Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra system to confirm your results. f(x, y) = x^2 - 4xy + 6 R = {(x, y): 1 lessthanorequalto x lessthanorequalto 4, 0 lessthanorequalto y lessthanorequalto 2} absolute maximum (x, y, z) = () absolute minimum (x, y, z) = ()

Answer:

Base=8 feet

Height=17 feet

Step-by-step explanation:

Let

Base=x

Height=3x-7

Area=68 square feet

Area of the sail boat=1/2 * base * height

68 = 1/2 * x * (3x-7)

Cross product

68 * 2 =(1) * (x) * (3x-7)

136 = 3x^2 - 7x

3x^2 - 7x - 136=0

Using quadratic formula

x= -b +or- √b^2 - 4ac / 2a

= -(-7) +or- √(-7)^2 - (4)(3)(-136) / 2(3)

= 7 +or- √49 - (-1632) / 6

= 7 +or- √49+1632) / 6

= 7 +or- √1681 / 6

=7 +or- 41 /6

x= 7+41 / 6 or 7-41 / 6

=48/6 or -34/6

=8 or -17/3

Answer:

Step-by-step explanation:

Let

Base=x

Height=3x-7

Area=68 square feet

Area of the sail boat=1/2 * base * height

68 = 1/2 * x * (3x-7)

Cross product

68 * 2 =(1) * (x) * (3x-7)

136 = 3x^2 - 7x

3x^2 - 7x - 136=0

Base of the boat can't be a negative value

Therefore,

Base = x = 8 feet

Height= 3x-7

=3(8)-7

=24-7

=17 feet

Answer:

5m  the last option is correct

Step-by-step explanation:

by phythagorean theorem

hypotenuse^2=base^2+altitude^2

hypotenuse ^2= (4)^2+(3)^2

                        =16+9

                        =25

taking square root on both isdes

 hypotenuse=5 m

Glow costs 16/27 dollars, which is equal to 59.3 cents per volume unit.

Let's start by assigning variables to the unknown prices and volumes of the toothpastes. Let x be the price per unit volume of Fresh, y be the price per unit volume of Glow, and z be the price per unit volume of Bright. Let v1 be the volume of Fresh, v2 be the volume of Glow, and v3 be the volume of Bright. From the information given in the problem, we can set up the following equations:

z = 1.6y (a tube of Bright is 60% more expensive than a tube of Fresh)

v3 = 0.75v2 (a tube of Bright has 25% less volume than Glow)

y = 0.75z (a tube of Glow is 25% less expensive than a tube of Bright)

v2 = v1 + 100/3 (a tube of Glow has 100/3 more volume than Fresh)

We can substitute the first equation into the second equation to eliminate z:

v3 = 0.75v2

(substitute v2 = 0.75z and v1 = 1)

0.75v2 = 0.75(0.75z + 100/3)

0.75v2 = 0.5625z + 25

(substitute z = 1.6y and v2 = v1 + 100/3)

0.75(v1 + 100/3) = 0.5625(1.6y) + 25

0.75v1 + 25/3 = 0.9y + 25

0.75v1 = 0.9y + 50/3

We can substitute the third equation into the fourth equation to eliminate y:

v2 = v1 + 100/3

(substitute y = 0.75z)

0.75z = 0.75(0.75y) + 100/3

z = y + 16/9

(substitute z = 1.6y)

1.6y = y + 16/9

y = 16/27

Therefore, the price per unit volume of Glow is 16/27 dollars, or 59.3 cents per unit of volume.

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A simple random sample of tanks is selected and the sample mean capacity is found to be 8550 gallons. Therefore, The z score corresponding to a tank with a capacity of 8550 gallons is z = 0.50.

We can see that the actual capacity of the tank is normally distributed with a mean of 8544 gallons and a standard deviation of 12 gallons.

The actual capacity of the tank is normally distributed.

Let X = the actual volume of the tank

SO, X ~ Normal(μ = 8544 , σ² = (12)²)

The normal z-score probability distribution is given by:

                   Z = ~ N(0,1)

where μ = average capacity = 8544 gallons

           σ = standard deviation = 12 gallons

Z score measures how many standard deviations the measurements are from the mean To do. Once you have determined the Z-score, look at the Z-score table to find the p-value (area) associated with that Z-score. This p-value is the probability that the value of the measure is less than X. which means that Percentile of X.

Now,

The probability of a randomly selected tank having a capacity of less than 8550 gallons is given by = P(X < 8550 gallons)

   P(X < 8550 gallons) = P ( X - μ /σ < 8550 - 8544/12 )

                                     = P(Z < 0.50)

                                      = 0.6915

The above probabilities are calculated considering the value of x = 0.50 in a z-table with an area of ​​0.6915.

Therefore,  The Z value corresponding to a tank with a capacity of 8550 gallons is z=0.

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

Step-by-step explanation:

\(\frac{X}{2} =\frac{X+2}{3} \\\\3x=2x+4\\\\x=4\)

hope it helps....

Answer:

Wat w Polsce i w sumie to nic innego niż

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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Answer: 12 people or less

Step-by-step explanation:

114≥30+5x+2x

114-30≥5x+2x

84≥7x

84/7≥7x/7

12≥x

There can be at  12 people or less who can attend the Friday night

Work Shown:

C = 2*pi*r

78.5 = 2*3.14*r

78.5 = 6.28r

r = (78.5)/(6.28)

r = 12.5

Since triangles abc and xyz are similar, their corresponding sides are proportional.

Let's label the sides of triangle xyz as a, b, and c. We know that the smallest side of xyz (side a) is 52 cm. We need to find the length of the longest side of xyz (which we can label as side c).
We can set up a proportion to solve for c:  121/52 = 105/b = 98/c
Solving for b, we get:  121/52 = 105/b
b = (105*52)/121
b ≈ 45.6
Now we can set up a new proportion to solve for c:  121/52 = 98/c
Multiplying both sides by c, we get:  121c/52 = 98
Solving for c, we get:
c = (98*52)/121
c ≈ 42.3
Therefore, the length of the longest side of xyz is approximately 42.3 cm.

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These are the true sentences that can be constructed using the symbols:

Increasing function:

If for all x in the open interval containing x₁ and x₂ such that x₁ < x < x₂, then f(x₁) < f(x).

Decreasing function:

If for all x in the open interval containing x₁ and x₂ such that x₁ < x < x₂, then f(x₁) > f(x).

Constant function:

If for all x in the open interval containing x₁ and x₂, then f(x₁) = f(x).

These symbols can be used in constructing true sentences:

Increasing function:

x₁ < x₂ and f(x₁) < f(x₂)

x₁ < x₂ and f(x₁) ≤ f(x₂)

x₁ < x₂ and f(x) < f(x₂) for all x in the open interval containing x₁ and x₂

Decreasing function:

x₁ < x₂ and f(x₁) > f(x₂)

x₁ < x₂ and f(x₁) ≥ f(x₂)

x₁ < x₂ and f(x) > f(x₂) for all x in the open interval containing x₁ and x₂

Constant function:

f(x₁) = f(x₂)

f(x) = f(x₁) for all x in the open interval containing x₁ and x₂

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Answer:

-1 infinite

Step-by-step explanation:

The most effective way to represent the relative distance between star systems within a galaxy is by using  logarithmic scale.

By compressing the vast distances in space logarithmically, we can create a manageable visual representation that allows for a better understanding of the relative proximity of different star systems.

Using the scale allows us to capture the immense distances involved in interstellar space while maintaining a manageable visual representation. By assigning increasing increments of distance to logarithmic intervals, we can create a proportional representation that preserves the relative distances between star systems.

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Answer:

---------------------

Solve in below steps:

No solutions as we ended up with false equality.

Answer:

no solution

Step-by-step explanation:

0.5 ( -2 + 4d ) - 2d = -13

Solve the brackets.

-1 + 2d - 2d = -13

The term "-2d" cancels out, leaving us with:

-1 = -13

Since this equation is not true (the left side does not equal the right side), there is no solution to the equation.

In other words, there is no value of "d" that satisfies the equation.

The measure of reliability of a statistical inference is the significance level. The significance level, also known as alpha, is the probability of rejecting the null hypothesis when it is actually true. It determines the threshold for accepting or rejecting a hypothesis.

A lower significance level indicates a higher level of confidence in the results. A descriptive statistic provides information about the data, but it does not directly measure the reliability of a statistical inference. It simply summarizes and describes the characteristics of the data.

A sample statistic is a numerical value calculated from a sample, such as the mean or standard deviation. While it can be used to make inferences about the population, it does not measure the reliability of those inferences.
A population parameter is a numerical value that describes a population, such as the population mean or proportion.

While it provides information about the population, it does not measure the reliability of inferences made from a sample. In conclusion, the significance level is the measure of reliability in a statistical inference as it determines the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

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The statement AA\B)=B is proven by showing that every element in AA\B is also in B. A counterexample is provided to demonstrate its invalidity without assuming B⊂A.

To prove that AA\B)=B, we need to show that every element in AA\B is also in B, and vice versa.

Step 1: Let x be an arbitrary element in AA\B. This means that x is in A but not in B. Since B⊂A, x must be in A but not in B, which implies that x is also in A. Therefore, x is in both A and A, so x is in AA.

Step 2: Since x is in AA and not in B, x is not in A\B. This means that x is either not in A or in B. However, since we know that x is in A, it must be the case that x is in B.

Therefore, we have shown that every element in AA\B is also in B. Hence, we can conclude that AA\B)=B.

To provide an example that demonstrates the statement is not true without assuming B⊂A, consider the following:

Let A = {1, 2, 3} and B = {2, 3, 4}. In this case, B is not a subset of A.

Now, let's calculate AA\B and see if it equals B:

AA = {{1, 1}, {1, 2}, {1, 3}, {2, 1}, {2, 2}, {2, 3}, {3, 1}, {3, 2}, {3, 3}}

AA\B = {{1, 1}, {2, 1}, {3, 1}}

However, B = {2, 3, 4}

Since AA\B is not equal to B, this example illustrates that the statement AA\B)=B is not true without assuming B⊂A.

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Answer:

x = 9

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) ⇔ \(a^{(m+n)}\)

Given

\(11^{x}\) = \(11^{4}\) × \(11^{5}\) = \(11^{(4+5)}\) = \(11^{9}\)

Since the bases on both sides are common, then equate the exponents

x = 9

Answer:

68%

Step-by-step explanation:

In normal distribution, the empirical rule (aka 68-95-99.7 rule) describes the approximate proportion of data that falls within certain distances from the mean of a normal distribution. Specifically, the rule states that:

A sample distribution with n = 20 and a five-number summary of 2, 4, 6, 8, and 10 can be generated by arranging the values in increasing order as follows: 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10.

To construct a sample distribution with a specific five-number summary, we need to determine the arrangement of values within the dataset. The five-number summary consists of the minimum value (2), the first quartile (Q1, 4), the median (Q2, 6), the third quartile (Q3, 8), and the maximum value (10).

Since the dataset has 20 observations, we need to arrange these values in increasing order while ensuring that they match the given five-number summary. In this case, we can start by placing the minimum value of 2 at the beginning of the dataset. Next, we need to include additional values between 2 and 4 to represent the first quartile. We can add two 2's, a 3, and two 4's to achieve this.

Moving forward, we continue adding values to match the remaining quartiles. For Q2, we include values 5 and 6, and for Q3, we include three 8's and four 9's. Finally, we add four 10's to represent the maximum value.

By arranging the values in this manner, we obtain a sample distribution with n = 20 and a five-number summary of 2, 4, 6, 8, and 10.

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Answer:

Step-by-step explanation:

\(\sf 6(9-6)-23+4\)

\(\sf (6)(3)-23+4\)

\(\sf 18-23+4\)

\(\sf -5+4\)

\(\sf -1\)

Answer:

First you are to do what is in the parenthesis first:

9 - 6 = 3

The equation is now:

6 * 3 - 23 + 4

Then you do the multiplcation:

6 * 3 = 18

18 - 23 + 4

23 + 4 = 27

27 - 18 = 9

Step-by-step explanation:

Hope it helps! =D

Answer:

When x < 0 (Option 1)

Step-by-step explanation:

The answer to your question would be Option 1, or when x < 0. When you create a table with f(x) and g(x), they're only ever equal when x = 0, which is when f(x) and g(x) both equal 1. When the numbers go into negatives for each equation, f(x) becomes exponentially bigger. Making f(x) > g(x) true when x < 0.

Hope this helps!

Answer:

A: i

Step-by-step explanation:

i^57=i use the calculator

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

540 is the answer

Step-by-step explanation:

Move the decimal point 2 places to the right.

I hope my answer was helpful!:)

3/4 and 5 18 is fraction have a leat common denominator of 36.

3/4 and 5 18 is fraction have a leat common denominator of 36.

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The five elements to be assessed during sample selection in audit sampling are Sapmlinf Frame, Sample Size, Sampling Method, Sampling Interval, Sampling Risk.

1. Sampling Frame: The sampling frame is the list or source from which the sample will be selected. It is important to ensure that the sampling frame represents the entire population accurately and includes all relevant elements.

2. Sample Size: Determining the appropriate sample size is crucial to ensure the sample is representative of the population and provides sufficient evidence for drawing conclusions. Factors such as desired confidence level, acceptable level of risk, and variability within the population influence the determination of the sample size.

3. Sampling Method: There are various sampling methods available, including random sampling, stratified sampling, and systematic sampling. The chosen sampling method should be appropriate for the objectives of the audit and the characteristics of the population.

4. Sampling Interval: In certain sampling methods, such as systematic sampling, a sampling interval is used to select elements from the population. The sampling interval is determined by dividing the population size by the desired sample size and helps ensure randomization in the selection process.

5. Sampling Risk: Sampling risk refers to the risk that the conclusions drawn from the sample may not be representative of the entire population. It is important to assess and control sampling risk by considering factors such as the desired level of confidence, allowable risk of incorrect conclusions, and the precision required in the audit results.

During the sample selection process, auditors need to carefully consider these elements to ensure that the selected sample accurately represents the population and provides reliable results. By assessing and addressing these elements, auditors can enhance the effectiveness and efficiency of the audit sampling process, allowing for meaningful generalizations about the population.

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