To minimize the function Q=x^2+2y^2, substitute x=3-y and expand the expression. Use the vertex formula to find the minimum value of Q. The minimum value is 13.5 when x=1.5 and y=1.5.
Explanation:To minimize the function Q=x^2+2y^2, where x+y=3, we can substitute x=3-y into the function to get Q=(3-y)^2+2y^2. Expanding this expression gives Q=9-6y+y^2+2y^2. Combining like terms, we have Q=3y^2-6y+9.
To find the minimum value of Q, we can use the vertex formula. The x-coordinate of the vertex of the parabola represented by Q=a(x-h)^2+k is x=-h. In our case, h=-(-3)/2=1.5. Substituting this value of x into the equation Q=3y^2-6y+9 gives Q=3(1.5)^2-6(1.5)+9=13.5-9+9=13.5.
Therefore, the minimum value of Q is 13.5 when x=1.5 and y=1.5.
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When making a statistical inference about the mean of a normally distributed population based on a sample drawn from that population, which of the following statements is correct, all else being equal?
The 68% confidence interval is wider than the 90% confidence interval.
The 90% confidence interval is narrower than the 95% confidence interval.
The 90% confidence interval is wider than the 99% confidence interval.
The 99% confidence interval is narrower than the 68% confidence interval
Vanessa deposited money into a bank account that earned 1.25% simple interest each year. After 1/2 year, she had earned $5.00 in interest on the account. If no other money was deposited into or withdrawn from the account, how much was her initial deposit
why wouldn't the man stand in line to step on the scale ?
answer ?
The man wouldn't stand in line to step on the scale because the scale measures weight, not mass. When you stand on a bathroom scale, it measures the force exerted on it due to your weight. Weight is the force of gravity acting on an object, while mass is the amount of matter in an object.
Explanation:The man wouldn't stand in line to step on the scale because the scale measures weight, not mass. When you stand on a bathroom scale, it measures the force exerted on it due to your weight. Weight is the force of gravity acting on an object, while mass is the amount of matter in an object. So, if the man were on the Moon or in an elevator accelerating, the scale reading would be different because the force of gravity on him would be different, but his mass would remain the same.
Samantha had 7/8 of a yard of ribbon. She used 1/6 of a yard for a bow. How much ribbon does Samantha have left?
Which word phrase represents this expression?
g + 24
A.the sum of g and 24
B.the sum of g and 26
C.the difference of 24 and some g
D. the difference of g and 24
What is the difference between 7 and -8?
Farmer Ed has 7000 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed? ...?
Let
x--------> the length side of the rectangular plot (assume side along the river)
y------> the width side of the rectangular plot
we know that
the perimeter of the rectangular plot is equal to
[tex]P=x+2y[/tex]
[tex]P=7,000\ m[/tex]
so
[tex]7,000=x+2y[/tex]
Clear variable y
[tex]y=(7,000-x)/2[/tex] -------> equation [tex]1[/tex]
The area of the rectangular plot is
[tex]A=x*y[/tex] ------> equation [tex]2[/tex]
substitute equation [tex]1[/tex] in equation [tex]2[/tex]
[tex]A=x*[(7,000-x)/2][/tex]
[tex]A=x*[(7,000-x)/2]\\\\ A=3,500x-0.5x^{2}[/tex]
we know that
To find the larger area that can be enclosed------> Find the vertex of the quadratic equation
The quadratic equation is a vertical parabola open down
so
the vertex is a maximum
using a graphing tool
see the attached figure
the vertex is the point [tex](3,500,6,125,000)[/tex]
that means
For [tex]x=3,500\ m[/tex]
the largest area is [tex]6,125,000\ m^{2}[/tex]
Find the value of y
[tex]y=(7,000-3,500)/2=1,750\ m[/tex]
the dimensions of the rectangular plot are
[tex]Length=3,500\ m\\Width=1,750\ m[/tex]
therefore
the answer is
The largest area that can be enclosed is [tex]6,125,000\ m^{2}[/tex]
The cone pictured has a surface area of ______ square centimeters. (Use 3.14 for π.)
A friend rewrote the expression 5(x 2) as 5x 2.write a few sentences to your friend explaining the error. then rewrite the expression 5(x 2) correctly
What are the x and y intercept of (0,0), (10,106), (15,159), (20,212), (30, 318) ?
Solve Equation
x^2 -4x +8 = 0
Let h(x)=xg(x), where g(x)=the inverse of f(x). Find h'(5) using the chart.....(type that in a minute) ...?
Which is the graph of the linear inequality y < 3x + 1?
Answer:
Graph is attached below
Step-by-step explanation:
[tex]y < 3x + 1[/tex]
To graph the inequality , we replace < symbol by = sign
[tex]y=3x + 1[/tex]
Now we graph the given equation by making a table
x y=3x+1
-1 -2
0 1
1 4
Graph all the points (-1,-2) (0,1) (1,4) and make a line
Now we do shading using test point (0,0)
[tex]0< 3(0) + 1[/tex]
[tex]0<1[/tex] True
So we shade the region that has test point (0,0)
the graph is attached below
Regular hexagon ABCDEF is inscribed in a circle with a radius of 2 units.
Find measure of central angle AGF
apothem a=GH
side length s=
perimeter P=
hexagon area A=
Add.
(3x4 – 2x3 + 1) + (12x4 + x2 – 11)
Answer
15x4 – 2x3 + x2 + 10
15x4 – x3 – 10
15x4 – x2 – 10
15x4 – 2x3 + x2 – 10
...?
11-8 The Choi Company's next expected dividend, D1, is $3.18; its growth rate is 6 percent; and its stock currently sells for $36. New stock can be sold to net the firm $32.4 per share.
a. What is Choi's percentage flotation cost, F?
b. What is Choi's cost of new common stock, Re ?
Choi's percentage flotation cost is 10%, and the cost of new common stock is 15.81%, calculated using the difference in current stock price and net price per share for the flotation cost, and the dividend discount model for the cost of new common stock.
Explanation:Calculating Choi's Flotation Cost and Cost of New Common Stock
The percentage flotation cost of Choi Company's new stock is 90.28% and the cost of new common stock is 15.94%.
To calculate Choi's percentage flotation cost (F), we start by looking at the difference between the price the stock currently sells for and the net amount the firm receives when selling new stock. The current stock price is $36, and the firm can net $32.4 per share from selling new stock, so the flotation cost per share is $36 - $32.4 = $3.6 per share. To find the percentage flotation cost, we divide this amount by the market price of the stock:
F = Flotation cost per share / Current stock price = $3.6 / $36 = 0.10 or 10%
Next, to calculate Choi's cost of new common stock (Re), we use the dividend discount model (DDM), which claims that the price of a stock is the present value of all future dividends. The expected dividend, D1, is $3.18 and the growth rate, g, is 6%. The cost of new common stock, taking into account the flotation cost, is calculated using the formula:
Re = (D1 / Net price per share) + g = ($3.18 / $32.4) + 0.06 = 0.0981 + 0.06 = 0.1581 or 15.81%
if p= 1/3 what is the answer to 9p2=
When p equals 1/3, 9p^2 calculates to 1 after squaring p and multiplying by 9.
The question involves calculating the expression 9p^2 given that p = 1/3. First, we square the value of 'p' and then multiply it by 9. Following the process, we have:
[tex](\frac{1}{3} )^2 = \frac{1}{9} \\9 \times (\frac{1}{9} ) = 1[/tex]
Therefore, 9p^2 is equal to 1 when p is equal to 1/3.
In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
A. 20 degrees
B. 30 degrees
C. 120 degrees
D. 180 degrees
You have a gift card for your favorite clothing store for the amount of $60. You have found a shirt you want for $15. You don't want to spend more than the amount of the gift card, which of the following inequalities could be used to determine the amount you have left to spend?
x+15 is greater than or equal to 60
x-15 is greater than or equal to 60
x+15 is less than or equal to 60
x-15 is less than or equal to 60
Let
x--------> the amount you have left to spend
y--------> the cost of a shirt you want
z------> the amount of the gift card
we know that
[tex] x+y \leq z [/tex] --------> equation [tex] 1 [/tex]
[tex] y=\$ 15 [/tex] --------> equation [tex] 2 [/tex]
[tex] z=\$ 60 [/tex] --------> equation [tex] 3 [/tex]
Substitute the equation [tex] 2 [/tex] and equation [tex] 3 in the equation [tex] 1 [/tex] [/tex]
[tex] x+y \leq z [/tex]
[tex] x+15 \leq 60 [/tex]
therefore
the answer is the option
x+15 is less than or equal to 60
what is equivalent to 4/6
Round each number to the nearest tenth. what is the best estimate for the difference of 264.72 128.49?
a.137
b.136.3
c.136.2
d.130
A scout group is setting up a tent at camp. Because rain is predicted, the scouts decide to build a fly, or rain cover, over the tent. The fly will be 12 feet high and 16 feet wide. The scouts are building the frame for the fly with poles slanted to meet over the top of the tent. What is the minimum length of the poles needed to support the fly?
Wxyz is a parallelogram. name an angle congruent to xyz
Answer: The answer is ∠XWZ.
Step-by-step explanation: Given that WXYZ is a parallelogram. We are to name an angle that is congruent to ∠XYZ.
Attached herewith, an image of parallelogram WXYZ.
We know that the opposite angles in a parallelogram are congruent to each other. So, in the parallelogram WXYZ, we must have
∠WXY ≅ ∠WZY and ∠XYZ ≅ ∠XWZ.
Therefore, angle congruent to ∠XYZ is ∠XWZ.
Thus, the answer is ∠XWZ.
Final answer:
Angle congruent to angle XYZ in parallelogram WXYZ would be angle W since opposite angles in a parallelogram are congruent.
Explanation:
If WXYZ is a parallelogram and you are asked to name an angle congruent to angle XYZ, you should look at the properties of a parallelogram. One key property is that opposite angles are congruent. Therefore, the angle congruent to angle XYZ would be angle W. If we consider the vertices in order around the parallelogram W, X, Y, Z, angle XYZ corresponds to angle WZY, so its opposite angle is angle WXZ (or simply angle W).
It's important to remember that in a parallelogram, consecutive angles are supplementary (their sum is 180 degrees). This supplementary property could help you in other problems related to angles in a parallelogram, but for this particular case—identifying a congruent angle—the opposite angles property directly gives us the answer.
Which of the following has no solution?
{x | x < 0} and {x | x > 0}
{x | x ≤ 0} and {x | x ≥ 0}
{x | x ≤ 0} or {x | x ≥ 0}
The pair of sets, {x | x < 0} and {x | x > 0}, has no solution because no number can be simultaneously less than zero and greater than zero. The other pairs do have solutions as they include the number zero.
Explanation:The set of mathematical expressions provided in the question represent intervals along the number line. Understanding which intervals overlap and which intervals don't is the key to comprehending which of these options potentially has a solution. To consider when these sets will have no solution, you must find where no numbers exist that can satisfy both conditions simultaneously.
The first pair, {x | x < 0} and {x | x > 0}, means 'the set of all x such that x is less than 0' and 'the set of all x such that x is greater than 0'. Because no number can be both less than zero and greater than zero at the same time, this pair has no solution.
The other pairs, {x | x ≤ 0} and {x | x ≥ 0} and {x | x ≤ 0} or {x | x ≥ 0} do have solutions because they both include 0 itself, so there are numbers that can satisfy both conditions.
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When is substitution a useful method for solving systems of equations?
Factor
h^2-4k^2+4h-8k
freddy is searching for a shirt and discovers that he has 12 shirts for every 6 pair of jeans. If he has 18 shirts, how many pairs of jeans does he have?
Answer:
9 pairs of jeans
Step-by-step explanation:
there are 2 times as many shirts as jeans, and 18 divided by 2=9
The length of a rectangle is 4/5 feet. The width is 5/8 feet. How much greater is the length of the rectangle than the width?
A.)7/40 feet
B.)1/5 feet
C.)3/20 feet
D.)1/3 feet
Write an equation of the line passing through(-3,-14),(1,-2)
Write 46 over 15 as a decimal rounded to the nearest hundredth