Several hours after departure the two ships described to the right are 340 miles apart. If the ship traveling south traveled 140 miles farther than the other, how many mile did they each travel?
Answers
The ship traveling south traveled 240 miles, and the other ship, which traveled 140 miles less, traveled (240 - 140) = 100 miles.
Let's denote the distance traveled by the ship traveling south as x miles. Since the other ship traveled 140 miles less than the ship traveling south, its distance traveled can be represented as (x - 140) miles.
According to the information given, after several hours, the two ships are 340 miles apart. This implies that the sum of the distances traveled by the two ships is equal to 340 miles.
So we have the equation:
x + (x - 140) = 340
Simplifying the equation, we get:
2x - 140 = 340
Adding 140 to both sides:
2x = 480
Dividing both sides by 2:
x = 240
Therefore, the ship traveling south traveled 240 miles, and the other ship, which traveled 140 miles less, traveled (240 - 140) = 100 miles.
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Related Questions
Function of a Function
Answers
Answer:
B. 8
Step-by-step explanation:
Step 1: Find g(-2)
g(-2) = (-2)² + 1
g(-2) = 4 + 1
g(-2) = 5
Step 2: Find f(5)
f(5) = 2(5) - 2
f(5) = 10 - 2
f(5) = 8
if f is a differentiable function and y=sin(f(x2)) what is dydx when x = 3 ?
Answers
At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.
How we can use the chain rule to find the derivative of y?We can use the chain rule to find the derivative of y = sin(f(x^2)) with respect to x:
dy/dx = cos(f(x^2)) * d/dx[f(x^2)]
To find d/dx[f(x^2)], we can use the chain rule again:
d/dx[f(x^2)] = f'(x^2) * d/dx[x^2] = 2xf'(x^2)
So, putting it all together:
dy/dx = cos(f(x^2)) * 2xf'(x^2)
At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.
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a polling organization conducts a telephone poll of 850 registered voters and asks which candidate they will vote for in the upcoming presidential election. forty-three percent of the respondents prefer candidate a and 45% prefer candidate b. a.what is the population being studied? b.what is the sample being studied? c.based on the sample, what percentage of the population do you think would vote for candidate b?
Answers
For a polling organization that conducts a telephonic poll from 850 registered votes and ask them to whom they will vote in coming presedential election. In the context of question, population size, sample and percentage of voter preference is given below.
a. The population being studied is the population of registered voters who will vote in the upcoming presidential election.
b. The sample being studied is the group of 850 registered voters who were surveyed by telephone.
c. Based on the sample, it is estimated that 45% of the population would vote for candidate B. However, it's important to note that this is only an estimate based on a sample of registered voters, and it may not accurately reflect the views of the entire population. Additionally, since the sample size is only 850, the estimate may have a margin of error associated with it. To get a more accurate estimate of the percentage of the population that would vote for candidate B, a larger sample size or a different method of polling would be necessary.
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approximately what percentage of u.s. adults is overweight? select one: a. 24 percent b. 44 percent c. 64 percent d. 84 percent
Answers
According to the Centers for Disease Control and Prevention (CDC), about 73.6 percent of adults in the United States are overweight or obese. So, the correct answer is D).
This means that a majority of adults in the U.S. have a body mass index (BMI) above the healthy range, which is defined as a BMI of 18.5-24.9, which puts them at increased risk for a range of health issues, including heart disease, diabetes, and some types of cancer.
The prevalence of overweight and obesity has been increasing in the United States in recent decades, and it is a significant public health concern. Obesity is a complex issue with many causes, including genetics, environment, and lifestyle factors such as diet and physical activity levels. So, the correct answer is D).
