Consider the function f(x,y) = 18y² + 497 +29xy + 82x+y (a) What is the value of the function at the point (x, y) = (8,4)? f(x, y) = The total differential of the function can be written as df(x, y) = Ady + Bd. (b) Find the values of A and B around the expansion point (x, y) = (8,4). A= B = at the point (2,y) = (8,4). (c) Find the derivative (4 decimal places) dz (d) Find the approximate new value of f(x,y) at the point (x, y) = (8.078, 3.934).(4 decimal places) 9 New approx value of f(x, ) = (e) Find the actual new value of f(x,y) at the point (x, y) = (8.078, 3.934) (4 decimal places) Answer (f) What is the percentage error in the approximation?

Answer:

Second option: 5E 10 = 5*10^(10) galaxies.

Step-by-step explanation:

The exponential notation is used as:

AE N

This is equal to:

A*10^(N)

And we need to add N zeros to the right of A.

While if we had:

AE - N

A*10^(-N)

We need to add N - 1 zeros at the left of A.

Now we have the number:

50,000,000,000

Let's count the number of zeros at the right of the 5, we have 10 zeros.

Then we would write this as:

5*10^(10)

OR

5E 10

Then the correct option is the second one.

Answer:

2. 5E10

Step-by-step explanation:

Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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The inequality that represents this situation is, (1 + x) > 2.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old.

Ava adopted her pig when it was 1 year old, and she has had it for x years.

∴ The inequality that represents this situation is,

(1 + x) > 2.

x > 2 - 1.

x > 1.

Ava adopted her pig for more than one year.

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Answer:

5g

Step-by-step explanation:

1. 0.04

2. 0.15

i just finished that assignment for properties of probability distributions.

i hope this is what you were looking for!

We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Two alternators are being connected to supply power to a load. After the connection is made, in order to make the added alternator share the load, the input torque to the alternator being added must be increased.

Tο supply pοwer tο a lοad using multiple alternatοrs, the input tοrque tο the added alternatοr shοuld be adjusted tο match the pοwer demand οf the lοad. The added alternatοr shοuld be synchrοnized with the existing alternatοrs and cοnnected in parallel tο share the lοad.

The input tοrque tο the added alternatοr will depend οn the pοwer required by the lοad and the characteristics οf the alternatοrs, such as their pοwer ratings and efficiency. By prοperly adjusting the input tοrque οf the added alternatοr, it can cοntribute tο supplying pοwer tο the lοad alοng with the existing alternatοrs.

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If you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

To determine the probability that you have tetrachromacy given a positive test result, we can use Bayes' theorem. Let's define the following probabilities:

P(T) = Probability of having tetrachromacy (10% or 0.1)

P(¬T) = Probability of not having tetrachromacy (90% or 0.9)

P(Pos|T) = Probability of a positive test result given tetrachromacy (true positive rate, 70% or 0.7)

P(Pos|¬T) = Probability of a positive test result given no tetrachromacy (false positive rate, 14% or 0.14)

We want to find P(T|Pos), the probability of having tetrachromacy given a positive test result.

According to Bayes' theorem:

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

To find P(Pos), the probability of a positive test result, we can use the law of total probability:

P(Pos) = P(Pos|T) * P(T) + P(Pos|¬T) * P(¬T)

Plugging in the values:

P(Pos) = (0.7 * 0.1) + (0.14 * 0.9)

= 0.07 + 0.126

= 0.196

Now we can calculate P(T|Pos):

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

= (0.7 * 0.1) / 0.196

= 0.07 / 0.196

≈ 0.3571

Therefore, if you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

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Answer: solutions are the same, just written differently, inequality sign is reversed when multiplying by a negative. Yes, both students are correct.Jul 8, 2018

Step-by-step explanation:

Answer:

probably about like 2 feet

Step-by-step explanation:

beetlejuice

The correct confidence interval for the mean lifetime of this type of battery is (114.56, 125.64).

