By using the concept of maxima, it can be determined that
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
Critical point with the smallest x - coordinate
(0, [tex]\frac{11}{2}[/tex])
Classification cannot be determined
Critical point with the next smallest x - coordinate
(1, 6)
Classification is local maxima
What is maxima of a function?
Maxima of a function gives the maximum value of a function in a given interval or within the whole domain.
f(x, y) = [tex]y\sqrt{x} -y^2 -3x + 11y[/tex]
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
Putting x = 0 in [tex]f_y(x, y) = 0[/tex],
-2y + 11 = 0
[tex]y = \frac{11}{2}[/tex]
[tex](0, \frac{11}{2})[/tex] is a critical point
Putting [tex]f_x(x, y) = 0[/tex] and [tex]f_y(x, y) = 0[/tex]
[tex]\frac{y}{2\sqrt{x}} - 3 = 0\\\frac{y}{2\sqrt{x}} = 3\\y = 6\sqrt{x}[/tex]
[tex]\sqrt{x} - 2y+11 = 0\\\sqrt{x} -2\times 6\sqrt{x}+11=0\\\sqrt{x}-12\sqrt{x} + 11 = 0\\11\sqrt{x} = 11\\\sqrt{x} = \frac{11}{11}\\\sqrt{x} = 1\\x = 1[/tex]
When x = 1, y = [tex]6 \times \sqrt{1} = 6[/tex]
(1, 6) is a critical point
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
The point (0, [tex]\frac{11}{2}[/tex]) is undefined in the second order partial derivative
For the critical point (1, 6)
[tex]f_{xx}(1, 6) = -\frac{1}{4}\\f_{yy}(1, 6) = -2\\f_{xy}(1, 6) = \frac{1}{2}[/tex]
[tex]f_{xx}f_{yy}-(f_{xy})^2[/tex]
[tex]-\frac{1}{4}\times -2-(\frac{1}{2})^2\\\frac{1}{2} - \frac{1}{4}\\\frac{1}{4} > 0[/tex]
[tex]f_{yy} = -2 < 0[/tex]
Hence (1, 6) is a point of local maxima
So it can be determined that
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
Critical point with the smallest x - coordinate
(0, [tex]\frac{11}{2}[/tex])
Classification cannot be determined
Critical point with the next smallest x - coordinate
(1, 6)
Classification is local maxima
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A survey conducted asked 110 people what type of pets they owned. The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat. What is the probability of choosing a person who owns a dog or a cat? Enter your answer as a simplified fraction
The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Number of peoples in survey = 110
And, The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat.
Now,
Since, Number of peoples in survey = 110
And, Number of peoples owns a dog or a cat = 72 + 58 - 37
= 93
Thus, The probability of choosing a person who owns a dog or a cat is,
Probability = 93 / 110
= 0.845
Therefore, The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 438 gram setting. is there sufficient evidence at the 0.02 level that the bags are underfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
The required hypothesis are as follows , H0: μ = 438 and Ha: μ ≠ 438
The null hypotheses for the above scenario will be the statement of no effect and it'll be the mean weight of the bag that filled will be 438grams.
H0: μ = 438
The alternative hypotheses for the above scenario will be that the bag isn't filled with 438grams. They are either underfilled below 438grams or overfilled above 438grams.
Ha: μ ≠ 438
Statistics is the study of surveys and research on numerical data. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.
The null hypothesis is a broad assertion or default condition that there is nothing happening. For instance, there is no relationship between two measured occurrences or a connection between groups.
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math how to answer twice the sum of five times a number increased by one is twelve. determine the number
After solving the expression, the number is 5.
In the given question we have to answer twice the sum of five times a number increased by one is twelve.
We have to determine the number by solving the given statement.
To solve the question we have to read the statement carefully. Then write the expression according to the statement. Then solve the statement according the rules.
In the given statement given that five time a number.
Let the number be x. So the expression should be 5x.
Again says that five times a number increased by one. So the expression 5x+1.
Then says that twice the sum of five times a number increased by one. Now the expression should be 2(5x+1).