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--The given question is incomplete, the complete question is given
" According to the Centers for Disease Control and Prevention (CDC), approximately what percentage of u.s. adults is overweight? select one: a. 24 percent b. 44 percent c. 64 percent d. 73.6 percent "--
I'm bad at math helpppppp
Answers
Answer:
2x + y = 18
y = 4x - 12
x = 5, y = 8
Step-by-step explanation:
x = 1st number
y = 2nd number
We can use the substitution method as we know what 'y' equals; that value will get plugged in for 'y' in the first equation as follows:
2x + 4x - 12 = 18
6x - 12 = 18
6x = 30
x = 5
y = 4(5) - 12 which is 20-12 or 8
y = 8
1. Find the median, mean, and range of the elephant ages.
a) Median
b) Mean:
c) Range:
years
11:39:13, 12:08 PM
years
years
2. Fill out the table to find the standard deviation of the elephant ages. Check your calculations by finding
the standard deviation on a graphing calculator.
X
2
8
2.8 14, 19, 20, 21, 26, 33, 36, 41
14
19
20
21
26
33
Age Ling-Rese
-20
-14
-8
(x-x)2
400
196
64
Answers
1) Note that the measures of dispersion are given as follows;
Mean = 22
Median = 20
Range = 39
2) The standard deviation based on the completed table is 11.696. See table attached.
Mean:
To find the mean, you add up all the ages and divide by the total number of ages:
= (2 + 8 + 14 + 19 + 20 + 21 + 26 + 33 + 36 + 41) /10
thus
Mean = 22.0
Median:
To find the median, you need to find the middle number when the ages are arranged in order:
2, 8, 14, 19, 20, 21, 26, 33, 36, 41
The middle numbers are (20 + 21)/2 = 20.5
so the median age is 20.5
Range:
To find the range, you subtract the smallest age from the largest age:
41 - 2 = 39
Therefore:
Mean = 22
Median = 20.5
Range = 39
2)
To find the standard deviation of the elephant ages, we first need to calculate the variance:
Find the mean (X):
X = (2 + 8 + 14 + 19 + 20 + 21 + 26 + 33 + 36 + 41)/ 10
X = 22
Subtract the mean from each value and square the result:
(x - X)²:
(2 - 22)² = 400
(8 - 22)² = 196
(14 - 22)² = 64
(19 - 22)² = 9
(20 - 22)² = 4
(21 - 22)² = 1
(26 - 22)² = 16
(33 - 22)² = 121
(36 - 22)² = 196
(41 - 22)² = 361
Sum up all the squared differences:
400 + 196 + 64 + 9 + 4 + 1 + 16 + 121 + 196 + 361 = 1368
Divide the sum by the number of values (n):
1368 / 20 = 136.8
Take the square root of the variance to get the standard deviation:
√136.8 = 11.696
Thus, the standard deviation = 11.696
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evalue 3a -4b for a =a and b=6
Answers
3a - 4b
substitute a = a and b= 6 in the above
3a - 4(6)
3a - 24
What is the measure of the angle shown
will give brainliest
Answers
It is between 0°and 45°.
The left ray of the angle (The left arrow) is facing up and is at zero. THe right ray is at 45.
let s 5 {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s. must there be two integers whose sum is 15? why?
Answers
The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.
In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.
We have to check there be two integers whose sum is 15.
As we know that,
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.
There are total 10 elements.
We have to choose two element from the given set which sum is equal to 15.
If we choose 3 and 12 then there sum is 15.
Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.
So the given set have two integers whose sum is 15.
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For the following pairs of assertions, indicate which do not
comply with our rules for setting up hypotheses and why (the
subscripts 1 and 2 differentiate between quantities for two
different populations or samples): (a) H0: μ = 100, Ha: μ > 100
These hypotheses comply with our rules. H0 cannot include equality,
so these hypotheses are not in compliance. Each μ is a statistic,
so these hypotheses do not comply with our rules. The asserted
value in H0 should not appear in Ha, so these hypotheses are not in
compliance. (b) H0: σ = 20, Ha: σ ≤ 20 These hypotheses comply with
our rules. Ha cannot include equality, so these hypotheses are not
in compliance. Each σ is a statistic, so these hypotheses do not
comply with our rules. The asserted value in H0 should not appear
in Ha, so these hypotheses are not in compliance. (c) H0: p ≠0.25,
Ha: p = 0.25 These hypotheses comply with our rules. Ha cannot
include equality, so these hypotheses are not in compliance. Each p
is a statistic, so these hypotheses do not comply with our rules.