Explanation:
We know that the sample size n is 50, the sample mean x is 120.1, and the population standard deviation is 20. We want to construct a 99% confidence interval for the mean lifetime of this type of battery.

The formula for the confidence interval is:

x ± z*(σ/√n)

where x is the sample mean,  is the population standard deviation, n is the sample size, and z is the z-score that corresponds to the desired confidence level.
   
For a 99% confidence interval, the z-score is 2.576 (using a z-score table or calculator).    
   
Plugging in the values, we get:

120.1 ± 2.576*(20/√50)

= (114.56, 125.64)

Therefore, the confidence interval for the mean lifetime of this type of battery is (114.56, 125.64) with 99% confidence.
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The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

To estimate the difference in earnings between Tamekia and Marsha, we can find the average hourly rates for each and use them to calculate an approximate earnings difference.

For Tamekia:

The hourly rate is between $6.00 and $6.25.

The average hourly rate is approximately $(6.00 + 6.25) / 2 = $6.125.

For Marsha:

The hourly rate is between $7.50 and $8.00.

The average hourly rate is approximately $(7.50 + 8.00) / 2 = $7.75.

If they each work 22 hours, Tamekia would earn approximately $6.125 x 22 = $134.75, and Marsha would earn approximately $7.75 x 22 = $170.50.

The difference in earnings between Marsha and Tamekia would be approximately $170.50 - $134.75 = $35.75.

Therefore, Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.

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In the given question both the options D and E are necessary for the Central Limit Theorem to hold.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that describes the behavior of sample means when the sample size is large. According to the CLT, the distribution of sample means approaches a normal distribution regardless of the shape of the original population distribution, given certain conditions.

Option A states that each individual measurement must be normally distributed. This is not a necessary condition for the CLT to hold. The original population distribution does not have to be normal; it can be any distribution shape.

Option B states that each individual measurement must be identically distributed. This is not a necessary condition for the CLT to hold. The measurements can have different distributions, as long as they satisfy the other conditions.

Option C states that each individual measurement must be independent of every other measurement. This is a necessary condition for the CLT to hold. The independence of measurements ensures that each observation contributes to the overall sample mean independently, without being influenced by other observations.

Therefore, options D and E are the correct choices. Both the independence of measurements (option C) and a sufficient sample size (option B) are necessary conditions for the Central Limit Theorem to hold.

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Answer:

\(k=\frac{6+z}{3}\)

Step-by-step explanation:

We are given the following equation:

6k - 2z = 12

We want to solve it for k.

To do that, we need to isolate the variable on one side.

6k - 2z = 12

To start, add 2z to both sides.

6k - 2z = 12

     +2z    +2z

______________

6k = 12 + 2z

now, divide by 6 on both sides. When dividing on the left, we're dividing the entire expression by 6.

6k = (12 + 2z)

÷6    ÷6

______________

\(k=\frac{12+2z}{6}\)

This can be simplified to become:

\(k=\frac{6+z}{3}\)

Answer:

\(\sf{k=2+\dfrac{1}{3}z}\)

Explanation:

Our equation is

\(\sf{6k-2z=12}\)

We need to solve it for k. So I am going to start by adding 2z on each side:

\(\sf{6k=12+2z}\)

Then, I'll divide each term by 6:

\(\sf{k=\dfrac{12}{6}+\dfrac{2z}{6}}\)

\(\sf{k=2+\dfrac{1}{3}z}\)

Hence, this is the equation.

Answer:

2, 7, 12.

Step-by-step explanation:

Substitute n = 1, n = 2 and n = 3:

First term = 5(1) - 3 = 5-3 = 2

Second = 5(2) - 3 = 7

Third = 5(3) - 3 = 12.

Some information that someone might use to solve problems related to a circle design is the Tangent Arc theorem.

The tangent arc theorem states that if an angle is formed by two secants, one secant, one tangent, or two tangents, and also intersects in a space outside of the circle, then the value obtained will be equal to the difference of the values of the intercepted arcs divided by one and a half.

Also, note that angles outside a circle are those whose vertex or arc is pointed outwards and their sides are either secants or tangents. With this information, it will be possible to solve problems related to tangent lines and arc measures.

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The number of ways of 3 volumes chosen at random is 455.

The number of ways that will include volume 1 and volume 2 is 13 and

The number of ways that will include volume 1 but not volume 2 is 156

Permutation and combination

In Mathematics, Permutation and combination are the ways of representing a group of objects by selecting from a set and forming subsets. These define the different types of ways to arrange a certain group of data.

When we select objects from a group, it is said to be permutations, whereas the combination is a way of selecting items, here the order of selection does not matter.

The formula for the combination of x things from a set of n things without replacement is given by

Here we have,

Number of volumes of  an encyclopedia = 15

Number volumes were chosen at a time = 3

From above formula

The number of ways of 3 volumes is chosen at random is

¹⁵C₃ = 15!/3!(15 - 3)!  

= 15!/3!(12)!  

= 15 × 14 × 13 × 12! / 6 (12!)

= 455  

(b) Including volume 1 and volume 2

To Include volume 1 and volume 2 in the set, first, we choose volume 1 and volume 2, and then we must choose the 3rd volume from the remaining volumes from 3 to 15 volumes [total 13 volumes].

Therefore the number of ways that will include volume 1 and volume 2

= 1 × 1 × 13 = 13  

(c) Including volume 1 but not volume 2

Here we are including volume 1 but not volume 2, for that in the first place we chose volume 1, for the second and third place we must choose from the remaining volumes 3 to 15 [total 13 volumes except 2 ]

The number of ways that will include volume 1 but not volume 2

= 1 × 13 × 12

= 156

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Answer:

The mistake is in step 2

Step-by-step explanation:

We are given h(x)=4-x

Note: Considering h(x)=4-x as in question given there is some issue. If value of h(x) is different the answer would be different.

and g(x)=2x+10

We need to find h(g(x))

h(g(x)) can be found by putting the value of g(x) in h(x)

Steps used by Mario are:

Step 1: h(g(x)) = 4 - x

Step 2: h(g(x)) = 4 - x + 10

Step 3: h(g(x)) = 14 - X

She did mistake in step 2:

The step 2 should be:

h(g(x))=4-(2x+10)

h(g(x))= 4-2x-10

h(g(x))=-6-2x

So, the mistake is in step 2

The expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.

We can calculate this by using the formula for the geometric series. The formula for the geometric series is given by S = a1(1-rn)/1-r, where a1 is the first term in the series, r is the common ratio, and n is the number of terms. In this problem, a1 = 1 (since the probability of finding the first applicant with advanced training is 1/8), and r = 1/8 (since the probability of finding the next applicant with advanced training is 1/8). Thus, plugging these values into the formula yields S = 1(1-(1/8)^n)/1-(1/8) = 8. Therefore, the expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.

S = a1(1-rn)/1-r

S =\(1(1-(1/8)^n)/1-(1/8)\)

S = 8

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The limit of the sequence (1) {2}, (2) {(-1)^n}, and (3) {n sin(n)}, converges to DNE (does not exist) or the sequence diverges. The limit of the sequence (4) {sin(nπ)} is undefined, as it oscillates between -1 and 1.

In the case of sequence (1) {2}, the limit is a constant value, and the sequence converges to that value. However, in the case of sequence (2) {(-1)^n}, the sequence oscillates between -1 and 1, and there is no single value that it approaches as n tends to infinity. Therefore, the limit does not exist, and the sequence diverges.

Sequence (3) {n sin(n)} also does not have a limit as n tends to infinity. The term n sin(n) oscillates between positive and negative values without approaching a specific value. Hence, the limit of this sequence is DNE, and it diverges.

In the case of sequence (4) {sin(nπ)}, the term sin(nπ) oscillates between -1 and 1 as n varies. Since there is no convergence to a specific value, the limit of this sequence is undefined.

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Answer:

A. 13/20

Step-by-step explanation:

The total area of the given shape is 71cm².

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.

The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.

Area of rectangle= 7*8= 56 cm²

Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²

Total area of shape = 56+15= 71 cm²

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The width of the walkway should be approximately 4.32 feet.

Let's call the width of the walkway "w". Then the width of the entire area (pool + walkway) will be:

15 + 2w (the original 15 feet of the pool plus the extra "w" feet of walkway on each side)

and the height of the entire area will be:

9 + 2w (the original 9 feet of the pool plus the extra "w" feet of walkway on each end)

So the total area of the entire area (pool + walkway) will be:

(15 + 2w) × (9 + 2w)

To find the width of the walkway that gives a total area of 567 square feet, we can set this expression equal to 567 and solve for w:

(15 + 2w) × (9 + 2w) = 567

Expanding the expression on the left side:

135 + 45w + 30w + 4w² = 567

Simplifying and rearranging:

4w² + 75w - 432 = 0

We can solve this quadratic equation using the quadratic formula:

w = (-b ± sqrt(b² - 4ac)) / 2a

where a = 4, b = 75, and c = -432. Plugging in these values, we get:

w = (-75 ± sqrt(75² - 4 × 4 × -432)) / 8

w ≈ 4.32 or w ≈ -25.07

Since we are looking for a width of a walkway, we should choose the positive solution:

w ≈ 4.32 feet

Therefore, the width of the walkway should be approximately 4.32 feet.

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Answer:

The drum capacity is 180 liters.

Step-by-step explanation:

Let the capacity of the drum be c.  Then the contents of the drum at the beginning are (3/4)c, and

if 30 liters are drawn out, then the contents are (3/4)c - 30 liters = (7/12)c.

Here the LCD is 12, and so we have (9/12)c - (7/12)c = 30 liters, or

(2/12)c = 30 liters, or c = (12/2)(30 liters) = 180 liters

The drum capacity is 180 liters.

Answer:

The capacity of the drum is 180 liters

Step-by-step explanation:

3/4x - 30 = 7/12x

3/4x - 7/12x = 30

9/12x - 7/12x = 30

2/12x = 30

1/6x = 30

x = 30*6

x = 180 liters

5 (2 cups of vinegar+ 2 cups of baking soda = 5 cups of fizzy mess)

or 4

Answer:

S = $10.20

Step-by-step explanation:

s = 12 - .15 (12)

s = 12 - 1.80

s = $10.20

If 15% comes off the price, then 85% of the price is left to pay. (100 - 15 = 85)

12 x .85 = $10.20

Answer:

\(Total\ Rent = 49 + 5m\)

Step-by-step explanation:

Given

Rent per day = $49

Addition = 5 cents per mile

Required

Determine the rent for a day and m miles

First, we need to generate a formula from the given parameters;

Let d represent number of days and m represent additional miles;

\(Total\ Rent = 49 * d + 5 * m\)

\(Total\ Rent = 49 d + 5 m\)

Solving for the rent for a day and m miles

We have that: d = 1 and m = m

Substitute these in the formula above

\(Total\ Rent = 49 * 1 + 5 * m\)

\(Total\ Rent = 49 + 5m\)

Hence, the total rent is

\(Total\ Rent = 49 + 5m\)

Answer:

Area=190.091 cm^2

Step-by-step explanation:

Area = 1/2(Pi x r^2)    one-half because it's a semi-circle

Area=1/2(3.14 x 11^2)

11^2=121 so, Area=1/2(3.14 x 121)

Area=1/2(379.94)

Area=189.97 cm^2

adjustment:

Area=1/2(3.142 x 11^2)

Area=1/2(3.142 x 121)

Area=1/2(380.182)

Area=190.091