Then says that twice the sum of five times a number increased by one is twelve. Now the statement is 2(5x+1)=12
Now solving the expression.
Divide by 2 on both side, we get
5x+1=6
Subtract 1 on both side, we get
5x=5
Divide by 5 on both side, we get
x=1
Now the number is 5.
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Can you guys please help me
Simplify and show work
Hence, the simplification is [tex]27-18i[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given equation is
[tex](-4+i)(-6+3i)[/tex]
then,
[tex]-4(-6+3i)+i(-6+3i)\\\\=24-12i-6i+3\\\\=24-18i+3\\\\=27-18i[/tex]
Hence, the simplification is [tex]27-18i[/tex].
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Help me please with my homework Find the b and r
rhambus has four equal sides
so r+l=2r-4
r=5
b-3=r+l=6
b=9
Diamond adjacent angle complementation
So (x+2x+6)=180*
3x=174
x=58
All in all r=5 b=9 x=58 4b-6r=21-4=r+l=b-3=6
2x+6=122
this is the answer thank you when you have th problem you can tell me
the combined perimeter of a circle and square is 16 cm. find the dimensions of the circle and square that produce a minimum total area.
the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
given that
the combined perimeter of a circle and square is 16cm
let side length of the square is s
let radius of the circle with r
So, the perimeter (P) and the area (A) of the shape are:
P= 4s + 2[tex]\pi[/tex]r
A = [tex]s^{2}[/tex] + [tex]\pi[/tex][tex]r^{2}[/tex]
given that perimeter is 16
so, 4s +2[tex]\pi[/tex]r = 16
divide by 4
s +0.5[tex]\pi[/tex]r = 4
s = 4 - 0.5[tex]\pi[/tex]r
substitute s value in area
A = [tex](4-0.5\pi r)^{2}[/tex] + [tex]\pi[/tex]r
A = 16 - 4[tex]\pi[/tex]r +0.25[tex](\pi r)^{2}[/tex] +[tex]\pi[/tex][tex]r^{2}[/tex]
A =16 - 4[tex]\pi[/tex]r + (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])[tex]r^{2}[/tex]
differentiate with respect to r
A' = 0 - 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r
A' = - 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r
now A' =0
- 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r =0
2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r = 4[tex]\pi[/tex]
divide both sides by 2
(0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r = 2[tex]\pi[/tex]
r = [tex]\frac{2\pi }{0.25\pi ^{2} +\pi }[/tex]
r = [tex]\frac{2\pi }{\pi (0.25\pi +1)}[/tex]
substitute [tex]\pi[/tex] =3.14
r = 2/(0.25(3.14)+1)
r = 1.12
substitute r value in s
s = 4 - 0.5 * 3.14 *1.12
s =2.24
Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
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Graph the function f(x)=(1/4)^x
[tex]f(x)=(\dfrac{1}{4} )^x[/tex]
Please refer to the following graph below:
a committee of 3 is selected from jillian, miles, mark, and nikia. how many committees contain 2 boys and 1 girl
The probability of committees contain 2 boys and 1 girl is 9.
In the given question,
A committee of 3 is selected from Jillian, Miles, Mark, and Nikia.
We have to find the how many committees contain 2 boys and 1 girl.
As we know that,
Simply put, probability is the likelihood that something will occur. If we don't know how such an occurrence will end out, we can discuss the possibility or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
There are total 3 selection.
Possibility of selecting 2 boys = [tex]^{3}C_{2}[/tex].
There are total 3 selection.
Possibility of selecting 1 girl = [tex]^{3}C_{1}[/tex].
So the probability of committees contain 2 boys and 1 girl is
P(C) = [tex]^{3}C_{2}\times^{3}C_{1}[/tex]
After solving
P(C) = 9
The probability of committees contain 2 boys and 1 girl is 9.
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A circle is centered on point B, Points A, C and D lie on its circumference. if ABC measures 61 degrees, what does ADC measures?
