Answer:
We have the coldest value of temperature [tex]T(\frac{3}{4},0) = -9/16 [/tex]. and the hottest value is [tex]T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}[/tex].
Step-by-step explanation:
We need to take the derivative with respect of x and y, and equal to zero to find the local minimums.
The temperature equation is:
[tex]T(x,y)=x^{2}+2y^{2}-\frac{3}{2}x[/tex]
Let's take the partials derivatives.
[tex]T_{x}(x,y)=2x-\frac{3}{2}=0[/tex]
[tex]T_{y}(x,y)=4y=0[/tex]
So, we can find the critical point (x,y) of T(x,y).
[tex]2x-\frac{3}{2}=0[/tex]
[tex]x=\frac{3}{4}[/tex]
[tex]4y=0[/tex]
[tex]y=0[/tex]
The critical point is (3/4,0) so the temperature at this point is: [tex]T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})[/tex]
[tex]T(\frac{3}{4},0)=-\frac{9}{16}[/tex]
Now, we need to evaluate the boundary condition.
[tex]x^{2}+y^{2}=1[/tex]
We can solve this equation for y and evaluate this value in the temperature.
[tex]y=\pm \sqrt{1-x^{2}}[/tex]
[tex]T(x,\sqrt{1-x^{2}})=x^{2}+2(1-x^{2})-\frac{3}{2}x[/tex]
[tex]T(x,\sqrt{1-x^{2}})=-x^{2}-\frac{3}{2}x+2[/tex]
Now, let's find the critical point again, as we did above.
[tex]T_{x}(x,\sqrt{1-x^{2}})=-2x-\frac{3}{2}=0[/tex]
[tex]x=-\frac{3}{4}[/tex]
Evaluating T(x,y) at this point, we have:
[tex]T(-(3/4),\sqrt{1-(-3/4)^{2}})=-(-\frac{3}{4})^{2}-\frac{3}{2}(-\frac{3}{4})+2[/tex]
[tex]T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}[/tex]
Now, we can see that at point (3/4,0) we have the coldest value of temperature [tex]T(\frac{3}{4},0) = -9/16 [/tex]. On the other hand, at the point [tex]-(3/4),\frac{\sqrt{7}}{4})[/tex] we have the hottest value of temperature, it is [tex]T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}[/tex].
I hope it helps you!
A company's stock was selling at
$30 a share. A month later, it was
selling at $33 a share. What is the
percent gain?
Answer:
10%
Step-by-step explanation:
What is the greatest common factor of all the terms: 6m and 18
Answer: 6
Step-by-step explanation:
Please help thank youu
Answer:
2√73 or 17.09 inches
Step-by-step explanation:
The small red square at the corner of the triangle symbolizes that the triangle is a right triangle. Therefore, to find the hypotenuse of the triangle, we can use the Pythagorean Theorem: a² + b² = c²
a = 6
b = 16
c = ?
Plug these values into the equation.
(6)² + (16)² = c²
Evaluate the exponents.
36 + 256 = c²
292 = c²
Take the square root of both sides to find c.
√292 = √c²
17.09 ≈ c
This is your answer.
You can also simplify the radical without using decimals.
4 • 73 = 292
Therefore,
√4 • √73 = √292
Which also means,
2•√73 = √292
So your answer is: 2√73
Hope this helps!
Answer:
We use the pythagorean theorem a²+b²=c² and in this question
a = 6
and
b = 16
so
36 + 256 = c²
so
c² = 292 so now we take the square root of it to get [tex]\sqrt{292}[/tex]
Hope this helps!
MULTIPLE CHOICE PLS ANSWER THANKS
Answer:
I think answer is B
B.10x+150=180
Why rotation, reflection, and translation are rigid motion?
Answer:
Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations". ... A reflection is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.
Hope it helps!!!
PLZZZ HELP
Triangle GHI is similar to triangle JKL. Find the measure of side KL Round your
answer to the nearest tenth if necessary.
8
L
H
K
A piece of rope 6.54 metres long is cut
into two pieces. One piece is twice as
long as the other. What is the length of
the longest piece?
If a rectangle has length x and width x+3, what is the perimeter of the rectangle in terms of x?
