The distance of a dog from a post and the cost of buying apples can be represented by functions. We can find the values of these functions by substituting specific values and calculating the corresponding outputs.
Explanation:In this question, we are given a function that represents the distance of a dog from a post as a function of time. To find the value of f(20), we substitute 20 into the function and calculate the corresponding distance. To find the value of f(140), we do the same thing, substituting 140 into the function.
f(20) = 20 feet
f(140) = 140 feet
In the second part of the question, we are given a function C that represents the cost of buying n apples. To find the meaning of each expression or equation, we substitute the given value of n and calculate the corresponding cost.
C(8) = $4.50
C(2) represents the cost of buying 2 apples.
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Pablo wishes to grow his baseball card collection to at least 3000 cards. He currently has 1200 and his favorite type of cards have 15 cards per package which inequality and solution represent the number of packages of cards that pablo wishes to buy , select all that apply
Answer:
x ≥ 120
Step-by-step explanation:
i) Let x be the number of packages of cards
ii) we know that Pablo currently has 1200 cards.
iii) Therefore the equation required is
15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards
iv) Solving the equation we get
15x + 1200 ≥ 3000
⇒ 15x ≥ (3000 - 1200)
⇒ 15x ≥ 1800
⇒ x ≥ (1800 ÷ 15)
∴ x ≥ 120
answer
x ≥ 120
Step-by-step explanation:
Step-by-step explanation:
i) Let x be the number of packages of cards
ii) we know that Pablo currently has 1200 cards.
iii) Therefore the equation required is
15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards
iv) Solving the equation we get
15x + 1200 ≥ 3000
⇒ 15x ≥ (3000 - 1200)
⇒ 15x ≥ 1800
⇒ x ≥ (1800 ÷ 15)
∴ x ≥ 120
Plot the points in the coordinate plane. Then find the perimeter and area of the polygon.
A(-3,5), B(1,6), C(3,-2), D(-1,-3)
Perimeter___________
Area__________________
Answer:
The answer to your question is below
Step-by-step explanation:
See the graph below
Process
1.- Find the distance from A to B, B to C, C to D, A to D
Formula
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
d AB = [tex]\sqrt{(1 + 3)^{2} + (6 - 5)^{2}} = \sqrt{17}[/tex]
dBC = [tex]\sqrt{(-2 -6)^{2} + (3 - 1)^{2}} = \sqrt{68}[/tex]
dCD = [tex]\sqrt{(-1 - 3)^{2} + (-3 +2)^{2}} = \sqrt{17}[/tex]
dAD = [tex]\sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}} = \sqrt{68}[/tex]
2.- Find the perimeter
Perimeter = 2[tex]\sqrt{17} + 2\sqrt{68}[/tex] = [tex]6\sqrt{17}[/tex] u
3.- Find the area
Area = [tex]\sqrt{17} x \sqrt{68}[/tex]
Area = [tex]\sqrt{17x68} = \sqrt{1156} = 34 u^{2}[/tex]
Adrienne's annual take-home pay is $57,000. What is the maximum amount that she can spend per month paying off credit cards and loans and not be in danger of credit overload?
A. $950.00
B. $1187.50
C. $4750.00
D. $3800.00
Answer:
Option C. is correct.
Step-by-step explanation:
Given:
Adrienne's annual take-home pay = $57,000
To find:
The maximum amount that she can spend per month on paying off credit cards and loans and not be in danger of credit overload.
Solution:
Number of months in a year = 12
So, amount she can spend per month =
Annual pay of Adrienne / Number of months in a year = [tex]\frac{57000}{12} =\frac{28500}{6}=\frac{14250}{3}=4750[/tex]
So, option C. is correct.