Answer:
61
Step-by-step explanation:
hope this helps
Answer the picture in 5 minutes, please
Answer:
area of the isosceles triangle is [tex]60cm^{2}[/tex]
Step-by-step explanation:
three sides are a=10, b=13, c=13
Area of Triangle:
[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\frac{a+b+c}{2}[/tex]
[tex]s=\frac{10+13+13}{2}[/tex]
s = 18
now,
[tex]A = \sqrt{18(18-10)(18-13)(18-13)}[/tex]
[tex]A =\sqrt{9(16)(5)(5)}[/tex]
A = 3x4x5
[tex]A =60cm^{2}[/tex]
help :(( pleaseeeeeee
Answer:
69.29 deg
Step-by-step explanation:
Recall that tan(x) = opposite/adjacent. This is helpful because we know the opposite and adjacent leg from the angle x! This gives us tan(x) = 43/18, so we can solve for x by taking tan^-1 of both sides, giving x = tan^-1(43/18), or 67.29 degrees.
Question at position 1
One serving of a fruit punch recipe serves 16 people.
Which of the following answer choices correctly lists the ordered pairs for 1, 2, 3, and 4 servings? (number of servings, number of people served)
(16, 1), (32, 2), (48, 3), (64, 4)
(1, 16), (2, 32), (3, 48), (4, 60)
(1, 16), (2, 32), (3, 48), (4, 64)
(1, 32), (2, 48), (3, 64), (4, 80)
Answer:
(1,16),(2,32),(3,48),(4,64)
Step-by-step explanation:
so 1=16
2×16=32
3×16=48
4×16=64
The correct answer is C. (1, 16), (2, 32), (3, 48), (4, 64)
How did we figure out this?For this equation we have to "multiply" each number that makes scene.
We got to work with what is given in the question.
Given options:
(16, 1), (32, 2), (48, 3), (64, 4)
(1, 16), (2, 32), (3, 48), (4, 60)
(1, 16), (2, 32), (3, 48), (4, 64)
(1, 32), (2, 48), (3, 64), (4, 80)
Therefore, the equation is:
[tex]2*16\\3*16\\4*16[/tex]
2 x 16 = 323 x 16 = 484 x 16 = 64Therefore, the correct answer is C. (1, 16), (2, 32), (3, 48), (4, 64)
In this lesson, you sketched polynomial functions using factors and rewrote them in general form.
1 Use the factors to sketch each cubic function and label the zeros. Then rewrite the function
in general form.
F(x) = (x+3)(-x + 5)2 - 2x)
Answer:
check the attached file
Step-by-step explanation:
polynomial functions- Part 1
The volume of a right rectangular prism is (10x³ +21x² 25x+6) cubic meters, and the area of its base is
(10x² - 9x+2) square meters.
What is the height of the prism?
Enter your answer in the box.
meters
Answer:
Below
Step-by-step explanation:
base * height = volume
volume / base = height
divide 10x^2-9x+2 INTO 10x^3 + 21x^2 MINUS 25x +6
( you left out the minus sign in your post)
to get height = x+3
Solve: -5/6 + m = -3 1/6
m= -4
m= -2
m= -2 1/6
m= -2 1/3
Answer: -2 1/3
Step-by-step explanation:
Okay
The ratio of cats to dogs in an animal
shelter is 2: 5, and there are 10 cats.
A group of animals arrive at the shelter and
the ratio of cats to dogs becomes 5 : 3.
Work out the smallest number of new
animals that could have arrived at the
shelter.
Answer:
5:8
Step-by-step explanation:
The ratio of dogs and cats is 5:8
The ratios always have a common multiple.
Let that common multiple is ‘a’
So dogs and cat are:
dogs=5a
cats=8a
total animals=5a+8a=13a
13a=52
a=52/13
= 4 ——- Means, the common multiple is ‘4’
So, number of cats = 8a
=8*4=32
Answer:
37
Step-by-step explanation:
HELP SOLVE!
name the property if 3x= 4 and 4=z then 3 =z
The name of the property is transitive property if 3x= 4 and 4=z then 3 =z.
What is a transitive property?According to the transitive property, "if two quantities are equal to the third quantity, then we can claim that all quantities are equal to each other." The term transitive refers to the act of transferring something. If a, b, and c are three quantities and an is connected to b by some rule and b is related to c by the same rule, then a and c are related to each other by the same rule; this is known as the transitive property of equality.
The transitive property of equality states that if a = b and b = c for any values of a, b, and c, then a = c. In other words, because a and c are both equal to the same item (in this case, b), they must be equal as well.
Given,
3x=4 and 4=z then 3=z
Here a=3, b=4, c=z
The name of the property is transitive property
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Identify the terms and like terms in the expression. 1/2s−4+3/4s+1/8−s3
HELP ME PLEASE TvT
1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³
What is Expression?An expression is combination of variables, numbers and operators.
Given expression is 1/2s−4+3/4s+1/8−s³
One by two times of s minus four plus three by four times of s plus one by eight minus s cube.
In the given expression minus, plus are the operators, s is the variable,
The expression has five terms
1/2s, -4, 3/4s, 1/8 and -s³ are the terms
Like terms contain the same variable which is raised to the same power.
In the given expression 1/2s and 3/4s are the like terms
Hence, 1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³
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Which pairs of rectangles are similar polygons? select each correct answer.
Pairs 1 &2 are not similar whereas pairs 3&4 are similar.
The term "similarities" refers to pairs of objects whose corresponding sides have the same ratio. When two figures, such as the rectangles A and B, are given:
length A/length B equals width A/width B
We enter the values of the pairs in the formula above to determine which pairs are similar:
Pair 1
169/1.3=130
49/0.7=70
130 ≠70
therefore the first pair is not similar
Pair 2
18.55/5.3=3.5
10.5/3.5=3
Pair 2 is not similar
Pair 3
120/24=5
60/12=5
this implies that pair 3 is similar
Pair 4
189/2.1=90
81/0.9=90
this means that pair 4 is similar.
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The mean of a set of normally distributed data is 600 with a standard deviation of 20. What percent of the data is between 580 and 620?.
We know that 68.26% of data is between 580 and 620 using a normal distribution table.
What is a normal distribution?A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution.
Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.
So, we know that:
μ = 600
σ = 20
Use the equation:
z - score = x-μ/σ
580 in the data's Z-score:
= 580-600/20
= -20/20
= -1
While the data's z-score in 620:
= 620-600/20
= 20/20
= 1
Using a table of the normal distribution:
P(580 < z) = 0.1587
Also, P(620 > z) = 0.8413
As a result, the percent of the data that falls between 580 and 620 is given by: P(620 > z) - P(580 z).
= 0.8413 - 0.1587
= 0.6826
= 68.26 %
Therefore, we know that 68.26% of the data is between 580 and 620 using a normal distribution table.
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i nee help please and thankyou
Question 7
Using the secant-secant theorem,
[tex]4(x+4)=3(8) \\ \\ x+4=6 \\ \\ \boxed{x=2}[/tex]
Question 8
Using the intersecting chords theorem,
[tex]8(4x+2)=9(4x) \\ \\ 32x+16=36x \\ \\ 16=4x \\ \\ \boxed{x=4}[/tex]
A video game store uses a markup rate of 40% on a shipment of video games. The store paid $24 for each video game in the shipment. What is the retail price of each video game?
The retail price of each video game is $33.6
How to determine the retail price of each video game?From the question, we have the following parameters that can be used in our computation:
Markup rate = 40%
Amount paid = $24
The retail price of each video game can be calculated using the following equation
Retail price = Amount paid * (1 + Markup rate)
Substitute the known values in the above equation, so, we have the following representation
Retail price = 24 * (1 + 40%)
Evaluate
Retail price = 33.6
Hence, the retail price is $33.6
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How much mut be depoited today into the following account in order to have $35,000 in 7 year for a down payment on a houe? Aume no additional depoit are made. An account with annual compounding and an APR of 4%
$17505 must be deposited today.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Variable principal payments, or the portion of your mortgage payment that goes toward the loan itself rather than interest, are what give compound interest its feel.
Simple or compound interest are also possible. A loan's or deposit's initial principal serves as the foundation for simple interest.
Contrarily, compound interest is calculated based on both the principal amount and the interest that is accrued on it each period. Simple interest is simpler to calculate than compound interest because it is only applied to the principal.
According to our question-
In order to calculate compound interest, we would use the formula A = P(1+r/n)nt.
Where A = the account's total balance at the end of t years, and r is the interest rate.
The periodic interval at which it was compounded is represented by n.
P stands for the principal, or the initial deposit amount.
Since it was compounded once a year, A = 30000 r = 8% = 8/100 = 0.08 and n = 1 according to the information provided.
t = year
In light of this, 30000 = P(1 + 0.08/1)1 7 30000 = P(1.08)7 30000 = 1.7138P
P = 30000/1.7138 \s P = $17505
Hence, $17505 must be deposited today
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The mass of a white-tailed deer is about 1.4 times the mass of a cougar. The average mass of a white-tailed deer is 98 kg. Calculate the mass of a cougar. Start with an equation that includes a variable. Show all work
The mass of the Cougar is 70 Kg using the concept of equations.
What are equations?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It demonstrates the equal relationship between the expressions presented on the left and right sides. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved. If there is no "equal to" symbol, a statement is not an equation.
Let the mass of white-tailed deer = d
Mass of cougar = c
According to the question,
d = 1.4 × c ....(1)
d = 98 kg ....(2)
So,
1.4 × c = 98
c = 98/1.4
c = 70
So, the mass of the Cougar = 70 Kg
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a waiter earned $300 in tips during his shift on friday. on saturday, he earned $335 in tips. what is the percent increase of his tips from friday to saturday?
The percent increase of his tips from Friday to Saturday is 35/3%.
T is equal to 112/3% as a mixed percentage fraction or 35/3% as an uncommon percentage fraction (decimal fraction: 0.116667)
PREMISES
T is the proportion of a waiter's tips that increased from $300 on Friday to $335 on Saturday.
CALCULATIONS
T=($335-$300)/$300
T=[($35/$300)100]%
T=[(7/60)100]%
T=[(7×100)/60]%
T=70/6%
A mixed percentage fraction of 112/3% or a percentage fraction of 35/3% (decimal fraction: 0.116667)
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38. WEATHER The temperature fell 16 degrees between noon and 3:00 P.M. At 3:00, the temperature was -3 degrees F. Write an equation to determine the temperature at noon.
Answer:
x - 16 = -3
Step-by-step explanation:
x - 16 = -3 Add 16 to both sides of the equation
x = 13
It was 13 degrees at noon
The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Responses
1/5
2/5
3/5
5/2
The ratio representing the number of votes for hot dogs to chicken is 2/5.
Define the term ratios of the number?An set of points of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing each data point (A) to some other data point (B).For the stated question.
Total votes = 20.
Pizza = 6
Chicken = 10
Hot dogs = 20 - 16 = 4
Then,
Ratio = votes for hot dogs/ votes for chicken
Ratio = 4/10
Ratio = 2/5
Thus, the ratio representing the number of votes for hot dogs to chicken is 2/5.
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an airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. if the airline sells 170 tickets for a flight that has only 165 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly? (round your answer to four decimal places.)
The probability that a seat will be available for every person holding a reservation and planning to fly s 0.9306.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given: An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight.
The airline sells 170 tickets for a flight that has only 165 seats.
The proportion of reservations that do not show up for the flight
P = 5% = 0.05.
Number of tickets sold n = 170
Number of seats in the flight = 165
If at least 5 people do not show up then we have enough seats for every person.
P(X ≥ 5) = Σ (from 5 to 170)[tex]170C_x(0.05)^x(0.95)^1^7^0^-^x[/tex]
P(X ≥ 5) ≈ 0.9306
Hence, the probability that a seat will be available for every person holding a reservation and planning to fly s 0.9306.
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An 8-ounce container of yogurt is on sale for $1.12. What is the cost of 1 ounce of yogurt?
Answer: $0.14
Step-by-step explanation: All we have to do is divide $1.12 by 8 to get our answer, that being $0.14.