The population of a town is 9,000, and it grows at a rate of 7% per year. What will the population be in 6 years?
Answer:
12,780
Step-by-step explanation:
Initial population = 9000
grows 7% of 9000= 630 people in a year
after 6 yrs, number of added people = 630× 6=3780 ...... totally, population = 9000+ 3780
= 12,780
The population of the town after 6 years will be 13506.
Concept:As the population grows at r% per year and if the Current population is P, then After 'x' years, the population will be [tex]P_x = P(1 + \frac{r}{100} )^x[/tex]How to solve the given question?Initial Population, P = 9000Rate of increase in population, r = 7% per yearPeriod , x = 6 years∴ The population after 6 years,[tex]P_x = P(1 + \frac{r}{100} )^x[/tex]Thus, the population of the town after 6 years will be 13506.
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Yolonda wanted to see if there was a connection between red hair and green eyes. She observed people walking past her on the street
Answer:
I saw one person that way
Step-by-step explanation:
she had red hair and green eyes with pale skin
Find the slope of the line. m =
Answer: m=4
Step-by-step explanation:
To find the slope, we use the formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. We can use the two points to find the slope. The points on the graph are (-2,1) and (-3,-3).
[tex]m=\frac{-3-1}{-3-(-2)} =\frac{-4}{-1} =4[/tex]
Determine the absolute maximum and minimum of f(x)= 2 cosx+ sin 2x
Answer:
2.598 and -2.598.
Step-by-step explanation:
f(x) = 2 cos x + sin 2x
f'(x) = -2 sin x + 2 cos 2x = 0 for turning points.
cos 2x = 1 - 2 sin^2 x so we have
-2 sin x + 2 - 4 sin^2 x = 0
4sin^2 x + 2 sin x - 2 = 0
2(2 sin^2 x + sin x - 1) = 0
2(2sinx - 1)(sinx + 1) = 0
sin x = 0.5, -1 when f(x) is at a turning point.
x = π/6, -π/2, 5pi/6
The second derivative is 2 cos x + 2 * -2 sin 2x
= 2 cos x - 4 sin 2x
When x = π/6, this is negative , when x = -π/2 it is positive
so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection
When x = π/6 , f(x) = 2.598
When x = 5pi/6, f(x) = -2.598.
c. Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $12 and $18
Answer:
0.0066
Step-by-step explanation:
The x has a distribution that is approximately normal. For normal distribution the probability of x will be,
u = 12 and 18
P (12 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 18)
P (- 2.3 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 2.85 )
P (0.9912 - 0.9978)
= 0.0066
How many feet of chain fence are necessary to enclosed a dog pen that is square and has a area of 64 sq feet
Answer:
32 feet
Step-by-step explanation:
area of square is given by side^2
Perimeter of square is given by 4*side
_______________________________
Given
area of square = 64 sq feet
side^2 = 64
side^2 = 8^2
side = 8
thus side = 8 feet
_______________________________________
The dog pen is fenced with chain, hence chain will be fence at the edge of square and at the perimeter.
Thus, length of chain required will be same as the Perimeter of square.
Perimeter of given dog pen with side length 8 feet = 4*8 = 32 feet.
Thus, 32 feet of chain fence is required.
Does anyone know the slope of this line?
Answer:
3/4
Step-by-step explanation:
Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.
listed below are costs in dollars of round trip flights between two cities. All flights involve one stop and a two week stay. Find a coefficient of variation for each of the two sets of data, then compare the variation.
30 days in advance: 250 286 305 256 288 282 254
1 day in advance: 454 619 557 912 619 1049 562
The coefficient of variation for the prices of tickets purchased 30 days in advance is ____% (round to the three decimal places as needed)
Answer:
coefficient of variation = 7.108%
Step-by-step explanation:
From the given information:
The objective is to determine the coefficient of variation for the prices of tickets purchased 30 days in advance is ____%
The mean [tex]\overline x[/tex] = [tex]\dfrac{250+286+305+256+288+282+254}{7}[/tex]
The mean [tex]\overline x[/tex] = [tex]\dfrac{1921}{7}[/tex]
The mean [tex]\overline x[/tex] = 274.4285714
The standard deviation also can be computed as follows:
[tex]\sigma =\sqrt{ \dfrac{\sum (x_i-\mu)^2}{N}}[/tex]
[tex]\sigma =\sqrt{ \dfrac{ (250-274.43)^2+(286-274.43)^2+(305-274.43)^2+...+(254-274.43)^2}{7}}[/tex][tex]\sigma =19.507[/tex]
Finally; the coefficient of variation can be calculated with the formula:
coefficient of variation = [tex]\dfrac{\sigma}{\overline x}[/tex]
coefficient of variation = [tex]\dfrac{19.507}{274.43}[/tex]
coefficient of variation = 0.07108
coefficient of variation = 7.108%
A shipment of 60 inexpensive digital watches, including 9 that are defective,is sent to a department store.The receiving department select's 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective.What is the probability that the shipment will be rejected?
