Find the best quadratic approximation, Q(x, y) of √1 – 5x – y for (x, y) near (0,0) Q(x, y) = ___

Answer: y=4x-9. --------------------->1

given (3,a) (x,y)

let the unknown be a

put the value of 3 in equation 1

y=4(3)-9

y=3

so the missing value is 3

Step-by-step explanation:

The coefficient of (3y² + 9)5 is 15.

A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.

Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.

a₀ is the leading coefficient.

In the question, we are asked to identify the coefficient of (3y² + 9)5.

First, we expand the given expression:

(3y² + 9)5

= 15y² + 45.

Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.

Thus, the coefficient of (3y² + 9)5 is 15.

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Answer:

C

Step-by-step explanation:

The probability that a college student selected at random has cheated on an exam is 0.3328 or 33.28% .

The given problem requires us to find the probability that a student has cheated on an exam given that the number of college students who have cheated on an exam is 855 and the number of students who have not cheated on an exam is 1717.

The total number of students is the sum of those who have cheated and those who have not cheated.

Total number of possible outcomes = Number of students who have cheated on an exam + Number of students who have not cheated on an exam

= 855 + 1717

= 2572

Therefore, the probability that a college student selected at random has cheated on an exam is:

P(C) = Number of outcomes favorable to event C / Total number of possible outcomes

= 855 / 2572

= 0.3328 or 33.28% (approx.)

Hence, the probability that the student has cheated on an exam is 0.3328 or 33.28% (approx.).

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Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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Answer:

144

Step-by-step explanation:

Answer:

The answer is 144.

Step-by-step explanation:

It's 144 quarts because there are 4 quarts in a gallon, multiply the 36 gallons by 4x as many quarts and get the answer 144.

The accountant's claim is: the proportion of tax filers that receive a refund is less than 25%. The Option B is correct.

The accountant's claim is based on their belief that the upcoming tax year will have a smaller proportion of tax refunds than the proportion from the previous year.

To test the claim, the accountant samples few of their clients and determines that proportion of clients receiving refund for the upcoming tax year is 19%.

This sample proportion of 19% is lower than the proportion of 25% from the previous year which supports the accountant's claim that the proportion of tax filers receiving a refund is less than 25%.

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Answer:

I got 0.84

Step-by-step explanation:

Answer:

0.60109487083

Step-by-step explanation:

Straight up can look it up or use calculator

Given data:

The expression for the equation of the line is 6x-8y=40.

The given equation can be written as,

6x-8y=40

8y=6x-40

y=6x/8-40/8

=3x/4-5

Thus, the slope intercept form is y=3x/4-5.

Answer:

option 6b):) is correct

The probability that all adjacent points differ in color is given as follows:

1/10. (second option).

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the total outcomes, we have an arrangement of 6 elements, due to the six points, with 3 and 3 repetitions, as 3 are green and 3 are red, hence the number of total outcomes is calculated as follows:

\(T = A_6^{3,3} = \frac{6!}{3!3!} = 20\)

For the desired outcomes, there are two, given as follows:

This means that the probability that all adjacent points differ in color is calculated as follows:

p = 2/20 = 1/10.

Hence the second option is the correct option.

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Answer:

Step-by-step explanation:

1 in: 30 km

4.3 inches * 30km= 129 km

Since every inch is the same as 30 km.

Second problem

20 test: 163 mins

8.15 mins per test

44*8.15= 358.6 mins round to the nearest whole is 359 mins

Answer:

Step-by-step explanation:

Divide: 1

3 : 14 = 13 · 4 1 = 1 · 4 3 · 1 = 43

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1

4 is 4 1

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - one third divided by one quarter = four thirds.

Answer:

11

Step-by-step explanation:

44/4 = 11

4/4 = 1

then:

44/4 = 11/1 = 11

(a) The revenue if 600 coats are sold is $66,000. (b) 500 coats must be sold to have a revenue of $55,000. (c) The y-intercept of the graph of the equation is (0,0). (d) The slope of the graph of the equation is 110.

(a) The revenue if 600 coats are sold is $66,000.

To find the revenue if 600 coats are sold, we simply plug in 600 for x in the given formula:

y = 110x
y = 110(600)
y = 66,000

Therefore, the revenue from the sale of 600 coats is $66,000.

(b) To find how many coats must be sold to have a revenue of $55,000, we set the revenue formula equal to 55,000 and solve for x:

y = 110x
55,000 = 110x
x = 500

Therefore, 500 coats must be sold to have a revenue of $55,000.

(c) The y-intercept of the graph of the equation is (0,0). This means that when no coats are sold, there is no revenue generated.

(d) The slope of the graph of the equation is 110. This means that for every additional coat sold, the revenue increases by $110. In other words, the slope represents the rate of change of revenue with respect to the number of coats sold.

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Answer:

22x-18

Step-by-step explanation:

Simplify: 6x+2(-9+8x)

Distribute:

=6x(2)(-9)+(2)(8x)

=6x+-18+16x

Combine like terms:

=6x+-18+16x

=(6x+16x)+(-18)

=22x+-18

Point C is located at (4,5)

It means

x= 4

y= 5

The only graph that has Point C at (4,5) is graph C.

Graph A, B, and D have point C on (5,5) , (5,4), and (4,-2)

Graph C also has the distance between A and B equal to 4 units, and the distance between B and C equal to 3 units.

Answer: C

Answer:

w

Step-by-step explanation:

If we randomly select 50 full-time college students in each of the 50 states, then a stratified type of sample is obtained.

Stratified sampling can be described as a kind of sampling in which smaller batches called strata are formed in which the given population is divided based on their characteristics. The population with common attributes is placed in the same subgroup or strata.

In this problem, the 50 states are the independent subgroups and are considered as 50 strata, and in each strata, 50 random samples which are college students in this case are selected randomly.

Random sampling is the simplest form of sampling in which a subset of individuals is chosen from a single, larger population. Systematic sampling also involves a single, larger population with a fixed periodic interval.

On the other hand, convenience sampling is a type of non-probability sampling, which doesn't include random selection.

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The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.

p = 0.69

1 - p = 0.31

n = 209

μp = p = 0.69

σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199

= 1 - p(p < 0.72)

= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)

= 1 - p(z < 0.94)

= 1 - 0.8264

= 0.1736

Hence, the probability is 0.1736.

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Answer:

\(x = p(m-n)\)

Step-by-step explanation:

m = n + \(\frac{x}{p}\)

Subtracting n to both sides

=> m-n = \(\frac{x}{p}\)

Multiplying p to both sides

=> \(x = p(m-n)\)

Answer:

x=p(m-n)

Step-by-step explanation:

m =n + x/p

x/p=m-n

x=p(m-n)

The amount of interest John will get after 12 years given his savings and interest rate is 1,680 Euros

Simple interest is a type of interest rate paid only on principal. It is called by multiplying principal by interest rate by time.

Simple interest = principal × rate × time

= 14,000 × 0.01 × 12

= 1,680 Euros

In conclusion, given John's savings and interest rate, he'll earn 1,680 Euros as interest after 12 years.

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Answer:

3^3 = 27, so C

Please give brainliest :)

Answer:

Step-by-step explanation:

We know that:

To find out if the LHS and the RHS are equal or not, we will need to simplify both sides of the equation.

Solution:

Hence, both sides of the equation are not equal.

\(\\ \tt\longmapsto 8+7-22\)

\(\\ \tt\longmapsto 15-22\)

\(\\ \tt\longmapsto -7\)

And

\(\\ \tt\longmapsto 3^2+2=9+2=11\)

Clear cut

Answer:

-55

Step-by-step explanation:

Substitute the given numbers for the variables; a = -6, b = -5

5(-6)+5(-5)

-30-25=-55

Hopefully this helps!

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ - 55}}}}}\)

Step-by-step explanation:

Given, a = -6 , b = -5

\( \sf{5a + 5b}\)

plug the value of a and b

⇒\( \sf{5 \times ( - 6) + 5 \times ( -5)}\)

Multiply the numbers

⇒\( \sf{ - 30 + ( - 25)}\)

We know that , \( \sf{( + ) \times ( - ) = ( - )}\)

⇒\( \sf{ - 30 - 25}\)

Calculate

⇒\( \sf{ - 55}\)

Hope I helped!

Best regards! :D

If we are standing at a personal distance from someone, you are typically 18 inches to 4 feet apart. This range allows for comfortable interaction while still maintaining a sense of personal space.

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If you are standing a personal distance from someone, you are typically 18 inches to 4 feet apart. This range is commonly referred to as the "personal space" or "social distance" zone.

personal distance can vary depending on cultural norms and individual preferences. However, in general, this distance is considered a comfortable distance for conversation and interaction with friends, family, and acquaintances.

If you are standing closer than 18 inches, it is considered the "intimate distance" zone and typically reserved for romantic partners or close family members. If you are standing farther than 4 feet, it is considered the "public distance" zone and typically used for formal interactions or public speaking.

the distance between you and someone else when standing a personal distance away is typically between 18 inches to 4 feet. However, it is important to remember that personal distance can vary and be influenced by cultural norms and individual preferences. This long answer provides a comprehensive explanation of personal distance and its various zones.

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a. Probability Mass Function: A probability mass function (pmf) is a function that is used to describe the probabilities of all possible discrete values in a probability distribution. Let X and Y be the initially diagnosed patient's score and after three months of treatment respectively.

The probability mass function of X is: f(x) = P(X = x), where x = 1, 2, 3, 4.From the given data, we can see that:P(X = 1) = 0.08 + 0.06 + 0.04 + 0.02 = 0.20P(X = 2) = 0.06 + 0.12 + 0.08 + 0.04 = 0.30P(X = 3) = 0.03 + 0.09 + 0.12 + 0.06 = 0.30P(X = 4) = 0.01 + 0.03 + 0.07 + 0.09 = 0.20Therefore, the probability mass function of X is:f(1) = 0.2, f(2) = 0.3, f(3) = 0.3, f(4) = 0.2Similarly, we can find the probability mass function of Y, which is: f(y) = P(Y = y), where y = 1, 2, 3, 4.From the given data, we can see that:P(Y = 1) = 0.08 + 0.06 + 0.03 + 0.01 = 0.18P(Y = 2) = 0.06 + 0.12 + 0.09 + 0.03 = 0.30P(Y = 3) = 0.04 + 0.08 + 0.12 + 0.07 = 0.31P(Y = 4) = 0.02 + 0.04 + 0.06 + 0.09 = 0.21Therefore, the probability mass function of Y is:f(1) = 0.18, f(2) = 0.3, f(3) = 0.31, f(4) = 0.21b.

Expected Value: The expected value is a measure of the central tendency of a random variable. It is the mean value that would be obtained if we repeated an experiment many times. The expected value of X is:E(X) = ∑xiP(X = xi) = 1(0.2) + 2(0.3) + 3(0.3) + 4(0.2) = 2.3The expected value of Y is:E(Y) = ∑yiP(Y = yi) = 1(0.18) + 2(0.3) + 3(0.31) + 4(0.21) = 2.33c. Variance: The variance is a measure of the spread of a random variable. It gives us an idea of how much the values in a distribution vary from the expected value.

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The radius of the circle is 3.12 inch.

A triangle having two sides of equal length. Additionally equal are the angles that face the equal sides. Triangle of isosceles. Having two identical sides and angles.

Calculation for the radius of the circle;

Consider the isosceles triangle ABC inscribed in a a circle (attached figure)

Sides AB = AC = 5 inches.

Side BC = 6 inches.

Join OB, OC and OA.

Draw perpendicular on BC from AD which passes from the centre O.

OD bisects BC at point D.

So, BD = DC = 3 inches.

In the right angled triangle ABC

AB² = AD² + BD²

5² = AD² + 3²

AD² = 16

AD = 4 inches.

Let the radius of the circle be r.

Then, OB = OC = OA =  r

OD = AD - AO

OD = 4 - r

In the right angled triangle OBD;

OB² = OD² + BD²

r² = (4-r)² + 3³

On solving,

r = 25/8 = 3.12

Therefore, the radius of the circle comes out to be 3.12 inches.

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