Answer:
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
Step-by-step explanation:
Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.
plz give me correct answers
Answer:
Step-by-step explanation:
greatest number=8643
smallest number=3468
difference=8643-3468=5175
6.1. DCCLVI
CDXCIV
(II) 74,746
For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 24 and p = 0.6.
Answer:
Since both np > 5 and np(1-p)>5, it is suitable to use the normal distribution as an approximation.
Step-by-step explanation:
When the normal approximation is suitable?
If np > 5 and np(1-p)>5
In this question:
[tex]n = 24, p = 0.6[/tex]
So
[tex]np = 24*0.6 = 14.4[/tex]
And
[tex]np(1-p) = 24*0.6*0.4 = 5.76[/tex]
Since both np > 5 and np(1-p)>5, it is suitable to use the normal distribution as an approximation.
If Aequals[Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column negative 4 2nd Row 1st Column negative 4 2nd Column 5 EndMatrix ] and ABequals[Start 2 By 3 Matrix 1st Row 1st Column negative 10 2nd Column 1 3rd Column 9 2nd Row 1st Column 7 2nd Column negative 15 3rd Column 8 EndMatrix ], determine the first and second columns of B. Let Bold b 1 be column 1 of B and Bold b 2 be colum
Answer:
[tex]b_1=\left(\begin{array}{ccc}-3\\3\end{array}\right),b_2=\left(\begin{array}{ccc}-\dfrac{65}{11}\\\\-\dfrac{19}{11}\end{array}\right)[/tex]
Step-by-step explanation:
Given matrix A and AB below:
[tex]A=\left(\begin{array}{ccc}1&-4\\-4&5\end{array}\right)\\\\\\ AB=\left(\begin{array}{ccc}-10&1&9\\7&-15&8\end{array}\right)[/tex]
For the product AB to be a 2 X 3 matrix, B must be a 2 X 3 matrix.
Let matrix B be defined as follows
[tex]B=\left[\begin{array}{ccc}a&c&e\\b&d&f\end{array}\right][/tex]
Therefore:
[tex]\left(\begin{array}{ccc}1&-4\\-4&5\end{array}\right)\left(\begin{array}{ccc}a&c&e\\b&d&f\end{array}\right)=\left(\begin{array}{ccc}-10&1&9\\7&-15&8\end{array}\right)[/tex]
This results in the equations
a-4b=-10-4a+5b=7c-4d=1-4c+5d=-15Solving the first two equations simultaneously
a-4b=-10 (a=-10+4b)
-4a+5b=7
Substitution of [tex]a=-10+4b[/tex] into the second equation
[tex]-4(-10+4b)+5b=7\\40-16b+5b=7\\-11b=-33\\b=3[/tex]
Recall that [tex]a=-10+4b[/tex]
[tex]a=-10+4(3)=-10+7\\a=-3[/tex]
Solving the other two equations
c-4d=1 (c=1+4d)
-4c+5d=-15
Substitution of c=1+4d into the second equation
[tex]-4(1+4d)+5d=-15\\-4-16d+5d=15\\-11d=19\\d=-\dfrac{19}{11}\\ Recall: c=1+4d\\c=1+4(-\frac{19}{11})\\c=-\dfrac{65}{11}[/tex]
Therefore, we have:
[tex]a=-3, b=3, c=-\dfrac{65}{11}, d=-\dfrac{19}{11}[/tex]
Thus:
[tex]b_1=\left(\begin{array}{ccc}-3\\3\end{array}\right)\\\\\\b_2=\left(\begin{array}{ccc}-\dfrac{65}{11}\\\\-\dfrac{19}{11}\end{array}\right)[/tex]
Answer:
option c
Step-by-step explanation:
it is said that a computer repairman makes 25 dollars per hour
this column shows the right amount of money he earns per hour
A comprehensive survey released by a college reports that the true proportion of all students at the college who use drugs is 0.3. You survey 100 students in your dorm and record that the proportion of students who use drugs is 0.15. The proportion of all students at this college who use drugs is a
Complete Question
The proportion of all students at this college who use drugs is a_____and the proportion of students who use drugs in your dorm is a _____ .
