A company manufactures and sells x VCRs per month. If the cost and revenue equations are C(x) = 200 + 2x, R(x) = 20x − (x^2/50) , use differentials to estimate the change, ∆P, in profit when the production is increased from 100 to 101.
Answer:
ΔP = 14
Step-by-step explanation:
Given
[tex]C(x) = 200 + 2x[/tex]
[tex]R(x) = 20x - \frac{x^2}{50}[/tex]
Required
Determine the change in profit
First, we need to determine the profit
[tex]P(x) = R(x) - C(x)[/tex]
[tex]P(x) = 20x - \frac{x^2}{50} - 200 - 2x[/tex]
Collect Like Terms
[tex]P(x) = - \frac{x^2}{50} + 20x - 2x- 200[/tex]
[tex]P(x) = - \frac{x^2}{50} + 18x- 200[/tex]
Differentiate wrt x
[tex]P'(x) = -\frac{x}{25} + 18[/tex]
When Profit increases from 100 to 101, the change becomes
ΔP [tex]= -\frac{x}{25} + 18[/tex]Δx
Δx[tex]= (x_2 - x_1)[/tex]
Where
[tex]x_2 = 101[/tex]
[tex]x_1 = x = 100[/tex]
So, the expression: ΔP [tex]= -\frac{x}{25} + 18[/tex]Δx becomes
ΔP [tex]= (-\frac{x}{25} + 18)(x_2 - x_1)[/tex]
ΔP [tex]= (-\frac{100}{25} + 18)(101 - 100)[/tex]
ΔP [tex]= (-4+ 18)(1)[/tex]
ΔP [tex]= (14)(1)[/tex]
ΔP = 14
In how many ways 50 people can handshake with each other?
Answer:
My estimate think it 1225
Step-by-step explanation:
49 / 2 * (49 + 1) = 1225
What’s 1.2983 rounded to the nearest hundredth
Answer:
1.30 :)
All you have to do is see if the number on your left is greater than 5 or not if it’s is round up 1 if not it stays the same !
Hope this helped !!!
Step-by-step explanation:
The R.D. Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by the machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed:_______.
14.25 13.7 14.02
14.13 13.99 14.0
Based on these sample data,which of the following is true if the significance level is .05?
A) No conclusion can be reached about the status of the machine based on a sample size of only six cups.
B) The null hypothesis cannot be rejected since the test statistic is approximately t = .29,which is not in the rejection region.
C) The null hypothesis can be rejected since the sample mean is greater than 14.
D) The null can be rejected because the majority of the sample values exceed 14.
Answer:
The null hypothesis cannot be rejected since the test statistic is approximately t = .20,which is not in the rejection region.
Step-by-step explanation:
Data: 14.25, 13.7, 14.02, 14.13, 13.99, 14.0
Mean = [tex]\frac{Sum}{n}=14.015[/tex]
Standard deviation =[tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n}}=0.1836[/tex]
Claim : Average number of fluid ounces in the cup should be 14.
Null hypothesis : [tex]H_0:\mu = 14[/tex]
Alternate hypothesis :[tex]H_a:\mu \neq 14[/tex]
n = 6
[tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}\\t=\frac{14.015-14}{\frac{0.1836}{\sqrt{6}}}\\t=0.20\\\alpha = 0.05t_{df,\alpha}=t_{(5,0.05)}=2.571[/tex]
t critical > t calculated
So, we failed to reject null hypothesis
So, Option B is true
Hence The null hypothesis cannot be rejected since the test statistic is approximately t = .20,which is not in the rejection region.
Jessica, Sarah, and Vincent are following music in Mr. Arnold's class. Jessica is playing the
triangle on every second beat. Sarah is playing the cymbals on every fourth beat. Vincent is
playing the tambourine on every seventh beat. On what beat will all three students all play
their instruments at the same time.
Answer:
28 beats?
