Answer:
-4
Step-by-step explanation:
First, we look at the order of operations. (Parentheses, exponents, multiplication and division, addition and subtraction.)
We don't have parentheses, but we do have an exponent. (6 squared)
6 squared just means six multiplied by itself.
6 x 6 = 36
Now, we have to multiply -3 by 3, since the product refers to the answer of a multiplication problem.
-3 x 3 = -9
Now, we do 36 ÷ -9
36 divided by -9 = -4
-4
-12x + 4y- 6y + 10x - 25 5x - 2(x - 12)
Answer:
=−259x−2y+24
Step-by-step explanation:
Distribute:
=−12x+4y+−6y+10x+−255x+(−2)(x)+(−2)(−12)
=−12x+4y+−6y+10x+−255x+−2x+24
Combine Like Terms:
=−12x+4y+−6y+10x+−255x+−2x+24
=(−12x+10x+−255x+−2x)+(4y+−6y)+(24)
=−259x+−2y+24
Answer:
=−259x−2y+24
Hope this helps emmy! or emma
(sorry I like calling you emmy)
(1) Determine the convergence of the series ∑[infinity]
n=1
(−1)n
4n.
(2) Determine the convergence of the series ∑[infinity]
n=1
n(−1)n
3.5n.
Both conditions are satisfied. Therefore, the series \(\sum_{n=1}^{\infty} \frac{(-1)^n}{4n}\) converges. The series \(\sum_{n=1}^{\infty} n \cdot (-1)^n \cdot \left(\frac{1}{3.5}\right)^n\) converges absolutely.
To determine the convergence of a series, we can apply various convergence tests. Let's analyze each series separately:
1. \(\sum_{n=1}^{\infty} \frac{(-1)^n}{4n}\)
This series is an alternating series since it alternates between positive and negative terms. To determine its convergence, we can use the Alternating Series Test. The Alternating Series Test states that if a series of the form \(\sum_{n=1}^{\infty} (-1)^{n-1} \cdot b_n\) satisfies the following conditions:
1. The terms \(b_n\) are positive and decreasing for all n.
2. The limit of \(b_n\) as n approaches infinity is zero.
In our case, \(b_n = 1/(4n)\). Let's check the conditions:
Condition 1: The terms \(b_n = 1/(4n)\) are positive for all n.
Condition 2: Let's calculate the limit of b_n as n approaches infinity:
\(\lim_{{n \to \infty}} \left(\frac{1}{{4n}}\right) = 0\)
Both conditions are satisfied. Therefore, the series \(\sum_{n=1}^{\infty} \frac{(-1)^n}{4n}\) converges.
2. \(\sum_{n=1}^{\infty} n \cdot (-1)^n \cdot \left(\frac{1}{3.5}\right)^n\)
To determine the convergence of this series, we can use the Ratio Test. The Ratio Test states that for a series \(\sum_{n=1}^{\infty} a_n\) , if the following limit exists:
\(\lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{{a_n}} \right| = L\)
1. If L < 1, the series converges absolutely.
2. If L > 1, the series diverges.
3. If L = 1, the test is inconclusive.
In our case, \(a_n = \frac{n \cdot (-1)^n}{3.5^n}\) . Let's apply the Ratio Test:
\(\left| \frac{{(n+1) \cdot (-1)^{n+1}}}{{3.5^{n+1}}} \div \frac{{n \cdot (-1)^n}}{{3.5^n}} \right|\)
\(\left| \frac{{(n+1)/n \cdot (-1)^2}}{{3.5}} \right|\)
\(\left| \frac{{n+1}}{{n}} \right| \cdot \frac{1}{3.5}\)
\(\frac{{n+1}}{{n}} \cdot \frac{1}{3.5}\)
Taking the limit as n approaches infinity:
\(\lim_{{n\to\infty}} \left(\frac{{n+1}}{n} \cdot \frac{1}{3.5}\right) = \frac{1}{3.5}\)
Since 1/3.5 < 1, the series \(\sum_{n=1}^{\infty} n \cdot (-1)^n \cdot \left(\frac{1}{3.5}\right)^n\) converges absolutely.
Therefore, both series converge.
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Part 1
The length of a persons stride (stride length is the distance a person travels in a single step) and the number of steps required to walk 100 yards.