The asserted value in H0 should not appear in Ha, so these
hypotheses are not in compliance. (d) H0: μ1 − μ2 = 25, Ha: μ1 − μ2
> 100 These hypotheses comply with our rules. H0 cannot include
equality, so these hypotheses are not in compliance. Each μ is a
statistic, so these hypotheses do not comply with our rules. The
asserted value in H0 should also appear in Ha, so these hypotheses
are not in compliance. (e) H0: S12 = S22, Ha: S12 ≠S22 These
hypotheses comply with our rules. H0 cannot include equality, so
these hypotheses are not in compliance. Each S is a statistic, so
these hypotheses do not comply with our rules. The asserted value
in H0 should not appear in Ha, so these hypotheses are not in
compliance. (f) H0: μ = 120, Ha: μ = 150 These hypotheses comply
with our rules. Ha cannot include equality, so these hypotheses are
not in compliance. Each μ is a statistic, so these hypotheses do
not comply with our rules. If μ appears in H0, then it should not
appear in Ha, so these hypotheses are not in compliance. (g) H0:
σ1/σ2 = 1, Ha: σ1/σ2 ≠1 These hypotheses comply with our rules. H0
cannot include equality, so these hypotheses are not in compliance.
Each σ is a statistic, so these hypotheses do not comply with our
rules. The asserted value in H0 should not appear in Ha, so these
hypotheses are not in compliance. (h) H0: p1 − p2 = −0.1, Ha: p1 −
p2 < −0.1 These hypotheses comply with our rules. H0 cannot
include equality, so these hypotheses are not in compliance. Each p
is a statistic, so these hypotheses do not comply with our rules.
The asserted value in H0 should not appear in Ha, so these
hypotheses are not in compliance.
Answers
a)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is right tailed. And null hypothesis can include equality. Further mu is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
b)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further sigma is not a statistics,
So option d) is correct and all other are incorrect.
C)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further p is not a statistics,
So option (b) is correct and all other are incorrect.
d)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further mu1 and mu2 is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
e)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further sigma is not a statistics,
So option (c) correct and all other are incorrect.
f)
Since alternative hypothesis can be of either right tailed or left tailed or a simple hypothesis. Here alternative hypothesis is a simple hypothesis And null hypothesis can include equality. Further mu is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
g)
Since alternative hypothesis can be of either right tailed or left tailed or two tailed. Here alternative hypothesis is two tailed. And null hypothesis can include equality. Further sigma1 and sigma 2 is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
h)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further p is not a statistics, and asseter value of H0 should not appear in asserted value in Ha.
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Help. What's 2(5x+3)=2?
Answers
Answer: X = -2/5
Step-by-step explanation:
Answer:
This has already been answered correctly (x = -2/5), but I'll add the steps required to arrive at that conclusion.
Step-by-step explanation:
Solving 2(5x+3)=2 requires that we use the order of operations, or PEDMAS, in going through the steps. PEDMAS is the acronym for Parentheses, Exponents, Division, Multiplication, Addition and Subtraction. These are the order in which math operations should be done when solving equations. This provides the "rules of the road" when interpreting how equations were meant to be read.
2(5x+3)=2
1. Parentheses: First, we should complete whatever is inside a set of parentheses, in this case (5x+3). There is nothing we can do with (5x+3) so go to the next step.
2. Exponents: none here, so continue
3. Division: none here, so continue
4. Multiplication: We can do the term 2(5x+3) by multiplying the 2 times each of the values within the parentheses.
2(5x+3) = 10x + 6
We now have:
10x + 6 = 2
5. Addition/Subtraction: Subtract 6 from both sides:
10x + 6 - 6 = 2 - 6
10x = - 4
We've gone through PEDMAS once, so start over again since we are still looking for the value of x.