Options
a. statistic; parameter b. parameter; statistic c. population; sample d. measure of central tendency, measure of variability e. none of the aboveAnswer:
b. parameter; statistic
Step-by-step explanation:
A parameter is a summary of data for an entire population.
Statistic, on the other hand, summarizes data for a sample of the population.
The proportion of all students at this college who use drugs is a parameter and the proportion of students who use drugs in your dorm is a sample.
The correct option is B
You can model that you expect a 1.25% raise each year that you work for a certain company. If you currently make $40,000, how many years should go by until you are making $120,000? (Round to the closest year.)
Answer:
94 years
Step-by-step explanation:
We can approach the solution using the compound interest equation
[tex]A= P(1+r)^t[/tex]
Given data
P= $40,000
A= $120,000
r= 1.25%= 1.25/100= 0.0125
substituting and solving for t we have
[tex]120000= 40000(1+0.0125)^t \\\120000= 40000(1.0125)^t[/tex]
dividing both sides by 40,000 we have
[tex](1.0125)^t=\frac{120000}{40000} \\\\(1.0125)^t=3\\\ t Log(1.0125)= log(3)\\\ t*0.005= 0.47[/tex]
dividing both sides by 0.005 we have
[tex]t= 0.47/0.005\\t= 94[/tex]
Find the sample size needed to estimate the percentage of Democrats among registered voters in Texas. Use a 0.01 margin of error, and use a confidence level of 96% and assume LaTeX: \hat{p}
p
^
=0.28.
Answer:
Step-by-step explanation:
Hello!
You have to determine the sample size to take to estimate the population proportion of Democrats among registered voters in Texas for a 96% interval with a margin of error of 0.01 and sample proportion p'= 0.28
The interval for the population proportion is
p' ± [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
The margin of error of the interval is:
d= [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex]\frac{d}{Z_{1-\alpha /2}}= \sqrt{\frac{p'(1-p')}{n} }\\(\frac{d}{Z_{1-\alpha /2}} )^2= \frac{p'(1-p)}{n} \\n*(\frac{d}{Z_{1-\alpha /2}} )^2= p'(1-p)\\n= p'(1-p)*(\frac{Z_{1-\alpha /2}}{d} )^2\\[/tex]
[tex]Z_{1-\alpha /2}= Z_{0.98}= 2.054[/tex]
[tex]n= 0.28*(1-0.28)*(\frac{2.054}{0.01} )^2= 8505.33[/tex]
n= 8506 voters
I hope this helps!
25% of a class do not play basketball.
27 children do play. How many
children are in the class?
Answer: 36 children
Step-by-step explanation:
3/4 of the class plays basketball. Thus 3/4x=27. Multiply each side by 4/3 to get x = 36
Use the data below, showing a summary of highway gas mileage for several observations, to decide if the average highway gas mileage is the same for midsize cars, SUV’s, and pickup trucks. Test the appropriate hypotheses at the α = 0.01 level.
n Mean Std. Dev.
Midsize 31 25.8 2.56
SUV’s 31 22.68 3.67
Pickups 14 21.29 2.76
Answer:
Step-by-step explanation:
Hello!
You need to test at 1% if the average highway gas mileage is the same for three types of vehicles (midsize cars, SUV's and pickup trucks) to compare the average values of the three groups altogether, you have to apply an ANOVA.
n | Mean | Std. Dev.
Midsize | 31 | 25.8 | 2.56
SUV’s | 31 | 22.68 | 3.67
Pickups | 14 | 21.29 | 2.76
Be the study variables :
X₁: highway gas mileage of a midsize car
X₂: highway gas mileage of an SUV
X₃: highway gas mileage of a pickup truck.
