The critical point of the function f(x, y) = x^2 + y^2 + 3xy - 7.5x is (0, 0) because the partial derivatives of f with respect to x and y are both equal to 0 at this point.
What is the critical point?In mathematics, a critical point is a location along a function or curve where the derivative of the function is either equal to 0 or undefined. Accordingly, a critical point occurs where the slope of the function is either 0 or not specified, producing a flat or vertical tangent line. Critical points are significant because they frequently point to locations where the function changes course or exhibits a local extreme value, such as a maximum or minimum. Taking the function's derivative and then solving for the values of x where the derivative equals zero or is undefined will help you locate key spots. The critical points of the function are at these values of x.
How to solve?
To use the Second Derivative Test, we need to calculate the Hessian matrix of the function at the point (0, 0).
The Hessian matrix for f(x, y) at (0, 0) is given by:
H = [2 3]
[3 2]
λ1 = 5, λ2 = -1
Since the Hessian matrix has one positive and one negative eigenvalue, the point (0, 0) is a saddle point.
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Bank of america's consumer spending survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. using data from a sample of credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). using the difference data, the sample mean difference was , and the sample standard deviation was . a. formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. is equal to 0 is not equal to 0 b. use level of significance. can you conclude that the population means differ? differ what is the -value? (to 6 decimals) c. which category, groceries or dining out, has a higher population mean annual credit card charge? groceries what is the point estimate of the difference between the population means? round to the nearest whole number. what is the confidence interval estimate of the difference between the population means? round to the nearest whole number. , hide feedback partially correct
The null hypothesis for the no difference test is 0 and the alternative hypothesis is 4.905 using the level of significance.
a)null hypothesis (H₀) = 0
Alternative hypothesis (H₀) ≠ 0
t = (d)/√n = 850 × √42 ÷ 1123 = 4.902
b) Now we calculate the degrees of freedom given by:
degrees of freedomf
= n-1
= 42 -1
= 41
Now we can calculate the p value, we have a left tailed test the p value is given by:
p=2× P(t₍₄₁₎>4.905) = 0.00015
We can therefore infer that we can reject the null hypothesis that the difference between the two groups is equal because the p value is less than the significance level indicated.
When there are two samples and the data in one sample can really be paired with observations in the other sample, a paired t-test is used to compare the two population means.
The system of the null and alternate hypothesis for this particular case are:
Null hypothesis: μ₁ - μ₂ = 0
Alternative hypothesis: μ₁ - μ₂ ≠ 0
Or equivalently
Null hypothesis: (H₀) = 0
Alternative hypothesis: (H₀) ≠ 0
c) now it is calculated that μ₁ - μ₂ = 0 , hence we can conclude that The standard deviation for the mean for groceries is more than the mean for dining out .
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what percentage of the national collegiate athletic association's (ncaa) men's basketball players enter the professional ranks
Answer: the answer is 1.2%
An employee worked 40. 3 hour and make $9. 94 per hour. How much money did the employee make?
The total amount of money that the employee made was $400.58
What is the hourly rate?
The amount that is paid per hour of work is known as an hourly rate.
The hourly rate can be calculated by:
The total amount of pay = hours worked * hourly rate of pay
Given, the rate per hour = $9.94
Total work duration = 40.3 hours
Now,
The total amount that the employee makes = $9.94*40.3 = $400.58
Hence, the employee made $400.58.
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What does a 1 2 1 phenotypic ratio mean?.
Phenotypic ratio helps us to predict gene expression in the future generations of organisms. In phenotypic ratio calculations, we map out specific parental alleles and predict the probability of how they will be expressed in their offspring.
Phonotypic ratio is a term that describes probability of finding the patterns and frequency of genetic trait outcomes in the offspring of organisms.
Phenotypic ratio is showing physical expression while the genotypic ratio shows genetic makeup. In complete dominance, the progeny shows the intermediate character of both the parents.
A cross of two hybrid F1 hybrids, heterogeneous for a single trait that displays incomplete dominance is predicted to give a 1:2:1 ratio among both the genotypes and phenotypes of the offspring.
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a ship proceeding southward in a straight course at a rate of 12 miles per hour is, at noon, 40 miles due north of a second ship, which is sailing west at 15 miles per hour. what is the minimum distance between the ships? at what time does this occur?
We have to calculate the minimum distance between the ships by using pythagoras theorem
Let us assume that we have to find the distance at 4 pm from the noon so,
Distance traveled by A in 4 hours = 15 X 4 = 60mi...........(a)
Distance traveled by B in 4 hours = 12 X 4 = 48...........(b)
Total distance between A and the initial point of B is = 40 + 60
=100 mi
[tex]c = \sqrt{100^{2} +48^{2}[/tex]
from pythagoras theorem we have,
[tex]a^{2} + b^{2} =c^{2}[/tex]
= [tex](a + 40)^{2} + b^{2} = c^{2}[/tex]
Diff, with respect to time we get the equation ,
[tex]2(a +40)da/dt + 2bdb/dt = 2c dc/dt\\(a+40)da/dt + db/dt = dc/dt\\dc/dt = (a+40)da/dt + b db/dt / c\\dc/dt = (60+40) X 15 + 48 X 12 / \sqrt60^{2}+48^{2} \\dc/dt = 2976 \//\sqrt{2304 +3600}\\dc/dt = 2976/ 76.83\\=38.73[/tex]{ after using equation (a) & (b) }
So, the distance between the ship at 4 pm is changing at 38.73 mph
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Use the Venn diagram to complete the missing values in the two-way table.
Thank you for helping.
Answer:
fishing + camping = 15
not fishing + camping = 10
Find the function which is parallel to y = 2x + 9.
5x-2y=8
O 7x+2y = 14
4y - 8x = 24
All of the choices
Answer:
4y - 8x = 24
Step-by-step explanation:
4y -8x = 24 Add 8x to both sides
4y = 8x + 24 Divide both sides by 4
y = 2x + 6
This slope is 2 which would great a line parallel to y = 2x + 9
Desmos is a free program that can help you graph. See the picture below. You just type in the equation and it graphs it for you. Cool
Bonnie measured a city and made a scale drawing. A neighborhood park is 115 inches long in the drawing. The actual park is 138 yards long. What is the scale of the drawing?.
Given:
Length of neighbourhood park = 115 inches
Length of actual park = 138 yards
Since 1 yard = 36 inch
Therefore , 138 yards = 138 × 36
= 4698 inches
What is an example of ASA triangle?.
ASA congruence postulate says that if the two angles and the included side of a triangle are congruent to two angles and the included side of another triangle then the triangles are congruent. ABC ≅ XYZ
What is Congruent triangles ?Congruent triangles are those with precisely the same dimensions and appearance. Congruent has the symbol. When the dimensions of one triangle's three sides and three angles match those of another triangle's three sides and three angles, the two triangles are said to be congruent.
Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below.
According to the ASA criterion, ABC = XYZ because BC = YZ and B = Y and C = Z, respectively. Due to the fact that ABC = XYZ, the third angle (A) and the other two sides (A) of ABC must be equal to the equivalent angle (X) and sides of XYZ.
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Can you expand 3(x+5)
Answer:
3x+15
Step-by-step explanation:
distribute by multiplying 3 to each term
3(x)+3(5)
3x+15
Hopes this helps please mark brainliest
In a lottery daily game, a player picks three numbers from 0 to 9. How many different choices does the player have if the order doesn't matter?
For the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.
As given in the question,
Total number have to pick by a player in a lottery daily game is equal to 3
Numbers from which player have to pick the three numbers is 0 to 9
Total numbers from which player have to pick the three numbers = 10
Given condition : Order of the number does not matter
Total number of choices to pick three numbers from 0 to 9
= ¹⁰C₃
= ( 10! ) / ( 10 - 3 )! (3!)
= 10! / 7! 3!
= ( 10 × 9 × 8 × 7! ) / ( 7!) ( 3 × 2 × 1 )
= 10 × 3 × 4
=120 choices
Therefore, for the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.
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What does Asa congruent triangle mean?.
ASA congruent triangle stands for Angle-Side-Angle.