Answer:
A. $950.00
Step-by-step explanation:
A p e x
Malcom coasted 32 miles from Moonridge to to Mentine and then pedaled back hard. If the round trip took 4 hours, what was Malcombs average speed in mph
Answer:
16 mph
Step-by-step explanation:
The relationship between distance, speed, and time is ...
speed = distance/time . . . . . "miles per hour"
Malcom's distance was 32 miles each way, for a total of 64 miles. Then his average speed was ...
speed = (64 mi)/(4 h) = 16 mi/h
Jeff wants to know how many miles it is from his house to school. On a map, the scale is 0.5 inches=2 miles. If his house island school are 3 inches apart on the map, how many miles is it to the school?
It is 12 miles from house to school
Solution:
Given that, Jeff wants to know how many miles it is from his house to school
On a map, the scale is 0.5 inches = 2 miles
His house island school are 3 inches apart on the map
So, from the given scale,
0.5 inches = 2 miles
Distance between school and house in map = 3 inches
Therefore,
0.5 inches = 2 miles
Muliply both sides by 6
[tex]0.5 \times 6\ inches = 6 \times 2\ miles\\\\3\ inches = 12\ miles[/tex]
Thus, it is 12 miles from house to school
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.81, 0.09, 0.08, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?
Answer:
$600
Step-by-step explanation:
Let the random variable [tex]X[/tex] denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of [tex]X[/tex] is given by
[tex]X : \begin{pmatrix}0 & 1000 & 5000 & 10\; 000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]
A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by
[tex]F(x) = \left \{ {{X+100, \quad \quad \quad \quad \quad \text{for} \; X = 0 } \atop {X-500+100} , \quad \text{for} \; X = 500,4500,9500} \right.[/tex]
For [tex]X = 0[/tex], we have
[tex]F(X) = 0+100 = 100[/tex]
For [tex]X = 500[/tex],
[tex]F(X) = 500-500+100 = 100[/tex]
For [tex]X = 4500[/tex],
[tex]F(X) = 4500-500+100 = 4100[/tex]
For [tex]X = 9500[/tex],
[tex]F(X) = 9500-500+100 = 9100[/tex]
Therefore, the probability distribution of [tex]F[/tex] is given by
[tex]F : \begin{pmatrix} 100 & 100 & 41000 & 91000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]
To determine the premium amount that the company should charge, we need to calculate the expected value of [tex]F.[/tex]
[tex]E(F(X)) = \sum \limits_{i=1}^{4} f(x_i) \cdot p_i = 100 \cdot 0.81 + 100 \cdot 0.09 + 4100 \cdot 0.08 + 9100 \cdot 0.02[/tex]
Therefore,
[tex]E(F) = 81+9+328+182 = 600[/tex]
which means the $600 is the amount the should be charged.
Players in any sport who are having great seasons, turning in performances that are much better than anyone might haveanticipated, often are pictured on the cover of Sports Illustrated. Frequently, their performances then faltersomewhat, leading some athletes to believe in a "Sports Illustrated jinx." Similarly, it is common for phenomenal rookies to have less stellar second seasons, the so-called "sophomore slump." While fans, athletes, and analysts have proposed many theories about what leads to such declines, a statistician might offer a simpler(statistical) explanation. Explain.
What would be a better explanation for the decrease in performance of the Sports Illustrated cover athlete?
A. People on the cover are usually there for outstanding performances. Because they are so far from the mean, the performance in the next year is likely to be closer to the mean.
B. The slope of the linear regression, predicting performance from years in the sport, must be negative because an athlete's performance always decreases over time. No matter how well an athlete performed one year, they must perform worse the next year.
C. People on the cover are usually considered the best of theyear, so naturally they reached the maximum level of athletic performance that year and it is impossible to improve upon that.
D. Once an athlete has made the cover of Sports Illustrated, they have reached their ultimate goal as an athlete and lack motivation to try the following year.
Answer:
I pick the reasoning of option A
Step-by-step explanation:
I like the reasoning given in B, however, there are many cases of Athletes that, after reaching the top, maintain supremacy and improve over the years, adapting to their old age. Usually speed and physical resistance are replaced by technique and experience in the case of the top athletes.
I dont like C and D argument too much because being the best in a sport doesnt mean either that you reach the maximum level possible (in many cases you can keep growing) or that you dont have more motivations. Many athletes are super competitive people and they try to improve themselves all the time to reach, and stay, in the top.