The only operation left is to divide both sides by 10:
10x = -4
10x/10 = -4/10
x= - 4/10 or -2/5
In general, PEDMAS works quite well. It defines how to interpret the manner in which equations are written. If there is any remaining ambiguity, always work from left to right. Solve the portion on the left first, then move right.
Also, it is always good, and edifying, to try the solution to see if the equation works for that solution. We can ask "Does a value of x=-(2/5) give the answer of "2" when used in 2(5x+3)?
2(5x+3)
2(5*(-2/5) + 3) = 2? for x = -(2/5)
2(5*(-2/5) + 3) = 2?
Use PEDMAS:
2(5*(-0.4) + 3) = 2?
2(-2 + 3) = 2?
2(1) = 2? YES, -(2/5) is correct
In the formula CL% confidence interval = x ZcL*
what is Z95% ?
Answers
In the formula for confidence interval; CI = X ± Z(s/√n)
what is Z95% ?
Answer:
>> Z95% means critical z value for 95% Confidence level.
>> Z95% = 1.96
Step-by-step explanation:
The formula for confidence interval is given as;
CI = x¯ ± Z(s/√n)
Where:
x¯ is the mean
Z is the critical value for a particular %CL
s is standard deviation
n is sample size
Thus, Z95% means critical z value for 95% Confidence level.
From tables, the z-value for a confidence level of 95% is 1.96
Answer:
The answer is 2 NOT 3. Ignore the answer listed above as 3. It is incorrect.
Step-by-step explanation:
Alberto conducted an experiment by rolling a fair six-sided number cube 60 times. He rolled a 2 fifteen times. Which statement about rolling a 2 in Alberto's experiment is correct?
Answers
Answer:
Step-by-step explanation:
Experimental probability is the probability of what actually happens in the given experiment.
We know that a fair six-sided cube is rolled 60 times and the outcome 2 has occurred 15 times out of 60 times.
Therefore, the experiment probability in the given experiment is:
Experimental probability of rolling 2
\(\frac{15}{60}=\frac{1}{4}\)
Now, the theoretical probability is the probability of what is expected from the random experiment. We know that a cube has 6 sides and the theoretical probability of getting 2 is given below:
Theoretical probability of rolling a 2
\(\frac{1}{6}\)
Therefore, the answer is:
The experimental probability of rolling a 2 is \(\frac{1}{4}\) and the theoretical probability of rolling a 2 is \(\frac{1}{6}\).
Answer:
The experimental probability of rolling a 2 is 1/4 and the theoretical probability of rolling a 2 is 1/6.
Step-by-step explanation:
Mrs kanja ,miss kanene and Mrs nyaga have to mark a form three contest for 160students .They take 5mins ,4mins and 12mins respectively to mark a script .If they all start to mark at 9.00am non-stop ,what is the shortest time they ca n take to complete the marking?
Answers
Answer:
300 minutes
2:00 p.m
Step-by-step explanation:
Given the following:
Time taken to mark a script :
Mrs Kanja = 5mins
Miss Kanene = 4mins
Mrs Nyaga = 12 mins
Number of scripts = 160
Start time = 9:00 a.m
Rate at which each of them mark:
Mrs Kanja = t / 5
Miss Kanene = t/4
Mrs Nyaga = t/12
Combined rate :
t/5 + t/4 + t/12 = 160
(12t + 15t + 5t) / 60 = 160
32t / 60 = 160
32t = 160 * 60
32t = 9600
t = 9600 / 32
t = 300 minutes
300 minutes = 300/60 = 5hrs
9:00 a.m + 5 hours = 2:00 p.m
What number could be a common denominator for 1/5 and 5/6?
6
5
11
30
Answers
Natalie saves $35 each month to buy a DVD player. The DVD player
costs $197.99. Will Natalie be able to buy the DVD player in 5 months?
If not, how much more money does she need?
Answers
Multiply amount she saves per month by 5 months:
35 x 5 = $175
$175 is less than the price of the player so she won’t have enough to buy it.
197.99 - 175 = $22.99
She needs $22.99.more
yo can someone do this for me ty i’m too lazy to do this myself
Answers
Answer:
1. 8 + 4 = 12 x 6 = 72
2. 9 + 6 = 15 x 4 = 60
3. 11 + 8 = 19 x 6 = 114
4. 4 + 6 = 10 x 5 = 50
5. 7 + 3 = 10 x 8 = 80
6. 8 + 12 = 20 x 9 = 180
7. 5 + 10 = 15 x 8 = 120
8. 19 + 13 = 32 x 10 = 320
9. 3 + 6 = 9 x 2 = 18
Area of a trapezoid:
Base 1 + Base 2 times Height times a half (basically dividing by 2).
The Bryants are moving to a new town and want to know about how much it will cost them to buy a house. The prices of five homes sold last week in the town were $125,500, $130,000, $132,500, $135,000, and $350,000. Which of these prices best represents the typical price of a home in this town?
A. the mode of the prices
B. the median price
C. the mean price
D. the average of the lowest and highest prices
Answers
Answer:
D
Step-by-step explanation:
Typical price is the average of highest and lowest
The best representation of the typical price of a home in this town is the median price, which is $132,500.
The best representation of the typical price of a home in the town can be determined using different measures of central tendency.
1. Mode: The mode represents the most frequent value in a dataset. In this case, none of the prices appear more than once, so there is no mode.
2. Median: The median is the middle value when the data is arranged in ascending or descending order.
To find the median, we arrange the prices in ascending order: $125,500, $130,000, $132,500, $135,000, and $350,000.
The middle value is $132,500, which is the median price.
3. Mean: In this case, the mean price is calculated as follows: ($125,500 + $130,000 + $132,500 + $135,000 + $350,000) / 5 = $174,800.
4. Average of the lowest and highest prices: To find the average of the lowest and highest prices, we add the lowest price ($125,500) and the highest price ($350,000) and divide by 2.
The average is ($125,500 + $350,000) / 2 = $237,750.
Therefore, the best representation of the typical price of a home in this town is the median price, which is $132,500. This value represents the middle price when all the prices are arranged in order.
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The probability that X is a 2, 11, or 12 is:
a.) 1/36
b.) 2/36
c.) 3/36
d.) 4/36
Answers
Answer:
The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.
Step-by-step explanation:
The Woodman Firewood Company delivers natural firewood to homes in Manhattan,
They charge a certain amount per cord for firewood and a fixed amount for each delivery,
no matter how many cords are delivered. My bill from WFC last winter was $155 for one
cord of wood, and my neighbor's bill was $215 for one and one-half cords. What is the
charge for each cord of wood and what is the delivery charge?
Answers
Answer:
step by step and the dog got 10 fire wood
Find the measure of angle K
K
N
M
17
27
63
36
Answers
9514 1404 393
Answer:
(b) 27
Step-by-step explanation:
It appears as though we're to assume that KM is a diameter, through circle center point N. That makes triangle KLM a right triangle, so angle K is the complement of angle M.
∠K = 180° -63° = 27°
an experiment may have: a. only one outcome b. only two outcomes c. two or more outcomes d. several events
Answers
Using the concepts of probability, we got that an experiment may have d) several events
Event is called one or more outcomes of an experiment. Example of this is -rolling a dice, we get a possible outcomes as {1,2,3,4,5,6}.
In an experiment there can be one outcome, two outcomes, more than two outcomes or several outcomes.
An event is the collection of one or more of the outcomes of an experiment. An event that actually includes one and only one of the (final) outcomes for an experiment is called the simple event and is denoted by Ei.
