The vector c for this SDP problem is (0, 1, 0).
The semidefinite programming problem (SDP) is given as follows:
{(x, y, z):〈c, x〉 + 2 〈(0, 0, 1), yz〉 → max; x ∈ R², y ∈ R³, yᵀ Q y + 〈(1, 0), x〉 ≤ 1},where Q is the matrix(1, 0, 0;0, 1, 0;0, 0, 0).
The given SDP problem is{(x, y, z):〈c, x〉 + 2 〈(0, 0, 1), yz〉 → max; x ∈ R², y ∈ R³, yᵀ Q y + 〈(1, 0), x〉 ≤ 1},where Q is the matrix(1, 0, 0;0, 1, 0;0, 0, 0).
We need to find the vector c that should be used in the SDP.
Let us consider each vector from the given options one by one.
(0, 0, 1): The first term of the objective function is zero because x ∈ R².
The second term becomes 2z, which is non-zero when z is non-zero.
Hence, this is not the correct choice.(1, 0): The first term of the objective function becomes x₁, which is non-zero in general.
Hence, this is not the correct choice.(0, 1):
The first term of the objective function becomes x₂, which is non-zero in general.
Hence, this is not the correct choice.(0, 1, 0): The first term of the objective function becomes x₃, which is zero in general.
Hence, this is the correct choice.
Therefore, the vector c for this SDP problem is (0, 1, 0).
Hence, option 4 is the correct choice.
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Which of the following functions is graphed below?
Answer:
non of the above thanks
don't ask me again please
Answer:
where are the functions ???
Step-by-step explanation:
A(n) ______________ is an approximate answer
Answer:
approximation
Step-by-step explanation:
A(n) approximation is an approximate answer.
Answer:
\(\boxed{\red{approximation}}
\)
Step-by-step explanation:
\(A(n)\blue{ \: \: approximation}
\: \: is \: \: \\ an \: \: \: approximate \: \: \: answer
\)
hope this helps you.
Archaeopteryx often is referred to as a transitional fossil because its fossils suggest that it is an intermediate organism between dinosaurs and birds. Transitional forms in the fossil record, such as Archaeopteryx, provide evidence for which pattern of evolution
Transitional forms in the fossil record, including Archaeopteryx, provide evidence for the pattern of evolution known as "gradualism."
This pattern suggests that species change over time through a slow and continuous process of accumulation of small, incremental changes. Transitional fossils like Archaeopteryx exhibit characteristics that are intermediate between two different groups of organisms, indicating a gradual transition from one form to another.
The presence of transitional fossils supports the idea that species do not undergo abrupt transformations but instead evolve gradually over long periods of time.
These fossils provide a tangible link between different groups of organisms, such as dinosaurs and birds in the case of Archaeopteryx, and offer evidence for the gradual transformation of one group into another. This supports the broader concept of evolution as a slow and continuous process of change in populations over generations.
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Here is my question.
Answer: True False True true
Step-by-step explanation:
Answer:
true
false
true
true
Step-by-step explanation:
What function is graphed below?
Answer:
\(y\ =\ \ \tan\theta\ +2\)
Step-by-step explanation:
20 Points. will give brainliest.
Which one doesn't belong?
Answer:
Depends, either option 3 or 4. I would say 4
Step-by-step explanation:
1,2,3 have the same line, just rotated, and 4's line is different
1,2,4 all start at the origin, tho
How long would it take R20000 invested today at a simple interest rate of 9% p.a. to reach an investment goal of R30000.
A Approximately 5.6 years
B Approximately 6.1 years
C Approximately 4.7 years
D Approximately 5.1 years
\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)
What numbers are least to greatest 1/2,1/4,1 and3/4, 1.5, 1.75
One way to solve the exercise is to view the fractions in decimal form and then order the numbers from least to greatest. So, you have
\(\begin{gathered} \frac{1}{2}=0.5 \\ \frac{1}{4}=0.25 \\ 1\frac{3}{4}=\frac{1\cdot4+3}{4}=\frac{4+3}{4}=\frac{7}{4}=1.75 \\ 1.5=1.5 \\ 1.75=1.75 \end{gathered}\)Now, to order the decimal numbers, first compare their whole part, then the tenths, and then the hundredths. So you have
\(\begin{gathered} 0.25 \\ 0.5 \\ 0.75 \\ 1.7 \\ 1.75 \\ 1.75 \end{gathered}\)Therefore,
-x = 10
I will____ both sides by_____
x= _____
Answer:
I will subtract both sides by 10. X=-10
Step-by-step explanation:
X= -10 because if you subtract it to -x it will cancel out the negative.
