x)]/sin(2x),
Using the trigonometric identity cos2x = cos²x - sin²x and sin2x = 2sinxcosx, we have that
[1 - cos(2x)]/sin(2x) = [1 - (cos²x - sin²x)]/2sinxcosx
= [1 - cos²x + sin²x)]/2sinxcosx
Now, 1 - cos²x = sin²x.
So, substituting this into the equation, we have that
[1 - cos²x + sin²x)]/2sinxcosx = [sin²x + sin²x)]/2sinxcosx
= [sin²x + sin²x)]/2sinxcosx
= 2sin²x/2sinxcosx
= sinx/cosx
= tanx
So, 1/sin(2x) - cos(2x)/sin(2x),= tanx
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