Answer:
[tex]4x+6[/tex] units
Step-by-step explanation:
Skills needed to solve: Order of Operations, Distributive Property, Perimeter Formula, Like Terms
1) To solve this problem, you need to understand the perimeter formula, and that is:
--> [tex]P = 2(L+W)[/tex]
P = Perimeter
L = Length
W = Width
2) Based on that, we are given that:
[tex]L = x[/tex] (since the length is x)
[tex]W = x+3[/tex] (since the width is x+3)
3) After that, we substitute in the values:
[tex]P = 2(L+W)[/tex]
[tex]P = 2(x+(x+3))[/tex]
[tex]x + (x+3) = x+x+3 = 2x+3[/tex] (with like terms and addition)
so: [tex]P=2(2x+3)[/tex]
Use distributive property, which is [tex]a(b+c) = ab+ac[/tex]
get: [tex]2(2x+3) = 2(2x) + 2(3)[/tex]
[tex]2(2x) = 4x[/tex]
[tex]2(3) = 6[/tex]
So: [tex]P = 4x+6[/tex]
Hope this helps and have a nice day!! :) :]
The table shows the rates for sending text messages. Are the rates proportional? Explain.
Answer:
Yes
Step-by-step explanation:
Remember in order for the rates to be proportional it has to have a constant rate of change and it has to go through the origin if graphed
For one this has a constant rate of change which is 3 dollars per 25 messages
Now we just have to find out if it would go through the origin (0,0)
To do so we subtract 3 dollars and then 25 messages
6-3=3
50 - 25 =25
then again 25-25=0
3-3=0
concluding that (0,0) is a solution
Thus meaning that this is a proportional relationship
4. Marcos wants to paint his skateboard ramp shown below. What is the total surface area of the skateboard ramp?
Answer:
yshshhshs
Step-by-step explanation:
shhshshsbbs
if anyone know the answers to this question i really need help.
Answer:
b.) 6
Step-by-step explanation:
2^6 = 64 because 2 * 2 * 2 * 2 * 2 * 2 = 64.
Pea plants contain two genes for seed color, each of which may be Y (for yellow seeds) or G (for green seeds). Plants that contain one of each type of gene are called heterozygous. According to a theory of genetics, if two heterozygous plants are crossed, each of their offspring will have probability 0.75 of having yellow seeds and probability 0.25 of having green seeds.
A) Out of 10 offspring of heterozygous plants, what is the probability that exactly 3 have green seeds?
B) Out of 10 offspring of heterozygous plants, what is the probability that more than 2 have green seeds?
C) Out of 100 offspring of heterozygous plants, what is the probability that more than 30 have green seeds?
D) Out of 100 offspring of heterozygous plants, what is the probability that between 30 and 35 inclusive have green seeds?
E) Out of 100 offspring of heterozygous plants, what is the probability that fewer than 80 have yellow seeds?
Answer:
a) 0.2503 = 25.03% probability that exactly 3 have green seeds.
b) 0.4744 = 47.44% probability that more than 2 have green seeds.
c) 0.1020 = 10.20% probability that more than 30 have green seeds.
d) 0.1414 = 14.14% probability that between 30 and 35 inclusive have green seeds.
e) 0.8508 = 85.05% probability that fewer than 80 have yellow seeds
Step-by-step explanation:
For questions a and b, the binomial probability distribution is used. For questions c, d and e, the binomial distribution is approximated to the normal.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A) Out of 10 offspring of heterozygous plants, what is the probability that exactly 3 have green seeds?
10 offspring of heterozygous plants means that [tex]n = 3[/tex]
Probability 0.25 of having green seeds means that [tex]p = 0.25[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.25)^{3}.(0.75)^{7} = 0.2503[/tex]
0.2503 = 25.03% probability that exactly 3 have green seeds.
B) Out of 10 offspring of heterozygous plants, what is the probability that more than 2 have green seeds?
This is
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.25)^{0}.(0.75)^{10} = 0.0563[/tex]
[tex]P(X = 1) = C_{10,1}.(0.25)^{1}.(0.75)^{9} = 0.1877[/tex]
[tex]P(X = 2) = C_{10,2}.(0.25)^{2}.(0.75)^{8} = 0.2816[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0563 + 0.1877 + 0.2816 = 0.5256[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.5256 = 0.4744[/tex]
0.4744 = 47.44% probability that more than 2 have green seeds.
C) Out of 100 offspring of heterozygous plants, what is the probability that more than 30 have green seeds?
Now
[tex]n = 100[/tex]
[tex]\mu = E(x) = np = 100*0.25 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.25*0.75} = 4.33[/tex]
Using continuity correction, this is [tex]P(X > 30 + 0.5) = P(X > 30.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 30.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 25}{4.33}[/tex]
[tex]Z = 1.27[/tex]
[tex]Z = 1.27[/tex] has a pvalue of 0.8980
1 - 0.8980 = 0.1020
0.1020 = 10.20% probability that more than 30 have green seeds.
D) Out of 100 offspring of heterozygous plants, what is the probability that between 30 and 35 inclusive have green seeds?
Using continuity correction, this is [tex]P(30-0.5 \leq X \leq 35 + 0.5) = P(29.5 \leq X \leq 35.5)[/tex], which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 29.5.
X = 35.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35.5 - 25}{4.33}[/tex]
[tex]Z = 2.42[/tex]
[tex]Z = 2.42[/tex] has a pvalue of 0.9922
X = 29.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29.5 - 25}{4.33}[/tex]
[tex]Z = 1.04[/tex]
[tex]Z = 1.04[/tex] has a pvalue of 0.8508
0.9922 - 0.8508 = 0.1414
0.1414 = 14.14% probability that between 30 and 35 inclusive have green seeds.
E) Out of 100 offspring of heterozygous plants, what is the probability that fewer than 80 have yellow seeds?
0.75 probability of yellow seeds, so [tex]p = 0.75[/tex]. So
[tex]\mu = E(x) = np = 100*0.75 = 75[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.75*0.25} = 4.33[/tex]
This probability is [tex]P(X < 80 - 0.5) = P(X < 79.5)[/tex], which is the pvalue of Z when X = 79.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{79.5 - 75}{4.33}[/tex]
[tex]Z = 1.04[/tex]
[tex]Z = 1.04[/tex] has a pvalue of 0.8508
0.8508 = 85.05% probability that fewer than 80 have yellow seeds
HELP ASAP I NEED HELP WITH THIS
Answer: 10/27
Step-by-step explanation:
Your multiplying the top and bottom yw :)
Answer:
I GOT YOU I GOT YOU
THE ANSWER IS 10/27
a farmer wants to fence in three sides of a rectangular field shown below with 960 feet of fencing. The other side of the rectangle will be a river. If the enclosed area is to be a maximum, find the dimensions of the field.
9514 1404 393
Answer:
240 ft by 480 ft
Step-by-step explanation:
Area is maximized when the long side is half the total length of the fence. That makes the short side (out from the river) be half the length of the long side.
The fenced field dimensions are 240 feet by 480 feet.
__
You can let x represent the length of the long side. Then the length of the short side is half the remaining fence: (960 -x)/2.
The total area is the product of these dimensions:
A = x(960 -x)/2
We note that this is the equation of a parabola with zeros at x=0 and x=960. The maximum will be found on the line of symmetry, halfway between the zeros. That is at x = (0 +960)/2 = 480.
The area is maximized for a long-side dimension of 480 feet. The short sides are 240 feet.
ill mark brainlist plss help
Answer:
A rectangle
Step-by-step explanation:
A rectangle is a quadrilateral ( 4 sided shape) and the opposite sides are always congruent therefore the answer is rectangle
PLEASE HELP ME!!!! HOW DO I GRAPH THIS??????
Answer:
draw the picture then put a box around it and label the body parts and that fun stuff
6x1/6 gente me ajudaaaa kakakkw e pra um teste de matematica
RESPONDE EM PORTUGUES PFV
6x1/6=6/6=1
---
hope it helps
TThe Education Trust publishes data on U.S. colleges and universities. Six-year graduation rates and student-related expenditures per full-time student for 2007 were reported for the seven primarily undergraduate public universities in California with enrollments between 10,000 and 20,000. Suppose that a 90% confidence interval for the prediction of student expenditures at a university with a graduation rate of 40% was (5,304, 8,686).
Required:
a. Determine the point estimate for the prediction of student expenditures at a university with a graduation rate of 40%.
b. Calculate the margin of error.
c. Calculate the standard error of the prediction of student expenditures at a university with a graduation rate of 40%.
Answer:
a) The point estimate is 6995.
b) The margin of error is of 1691.
c) The standard error is of 1000
Step-by-step explanation:
a. Determine the point estimate for the prediction of student expenditures at a university with a graduation rate of 40%.
The point estimate is the mean of the two bounds of the confidence interval. So
[tex]P = \frac{5304 + 8686}{2} = 6955[/tex]
The point estimate is 6995.
b. Calculate the margin of error.
The margin of error is the difference between the bounds and the point estimate. So
M = 8686 - 6995 = 6995 - 5304 = 1691
The margin of error is of 1691.
c. Calculate the standard error of the prediction of student expenditures at a university with a graduation rate of 40%.