The coreelation coefficent would be
A. be close to 1
B.not be close to 1 or -1
c. be close to -1
Part 2
The number of years of education completed and annual salary
The coreelation coefficent would be
A. be close to 1
B.not be close to 1 or -1
c. be close to -1
Part 3
The annual snowfall amount in the city and the number of residents
The coreelation coefficent would be
A. be close to 1
B.not be close to 1 or -1
c. be close to -1
Part 1: The correlation coefficient between the length of a person's stride and the number of steps required to walk 100 yards would likely not be close to 1 or -1.
Part 2: The correlation coefficient between the number of years of education completed and annual salary would likely not be close to -1.
Part 3: The correlation coefficient between the annual snowfall amount in a city and the number of residents would likely not be close to -1.
Part 1:
The correlation coefficient between the length of a person's stride and the number of steps required to walk 100 yards would likely not be close to 1 or -1. This is because the length of a person's stride and the number of steps are two different measurements and may not have a strong linear relationship.
Factors such as individual walking pace, terrain, and stride variability can affect the number of steps taken to cover a certain distance. Therefore, the correlation coefficient would likely fall between -1 and 1 but not be close to either extreme.
Part 2:
The correlation coefficient between the number of years of education completed and annual salary would likely not be close to -1. This is because a higher level of education generally corresponds to higher earning potential, so there tends to be a positive correlation between education and salary.
However, the correlation coefficient would also not be close to 1, as there are other factors besides education that can influence salary, such as job experience, industry, and individual performance. Therefore, the correlation coefficient would fall between -1 and 1 but not be close to either extreme.
Part 3:
The correlation coefficient between the annual snowfall amount in a city and the number of residents would likely not be close to -1. The number of residents in a city is not directly influenced by the amount of snowfall, as it is determined by various socioeconomic factors and population dynamics.
While cities in regions with heavy snowfall may have lower populations due to climate preferences, the correlation between snowfall and population is unlikely to be strong. Therefore, the correlation coefficient would not be close to -1. It would also not be close to 1, as there are other factors that influence population size. The correlation coefficient would fall between -1 and 1 but not be close to either extreme.
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What is 4 x 1,424 and show your work
Answer:4 x 1,424 = 5,696
Step-by-step explanation:
To multiply 4 by 1,424, we first multiply the ones digit of 1,424 by 4, which gives us 4 x 4 = 16. We write down the 6 and carry the 1.
Next, we multiply the tens digit of 1,424 by 4, which gives us 4 x 2 = 8. We add the carried 1 to get 9, and write down the 9 in the tens place. We carry the remaining 1.
Then, we multiply the hundreds digit of 1,424 by 4, which gives us 4 x 4 = 16. We add the carried 1 to get 17, and write down the 7 in the hundreds place. We carry the remaining 1.
Finally, we multiply the thousands digit of 1,424 by 4, which gives us 4 x 1 = 4. We add the carried 1 to get 5, and write down the 5 in the thousands place.
Putting it all together, we get 5,696 as the product of 4 and 1,424.
Answer: 5696
Step-by-step explanation:
1424 is 1000+400+ 20+4
multiply each by 4
4000+1600+80+16
This equals 5696
With enough practice, you'll be able to do it in your head!
Which statements can be used to justify the fact that two right angles are supplementary? Select two options.
A right angle measures 90°.
If two angles are complementary, the sum of the angles is 90°.
If two angles are supplementary, the sum of the angles is 180°.
A complementary angle is one-half the measure of a supplementary angle.
A supplementary angle is twice the measure of a complementary angle.
Answer:
Which statements can be used to justify the fact that two right angles are supplementary? Select two options.
* A right angle measures 90°.
If two angles are complementary, the sum of the angles is 90°.
* If two angles are supplementary, the sum of the angles is 180°.
A complementary angle is one-half the measure of a supplementary angle.
A supplementary angle is twice the measure of a complementary angle.
Step-by-step explanation:
(A) and (C)
A right angle measures 90°, hence the sum of two right angles is 180° (supplementary)
AnglesAn angle is formed when two lines intersect each other. Two angles are said to be supplementary if their measures add up to 180 degrees while Two angles are called complementary if their measures add up to 90 degrees.