Step-by-step explanation: i think you have to do LCM of 2,4 and 7
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.35°F and a standard deviation of 0.64°F. Using the empirical rule, find each approximate porcent
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F?
b. What is the approximate percentage of healthy adults with body temperatures between 97 71°F and 98.99°F?
a. Approximately % of healthy adults in this group have body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F
(Type an integer or a decimal. Do not round)
Answer:
a) 99.97%
b) 65%
Step-by-step explanation:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
Mean of 98.35°F and a standard deviation of 0.64°F.
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F?
μ - 3σ
98.35 - 3(0.64)
= 96.43°F
μ + 3σ.
98.35 + 3(0.64)
= 100.27°F
The approximate percentage of healthy adults with body temperatures is 99.97%
b. What is the approximate percentage of healthy adults with body temperatures between 97 .71°F and 98.99°F?
within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
μ - σ
98.35 - (0.64)
= 97.71°F
μ + σ.
98.35 + (0.64)
= 98.99°F
Therefore, the approximate percentage of healthy adults with body temperatures between 97.71°F and 98.99°F is 65%
Simplest form of 14/63
Answer:
2/9
Step-by-step explanation:
Answer:
2/9
Step-by-step explanation:
a bowl contains 4 yellow marbles, 5 red marbles, 1 blue marbles, and 3 green marbles. find the probabilityof the given outcome
Answer:
bowl of colorful marbels
Step-by-step explanation:
bowl+marbels
m. 2.7(2x + 3) –4.6 n. 2 3 (12 + 15z) – 4 1 2 z o. 9 10 + 1 4 ( 2 3 v+ 2 5 )–1
Answer:
go on
Step-by-step explanation:
math,way, ., com
Write each prime factorization using exponents.
1. 2×2×2×7
2. 2×3×3
3. 7×7×7×7
Kevin's wife sends him to the store to buy pickles and ice cream. Ice cream cost 5 dollars per pound and pickles costs 8 dollars per pound. Kevin has 80 dollars in his wallet. Let x be the number of pounds of ice cream and y be the number of pounds of pickles that Kevin purchases. State the inequality that represents his budget, and graph the solution that represents the possible combinations of x and y . Express your answer with the standard form a x + b y on the left side. The budget inequality is _____________________
Answer:
5x+8y≤80
Step-by-step explanation:
trust me ;)
Answer:
5x+8y< 80
Step-by-step explanation:
The total amount should be less than 80 or equal to
Make 3 1/2 cakes in 20 minutes how many cakes can you make in two hours
Answer:
17
Step-by-step explanation:
3 1/2+3 1/2=5 which is 40 min
5=40mins
5+3 1/2=81/2
1 hour=8 1/12
8 1/2+8 1/2= 17
17 in two hours
Am gonna give branliest!!!
Jeannine puts 10% of her paycheck into a savings account. If she makes $500 each week,
how much does she put in her savings account each week?
Answer:
$50
Step-by-step explanation:
a horizontal line , such as y=4, has a slope of what
Answer:
0
Step-by-step explanation:
A horizontal line has a slope of zero and a vertical line has an undefined slope
A bakery offers a sale of 3.50 for 6 muffins what’s is the price per dozen
Select the values that correctly complete the problem. a = b = c = d = e =
Answer: 2/3 = b/ac = d/e
Step-by-step explanation:
This is all I got if I got it right. Is this one of your answers?
Answer:
a= 2
b=4
c=3
d=2
e=3
Step-by-step explanation:
i hope this helps.
f(x) = 3x2 – 4x – 1
g(x) = –2x + 5
Find: (gof)(x)
Answer:
[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]
Step-by-step explanation:
The Composite Function
Given f(x) and g(x) real functions, the composite function, named (g\circ f)(x) is defined as:
[tex](g\circ f)(x)=g(f(x))[/tex]
For practical purposes, it's found by substituting f into g.
