find the extreme values of f(x,y) = xy 2y2 x4 −y4 on the circle x2 y2 = 1

The range of sales for the given condition is (25000, +∞), Hence Mrs. Dundee makes more from the second publisher than the first.

As per the question statement, Mrs. Dundee wants to sell the rights to her Cajun cookbook so one publisher offered to pay $80,000 and a $3 royalty for every book sold and publisher two offered to pay $30,000 and $5 for every book sold.

We are supposed to find the range of sales for the given conditions.

Let's suppose Mrs. Dundee sold "x" books

30,000 + 5x > 80,000 + 3x

2x > 50,000

x > 25,000

So, the range of sales for the given condition is (25000, +∞), Hence Mrs. Dundee makes more from the second publisher than the first.

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Answer:

(-7,-4)

Step-by-step explanation:

-6-1=-7

-9-(-5)=-4

At a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.

What is the null hypothesis in statistics?

The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely due to chance. The likelihood that the null hypothesis is true can be calculated using statistical tests.

Sample size, n =1500

The sample proportion of the chips that do not fail in the first 1000 hrs of their use, \(\hat{p} = 0.69\)

Null Hypothesis, H0: p=0.72

Alternate Hypothesis, \(Ha: p \neq 0.72\)

Test statistic,

\(z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} - \frac{0.69-0.72}{\sqrt{\frac{0.72(1-0.72)}{1500}}} = -2.5877\)

Critical Value,

\(Z_{0.05/2} =\)±1.96

Now, since the absolute value of the test statistic i.e, 2.5877 is greater than the absolute value of the critical value i.e, .1.96, thus we will reject the null hypothesis.

Thus at a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.

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An example of a sample space S could be rolling a fair six-sided die, where each face has a number from 1 to 6.
Let's define three events:
- E1: Rolling an even number (2, 4, or 6)
- E2: Rolling a number less than 4 (1, 2, or 3)
- E3: Rolling a prime number (2, 3, or 5)
To verify that these events are pairwise independent, we need to check that the probability of the intersection of any two events is equal to the product of their individual probabilities.
1. E1 ∩ E2: The numbers that satisfy both events are 2. So, P(E1 ∩ E2) = 1/6. Since P(E1) = 3/6 and P(E2) = 3/6, we have P(E1) × P(E2) = (3/6) × (3/6) = 9/36 = 1/4. Since P(E1 ∩ E2) = P(E1) × P(E2), E1 and E2 are pairwise independent.

2. E1 ∩ E3: The numbers that satisfy both events are 2. So, P(E1 ∩ E3) = 1/6. Since P(E1) = 3/6 and P(E3) = 3/6, we have P(E1) × P(E3) = (3/6) × (3/6) = 9/36 = 1/4. Since P(E1 ∩ E3) = P(E1) × P(E3), E1 and E3 are pairwise independent.

3. E2 ∩ E3: The numbers that satisfy both events are 2 and 3. So, P(E2 ∩ E3) = 2/6 = 1/3. Since P(E2) = 3/6 and P(E3) = 3/6, we have P(E2) × P(E3) = (3/6) × (3/6) = 9/36 = 1/4. Since P(E2 ∩ E3) ≠ P(E2) × P(E3), E2 and E3 are not pairwise independent.
Therefore, we have found an example where E1 and E2, as well as E1 and E3, are pairwise independent, but E2 and E3 are not pairwise independent. Hence, these events are not mutually independent.

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The value of \(c\) in the function \(P(t) = P_0(1+c)^t\) represents the growth rate of the population per year. In this case, with a growth rate of 6% per year, the value of \(c\) is equal to 0.06.

The value of \(c\) in the function \(P(t) = P_0(1+c)^t\) represents the growth rate of the population of animals per year. In this case, the population is growing at a rate of 6% per year.

To find the value of \(c\), we need to convert the growth rate from a percentage to a decimal. Since 6% is equal to 0.06, we can substitute this value into the formula:

\(P(t) = P_0(1+0.06)^t\)

Now, we can see that the value of \(c\) is equal to 0.06. This means that the population is growing by 6% per year.

Let's consider an example to understand this better. Suppose we have an initial population of 100 animals (represented by \(P_0 = 100\)) and we want to know the population after 5 years (represented by \(t = 5\)).

Using the formula with \(c = 0.06\), we can calculate the population after 5 years as follows:

\(P(5) = 100(1+0.06)^5\)

\(P(5) = 100(1.06)^5\)

\(P(5) \approx 133.82\)

So, after 5 years, the population would be approximately 133.82 animals.

In summary, the value of \(c\) in the function \(P(t) = P_0(1+c)^t\) represents the growth rate of the population per year. In this case, with a growth rate of 6% per year, the value of \(c\) is equal to 0.06.

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Answer:

52.26 cm

Step-by-step explanation:

Since the semicircle is a part of the rectangle, the side of the rectangle where the semicircle is put is eliminated. We know the diameter of the circle, if is 6 cm, but the formula of a semicircle is пr^2 / 2. To find the radius, we divide 6cm by 2, and then we square 3 (that's what we got), and get 9. We  simply multiply it by п, which would give us 28.26. The area of the rectangle is 4 * 6 = 24, and the area of the semicircle is 28.26. Now, we just need to add them: 24 + 28.26 = 52.26 cm, and that would be your answer.

Tell me if I'm wrong :)

A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

Given,

We must determine the kind of variable needed in the given problem to build a confidence interval for a population proportion.

Considering that;

The percentage of the entire population that possesses a specific quality is known as the population proportion (which is qualitative in nature). Therefore, a qualitative variable with two alternative outcomes must be used to generate the confidence interval for the population proportion.

Therefore, the nature of the various types of variables is used to choose the correct option. A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

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Question is incomplete. Completed question is given below;

What type of variable is required to construct a confidence interval for a population proportion?

A. Quantitative

B. Qualitative with any number of possible outcomes

C. Continuous

D. Qualitative with 2 possible outcomes

E. Discrete

F. Qualitative with 3 or more possible outcomes

Then,

Answer:

55

Step-by-step explanation:

An example of geometric series is  2 + 6 + 18 + 54.

When a set of numbers follow a particular order, they are said to be in sequence.

A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as

Sum of n terms = a, ar, ar², ar³,  ......, arⁿ⁻¹, arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

When the numbers in geometric sequence are added together, it is called a geometric series. The geometric series is presented as

Sum of n terms = a + ar + ar² + ar³ + ...... + arⁿ⁻¹ + arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

Let us take an example.

The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series.

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The number of cars that the dealer have for sale is 17 cars.

From the problem given, if the ratio of cars to trucks on the lot is 11 to 33, we can write this as: Cars/Trucks = 11/33

We can also simplify this ratio by dividing both sides by 11:

==> cars/51 = 11/33

Now we can solve for the number of cars:

Cars = (11/33) * 51

Cars = 17. Therefore, the dealer has 17 cars for sale.

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Answer:

2=x+6/7 would need to be linear which would now equal to 14=x+6 and since you need to isolate x, subtract 6 from 14 which is now 8 so 8=x, your welcome.

Step-by-step explanation:

\(3x-1=81x\\78x=-1\\x=-\dfrac{1}{78}\)

Answer:

\(\large \boxed{\displaystyle x=- \frac{1}{78}}\)

Step-by-step explanation:

\(3x-1=81x\)

Subtract 3x from both sides of the equation.

\(-1=78x\)

Divide both sides of the equation by 78.

\(\displaystyle \frac{-1}{78} =x\)

The values of k that satisfy the differential equation 64y" = -81y for the function y = cos(kt) are k = -4/3 and k = 4/3.

To determine the values of k that satisfy the given differential equation, we need to substitute the function y = cos(kt) into the equation and solve for k.

First, we find the second derivative of y with respect to t. Taking the derivative of y = cos(kt) twice, we obtain y" = -k^2 * cos(kt).

Next, we substitute the expressions for y" and y into the differential equation 64y" = -81y:

64(-k^2 * cos(kt)) = -81*cos(kt).

Simplifying the equation, we get -64k^2 * cos(kt) = -81*cos(kt).

We can divide both sides of the equation by cos(kt) since it is nonzero for all values of t. This gives us -64k^2 = -81.

Finally, solving for k, we find two possible values: k = -4/3 and k = 4/3.

Therefore, the smaller value of k is -4/3 and the larger value of k is 4/3, which satisfy the given differential equation for the function y = cos(kt).

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Answer:

The correct option is A.

Step-by-step explanation:

When we have two congruent figures, the correspondent sides of the figures are related by the same constant C.

In the case of the image.

h is the left side of the smaller triangle.

h + j is the left side of the larger triangle.

Then we have the relation:

(h + j) = C*h

If we isolate C, we get:

C = (h + j)/h

We can also write this for the other side (the bottom one)

k*C = (k + i)

C = (k + i)/k

Then we have:

(h + j)/h = (k + i)/k

We can rewrite this as:

h/h + j/h = k/k + i/k

1 + j/h = 1 + i/k

We can subtract 1 in each side to get:

j/h = i/k

This is almost the same we can see in option A (its inversed)

If we apply the inverse to both sides, we get:

(j/h)^-1 = (i/k)^-1

h/j = k/i

Which is the same equation that we can see in option A.

Then the correct option is A.

The amount theo had left in the account is £32.

We are given that;

Amount= £350

Rate= 2%

Time= 6months

Now,

Plugging these values into the formula, we get:

I = 350 x 0.02 x 6 I = 42

This means that Theo earned £42 in interest after 6 months. Adding this to the principal amount, we get the total amount in the account:

350 + 42 = 392

To find how much money Theo had left after buying the bike, we need to subtract the cost of the bike from the total amount in the account:

392 - 360 = 32

Therefore, by interest the answer will be £32.

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To determine the amount of salt in the tank after 60 minutes, we need the concentration of salt in the solution entering the tank.

The information provided, which is the salt concentration in terms of "zib salt /gal," is incomplete and does not specify the actual value of zib.

If you can provide the concentration of salt in the solution entering the tank (in terms of a specific numerical value), I can help you calculate the amount of salt in the tank after 60 minutes.

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a tank contains 100 gal of pure water inirially. a solution containing zib salt /gal enters into the tank at the vate of 3 gal/min. also a drain is open so that qhe volume of the solution is constant. tow much after salt is in the tank after 60 mins?

Answer:

5

Step-by-step explanation:

You add 5.49 until it almost goes past 30

Then count how many times you added

I hope this helps!

When two angles add to 90°, we say they "Complement" each other.

So if two angles are complementary,

then the sum of their measures is 90 degrees.

For example, if we had a 62 degree angle and an 18 degree angle,

these two angles are complementary because they add to 90 degrees.

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

By Pythagoras theorem :

\(\qquad \sf  \dashrightarrow \: hypotenuse = \sqrt{(perpendicular) {}^{2} + (base) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: h= \sqrt{15 {}^{2} + {8}^{2} } \)

\(\qquad \sf  \dashrightarrow \: h = \sqrt{225 + 64} \)

\(\qquad \sf  \dashrightarrow \: = \sqrt{289} \)

\(\qquad \sf  \dashrightarrow \: h = 17 \: \: units\)

Now, we know ~

\(\qquad \sf  \dashrightarrow \: \sin(A) = \dfrac{opposite \: \: side}{hypotenuse} \)

\(\qquad \sf  \dashrightarrow \: \sin(A) = \dfrac{8}{17} \)

Answer:

Step-by-step explanation:

Speed of student 1 = 180/30= 6 m/sec

speed of student 2= 180/32= 5.62 m/sec

speed of student 3= 180/33= 5.45 m/sec

speed of student 4= 180/35= 5.14 m/sec

speed of student 5= 180/37= 4.86 m/sec

speed of student 6= 180/38= 4.73 m/sec

speed of student 7= 180/40= 4.5 m/sec

speed of student 8= 180/32= 4 m/sec

average speed is = (6+5.62+5.45+5.14+4.86+4.73+4.5+4)/8

hence, average speed is= 5.04

hence, the average speed of student 1 = 6m/sec

how much faster is average speed of student 1 than average speed= 6- 5.04 = 0.96

hence, average speed of student 1 is 0.96 m/sec more thanthe average speed.

Answer:

Answer:

The cross product is 47 i - 61 j + 17 k.

Step-by-step explanation:

Given that-

a = < -1, -3, -8 > , b = < 7, 4, -5 >

The cross product is

a × b =\begin{gathered}\left[\begin{array}{ccc}i&j&k\\-1&-3&-8\\7&4&-5\end{array}\right]\end{gathered}⎣⎢⎡i−17j−34k−8−5⎦⎥⎤

        = i ( - 3 × -5 - 4 × -8 ) - j ( -1 × -5 - (-8) × 7 ) + k ( -1 × 4 - 7 × -3 )

        = i ( 15 + 32 ) -j ×( 5 + 56 ) + k ( -4 + 21 )

        = i ( 47) - j (61 ) + k (17)

        = 47 i -61 j + 17 k

As we know that if two vectors A & B are perpendicular then

A . B = 0

So here only the given vector b = < 7,4, -5> is perpendicular to the resulting vector .

Step-by-step explanation:

47, -61, 71>; yes

Answer:

AGDB

Step-by-step explanation:

1: 1 is alternate interior because the angles are on opposite sides of the interior of the transversal. (A)

2: 2 is alternate exterior because the angles are on opposite sides of the exterior of the transversal. (G)

3: 3 is same-side interior because the angles are on the same side of the interior of the transversal. (D)

4: 4 is same-side exterior because the angles are on the same side of the exterior of the transversal. (B)

The measure of an exterior angle of a regular polygon with 16 sides can be found by dividing 360 degrees (the sum of all exterior angles in any polygon) by the number of sides. Therefore, the measure of an exterior angle of a regular polygon with 16 sides is 22.5 degrees.

A regular polygon has equal side lengths and equal interior angles. The sum of the exterior angles of any polygon is always 360 degrees. In a regular polygon, each exterior angle has the same measure. To find the measure of an exterior angle of a regular polygon, we divide 360 degrees by the number of sides.
In this case, the polygon has 16 sides. Therefore, the measure of each exterior angle can be calculated as follows:
Measure of each exterior angle = 360 degrees / 16 sides = 22.5 degrees.
Hence, the measure of an exterior angle of a regular polygon with 16 sides is 22.5 degrees.

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Answer:

\( \sqrt{ {1}^{2} + {2}^{2} + {( - 2)}^{2} } = \sqrt{1 + 4 + 4} = \sqrt{9} = 3\)

(1, 2, -2) is 3 units away from the origin.

(0, 0, 5) is 5 units away from the origin.

So (0, 0, 5) is farther away from the origin.

Answer:

x = 61°

Step-by-step explanation:

From the image, we can see that we have an isosceles triangle.

We know that the other 2 angles will be equivalent to each other.

We also know that the sum of angles in a triangle adds up to 180°.

Step 1: Set up equation

58 + x + x = 180

Step 2: Solve

58 + 2x = 180

2x = 122

x = 61°

Answer:

[-0.25 1.25]

[ ]

[-0.75 2.75]

If not satisfied than..

You can write it in other way as show in step by step

Step-by-step explanation:

Step 1:

First of all find the determinate.

Cross multiply the number 11 ✖ -1

= -11 ---eq1

And now cross multiply the number 3 ✖ - 5

= -15 ---eq2

Now we use eq 1 and 2

detA = (-11)-(-15)

Minus cancels minus

So it becomes

detA = -11 + 15

= 4

Step 2:

We find adjacent of the given.

[11 -5]

adjA= [ ]

[3 -1 ]

We change the places. The number 11 goes to in place of -1. -1 goes in place of 11.

And we change the signs of -5 and 3. -5 becomes 5 and 3 becomes -3.

We get

[-1 5]

adjA = [ ]

[-3 11]

Step 3:

Now we use the following formula

1

A^-1 = -------- adjA

detA

1 [-1 5]

A^-1 = ------- [ ]

4 [-3 11]

And now multiply

1

---- with each number of adjA.

4

And than subtract..

And you will get the inverse matrix

If the answer comes same than that's the answer for inverse matrix

Thank you.

Answer:

7a) 1/6

7b) 7/12

7c) 3/2 or 1 1/2

7d) 61/10 or 6 1/10

Step-by-step explanation:

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