To justify the fact that two right angles are supplementary. Firstly a right angle measures 90°, hence the sum of two right angles is 180° (supplementary)
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1. An elevator in a tall building starts at a floor of the building that is 80 meters above the ground. The elevator descends2 meters every 0.5 seconds for 4 seconds. Identify the domain and range using the following formats and then graph.Inequality:Set Notation:
Let's begin by listing out the information given to us:
The elevator starts at 80 m
The elevator descends 2 meters every 0.5 seconds for 4 seconds
The inequality is given by:
\(\begin{gathered} y=80-2x \\ where\colon x=every\text{ 0.5}seconds \end{gathered}\)The set notation is given by:
\(undefined\)Customers can be served by any of three servers, where the service times of server i are exponentially distributed with rate mu_i, i = 1, 2, 3. Whenever a server becomes free, the customer who has been waiting the longest begins service with that server. a. If you arrive to find all three servers busy and no one waiting, find the expected time until you depart the system. b. If you arrive to find all three servers busy and one person waiting, find the expected time until you depart the system.
a. The expected time until departure from the system when arriving to find all three servers busy and no one waiting can be calculated as (3/2(mu_1+mu_2+mu_3)).
b. The expected time until departure from the system when arriving to find all three servers busy and one person waiting can be calculated as (5/2(mu_1+mu_2+mu_3)).
a. In order to calculate the expected time until departure from the system when arriving to find all three servers busy and no one waiting, we can use the following formula:
E(T) = 1/3 * [1/mu_1 + 1/mu_2 + 1/mu_3 + (1/(mu_1+mu_2+mu_3))]
where E(T) represents the expected time until departure and mu_1, mu_2, and mu_3 represent the service rates of each server.
By substituting the given values into the formula, we get:
E(T) = 1/3 * [1/mu_1 + 1/mu_2 + 1/mu_3 + (1/(mu_1+mu_2+mu_3))]
= 1/3 * [1/μ_1 + 1/μ_2 + 1/μ_3 + (1/(μ_1+μ_2+μ_3))]
= (1/μ_1 + 1/μ_2 + 1/μ_3 + (1/(μ_1+μ_2+μ_3)))/3
Simplifying this expression gives us:
E(T) = (3/2(mu_1+mu_2+mu_3))
Therefore, the expected time until departure from the system when arriving to find all three servers busy and no one waiting is (3/2(mu_1+mu_2+mu_3)).
b. When one person is already waiting in the system, the expected time until departure can be calculated using the following formula:
E(T) = 1/2(mu_1+mu_2+mu_3) + 1/μ_min
where μ_min is the smallest service rate among the three servers.
The reasoning behind this formula is that the customer who has been waiting the longest will begin service immediately when a server becomes free, while the customer who arrived most recently will wait until all the other customers ahead of them have been served.
Therefore, the expected time until departure in this case is the expected waiting time for the customer who has been waiting the longest plus the expected service time for the next customer in line.
Since the service times are exponentially distributed, the expected service time for a server with rate mu is 1/mu. Therefore, the expected service time for the customer who is next in line is 1/μ_min.
By substituting the given values into the formula, we get:
E(T) = 1/2(mu_1+mu_2+mu_3) + 1/μ_min
= (μ_min/2(μ_1+μ_2+μ_3)) + (1/μ_min)
Therefore, the expected time until departure from the system when arriving to find all three servers busy and one person waiting is (μ_min/2(μ_1+μ_2+μ_3)) + (1/μ_min), or equivalently, (5/2(mu_1+mu_2+mu_3)) if we substitute μ_min = min(μ_1, μ_2, μ_3).
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x-2√x ³ - x² - 4x+12
-x² - x( 3 + 2√x) + 12 is the simplified form of the expression
x-2√x ³ - x² - 4x+12.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given an expression that needs to be rewritten in simplified form
Equation is:
=> x-2√x ³ - x² - 4x+12
Solving the square root
=> x - 2 * x√x - x²- 4x + 12
=> -x² + x(-3 -2√x) + 12
=> -x² - x( 3 + 2√x) + 12
therefore, -x² - x( 3 + 2√x) + 12 is the simplified form of the expression
x-2√x ³ - x² - 4x+12.
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Need help asap please!!!
Answer:
Bottom Right = (2 x 10^-3) x (4 x 10^4) = 8 x 10^1
Step-by-step explanation:
a tree is cut down to the ground the trunk of the tree is cut into equal sections which geometric shape can be used to model the volume of the cut tree
Cylindrical shape.
To model the volume of the cut tree, the appropriate geometric shape is a cylinder.
This is because a cylinder's volume is equal to the product of the base's area and the height of the cylinder,
which can be determined by the length of the equal sections of the tree trunk.
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ANSWER PLEASE FINAL DUE IN 3 HOURS
Suppose a normal distribution has a mean of 120 and a standard deviation of 10. What is P(x ≥ 130)?
