Answer: 15/16
Step-by-step explanation:
There will be 16 outcomes for 4 coins=2^4
Probability of only head is : P(C)=1/16
P(C) + P(C') = 1
P(C') = 1 - P(C)
P(C') = 1 - 1/16
Take the l.c.m
P(C') = (16-1) / 16
P(C') = 15/16
So the probability of getting at least 1 tail is 15/16
Answer:
D 0.94
Step-by-step explanation:
when solved the answer is 15/16. This equals 0.9375 which rounded to the second decimal = 0.94
The function H described by H(x) =2.75x+71.48 can be used to predict the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long.
Predict the height of a woman whose humerus is 39 cm long.
Answer:
The predicted height of the woman is 178.73 cm.
Step-by-step explanation:
Consider the provided function.
[tex]H(x) =2.75x+71.48[/tex]
Where x represents the height of humerus and H(x) represents the height of woman.
Substitute x=39 in above function.
[tex]H(x) =2.75(39)+71.48[/tex]
[tex]H(x) =107.25+71.48[/tex]
[tex]H(x) =178.73[/tex]
Hence, the predicted height of the woman is 178.73 cm.
The height of the woman is 178.73 cm.
Given to us,
function describing the height of a woman, H(x) =2.75x+71.48,
where, x is humerus (the bone from the elbow to the shoulder).
Height of a woman whose humerus is 39 cm long,
We can find the height of the woman by substituting the value of x in H(x).
H(x) =2.75x+71.48,
substituting x = 39 cm,
H(39) =2.75(39)+71.48,
= 178.73 cm
Therefore, the height of the woman is 178.73 cm.
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A fair dice (six-sided) is rolled twice. What is the probability that the sum of the numbers rolled will add up to seven? List the outcomes representing the sum of 7?
When a fair dice is rolled twice, it has 36 possible outcomes. The sum of the numbers that amount to 7 can be got in 6 ways. Therefore, the probability of rolling a sum of 7 is 1/6.
Explanation:When solving a probability question, the first step is to determine all the possible outcomes. Since a dice has 6 sides, when you roll it twice, you have 6x6 = 36 possible outcomes.
We are looking for the outcomes where the sum of the numbers is exactly 7. There are six (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
The probability is then calculated by taking the number of desired outcomes and dividing it by the total number of outcomes. So, the probability of rolling a sum of 7 with two dice is 6 / 36 = 1 / 6.
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Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?
1) The probability that she will get a job offer from neither company is 0.3.2) The probability that she will get a job offer from exactly one of the two companies is 0.5.
Answer:0.2
Step-by-step explanation: Let the two companies be A and B
Pa = probability of getting a job offer from only company A
Pb = probability of getting a job offer from only company B
Pbb = probability of getting a job offer from both companies
Pn = ProbabityProbability of getting a job from neither companies
The relation could be combined using :
Pbb+Pa+Pb+Pn=1
Pn = 0.3
(Pa + Pb) =probability of offer from exactly one of A or B = 0.5
Pbb + 0.5 + 0.3 = 1
Pbb+0.8=1
Pbb=1-0.8
Pbb = 0.2
A researcher records the time it takes to complete a memory task in a sample of 25 participants. He finds that the average participant completed the test in 43 s. The average time to complete this task is called a(n) ______.
Answer: It is called a sample statistic.
Step-by-step explanation:
Since we have given that
A researcher records the time it takes to complete a memory task in a sample of 25 participants. He finds that the average participant completed the test in 43 s.
The average time to complete this task is called sample statistic.
As we know that
Sample statistic is the quantity which we get from the sample taken from a any specified population for using this quantity to calculate the same.
In our case, average participant completed the test = 43 sec.
It is sample statistic as we will use to find the average time for the population i.e. 25 participant to get the same calculation i.e. average time.
We will get average time is also equal to 43 sec.
Hence, it is called a sample statistic.
A box contains 80 balls numbered from 1 to 80. If 11 balls are drawn with replacement, what is the probability that at least two of them have the same number?
Final answer:
The student's question is about finding the probability that at least two of the 11 balls drawn with replacement from a box of 80 uniquely numbered balls are the same. We use the complement rule to find the probability of all balls being unique and subtract this from 1 to find the desired probability.
Explanation:
The student is asking about the probability of drawing at least two balls with the same number when 11 balls are drawn with replacement from a box containing 80 uniquely numbered balls. To solve this, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.
The probability of drawing 11 unique balls in a row with replacement from 80 can be calculated by multiplying the probabilities of drawing a unique ball at each draw after the first. For the first ball, the probability is 80/80 (since any ball can be drawn), for the second ball it's 79/80 as one unique ball is already drawn, for the third it's 78/80, and so on until the eleventh ball.
The probability of drawing 11 unique balls is therefore (80/80) * (79/80) * (78/80) *...* (70/80). The probability of at least two balls having the same number is 1 minus this product, which represents the probability of all balls being unique.
A plane flew between two cities at 330 mph, a car went the same distance at 55 mph . If the car took 7.5 hours longer how far apart were the two cities
Answer:
The cities are 495 miles apart.
Step-by-step explanation:
Let x represent the distance between the two cities.
Let t represent the time taken by the plane to fly between the two cities.
The plane flew between two cities at 330 mph.
Distance = speed × time
Distance covered by the plane would be
330 × t = 330t
A car went the same distance at 55 mph. If the car took 7.5 hours longer, means that the time spent by the car would be (t + 7.5) hours and distance travelled would be
55(t + 7.5) = 55t + 412.5
Since the distance is the same, then
330t = 55t + 412.5
330t - 55t = 412.5
275t = 412.5
t = 412.5/275
t = 1.5
the distance between the two cities would be
1.5 × 330 = 495 miles
Katie is starting a babysitters sitting business. She spent $26 to make signs to advertise. She charges her initial fee of five dollars and then three dollars for each hour of service right in Solve inequality to find the number of hours she want to babysit to make a profit interpret the solution any quality
Answer:
The Inequality representing the number of hours she want to babysit to make a profit is [tex]5+3x>26[/tex].
Katie should babysit for more than 7 hours in order to make profit.
Step-by-step explanation:
Given:
Money spent on advertising = $26
Initial fee = $5
Hourly charge = $3
We need to find the number of hours she want to babysit to make a profit.
Solution:
Let the number of hours be 'x'.
Now we can say that;
The sum of Initial fee and Hourly charge multiplied by number of hours should be greater than Money spent on advertising .
framing in equation form we get;
[tex]5+3x>26[/tex]
Hence The Inequality representing the number of hours she want to babysit to make a profit is [tex]5+3x>26[/tex].
On Solving the above Inequality we get;
Now Using Subtraction property of Inequality we will subtract both side by 5 we get;
[tex]5+3x-5>26-5\\\\3x>21[/tex]
Now Using Division Property of Inequality we will divide both side by 3 we get;
[tex]\frac{3x}{3}>\frac{21}{3}\\\\x>7[/tex]
Hence Katie should babysit for more than 7 hours in order to make profit.
Interpretation:
when x=7
Amount earned will be = [tex]5+3x=5+3\times7 =5+21=\$26[/tex]
Profit earned will be = Amount earned - Money spent on advertising = 26 -26 =0
when x= 8
Amount earned will be = [tex]5+3x=5+3\times8 =5+24=\$29[/tex]
Profit earned will be = Amount earned - Money spent on advertising = 29 -26 =$3
Hence at 7 hours of babysitting profit will be 0 and at 8 hours of babysitting profit will be $3.
I have 8 flavors of ice cream and 4 different toppings. How many different ice cream sundaes can I make if I choose one flavor of ice cream and only one topping?
A quartic polynomial P(x) has rational coefficients. If √7 and 6+i are roots of P(x)=0, what is one additional root?
The additional root is 6-i.
Here's why:
Conjugate Pairs for Rational Coefficients: When a polynomial with rational coefficients has a complex root of the form a + bi (where a and b are real numbers and i is the imaginary unit), its conjugate, a - bi, must also be a root. This ensures that the polynomial remains with rational coefficients.
Applying the Conjugate Pair Rule: In this case, we're given that 6 + i is a root. Therefore, its conjugate, 6 - i, must also be a root of the polynomial P(x) = 0.
Other Roots: The problem states that √7 is also a root. However, since it's a real number, it doesn't introduce any complex conjugate pairs.
Quartic Polynomial: A quartic polynomial has four roots in total. We've identified three of them: √7, 6 + i, and 6 - i. The fourth root could be either a real number or another complex conjugate pair, but the information provided is insufficient to determine its exact value.
A roller coaster starts down the slope at 4 m/s. But 3 seconds later at the bottom of the slope it's speed is 22 m/s. What is the average acceleration?
Answer: 6m/s²
Step-by-step explanation:
Let
Initial Velocity be V_0 = 4m/s
Time be t = 3s
Final Velocity be V_n = 22m/s
Acceleration be A = (Final Velocity - Initial Velocity) / time
A = (V_n - V_0) / t
= (22 - 4) / 3
= 18/3
= 6m/s²
The average acceleration of the roller coaster is 6 m/s².
Explanation:The average acceleration can be calculated by using the formula:
average acceleration = (final velocity - initial velocity) / time interval
In this case, the initial velocity is 4 m/s, the final velocity is 22 m/s, and the time interval is 3 seconds. So, the average acceleration is:
average acceleration = (22 m/s - 4 m/s) / 3 s = 6 m/s²
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Use the distributive property to remove the parentheses
(4n^2+2n-1)3
Answer:
The answer to your question is 12n² + 6n - 3
Step-by-step explanation:
Polynomial
3(4n² + 2n - 1)
Distributive property, this property lets us multiply a sum by multiplying each term of the sum separately and if possible simplify like terms.
Solution
3(4n²) + 3(2n) - 3(1)
12n² + 6n - 3
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars. R, that he is reimbursed and the number of miles, m, he drives in one day. Interpret the slope of the equation.
Answer:
The slope, 0.575, means that the total amount Bruce is reimbursed in one day increases by 0.575 of a dollar for each mile he drives on that day.
Step-by-step explanation:
The slope of equation R=0.575m+42 represents the rate of change of reimbursement with respect to miles driven. Thus, for each additional mile driven, the reimbursement increases by $0.575. This means that the slope essentially represents the reimbursement rate per mile.
Explanation:The equation R=0.575m+42 given in the question is a linear equation in the form of y = mx + b. In this equation R is the dependent variable symbolizing the reimbursement amount in dollars, m is the independent variable symbolizing the miles driven, 0.575 is the slope, and 42 is the y-intercept.
The slope in this case, 0.575, interprets as the rate of change of the reimbursement amount with respect to the miles driven. That is, for each additional mile driven, the reimbursement Bruce receives increases by $0.575. Hence, the slope or 'm' is actually the reimbursement rate per mile for Bruce's travels.
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Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keith drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Keith live from the mountains? Do not do any rounding.
Answer:
Keith live 280 miles far way from the mountains.
Step-by-step explanation:
Consider the provided information.
Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours.
Let the distance is D and average rate or speed is x miles.
[tex]Distance =Speed\times Time[/tex]
Substitute the respective values.
[tex]D=x\times 8\\D=8x[/tex]
When Keith drove home, there was no traffic and the trip only took 5
hours. The average rate was 21 miles per hour faster on the trip home,
The average rate or speed during return is x+21 miles.
Substitute the respective values in the above formula.
[tex]D =(x+21)\times 5\\D=5x+105[/tex]
Equate both the equations.
[tex]5x+105=8x\\3x=105\\x=35[/tex]
Substitute the value of x in [tex]D=8x[/tex]
[tex]D=8(35)\\D=280[/tex]
Hence, Keith live 280 miles far way from the mountains.
Final answer:
To find the distance Keith lives from the mountains, we need to set up and solve an equation using the given information about the trip duration and rates.
Explanation:
To find the distance Keith lives from the mountains, we can use the formula:
Distance = Rate * Time
Let's assume the rate Keith drove to the mountains is r. Therefore, the distance to the mountains would be 8r. We also know that on the return trip, Keith's rate was 21 miles per hour faster, so his rate on the return trip would be r + 21. The distance on the return trip would be 5(r + 21).
Since the distance to and from the mountains is the same, we can set up the equation:
8r = 5(r + 21)
Solving this equation will give us the value of r, and therefore, the distance Keith lives from the mountains.
For what value of a does (one-seventh) Superscript 3 a + 3 Baseline = 343 Superscript a minus 1?
–1
0
1
no solution
Answer:
a = 0
Step-by-step explanation:
I find a graphing calculator useful for such questions. It shows the solution to be a = 0. For the graph, we have rewritten the equation from
(1/7)^(3a+3) = 343^(a-1)
to
(1/7)^(3x+3) -343^(x-1) = 0 . . . . . this graphing calculator likes x for the independent variable
__
If you recognize that 343 is the cube of 7, you might solve this by taking logarithms to the base 7.
(7^-1)^(3a+3) = (7^3)^(a-1)
Equating exponents of 7*, we get ...
-(3a+3) = 3(a -1)
-3a -3 = 3a -3 . . . . . eliminate parentheses
0 = 6a . . . . . . . . . . . add 3+3a
0 = a . . . . . . . . . . . . divide by 6
_____
* Equating exponents of 7 is the same as taking logarithms to the base 7. Here, we use the rules of exponents ...
1/a^b = a^-b
(a^b)^c = a^(bc)
Answer:
B. 0
Step-by-step explanation:
:)
A model of a car is available in 4 colors (black blue silver and white.) and 3 body styles(coupe sedan and wagon) there are also 2 engines to choose from , (16 cylinders, called V6 and four cylinder called l4) what is the probability of choosing a vehicle that is V6 sedan
Answer:
Step-by-step explanation:
P=1/2 *1/3=1/6
A relationship in which both the independent and dependent variables are influenced by a causally prior control variable such the original relationship is "explained away" by the control variable is referred to as:
a. spuriousness
b. statistical significance
c. percentage difference
d. dependence
Answer: (a) spuriousness relationship
Step-by-step explanation:
Spurious occurs between two variables that are actually caused by a third variable. Examples is like a number of teachers in region and number of people learn from college.
A team of dogs drags a 70.9 kg sled 1.24 kmover a horizontal surface at a constant speed.The coefficient of friction between the sledand the snow is 0.193.The acceleration of gravity is 9.8 m/s2.Find the work done by the dogs.Answer in units of kJ.
Answer:
166.284 KJ
Step-by-step explanation:
We are given that
Mass of sled =70.9 kg
Displacement of sled=1.24 km
Coefficient of friction=[tex]\mu=[/tex]0.193
Acceleration due to gravity=[tex]g=9.8m/s^2[/tex]
We have to find the work done by the dogs in units KJ
Friction force=[tex]\mu mg[/tex]
Friction force =f=[tex]0.193\times 70.9\times 9.8=134.1N[/tex]
Force applied by team of dogs=Friction force
F=f=134.1 N
Work done=[tex]F\times s[/tex]
We have s=1.24 km=[tex]1.24\times 1000=1240m[/tex]
1 km= 1000 m
Work done=[tex]134.1\times 1240=166284 J[/tex]
1 KJ=1000J
Work done=[tex]\frac{166284}{1000}=166.284KJ[/tex]
Hence, the work done by the dogs=166.284 KJ
A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet . The width of the banner is 1/4 the length of the banner. What are the dimensions of the banner?
Answer:
The answer to your question is width = 6 ft; length = 24 ft
Step-by-step explanation:
Data
Area = 144 ft²
width = w
length = l
The width is 1/4 of the length
Formula
Area = width x length = w x l
Length = 4 width l = 4w
Process
1.- Substitute length in the first equation
Area = w(4w)
Simplify
Area = 4w²
2.- Solve for w
w = [tex]\sqrt{\frac{Area}{4}}[/tex]
Substitution
w = [tex]\sqrt{\frac{144}{4}}[/tex]
Simplification
w = [tex]\sqrt{36}[/tex]
Result
w = 6 ft
3.- Find l
l = 4(6)
l = 24 ft
A car traveling at 88 km an hour over takes a bus traveling at 64 km an hour if the bus has a 1.5 hour Headstart how far from the starting point does the car over take the bus
Answer: 352 miles
Step-by-step explanation:
At the point where the car overtook the bus, the car and the bus would have travelled the same distance.
Let x represent the distance covered by bus and the car before the car overtook the bus.
Let t represent the time taken by the bus to travel x miles.
The bus was traveling at 64 km an hour.
Distance = speed × time
Distance travelled by the bus in t hours would be
x = 64 × t = 64t
if the bus has a 1.5 hour Headstart, it means that the car started moving 1.5 hours after the bus has moved.
Therefore, time spent by the car would be t - 15 hours.
The car traveling at 88 km an hour
Distance covered by the car in t - 1.5 hours would be
x = 88(t - 1.5) = 88t - 132
Since the distance covered is equal, then
88t - 132 = 64t
88t - 64t = 132
24t = 132
t = 132/24
t = 5.5 hours
Therefore, the distance from the starting point when the car overtook the bus would be
x = 64 × 5.5 = 352 miles
What is the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards?
Answer: [tex]\dfrac{11}{221}[/tex]
Step-by-step explanation:
We know that the total number of cards in a standard deck = 52
Then the number of ways to draw any two card = 52 x (52-1)
= 52 x 51 = 2652 [By Multiplicative principle]
Also , there are 12 face cards in a standard deck , so the number of ways to draw two face cards in succession = 12 x (12-1)
12 x 11= 132 [By Multiplicative principle]
Then, the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards would be
[tex]\dfrac{\text{ Number of ways to draw 2 face cards}}{\text{Total number of ways to draw two cards}}[/tex]
[tex]=\dfrac{132}{2652}=\dfrac{11}{221}[/tex]
Hence, the required probability is [tex]\dfrac{11}{221}[/tex] .
A company repaid a long-term debt during the year. They will report this as an (increase/decrease) in the activities section on the statement of cash flows.
Answer:
Decrease and financing section
Step-by-step explanation:
The cash flows statement categorizes activities into 3 groups namely; Operating, Investing and Financing.
Operating activities captures the changes to current assets and liabilities such as inventory, trade payables and trade receivables, net income, depreciation etc.
Investing has elements such as sale and purchase of fixed asset. While financing dealings with elements around equity changes and long term debts.
As such the payment of long term debt will be reported in the financing activities section as a decrease because it results in the out flow of cash.
Repayment of a long-term debt during the year is reported as a decrease in the cash flows from financing activities section on the statement of cash flows. This reflects the money used to repay the debt.
When a company repays a long-term debt during the year, it is reported as a decrease in the cash flows from financing activities section on the statement of cash flows.
This decrease reflects the outgoing funds used to repay the debt. For example, in the case of Singleton Bank's change in business plan, their balance sheet would reflect the change in assets from the repayment of a loan, such as the one to Hank's Auto Supply for $9 million.
As a result, there would be a corresponding decrease in cash flows from financing activities by the same amount in the statement of cash flows. The decrease would indicate the outflow of money used to retire the long-term debt.
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A recent survey reported that out of 50 teenagers, 9 said they get most of their news from a newspaper. At this rate, how many out of 300 teenagers would you expect to get their news from a newspaper?
Answer:
Out of 300 teenagers 54 would be expected to get their news from a newspaper.
Step-by-step explanation:
Given:
A recent survey reported that out of 50 teenagers, 9 said they get most of their news from a newspaper.
Now, at this rate, out of 300 teenagers to find the number of teenagers to get their news from a newspaper.
So, as given 9 out of 50 teenagers said they get most of their news from a newspaper.
Thus, 9 : 50 is the ratio.
At this rate, out of 300 teenager.
Let the number of teenagers to get their news from a newspaper be [tex]x.[/tex]
Thus, the ratio is [tex]x:300.[/tex]
Now, to get the number of teenagers we set proportion:
[tex]\frac{9}{50} =\frac{x}{300}[/tex]
So, to solve by using cross multiplication method:
[tex]\frac{9}{50} =\frac{x}{300}[/tex]
By cross multiplying we get:
[tex]2700=50x[/tex]
Dividing both sides by 50 we get:
[tex]54=x[/tex]
[tex]x=54.[/tex]
Therefore, out of 300 teenagers 54 would be expected to get their news from a newspaper.
The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. 95% of all people work between ___ and ___ hours per day? a.7 and 9 hours (T/F)
Answer: 95% of all people work between 7 hours and 9 hours per day and It is true.
Step-by-step explanation:
Since we have given that
Mean = 8 hours
Standard deviation = 0.5 hours
According to Empirical Rule,
at 95% confidence, it lies within 2 standard deviations from the mean
so, lower value is given by
[tex]mean-2\times sd\\\\=8-2\times 0.5\\\\\=8-1\\\\=7\ hours[/tex]
upper value is given by
[tex]mean+2\times s.d\\\\=8+2\times 0.5\\\\=8+1\\\\=9\ hours[/tex]
Hence, 95% of all people work between 7 hours and 9 hours per day.
Therefore , it is true.
Final answer:
95% of people work between 7 and 9 hours per day according to the empirical rule of the normal distribution. The statement is true.
Explanation:
The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. Since the distribution is symmetric, and we are looking for the range that includes 95% of the distribution for a standard normal distribution, we can use the empirical rule. The empirical rule states that approximately 95% of the data in a normal distribution falls within two standard deviations of the mean.
To find the range, we calculate as follows:
Lower bound = Mean - 2(Standard Deviation) = 8 - 2(0.5) = 7 hoursUpper bound = Mean + 2(Standard Deviation) = 8 + 2(0.5) = 9 hoursTherefore, 95% of all people work between 7 and 9 hours per day. The statement is true.
Evaluate the amount of work done by the force field F(x,y)=1x2i+yexjF(x,y)=1x2i+yexj on a particle that moves along the curve C:x=y2+1C:x=y2+1 from (1,0)(1,0) to (2,1)(2,1).
Answer:
[tex]\frac{7}{3} + \frac{e^2 - e}{2}[/tex]
Step-by-step explanation:
By definition:
Work done along the path is the line integral along that path denoted as:
Work Done = [tex]\int\limits^C {F} \, dr[/tex]
Note: dr = dx i + dy j
Given that: [tex]F (x,y) = x^2 i + ye^x j[/tex]
F (x, y) dot product with dr = [tex] x^2 dx + ye^x dy[/tex]
Work done = [tex]\int\limits^C {(x^2 dx + ye^x dy)}[/tex] ... Eq 1
Given that C: [tex]y = \sqrt{x-1}[/tex]
[tex]dy = \frac{dx}{2\sqrt{x-1} }[/tex]
Replace the value of y and dy in Eq 1
[tex]Work done = \int\limits^C ({x^2 + \frac{e^x}{2} }) \, dx[/tex]
Limits of x are 1 to 2 respectively
[tex]Work done = \int\limits^2_1 ({x^2 + \frac{e^x}{2} }) \, dx[/tex]
= [tex](\frac{x^3}{3} + \frac{e^x}{2})\limits^2_1[/tex]
Evaluate limits to obtain
Work Done = [tex]\frac{7}{3} + \frac{e^2 - e}{2}[/tex]
John and Monica are paid $41.25 for their work. John worked 2.5 hours, and Monica worked 3 hours. They split the money according to the amount of time each of them worked. How much is John's share of the money?
John worked for a portion of the total hours, so he should get a proportionate share of the payment. His share of the total hours is 2.5/5.5, so his share of the total payment is (2.5/5.5) times $41.25, which is about $18.75.
Explanation:The subject of this question is Mathematics, specifically a scenario about division and ratios. To find out how much money John gets, we need to know the total number of hours worked and how this correlates to the total payment.
John and Monica collectively worked for 2.5 + 3 = 5.5 hours. John worked 2.5 out of these 5.5 hours. So, the proportion of time John worked is 2.5/5.5. Then, multiply this proportion (2.5/5.5) by the total payment of $41.25 to get John's share.
John's share is thus (2.5/5.5) * $41.25 ≈ $18.75.
This approach represents a principle of fair division, where the money is divided according to the proportion of hours worked by each person.
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Japanese bullet trains travel at an average speed of 150 miles per hour. If you take the bullet train and leave Tokyo at 9:00 AM, how many miles you have travelled at 12:20
Answer: you would have travelled 500 miles.
Step-by-step explanation:
Distance travelled = speed × time
Japanese bullet trains travel at an average speed of 150 miles per hour.
If you take the bullet train and leave Tokyo at 9:00 AM, by 12:20, it would be noon. The time that you would have spent would be
12:20 - 9:00 = 3 hours 20 minutes.
Converting to hours, it becomes
3 + 20/60 = 3 + 1/3 = 10/3 hours
Therefore, the number of miles that you would have travelled would be
10/3 × 150 = 500 miles
Finding the Break-Even Point and the Profit Function Using Substitution Given the cost function C(x)=0.85x+35,000 and the revenue function R(x)=1.55x,find the break-even point and the profit function?
Answer:
[tex]x=50000[/tex]
[tex]P(x)=0.7x-35000[/tex]
Step-by-step explanation:
Given cost function is
[tex]C(x)=0.85x+35000[/tex]
and revenue function is
[tex]R(x)=1.55x[/tex]
At break even point, revenue is equal to cost
R(x)= C(x)
[tex]1.55x=0.85x+35000[/tex]
Subtract 0.85 from both sides
[tex]0.7x=35000[/tex]
divide by 0.7 on both sides
[tex]x=50000[/tex]
Profit function
P(x)= R(x)- C(x)
[tex]P(x)=1.55x-(0.85x+35000)[/tex]
[tex]P(x)=1.55x-0.85x-35000[/tex]
[tex]P(x)=0.7x-35000[/tex]
The break-even point is found by setting the revenue function equal to the cost function, which results in the sale of 50,000 units. The profit function is calculated by subtracting the cost function from the revenue function, resulting in π(x) = 0.70x - 35,000.
Explanation:To find the break-even point where the cost and revenue functions are equal, we substitute these functions and solve for Q:
R(x) = C(x)
1.55x = 0.85x + 35,000
This gives us 1.55x - 0.85x = 35,000
0.70x = 35,000
x = 35,000 / 0.70
x = 50,000 units (break-even point)
The profit function (π) is found by subtracting the cost function from the revenue function:
π(x) = R(x) - C(x)
π(x) = 1.55x - (0.85x + 35,000)
π(x) = 1.55x - 0.85x - 35,000
π(x) = 0.70x - 35,000
Hence, the profit function is π(x) = 0.70x - 35,000.
Jessica is walking home from a friend's house. After two minutes she is 1 mile from home. Twelve minutes after leaving, she is 0.5 miles from home. What is her rate in miles per hour?
Step-by-step explanation:
In ten minutes she walked 1-0.5=0.5 miles.
60 minutes/10 minutes=6. So 0.5 miles ×6=3 miles per hour
Find the midpoint of (5,9) and (-1,9)
Answer:
The answer to your question is (2, 9)
Step-by-step explanation:
Data
A (5, 9)
B (-1, 9)
Formula
Xm = [tex]\frac{1 + x2}{2}[/tex]
Ym = [tex]\frac{y1 + y2}{2}[/tex]
Substitution
Xm = [tex]\frac{5 - 1}{2}[/tex]
Xm = [tex]\frac{4}{2} = 2[/tex]
Ym = [tex]\frac{9 + 9}{2} = \frac{18}{2} = 9[/tex]
Midpoint = (2, 9)
On the beach Broadwalk ,there are 20 different places to get food.Twenty percent of them are ice cream shops . How many ice cream shops are in the park
Answer:
4
Step-by-step exp
You figure out what is 20 percent of 20 and that is 4.