Answer:
I will divide both sides by -1.
x = -10
Step-by-step explanation:
To solve this, we have to isolate x on one side of the equation. In this equation, 10 = -x.
Remember that the coefficient of a single variable is always 1, so 1x = x. We have -x, which means it's actually -1x. Solve using -1x instead of -x.
\(-x=10\)
\(-1x=10\)
Divide both sides by -1 to isolate x.
\(\frac{-1x}{-1} =\frac{10}{-1}\)
Simplify.
\(x = -10\)
x is equal to -10.
The answer is I will divide both sides by -1.
x = -10
I hope this helps :)
Using technology, we found that Juan's investment account can be modeled by the function, c(x)=3x2-2x+10, in
thousands of dollars. What was Juan's initial investment?
O $5
o $10
o $5,000
$10,000
Answer:
$10
Step-by-step explanation:
"Initial" here means "beginning." That is, time = x = 0. If we let x = 0 here we get c(0) = 10, which is the desired answer. Juan's initial investment was $10.
Pls help me thanks :)))
Answer:
y = - 1 , y = 17
Step-by-step explanation:
y² - 16y + 64 = 81 ← y² - 16y + 64 is a perfect square
)y - 8)² = 81 ( take the square root of both sides )
y - 8 = ± \(\sqrt{81}\) = ± 9 ( add 8 to both sides )
y = 8 ± 9
then
y = 8 - 9 = - 1
x = 8 + 9 = 17
which is the largest living thing?
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1210 1331
Option 2 (amount in dollars) 1100 1200 1300
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.
B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;
Option 1; f(n) = n + 100
Option 2; f(n) = n + 100x
C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900
How to solve Linear functions?A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.
For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.
B) For option 1, the function is;
f(n) = n + 100
For option 2, the function is;
f(n) = n + 100x
C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.
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If the length of a is 6, the length of b is 4, and the length of c is 7, what is the measure of angle B
Answer:
B = 34.77°
Step-by-step explanation:
For this problem you are given all three side lengths and asked to find an angle. To do this you can use the law of cosines which is written:
\(b^{2} =a^{2} +c^{2} -2ac Cos(B)\)
This can be rearranged to find the angle B:
\(b^{2} -a^{2} -c^{2} /-2ac = Cos(B)\)
With lowercase letters being sides and uppercase being angles.
We simply plug in the sides and solve:
\(4^{2} -6^{2} -7^{2}/-2*6*7= Cos(B)\)
0.8214 = Cos (B)
Then you use inverse cosine to get angle B alone.
B = 34.77°
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the circle graph shown below to answer the question.
A pie chart labeled Favorite Sports to Watch is divided into three portions. Football represents 42 percent, baseball represents 33 percent, and soccer represents 25 percent.
If 210 people said football was their favorite sport to watch, how many people were surveyed?
Natalie picked 135 berries in 15 minutes. If she continues picking at that rate, how many total minutes will it take her to pick 486 berries?
a. Find the unit price for each option shown below. Round to the nearest cent when necessary.
Option I: 10 candy bars for $6.75
Option II: 12 candy bars for $7.25
b. Which option is the better buy.
Solve the proportion.
16
50
=
x
156
.
25
A jacket's original price is $65.00. It is on sale for 40% off. You have to pay 5% sales tax. What is the final price for the jacket?
A) 500
B) 54 minutes
C) 68cents and 60 cents
D)
E) $40.95
ProportionsA proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.
Proportions can be written as equivalent fractions or as equal ratios.
A) 42% = 210
100% = (210 x 100)/42
= 500 people
B) 135 berries = 15 minutes
486 berries = ??minutes
= (486 x 15)/135
= 54 minutes
C) unit price = $6.75/10 = 0.675cents or 68cents
ii) unit price = $7.25/12 = 0.604cents or 60cents
D) Inconclusive question.
E) 40% of 65 = $26
65 - 26 = $39
Tax = 5% = $1.95
Total = $39 + 1.95
Final Price of jacket = $40.95
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You have a coin collection of nickels and dimes containing 63 coins. If you have
$5.05, how may of each coin do you have?