A.
0.475
B.
0.84
C.
0.16
D.
0.975
Answer:
B
Step-by-step explanation:
First thing to do here is to calculate the z-score
Mathematically;
z-score = (x-mean)/SD
here, x = 130, mean = 120 and SD = 10
Substituting these values
z-score = (130-120)/10 = 10/10 = 1
So the probability we want to calculate is;
P(z ≥ 1) = 1 - P(z <1)
From standard score table, P(z <1) = 0.15866
P(z ≥ 1) = 1-0.15866 = 0.84134
Answer:
0.16
Step-by-step explanation:
The following table shows how many pizzas Dave’s pizzeria has sold each hour.
Write the slope intercept equation, and find the constant rate of change and the vertical intercept of the line. Explain how they are related to this situation.
Answer:
x=3.3333333333333333333333333333333
How do I evaluate P(3,3)
Answer:
The value of P(3,3) is 6
Step-by-step explanation:
We have to evaluate P(3,3)
As permutation can be calculated by the formula
Hence, the value of P(3,3) is 6
Find y. Simplify completely.
y=√9+√25
3+5
=8
division is addition
The perimeter of a rectangular lawn i 50 meter. It' 16 meter long how wide i it?
The width of the rectangle is 9 meter.
Now, According to the question:
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.
Now, Solving the problem:
Perimeter of rectangle is 50 meter sq.
Length of the rectangle(L) is 16 meter.
We have to find the width (W) of the rectangle.
We know that,
Perimeter of rectangle is = 2 (L + W)
50 = 2(16 + W)
50 = 32 + 2W
2W = 50 - 32
2W = 18
W = 18/2
W = 9
Hence, The width of the rectangle is 9 meter.
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17 The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6
Number on dice
Probability
1
2
0.17
3
4
0.18 0.09
5
0.15
6
0.1
Neymar rolls the biased dice 200 times.
Work out an estimate for the total number of times the dice will land on 1 or on 3
The total number of occasions the dice would land on 1 or 3 is 98.
What are the components of probability?The probability space associated with a randomly chosen experiment is established by three components: the result space, whose element is an experiment outcome, a collection of events F whose elements represent subsets of, and a probability measure IP assigned towards the elements in F.
How do you get good at probability?As a result, for problems like Cards, Coins, and Dices, it is preferable to record the potential scenarios and determine the individual probabilities of each case before ORing/ANDing them in accordance with the problem demand. If done correctly, this will provide a great solution that will never fail you.
According to the given data:All of the probability will add upto 1.
this give us the equation:
P(1)+0.17 + 0.18 + 0.09 + 0.15 + 0.1 = 1
P(1) + 0.69 = 1
P(1) = 1 - 0.69
P(1) = 0.31
We now need to find the probability of 1 or 3
P(1 or 3) = P(1) + P(3)
= 0.31 + 0.18
= 0.49
We now use the predicting outcomes formula.
expected = P(1 or 3) x no. of times.
= 0.49 x 200
= 98
the total number of times the dice will land on 1 or on 3 = 98.
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A shoe repairman is working with his assistant, who takes 1.5 times as long to repair a pair of shoes.
Together they can fix 10 pairs of shoes in six hours. How long does it take the repairman to fix one pair
of shoes by himself?
Answer:
1/2 or 0.5 hours
Step-by-step explanation:
r = time for repairman to fix one pair of shoes.
a = time for assistant to fix one pair of shoes.
a = r×1.5
x×r + y×a = 6
x = number of pairs of shoes repaired by repairman.
y = number of pairs of shoes repaired by assistant.
x+y = 10
y = 10-x
x = y×1.5 (based on the a/r ratio : as the assistant needs 1.5 times longer, the repairman will have repaired 1.5 times more pair of shoes in the same time)
y = 10 - y×1.5
y + y×1.5 = 10
2.5×y = 10
y = 4
=> x = 6
6×r + 4×r×1.5 = 6
6×r + 6×r = 6
12×r = 6
r = 6/12 = 1/2 or 0.5 hours
There Are 13 Girls And 17 Boys In Juan's Math Class Girls Are What Fraction Of The Class? Boys Are What Fraction? Girls= Boys=
Answer:
girls: 13/30
boys:17/30
Step-by-step explanation:
Answer:
13/30(girls) =0.43333333 repeating
Step-by-step explanation:
17/30(boys)=0.56666666 repeating
Hope this helped :D
The peace center is ready to reopen with a special rate. Tickets for the opening show cost 4.00 for adults and 1.50 for students. If 450 tickets were sold for a total of 925 on opening night, how many adults and students tickets were sold?
Answer:there were 100 adults and 350 children tickets sold .
Step-by-step explanation:
Step 1
let number of adult tickets sold be represented as x
and that of children be y
such that the total number of adult and children who attended the center will be expressed as
x+ y = 450------equation 1
and the total cost of tickets sold can be expressed as
4x+ 1.50 y= 925,...equation 2
Step 2--Solving
x+ y = 450------eqn1
4x+ 1.50 y= 925,...eqn 2
By elimination method , Multiply equation 1 by 4 and subtract equation 2 from the new equation formed
4x+ 4y= 1800 ----- eqn 3
-4x+ 1.50 y= 925 eqn 2
2.5y=875
y= 875/2.5
y=350
to fnd x
x+ y= 450
x= 450- 350
x= 100
Therefore there were 100 adults and 350 children tickets sold .
The population of a town,
y
,
increases at a rate of
4.6
%
each year. If the population of the town in the year
2000
was
57
,
000
people, which equation represents the population of the town
x
years after
2000
?
Answer:
hi
Step-by-step explanation:
The equation that represents the growth of the population of a town will be y = 57,000 × (1.046)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and r be the increasing rate.
The exponent is given as,
y = a(1 + r)ˣ
A town's (y) population grows at a pace of 4.6% each year. If the town had a population of 57,000 inhabitants in the year 2000.
Let 'x' be the number of years from 2,000. Then the equation is given as,
y = 57,000 × (1 + 0.046)ˣ
y = 57,000 × (1.046)ˣ
The equation that represents the growth of the population of a town will be y = 57,000 × (1.046)ˣ.
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Three circles of radius $s$ are drawn in the first quadrant of the $xy$-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the $x$-axis, and the third is tangent to the first circle and the $y$-axis. A circle of radius $r>s$ is tangent to both axes and to the second and third circles. What is $r/s$
Three circles of radius s are drawn in the first quadrant of the xy-plane.
\($r/s$\\\) =9/1 =9
Set \($s$\) =1 so that we only have to find \($r$\).
Draw the segment between the center of the third circle and the large circle; this has length \($r+1$\). We then draw the radius of the large circle that is perpendicular to the x-axis, and draw the perpendicular from this radius to the center of the third circle.
This gives us a right triangle with legs \($r-3,r-1$\)and hypotenuse \($r+1$.\)
The Pythagorean Theorem yields:
\($(r-3)^2 + (r-1)^2 = (r+1)^2$$r^2 - 10r + 9 = 0$$r = 1, 9$Quite obviously $r > 1$, so $r = 9 \boxed{(D)}$.\)
Three circles of radius s are drawn in the first quadrant of the x y -plane.
\($r/s$\\\) =9/1 =9
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Using the same facts as #16, how long would it take to pay off 60% of the a. About 45 months b. About 50 months c. About 55 months d. About 37 months
To calculate how long it would take to pay off 60% of the debt,
we can use the same facts as in problem #16. Let's go through the steps:
1. Determine the total amount of debt: Find the original debt amount given in problem #16.
2. Calculate 60% of the debt: Multiply the total debt by 0.6 to find the amount that represents 60% of the debt.
3. Divide the amount obtained in step 2 by the monthly payment: This will give us the number of months it will take to pay off 60% of the debt.
Now, let's apply these steps to the options provided:
a. About 45 months: To determine if this is the correct answer, we need to perform the calculations outlined above using the original debt amount and the monthly payment given in problem #16.
b. About 50 months: Same as option a, perform the calculations using the original debt amount and the monthly payment.
c. About 55 months: Perform the calculations outlined above using the original debt amount and the monthly payment.
d. About 37 months: Perform the calculations outlined above using the original debt amount and the monthly payment.
After performing the calculations for each option, compare the results with the options provided to find the correct answer.
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suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. what is the probability that the number will be more than 4 or odd? (enter your probability as a fraction.) 6/10 incorrect: your answer is incorrect.
Therefore, the probability of choosing a number that is more than 4 or odd is 1 or 100%.
To find the probability that the number chosen is more than 4 or odd, we need to add the probabilities of choosing a number that is more than 4 and the probability of choosing a number that is odd and subtract the probability of choosing a number that is both more than 4 and odd, since we would be double-counting this case.
The numbers more than 4 are 5, 6, 7, 8, 9, and 10. The odd numbers are 1, 3, 5, 7, and 9. The number that satisfies both conditions is 5, so we must subtract the probability of choosing 5 once.
Therefore, the probability of choosing a number that is more than 4 or odd is:
(6 + 5 - 1) / 10
= 10/10
= 1
So the probability is 1 or 100%.
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Factor the following binomials
I’ll give the Brainliest to who answers the question with and reasonable explanation.
When is the constant of proportionality the same as the unit rate when comparing two quantities?
A. Only when the two quantities are indirectly proportional
B. Only when the two quantities are directly proportional
C. Always
D. Never
Thank you!
Answer:
it's A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Just got it correct
The Point class represents x,y coordinates in a Cartesian plane. Which line of code appears completes this operator which transforms a Point by dx and dy? (Members written inline for this problem.) class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return _________________________;}
The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.
The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`
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A rectangular wooden chest is twice as long as it is wide. The top and sides of the chest are made of oak and the bottom is made of pine. The volume of the box is 0.25 cubic metres. The oak costs $2/m2 and the pine is $1/m2 Find the dimensions that will minimize the cost of making the chest. A cardhon
The cost of making the chest with these dimensions is approximately $3.83.
Let's start by finding an expression for the cost of making the chest in terms of its dimensions. The cost of the oak top and sides is given by:
cost of oak = 2lw + 2lh
where l is the length and w is the width of the chest, and h is the height (which we don't know yet). The cost of the pine bottom is given by:
cost of pine = lw
The total cost of making the chest is the sum of these two costs:
total cost = cost of oak + cost of pine
= 2lw + 2lh + lw
We want to minimize this cost subject to the constraint that the volume of the chest is 0.25 cubic metres. The volume of a rectangular box is given by:
volume = length × width × height
= lwh
Since the volume is given as 0.25 cubic metres, we have:
lwh = 0.25
We also know that the length is twice the width, so we can write:
l = 2w
Substituting this into the expression for volume, we get:
\(2w^{2h} = 0.25\)
Solving for h, we get:
\(h = 0.125/w^2\)
Substituting this expression for h into the expression for the total cost, we get:
total cost = \(2lw + 2(0.125/w^2)w + lw\)
= 2lw + 0.25/w
To minimize this cost, we can take the derivative with respect to w and set it equal to zero:
d(total cost)/dw =\(2l - 0.25/w^2 = 0\)
Solving for w, we get:
w = \(\sqrt{0.125/l)}\)
Substituting this value for w back into the expression for h, we get:
h = \(0.125/w^2 = 8l\)
Therefore, the dimensions that will minimize the cost of making the chest are:
length = 2w = \(2\sqrt{(0.125/l)}\)
width = w =\(\sqrt{0.125/l)}\)
height = h = 8
To find the cost of making the chest, we can substitute these values into the expression for the total cost:
total cost = 2lw + 0.25/w
= \(2\sqrt{(0.125/l} ) \times \sqrt{0.125/l)} \times 2 + 0.25/\sqrt{(0.125/l)}\)
= 4 × 0.125 + 0.25 × sqrt(l/0.125)
= 0.5 + 2\(\sqrt{2\) ≈ 3.83
Therefore, the cost of making the chest with these dimensions is approximately $3.83.
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A biologist studying ants started on day 1 with a population of 1500 ants. On day 2, there were 3000 ants, and on day 3, there were 6000 ants. The increase in an ant population can be represented using a geometric sequence.
What is the value of the account after 8 years, if interest is being paid at 2.3%, if no
other deposits or withdrawals are made? Write answer with just numbers, do not
type $ or use commas. Round to the nearest hundredth.
The value of the account after 8 years, if no other deposits or withdrawals are made is $1199.51
Calculating the amount after eight yearsTo calculate the value of an account after a certain period of time with a fixed interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial amount or principal
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)
Plugging in the values into the formula, we get:
A = 1000(1 + 0.023/1)^(1*8)
Evaluate
A = 1199.51
Therefore, the value of the account after 8 years with an interest rate of 2.3%, assuming an initial investment of $1,000 and no other deposits or withdrawals, is approximately $1199.51.
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A recipe for banana bread calls for 5 1/4 cups of flour to make 3 loaves of banana bread. how much is used to make 1 loaf of bread?
Answer:
1 3/4
Step-by-step explanation: