Final answer:
It takes 30 minutes for the moon's shadow to travel 1150 miles during a solar eclipse based on the speed of 2300 miles per hour.
Explanation:
The question asks us to calculate the amount of time it takes the moon's shadow to travel a certain distance during a solar eclipse, based on given speeds and distances. We know that the shadow travels 2300 miles in one hour, so the speed of the shadow is 2300 miles per hour. In the first 20 minutes, the shadow traveled 766 ⅓ miles. To find the time it takes the shadow to reach 1150 miles, we set up a proportion since the motion of the shadow is at a constant speed.
First, let's convert the 20-minute travel time to hours by dividing by 60, which is ⅓ of an hour (20 / 60 = ⅓). Then we can set up the proportion as follows:
766 ⅓ miles is to ⅓ hour, as 1150 miles is to T hours. Which gives us:
(766 ⅓ / 2300) = (⅓ / 1)
(1150 / 2300) = (T / 1)
Now, we solve for T:
⅓ = 1150 / 2300
T = ⅓
So, T is ⅓ of an hour, which means that it takes ⅓ of an hour for the shadow to reach 1150 miles. We can convert ⅓ of an hour to minutes by multiplying by 60, thus:
T = ⅓ × 60
T = 30 minutes
Therefore, it takes 30 minutes for the shadow to reach 1150 miles.
A metalworker has a metal alloy that is 15% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 51% copper alloy?
18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.
Step-by-step explanation:
Let x = kg of 15% copper alloy
Let y = kg of 60% copper alloy
Since we need to create 90 kg of alloy we know:
x + y = 90
51% of 90 kg = 45.9 kg of copper
So we're interested in creating 45.9 kg of copper
We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:
0.15x + 0.60y = 45.9
but
x + y = 90
x= 90 - y
substituting that value in for x
0.15(90 - y) + 0.60y = 45.9
13.5 - 0.15y + 0.60y = 45.9
0.45y = 32.4
y = 72
Substituting this y value to solve for x gives:
x + y = 90
x= 90-72
x=18
Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
Use technology to find the P-value for the hypothesis test described below. The claim is that for 12 AM body temperatures, the mean is μ > 98.6°F. The sample size is n = 6 and the test statistic is t = 1.965.
Answer:
[tex]p_v =P(t_5>1.965)=0.0533[/tex]
We can use the following excel code to find it :"=1-T.DIST(1.965,5,TRUE) "
Step-by-step explanation:
Data given and notation
[tex]\bar X[/tex] represent the average score for the sample
[tex]s[/tex] represent the sample standard deviation
[tex]n=6[/tex] sample size
[tex]\mu_o =98.6[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a one upper tailed test.
What are H0 and Ha for this study?
Null hypothesis: [tex]\mu \leq 98.6[/tex]
Alternative hypothesis :[tex]\mu > 98.6[/tex]
Compute the test statistic
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
The calculated value on this case is given t=1.965
Give the appropriate conclusion for the test
First we need to calculat ethe degrees of freedom given by:
[tex]df=n-1=6-1=5[/tex]
Since is a one side right tailed test the p value would be:
[tex]p_v =P(t_5>1.965)=0.0533[/tex]
We can use the following excel code to find it :"=1-T.DIST(1.965,5,TRUE) "
Conclusion
If we compare the p value and a significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 98.6 at 5% of significance.
For how many positive values of n are both n3 and 3n four-digit integers?
Answer:
No positive value of n
Step-by-step explanation:
we have to find out for how many positive values of n are both
[tex]n^3 , 3^n[/tex] our-digit integers
Let us consider first cube
we get 4digit lowest number is 1000 and it has cube root as 10.
Thus 10 is the least integer which satisfies four digits for cube.
The highest integer is 9999 and it has cube root as 21.54
or 21 the highest integer.
Considering 3^n we get,
3^10 is having 5 digits and also 3^21
Thus there is no positive value of n which satisfy that both n cube and 3 power n are four digits.
state of the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement
Answer: UTS is similar to UQR, second choice
The other choices refer to the same triangle but we have to have corresponding vertices in the same order. U corresponds to itself, so has to be listed first in the similar triangle. T corresponds to Q and S to R, so UQR is our answer.
find the center and radius of the circle that has the equation ( +7)^2 +(−4)^2 = 49
Answer:
For the given circle, the center is at (-7,4) and radius is 7
Step-by-step explanation:
Given equation of the circle is [tex](x+7)^2+(y-4)^2=49\hfill (1)[/tex]
To find the center and radius of given circle with the help of its equation:
Equation of the circle is of the form
(x-h)^2+(y-k)^2=r^2\hfill (2)[/tex] with center at (h,k) and radius is r.
Given [tex](x+7)^2+(y-4)^2=49[/tex]
The above equation can be written as,
[tex](x-(-7))^2+(y-4)^2=7^2\hfill (3)[/tex]
Now comparing the equations (2) and (3) we get
h=-7, k=4 and r=7
Therefore center at (h,k) is (-7,4) and radius is 7
For the given circle, the center is at (-7,4) and radius is 7
Fill in the code to complete the following function for computing a Fibonacci number. public static int fib(int index) { if (index == 0 || index == 1) // Base case ________ else // Reduction and recursive calls return fib(index - 1) + fib(index - 2); }
Final answer:
The student asked for the completion of a Java function to compute the nth Fibonacci number using recursion. The base case for the function is missing, which should return the index when it is either 0 or 1. Two alternatives to improve runtime are memoization and dynamic programming, with an example provided for the latter technique.
Explanation:
The student is asking for the missing code in a recursive Java function to compute the nth Fibonacci number. To complete the base case of the provided function, we should return the index itself because the 0th and 1st Fibonacci numbers are defined as 0 and 1, respectively.
The function should look as follows:
public static int fib(int index) {
if (index == 0) return 0; // Base case for 0
if (index == 1) return 1; // Base case for 1
else // Reduction and recursive calls
return fib(index - 1) + fib(index - 2);
}
Using this recursive algorithm is inefficient due to its exponential time complexity, represented by O(2^n). To illustrate the concept of reducing computation time, two alternative approaches can be used: memoization and dynamic programming. Memoization stores the results of expensive function calls and reuses them when the same inputs occur again, thus avoiding the need to recompute them. Dynamic programming approaches the problem from a bottom-up perspective, computing and storing the result of smaller subproblems first, which then are used to compute larger ones.
An example of a dynamic programming approach is to use a loop to calculate the sequence iteratively:
public static int fib_loop(int index) {
if (index == 0) return 0;
if (index == 1) return 1;
int a = 0, b = 1, sum;
for (int i = 2; i <= index; i++) {
sum = a + b;
a = b;
b = sum;
}
return b;
}
The time complexity for the iterative solution is O(n), which is significantly faster than the recursive approach. Therefore, fib_loop() can compute Fibonacci numbers much quicker than the recursive fib(). For example, calculating fib(40) using the recursive method can take a significant amount of time, while fib_loop(40) will complete in a fraction of the time due to its linear time complexity.
Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards he gets 20 by 10 yards. Is that enough and if so how much more does he need?
Answer:
Step-by-step explanation:
Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards. This means that the total area of the lawn is
30 × 30 = 900 yards^2
he gets 20 by 10 yards. This means that the total area of what he got would be
20 × 10 = 200 yards^2
Since what he needs is 900 yards^2 and it is greater than what he got, 200 yards^2, then it won't be enough.
What he needs more would be
900 - 200 = 700 yards^2
Karl and Pete produce cars and trucks. Karl can produce 10 cars per hour or 5 trucks per hour. Pete can produce 12 cars per hour or 4 trucks per hour.Based on the scenario, Pete’s opportunity cost of one truck is:a. 6 cars.b. 4 cars.
c. 1 1/3 cars.d. 3 cars.e. 3/4 car.
Answer:
The opportunity cost will be 3 cars
So option (d) will be correct answer
Step-by-step explanation:
The opportunity is cost is best characterized as the following best action done without, it is something we give up to gain another.
For instance the opportunity cost of going to class can be the pleasure from watching movie, or spending time with companions or something different. The opportunity cost can be determined by isolating what you forgone by what you gain.
So opportunity cost [tex]=\frac{12}{4}=3cars[/tex]
So option (d) will be the correct answer
Final answer:
Pete's opportunity cost of producing one truck is 3 cars, which is found by dividing Pete's car production rate by his truck production rate (12 cars per hour / 4 trucks per hour).
Explanation:
Pete's opportunity cost of producing one truck can be determined by looking at the alternative production of cars he could have achieved in the same amount of time. Since Pete can produce 12 cars per hour or 4 trucks per hour, we can set up a ratio of cars to trucks based on his production abilities. To find the opportunity cost of one truck, we divide the number of cars Pete can make by the number of trucks, which is 12/4, giving us 3. Hence, Pete's opportunity cost of one truck is 3 cars. This calculation is similar to how opportunity cost is determined in examples such as the production possibility frontier, where the slope shows the trade-off between two different products.
You are buying fruit to make fruit baskets apples come in bags of 20. Ornages come in bags of 16. And bananas come in bags of 32. You have one bag of each fruit each fruit basket must be identical. A) what is the greates t number of fruit baskets that you can make using all fruit ?
Answer:
160 basket of each fruit baskets we can make using all fruit.
Step-by-step explanation:
Given:
Oranges comes in bags = 16
Apples comes in bags = 20
bananas come in bags = 32
We need to find the greatest number of fruit baskets that you can make using all fruit.
Also Given:
You have one bag of each fruit basket must be identical.
So we will first find the least common multiple of all the numbers we get;
20 = 20,40,60,80,100,120,140,160
16 = 16,32,48,64,80,96,112,128,144,160
32 = 32,64,96,128,160
The least common multiple is 160.
Hence we can say that, 160 basket of each fruit baskets we can make using all fruit.
Find the relative minimum of
y = 3x^3 + 14x^2 - 11x - 46
(___ , ____)
Round your answers to the nearest tenth when applicable.
Write your answer in the format (a, b).
Answer:
Step-by-step explanation:
The max and min values exist where the derivative of the function is equal to 0. So we find the derivative:
[tex]y'=9x^2+28x-11[/tex]
Setting this equal to 0 and solving for x gives you the 2 values
x = .352 and -3.464
Now we need to find where the function is increasing and decreasing. I teach ,my students to make a table. The interval "starts" at negative infinity and goes up to positive infinity. So the intervals are
-∞ < x < -3.464 -3.464 < x < .352 .352 < x < ∞
Now choose any value within the interval and evaluate the derivative at that value. I chose -5 for the first test number, 0 for the second, and 1 for the third. Evaluating the derivative at -5 gives you a positive number, so the function is increasing from negative infinity to -3.464. Evaluating the derivative at 0 gives you a negative number, so the function is decreasing from -3.464 to .352. Evaluating the derivative at 1 gives you a positive number, so the function is increasing from .352 to positive infinity. That means that there is a min at the x value of .352. I guess we could round that to the tenths place and use .4 as our x value. Plug .4 into the function to get the y value at the min point.
f(.4) = -48.0
So the relative min of the function is located at (.4, -48.0)
You chose a college loan plan that is compounded annually. You take out $10,000 on the loan, and it has an interest rate of 5.75%. If it takes you six years to pay off the loan, how much money will you have paid back by the end of the six years?
Answer:
At the end of 6 years, he would have paid $13985.6
Step-by-step explanation:
Initial amount taken as load is $10,000 This means that the principal
P = 10000
It was compounded annually. This means that it was cam pounded once in a year. So
n = 1
The rate at which the principal was compounded is 5.75%. So
r = 5.75/100 = 0.0575
it takes you six years to pay off the loan. So
t = 6
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount of money that you would have paid back by the end of the six years. Therefore
A = 10000 (1+0.0575/1)^1×6
A = 10000(1.0575)^6 = $13985.6
Anthony has a bag that contains 4 blue candies, 6 green candies, and 10 yellow candies. * Without looking, he pulls out a piece of candy, records the color, and then puts it back in the bag. * He does this 150 times. How many times could Anthony expect to pull out a blue candy?
Answer:
0.03
Step-by-step explanation:
Anthony can expect to pull out a blue candy 30 times in 150 draws, as each draw has a 1/5 probability of being blue, and the total number of draws is 150.
The question can be answered by calculating the expected frequency of pulling a blue candy based on the probability of drawing a blue candy from the bag. Anthony has 4 blue candies, 6 green candies, and 10 yellow candies, making a total of 20 candies in the bag. Since each draw is independent and the candies are replaced each time, the probability of drawing a blue candy is 4/20 or 1/5.
To find the expected number of times Anthony could pull out a blue candy in 150 tries, we multiply the probability by the number of trials:
Expected blue candies = (Probability of blue candy) x (Number of trials)
Expected blue candies = (1/5) x 150
Expected blue candies = 30
Therefore, Anthony can expect to pull out a blue candy 30 times in 150 draws.
Derek's math teacher put some candy in a brown paper bag. The bag contains 4 lemon, 6 lime, 8 cherry, 2 pineapple, 5 orange, and 5 grape candies. All 14 students ahead of Derek selected a candy to eat, but no one got pineapple. What is the probability that Derek will draw out a pineapple candy?
Answer:
Even though 14 candies were gone there still is a very low change of getting pineapple. out of 12 candies 2 are pineapple.
Step-by-step explanation:
It is estimated that almost ___% of collisions involving a vehicle and a train were at crossings where warning devices such as lights, gates and bells were in working order.
Answer: 50%
Step-by-step explanation:
It is estimated that almost 50% of collisions involving a vehicle and a train were at crossings where warning devices such as lights, gates and bells were in working order. This high percentage may be as a result of malfunction of warning devices, because when warning devices malfunction they give wrong signals that could lead to accidents. It could also be as a result of violation or ignorance of traffic rules and warning signals which can also lead to collision.
The question discusses the number of accidents happening at railway crossings despite working warning systems, akin to a problematic intersection at Clay Street and Eagle Avenue that saw many accidents despite traffic rules. While specific statistics aren't given, such cases highlight the importance of adhering to traffic signals and safety measures for both drivers and pedestrians.
Explanation:The question seems to be related to railroad crossing safety, specifically the effectiveness of warning devices like bells, lights, and gates. While the exact percentage is not provided, studies show that a significant proportion of vehicle-train collisions occur at crossings where these warning systems are fully functional. Like the traffic signal installed at the intersection of Clay Street and Eagle Avenue to prevent the high number of accidents, these warning devices aim to control vehicular and pedestrian traffic. Unfortunately, they may not always be heeded, and thus accidents occur.
Similar to the situation in the Clay Street and Eagle Avenue intersection, safety measures only work if they're respected. A traffic signal might reduce accidents, but only if drivers and pedestrians heed it. Unfortunately, despite railroad crossing warnings, accidents still occur, often due to negligence, recklessness, or distraction.
It emphasizes the importance of traffic rules and safety measures in our day to day life. Be it the students crossing the road or vehicles moving in traffic, the role of traffic signals and warning signs is critical. We must remember these are not there to restrict us, but to ensure everyone's safety.
Learn more about road safety here:https://brainly.com/question/33417376
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Albert has $105 to spend, the prices varying from $80 to $180 worth delivery being one-twentieth of the price. Total cost can be modeled by the function f(c) c representing the price. Domain is:
Answer
Domain=[80, 100] ie. both of them inclusive.
Step-by-step explanation:
Albert has total $105.
Let the cost of a product be c.
Therefore, the total cost of a product after the delivery and all is represented by a function f(c)
f(c)=c+[tex]\frac{c}{20}[/tex]
f(c)=[tex]\frac{21c}{20}[/tex]
The domain, of the function is the no. of possible values of c that can satisfy the equation.
Now, lets check the maximum price of the product that Albert can buy.
f(c)=105
[tex]\frac{21c}{20}[/tex]=105
c=$100
As, the minimum price of a product of is $80 , the domain needs to start from here. And it will go on till $100.
Domain=[80, 100]
Twenty types of beef hot dogs were tested for calories and sodium content (mg). the hot dogs average 156.85 calories with a standard deviation of 22.64, and the sodium level average 401.15 mg with a standard deviation of 102.43 mg. the correlation given as r = 0.887. the equation of the lsrl predicting sodium level from number of calories is:________
The equation of the least squares regression line (LSRL) predicting sodium level from the number of calories in beef hot dogs is Sodium Level (mg) = 37.77 mg + 4.077 mg/calories × Calories.
Explanation:The equation of the least squares regression line (LSRL) predicting sodium level from the number of calories in beef hot dogs can be determined using the given statistics and the formula for the slope (b) of the LSRL:
b = r (sy/sx)
Where r is the correlation coefficient, sy is the standard deviation of the y-values (sodium levels), and sx is the standard deviation of the x-values (calories).
Given that r = 0.887, sy = 102.43 mg, and sx = 22.64 calories, we can calculate the slope (b):
b = 0.887 (102.43 mg / 22.64 calories) = 4.077 mg/calories
Then, we can use the y-intercept (a) in the equation y = a + bx, where a = y-bar - b*x-bar.
Given that the average sodium level y-bar = 401.15 mg and the average number of calories x-bar = 156.85 calories, the y-intercept (a) will be:
a = 401.15 mg - (4.077 mg/calories * 156.85 calories) = 37.77 mg
Therefore, the equation of the LSRL is:
Sodium Level (mg) = 37.77 mg + 4.077 mg/calories × Calories
Assuming you start with just one microbe that divides every 30 minutes, how many microbes would you have after 8 hours?
Answer: 1/16,384 microbes
Step-by-step explanation:
Since the microbes divides every 30minutes, if the microbes divides by half every 30minutes, then after an hour it will divides by another half that is (1/2)of 1/2 to give 1/4.
Subsequently after another hour, the microbes will reduces to 1/4 of its remains (i.e 1/4) to give 1/16.
Since the denominator is increasing geometrically each hour.
Looking at the trend;
After 1hr = 1/4 of the original microbe = 1/4
After 2 hrs = 1/4 of the remaining microbe = 1/4 of 1/4 = 1/16
Generalizing, we will let the number of hours be n
According to the progression, 1, 1/4,1/16,...n
Since its a Geometric Progression, nth term = ar^n-1
Where a is the first term = 1
r is the common ratio = 1/4
n is the number of hours of decay
After 8hours, the microbes will have been divided by
(1)(1/4)^8-1
= (1/4)^7
= 1/16,384 microbes
Answer:
1/2^16 or 0.0000152588 microbes
Step-by-step explanation:
Assuming you start with just one microbe that divides every 30 minutes.
This means that the half life of the microbe is 30 minutes or 0.5hours
The interpretation of this half life is that after every half-life, which in this case is 30 minutes, half of the microbe will be gone, and half will remain.
It follows that after another half hour the amount remaining will be
1/2 of 1/2= 1/4 microbes
Thus after 8 hours, there would have been (8/0.5)=16 half lives.
Therefore the amount of microbes remaining will be 1/2^16 of 1 = 0.0625
Alternatively, we could solve the differential equation
dM/dt=kM, where dM/dt is the rate of decay, and M is the amount at any time t, k is the decay constant
Solution of this first order differential equation by separating the variables and integrating yields {dM/M={kt+c, lnM=kt+c, and ......
M=Moexp(-kt)
The initial value Mo=1, when t=0, and given value M=0.5, t=0.5h yields the value of k as follows
0.5=exp(-k*0.5)
ln(0.5)=-k*0.5
k=1.386
After any time time, thus the given expression holds
M=exp(-1.386t)
Thus after 8 hours, the microbes remaining will be
M=exp(-1.386t)=exp(-1.386*8)=0.000152588 microbes.
The average 8 year old gets 30 questions right on an intelligence test, whereas the average 12 year old gets 50 questions right.
What is the mental age of an 8 year old who gets 50 questions right?
Answer:
12 years.
Step-by-step explanation:
We have been given that the average 8 year old gets 30 questions right on an intelligence test, whereas the average 12 year old gets 50 questions right. We are asked to find the mental age of an 8 year old who gets 50 questions right.
Since the 8 year old boy gets 50 questions right and the average 12 year old also gets 50 questions right, so the mental age of 8 year old (getting 50 questions right) will be equal to the mental age of 12 years old.
Therefore, the mental age of an 8 year old who gets 50 questions right would be 12 years.
Answer:
The answer is either 9 or 12
Step-by-step explanation:
The local deli charges a fee, f, for delivery. On Monday, they delivered two dozen bagels, b, to an office at a total cost of 58. On Tuesday, three dozen bagels were delivered at a total cost of $11. Which system of equations could be used to find the cost of a dozen bagels?
Answer:
[tex] 2b+f = 8[/tex] (1)
[tex]3b+f=11[/tex] (2)
[tex] b = 11-8=3[/tex]
[tex]f= 8-2(3) = 8-6 =2[/tex]
Step-by-step explanation:
For this case we can put some notation
Let b= dozen bagels and f= delivery fee
And for this case we know that "On Monday, they delivered two dozen bagels, b, to an office at a total cost of $8", so then the total taling in count the delivery fee we have this:
[tex] 2b+f = 8[/tex]
And for the other part "On Tuesday, three dozen bagels were delivered at a total cost of $11", we can write the expression like this:
[tex]3b+f=11[/tex]
And our system of equations would be:
[tex] 2b+f = 8[/tex] (1)
[tex]3b+f=11[/tex] (2)
If we solve for f from equation (1) we got:
[tex]f= 8-2b[/tex]
And if w replace this into equation (2) we got:
[tex]3b+8-2b=11[/tex]
[tex] b = 11-8=3[/tex]
And solving for f we got:
[tex]f= 8-2(3) = 8-6 =2[/tex]
During a football game a concession stand sold a family three hamburgers and two hotdogs for a total of $13 it's sold another family two hamburgers and five hotdogs for a total of $16 what are the prices of a hamburger and a hotdog
Answer:
The price of each hamburger is $3
The price of each hot dogs is $2 .
Step-by-step explanation:
Given as :
The total price of 3 hamburger and 2 hot dogs = $13
The total price of 2 hamburger and 5 hot dogs = $16
Let The price of each hamburger = $x
Let The price of each hot dogs = $y
Now, According to question
3 x + 2 y = 13 .........A
2 x + 5 y = 16 .......B
Now, Solving to eq A and B
3 × (2 x + 5 y ) - 2 × (3 x + 2 y ) = 3 × 16 - 2 × 13
Or, (6 x + 15 y) - (6 x + 4 y) = 48 - 26
Or, (6 x - 6 x) + (15 y - 4 y) = 22
Or, 0 + 11 y = 22
∴ y = [tex]\dfrac{22}{11}[/tex]
i.e y = $2
so, The price of each hot dogs = y = $2
Now, Put the value of y into eq B
i.e 2 x + 5 y = 16
or, 2 x + 5 × 2 = 16
or, 2 x = 16 - 10
or, 2 x = 6
∴ x = [tex]\dfrac{6}{2}[/tex]
i.e x = $3
So, The price of each hamburger = x = $3
Hence, The price of each hamburger is $3 and The price of each hot dogs is $2 . Answer
ABC is an equilateral triangle with sides equal to 2 cm. BC is extended its own length to D, and E is the midpoint of AB. ED meets AC at F. Find the area of the quadrilateral BEFC in square centimeters in simplest radical form.
Answer:
[tex]\frac{2\sqrt3}{3}[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
Since [tex]\triangle ABC[/tex] is equilateral triangle, then [tex]\angle A = \pi /3[/tex]
So,
[tex]S_{\triangle ABC} = \frac{2 * 2 * sin(\pi /3)}{2} = \frac{2 * 2 * \sqrt{3}/2}{2} = \sqrt{3}[/tex] [tex]cm^2[/tex]
Then we need to find [tex]S_{\triangle AEF}[/tex] which can be computed by finding length_AF.
Let's call x = length_AF.
By Menelao's Theorem,
[tex]\frac{BE*x*CD}{AE*(2-x)*BD} = \frac{1*x*2}{1*(2-x)*4} = 1[/tex]
⇒ x = 4/3 cm
Thus,
[tex]S_{\triangle AEF} = \frac{1 * x * sin(\pi /3)}{2} = \frac{1 * 4/3 * \sqrt{3}/2}{2} = 1/\sqrt{3}[/tex] [tex]cm^2[/tex]
To find the area of quadrilateral [tex]BEFC[/tex], we have to subtract [tex]S_{\triangle AEF}[/tex] from [tex]S_{\triangle ABC}[/tex]
Hence,
[tex]S_{BEFC} = S_{\triangle ABC} - S_{\triangle AEF} = \sqrt3 -1/\sqrt3 = \frac{2\sqrt3}{3}[/tex] [tex]cm^2[/tex]
Two identical rubber balls are dropped from different heights. Ballroom is dropped from a height of 154 feet, and ball to is dropped from a height of 271 feet. Use the function f(t) = -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over the given time t.
Write a function for the height of ball 1.
h_1(t) = _____
Answer:
[tex]h_1(t)=-16t^2+154[/tex]
Step-by-step explanation:
Put the initial height of ball 1 into the given formula:
[tex]h_1(t)=-16t^2+154[/tex]
Six different airlines fly from New York to Denver and seven flies from Denver to San Francisco. How many different pairs of airlines can you choose on which to book a trip from New York to San Francisco via Denver, when you pick an airline for the flight to Denver and air line for the continuation flight to San Francisco?
Answer:
Step-by-step explanation:
6 flights from New York to Denver
7 flights from Denver to San Francisco.
total number of combination
6*7= 42
Final answer:
For a trip from New York to San Francisco via Denver, with six airlines on the first segment and seven on the second segment, there are 42 different pairs of airlines that can be chosen.
Explanation:
The question asks how many different pairs of airlines can be chosen for a trip from New York to San Francisco via Denver, considering one airline for the leg from New York to Denver and another airline for the continuation from Denver to San Francisco. Since there are six different airlines that fly from New York to Denver and seven that fly from Denver to San Francisco, the total number of combinations of airlines for both segments of the journey is a simple multiplication of the two separate choices. Therefore, the number of unique airline pairs is 6 airlines from New York to Denver multiplied by 7 airlines from Denver to San Francisco.
To calculate this, we use the formula for the number of combinations for two independent choices, which is:
Total combinations = (Choices for first segment) × (Choices for second segment)
Total combinations = 6 × 7 = 42 different pairs of airlines.
Thus, a traveler could choose from 42 different combinations of airlines for their trip from New York to San Francisco via Denver.
Joe owns a coffee house and produces coffee drinks under the production function q = 5KL where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). What is the marginal product of labor?
Answer:
Marginal Product of Labour = 5K
Step-by-step explanation:
Marginal product of labor is the change in output when additional labor is added,
To calculate marginal product of labor you simply divide the change in total product by the change in labour.
Marginal product of labour (MPL) = Change in total products/ Change in labour
Here, change in labour = 5KL
Change in labour = L
MPL = 5KL/L
MPL = 5K
The marginal product of labor for Joe's coffee house, where the production function is q = 5KL, is found by differentiating q with respect to L, resulting in 5K, which indicates that each additional employee increases output by 5 times the number of coffee machines available.
Explanation:The marginal product of labor (MP) is the additional output generated by employing one more unit of labor while holding other factors of production constant. In Joe’s coffee house, where the production function is given by q = 5KL (with q as the number of cups produced per hour, K as the number of coffee machines, and L as the number of employees), the marginal product of labor can be found by differentiating the production function with respect to labor. As capital (K) is held constant, the marginal product of labor will be calculated as follows:
MP = d(q)/d(L) = d(5KL)/d(L) = 5K
This equation indicates that the marginal product of labor is 5 times the number of coffee machines in use because K is constant in the short run. Therefore, every additional employee hired will increase the output (q) by an amount equal to 5 times the number of coffee machines that Joe has in his coffee house.
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Charles owns a toy store and to store his inventory of toys at his home office he keeps them in plastic containers. Each container holds 12 toy boxes and he has 278 toy boxes how many containers does he need?
Answer:
He needs 23 containers
Step-by-step explanation:
1 container = 12 toy boxes
X container= 278 toy boxes
12x= 278
X= 278/12
X= 23 containers
A cell phone company charges a flat Rate of 4.75 per month with an additional charge .19 per minute. How many minutes did alexandra talk on her cell phone if your monthly bill was 27.55
Answer:The number of minutes that Alexandra talked on her cell phone is 120
Step-by-step explanation:
A cell phone company charges a flat rate of 4.75 per month with an additional charge 0.19 per minute. Assuming the total number of minutes of call made for the month is represented by x and the total cost of x minutes of call is y, then
y = 0.19x + 4.75
To determine how many minutes that Alexandra talked on her cell phone if his monthly bill was 27.55, we would substitute y = 27.55 into the equation. It becomes
27.55 = 0.19x + 4.75
0.19x = 27.55 - 4.75 = 22.8
x = 22.8/0.19 = 120 minutes.
Chanice and destiny went shopping at new fashion shop. Everything in the store was at a 30% discount. Chanice found a dress that was originally $65.00. What was the sale price
Answer: the sale price of the dress is $87.75
Step-by-step explanation:
Chanice and destiny went shopping at new fashion shop. Everything in the store was at a 30% discount. Chanice found a dress that was originally $65.00. This means that
the sale price would be the original price + 35% of the original price. It becomes
65 + 35/100×65
= 65 + 0.35×65
= 65 + 22.75
= 87.75
Sarah buys a new bike. The total cost of the bike including taxes is $349. She pays $100 down and then agrees to pay the balance in 6 equal payments.
Which of the following values is an appropriate representation of the amount of each of the 6 payments?
A
$58.17
B
$42
C
$41.50
D
$41
The amount of each of the 6 payments will be $41.50
Step-by-step explanation:
Given,
Cost of bike including taxes = $349
Down payment = $100
Amount left to pay = Cost of bike - Down payment
Amount left to pay = 349 - 100
Amount left to pay = $249
She agrees to pay in 6 equal payments, therefore, we will divide the total amount to pay by 6.
Amount to pay for one month = [tex]\frac{Amount\ left\ to\ pay}{No.\ of\ months}[/tex]
Amount to pay for one month = [tex]\frac{249}{6} = \$41.50[/tex]
The amount of each of the 6 payments will be $41.50
Keywords: division, subtraction
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A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded. What is the probability that one spin of the spinner will land in a shaded sector?
Answer:
2/3
Step-by-step explanation:
A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded.
Probability is the likelihood that an event will occur. Probability is a selection over the number of observation.
There are 4 shaded portion of the spinner and two unshaded portion.
The probability that when the spinner is spinned the portion will liand on four is simply
4/6, divided to its lowest term.
2/3
The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].
Given information:
A certain spinner is divided into [tex]6[/tex] sectors of equal size, and the spinner is equally likely to land in any sector. Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.
According to question,
[tex]P(E)=\frac{\rm{No\;of\;favourable\;outcomes}}{\rm{Total\;no\;of\;outcomes}}[/tex]
Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.
There are [tex]4[/tex] shaded portion of the spinner and two unshaded portions.
[tex]P(E)=\frac{4}{6}=\frac{2}{3}[/tex]
Hence, The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].
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what is the measure of this angle ? I think 180 or i’m completely wrong
Answer:
It is an obtuse angle.
Step-by-step explanation:
It is not a 180° angle. Because 180° angle forms a straight line.
The given angle is an obtuse angle which means it is greater than 90° and less than 180°
Note that 90° angle is perpendicular angle(interior angles of a rectangle)
That angle can be measured using a protractor.