The yield to maturity on Bond B is 9%
How to calculate the yield to maturityWe know that Zero Coupon Bond Value= F/(1+r)^t
F= Face Value =100
r= Rate of interest
t= time to maturity =2Yrs
Price= F/(1+r)^t
84.18 = 100/(1+r)^t
(1+r)^t=100/84.18
(1+r)^2=1.18793
1+r=(1.18793)^(1/2)
r = 1.089922 - 1
r = 8.9922%
r = 9% (Approx)
In conclusion, the yield to maturity on Bond B is 9%
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Explain how to determine the zeros of g (x) = -(x+2) (x-3) (x-3)
The zeros of g(x)= -(x+2) (x-3) (x-3) are -2 and 3.
We are given that;
g (x) = -(x+2) (x-3) (x-3)
Now,
To determine the zeros of g(x) = -(x+2)(x-3)(x-3), we need to find the values of x that make g(x) equal to zero. This means that we need to solve the equation:
−(x+2)(x−3)(x−3)=0
To solve this equation, we can use the zero product property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x:
x+2=0orx−3=0
Subtracting 2 from both sides of the first equation, we get:
x=−2
Adding 3 to both sides of the second equation, we get:
x=3
Therefore, by the given equation the answer will be -2 and 3.
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the lowest common multiple of 36 30
Answer:
180
Step-by-step explanation:
To find the lowest common multiple (LCM) of 36 and 30, we can use the prime factorization method:First, we can find the prime factorization of each number:36 = 2^2 * 3^230 = 2 * 3 * 5Next, we can take the highest power of each prime factor that appears in either number and multiply them together.The highest power of 2 is 2^2 = 4.The highest power of 3 is 3^2 = 9.The highest power of 5 is 5^1 = 5.Multiplying these together, we get:LCM(36, 30) = 2^2 * 3^2 * 5 = 180Therefore, the lowest common multiple of 36 and 30 is 180.
Answer: 180
Step-by-step explanation:
To find the lowest common multiple (LCM) of two numbers, we need to find the smallest number that is a multiple of both of them.
One way to do this is to find the prime factorization of each number and then take the product of all the prime factors, with each factor occurring as many times as it appears in the factorization of either number.
The prime factorization of 36 is 2^2 × 3^2, and the prime factorization of 30 is 2 × 3 × 5. Therefore, the LCM of 36 and 30 can be found by taking the product of the highest power of each prime factor that appears in either factorization:
LCM(36, 30) = 2^2 × 3^2 × 5 = 180
Therefore, the lowest common multiple of 36 and 30 is 180.
How do you calculate this???
Picture below. Thank you.
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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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%.
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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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.
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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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
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.
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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Jake and Rafael are training for a bike race. Jake is a beginner and starts by riding up a hill with a 7.9° incline. Rafael is more experienced and rides up a hill with an 18.3° incline. If Jake and Rafael ride 100 ft., how much more horizontal distance did Jake cover?
Responses
4.1 ft.
4.1 ft.
9.6 ft.
9.6 ft.
17.7 ft.
17.7 ft.
19.2 ft.
The horizontal distance more that Jake was able to cover, given the incline, would be A.4.1 ft.
How to find the horizontal distance ?We can find the horizontal distance that both Jake and Raphael covered .
Jake's distance was:
cos ( 7.9 ° ) = adjacent / 100
adjacent = 100 x 0.989
adjacent = 98.9 ft
Rafael's distance was :
cos ( 18. 3° ) = adjacent / 100
adjacent = 100 x 0.951
adjacent = 95.1 ft
The difference and the distance covered in addition by Jake would be:
= 98. 9 - 95. 1
= 3. 8 ft
The closest option is 4. 1 ft.
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What is 2x-5y=9 in slope intercept form?
In circle R, find arc length of arc GH
The length of the arc GH is 13.3 cm
What is length of an arc?The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 360-( 170+80)
R = 360-250
R = 110°
l = 110/360 × 2 × 3.14 × 6.4
l = 4787.2/369
l = 13.3 cm (1.dp)
therefore the length of the arc GH is 13.3 cm
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Select the smaller fraction. 1/10 or 1/2
Answer:
1/10
Step-by-step explanation:
Select the smaller fraction. 1/10 or 1/2
1/10 = 1 : 10 = 0.1
1/2 = 1 : 2 = 0.5
so your answer is 1/10
A bakery sold 107 cupcakes in one day. The head baker predicted he would sell 87 cupcakes that day. What was the percent error of the baker's prediction?
Answer:
First, we need to calculate the absolute error, which is the difference between the predicted value and the actual value:
Absolute error = |predicted value - actual value| = |87 - 107| = 20
Then, we can calculate the percent error using the formula:
Percent error = (absolute error / actual value) x 100%
Plugging in the values, we get:
Percent error = (20 / 107) x 100% ≈ 18.69%
Therefore, the percent error of the baker's prediction is approximately 18.69%.
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.
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?
The length of one of the legs of a right triangle is 17. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides (the second leg).
The value of the smaller of the two missing sides (the second leg) is,
⇒ 144 units
We have to given that;
The length of one of the legs of a right triangle is 17.
And, The lengths of the other two sides are consecutive integers.
Hence, Let the smallest of the other legs be x,
And, the hypotenuse be x + 1.
So, By using the Pythagorean theorem as;
⇒ 17² + x² = (x + 1)²
⇒ 289 + x² = x² + 1 + 2x
⇒ 2x = 288
⇒ x = 144
Thus, The value of the smaller of the two missing sides (the second leg) is,
⇒ 144 units
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Need help I have 20 min! x=In^20 Write in exponential form.
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 number of runs scored by the Stars for six games is shown below.
4,9, 2, 4, 1,6
If the Stars scored 14 runs in their seventh game, which of the following statements is true?
OA. The mean increases and the median remains the same.
OB. The median increases and the mean remains the same.
OC. The mean and the median both increase.
O D. The median and the mean both remain the same.
A train moving 50 miles per hour meets and passes a train moving 50 miles per hour in the opposite direction. A passenger in the first train sees the second train pass in 5 seconds. How long is the second train?
Answer:
The length of the second train is 416.67 meters.
Step-by-step explanation:
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PLEASE HELP ME SOLVE THIS!!!!
The meaning of the absolute value of -5.5 is given as follows:
The temperature decreases 5.5 degrees.
What is the absolute value of a number?The absolute value of a number is the number without the signal, for example:
|-2| = |2| = 2.
The number in this problem is given as follows:
-5.5.
Hence:
The negative sign means that the temperature decreased.The absolute value of 5.5 means that the temperature decreased by 5.5 degrees.Hence the second option is the correct option in the context of this problem.
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What is two ten thousandths in decimal form
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
IQR of 28 22 15 16 15 13 19 18
Answer: The IQR of this data set is 5.5
Step-by-step explanation: Ok so first you line the data set up in correct order.
Here's the correct order:
13, 15, 15, 16, 18, 19, 22, 28
Then you find the median and since there's even amount of numbers you add the two numbers in the middle which is 16 and 18 and divide that by 2 which is 17. So the median is 17. Then you split the data set into halves. The first quartile is 15 and the third quartile is 20.5. Then to find the IQR, you would minus 20.5 - 15 = 5.5. Hope this helps!
Helppppp
I really neeed this answer
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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Given f(x) = 7 - 4x and f(x) = 27, what is the value of x?
Answer: x = -5
Step-by-step explanation:
Answer:
x=-5
7 - 4 * (-5)
Negative times a negative equals a positive
-4*-5=20
7+20=27
Which expression is equivalent to
1/sin(2x)-cos(2x)/sin(2x)?
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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Solve the equation.
22
= 6
2 =
Need help with his page 20 points
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]
__________________________________________
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−−√
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.
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
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]
A
The bottom of this cylinder, called the
base, has an area of 22 in.² It takes
22 in. of sand to cover the base.
The cylinder has a height of 3 in.
How much sand can the cylinder hold?
B
Which can be used to find the volume of a cylinder?
v=Area of the base + height of the cylinder
V= (Area of the base)2 x height of the cylinder
v=Area of the base x height of the cylinder
V = Area of the base
Answer: 1) 66 2)
Step-by-step explanation:
1) 22x3=66
2) C
Hope this helps! :)
The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every 8 minutes. The waiting times for the train are known to follow a uniform distribution.
What is the probability of waiting less than 2 minutes and more than 6 minutes?
The 30th percentile in the uniform distribution is 2.4 min.
The correct option is (b)
Probability :The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), :
P(E)= Number of favorable outcomes/ Number of total outcomes
[tex]\mu=\frac{a +b}{2}[/tex]
[tex]\sigma=\sqrt{\frac{(b-a)^2}{12} }[/tex]
P(x) = 1/ b - a if a < x < b
P(X < a) = 0
and
P(X > b) = 0
In this case, a = 0 and b = 8
The 30th percentile in the uniform distribution, this means that the probability is 0.30. Therefore:
0.3 = [tex]\frac{1}{8-0}.x[/tex]
0.3 (8 -0) = x
2.4 = x
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The given question is incomplete, complete question is :
The Sky Train from the terminal to the rental-car and long-term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. Find the 30th percentile for the waiting times (in minutes).
a. 2
b. 2.4
c. 2.75
d. 3