Answer: 0.627 or 62.7 %
Step-by-step explanation:
The probability that shipment will be rejected P(rejected) = 1- probability that shipment will be accepted.
P(rejected)= 1-P(accepted)
P(accepted) is equal to probability when all 10 watches are not defective.
The probability that 1st one randomly selected watches are not defective is 51/60 (51 watches are not defective and 9 are defective)
The probability that 2-nd one randomly selected watches are not defective is 50/59 ( because the total number of the watches now is 1 unit less 60-1=59, and the total number of not defective watches is 1 unit less 51-1=50 units)
The probability that 3rd one randomly selected watches are not defective is 49/58 (49 watches are not defective total number of watches is 58)
Similarly P(4th)= 48/57 P(5th)=47/56 P(6th)=46/55 P(7th)=45/54
P(8th)=44/53 P(9th)=43/52 P(10th)=42/51
So P(accepted)= P(1st)*P(2nd)*P(3rd)*P(4th)*P(5th)*P(6th)*P(7th)*P(8th)*P(9th)*P(10th)=
=51*50*49*48*47*46*45*44*43*42/(60*59*58*57*56*55*54*53*52*51)=
= approx= 0.373
So P(rejected)=1-0.373=0.627
what is the solution of the inequality shown below
Answer:
there is no inequality..
Step-by-step explanation:
Answer:
???
Step-by-step explanation:
9) brainliest & 10 + points!
Answer:
no supplement
Step-by-step explanation:
Supplementary angles add to 180 degrees,
This angle is larger than 180 degrees by itself, so it has no supplement
What is the value of $x$ if $-\frac23(x-5) = \frac32(x+1)$?
Answer:
x = (-29)/5
Step-by-step explanation:
Solve for x:
(2 (x - 5))/3 = (3 (x + 1))/2
Multiply both sides by 6:
(6×2 (x - 5))/3 = (6×3 (x + 1))/2
6/3 = (3×2)/3 = 2:
2×2 (x - 5) = (6×3 (x + 1))/2
6/2 = (2×3)/2 = 3:
2×2 (x - 5) = 3×3 (x + 1)
2×2 = 4:
4 (x - 5) = 3×3 (x + 1)
3×3 = 9:
4 (x - 5) = 9 (x + 1)
Expand out terms of the left hand side:
4 x - 20 = 9 (x + 1)
Expand out terms of the right hand side:
4 x - 20 = 9 x + 9
Subtract 9 x from both sides:
(4 x - 9 x) - 20 = (9 x - 9 x) + 9
4 x - 9 x = -5 x:
-5 x - 20 = (9 x - 9 x) + 9
9 x - 9 x = 0:
-5 x - 20 = 9
Add 20 to both sides:
(20 - 20) - 5 x = 20 + 9
20 - 20 = 0:
-5 x = 9 + 20
9 + 20 = 29:
-5 x = 29
Divide both sides of -5 x = 29 by -5:
(-5 x)/(-5) = 29/(-5)
(-5)/(-5) = 1:
x = 29/(-5)
Multiply numerator and denominator of 29/(-5) by -1:
Answer: x = (-29)/5
Answer:
Step-by-step explanation:
Multiplying both sides by $6$ to get rid of the fractions gives\[6\left(-\frac23\right)(k-6) = 6\left(\frac32\right)(k+6),\]so\[-4(k-6) = 9(k+6).\]Expanding both sides gives $-4k+24 = 9k + 54.$ Adding $4k$ to both sides gives $24 = 13k+54.$ Subtracting $54$ from both sides gives $-30=13k.$ Dividing both sides by $13$ gives $k =-30/13}.$
Multiply: (−2x2 + 9x − 3) * (7x2 − 4x + 2)
Answer:
[tex]-14x^4+71x^3-61x^2+30x-6[/tex]
Step-by-step explanation:
All we are doing is distributing each number of the 1st equation to the 2nd equation to get our answer. Once we do so, we combine like terms and we get our answer.
