In January,the depth of a lake was 1,098 feet. In august, the depth of the lake was 988.2 feet. What is the percentage decrease of the depth of the lake from January to august

a. To calculate the expected value of the monthly demand, multiply each unit demand by its probability and then sum the results:

Expected value = (300 * 0.20) + (400 * 0.30) + (500 * 0.35) + (600 * 0.15) = 60 + 120 + 175 + 90 = 445 units

Carolina's monthly order quantity should be 445 units for this product.

b. If Carolina orders 445 units and the actual demand is 300 units, the revenue and cost can be calculated as follows:

Revenue: 300 units * $70 = $21,000
Cost: 445 units * $50 = $22,250

Gain/loss = Revenue - Cost = $21,000 - $22,250 = -$1,250

The company will lose $1,250 in a month if it places an order based on the expected value and the actual demand is 300 units.

c. To calculate the variance and standard deviation for the number of units demanded, first calculate the squared deviation of each demand value from the expected value (445):

(300 - 445)^2 = 21,025
(400 - 445)^2 = 2,025
(500 - 445)^2 = 3,025
(600 - 445)^2 = 24,025

Now, multiply the squared deviations by their respective probabilities and sum the results to obtain the variance:

Variance = (21,025 * 0.20) + (2,025 * 0.30) + (3,025 * 0.35) + (24,025 * 0.15) = 4,205 + 607.5 + 1,058.75 + 3,603.75 = 9,475

Standard deviation = √Variance = √9,475 ≈ 97.34 units

The variance and standard deviation for the number of units demanded are 9,475 and 97.34 units, respectively.

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The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.

To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).

Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.

Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.

Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).

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Answer:

Temperature at midnight = -8°F

Temperature at noon = 23°F

So increase in temperature is

= |-8 - 23|

= 31 °F

Answer:

1.) isosceles triangle x=11.3

2.) scalene triangle   x=14.1

3.) isosceles triangle  x=6.02

4.) isosceles triangle   x=15

5.) scalene triangle   x=12

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

The line is vertical and/or undefined and it passes through the point (-2,5).

Answer:

C (is greater than it equal to) 31

Step-by-step explanation:

Isolate the c by adding 11 to both sides (cancels out the 11 and turns 20 into 31). Keep the sign the same!! Hope this helped! <33

Answer:

B

Step-by-step explanation:

There are other methods to write a division issue, such as using a / or a to denote "divided by." As a result, in the equation 473 / 2 = 1 the divisor is the quotient, the remainder is 236, and the divisor is 2.

Divide the dividend's first digit, which should be on the left, by the divisor, then write the result as the quotient on top. Write the difference below after subtracting the outcome from the digit. Bring down the dividend's next digit (if present).

Long division strategy: lengthy division techniques. The same symbols are used for long division as they are for short division: dividend (the number being divided) under the "bus stop," divisor (the number the dividend is being divided by), quotient (the solution) on top, and each place value aligned with the dividend.

Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

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The complete question is "Divide the given numbers 473 and 6 using our free online Long Division Calculator and determine the Quotient and Remainder as Q 78 R 5 instantly without any hurdles."

Answer: (-8.5, 0), (0, 34), and (2, 42)

(-6,9)

Step-by-step explanation:

The probability that the student would choose to be playing a videogame is given as follows:

0.3559 = 35.59%.

The parameters that are needed to calculate a probability are listed on the bullet points as follows:

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

The parameters for this problem are given as follows:

Hence the probability is given as follows:

p = 21/59 = 0.3559 = 35.59%.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

l ll k

angles = ?

Step 02:

We must analyze the figures to find the solution to the exercise.

Hexagon

angle a = 120°

angle b = 180 - 120 = 60°

angle c = angle b = 60°

angle e = angle b = 60°

angle f = 180 - 90 - 60 = 30°

angle d = 60 + 60 = 120°

Pentagon

angle g = 108°

angle m = 180 - 90 - 72 = 18°

angle p = 90°

The full solution is:

angle a = 120°

angle b = 60°

angle c = 60°

angle d = 120°

angle e = 60°

angle f = 30°

angle g = 108°

angle m = 18°

angle p = 90°

Answer:

Step-by-step explanation:

we want this to be in one inch units.   we are told 3/10  of an inch is 7/8 of a mile.  so use the reciprocal of 3/10 or   10/3  to get to one.

7/8* 10/3 = 70/24   mile is equal to one inch.

Now figure out how much 70/24th miles is.

2.91666666 miles = 1 inch

The correct answer is: The product of a constant factor 12 and a 2-term factor x + 3.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that is written using mathematical symbols and conventions.

The expression 12(x + 3) can be simplified by distributing the constant factor 12 over the 2-term factor x + 3.

This would give us:

12(x + 3) = 12x + 36

So, the expression 12(x + 3) can be described as "the product of a constant factor 12 and a 2-term factor x + 3".

Therefore, the correct answer is: The product of a constant factor 12 and a 2-term factor x + 3.

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Answer:

Cada 12 días comería este menú (días comunes)

Step-by-step explanation:

En este caso la pregunta sería cuando vuelve a comer postre  de flan y pasta el mismo día.

Tenemos que come pasta cada 4 días y postre de flan cada 6 días, por lo tanto debemos calcular el m.c.m. (mínimo común múltiplo) entre 4 y 6, así:

4     6  | 2

2      3 | 2

1       3 | 3

1        1

Por lo tanto el m.c.m. sería:

2*2*3 = 12

Lo que quiere decir en 12 días vuelve a coincidir este menú, de pastas y postre de flan, por esto, los días comunes sería que cada 12 días coma este mismo menú.  

Answer:

57000

Step-by-step explanation:

56709 = 50000 + 6000 + 700 + 9

6709 is closer to 7000 that 6000

The answer is 57000

Hope this helps :)

Have a nice day!

To find the point(s) on the plane x−2y+z=3 where the expression x^2+4y^2+2z^2 is minimum, we can use the method of Lagrange multipliers.

Let's define the function f(x, y, z) = x^2 + 4y^2 + 2z^2, and the constraint g(x, y, z) = x − 2y + z − 3 = 0.

We set up the Lagrange function L(x, y, z, λ) = f(x, y, z) + λg(x, y, z).

Taking partial derivatives and setting them to zero, we get:

∂L/∂x = 2x + λ = 0

∂L/∂y = 8y - 2λ = 0

∂L/∂z = 4z + λ = 0

∂L/∂λ = x - 2y + z - 3 = 0

Solving these equations simultaneously, we find x = -2/3, y = 1/3, z = 2/3, and λ = -4/3.

Therefore, the point(s) on the plane x−2y+z=3 where x^2+4y^2+2z^2 is minimum is (-2/3, 1/3, 2/3).

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Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

She will need 3 more of every ingrediant.

Step-by-step explanation:

7x3=21 so 3 more of everything

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

The cost foe producing 1700 key chains is $1,620

Explanation:

Given that cost of production key chains can be calculated using the formula:

C = 260 + 0.80p

The cost for producing 1700 key chains can be obtained by substituting p by 1700 in the given formula.

C = 260 + 0.80(1700)

= 260 + 1360

= 1620

The cost is $1,620

Answer:

the answer would be 25

Step-by-step explanation:

Answer:

Find the rate of sales tax

R= 9000/120000

=0.075

=7.5%

So, the rate is 7.5%

Answer:

140

Step-by-step explanation:

20.82 = 21 when rounded to the nearest whole number

6.94 = 7

21*7 = 147

The best estimate is 140

Answer:

x=1 or x=3

Step-by-step explanation:

x2−4x+3=0        (x−1)(x−3)=0       x−1=0 or x−3=0      x=1 or x=3                                                                                                                  

The angle at which golf ball should be hit to land in the hole is 13.65°.

Given information is,
Horizontal distance of golf ball from hole = 420 ft or 140 yd
Height of golf ball from hole = 55 ft
Initial velocity of golf ball = 120 ft/s
Let, Angle at which golf ball should be hit to land in the hole is θ.The range of golf ball is given by:
R = u²/g × sin2θ
Where,u = Initial velocity of golf ball
g = acceleration due to gravity= 32 ft/s²
R = Range of golf ball
Therefore,420 = 120²/g × sin2θ
By solving this equation, the value of sin2θ is obtained,2 sinθ cosθ = 8400/g
The value of sinθ can be determined by solving the above equation, sinθ = (8400/g)/√(4 + (8400/g)²)
Therefore,θ = 0.5sin⁻¹(8400/g√(4 + (8400/g)²))
The value of θ can be calculated,θ = 0.5sin⁻¹(8400/32√(4 + (8400/32)²))= 0.5sin⁻¹(8400/32√(4 + 2625))= 0.5sin⁻¹(8400/32√(2629))= 0.5sin⁻¹(8400/181.33)= 0.5sin⁻¹(46.337)= 0.5 × 27.31= 13.65°

Therefore, the angle at which golf ball should be hit to land in the hole is 13.65°.

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The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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a) The relation R from set A={13, 17, 29, 45} to set B={4, 6, 22, 60} is {(13,4), (13,6), (13,60), (17,6), (17,22), (29,22)}.

b) R is a function from A to B.

a) We need to find all pairs of elements (a, b) such that aRb, where a is an element of set A and b is an element of set B. According to the definition of R, aRb if and only if a+b is a prime number.

Let's start with the first element of set A, which is 13. We need to find all elements of set B that satisfy the condition a+b is a prime number, where a=13. We have:

13+4=17 (prime)

13+6=19 (prime)

13+22=35 (not prime)

13+60=73 (prime)

So, for a=13, the elements of set B that satisfy the condition are 4, 6, and 60. We can repeat this process for the other elements of set A to find all pairs of elements (a, b) such that aRb. The results are:

For a=17, the elements of set B that satisfy the condition are 6 and 22.

For a=29, the element of set B that satisfies the condition is 22.

For a=45, there are no elements of set B that satisfy the condition.

Therefore, the relation R from set A to set B is {(13,4), (13,6), (13,60), (17,6), (17,22), (29,22)}.

b) To determine if R is a function from A to B, we need to check if each element of set A is related to at most one element of set B. In other words, we need to check if there are any duplicate elements in the first coordinate of the ordered pairs in R.

In our case, there are no duplicates in the first coordinate, so each element of set A is related to at most one element of set B. Therefore, R is a function from A to B.

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Answer:

15x, 19x, 26x, and 3x

Step-by-step explanation:

To figure this out, we just need to figure out which sort of value can be combined. Every choice except 49 has a variable attached. The different variables are a, y, x, h, and g. There is only one of each variable except for x. So, you would combine each like term with x as an variable.

Hope this helps!!! Have a wonderful day :D

The other side length is √20 after applying the Pythagoras and other two sides are 2 and 2√3.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

One side length = 2

Other side length = 2√3

Apply Pythagoras

x^2 = 2^2 + (2√3)^2

x^2 = 4 + 12

x = √20

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