Now I have to expand a bit into the confidence interval.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs[/tex]
In which s is the margin of error.
We have that M = 1691. So
[tex]M = zs[/tex]
[tex]s = \frac{M}{z} = \frac{1645}{1.645} = 1000[/tex]
The standard error is of 1000
Mindy is playing a game. She notices that the ratio of red tokens to purple tokens is 2 to 3. She counts 6 red tokens. Draw numbers to complete the diagram to the number of purple tokens. Numbers may be used once, more than once, or not at all.
What is the measure of CED?
The measure of CED is p degree. By AA rule of similarity, Corresponding angles of similar triangles are same. Therefore the measure of CED is p degree.
PLEASE MARK BRAINLIST
the illustration below shows the graph of y as a function of x complete the following sentences based on the graph of the function
Answer:
*This is the graph of a [NON-LINEAR].
*The y-intercept of the graph is the function value y=[0]. *The smallest positive x-intercept of the graph is located at x=[π/2]. *The greatest value of y is y=[2]. *For x between x= -π and x= -π/2, the function value y[>]0.
This is the graph of a sin function.
The y-intercept of the graph is the function value y = 0
The smallest positive x-intercept of the graph is located at x = π/2
The greatest value of y is y = 2
For a between x = -π and x = -π/2 the function value y > 0
How to identify sin functionsA sine function graph represents the behavior of the sine function over a specific interval. The graph of a sine function has the following characteristics:
Shape: The graph of a sine function resembles a wave. It consists of a series of repeated crests (peaks) and troughs (valleys) that oscillate above and below a central line called the midline.
Period: The graph repeats itself over a specific interval called the period. The standard period of the sine function is 2π radians or 360 degrees. This means that the graph completes one full wave cycle in this interval.
Amplitude: The amplitude determines the vertical distance between the midline and the maximum or minimum points of the graph. It represents the maximum deviation of the function from the midline. The amplitude of the sine function is always positive.
Midline: The midline is the horizontal line that the sine function oscillates around. It is located between the maximum and minimum points of the graph and has a constant y-value.
Learn more about sin function at
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Write the recurring decimal 0.67
as a fraction
2/3 I hope this helps!! :3
What is the feet....
Answer: 29 feet from across the kitchen to one hole to the other.
Solve
Root 3x+5 - root x-1 =0
Answer:
undefined
Step-by-step explanation:
3x+5=x-1
2x=-6
x=-3
but when u check its undefined
If 15 people can fit comfortably in a 5 ftby 5 squarewhat is the ratio of the people to the rectangle's area ?
Answer: 15:25
Step-by-step explanation: the number of people is 15 and the area would be 25
Y’all help meeeee :(
Solve the exponential equations: 2^3x =11
Answer:
x = 3
Step-by-step explanation:
2 + 3x = 11
3x = 11 - 2
3x = 9 (divide both sides by 3 to get x)
3x/3 = 9/3
x = 3
In the given exponential equations: [tex]2^3x[/tex] = 11, the value of x is [tex]\frac{log_211}{3}[/tex].
Mathematically, an equation is a statement that asserts the equivalency of two expressions. It consists of two hands, the left-hand side( LHS) and the right-hand side( RHS), separated by an equal sign( =). The LHS and RHS can be numbers, variables, constants, or further complex fine expressions.
Equations can be classified based on their degree, which corresponds to the highest power of the variables involved. For example, linear equations have a degree of 1, quadratic equations have a degree of 2, and so on.
Given the equation:
[tex]2^3^x[/tex] = 11
Take the logarithm of both sides,
log [tex]2^3^x[/tex] = log 11
3x log2 = log 11
3x = [tex]\frac{log 11}{log2}[/tex]
3x = [tex]log_211[/tex]
x = [tex]\frac{log_211}{3}[/tex].
So, the value of x is [tex]\frac{log_211}{3}[/tex].
Learn more about Equations here:
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The probability of an archer hitting her target is 83%. Suppose she has 20 shots to take, and each shot is independent of the others. Let X represent the number of targets hit. What is the mean of X?
4.1
8.3
16.6
83
Answer:
16.6
Step-by-step explanation:
Edge
need help geometry question central angles and arcs???pls
Answer:
84.96 G
Step-by-step explanation:
cuz im connected to einstine and im smart like him
Which inequality represents: 3 is less than y minus 2
Answer:
3>y-2
Step-by-step explanation:
your welcome i think