Hence, an experiment may have d)several events
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Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.75 feet and
Eric jumped 37 feet and 1 1 inches. Who was closer to the state record if the 4
eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches?
Answers
The distance Alex jumped and the distance Eric jumped compared with the state records indicates that the magnitude of Eric's score was closer to their grades state record
What is the magnitude of a value?The magnitude of a value is the value itself, indicating the distance of the number from zero.
Alex is an eight grader
Eric is a seventh grader
The distance Alex jumped = 39.75 feet
The distance Eric jumped = 37 feet 11 inches
The eight grade record = 42.25 feet
The seventh grade record = 39 feet 3 inches
Each athlete distance jumped is compared with the record for the grade at which they jumped
The deviation of the distance jumped from the record scores are;
Alex's difference between distance jumped and the record = 39.75 - 42.25 = -2.5
The difference between the distance Eric jumped and the record = 37 feet + 11 inches - (39 feet + 3 inches) = -(1 feet + 4 inches)
-(1 feet + 4 inches) = -1.\(\overline 3\) inches
The magnitude of the difference between the distance Eric jumped and the state record is smaller, therefore, Eric was closer to the state record
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Answer: I can confirm that Eric is closer!
Step-by-step explanation:
Please please help me please
Answers
Step by step explanation: divide 5025 by 220 and it should give you a decimal answer then divide it by 10,050 then you have your answer
Consider a cost-benefit-trade-off problem having the following data. Benefit Contribu tion per Unit of Each Activity Accept able Level Benefit 2 60 30 126 Unit cost$60 $50 a. Formulate a linear programming model for this problem on a spreadsheet. b. Use the spreadsheet to check the following solutions: (x1,32)(7,7. (7. 8), (8. 7), (8, 8) (8, 9), (9, 8). Which of these solutions are feasible? Which of these feasible solutions has the best value of the objective function? c. Express the model in algebraic fom. d. Use the graphical method to solve this model.
Answers
The value of the objective function at this point is Z = 840. The solution (7, 7) is feasible.
a. Formulation of linear programming model:To solve this problem, the following linear programming model can be used:x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)Step-by-step explanation is given below:Function: Linear Programming modelSolution:
a. Formulation of linear programming model:To solve this problem, the following linear programming model can be used:x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)
b. Checking for feasible solutionsWe need to check the following solutions:(x1, 32) (7, 7) (7, 8) (8, 7) (8, 8) (8, 9) (9, 8)Let us substitute the values in the linear programming model for each solution:Solution: (x1, 32)30x1 + 126(32) = 4,752 + 4,032 = 8,784 > 4,752 (Infeasible)Solution: (7, 7)30(7) + 126(7) = 966 < 4,752 (Feasible)60(7) + 126(7) = 1,092 < 8,436 (Feasible)Solution: (7, 8)30(7) + 126(8) = 5,070 > 4,752 (Infeasible)Solution: (8, 7)30(8) + 126(7) = 5,016 > 4,752 (Infeasible)Solution: (8, 8)30(8) + 126(8) = 5,196 > 4,752 (Infeasible)Solution: (8, 9)30(8) + 126(9) = 5,322 > 4,752 (Infeasible)Solution: (9, 8)30(9) + 126(8) = 5,358 > 4,752 (Infeasible)Therefore, only the solution (7, 7) is feasible.
c. Expressing the model in algebraic form:We have,x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)The solution x = (7, 7) is feasible and optimal, with Z = 60(7) + 50(7) = 840.d. Using the graphical method:Below is the graph plotted for the above linear programming model:graph{(y-4752)/126<=-(3/2)x+316}The feasible region is given by the shaded region in the graph. The optimal solution is (7, 7), which is at the point of intersection of the two lines. The value of the objective function at this point is Z = 840.
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What is the property of 2x=10
Answers
Answer:
2x(3x-1) = 6x2-2x because of the distributive property.
Step-by-step explanation:
The property of the equation 2x = 10 is that it has a solution where x equals 5.