Given the functions:
[tex]f(x) = 3x^2 - 4x - 1[/tex]
[tex]g(x) = -2x + 5[/tex]
We need to find
[tex](g\circ f)(x)=g(f(x))[/tex]
Replace f into g:
[tex](g\circ f)(x)=-2(3x^2 - 4x - 1) + 5[/tex]
Operating:
[tex](g\circ f)(x)=-6x^2 +8x +2 + 5[/tex]
Reducing:
[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]
Thus,
[tex]\boxed{(g\circ f)(x)=-6x^2 +8x +7}[/tex]
Drove 260 km using 12 liters of gas at this rate how many liters of gas would he need to drive 286km
Answer:
We calculate the amount of gas used per km and multiply it by 286
Step-by-step explanation:
If we drive for 260km and use 12 litres of gas that means that we use
[tex]\frac{12}{260}[/tex] litres per km.
Now we multiply it by 286:
[tex]\frac{12}{260} *286 = \frac{858}{65} = 13.2[/tex]
So, the answer is 13.2 litres.
division 6=7??????????
Valerie runs track and field. At meets, Valerie lkes to buy protein bars, bananas and sports drinks Protein bars are $1. bananas are S0.50, and sports drinks are S2. Valerie has S10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars. Let represent the number of protein bars. represent the number of bananas. and represent the number of sports drinks that Valerie buys. Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p
Complete Question
Valerie runs track and field. At meets, Valerie likes to buy protein bars, bananas, and sports drinks. Protein bars are $1, bananas are $0.50, and sports drinks are $2. Valerie has $10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars.
Let p represent the number of protein bars, b represent the number of bananas, and d represent the number of sports drinks that Valerie buys.
Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p
Answer:
The statements that are true regarding Valerie's situation:
A: p + 0.5b + 2d < 10
C: d < 2b
D: b > 3p
Step-by-step explanation:
Lets represent
The number of protein bars as p.
The number of bananas as b.
The number of sports drinks that Valerie buys as d.
From the question:
We are told
Protein bars are $1
Bananas are $0.50
Sports drinks are $2.
She will spend no more than twice as much on sports drinks as bananas
d ≤ 2b = d < 2b
At least three times as much on bananas as protein bars.
b ≥ 3p = b > 3p
We are also told that:
Valerie has $10 to spend.
Hence:
$1 × p + $0.50 × b + $2 × d < $10
= p + 0.5b + 2d < 10
Therefore, the statements that are true regarding Valerie's situation:
A: p + 0.5b + 2d < 10
C: d < 2b
D: b > 3p
NEED HELP ASAP Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberries less than Ann and Ben together, what is the total number of strawberries the three of them ate?
Answer:
170Step-by-step explanation:
given:
Ann, Ben, and Cindy were eating strawberries.
The ratio of the numbers of berries they ate is 5:5:7.
If Cindy ate 30 strawberries less than Ann and Ben together,
find:
what is the total number of strawberries the three of them ate?
solution:
add the ratios 5 + 5 + 7 = 17
since Cindy ate 30, less than Ann and Ben together so, the equation is
7x = 5x + 5x - 30
7x - 10x = -30
x = 30/3
x = 10
ann 5 x 10 = 50
ben 5 x 10 = 50
cindy 7 x 10 = 70
total = 170
==============================================
Explanation:
A = number Ann ate
B = number Ben ate
C = number Cindy ate
Let x be some positive whole number
Since A,B,C is in the ratio 5:5:7, this means
A = 5x
B = 5x
C = 7x
Note how A:B:C = 5x:5x:7x = 5:5:7. We divide all parts by x to simplify the ratio.
-------------------
Cindy ate 30 strawberries less than Ann and Ben, so
C = A+B-30
C = 5x+5x-30
C = 10x-30
Earlier in the last section we had C = 7x, and now we found C = 10x-30
Since we're talking about the same C value, we can equate and solve
C = 7x
10x-30 = 7x ... replace C with 10x-30
10x-7x = 30
3x = 30
x = 30/3
x = 10
------------------
With this x value, we now know that...
A = 5x = 5*10 = 50
B = 5x = 5*10 = 50
C = 7x = 7*10 = 70
Cindy's count (70) is 30 less than Ann and Ben's combined count (50+50 = 100), so that helps confirm the answer.
Further confirmation comes from 50:50:70 reducing to 5:5:7 when you divide all parts by the GCF 10.
--------------------
The last step is to add the values of A, B and C.
A+B+C = 50+50+70
A+B+C = 100+70
A+B+C = 170
---------------------
Side note: since A+B+C = 5x+5x+7x = 17x, this means that the final answer is a multiple of 17.
10a^2b^0 for a=–3, b=–8
Answer:
90Step-by-step explanation:
Substitute a = -3 and b = -8 to the expression 10a²b⁰:
10(-3)²(-8)⁰ = 10(9)(1) = 90
a⁰ = 1 for any real number
Answer:
90
Step-by-step explanation:
10a^2b^0
Let a=–3, b=–8
10 (-3)^2 ( -8)^0
10 * 9 *1
90
Darren and Carl each go for a morning jog before work. Darren's jogging pace
is represented by the equation y = 5x where y is the number of miles he jogs
and x is the number of hours he jogs. Carl's pace is given by the graph.
35
28
Distance (miles)
21
14
2
3
5
Time (hours)
Choose the statement that correctly compares their unit rates.
O A. Carl's unit rate is equal to Darren's unit rate.
O B. Carl's unit rate is 2 fewer miles per hour than Darren's unit rate.
O C. Carl's unit rate is 1 more mile per hour than Darren's unit rate.
D. Carl's unit rate is 2 more miles per hour than Darren's unit rate.
Answer: d
Step-by-step explanation:
Answer:
D. Carl's unit rate is 2 more miles per hour than Darren's unit rate.
Step-by-step explanation:
A table marked at ₹ 15,000 is available for ₹ 14,400. Find the discount given and the discount percentage.
Answer: ₹ 600 and 15% discount rate i believe
Step-by-step explanation:
escribe el número igaul a 5 decenas y 13 unidades
Answer:
63
Step-by-step explanation:
Last week, Tanya had $43 in her checking
account. She deposited $50 and wrote a check
for $92. How much money is left in her account?
Answer:
She would have $1 left in her account.
Step-by-step explanation:
43 + 50 = 93
93 - 92 = 1
Hope this helps..?
Answer:
$1
Step-by-step explanation:
We start off with $43.
Tanya deposits $50 to her account.
50+43=93.
She has $93 now.
She writes a check for $92.
93-92=1.
Man, Tanya is broke no cap.
Given that BD is an angle bisector
Solve for m
Answer:
24 degrees
Step-by-step explanation:
since BD is an angle bisector, the given numbers are equal to each other
this means that you can write the equation as: 6x = x + 20
subtract x from both sides to move the variable to one side, this leaves you with: 5x = 20
then divide both sides by 5 to find x: x = 4
now substitute this into the value given for angle ABD: 6(4)
this gives you 24 degrees
g Find the standard deviation for the number of female college students out of 15 that plan to graduate with a STEM degree.
Complete question is;
In a recent poll of female college students, 70% stated that they plan to graduate with a STEM degree. A math teacher at ODU decides to randomly sample 15 female college students. Find the standard deviation for the number of female college students out of 15 that plan to graduate with a STEM degree.
Answer:
σ = 1.77
Step-by-step explanation:
We are told that 70% stated that they plan to graduate with a STEM degree.
This means that probability of success is; p = 70% = 0.7
A sample of 15 female college students were randomly selected, this means that number of trials is;
n = 15
Now,in binomial distribution formula for standard deviation is;
σ = √(np(1 - p))
Plugging in the relevant values, we have;
σ = √(15 × 0.7 × (1 - 0.7))
σ = √(15 × 0.7 × 0.3)
σ = √3.15
σ ≈ 1.77
Solve the following 3x + 7 = 2x + 13 over 3
Answer:
3x+7=2x+13 over 3
3 (3x )+3 (7)=2x +13 over 3×3
9x+21=2x +13
9x- 2x=13-21
7x=-8
x=8/7
Step-by-step explanation:
Step 1:Multiply both sides by the denominator
Step 3:Group like terms
Step 5: Divide both sides to find for x