Let ????(t)=⟨t2,1−t,4t⟩r(t)=⟨t2,1−t,4t⟩. Calculate the derivative of ????(t)⋅????(t)r(t)⋅a(t) at t=2t=2, assuming that ????(2)=⟨2,5,−3⟩a(2)=⟨2,5,−3⟩ and ????′(2)=⟨4,−3,9⟩
Answer:
The derivative is [tex]\frac{ d (r(t) \cdot a(t))}{dt} = 82[/tex]
Step-by-step explanation:
From the question we are told that
[tex]r(t) = (t^2 ,1 - t , 4t)[/tex]
[tex]a(2) = (2, 5, -3)[/tex] and [tex]a'(2) = (4,-3 , 9)[/tex]
At t = 2
[tex]r(t) = (2^2 ,1 - 2 , 4(2))[/tex]
[tex]r(t) = (4 ,-1 , 8 )[/tex]
Now the derivative of r(t) is
[tex]r'(t) = (2t, -1 ,4)[/tex]
At t = 2
[tex]r'(t) = (2(2), -1 ,4)[/tex]
[tex]r'(t) = (4, -1 ,4)[/tex]
Now the derivative of [tex]r(t) \cdot a(t)[/tex] At t = 2 is
[tex]= r'(2) a(2) + a'(2)r(2)[/tex]
[tex]= (4,-1,4)(2,5,-3) + (4,-3,9)(4,-1,8)[/tex]
[tex]= (8 - 5 -12) + (16+3+72)[/tex]
[tex]= -9 + 91[/tex]
[tex]\frac{ d (r(t) \cdot a(t))}{dt} = 82[/tex]
an experiment consists of rolling two fair dice and adding the dots on the two sides facing u. Find the probability of the sum of the dots indicate. A sum less than or equal to 6
Answer:
41.67% probability of the sum of the dots indicate a sum less than or equal to 6
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes:
In this problem, we have these possible outcomes:
Format(Dice A, Dice B)
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes.
Desired outcomes:
Sum of 6 or less. They are:
(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)
15 desired outcomes
15/36 = 0.4167
41.67% probability of the sum of the dots indicate a sum less than or equal to 6
To decide whether two different types of steel have the same true average fracture toughness values, n specimens of each type are tested, yielding the following results.
Type Sample Average Sample SD
1 60.7 1.0
2 60.5 1.0
Required:
a. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 100. (Round your answer to four decimal places.)
b. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 500. (Round your answer to four decimal places.)
c. Is the small P-value for n = 500 indicative of a difference that has practical significance
Answer:
a. P-value = 0.1589
b. P-value = 0.0016
Step-by-step explanation:
a. This is a hypothesis test for the difference between populations means.
The claim is that the two types of steel have different true average fracture toughness values.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is α=0.05.
The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1. The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.
The difference between sample means is Md=0.2.
[tex]M_d=M_1-M_2=60.7-60.5=0.2[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=100+100-2=198[/tex]
This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t>1.4142)=0.1589[/tex]
As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.
b. As the sample size changes, the standard error and the degress of freedom change.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=500+500-2=998[/tex]
This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t>3.1623)=0.0016[/tex]
As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.
to prove triangleABC is isosceles, which of the following statements can be used in the proof?
(idk the answer)
Answer:
Step-by-step explanation:
An isosceles triangle is a triangle in which two of its sides are equal. This also means that in the triangle, two angles are equal. The angles are usually the base angles. Looking at the given triangle ABC, the base angles are angle Angle A and Angle B, thus angle A = ang B
Therefore, the statement that can be used in the proof is
Angle CAB = angle CBA
two lines, 3y-2x=21 and 4y+5x=5, intersect at the point Q. find the coordinates of Q.
Answer:
Q = (- 3, 5 )
Step-by-step explanation:
Given the 2 equations
3y - 2x = 21 → (1)
4y + 5x = 5 → (2)
Multiplying (1) by 5 and (2) by 2 and adding will eliminate the x- term.
15y - 10x = 105 → (3)
8y + 10x = 10 → (4)
Add (3) and (4) term by term to eliminate x
23y = 115 ( divide both sides by 23 )
y = 5
Substitute y = 5 into either of the 2 equations and solve for x
Substituting into (2)
4(5) + 5x = 5
20 + 5x = 5 ( subtract 20 from both sides )
5x = - 15 ( divide both sides by 5 )
x = - 3
Solution is (- 3, 5 )
Does the point (3.28) lie on the line y = 19+ 3x
Answer:
yes
Step-by-step explanation:
y = 19+ 3x
Let x = 3 and y = 28
28 = 19 + 3*3
28 =19+9
28 = 28
This is true so the point is one the line
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustain-ability perspective, PHB offers many attractive proper-ties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in the article "The Melting Behaviour of Poly(3-1-1ydroxybutyrate) by DSC. Reproducibility Study" (Polymer Testing, 2013: 215-220).
180.5 181.7 180.9 181.6 182.6 181.6
181.3 182.1 182.1 180.3 181.7 180.5
Compute the following:
a. The sample range
b. The sample variance S2 from the definition (Hint: First subtract 180 from each observation.]
c. The sample standard deviation
d. S2 using the shortcut method
Answer:
(a) 2.3
(b) 0.5245
(c) 0.7242
(d) 0.5245
Step-by-step explanation:
The data provided is:
S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6, 181.3, 182.1, 182.1, 180.3, 181.7, 180.5}
(a)
The formula to compute the sample range is:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
The data set arranged in ascending order is:
S' = {180.3 , 180.5 , 180.5 , 180.9 , 181.3 , 181.6 , 181.6 , 181.7 , 181.7 ,, 182.1 , 182.1 , 182.6}
The minimum value is, 180.3 and the maximum value is, 182.6.
Compute the sample range as follows:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
[tex]=182.6-180.3\\=2.3[/tex]
Thus, the sample range is 2.3.
(b)
Compute the sample variance as follows:
[tex]S^{2}=\frac{1}{n-1}\sum(x_{i}-\bar x)^{2}[/tex]
[tex]=\frac{1}{12-1}\times [(180.5-181.41)^{2}+(181.7-181.41)^{2}+...+(180.5-181.41)^{2}]\\\\=\frac{1}{11}\times 5.7692\\\\=0.524473\\\\\approx 0.5245[/tex]
Thus, the sample variance is 0.5245.
(c)
Compute the sample standard deviation as follows:
[tex]s=\sqrt{S^{2}}[/tex]
[tex]=\sqrt{0.5245}\\\\=0.7242[/tex]
Thus, the sample standard deviation is 0.7242.
(d)
Compute the sample variance using the shortcut method as follows:
[tex]S^{2}=\frac{1}{n-1}\cdot [\sum x_{i}^{2}-n(\bar x)^{2}][/tex]
[tex]=\frac{1}{12-1}\cdot [394913.57-(12\times (181.41)^{2}]\\\\=\frac{1}{11}\times [394913.57-394907.80]\\\\=\frac{5.77}{11}\\\\=0.5245[/tex]
Thus, the sample variance is 0.5245.
Let $x$ be the smallest multiple of $11$ that is greater than $1000$ and $y$ be the greatest multiple of $11$ less than $11^2$. Compute $x - y$.
Answer:
891
Step-by-step explanation:
x has to be 1001 and y has to be 11 * 10 = 110 so x - y = 1001 - 110 = 891.
Answer:
891
Step-by-step explanation:
[tex]$1001$ is the smallest integer greater than $1000$. It also happens to be a multiple of $11$, since $1001 = 11 \cdot 91$. So $1001$ is the smallest multiple of $11$ greater than $1000$ and thus $x = 1001$.The greatest multiple of $11$ that is less than $11^2 = 11 \cdot 11$ is$$11 \cdot (11 - 1) = 11 \cdot 10 = 110$$Thus $y = 110$, and we compute$$x - y = 1001 - 110 = \boxed{891}$$[/tex]
Hope this helped! :)
Find measure of arc or angle indicated
A large mixing tank initially contains 1000 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 pounds of salt per gallon. If represents the amount of salt in the tank at time t, the correct differential equation for A is:__________.A.) dA/dt = 4 - .08AB.) dA/dt = 8 -.04AC.) dA/dt = 4-.04AD.) dA/dt = 2-.04AE.) dA/dt = 8-.02A
Answer:
(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]
Therefore:
The rate of change of amount of salt in the tank,
[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]
Let x be a variable, and let n be an arbitrary constant. What is the derivative of x^n?
Answer:
nx^(n-1)
Step-by-step explanation:
5x + 7y = -29 y = x + 1
Answer:
(x, y) = (-3, -2)
Step-by-step explanation:
Perhaps this is a system of equations you want the solution for.
Since you have an expression for y, substitution is a viable approach.
5x +7(x+1) = -29 . . . . . . substitute for y
12x = -36 . . . . . . subtract 7 and simplify
x = -3 . . . . . . . . . divide by 12
y = (-3) +1 = -2 . . . use the expression for y
The solution is (x, y) = (-3, -2).
Define f(0,0) in a way that extends f(x,y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.
Answer:
It cannot be extended.
Step-by-step explanation:
Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.
In this case, consider the case in which y =0. When y=0 then
[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]
But, when x=0, we get
[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].
So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.
Please answer this correctly
Answer:
5/12
Step-by-step explanation:
The probability of rolling a number greater than 1 is 5/6, because 5 numbers on a 6-sided dice are greater than 1.
The probability of rolling an even number is 3/6, because 3 numbers on a 6-sided dice are even numbers.
[tex]5/6 \times 3/6[/tex]
[tex]=15/36[/tex]
[tex]=5/12[/tex]
The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock that pay $2.85 per share and 2,500,000 shares of common stock. After finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock.
Answer:
$1,06
Step-by-step explanation:
Calculation for dividend per share of common stock for board of directors of Midwest Foods
First step is to find the amount of dividends due to the preferred shareholders
Using this formula
Total Dividend =Dividend- (Preferred stock *Per share of preferred stock )
Let plug in the formula
Total Dividend =$3,500,000-($300,000*$2.85)
Total Dividend =$3,500,000-$855,000
Total Dividend =$2,645,000
The second step is to find Dividend per share of common stock
Using this formula
Dividend per share of common stock=Total dividend/Shares of common stock
Let plug in the formula
Dividend per share of common stock=$2,645,000/$2,500,000
Dividend per share of common stock=$1.06
Therefore the dividend per share of common stock for board of directors of Midwest Foods will be $1.06
You would like to have extra spending money, so you decided to work part-time at the local gym. The job pays $15.00 per hour and you work 20 hours per week. Your employer withholds 10% of your gross pay for federal taxes, 7.65% for FICA taxes, and 3% for state taxes.
Required:
a. What is your weekly gross pay?
b. How much is withheld per week for federal taxes?
c. How much is withheld per week for FICA taxes?
d. How much is withheld per week for state taxes?
e. What is your weekly net pay?
f. What percentage of your gross pay is withheld for taxes? Round to the nearest tenth of a percent.
Answer:
a. Weekly gross pay = $300
b. Federal taxes, F = $30
c. Fica taxes, K = 22.95
d. State taxes, S = $9
e. Weekly net pay = 238.05
Step-by-step explanation:
Gross pay, G = 15 $/h * 20 h = 300 / week
Fed taxes, F = 10%*G = $30
FICA, K = 7.65%*G = $22.95
State taxes, S = 3%*G = $9
a. Weekly gross pay = $300
b. Federal taxes, F = $30
c. Fica taxes, K = 22.95
d. State taxes, S = $9
e. Weekly net pay = 300 - (30+22.95+9) = 300 - 55.95 = 238.05
To compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected.This study uses_________ design
Answer:
An independent sample.
Step-by-step explanation:
In this scenario, to compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected. We can safely conclude that this study uses an independent sample design.
An independent sample design can be defined as a research method that usually involves the use of multiple experimental groups (two or more). The samples or participants are only in one group and as such each group has no relationship with the other. This simply means that, the samples in a particular group is having no relationship with the other samples in another group.
Ultimately this implies, each samples are independent and satisfies only one condition of the independent sample design during the experiment to compare the production technique used by foreign and local firms in Brazil.
Hence, the researcher would use only two variables or conditions: a random sample of 80 foreign firms and a random sample of 80 local firms are selected.