I choose option A as answer because people on the cover doesnt neccesarily mean that they are the absolute best. Their performance was way better than their usual performance, and that may be due to either real skill growth, heavy training or a lucky streak. If it is a lucky streak, it is natural for that player's performance to go down into more terrenal levels for him. On the other hand, If he trained heavily, then he might have big injuries on later seasons and his performance wont be able to keep up for long. Thats why 'surprises' (that also sell better due to be a novelty) tend to go downhill after they reach the cover of sports illustrated.
The decrease in performance after an athlete's phenomenal season could be due to a statistical phenomenon called regression to the mean. This principle suggests that if a variable (e.g., athletic performance) is extreme on its first measurement, it will tend to be closer to the average on its subsequent measurement, which could explain why some athletes have less stunning seasons after achieving outstanding performances.
Explanation:A better explanation for the decrease in performance of the Sports Illustrated cover athlete could be option A. People on the cover are usually highlighted for their outstanding performances, which are far from the mean. Due to a phenomenon called regression to the mean, it is likely that their performance in the next season would be closer to the mean (average).
Regression to the mean is a statistical concept that suggests that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement, and vice-versa.
This has nothing to do with a jinx, but rather with the statistical principle that performances, both good and bad, tend to cluster around the mean over time. So, outstanding performance is often followed by less exceptional performance, not necessarily because the player got worse, but because the original performance was likely above their true average.
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A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of 72000$ in one week what was the salesperson paid that week
Answer:
Step-by-step explanation:
A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of $72000 in one week, it means that the amount of commission that was received by the salesperson would be
3/100 × 72000 = 0.03 × 72000 = $2160
Therefore, the total amount of pay that the salesperson would receive for the week would be
900 + 2160 = $3060
A stadium has 10500 seats and 8 VIP boxes. The stadium is divided into 12 equal sections: 2 premium sections and 10 standard sections. A seat at the premium section costs $48 per game. A seat at the standard section costs $27 per game.
Answer:
1). 875 seats
2). 25 rows in each section
3). $8400
4). Saving of $360
5). 2105 tickets remained unsold
6). x = 16
Step-by-step explanation:
This question is incomplete; here is the complete question.
A stadium has 10,500 seats and 8 VIP boxes. The stadium is divided into 12 equal sections: 2 premium sections and 10 standard sections. A seat at the premium section costs $48 per game. A seat at the standard section costs $27 per game.
1. How many seats are there in each section?
2. If there are 35 seats in each row, how many rows are in each section?
3. If all the seats in the premium section are sold out for a game, how much will the stadium get from those ticket sales?
4. There are 50 games in each season. A season pass costs $2,040. A season pass holder can go to all the games and have a seat in the premium section. How much can a fan save by buying the season pass?
5. For the night game on Tuesday, 8,395 tickets were sold. How many tickets were left?
6. Write an equation using “x” and then solve the equation. Each VIP boxes can seat X people. If all the seats and VIP boxes are filled up, there are 10,628 audience in the stadium.
1). Number of seats in the stadium = 10500
Number of sections = 2 premium + 10 standard = 12
Number of seats in each section = [tex]\frac{10500}{12}=875[/tex]
2). If the number of seats in each row = 35
Then number of rows in each section = [tex]\frac{875}{35}=25[/tex]
3). Number of seats in 2 premium sections = 2×875 = 1750
Cost of 1750 seats at the rate of $48 per game = 1750 × 48 = $84000
4). Cost of one ticket in premium section = $48 per game
If the games planned in one season = 50
Then cost of the tickets = 48×50 = $2400
Cost of the season ticket = $2040
Saving on the purchase of one season ticket = 2400 - 2040 = $360
5). For a night game number of tickets sold = 8395
Total number of seats in the stadium = 10500
Tickets remained unsold = 10500 - 8395 = 2105
6). Number of seats in each VIP box = x
Number of VIP boxes = 8
Number of seats in 8 VIP boxes = 8x
Total number of tickets sold = 10500 + 8x
Total number of audience in the stadium = 10628
Then the equation will be
8x + 10500 = 10628
8x = 10628 - 10500
x = [tex]\frac{128}{8}=16[/tex]
The subject of this question is Mathematics, specifically dealing with seating capacity and pricing in a stadium. To determine the maximum seating capacity of the stadium, add up the number of seats in each section. To calculate the total revenue from a single game, multiply the number of seats in each section by the corresponding ticket price, and then sum up the results.