Assuming these variables have a normal distribution and are independent.
The hypotheses are:
H₀: μ₁ = μ₂ = μ₃
H₁: At least one of the population means is different.
α: 0.01
The statistic for this test is:
[tex]F= \frac{MS_{Treatment}}{MS_{Error}}[/tex]~[tex]F_{k-1;n-k}[/tex]
Attached you'll find an ANOVA table with all its components. As you see, to manually calculate the statistic you have to determine the Sum of Squares and the degrees of freedom for the treatments and the errors, next you calculate the means square for both and finally the test statistic.
For the treatments:
The degrees of freedom between treatments are k-1 (k represents the amount of treatments): [tex]Df_{Tr}= k - 1= 3 - 1 = 2[/tex]
The sum of squares is:
SSTr: ∑ni(Ÿi - Ÿ..)²
Ÿi= sample mean of sample i ∀ i= 1,2,3
Ÿ..= grand mean, is the mean that results of all the groups together.
So the Sum of squares pf treatments SStr is the sum of the square of difference between the sample mean of each group and the grand mean.
To calculate the grand mean you can sum the means of each group and dive it by the number of groups:
Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (25.8+22.68+21.29)/3 = 23.256≅ 23.26
[tex]SS_{Tr}[/tex]= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (25.8-23.26)² + (22.68-23.26)² + (21.29-23.26)²= 10.6689
[tex]MS_{Tr}= \frac{SS_{Tr}}{Df_{Tr}}= \frac{10.6689}{2}= 5.33[/tex]
For the errors:
The degrees of freedom for the errors are: [tex]Df_{Errors}= N-k= (31+31+14)-3= 76-3= 73[/tex]
The Mean square are equal to the estimation of the variance of errors, you can calculate them using the following formula:
[tex]MS_{Errors}= S^2_e= \frac{(n_1-1)S^2_1+(n_2-1)S^2_2+(n_3-1)S^2_3}{n_1+n_2+n_3-k}= \frac{(30*2.56^2)+(30*3.67^2)+(13*2.76^2)}{31+31+14-3} = \frac{695.3118}{73}= 9.52[/tex]
Now you can calculate the test statistic
[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Error}} = \frac{5.33}{9.52}= 0.559= 0.56[/tex]
The rejection region for this test is always one-tailed to the right, meaning that you'll reject the null hypothesis to big values of the statistic:
[tex]F_{k-1;N-k;1-\alpha }= F_{2; 73; 0.99}= 4.07[/tex]
If [tex]F_{H_0}[/tex] ≥ 4.07, reject the null hypothesis.
If [tex]F_{H_0}[/tex] < 4.07, do not reject the null hypothesis.
Since the calculated value is less than the critical value, the decision is to not reject the null hypothesis.
Then at a 1% significance level you can conclude that the average highway mileage is the same for the three types of vehicles (mid size, SUV and pickup trucks)
I hope this helps!
Can somebody help me i have to drag the functions on top onto the bottom ones to match their inverse functions.
Answer:
1. x/5
2. cubed root of 2x
3.x-10
4.(2x/3)-17
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. Lets find the inverse function for function f(x)=2*x/3-17
To do that first express x through f(x):
2*x/3= f(x)+17
2*x=(f(x)+17)*3
x=(f(x)+17)*3/2 done !!! (1)
Next : to get the inverse function from (1) substitute x by f'(x) and f(x) by x.
So the required function is f'(x)=(x+17)*3/2 or f'(x)=3*(x+17)/2
This is function is No4 in our list. So f(x)=2*x/3-17 should be moved to the box No4 ( on the bottom) of the list.
2. Lets find the inverse function for function f(x)=x-10
To do that first express x through f(x):
x= f(x)+10
x=f(x)+10 done !!! (2)
Next : to get the inverse function from (2) substitute x by f'(x) and f(x) by x.
So the required function is f'(x)=x+10
This is function is No3 in our list. So f(x)=x-10 should be moved to the box No3 ( from the top) of the list.
3.Lets find the inverse function for function f(x)=sqrt 3 (2x)
To do that first express x through f(x):
2*x= f(x)^3
x=f(x)^3/2 done !!! (3)
Next : to get the inverse function from (3) substitute x by f'(x) and f(x) by x.
So the required function is f'(x)=x^3/2
This is function No2 in our list. So f(x)=sqrt 3 (2x) should be moved to the box No2 ( from the top) of the list.
4.Lets find the inverse function for function f(x)=x/5
To do that first express x through f(x):
x=f(x)*5 done !!! (4)
Next : to get the inverse function from (4) substitute x by f'(x) and f(x) by x.
So the required function is f'(x)=x*5 or f'(x)=5*x
This is function No1 in our list. So f(x)=x/5 should be moved to the box No1 ( on the top) of the list.
a bank teller has 340 one hundred dollar bills. how much money does the bank teller have?
Answer:
$34,000
Step-by-step explanation:
Since a one hundred dollar bill is equal to 100, we simply multiply 340 and 100 together:
340(100) = 34000
2-x=-3(x+4)+6 please help
Answer:
2-x=-3x-12+6
2-x=-3x-6
8=-3x+x
8=-2x
x=-4
hope it's clear
mark me as brainliest
Answer:
X = -4Option B is the correct option.
Step by step explanation
2 - x = -3 ( x + 4) +6
Distribute -3 through the paranthesis
2 - x = - 3x - 12 + 6
Calculate
2 - x = - 3x - 6
Move variable to LHS and change its sign
2 - x + 3x = -6
Move constant to R.H.S and change its sign
- x + 3x = -6 - 2
Collect like terms and simplify
2x = -8
Divide both side by 2
2x/2 = -8/2
Calculate
X = -4
Hope this helps....
Good luck on your assignment..
help please this is important
Answer:
D. [tex]3^3 - 4^2[/tex]
Step-by-step explanation:
Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amounts she spent in each category are pictured here. Rent $433 Food $320 Fun $260 Other $487 What percent of her total spending did she spend on Rent? % (Please enter your answer to the nearest whole percent.) What percent of her total spending did she spend on Food? % (Please enter your answer to the nearest whole percent.) What percent of her total spending did she spend on Fun? % (Please enter your answer to the nearest whole percent.)
Answer: Rent = 29%, Food = 21%, Fun = 17%
Step-by-step explanation:
Rent = $433
Food = $320
Fun = $260
Other = $487
TOTAL = $1500
[tex]\dfrac{Rent}{Total}=\dfrac{433}{1500}\quad =0.2886\quad =\large\boxed{29\%}\\\\\\\dfrac{Food}{Total}=\dfrac{320}{1500}\quad =0.2133\quad =\large\boxed{21\%}\\\\\\\dfrac{Fun}{Total}=\dfrac{260}{1500}\quad =0.1733\quad =\large\boxed{17\%}[/tex]
please help me, i will give you brainliest
Answer:
52°i think
Step-by-step explanation:
148°-96°=52°
Answer:
The answer is below
Step-by-step explanation:
The answer is 52 degrees
The third option in the line
Hope the answer helps
What is the simplified form of this expression?
(-3x^2+ 2x - 4) + (4x^2 + 5x+9)
OPTIONS
7x^2 + 7x + 5
x^2 + 7x + 13
x^2 + 11x + 1
x^² + 7x+5
Answer:
Option 4
Step-by-step explanation:
=> [tex]-3x^2+2x-4 + 4x^2+5x+9[/tex]
Combining like terms
=> [tex]-3x^2+4x^2+2x+5x-4+9[/tex]
=> [tex]x^2+7x+5[/tex]
. If α and β are the roots of
2x^2+7x-9=0 then find the equation whose roots are
α/β ,β/α
Answer:
[tex]18x^2+85x+18 = 0[/tex]
Step-by-step explanation:
Given Equation is
=> [tex]2x^2+7x-9=0[/tex]
Comparing it with [tex]ax^2+bx+c = 0[/tex], we get
=> a = 2, b = 7 and c = -9
So,
Sum of roots = α+β = [tex]-\frac{b}{a}[/tex]
α+β = -7/2
Product of roots = αβ = c/a
αβ = -9/2
Now, Finding the equation whose roots are:
α/β ,β/α
Sum of Roots = [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]
Sum of Roots = [tex]\frac{\alpha^2+\beta^2 }{\alpha \beta }[/tex]
Sum of Roots = [tex]\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }[/tex]
Sum of roots = [tex](\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}[/tex]
Sum of roots = [tex]\frac{49}{4} + 9 /\frac{-9}{2}[/tex]
Sum of Roots = [tex]\frac{49+36}{4} / \frac{-9}{2}[/tex]
Sum of roots = [tex]\frac{85}{4} * \frac{2}{-9}[/tex]
Sum of roots = S = [tex]-\frac{85}{18}[/tex]
Product of Roots = [tex]\frac{\alpha }{\beta } \frac{\beta }{\alpha }[/tex]
Product of Roots = P = 1
The Quadratic Equation is:
=> [tex]x^2-Sx+P = 0[/tex]
=> [tex]x^2 - (-\frac{85}{18} )x+1 = 0[/tex]
=> [tex]x^2 + \frac{85}{18}x + 1 = 0[/tex]
=> [tex]18x^2+85x+18 = 0[/tex]
This is the required quadratic equation.
Answer:
α/β= -2/9 β/α=-4.5
Step-by-step explanation:
So we have quadratic equation 2x^2+7x-9=0
Lets fin the roots using the equation's discriminant:
D=b^2-4*a*c
a=2 (coef at x^2) b=7(coef at x) c=-9
D= 49+4*2*9=121
sqrt(D)=11
So x1= (-b+sqrt(D))/(2*a)
x1=(-7+11)/4=1 so α=1
x2=(-7-11)/4=-4.5 so β=-4.5
=>α/β= -2/9 => β/α=-4.5
The solutions to the inequality y < to -x+1 sre shaded on the graph. Which point is a solution
There are two ways to confirm this is the answer. The first is to note that (3,-2) is on the boundary, so it is part of the solution set. This only works if the boundary line is a solid line (as opposed to a dashed or dotted line).
The second way is to plug (x,y) = (3,-2) into the given inequality to find that
[tex]y \le -x+1\\\\-2 \le -3+1\\\\-2 \le -2[/tex]
which is a true statement. So this confirms that (3,-2) is in the solution set of the inequality.
Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9,8 and 7(separate number sum for each multiple). What is the sum of these three numbers?
Answer:
Sum of 2 digit = 48
Sum of 3 digit = 317
Sum of 4 digit = 3009
Total = 3374
Step-by-step explanation:
Given:
9, 8 and 7
Required
Sum of Multiples
The first step is to list out the multiples of each number
9:- 9,18,....,99,108,117,................,999
,1008
,1017....
8:- 8,16........,96,104,...............,992,1000,1008....
7:- 7,14,........,98,105,.............,994,1001,1008.....
Calculating the sum of smallest 2 digit multiple of 9, 8 and 7
The smallest positive 2 digit multiple of:
- 9 is 18
- 8 is 16
- 7 is 14
Sum = 18 + 16 + 14
Sum = 48
Calculating the sum of smallest 3 digit multiple of 9, 8 and 7
The smallest positive 3 digit multiple of:
- 9 is 108
- 8 is 104
- 7 is 105
Sum = 108 + 104 + 105
Sum = 317
Calculating the sum of smallest 4 digit multiple of 9, 8 and 7
The smallest positive 4 digit multiple of:
- 9 is 1008
- 8 is 1000
- 7 is 1001
Sum = 1008 + 1000 + 1001
Sum = 3009
Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit
Sum of All = 48 + 317 + 3009
Sum of All = 3374
The first step in solving for the variable / in the equation P= 21 + 2w is:
A. Add the 2w to both sides of the equal sign.
B. Subtract the 2w to both sides of the equal sign.
C. Divide the 2 to both sides of the equal sign.
D. None of these choices are correct.
Find AC. (Khan Academy-Math)
Answer:
[tex]\boxed{11.78}[/tex]
Step-by-step explanation:
From observations, we can note that BC is the hypotenuse.
As the length of hypotenuse is not given, we can only use tangent as our trig function.
tan(θ) = opposite/adjacent
tan(67) = x/5
5 tan(67) = x
11.77926182 = x
x ≈ 11.78
3/(2x-1)+4=6x/(2x-1)
Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level 0.01 to test H0: μ1 − μ2 = −10 versus Ha: μ1 − μ2 < −10 for the following data: m = 8, x = 115.6, s1 = 5.04, n = 8, y = 129.3, and s2 = 5.32.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = ________
P-value = _________
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. Given that μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems, the hypothesis are
For null,
H0: μ1 − μ2 = - 10
For alternative,
Ha: μ1 − μ2 < - 10
This is a left tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 115.6
x2 = 129.3
s1 = 5.04
s2 = 5.32
n1 = 8
n2 = 8
t = (115.6 - 129.3)/√(5.04²/8 + 5.32²/8)
t = - 2.041
Test statistic = - 2.04
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [5.04²/8 + 5.32²/8]²/[(1/8 - 1)(5.04²/8)² + (1/8 - 1)(5.32²/8)²] = 45.064369/3.22827484
df = 14
We would determine the probability value from the t test calculator. It becomes
p value = 0.030
Since alpha, 0.01 < the p value, 0.03, then we would fail to reject the null hypothesis.
A group of 20 people were asked to remember as many items as possible from a list before and after being taught a memory device. Researchers want to see if there is a significant difference in the amount of items that people are able to remember before and after being taught the memory device. They also want to determine whether or not men and women perform differently on the memory test. They choose α = 0.05 level to test their results. Use the provided data to run a Two-way ANOVA with replication.
A B C
Before After
Male 5 7
4 5
7 8
7 8
7 8
7 8
5 6
7 7
6 7
Female 5 8
5 6
8 8
7 7
6 6
8 9
8 8
6 6
7 6
8 8
Answer:
1. There is no difference in amount of items that people are able to remember before and after being taught the memory device.
2. There is no difference between performance of men and women on memory test.
Step-by-step explanation:
Test 1:
The hypothesis for the two-way ANOVA test can be defined as follows:
H₀: There is no difference in amount of items that people are able to remember before and after being taught the memory device.
Hₐ: There is difference in amount of items that people are able to remember before and after being taught the memory device.
Use MS-Excel to perform the two-way ANOVA text.
Go to > Data > Data Analysis > Anova: Two-way with replication
A dialog box will open.
Input Range: select all data
Rows per sample= 10
Alpha =0.05
Click OK
The ANOVA output is attaches below.
Consider the Columns data:
The p-value is 0.199.
p-value > 0.05
The null hypothesis will not be rejected.
Conclusion:
There is no difference in amount of items that people are able to remember before and after being taught the memory device.
Test 2:
The hypothesis to determine whether or not men and women perform differently on the memory test is as follows:
H₀: There is no difference between performance of men and women on memory test.
Hₐ: There is a difference between performance of men and women on memory test.
Consider the Sample data:
The p-value is 0.075.
p-value > 0.05
The null hypothesis will not be rejected.
Conclusion:
There is no difference between performance of men and women on memory test.
