The number of cases of a new disease can be modeled by the quadratic regression equation y = –2x2 + 36x + 6, where x represents the year.
Which is the best prediction for the number of new cases in year 15?
A. 194
B. 96
C. 328
D. 614
Answer: B 96
Step-by-step explanation:
By evaluating the function in x = 15, we will see that in the year 15 there will be 96 cases.
Which is the best prediction for the number of new cases in year 15?
The function that predicts the number of cases in the year x is given by:
[tex]y = -2x^2 + 36x + 6[/tex]
So we just need to evaluate that function in x = 15, this means replacing x by 15.
[tex]y = -2*15^2 + 36*15 + 6 = 96[/tex]
So we can expect that in the year 15, there will be around 96 cases. Then the correct option is B.
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(4) use the method of lagrange multipliers to determine the maximum value of f(x, y) = x a y b (the a and b are two fixed positive constants) subject to the constraint x + y = 1. (assume x, y > 0.)
The maximum value of [tex]\(f(x, y)\)[/tex] is given by:
[tex]\(f\left(\frac{b}{a+b}, \frac{a}{a+b}\right) = \left(\frac{b}{a+b}\right)^a \left(\frac{a}{a+b}\right)^b\)[/tex]
To find the maximum value of the function [tex]\(f(x, y) = x^a y^b\)[/tex] subject to the constraint (x + y = 1, use the method of Lagrange multipliers.
Let's set up the Lagrangian function:
[tex]\(L(x, y, \lambda) = x^a y^b + \lambda(x + y - 1)\)[/tex]
Taking the partial derivatives and setting them to zero:
Equation 1: [tex]\(\frac{\partial L}{\partial x} = a x^{a-1} y^b + \lambda = 0\)[/tex]
Equation 2: [tex]\(\frac{\partial L}{\partial y} = b x^a y^{b-1} + \lambda = 0\)[/tex]
Equation 3: [tex]\(\frac{\partial L}{\partial \lambda} = x + y - 1 = 0\)[/tex]
From equations (1) and (2) it can be written as
Equation 4: [tex]\(a x^{a-1} y^b = -\lambda\)[/tex] ... (4)
Equation 5: [tex]\(b x^a y^{b-1} = -\lambda\)[/tex] ... (5)
Dividing equation (4) by equation (5) gives
[tex]\(\frac{a}{b} \frac{x^{a-1}}{x^a} \frac{y^b}{y^{b-1}} = 1\)[/tex]
[tex]\(\frac{a}{b} \frac{y}{x} = 1\)[/tex]
From equation (3) [tex]\(y = 1 - x\)[/tex].
Substituting [tex]\(y = 1 - x\)[/tex] into the equation [tex]\(\frac{a}{b} \frac{y}{x} = 1\)[/tex]
[tex]\(\frac{a}{b} \frac{1-x}{x} = 1\)[/tex]
[tex]\(a x = b (1-x)\)[/tex]
[tex]\((a + b) x = b\)[/tex]
[tex]\(x = \frac{b}{a+b}\)[/tex]
Substituting [tex]\(x = \frac{b}{a+b}\)[/tex] into the constraint equation (3):
[tex]\(y = 1 - x[/tex]
[tex]= 1 - \frac{b}{a+b} = \frac{a}{a+b}\)[/tex]
Therefore, the critical point (x, y) that satisfies the constraint equation is:
[tex]\(x = \frac{b}{a+b}\) and \(y = \frac{a}{a+b}\)[/tex]
Therefore, the critical point gives the maximum value of the function [tex]\(f(x, y) = x^a y^b\)[/tex] subject to the constraint x + y = 1.
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Combine like terms: –10.9p + 3.9 = –9.18 Apply the next steps to solve the equation. What is the solution? p =
Answer:
P=1.2
Step-by-step explanation:
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If you know that a < b, and both a and b are positive numbers, then what must be true about the relationship between the opposites of these numbers? Explain.
Answer: just copy and paste
We want to find the relationship between the opposites of a and b, given that both are positive and a < b.
That relation is:
-a > -b.
Remeber that the opposite of a real number is just -1 times that number.
The opposite of a is: -a
The opposite of b is: -b
Remember that for negative numbers, the closer the number is to zero, the larger is the number.
Because we know that a and b are positive, and a < b, then we know that a is closer to zero.
So for -a and -b, we know that -a is also closer to zero (then -a is larger than -b), so the relationship between these two is:
-a > -b.
When a < b and both a and b are positive numbers, the opposites of these numbers will have opposite signs.
Explanation:In mathematical terms, when two positive numbers add, the answer has a positive sign. Similarly, when two negative numbers add, the answer has a negative sign. However, when a negative number is added to a positive number, the answer will depend on the magnitudes of the numbers:
If the positive number is greater than the negative number, the answer will have a positive sign.If the positive number is smaller than the negative number, the answer will have a negative sign.So, in the given scenario where a < b, if both a and b are positive numbers, the opposites of these numbers will have opposite signs.
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Solve the system of equations using elimination. 2x + y = 9 8x – 2y = 6
A $15,000, 11%, 120-day note dated Sept. 3, is discounted on Nov. 11. Assuming a bank discount rate of 9%, the proceeds would be
write the rule that applies to the following number:0÷7=0
Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?
Which function can be used to find the nth term of the arithmetic sequence?
Complete the following statements in relation to the third term in the expansion of the binomial (2x+y^2)^5
Answer:
coefficient = 80
The power of x = 3
The power of y = 4
Step-by-step explanation:
did the test on plato/edmentum and got it right
Section J in an arena has 20 rows. Each row has 15 seats. Our tickets cost $18 each. If all the seats are sold, how much money with the Arena collect the section J
Δ ABC is isosceles. Angles B and C are congruent. If m∠B = (5x + 5)° and m∠C = (7x - 25)°, Find m∠A. A) 10° B) 15° C) 20° D) 80°
Answer:
option C
[tex]20\°[/tex]
Step-by-step explanation:
we know that
An isosceles triangle has two equal angles and two equal sides. The two equal angles are the base angles and the third angle is the vertex angle
In this problem the base angles are angle B and angle C
so
m∠B=m∠C
substitute
[tex](5x+5)\°=(7x-25)\°[/tex]
[tex](7x-5x)\°=(5+25)\°[/tex]
[tex]2x=30\°[/tex]
[tex]x=15\°[/tex]
m∠B=[tex](5x+5)\°=5*15+5=80\°[/tex]
Remember that the sum of the internal angles of the triangle is equal to [tex]180\°[/tex]
Find m∠A
m∠A=[tex]180\°-2*80\°=20\°[/tex]
Suppose your statistics professor reports test grades as z-scores, and you got a score of 2.20 on
ron has a 4 1/2 pound bag of beans. he wants to sell the beans in 2/3 pound bags. how many whole bags can he fill?
what is the perimeter of the trapezoid graphed below?
fill in the table using this function rule. y=-4x+2
x y
-1
0
1
2
To fill in the table using the function rule y = -4x + 2, substitute the given x-values into the equation and solve for y.
To fill in the table using the function rule y = -4x + 2, substitute the given x-values into the equation and solve for y.
For x = -1, substitute x = -1 into the equation: y = -4(-1) + 2
For x = 0, substitute x = 0 into the equation: y = -4(0) + 2
For x = 1, substitute x = 1 into the equation: y = -4(1) + 2
For x = 2, substitute x = 2 into the equation: y = -4(2) + 2
By evaluating the expressions, you will obtain the corresponding y-values for each x-value.
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Bennett tried to solve exercise 1 a few different ways. Which of his methods are correct? Of the other methods, which makes the most sense to you? Explain
A. 5% sales tax means that for every dollar you spend, you need to pay a nickel in tax. If you buy a nickel tax. If you buy something for $21, you need to pay 21 nickels in tax.
B. You can set up a promotion and solve for the missing value.
$.05 = x <-- (These are fractions)
___ __
$1.00 $21.00
C. If you know that 10% of $21 is $2.10, so 5% should be half of $2.10
D. 5% is equal to 1/20. To find the amount of tax on $21, find $21 ÷ 20
E. 1% of $21.00 is $0.21 so 5% of $21.00 is 5 x $ 0.2
what is the answer to this including shown work?
Solve 5x + 7 > 17. {x | x < 2} {x | x > 2} {x | x < -2} {x | x > -2}
Answer:
The solution set for the provided inequity is {x | x > 2}.
Step-by-step explanation:
Consider the provided inequity.
[tex]5x+7>17[/tex]
Subtract both the side by 7.
[tex]5x+7-7>17-7[/tex]
[tex]5x>10[/tex]
Now divide both the side by 5.
[tex]\frac{5x}{5}>\frac{10}{5}[/tex]
[tex]x>2[/tex]
Hence, the solution set for the provided inequity is {x | x > 2}.
Find the equation of the tangent plane to (a) z = 4x 2 − y 2 + 2y at (−1, 2, 4)
Mrs. Carothers is considering reserving a room at the Hotel Indigo for a trip to Fox Theater. Hotel Indigo charges $717 for a 3 night stay.
Mrs. Carothers looked at another hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and show your work
At a certain college, the probability that a student attends full-time is 0.320 and the probability that the student attends part-time is 0.680. At the same college, the probability that a student receives financial aid is 0.570 while the probability that a student does not receive financial aid is 0.430. If a student is randomly selected, what is the probability that the student attends full-time and does not receive financial aid?
the probability that a randomly selected student attends full-time and does not receive financial aid is ( 0.1376 ), or ( 13.76% ).
To find the probability that a student attends full-time and does not receive financial aid, we can use the multiplication rule for independent events.
Given:
- Probability of attending full-time: [tex]\( P(\text{full-time}) = 0.320 \)[/tex]
- Probability of not receiving financial aid:[tex]\( P(\text{no financial aid}) = 0.430 \)[/tex]
By the multiplication rule, the probability of both events occurring is the product of their individual probabilities:
[tex]\[ P(\text{full-time and no financial aid}) = P(\text{full-time}) \times P(\text{no financial aid}) \][/tex]
[tex]\[ = 0.320 \times 0.430 \][/tex]
[tex]\[ = 0.1376 \][/tex]
Therefore, the probability that a randomly selected student attends full-time and does not receive financial aid is ( 0.1376 ), or ( 13.76% ).
Which fraction is equal to 0.20%? 1/20 1/40 1/50 1/400 1/500
Henry invest 4500 at a compound interest rate of 5% per annum. At the end of n complete years the investment has grown to 5469.78. Find the value of n
The value of n is 4. This means that it took 4 years for the investment to grow to £5469.78.
How to calculate the value of nWe can use the compound interest formula to solve this problem:
A = P(1 + r/n)nt
where:
A is the future value of the investment
P is the principal amount invested
r is the annual interest rate
n is the number of times per year the interest is compounded
t is the number of years
In this problem, we have the following information:
A = 5469.78
P = 4500
r = 0.05 (5%)
n = ?
t = n
We can plug these values into the formula and solve for n:
5469.78 = 4500(1 + 0.05/n)n
1.2155066 = (1.05)n
n = 4
Therefore, the value of n is 4. This means that it took 4 years for the investment to grow to £5469.78.
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a graduated cylinder is filled to 41.5 ml with water and a piece of granite is placed in the cylinder displacing the level to 47.6 ml what is the volume of the granite piece in cubic centimeters?
The volume of the piece of granite is 6.1 cubic cm if the graduated cylinder is filled to 41.5 ml with water and a piece of granite is placed in the cylinder, displacing the level to 47.6 ml.
What is volume?
It is defined as a three-dimensional space enclosed by an object or thing.
We have:
Volume of the water filled in the cylinder = 41.5 ml
Volume after placing the piece of granite = 47.6 ml
The volume of the piece of granite = 47.6 - 41.5 = 6.1 ml
As we know 1 ml = 1 cm³
The volume of the piece of granite = 6.1 cubic cm
Thus, the volume of the piece of granite is 6.1 cubic cm if the graduated cylinder is filled to 41.5 ml with water and a piece of granite is placed in the cylinder displacing the level to 47.6 ml.
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Write the steps for how to use a number line to multiply a 2 digit number by 20
A combination lock uses three distinctive numbers between 0 and 49 inclusive. how many different ways can a sequence of three numbers be selected? (show work)
solve for w w- 8=32
answer choices
4
24
40
256
On a map, 12 inch represents 45 mile.
What distance on the map represents 1 mile?
A 2/5 in.
B 5/8 in.
C 1 3/5 in.
D 2 1/2 in.
5/8 in.
i just took a test.
Bills had enough to buy no more than 1/2 pound of cheese. How much cheese could he buy?
Bill can buy less than or equal to (≤) a 1/2 pound of cheese.
Hope this answers the question.