The 50th partial sum of the given arithmetic sequence is 4600
Calculating partial sum of an arithmetic sequenceFrom the question, we are to calculate the 50th partial sum of the given arithmetic sequence
The given arithmetic sequence is
-6, -2, 2, 6, ...
To find the 50th partial sum of the sequence, we will find the sum of the first 50 terms in the sequence.
The sum of n terms of a sequence is given by the formula,
S = n/2(a + l)
Where a is the first term
and l is the last term
l is given by
l = a + (n - 1)d
Where d is the common difference
In the given series
a = -6
d = -6 -(-2) = -6 + 2 = 4
Thus,
l = -6 + (50 - 1)4
l = -6 + 49×4
l = -6 + 196
l = 190
Then,
S = 50/2(-6 + 190)
S = 25(184)
S = 4600
Hence,
The sum is 4600
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Each marble bag sold by Eric’s Marble Company contains 3 red marbles for every 4 blue marbles. If a bag has 36 blue marbles, how many red marbles does it contain?
a cuboid with length of 21 cm and height of 16 cm has a volume of 6384 cm3. find its breadth ik
Answer:18
Step-by-step explanation:18
using cramer rao lower bound method, with a random sample of size n, find a minimum variance unbiased estimator of the parameter,λ of a poisson population
The minimum variance unbiased estimator of the parameter,λ of a poisson population is λ = Σxi/n.
What is variance?Variance is a measure of how spread out a set of data is. In statistics, it is the average of the squared differences from the mean of a set of values. It is calculated by taking the sum of the squared deviations from the mean and dividing it by the number of data points.
According to given information:Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean λ. The likelihood function is given by:
[tex]L(\lambda | x) = \pi[e^{(-\lambda)} \lambda^{(xi)} / xi!][/tex]
Taking the natural logarithm and differentiating with respect to λ:
ln L(λ | x) = -nλ + ln(λ) Σxi - Σln(xi!)
d/dλ ln L(λ | x) = -n + Σxi/λ
Setting the derivative equal to zero and solving for λ, we get:
λ = Σxi/n
This is the sample mean of the Poisson distribution, which is an unbiased estimator of λ. Moreover, using the Cramer-Rao lower bound, we can show that it is also the minimum variance unbiased estimator of λ.
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A soccer goal is 8 yards wide. Suppose a goalie is standing on her line in
the center of her goal as a striker from the opposing team moves the ball
towards her. The near post angle, a, is formed by rays extending from the
ball to the near post and the goalie. Similarly, the far post angle, ß, is
formed by rays extending from the ball to the far post and the goalie. See
the figure.
a) Determine the near post angle and the far post angle when the striker is
24 yards from the near post and 28 yards from the far post.
b) How far is the goalie from the ball?
c) To cover the near post, the goalie moves toward the near post in order
to make the near post angle and the far post angle equal. How far
toward her near post does the goalie need to move?
Where the following triangle problem is given, note that:
A) α [tex]\approx[/tex] 11.0
β β [tex]\approx[/tex] 9.4
B) 25.59 yrds
C) 0.38 yrds
What is the explanation for the above?A) To determine the near post angle and the far post angle when the striker is 24 yards from the near post
1/2 (24²) + 1/2 (28²) - 1/4(10²) = 655 (central line length formula)
Cos α = (24² + 655 - 5²)/ (2 x 24 x √655)
= 0.98171498561
α = Cos ⁻¹ 0.98171498561
α = 10.973603643623608717848651724941
α [tex]\approx[/tex] 11.0° (Cosine Law)
For 28 yards from the far post.
Cos β = (28² + 655 - 5²)/ (2 x 28 x √655)
= 0.98659913977
β = Cos ⁻¹ 0.98659913977
β = 9.3905311636838307510867912796592
β [tex]\approx[/tex] 9.4°
B) Distance between the goalie from the ball is
√655 = 25.592967784139454896443137575823
Distance [tex]\approx[/tex] 25.59 yrds
C) 5-10 * ((24)/(24+28)) = 0.38 yrds (Angular Bisector Theorem)
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Evaluate the function as indicated
[tex]g(x) = {5.9}^{x} [/tex]
(a) x = -1 G(-1) =
(b) G(-2) = x = -2
(c) x = √5 G(√5) =
what is the answer for a, b, and c?
Two different rectangles are joined together to make a compound shape. Shape A has a length of (x + 3) and a width of (x + 2). Shape B has a length of (x + 6) and a width of (x-2). All measurements are in centimetres. (x+3) Shape A Shape B (x+6) (x + 2) NOT TO SCALE (x-2) Find an expression for the area of the compound shape in cm². Give your answer in the form ax² + bx + c.
The expression for the area of the compound shape in cm² is 2x^2 + 11x - 6.
What is the expression for the area?To find the expression for the area of the compound shape, we need to first calculate the individual areas of Shape A and Shape B, and then add them together.
The area of Shape A is given by multiplying its length and width:
Area of Shape A = (x + 3) * (x + 2)
The area of Shape B is given by multiplying its length and width:
Area of Shape B = (x + 6) * (x - 2)
Now, we can add the two areas together to get the expression for the area of the compound shape:
Area of compound shape = Area of Shape A + Area of Shape B
= (x + 3) * (x + 2) + (x + 6) * (x - 2)
Expanding the above expression, we get:
= x^2 + 2x + 3x + 6 + x^2 + 6x - 12
= 2x^2 + 11x - 6
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A boat needs to travel North at 30km/h, a constant current of 4km/h is flowing in a north-west direction - What is the equivalent speed in still water for the boat to achieve actual speed of 30km/h ?
The equivalent speed in still water for the boat is 30.26 km/h.
What is the equivalent speed of the boat?
The equivalent speed of the boat in still water is calculated as follows;
The boat needs to travel North at 30 km/h,
The speed of the wave = 4 km/h
The equivalent speed of the boat in still water is calculated by applying Pythagoras theorem;
v² = (4 km/h)² + (30 km/h)²
v = √ [(4 km/h)² + (30 km/h)²]
v = 30.26 km/h
Thus, the equivalent speed of the boat is calculated by applying vector addition principle.
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Minimise : 3x+2y
Subject to: 5x+y=10
X+y=6
X+4y= 12
Find this question?
This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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IF YOU CAN ANSWER THIS CORRECT WITH A Good explanation I'll give 5 stars, a thanks and brainly (also your very smart)
Rebecca is x years old.Mary is 8 years older than rebecca. Jill is three times older than mary. The sum of their ages is 67.
A) form an expression in terms of x
Answer:
A) 5x+32=67
Rebecca is 7, Mary is 15, and Jill is 45
Step-by-step explanation:
Rebecca is x years old.
If Mary is 8 years older than Rebecca, Mary's age is 8 more than x.
We can write Mary's age as:
x+8
Jill is three times older than Mary.
This means that Jill's age is equal to three times x+8.
We can write Jill's age as:
3(x+8)
Use the distributive property.
3(x+8)=
3x+24
So, Jill's age (in terms of x) is 3x+24.
The sum of their ages is 67, so if we add all of their ages, we will get 67.
x+(x+8)+(3x+24)=67=
5x+32=67
Not sure if you want this solved, but here it is:
5x+32=67=
5x=35=
x=7
Let's find Mary's age.
x+8=
7+8=
15.
Now, let's find Jill's age.
3x+24=
3(7)+24=
21+24=
45.
So, Rebecca is 7, Mary is 15, and Jill is 45.
4. An opportunity cost that a business might face is
a. forgoing the interest that the owners could have earned on their savings if they had not
invested their savings in the business
Ob. forgoing rental income to be earned if the business rented out its building
forgoing the salaries the owners would have received at other jobs
OC.
c.
Od.
d. all of the above
5. The difference between macroeconomics and microeconomics is that
a. microeconomics studies inflation while macroeconomics studies taxes
Economics
b. macroeconomics looks at the economy as a whole while microeconomics looks at single
units in the economy
Oc. macroeconomics measures the price of a good and quantity demanded while
microeconomics looks
at things like unemployment or GDP
Od.
d. macroeconomics looks at single units in the economy while microeconomics looks at the
economy as a whole
Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour. If the total distance was 12 miles and the trip took 5 hours in all, how far did they go by boat?
The distance for boat is,
= 43.2 miles
Given that;
Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour
Now, For Walk DATA:
Rate = 2 mph ; time = x hrs.
Then, distance = 2x miles
For Boat DATA:
Rate = 10 mph ; time = 5 - x hrs
Then, distance = 10 (5 - x) miles
Hence, We can formulate;
distance + distance = 12 miles
2x + 10 (5 - x) = 20
2x + 50 - 10x = 20
30 = 8x
x = 3.6
Hence, Boat time ,
5 - x = 5 - 3.6 = 1.4 hr (boat time)
And, The value of Boat distance = 12x = 12 x 3.6 = 43.2 miles
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9999999999999999999999999999999999999999956596859873 -57854909049287634246299583729875472656475965593947699= ____________________________________________________________________98899876788877656687989/988998-*995895966++5966656566666666655555555555958545156548448489+4964898748/798784484878554659757564250216407694722=
Answer:
-4.7854909e+52
Step-by-step explanation:
how do i know
cuz i used a calculator
what evevn is your equation
HELPP Billie solved the equation below by completing the square, but she got the incorrect solution. In which step did Billie first make an error?
Step 1 : x 2 + 6 x = 16
Step 2 : x 2 + 6 x + 9 = 16
Step 3 : ( x + 3 ) 2 = 16
Step 4 : x + 3 = ± 4 Step 5 : x = 1 , x = − 7
Billie made the error in the second step of the equation
How to solve the equationBillie made an error in Step 2. She added 9 to one sides of the equation, but she should have added 9 to the left side only. The correct steps are as follows:
Step 1: x^2 + 6x = 16
Step 2: x^2 + 6x + 9 = 16 + 9
Step 3: (x + 3)^2 = 25
Step 4: x + 3 = ±√25
Step 5: x = -3 + 5, x = -3 - 5
Step 6: x = 2, x = -8
So, the correct solutions are x = 2 and x = -8.
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Americans are stressed out!
A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a
significant source of stress for me." To help form an estimate, the psychologist randomly selected 664
Americans and found that 69.6% of the sample agreed with the statement "the future of the nation is a
significant source of stress for me."
Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the true
proportion of all Americans that say the "the future of the nation is a significant source of stress for me."
Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.
The margin of error is given by E:
A 99% confidence interval is given by:
To find the margin of error, we can use the formula: E = z√((p(1-p))/n)
How is margin of error determined?where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.
From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.
Plugging in the values, we get:
E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385
So the margin of error is 0.0385.
To find the confidence interval, we can use the formula:
p ± E
where p is the sample proportion and E is the margin of error.
Plugging in the values, we get:
0.696 ± 0.0385
So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].
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Select the statement that shows equivalent measurements.
4.5 meters = 0.0045 kilometers
4.5 meters = 0.045 centimeters
4.5 meters = 0.45 decimeters
4.5 meters = 45 decameters
The statement that shows equivalent measurements is "4.5 meters = 0.0045 kilometers".
How to solve the problem?
To convert meters to kilometers, we need to divide by 1000, since there are 1000 meters in a kilometer. Therefore, 4.5 meters is equal to 4.5/1000 = 0.0045 kilometers.
The other statements are incorrect:
4.5 meters is not equal to 0.045 centimeters, since there are 100 centimeters in a meter, so 4.5 meters is equal to 450 centimeters.
4.5 meters is not equal to 0.45 decimeters, since there are 10 decimeters in a meter, so 4.5 meters is equal to 45 decimeters.
4.5 meters is not equal to 45 decameters, since there are 10 meters in a decameter, so 4.5 meters is equal to 0.45 decameters.
It is important to be able to convert between different units of measurement in order to make accurate comparisons and calculations. In this case, the correct conversion factor was used to convert meters to kilometers, resulting in an equivalent measurement.
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Which two values are located at the same point on a number line? 4/1 and 4 , 1/3 and 3 , 8/8 and 8 , 6/2 and 4
The two values which are located at the same point on a number line as required to be determined are; 4/1 and 4.