According to the question,
We have the following information:
ASA congruent triangle
We know that ASA is a property to prove that two triangles are congruent in the same way the properties are used to prove that two triangles are similar.
ASA stands Angle-Side-Angle which means that two triangles can be congruent if the two angles and one side of one triangle is equivalent to the corresponding two angles and side of the other triangle.
There are other properties to prove two triangles are congruent. For example, there is SSS and SAS.
Hence, ASA congruent triangle stands for Angle-Side-Angle.
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The product of two numbers is negative. Which statement is true? Select all that apply.
A The quotient of the two numbers is positive.
B The quotient of the two numbers is negative.
C No conclusion can be drawn about the quotient.
D The signs of both numbers are negative.
E The sign of one number is positive and the sign of the other is negative.
F Neither number is equal to zero.
The product of two numbers is negative. Which statement is true
B and E
How does the law of signs for multiplication work?
For division and multiplication: Positive results are obtained if the symptoms are same. If the signs disagree, the outcome is adverse.
Detailed explanation:
Let a and b be two separate numbers. A and B together have a negative product. The reason why the product of a and b is negative, according to the law of signs for multiplication, is because a and b have distinct signs—one is positive and the other is negative.
which claim is accurate?
A. The two numbers' quotient is a positive number. NO.
B. The two numbers' quotient is negative. YES. The quotient of two numbers with different signs is negative in accordance with the law of signs for division.
C. The quotient cannot be used to infer any conclusions. NO.
D. Both numbers have negative signs. NO.
E. One number has a positive sign, whereas the other has a negative sign. YES.
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What is an outlier example?.
If the data collection contains the following numbers: 3, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85 , Here 3 and 85 represents the outlier.
What is characteristics of statistics ?The important characteristics of Statistics are given as follows:
Statistics are always numerically expressed.It had an aggregate of facts and dataData are to be collected in systematic way.It should be always comparable to each otherData are collected for a pre planned purposeOutliers are the data's most wildly divergent values.
For instance, if the data collection contains the following numbers: 3 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85
The display of data and outliers
The numbers 3 and 85, which are at the extremes and are hence outliers in the number line above, may be seen to be at these extremes.
The group's outliers are a part of it, but they are not close to the other group members.
Outliers are a concern since they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=−3x^2+152x−1150
The price of the widgets for which it should be sold to make the maximum profit is $25.4 .
We know that the quadratic equation ax² + bx + c ,
if a < 0 , then the maximum value of the quadratic equation will be at x = -b/2a .
In the question ,
it is given that ,
a company is selling a widget ,
the selling price of each widget is = x ,
the profit made by the company = y ,
the equation of profit is given as y = −3x² + 152x − 1150 ,
where a = -3 , b = 152 and c = -1150,
we can see that in the given quadratic equation ,
a < 0 , so , the maximum will be at
x = -b/2a
x = -152/2(-3)
x = 152/6
x = 25.333
x ≈ 25.4
Therefore , the price of the widget is $25.4 .
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How can you determine if the two triangles are congruent by SAS?.
Answer:The SAS criterion for triangle congruence states that if two triangles have two pairs of congruent sides and the included angle (the one between the congruent sides) in one triangle is congruent to the included angle in the other triangle, then the triangles are congruent.
Step-by-step explanation:
How do you prove two triangles are congruent using SAS?
SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.
How can you determine if the two triangles are congruent?
So we know that two triangles are congruent if all of their sides are the same-- so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.
It cot Camp, Inc. $38 per unit to manufacture 1,000 unit per month of a product that it can ell for $54 each. Alternatively, Camp could proce the unit further into a more complex product, which would cot an additional $33 per unit. Camp could ell the more complex product for $81 each. How would proceing the product further affect Camp' profit?
There will be a loss of $6000.
What is loss?
In Maths, Loss share formula is that the formula to calculate the proportion loss happened in any business.
Loss = Cost Price – Selling Price
Main body:
Total unit produced = 1000
cost price of 1 unit = $38
Selling price of 1 unit = $54
profit on 1 unit = $54-$38
profit = $16
total profit on 1000 units = 16*1000
= $16000
After additional cost , cost price = 38+ 33 = $71
cost price after = $81
Profit on 1 unit = $10
profit on 1000 units = 10*1000
= $10000
Total profit/ loss after further addition = 16000-10000
therefore , loss of $6000 will be there.
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A, B and C are faces of the cuboid below. Calculate the area of each labelled face. Give your answers in m²
The Area of Face A is 12 m² and face B is 18 m² and face C is 54 m².
What is Area?Area is a measure of the amount of space enclosed by a two-dimensional shape or surface. It is a fundamental concept in geometry and is expressed in square units.
We have,
length = 9m
width = 6 m
height = 2m
So, the Area of face A
= l w
= 6 x 2
= 12 m²
and, area of Face B
= 9 x 2
= 18 m²
and, Area of face C
= 9 x 6
= 54 m²
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When the scale factor is greater 1 The image is an?.
When the scale factor is greater than 1, the image is larger than the pre-image.
What do dilations mean?Dilatation is a transformation that modifies a figure's size without changing its shape. Due to dilatation, a figure may grow or shrink. The preimage refers to the first figure in dilatation. It shows an expanded figure. Figures are warped from a fixed point called the center of dilatation.
What do enlargements and reductions mean?When you enlarge or reduce a figure, the scale factor indicates how much smaller or larger the result will be.
• When the scaling factor is between 0 and 1, the picture is smaller than the preimage. On a scale of 0 to 1, dilations are referred to as reductions.
• If the scale factor is more than 1, the image is bigger than the preimage. The definition of enlargement is a dilatation with a scale factor higher than 1. Each new point in a dilated figure is denoted by the prime sign, ". As an illustration, point', which denotes "prime," would be the enlarged version of point.
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please answer this question
Answer: (a 0.35) (b 33.18) (c 2.1) (d 0.0861) (e 0.322) (f 48) (g 5.491) (h 183.372)
Step-by-step explanation: what i did here is just take out the decimal and then multiply then after i put it where it makes more sense.
Bria wants to put a fence around the dog run in her back yard in Detroit. Since one side is adjacent to the house, she will only need to fence three sides. There are two long sides and one shorter side parallel to the house, and she needs 119 feet of fencing to enclose the dog run. The length of the long side is 3 feet less than two times the length of the short side. Find the dimensions of the sides of the fence. The length of the long side is __________ feet, and the length of the short side is __________ feet.
The length of the long and short side of Brian's fence in backyard in Detroit is 47 and 25 respectively.
Total length = length of two long sides + length of short side
Let the length of short side be x. So, length of long side = 2x - 3
Keep the values in formula
x + 2 (2x - 3) = 119
Performing multiplication on Left Hand Side
x + 4x - 6 = 119
Rewriting the equation
x + 4x = 119 + 6
Performing addition on both sides of equation
5x = 125
x = 125/5
Performing division on Right Hand Side
x = 25
Length of short side = 25
Length of long side = 2×25 - 3
Length of long side = 50 - 3
Length of long side = 47
Hence, the lengths are 25 and 47.
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What is radius r length?.
Radius defines the length between the center and corner point of the circle.
Circle:
Circle means a round shape that has no corners or line segments and it is a closed curve shape in geometry.
Given,
Here we have to define what is radius
As per the concept of the circle, radius is the half of the diameter.
Where the diameter a line segment through the center of a circle with its ends on the circle's circumference.
And the radius refers the straight line from the center to the circumference of a circle or sphere.
In order to find the radius, simply divide the diameter by 2.
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How do you know when the divisor is a factor of the dividend?.
The divisor is referred to as a dividend factor if it totally divides the payout, leaving no residual.
A divisor in a calculation is a number that divides the other number. According to the definition of a divisor, it is the term used to divide a dividend. For any division procedure, the remainder is always less than the divisor. All integers can be divided by 1, which is. The divisor will always equal one if the quotient and dividend are equal. The quotient will always equal one if the dividend and the divisor are equal. If there is no residue, the number can be divided evenly and is hence a perfect divisor of the dividend. The quotient will always equal a decimal number if the divisor is greater than the dividend.
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What is the GCD of 10 and 50?.
The greatest common divisor(GCD) of 10 and 50 is 10.
What is meant by GCD?The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.
In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.
Foe calculating the GCD of 10 and 50, we have to find the factors of 10 and 50.
Factors of 10:
1, 2, 5, 10
Factors of 50:
1, 2, 5, 10, 25, 50
From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 50 are 1, 2, 10, and 5.
So, the greatest factor of 10 and 50 is 10.
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in bowl of fruit there are green grapes and black grapes in the ratio 3:4.
if there are 24 grapes,how many black grapes are there
Answer:
32 black grapes
Step-by-step explanation:
24 green grapes
3:4
24÷3=8
8×4=32
there are 32 grapes
What is the 75 percentage of 25?.
in general, the duration of a bank's zero-coupon securities with short maturities is than the duration of its zero-coupon securities with long maturities.
In general, the duration of a bank's zero-coupon securities with short maturities is lower than the duration of its zero-coupon securities with long maturities.
What is zero coupon securities?Bonds with no interest payments are those whose face value is paid back at maturity. The phrase "zero-coupon bond" refers to a bond that does not have so-called coupons or periodic interest payments like conventional bonds do. The investor of the bond receives the bond's par value when it matures. Bonds with zero coupon rates do not accrue interest throughout the course of their lifetime. Instead, buyers purchase zero-coupon bonds at a significant discount to face value, which represents the sum the buyer will get when the bond "matures" or becomes due.
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A principal buys 30 boxes of markers and evenly divides the boxes among 12 teachers. What
fraction of a box of markers does each teacher receive?
Answer: [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Divide the boxes among the teachers will result in:
[tex]\frac{30}{12} =\frac{6(5)}{6(2)} =\frac{5}{2}[/tex]
So, each teacher will receive [tex]\frac{5}{2}[/tex] or 2.5 boxes of markers.
In a club of 13 members, 8 male and 5 female, how many ways can we form a committee of 5 male and 2 female with at least 3 men that must be at the committee?
This problem involves a series of Combinations
8 males, 3 at a time = Comb (8,3) = 56, which is multiplied by
5 females, 2 at a time = Comb (5,2) = 10
So, the base combination of 5 males & 2 females from 8 possible males and 5 possible females = 56 x 10 = 560.
However, the total combinations are further expanded by the condition that 3, 4 or 5 of the 5 male members must be present, which means that the 560 base combinations must be further multiplied by the subset combinations of 3 - 5 males that must be present out of the 5 male committee members. This expansion factor, then, is the Comb (5,3) x Comb (5,4). [Note that all 5 of 5 can be ignored as Comb (5,5)=1]. So, Comb (5,3) x Comb (5,4) = 10 x 5 = 50
The combined total are 560 x 50 = 28,000 possible combinations of 5 of 8 possible males & 3 females of 5 possible females with 3, 4 or 5 of the males being present.
Possible combinations that can be formed a committee of 5 male and 2 female with at least 3 men that must be at the committee from 13 members is 28000.
What is combination?
Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
C (n, r) = n! (r! n-r!)
According to the given question:
8 males, 3 at a time = Comb (8,3) = 56
5 females, 2 at a time = Comb (5,2) = 10
So, the base combination of 5 males & 2 females from 8 possible males and 5 possible females = 56 x 10 = 560.
However, the total combinations are further expanded by the condition that 3, 4 or 5 of the 5 male members must be present
This expansion factor is the Comb (5,3) x Comb (5,4).
So, Comb (5,3) x Comb (5,4) = 10 x 5 = 50
Therefore, the combined total are 560 x 50 = 28,000 possible combinations of 5 of 8 possible males & 3 females of 5 possible females with 3, 4 or 5 of the males being present.
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How much 93 is more than 47?.
93 is more than 47 by 46
Subtraction is an arithmetic operation that represents the operation of removing a number from another number. Subtraction is represented by the minus sign,
Other arithemetic operations are addition, multiplication and division.
The mathemetical properties that it follows is Identity Property.
Commutative Property and Associative Property.
Let the number by how much 47 is less than 93 be x,
then
47 + x = 93
x = 93 - 47
x = 46
Therefore, By subtracting it is found that 93 is greater than 47 by 46
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