Answer:
We know that:
[tex]C_{(N)}=15000+8000N[/tex]
So first we need to substitute the next equation in the C(N) equation
[tex]N_{(t)} = 100t-5t^{2}[/tex]
And therefore we have:
[tex]C_{(t)}=15,000 + 8000*(100t-5t^{2})\\C_{(t)}=15,000 + 800000t-40000t^{2}[/tex]
Finally we replace at t = 5 in the equation above and we have:
[tex]C_{(5)}=15,000 + 800000*5-40000*5^{2}\\C_{(5)}= 3015000[/tex]
The interpretation is that after 5 hours of operation, we have wasted 3015000 dollars producing cars.
To calculate the cost of production as a function of time, substitute the production function N(t) into the cost formula C(N). After simplifying, the cost function is C(t) = 15,000 + 800,000t - 40,000t². At 5 hours, the cost is 3,015,000 dollars.
Explanation:To find the cost C as a function of the time t of operation of the factory, we first use the formula for the number of cars produced N(t) = 100t - 5t². Then we substitute the expression for N(t) into the cost function C(N) = 15,000 + 8000N.
Substituting N(t) into C(N), we get:
C(N(t)) = 15,000 + 8000(100t - 5t²)C(t) = 15,000 + 8000(100t) - 8000(5t²)C(t) = 15,000 + 800,000t - 40,000t²This is the cost C as a function of time t.
When t = 5 hours, the function becomes:
C(5) = 15,000 + 800,000(5) - 40,000(5²)C(5) = 15,000 + 4,000,000 - 1,000,000C(5) = 3,015,000 dollarsThis result means that the cost of production after 5 hours of operation is 3,015,000 dollars.
Lines AB and EB share a common point at B therefore we say that these lines
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5 rubber stamps cost $9.70 Which equation would help determine the cost of 11 rubber stamps?
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3.582x 10(-6) in standard form
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Find the product and quotient of each pair of numbers
a. 24.6 and 1.2
b. 1.95 and .25
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Is 5/8 more than 2/3
mario has less than $50. he has six bills in all. four of them are are tens. how many ones does he have????
6/10 in simplest form
T is the midpoint of su. If st=16 the su=?
can 50 go into 100 and 250
yes:
100/50 = 2
250/5 = 5
What are the whole number dimensions of 180
Susan and John are buying cold drinks for a neighborhood picnic. Each person is expected to drink one can of soda. Susan says that if you multiply the unit price for a can of soda by the number of people attending the picnic, you will be able to determine the total cost of the soda. John says that if you divide the cost of a 12 pack of soda by the number of sodas, you will determine the total cost of the sodas. Who is right, and why?
Dr.Baker and 2 other dentists work in the same office.In one day,the three dentists saw a total 51 patients.Suppose each dentist saw the same number of patients .How many patients dud each dentist see?
Drag a reason to each box to complete the flowchart proof.
From linear pair postulate, if two angles are in linear pair, then they are supplementary.
Also, the definition of supplementary angles states that the sum of the angles is 180 degrees.
Hence, the correct option is Definition of supplementary angles.
Multiply: 3x4(4x4 − x5 + 2) 7x8 − 3x9 + 6x4
2. AB and DE are parallel. Angle BAC = 30 , angle CDE = 50. What is the measure of angle ACD?
A. 100
B. 90
C. 80
D. 70
E. cannot be determined from the information
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For his parents’ anniversary, Danny spends $5.87 on a photo.He also buys a balloon for $2.49 and a box of strawberries for $4.50. How much money does he spend all together
The total amount of money spent by Danny is [tex]\fbox{\$12.86}[/tex].
Further explanation:
Given:
Danny spends $5.87 on a photo, $2.49 for balloon and $4.50 on strawberries.
Calculation:
Consider the total money spent as [tex]S[/tex], money spends on photo as [tex]x[/tex], money spends on balloons as [tex]y[/tex] and money spend on strawberries as [tex]z[/tex].
Total money spent [tex]S[/tex] is written as the sum of the money spent on photo [tex]x[/tex], balloons [tex]y[/tex] and strawberries [tex]z[/tex] as follows:
[tex]S=x+y+z[/tex] …… (1)
Substitute, 5.87 for [tex]x[/tex], 2.49 for [tex]y[/tex] and 4.50 for [tex]z[/tex] in equation (1) to obtain the total money spent by Danny as follows:
[tex]\begin{aligned}S&=5.87+2.49+4.50\\&=8.36+4.50\\&=12.86\\\end{aligned}[/tex]
Thus, the total amount of money spent by Danny is [tex]\fbox{\$12.86}[/tex].
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1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
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Answer Details :
Grade: Middle School
Subject: Mathematics
Chapter: linear equation
Keywords:
Money, Danny, anniversary, photo, balloon, strawberries, dollar, spent, x+y+z, function, substitution, direct substitution, elimination, graph, middle term factorization, scientific notation.
A moving company charges a $2,000 fee plus $100 per hour. Another moving company charges an $1,800 fee plus $150 per hour. How long is a job for which the two companies' costs are the same?