Explanation:The subject of this question is Mathematics, specifically dealing with the concepts of seating capacity and pricing in a stadium.
To determine the maximum seating capacity of the stadium, we add up the number of seats in each section: 2 premium sections with 48 seats each, 10 standard sections with 900 seats each, and 8 VIP boxes with a capacity of 12 seats each. This gives us a total of 1116 seats.
To calculate the total revenue from a single game, we multiply the number of seats in each section by the corresponding ticket price, and then sum up the results. For the premium sections, the revenue is $48 per seat multiplied by 96 seats, and for the standard sections, the revenue is $27 per seat multiplied by 900 seats. Adding up these two amounts gives us the total revenue from a single game.
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A buyer paid $55 comma 68055,680, including the buyer's premium, for a car auction. If the auction adds a 1616% buyer's premium to the sale price of the car, then what was the sale price of the car?
Answer:
The sale price of the car is $48000.
Step-by-step explanation:
i) let the sale price of the car be = $x
ii) the premium is given as 16%
therefore the premium of the car will be equal to = 16% of $x
the premium of the car will be = $0.16x
iii) therefore total price of car in terms of sale price x = $x + $0.16x
therefore total price = $1.16x
iv) total price is given as $55,680
Therefore $55,680 = $1.16x, therefore $x = [tex]\dfrac{55,680}{1.16} = \$\hspace{0.15cm}48000[/tex].
Therefore the sale price of the car is $48000.
When you graph a square root does it curve
Answer:
yes
Step-by-step explanation:
because it is not a whole number so you cant tell
A box with a square base and open top must have a volume of 32,000cm^3. How do you find the dimensions of the box that minimize the amount of material used?
Answer:
Side of 40 and height of 20
Step-by-step explanation:
Let s be the side of the square base and h be the height of the box. Since the box volume is restricted to 32000 cubic centimeters we have the following equation:
[tex]V = hs^2 = 32000[/tex]
[tex]h = 32000/ s^2[/tex]
Assume that we cannot change the thickness, we can minimize the weight by minimizing the surface area of the tank
Base area with open top [tex]s^2[/tex]
Side area 4hs
Total surface area [tex]A = s^2 + 4hs[/tex]
We can substitute [tex]h = 32000/ s^2[/tex]
[tex]A = s^2 + 4s\frac{32000}{s^2}[/tex]
[tex]A = s^2 + 128000/s[/tex]
To find the minimum of this function, we can take the first derivative, and set it to 0
[tex]A' = 2s - 128000/s^2 = 0[/tex]
[tex]2s = 128000/s^2[/tex]
[tex]s^3 = 64000[/tex]
[tex]s = \sqrt[3]{64000} = 40[/tex]
[tex]h = 32000/ s^2 = 32000/ 40^2 = 20[/tex]
Shane's neighbor pledged $1.25 for every 0.5 miles that Shane swims and the charity swim-a-thon. If Shane swims 3 miles how much money would his neighbors donate
Answer:
7.5
Step-by-step explanation:
1.25/ (.5) = 2.5
2.5 x 3 = 7.5
A typical marathon has 26.2 miles. allan makes an average of 12 kilometers per hour when running marathons. Determine how long it would take allan to complete a marathon at the nearest tenth of an hour.
Answer:
3hr 31mins
Step-by-step explanation:
First we convert miles to kilometers
1 miles to km = 1.60934 km
26.2 miles = 26.2 x 1.60934 = 42.164708
A typical marathon approx = 42.165km
If our runner covers 12 km = 1 hr
then he'll cover 42.165km = 42.165/12 = 3.5137 hrs
= 3 hrs + (0.514 * 60 mins) = 3hrs + (30.84mins)
Allan going at that speed would complete the marathon in appox = 3hrs : 31mins.
Answer:
2.34m2
Step-by-step explanation:
boom
A pilot knows she descended 1,000 feet and traveled a diagonal distance of 18,000 feet.
What was the horizontal distance covered by the pilot?
A-17.9722 ft
B-18027.8 ft
C-16.000 ft
D-15.457 8 ft
The horizontal distance covered by pilot is 17,972.2 feet.
Step-by-step explanation:
Given,
Distance covered descending = 1000 feet
Diagonal distance = 18,000 feet
The horizontal distance will form a right triangle, therefore, we can find the horizontal distance by using pythagoras theorem.
Here,
a = 1000
b = horizontal distance
c = 18000
[tex]a^2+b^2=c^2\\(1000)^2+b^2=(18000)^2\\1000000+b^2=324000000\\b^2 = 324000000-1000000\\b^2=323000000[/tex]
Taking square root on both sides
[tex]\sqrt{b^2}=\sqrt{323000000}\\b=17972.2[/tex]
The horizontal distance covered by pilot is 17,972.2 feet.
Keywords: pyathoras theorem, square root
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Suppose that a chemist is mixing two acid solutions, one of 20% concentration and the other of 30% concentration. Which of the following concentrations could not be obtained?
1. 22%,
2. 24%,
3. 28%,
4. 34%
Final answer:
A chemist cannot achieve a 34% concentration by mixing 20% and 30% acid solutions, as it is outside the possible range of concentrations achievable by combining these two solutions, option no 4.
Explanation:
When a chemist is mixing two acid solutions, one with a 20% concentration and the other with a 30% concentration, they can obtain a range of concentrations between the two provided percentages by varying the proportions of each solution mixed. The concentrations that could not be obtained would be any value outside of the 20% to 30% range because the resulting mixture cannot exceed the concentration of the higher concentrated solution or be lower than the concentration of the less concentrated solution. Therefore, a 34% concentration could not be obtained by mixing a 20% solution with a 30% concentration.
1 question 60 points need help now
Solve the equation and show all your work
[tex]\frac{x}{x-2} + \frac{x-1}{x+1} =-1[/tex]
Answer:
The answer to your question is x = 0 and x = 1
Step-by-step explanation:
Equation
[tex]\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1[/tex]
1)
[tex]\frac{x(x + 1) + (x - 2)(x - 1)}{(x - 2)(x + 1)} = - 1[/tex]
Expand
2) x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)
Simplify
3) 2x² -2x + 2 = -1(x² + x - 2x - 2)
4) 2x² - 2x + 2 = -x² + x + 2
Equal to zero
5) 2x² - 2x + 2 + x² - x - 2 = 0
6) 3x² - 3x = 0
Factor
7) 3x(x - 1) = 0
8) 3x₁ = 0 x₂ - 1 = 0
9) x₁ = 0/3 x₂ = 1
10) x₁ = 0 x₂ = 1
A scatter plot shows a set of data points that are clustered close to a line that slopes down to the right. Which of the following values would be closest to the correlation for these data? a. -0.40 b. 0.40 c. 0.80 d. -0.80
Answer:
Option D. -0.80
Step-by-step explanation:
A scatter plot that shows a set of data points having two properties
1). If the points are clustered close to the line that reveals the high correlation.
2). Data points are clustered close to the line having slope down to the right or negative slope.
Therefore, Option D. has the highest correlation with negative slope.
Ms Thomas drove at a constant rate for 45. She drove 39 miles during that time. If distance is determined by the equation d=rt where r is the constant rate in miles per hours what was ms Thomas constant rate?
Answer:
Ms. Thomas was driving at constant rate of 52 miles/hour.
Step-by-step explanation:
Given:
Total time to travel (t) = 45 minutes
Distance drove (d) = 39 miles
we need to find the constant rate in miles per hour at which she was driving.
Solution:
Now we know that;
We need to find constant rate at miles per hour;
But time is given in minutes.
So we will convert minutes into hour by dividing by 60 we get;
time [tex]t =\frac{45}{60}= 0.75\ hrs[/tex]
Now we know that;
Distance is equal to rate times time.
framing in equation form we get;
distance [tex]d =rt[/tex]
Or
rate [tex]r= \frac{d}{t} = \frac{39}{0.75}= 52 \ mi/hr[/tex]
Hence Ms. Thomas was driving at constant rate of 52 miles/hour.
Evaluate the expression x^3 - (3 + x)^2x 3 −(3+x) 2 x, cubed, minus, left parenthesis, 3, plus, x, right parenthesis, squared for x=4x=4x, equals, 4.
Answer:
15
Step-by-step explanation:
Put the given value of x where x is in the expression and do the arithmetic.
4^3 -(3 +4)^2 = 64 -49 = 15
The value of the expression for x=4 is 15.
Final answer:
The expression x³ - (3 + x)² for x = 4 simplifies to 64 - 49, resulting in a final answer of 15.
Explanation:
The student has asked to evaluate the expression x³ - (3 + x)² for x = 4. To do this, we will substitute x with 4 and simplify the expression step by step. First, calculate the value inside the parentheses: (3 + 4) = 7. Then, we square this value to get 7² = 49. After that, subtract the squared value from 4³ (which is 64), to get the final answer.
The final answer is 15
Suppose that the number of worker-hours required to distribute new telephone books to x% of the households in a certain rural community is given by the function W(x)=250x/(400−x). (a) What is the domain of the function W? (Give the domain in interval notation. If the answer includes more than one interval write the intervals separated by the "union" symbol, U.) (b) For what values of x does W(x) have a practical interpretation in this context? (c) How many worker-hours were required to distribute new telephone books to the first 70% of the households? (d) How many worker-hours were required to distribute new telephone books to the entire community? (e) What percentage of the households in the community had received new telephone books by the time 3 worker-hours had been expended?
Answer:
a) Domain = [tex](-\infty,400)\cup (400,\infty)[/tex]
b) [tex]x \in [0,100][/tex]
c) 53.03 worker hours
d) 83.33 worker hours
e) 83.33 worker hours
Step-by-step explanation:
We are given the following in the question:
[tex]W(x) = \dfrac{250x}{(400-x)}[/tex]
where W(x) is the number of worker-hours required to distribute new telephone books to x% of the households in a certain rural community.
a) Domain of function.
The domain is the all the possible values of x that the function can take.
Domain = [tex](-\infty,400)\cup (400,\infty)[/tex]
b) Values of x
Since x is a percentage in reference to context, it can only take value upto 100. Also it cannot take any negative value.
So domain n reference to context will be
[tex]x \in [0,100][/tex]
c) worker-hours were required to distribute new telephone books to the first 70% of the households
[tex]W(70) = \dfrac{250(70)}{(400-70)} = 53.03[/tex]
53.03 worker hours were required to distribute new telephone books to the first 70% of the households.
d) Worker hour for entire community
For entire community, x = 100
[tex]W(100) = \dfrac{250(100)}{(400-100)} = 83.33[/tex]
83.33 worker hours were required to distribute new telephone books to the entire households.
e) Percentage of the households in the community for 3 worker hours
[tex]3 = \dfrac{250x}{(400-x)}\\\\1200-3x = 250x\\253x = 1200\\\\x = \dfrac{1200}{253} = 4.74\%[/tex]
Thus, 4.74% of the households in the community had received new telephone books by the time 3 worker-hours had been expended.
Final answer:
The domain of the function W(x) is (-∞, 400) U (400, +∞). The values of x that have a practical interpretation in this context are in the interval [0, 100]. Approximately 53.03 worker-hours were required to distribute new telephone books to the first 70% of households, and approximately 83.33 worker-hours were required to distribute to the entire community. After 3 worker-hours, approximately 4.73% of the households had received new telephone books.
Explanation:
(a) The domain of the function W is the set of all possible values of x that make the function defined and meaningful. In this case, the function W(x) is defined except when the denominator 400-x is equal to zero. So, we need to find the values of x that make the denominator zero.
To do that, we solve the equation 400-x = 0, which gives x = 400.
Therefore, the domain of the function W is the set of all real numbers except x = 400. We can express this in interval notation as (-∞, 400) U (400, +∞).
(b) In this context, the function W(x) represents the number of worker-hours required to distribute new telephone books to x% of the households in the rural community. A practical interpretation is only meaningful when x represents a valid percentage, meaning that it is between 0% and 100%, inclusive. So, the values of x that have a practical interpretation in this context are in the interval [0, 100].
(c) To find the worker-hours required to distribute new telephone books to the first 70% of households, we substitute x = 70 into the function W(x). Evaluating the expression, we get: W(70) = 250(70) / (400 - 70) = 17500 / 330 = 53.03.
Therefore, approximately 53.03 worker-hours were required to distribute new telephone books to the first 70% of households.
(d) To find the worker-hours required to distribute new telephone books to the entire community, we substitute x = 100 into the function W(x). Evaluating the expression, we get: W(100) = 250(100) / (400 - 100) = 25000 / 300 = 83.33.
Therefore, approximately 83.33 worker-hours were required to distribute new telephone books to the entire community.
(e) To find the percentage of households that had received new telephone books after 3 worker-hours, we rearrange the function W(x) to solve for x. We have:
W(x) = 250x / (400 - x)
3 = 250x / (400 - x)
3(400 - x) = 250x
1200 - 3x = 250x
1200 = 253x
x = 1200 / 253 ≈ 4.73
Therefore, approximately 4.73% of the households in the community had received new telephone books after 3 worker-hours.
what is the value of x? pls help!
Answer:The procedure to use the find the value of x calculator is as follows:
Step 1: Enter the values in the divisor and the product field
Step 2: Now click the button “Solve” to get the output
Step 3: The dividend or the x value will be displayed in the output field
Step-by-step explanation: In algebra, it is easy to find the third value when two values are given. Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication, and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Tiwa spent 1 1/2 hours setting up her computer. It took her 3 times as long to install the software. How long did it take Tiwa to set up the computer and install the software
Answer:
Total time spent by Tiwa to set up the computer and install software = 6 hours
Step-by-step explanation:
Given:
Time spent by Tiwa to set up her computer = [tex]1\frac{1}{2}\ hours[/tex]
Time spent to install the software is 3 times the time she took to set up the computer.
To find the total time Tiwa took to set up her computer and install the software.
Solution:
Time spent by Tiwa to install the software can be given as:
⇒ [tex]3\times 1\frac{1}{2} \ hours[/tex]
In order to multiply mixed numbers we first change them to fractions.
We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.
So, [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
So, we have:
⇒ [tex]3\times \frac{3}{2}\ hours[/tex]
⇒ [tex]\frac{9}{2}\ hours[/tex]
Total time spent by Tiwa to set up the computer and install software can be given as:
⇒ [tex]\frac{3}{2}\ hours+\frac{9}{2}\ hours[/tex]
Since denominators are same, so we simply add the numerators.
⇒ [tex]\frac{3+9}{2}\ hours[/tex]
⇒ [tex]\frac{12}{2}\ hours[/tex]
⇒ [tex]6\ hours[/tex]
help in anyway in this ixl
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle shown,
AB represents the hypotenuse of the right angle triangle.
With 45 degrees as the reference angle,
AC represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine QR, we would apply trigonometric ratio
Sin θ = opposite side/hypotenuse side. Therefore,
Sin 45 = BC/6√2
√2/2 = BC/6√2
BC = √2/2 × 6√2
BC = 6
. Solve the equation. 3/7x + 5 = 8 1 2/7 7 7 2/7 –7
Answer:
x= −5621/201
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3 /7x+5 = 812/7772/7-7
3 /7x+5= 1/67+−7
3 /7x+5=( 1/67+-7)(Combine Like Terms)
3 /7x+5= −468 /67
3 /7x+5= −468/67
Step 2: Subtract 5 from both sides.
3 /7x+5−5=−468/67−5
3 /7x=−803/67
Step 3: Multiply both sides by 7/3.
( 7/3)*(3/7x)=(7/3)*(−803/67)
x= −5621/201
For #1-4, graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the Pre-image and image using the correct notation.
See the attached picture:
Edited graph 4. I missed the negative sign in front of the one. The new graph is attached.
Working together, two people can cut a large lawn in 4 hr. One person can do the job alone in 1 hr less than the other. How long would it take the faster person to do the job? the faster person would do the job alone in hours.
Answer:The faster person will do the job in 7.53hours
Step-by-step explanation:
Let t=faster person
Let t-1= the other person
The job to be done =1
Each person will do a fraction of the job
4/t+4/t-1=1
Multiply both sides wit t(t-1)
4(t+1)+4t=t(t-1)
4t+4+4t=t^2+t
8t+4=t^2+t
0=t^2+t-8t-4
t^2-7t-4=0
Use Almighty formular to solve d quadratic equation
X=-b+- rootb^2-4ac/2a
X=t,a=1,b=-7 c=4
Substituting the values you get:
t=-7 +- root 49+16/2
t=-7 +- root 65/2
t=7 +8.06/2=15.06/2
t=7.53 hours
What is the slope of the line through (-9,6)(−9,6)(, minus, 9, comma, 6, )and (-3,9)(−3,9)(, minus, 3, comma, 9, )?
Answer:
0.5
Step-by-step explanation:
The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5
Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through
The number of question on a math test is represented (3x+1). The number of questions on the spelling test is represented by (x+12). Write an expression to find how many more questions were on the math test. Then evaluate the expression if the value x is 8
Answer:
Step-by-step explanation:
The number of questions on a math test is represented (3x+1). The number of questions on the spelling test is represented by (x+12).
An expression to find how many more questions were on the math test would be
= 3x + 1 - (x + 12)
= 3x + 1 - x - 12
= 3x - x + 1 - 12
= 2x - 11
When the value of x = 8, then the expression becomes
2× 8 - 11 = 16 - 11 = 5
Final answer:
To find how many more questions are on the math test compared to the spelling test, you subtract the spelling test expression from the math test expression. Simplifying this gives 2x - 11. Evaluating this expression for x = 8 shows there are 5 more questions on the math test.
Explanation:
The question asks you to write an expression to find out how many more questions are on the math test compared to the spelling test, and then evaluate this expression for x = 8.
Step 1: Write the expression
To find how many more questions are on the math test, you subtract the number of questions on the spelling test from the number of questions on the math test. Therefore, the expression is:
(3x + 1) - (x + 12)
Step 2: Simplify the expression
First, distribute the negative sign: 3x + 1 - x - 12. Simplify by combining like terms: 2x - 11. This simplified expression represents how many more questions are on the math test compared to the spelling test.
Step 3: Evaluate the expression for x = 8
Plug in x = 8 into the simplification, 2x - 11. So, you get: 2(8) - 11 = 16 - 11 = 5.
Therefore, there are 5 more questions on the math test than on the spelling test when x = 8.
At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. In how many ways a voter can vote?
Answer:
Voters can select their members in 10possible ways
Step-by-step explanation:
According to the question, the voters are to elect 3members out of 5 candidates, this means they are to select any 3 candidates of their choice from a pool of 5 candidates. Since "combination" has to do with selection, we use the combination formula.
To select 'r' objects from 'n' pool of objects, we have;
nCr = n!/(n-r)!r!
5C3 = 5!/(5-3)!3!
5C3 = 5!/2!3!
5C3 = 5×4×3×2×1/2×3×2
= 120/12
5C3 = 10
Candidates can therefore vote in 10 possible ways