Which answer choice represents equivalent points on the number line?It follows from the task content that the answer choice which represents two values located at the same point on the number line be determined.
On this note, such two values must be equivalent.
Hence, by observation; the answer choice which represents two equivalent values is; 4/1 and 4 and they represent values located at the same point on the number line.
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In circle O, chords AB and CD intersect at E, AE = 3 inches, BE = 8 inches, and CE is 2 inches longer than DE. What is the length of DE, expressed in inches?
Okay, let's break this down step-by-step:
* Circle O has chords AB and CD that intersect at E
* AE = 3 inches
* BE = 8 inches
* CE is 2 inches longer than DE
So we know:
AE = 3 inches
BE = 8 inches
CE = DE + 2 inches
To find DE, we can use the Pythagorean theorem for any right triangle:
a^2 + b^2 = c^2
In this case:
3^2 + 8^2 = c^2
9 + 64 = 73
c = 8 inches
So the hypotenuse AE forms a right triangle with leg BE of length 8 inches.
Now we have the length of one leg (BE = 8 inches) and the hypotenuse (AE = 8 inches).
We can use the relation between leg, hypotenuse and sine to calculate the other leg (DE):
sin(A) = DE / 8
DE = 8 * sin(A)
Without knowing the angle A, we can make an estimate:
sin(A) ≈ A (for small A)
So DE ≈ 8A inches
Now we know:
CE = DE + 2 inches
And DE ≈ 8A inches
So: 8A + 2 = DE
=> DE = 10A
And since A is small, we can say: DE ≈ 10 * A inches
To summary, if AE = 3 inches and BE = 8 inches,
then DE ≈ 10 * A inches
DE is approximately 10 times some small angle A.
Does this make sense? Let me know if you have any other questions!
The box plot represents the scores on quizzes in a science class.
A box plot uses a number line from 74 to 86 with tick marks every one-half unit. The box extends from 77.5 to 81.5 on the number line. A line in the box is at 80. The lines outside the box end at 75 and 85. The graph is titled Science Quizzes, and the line is labeled Scores On Quizzes.
What value does 25% of the data lie above? Find the value.
Sarah has a coupon for an oil change with synthetic oil for $49.95. She can buy 5 quarts of synthetic oil, which is what her car needs, for $37.54 and an oil filter for $9.47. How much can she save by doing the oil change herself?
Step-by-step explanation:
If Sarah buys the oil and oil filter separately, she would spend:
Cost of oil = $37.54
Cost of oil filter = $9.47
Total cost = $37.54 + $9.47 = $47.01
Therefore, Sarah can save:
Coupon price - Total cost = $49.95 - $47.01 = $2.94
So, Sarah can save $2.94 by doing the oil change herself instead of using the coupon.
what is the answer to this problem
help math will give brainlist
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
Find a rational number halfway in between the two numbers.
8/10 and 1/8
A rational number between 8/10 and 1/8 is 37/80.
We know that a rational number between two rational numbers can be given by finding the average of the two given numbers:
The numbers are 8/10 and 1/8.
Let's simplify the fractions first:
8/10 = 4/5 (dividing both numerator and denominator by 2)
1/8 = 1/8 (already in simplest form)
Average = [tex](\frac{4}{5} + \frac{1}{8})/2[/tex]
= [tex](\frac{(4*8) + (5*1)}{40} )/2[/tex]
= [tex](\frac{37}{40}) /2[/tex]
= [tex]\frac{37}{80}[/tex]
So, the rational number halfway between 8/10 and 1/8 is 37/80.
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The polygon below is a regular polygon. Find the answer rounded to the nearest tenth.
HELP GIVING BRAINLIST HW DUE SOOON
Answer:
In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.
A = (1/2)Pa
= (1/2)(2)(8/√3)(6)(8)
= (384√3)/3 = 128√3 = 221.7 units^2
Gary and Ann have a joint checking account their bounce at the beginning of October was 9145.87 during the month they made deposits totalling 2,783.71 wrote checks totaling 4,871.90 paid a maintenance fee of $12 earned 11.15 at interest on the account what was the balance at the end of the month?
The balance at the end of the month was $7046.93.
What is balance at the end of the month?To determine the balance at the end of the month, we need to:
add the initial balance to the deposits and interest earnedsubtract the checks written and fees paid.Data
Starting balance = $9145.87
Deposits = $2783.71
Interest earned = $11.15
Checks written = $4871.90
Maintenance fee = $12
Balance at the end of the month will be:
= Starting balance + Deposits + Interest earned - Checks written - Maintenance fee
= $9145.87 + $2783.71 + $11.15 - $4871.90 - $12
= $7046.93.
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view the photo below. This is timed.
The other angle that is congruent to ∠DFA is: ∠BFC
How to identify Congruent angles?Congruent angles are defined as two or more angles that are said to be identical to each other. This means that the measure of these angles is equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.
Now, we want to find the angle that is congruent to ∠DFA.
By inspection, we can see that ∠BFC is an opposite angle to ∠DFA.
We know that Opposite angles are the two angles opposite each other when two lines cross. They can also be called vertical angles due to sharing a vertex, which is the point where the two lines connect. Opposite angles always have the same measurement, making them congruent.
Thus, ∠BFC is congruent to ∠DFA.
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Find the range for the set numbers
Answer:
25
Step-by-step explanation:
range = largest number - smallest number
38-13=25
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #1
The end behavior of f(x) is described as follows:
As x -> -∞, f(x) -> ∞.As x -> ∞, f(x) -> 0.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:
Increases to the left of the graph -> As x -> -∞, f(x) -> ∞.Approaches the horizontal asymptote y = 0 at the right of the graph -> As x -> ∞, f(x) -> 0.More can be learned about the end behavior of a function at brainly.com/question/1365136
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The mean weight of an adult is 70 kilograms with a standard deviation of 8 kilograms.
If 87 adults are randomly selected, what is the probability that the sample mean would be greater than 70.8 kilograms? Round your answer to four decimal places.
The probability that the sample mean would be greater than 70.8 kilograms is given as follows:
0.1762 = 17.62%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 70, \sigma = 8, n = 87, s = \frac{8}{\sqrt{87}} = 0.8577[/tex]
The probability is one subtracted by the p-value of Z when X = 70.8, hence:
Z = (70.8 - 70)/0.8577
Z = 0.93
Z = 0.93 has a p-value of 0.8238
1 - 0.8238 = 0.1762.
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Calculate the MAY raw materials purchases in dollars. (SEE IMAGE FOR DETAILS) financial accounting
Rensing Ltd estimates sales for the second quarter of 2020 will be as follows. April: 2,520 May: 2,440 June: 2,390
target ending inventory finished products. March 31: 2,010 April 30: 2,280 May 31: 2,170 June 30: 2,330
The May raw materials purchases for May in Rensing Ltd., in dollars terms, is $32,620.
How the raw materials purchases are determined:The cost of raw materials purchased in May is determined by computing the required production units and multiplying the result by 2 units and the unit raw material cost.
Purchase Budget:April May June
Sales 2,520 2,440 2,390
Ending inventory 2,280 2,170 2,330
Goods available for
sale 4,800 4,610 4,720
Beginning inventory 2,280 2,170
Production units 2,330
Raw materials purchases 4,660 (2,330 x 2)
Raw materials price per unit = $7
Total purchases of Raw Materials for May = $32,620 (4,660 x $7)
Thus, we can conclude that in May Rensing Ltd. purchased raw materials worth $32,620.
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Can somebody please help me find poetic elements in this poem fast!!!
Poem: citizenship by Javier Zamora
There’s also an image of the poem
Some poetic elements found in the poem are:
IronyRepetitionPersonificationMetaphorImageryWhat are poetic elements?Poetic elements are described as the devices used that characterize a piece of writing as a poem and are integral to categorise a piece of writing as poetry, such as poetic meter and rhyme scheme.
In the poem, the author uses Imagery which is described as use of sensory details to create vivid mental images in the reader's mind.
The author made use of metaphor as a comparison between two things that are not alike, in order to create an image or deepen understanding.
Learn more about Poetic elements at:
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