2 hours
4 hours
3 hours
5 hours
The two moving companies' costs would be equal for a job that takes 4 hours to complete.
Explanation:The cost for each moving company can be represented as a linear equation. For the first company, the cost equation is C = 2000 + 100h and for the second company, the equation is C = 1800 + 150h. We want to know when these two costs are equal, so we can set the two equations equal to each other and solve for 'h' (which represents the number of hours):
2000 + 100h = 1800 + 150h.
Solving for h, you'll find h = 4 hours. This means that the costs of the two companies will be the same if the job takes 4 hours to complete.
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Aidan drives to school and back each day. The school is 16 miles from his home. He averages 40 miles per hour on his way to school. If his total trip takes 1 hour, at approximately what speed does Aidan drive home?
17 mph
27 mph
32 mph
56 mph
Answer:
The correct option is 2.
Step-by-step explanation:
The formula form speed is
[tex]speed=\frac{distance}{time}[/tex]
[tex]time=\frac{distance}{speed}[/tex]
It is given that the school is 16 miles from his home. He averages 40 miles per hour on his way to school. Time taken by Aidan to reach school from the home is
[tex]t_1=\frac{16}{40}[/tex]
Let speed at which Aidan drive home be s. Time taken by Aidan to reach home from the school is
[tex]t_2=\frac{16}{s}[/tex]
It is given that his total trip takes 1 hour.
[tex]\frac{16}{40}+\frac{16}{s}=1[/tex]
[tex]\frac{16s+640}{40s}=1[/tex]
[tex]16s+640=40s[/tex]
[tex]640=40s-16s[/tex]
[tex]640=14s[/tex]
Divide both sides by 14.
[tex]\frac{640}{24}=s[/tex]
[tex]s=26.666667[/tex]
[tex]s\approx 27[/tex]
Aidan return with speed about 27 mph Therefore the correct option is 2.
Answer:
B
Step-by-step explanation:
did it on edg
Diagram 6(b)(i) shows a regular pentagon PQRST and a right-angled triangle RUV. Find the value of x.
Last year at this time we had 250 employees. Due to attrition , we lost 12% of our workforce. How many employees are working now
Answer: There are 220 employees working now.
Step-by-step explanation:
Hi, to answer this question, first, we have to multiply the number of employees by the percentage in decimal form.
12% = 12/100= 0.12 (decimal form)So, mathematically speaking:
250 x 0.12 = 30 employees lessFinally, we subtract the number obtained to the initial number of employees.
250 -30 = 220 employees.There are 220 employees working now.
Feel free to ask for more if needed or if you did not understand something.
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17. A local university accepted 2,300 students out of 4,500 applicants for admission. What was the acceptance rate, expressed as a percent? Show your work.
The acceptance rate of the students is 51.1%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a local university accepted 2,300 students out of 4,500 applicants for admission.
The acceptance rate will be calculated as,
Acceptance rate = ( 2300 x 100 ) /4500
Acceptance rate = 51.1 %
Therefore, the acceptance rate of the students is 51.1%.
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what's 763 thousandths in scientific notation
The scientific notation of 763 thousandths is [tex]\boxed{7.63 \times {{10}^{ - 1}}}.[/tex]
Further explanation:
Given:
The number is 763 thousandths.
Explanation:
The place values are only natural numbers.
The base ten systems represent the position of a place value.
The first digit from the right is the ones place, the second digit from the right is the tens place, the third digit from the right is the hundreds, the fourth digit from the right is the thousands.
After decimal the first place is the tenth place, the second place is the hundredth and the third place is the thousandth.
763 thousandths in base 10 can be expressed as follows,
[tex]\begin{aligned}763{\text{ thousandths}}&= \frac{{763}}{{1000}} \\&= 763 \times {10^{ - 3}} \\ &= 0.763 \\\end{aligned}[/tex]
The scientific notation of 763 thousandths can be obtained as follows,
[tex]\boxed{0.763 = 7.63 \times {{10}^{ - 1}}}[/tex]
The scientific notation of 763 thousandths is [tex]\boxed{7.63 \times {{10}^{ - 1}}}.[/tex]
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Decimals
Keywords: value, scientific notation, 763, digit, place value, tens, hundreds, thousandth, ones, digit, place, base ten.
Tyler orders a meal that costs $15, if the tax rate is 6.6%, how much will the sales tax be on Tyler's meal?
Answer:
The sales tax on Tyler's meal will be approximately $0.99.
Explanation:
To calculate the sales tax on Tyler's meal, you can first find the amount of tax by multiplying the cost of the meal by the tax rate (in decimal form). Then, you can simply add this tax amount to the cost of the meal.
Tax amount = Cost of the meal × Tax rate
Given:
Cost of the meal = $15
Tax rate = 6.6% = 0.066 (in decimal form)
Now, let's calculate the tax amount:
Tax amount = $15 × 0.066
≈ $0.99
So, the sales tax on Tyler's meal will be approximately $0.99.