The equation 2x = 10 represents a linear relationship between the variable x and the constant value 10. To determine the property of this equation, we can solve it to find the value of x.
To solve for x, we can isolate it on one side of the equation by performing inverse operations. In this case, since 2x is equal to 10, we can isolate x by dividing both sides of the equation by 2:
2x/2 = 10/2
Simplifying further:
x = 5
The property of this equation is that when x is equal to 5, the equation is satisfied. In other words, if you substitute x with 5 in the equation 2x = 10, both sides of the equation will be equal.
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Cafe A offers 2 free bottled waters or juices for every 20 purchased. Cafe B offers 3 free bottled waters or juices for every 25 purchase. If you purchased 50 drinks at each cafe how many drinks would you get?
Answers
Answer:
Cafe A - 54
Cafe B - 56
Step-by-step explanation:
the length of a rectangle is 3 yd less than double the width, and the area of the rectangle is 14 yd^2. find the dimensions of the rectangle.
Answers
Answer:
The rectangle is 3.5 yd x 4 yd
Step-by-step explanation:
Area = length x width = lw
l = length = 2w - 3
w = width
Area = 14(2w - 3)(w) = 14
2w² - 3w - 14 = 0
Use quadratic equation to find the 2 roots of w: a = 2, b = -3, c = -14
w = 3.5, -2 disregard the negative root
width = 3.5 yd
length = 2(3.5) - 3 = 4 yd
The dimensions of the rectangle are approximately 2.23 yards by 1.46 yards.
We are assuming the width of rectangle to be "x" yards. Then, the length would be (2x - 3) yards, since it is 3 yards less than double the width. The formula for the area of a rectangle is A = l x w, so we can plug in the values we know:
14 = (2x - 3) x x
Expanding the brackets:
14 = 2x² - 3x
Put this equation=0:
2x² - 3x - 14 = 0
Using the quadratic formula:
x = (3 ± √(3² + 4 x 2 x 14)) / (2 x 2)
x = (3 ± √97) / 4
We can ignore the negative root, since the width cannot be negative. Therefore,
x ≈ 2.23
This is the width of the rectangle. To find the length, we can plug this value back into the expression we derived earlier:
length = 2x - 3
length ≈ 1.46
Therefore, the dimensions of the rectangle are approximately 2.23 yards by 1.46 yards
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A truck covers 40 km with an average speed of 80 km/h. It then travels
another 40 km with a speed of 40 km/h. What was the time taken to
complete the entire journey?
Answers
Answer: 53.33 km/hr
Step-by-step explanation:
The total distance covered by car is 80 KM(40+40).
Now their are two cases:
Case 1) Distance covered 40km, speed 80km/h. Now we all know speed=Distance/ time
So Time taken is 0.5 hour.
Case 2) Now again distance covered is 40 km but speed is 40Km/h
So time taken is 1 hr
Now total distance traveled is 80KM. Total time taken is 1.5 hrs (0.5+1)
Average speed =Total Distance/Total Time
Average Speed = 80/1.5
Which is equal to 53.33km/h
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 57:18 Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is 5 and the length of B D is 12. What is the length of Line segment B C, rounded to the nearest tenth? 13.0 units 28.8 units 31.2 units 33.8 units
Answers
Answer:
28.8 units
Step-by-step explanation:
In order to further explain the description of the right angled triangle ABC above, I have attached a hand drawn diagram for easier understanding.
The length of A D is 5 units
The length of B D is 12 units.
From the above triangle ABC, to solve for BC we have the following ratios.
BD : BC = AD : BD
Hence,
BD/ BC = AD/BD
= 12/BC = 5/12
Cross Multiply
12× 12 = BC × 5
BC = 12 × 12/ 5
BC = 144/5
BC = 28.8 units
Therefore, the length of Line segment B C, rounded to the nearest tenth is 28.8 units
Answer:
c.31.2
Step-by-step explanation: