Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Answer:

Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.

Therefore, what can be used as a reason in a two-column proof are:

Postulates

Definitions

Profit on each kite that Allan sells= $ 20 per kite

Amount paid by Allan for his Website = $ 20 per day

Let number of kites sold by Allan per day = x

In 7 days , number of kites sold = 7 x

Amount paid by Allan for his Website in 7 seven days = 20 × 7=$140

We have to make an equality describing number of kites Alan needs to sell to make at least $900 per week.

The Inequality is

→20×7 x -140 ≥ 900

→ 140 x ≥ 900 + 140

→ 140 x ≥1040

→ 7 x ≥ 52 (Minimum number of kites that allan should sell in a week)

Dividing both sides by 140,we get

→ x ≥ [tex]\frac{1040}{140}=7.43[/tex]= 8 kites in a day(approx)

Final answer:

The question involves creating unordered lists with various bullet options such as disc, square, circle, and triangle. While disc, square, and circle are commonly available, the triangle may need to be created as a custom bullet option in advanced editors. The process includes selecting the Bullets icon in the Paragraph section and choosing or customizing the bullet style.

Explanation:

The question refers to the process of creating unordered lists in document editing or web development environments, where you have the option to format lists using different types of bullets. When you want to organize information without a specific order of importance, an unordered list can be used. These lists are often formatted with bullet points to improve readability and structure.

Steps to Create an Unordered List with Different Bullet Options:

Go to the Home menu item.

In the Paragraph section, select the Bullets icon for unordered lists.

To choose a different bullet format, select the arrow beside the icon.

Select a format from the format Library that appears in the drop-down menu. Common bullet styles include disc, square, and circle. However, the question mentions 'triangle' which is not a standard option in most document editors but can be created as a custom bullet in some advanced editing tools.

Using different bullet styles like disc, square, and circle can help distinguish or organize your content more effectively. While the 'triangle' option might not be directly available, it represents the possibility to define new custom bullets, adding a unique aspect to your document's design.

The volume of the rectangular prism completely packed with 200 cubes of edge length 1/5in is approximately 1600 cubic inches.

The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism. In this case, the prism is completely packed with cubes of edge length 1/5in. Since there are 200 cubes, the length, width, and height of the prism would be the number of cubes in each respective direction. Therefore, the volume of the rectangular prism is:

(200 cubes in length) x (200 cubes in width) x (200 cubes in height) x (1/5in cube)^3

To simplify the calculation, we can express the volume in terms of the number of cubes:

200 x 200 x 200 x (1/5)^3 in³

Converting the units, we find that the volume of the rectangular prism is approximately 1600 cubic inches.

To solve this, we need to use the z statistic. The formula for z score is:

z = (x – u) / s

where x is sample value = less than 90, u is the sample mean = 90.6, s is the standard deviation = 17.2

z = (90 – 90.6) / 17.2

z = -0.035

From the standard distribution tables:

P (z = -0.035) = 0.4860

Therefore there is about 48.60 % chance that it will be less than 90 pounds

Answer: The required pattern is 13, 37, 109, 325, 973

Step-by-step explanation:

Since, each number in the sequence follows the following rule,

2 less than the 3 times of the previous number.

If we start from 5,

Then first number of the sequence = 3×5 - 2 = 15 - 2 = 13

Second number = 3× 13 - 2 = 39 - 2 = 37

Third number = 3× 37 - 2 = 111 - 2 = 109

Fourth number = 3×109 - 2 = 327 - 2 = 325

Fifth number = 3× 325 - 2 = 975 - 2 = 973

Hence, The required sequence is,

13, 37, 109, 325, 973

To solve the equation 25 1/7 - 12 5/7, subtract the whole numbers and fractions separately, and combine them back into a mixed number to get the solution, which is 12 3/7

To solve the equation 25 1/7 - 12 5/7, follow these steps:

The solution to the equation is 12 3/7

Answer:

Step-by-step explanation:

Okay. So first 8.25 * 20 = 165. Then you multiply 165 by 3 (165*3). 165 * 3 = 495.

Dan will earn $495 in three weeks.

146.54 units are the total units will she sell her ninth year.

Here, we have,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

where,

A = amount

I = initial amount

r = rate

t = time

p = period

we know, the first year she sold 400 units,

thus year 0, 400 units, t = 0, A = 400.

so, we get,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

=> 400 = I × 1

=> 400 = I

therefore then, when, rate = 20 %

we get,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

[tex]= > A = 400(1-0.2)^{t/2}[/tex]

now, how many units will it had decreased by the 9th year?  t = 9

so, we get,

[tex]= > A = 400(1-0.2)^{9/2}[/tex]

=> A = 146.54

Learn more about exponential function here:

brainly.com/question/14355665

#SPJ6

Final answer:

The fair price to play this game is 10.5 cents.

Explanation:

To find the fair price to play this game, we need to calculate the expected value. The expected value is calculated by multiplying each outcome by its probability and summing them up.

Let's calculate the expected value:

Now, we calculate the expected value:

(1/8) * 28 + (3/8) * 16 + (3/8) * 4 = 3.5 + 6 + 1 = 10.5 cents

Therefore, the fair price to play this game is 10.5 cents.

(2x² +3x -4) + (8 -3x) + (-5x² +2)

= x²(2 -5) +x(3 -3) +(-4 +8 +2)

= -3x² +6

_____

The process here is called "collecting terms", which means you add the coefficients of "like" terms. Terms are "like terms" when they have the same constellation of variables. Here, there are three different kinds of like terms:

• x² terms

• x terms

• constants

This process is an application of the distributive property, as you can see on the second line of the solution above.

x + 6 =y

8 =2y ........ y = 8/2 = 4

4+6 =10

John is four & Jose is 10