Answer: 25 nickels
Step-by-step explanation:
EQUATIONS:
quantity: n + d = 63
value: 5n + 10d = 505
-------------------------
Divide thru the 2nd equation by 5 to get:
n + 2d = 101
----------------
Subtract that from the 1st equation:
-d = -38
d = 38 (# of dimes)
---------------
Substitute that into n+d=63 to solve for "n":
n + 38 = 63
n = 25 (# of nickels)
suppose we want to estimate the mean quality ratings for the dfw airport. a simple random sample of 25 travelers at this airport is selected and each traveler is asked to provide a rating for this airport. the maximum possible rating is 5. the sample provided a mean of 3.84 and a standard deviation of 0.55. assume the population of ratings is approximately normal. an 80% confidence interval estimate of the population mean rating is:
The 80% confidence interval estimate of the population mean rating for DFW airport can be calculated using the formula:
Margin of error = (Z-score)*(standard deviation/sqrt(sample size))
where the Z-score for 80% confidence level is 1.28.
So, the margin of error = (1.28)*(0.55/sqrt(25)) = 0.28.
Therefore, the confidence interval estimate can be calculated by subtracting and adding the margin of error to the sample mean:
Confidence interval = sample mean ± margin of error
Confidence interval = 3.84 ± 0.28
Confidence interval = (3.56, 4.12)
The question requires us to find an 80% confidence interval estimate for the population mean rating of DFW airport using a sample of 25 travelers. The formula for the margin of error is used to calculate the range of values within which the population mean is likely to fall. The Z-score for the 80% confidence level is used in the formula. We then use this margin of error to calculate the confidence interval estimate by adding and subtracting it from the sample mean. This gives us a range of values within which we can be confident that the population mean rating falls.
The 80% confidence interval estimate for the population mean rating of DFW airport is (3.56, 4.12). This means that we can be 80% confident that the population mean rating falls within this range of values. The sample mean of 3.84 is the best estimate of the population mean rating, and the margin of error of 0.28 indicates the level of uncertainty in this estimate.
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Use properties of parallel lines to find the value of x.
Answer:
x = 73
Step-by-step explanation:
x-5 = 68 due to parallel lines
Which of the following is a factor of x
3
+ 1000?
Answer:
can you please make your question clear
1. Solve.
: 1/2 divided by 2/1
Answer:
The answer to this one is 0.25
A company has a machine that makes "acceptable" products 98% of the time. If 600 random products are tested, what is the varlance for acceptable products in the sample?
The variance for acceptable products in the sample is 11.76.
How to find the variance for acceptable products in the sample?The variance for a random variable X representing the number of acceptable products in the sample can be determined using the formula:
Var(X) = n * p * (1 - p)
Where:
n is the number of products in the sample
p is the probability of a product being acceptable
In this case, n = 600 and p = 98% = 0.98
Substituting the values into the formula:
Var(X) = 600 * 0.98 * (1 - 0.98)
Var(X) = 600 * 0.98 * 0.02
Var(X) = 11.76
Therefore, the variance for acceptable products in the sample is 11.76.
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a marksman has a probability of 0.623 for hitting a certain long range target. what is the probability that it takes 4 shots for the marksman to hit the long range target?
The probability that it takes 4 shots for the marksman to hit the long-range target is approximately 0.1466, or 14.66%.
To calculate the probability that it takes 4 shots for the marksman to hit the long-range target, we assume each shot is independent and has a success probability of 0.623. The probability of hitting the target on the fourth shot can be calculated using the binomial distribution. The formula for the probability mass function (PMF) of the binomial distribution is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of exactly k successes,
n is the number of trials,
k is the number of successful trials,
p is the probability of success on a single trial, and
C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! * (n - k)!)
In this case, n = 4 (the number of shots), k = 4 (the number of successful shots), and p = 0.623 (the probability of hitting the target on each shot). Substituting these values into the formula, we can calculate the probability:
P(X = 4) = C(4, 4) * 0.623^4 * (1 - 0.623)^(4 - 4)
C(4, 4) = 4! / (4! * (4 - 4)!) = 1
P(X = 4) = 1 * 0.623^4 * (1 - 0.623)^(4 - 4)
= 1 * 0.623^4 * 1
= 0.623^4
= 0.1466
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find the product of the integers 2(-4)
Answer:
-8
Step-by-step explanation:
2(4)=8, and a negative number times a positive number results in a negative number.
At the rate shown in the table, how many weeks did it take to sell 700 books? [Type your answer as a number.]
Answer:
3
Step-by-step explanation:
Answer:
10 weeksI hope this help you
To prove angle ABC is isosceles?
Step-by-step explanation:
m < (CAB ) = m < ( c B A ).....
A doctor is using a treadmill to assess the strenght of a patient's heart. He sets the 48-inch long treadmil at an incline of 10⁰,how high is the end of the treadmill raised
The end of the 48-inch long treadmill is raised approximately 8.36 inches.
The incline of the treadmill is given as 10 degrees.
We can use trigonometry to calculate the height of the end of the treadmill.
The height (h) can be found using the formula h = l * sin(θ), where l is the length of the treadmill and θ is the angle of inclination.
Substitute the values into the formula:
h = 48 inches * sin(10 degrees)
Calculate the sine of 10 degrees using a calculator:
sin(10 degrees) ≈ 0.1736
Multiply the length of the treadmill by the sine of the angle:
h = 48 inches * 0.1736 ≈ 8.36 inches
The end of the 48-inch long treadmill is raised approximately 8.36 inches when set at an incline of 10 degrees.
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Two customers took out loans from a bank.
Jacob took out a 3-year loan for $8,000 and paid 4.2% annual simple interest
Christian took out a 5-year loan for $8,000 and paid 3.9% annual simple interest.
What is the difference between the amounts of interest Jacob and Christian paid for their loans?
A.635.59
B.1560.00
C.1008.00
D.552.00
The difference between the amounts of interest Jacob and Christian paid for their loans is $552.
To calculate the amount of interest paid by Jacob and Christian, we can use the simple interest formula:
Interest = Principal x Rate x Time
Where,
Principal: the amount of the loan
Rate: the annual interest rate
Time: the duration of the loan in years
For Jacob's loan:
Principal = \(\$8,000\)
Rate = 4.2%
Time = 3 years
Interest = \(\$8,000 * 4.2\% * 3 = \$1,008\)
Therefore, Jacob paid $1,008 in interest.
For Christian's loan:
Principal = \(\$8,000\)
Rate = 3.9%
Time = 5 years
Interest = \(\$8,000 * 3.9\% * 5 = \$1,560\)
Therefore, Christian paid $1,560 in interest.
The difference between the amounts of interest Jacob and Christian paid for their loans is:
\(\$1,560 - \$1,008 = \$552\)
Therefore, the answer is D. \(\$552\).
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sarah has a coupon 25% off any item at the big fish store. If she buys an item reguarly marked $60, What is her sale price?
Answer:
$45
Step-by-step explanation:
60×0.75=45
Hope this helps
At the big fish store, Sarah has a coupon good for 25% off any purchase. She will pay $45 for a $60 item if she purchases it at a reduced price.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that Sarah has a coupon for 25% off any item at the big fish store. If she buys an item regularly marked $60,
Sale price =Original price - discount
Sale price = $60 - 25% of $60
Sale price = $60 - $ 15
Sale price = $45
Thus, at the big fish store, Sarah has a coupon good for 25% off any purchase. She will pay $45 for a $60 item if she purchases it at a reduced price.
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Jane belongs to a book club. She pays a flat fee of $8 to ship any number of books. She is able to purchase
the books for $10 each. Which of the following choices shows the expression that represents
1. Jane's situation and
2. how much it would cost her if she bought 8 books?
a. 10+8b, the cost would be $88.
b. 8+10b, the cost would be $88.
C. 8+10b, the cost would be $74.
d. 10+8b, the cost would be $74.
Answer:
b.8+10b,the cost would be $88
Step-by-step explanation:
if she buys 8 books worth $10 each
so 8×10= 80
plus $8 for shipment
so $80 +$8 =$88
Robert and Tony love to read. Robert reads 30 pages the first day and 20 pages each day after that. Tony reads 40 pages the first day and 15 pages each day after that. Will the boys ever read the same amount of pages? If so, how many days will it take them to read the same number of pages? A. Yes. They will read the same amount of pages in 3 days. B. Yes. They will read the same amount of pages in 5 days. C. Yes. They will read the same amount of pages in 6 days. D. No. They will never read the same amount of pages.
Answer:
Yes they will read the same amount of pages in 3 days
Step-by-step explanation:
Because when you do the math they add up to the same amount of pages.
The correct statement is;
''Yes. They will read the same amount of pages in 2 days.''
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Robert reads 30 pages the first day and 20 pages each day after that.
And, Tony reads 40 pages the first day and 15 pages each day after that.
Now,
Let the number of days for same pages read = x
So, We can formulate;
For Robert;
Number of pages = 30 + 20x
For Tony;
Number of pages = 40 + 15x
For equal days, we get;
⇒ 30 + 20x = 40 + 15x
Solve for x as;
⇒ 20x - 15x = 40 - 30
⇒ 5x = 10
⇒ x = 2
Thus, The correct statement is;
''Yes. They will read the same amount of pages in 2 days.''
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