The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p)= -80p + 3440p -36,000, where p is the price per frame and f(p) is the monthly profit based on that price.
Requried:
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
Answer:
a. $21.50
b. $980
c. $25 and $18
Step-by-step explanation:
a. The price that generates the maximum profit is
In this question we use the vertex formula i.e shown below:
[tex](-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\[/tex]
where a = -80
b = 3440
c = 36000
hence,
P-coordinate is
[tex](-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\[/tex]
[tex]= \frac{3440}{160}[/tex]
= $21.5
b. Now The maximum profit could be determined by the following equation
[tex]f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\[/tex]
= $980
c. The price that would enable the company to break even that is
f(p) = 0
[tex]f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0[/tex]
By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come
(p - 25) = 0 or (p - 18) = 0
so we can write in this form as well which is
p = 25 or p = 18
Therefore the correct answer is $25 and $18
If the area of a circular cookie is 28.26 square inches, what is the APPROXIMATE circumference of the cookie? Use 3.14 for π.
75.2 in.
56.4 in.
37.6 in.
18.8 in.
Answer:
Step-by-step explanation:
c= 2(pi)r
Area = (pi)r^2
28.26 = (pi) r^2
r =[tex]\sqrt{9}[/tex] = 3
circumference = 2 (3.14) (3)
= 18.8 in
Answer: approx 18.8 in
Step-by-step explanation:
The area of the circle is
S=π*R² (1) and the circumference of the circle is C= 2*π*R (2)
So using (1) R²=S/π=28.26/3.14=9
=> R= sqrt(9)
R=3 in
So using (2) calculate C=2*3.14*3=18.84 in or approx 18.8 in
What is the equation of a line passes thru the point (4, 2) and is perpendicular to the line whose equation is y = ×/3 - 1 ??
Answer:
Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.
y= -3x+b
Now, we can substitute in the point given to find the intercept.
2= -3(4)+b
2= -12+b
b=14
Finally, put in everything we've found to finish the equation.
y= -3x+14
Answer:
y = -3x + 14
Step-by-step explanation:
First find the reciprocal slope since it is perpendicular. Slope of the other line is 1/3 so the slope for our new equation is -3.
Plug information into point-slope equation
(y - y1) = m (x-x1)
y - 2 = -3 (x-4)
Simplify if needed
y - 2 = -3x + 12
y = -3x + 14
8. What is the lateral area of the cone?
Answer:
[tex]190.07 \: {yd}^{2} [/tex]Option D is the correct option.
Step-by-step explanation:
Diameter (d) = 10 yd
Radius(r) = 10/2 = 5 yd
Slant height (l)= 12.1 yd
We know,
Lateral surface area of cone:
[tex]\pi \: r \: l[/tex]
[tex] = 3.14 \times 5 \times 12.1[/tex]
[tex] = 189.97 \: {yd}^{2} [/tex]
which is nearly 190.07 square yards.
Hope this helps...
Good luck on your assignment..
Answer:
[tex]190.07 {yd}^{2} [/tex]
Step-by-step explanation:
[tex]lateral \: \: area \\ = \pi \: rl \\ = 3.14 \times 5 \times 12.1 \\ = 189.97[/tex]
189.97 square yards which is nearly 190.07 square yards
what's the equivalent expression
Answer:
2^52
Step-by-step explanation:
(8^-5/2^-2)^-4 = (2^-15/2^-2)^-4= (2^-13)^-4= 2^((-13*(-4))= 2^52
What is the sum of the measures of the interior angles of the stop sign?
Answer:
Sum of Interior Angles = (Number of Sides -2) • 180 degrees
Sum of Interior Angles = (8 -2) * 180 = 1,080
A piece of string is 120 centimeters long. How long would the piece of string measure in meters?. Enter your answer in the box.
Answer:
1.2 metres
Step-by-step explanation:
1 metre = 100cm
so 120cm has 120 cm * 1 m/ 100cm = 1.2 m