Estimate how many times larger 2 x 10-5 is than 4 x 10-12 in the form of a single digit times an integer power of 10.

Answer:

this is why you pay attention in school kids.

Step-by-step explanation:

any ways i never learned how to do long division but the answer is a decimal

Given, The function f(x, y, z) = 8x - 4zTo find:The extreme values of the given function using Lagrange's multiplier method. Solution: According to the Lagrange's multiplier method,Let us consider a function g(x, y, z) = x² + y² + z² - 9, as a constraint equation and the function f(x, y, z) = 8x - 4z.

Let λ be the Lagrange's multiplier. Since the extreme values of f(x, y, z) are to be found, therefore,∇f(x, y, z) = λ∇g(x, y, z)Where, ∇ is the nabla operator.\(∇f(x, y, z) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k= 8i + 0j - 4k= 8i - 4k∇g(x, y, z) = (∂g/∂x)i + (∂g/∂y)j + (∂g/∂z)k= 2xi + 2yj + 2zk= 2xi + 2yj + 2kλ= ∇f(x, y, z) / ∇g(x, y, z)\)

Now, solving for x and \(z.8 / 2λ = x ⇒ x = 4λ-4 / 2λ = z ⇒ z = -2λHence, y = 0 from g(x, y, z) = x² + y² + z² - 9 = 0i.e. x² + z² = 9 ⇒ (4λ)² + (-2λ)² = 9 ⇒ 16λ² + 4λ² = 9 ⇒ 20λ² = 9λ = ±√(9/20)\) Now, put the values of x, y and z in the function f(x, y, z) = 8x - 4z.8x - 4z = 8(4λ) - 4(-2λ)= 32λ + 8λ= 40λ and - 40λThus, the extreme values of the function f(x, y, z) = 8x - 4z are 40λ and -40λ, respectively.  Answer:

Therefore, the required answer is that the extreme values of the function f(x, y, z) = 8x - 4z using Lagrange's multiplier method are 40λ and -40λ, respectively.Read more on Lagrange's multiplier method from reference:

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ANSWER

EXPLANATION

We want to express the given decimal as a fraction in its lowest terms:

To do this, first convert it to a fraction:

Now, divide the numerator and denominator by common numbers until they cannot be divided further:

That is the fraction in lowest terms.

The value is -6

We are given a sequence {an} such that sn = 3n - 9. We can find an by using the formula sn = an + d(n - 1).

Substituting the values for sn and d (which is 1 in this case), we get

an = 3n - 9 - (n - 1)

an = 2n - 10

Therefore, when k = 1, an = 2(1) - 10 = -6.

The answer value is -6.

Expand it to 2 liens

The answer is -6, which can be obtained by using the formula an = 3n - 9 - (n - 1).

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The equation in point-slope form for the  perpendicular line is y-5= x+1.

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The slope of the line y= -x-6 is   -1.

Perpendicular lines slopes satisfy the condtion:

\(m_{1} m_{2} = -1\)

then the slope of the perpendicular line is 1.

The equation in point-slope form of the line that passes through the point (-1, 5) is

y-y1=m(x-x1)

y-5=1(x-(-1))

y-5= x+1

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Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.

1. Solve operations in parentheses:

2. Solve exponentials:

3. Solve division:

4. Solve multiplication:

5. Solve subtraction:

Answer: Answer is 20( please make me brainliest i just did this all in my head)

Step-by-step explanation: soo (14-2) =12  12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)

A) The probability that a person eating ice cream complies European Championship in soccer is 6/13.B) The probability that a person who is watching the European Football Championship eats ice cream is 6/11.C) The two events are not independent.

a) The probability of a person eating ice cream follows European Championship in soccer is to be determined. Given that 30% of the people follow soccer World Cup and eat ice cream. Then, using the formula of conditional probability, we get P(A|B) = P(A and B) / P(B).

Here, A: Eating ice cream follows European Championship B: Follow soccer World Cup

P(A and B) = 30%

P(B) = 65%

P(A|B) = P(A and B) / P(B) = 30/65 = 6/13

So, the probability that a person eating ice cream complies European Championship in soccer is 6/13.

b) The probability of a person who is watching the European Football Championship eating ice cream is to be determined. Again, using the formula of conditional probability, we get P(A|B) = P(A and B) / P(B).

Here, A: Eating ice creamB: Watching European Football Championship

P(A and B) = 30%

P(B) = 55% (As 55% eat ice cream)

P(A|B) = P(A and B) / P(B) = 30/55 = 6/11.

So, the probability that a person who is watching the European Football Championship eats ice cream is 6/11.

c) To check whether two events are independent or not, we need to see if the occurrence of one event affects the occurrence of another. So, we need to check whether the occurrence of eating ice cream affects the occurrence of following soccer World Cup.

Using the formula for the probability of independent events, we get

P(A and B) = P(A) x P(B) = 55/100 x 65/100 = 3575/10000 = 0.3575

But P(A and B) = 30/100 ≠ 0.3575

Hence, the two events are not independent.

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The number of cows needed to satisfy the beef appetite would be 5263

With an average yield of 570 pounds (258.1 Kg.) of prepared beef per cow, we need to determine how many people can be fed from this amount. The number of people fed per cow can vary depending on various factors such as portion sizes and individual dietary preferences. Assuming a reasonable estimate, let's consider that one pound (0.45 Kg.) of prepared beef can feed about three people.

To find the number of cows needed to satisfy the beef appetite for New York City's population of approximately 9,000,000 people, we divide the population by the number of people fed by one cow. Thus, the calculation becomes 9,000,000 / (570 pounds x 3 people/pound).

After simplifying the equation, we get 9,000,000 / 1710 people, which equals approximately 5,263 cows. However, it's important to note that this is a rough estimate and does not consider factors such as variations in consumption patterns, distribution logistics, or other sources of meat supply. Additionally, individual dietary choices and preferences may result in different consumption rates. Therefore, this estimate serves as a general indication of the number of cows needed to satisfy the beef appetite for New York City's population.

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Complete question :

A college is funded depending on the mean number of credit units a student takes. A survey involving 16 students yielded the mean number 12 units with a standard deviation 3 units. Assume normal population

If th ere are 10,000 stu dents enrolled in the college an d the institution is funded at the rate of $300 per student unit. At the 95 % confidence level, estimate the interval th at covers the total funding of the college . for full credit, round the answer to TWO decimal places!

Answer: (35823600 , 36176400)

Step-by-step explanation:

Mean number of units = 12

Standard deviation = 3

Number of samples (n) = 10000

Fund rate = 300

Mean = 10000 * 300 * 12 = 36000000

Standard deviation = 10000^0.5 * 300 * 3 = 90000

Fir 95% C. I

Z0.05 = 1.96

Interval = mean ± 1.96 * SE

(36000000 - 1.96*90000) ; (36000000 + 1.96*90000)

(35823600 , 36176400)

To finf this, we simply divide 25.5 by 51, and then multiply the result by 100.

This is done as follows:

Therefore 25.5 is 50% of 51

Answer:

Step-by-step explanation:

Just subtract all the numbers from 38.75

Solving for C(t), we get:C(t) = 0.05 kg/LAt steady state, the concentration of salt in the tank is 0.05 kg/L or 50 g/L. Note that the units are converted from kg/L to g/L for convenience.

In order to solve the problem, we can start by finding out how much salt is entering the tank every minute. This can be done by multiplying the concentration of the solution by the rate at which it is entering the tank:

0.05 kg/L x 8 L/min = 0.4 kg/min

So, for every minute that the solution is entering the tank, 0.4 kg of salt is being added to the original 100 kg. The total amount of salt in the tank at any given time can be represented by the equation:

S(t) = 100 + 0.4t, where S(t) is the amount of salt in kg at time t in minutes.We can also find the total amount of liquid in the tank at any given time using the rate at which the solution is entering and leaving the tank:

V(t) = 1000 + 8t.

Next, we can find the concentration of salt in the tank at any given time by dividing the amount of salt by the amount of liquid:C(t) = S(t)/V(t) = (100 + 0.4t)/(1000 + 8t)Finally, we can find the concentration of salt in the tank when it reaches a steady state, which occurs when the amount of salt entering the tank equals the amount leaving the tank. At steady state, the rate of salt entering the tank is 0.4 kg/min and the rate of salt leaving the tank is:C(t) x 8 L/min.

Therefore, we can set up the equation:0.4 = C(t) x 8Solving for C(t), we get:

C(t) = 0.05 kg/LAt steady state, the concentration of salt in the tank is 0.05 kg/L or 50 g/L.

Note that the units are converted from kg/L to g/L for convenience.

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Answer:

(5π/12)(11) = about 14.4 inches

Answer:

if you mean the formula it is (1/2) · b · (6 · h + sqrt(3) · b)

Step-by-step explanation:

Answer:

0630 is the only thing I can come up with.

For maximum strength training, it is recommended to perform 1 to 5 repetitions per set, with heavier weights and longer rest periods between sets. This type of training focuses on increasing muscle strength and power.

Maximum strength training is a type of resistance training that is designed to increase muscle strength and power. The number of repetitions per set is an important factor in developing maximum strength, and the recommended range is between 1 and 5 repetitions. For this type of training, heavier weights and longer rest periods between sets are used. This allows the muscles to recover and build strength. During each set, the goal is to lift the weight as fast and explosively as possible, to help increase muscle power. It is important to also keep proper form and technique when performing exercises, as any incorrect movements can result in injury. Maximum strength training should be done with a gradual increase in weight, so that the body can properly adjust to the new load. It is also important to vary the exercises and the intensity level to help the body adapt to the training and to avoid plateaus in progress. To ensure optimal results, it is recommended to consult with a professional trainer or physical therapist.

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Answer:

y(t) = 494 (1.03)^t

y(10) = 663,89

Step-by-step explanation:

An increase in population by 3% each year means that at the end of each year, the population is 1.03 times what it was at the start of the year

This increase in population continues for t years

Exponential growth model that represents the population y (in thousands) t years after the beginning of the decade is

y(t) = 494 (1.03)^t

Where,

y = population

t = number of years

Find y when t = 10

y(t) = 494 (1.03)^t

y(10) = 494 (1.03)^10

= 494 ( 1.3439)

= 663.8866

Approximately y(10) = 663.89

This means that after 10 years from when the population was 494,000, it increased to 663,89.

Answer:

2684 \(units^{2}\)

Step-by-step explanation:

We find the area of the 4 triangles

area = 1/2 base x height  All the bases area the same measurement

a = 1/2(22)(61)

a = 671

There are 4 sides

671 x 4 = 2684

The Board of Trustees can choose a president and a provost in 1000 different ways because there are 1000 professors on the college's faculty. The concept used in this is permutations and combinations.

What are combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical.

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Correct question:

Suppose that a college has 1000 professors.

a) In how many ways can the Board of Trustees pick a president? The president should be one of the 1000 professors.

The change in average cost is approximately 11.98 dollars.

To estimate the change in average cost as production goes from 250 units to 251 units, we need to calculate the difference between A(251) and A(250).

A(250) = 12(250) + 1250/250 = 300 + 5 = 305

A(251) = 12(251) + 1250/251 = 301.03

Therefore, the change in average cost is approximately:

A(251) - A(250) = 301.03 - 305 = -3.97 dollars (rounded to two decimal places)

So the change in average cost is approximately negative 3.97 dollars.

To estimate the change in average cost as production goes from 250 units to 251 units, we need to find the difference between the average cost at 251 units and the average cost at 250 units using the given function A(x) = 12x + 1250/x.

First, find the average cost for 250 units:
A(250) = 12(250) + 1250/250 = 3000 + 5 = 3005 dollars.

Next, find the average cost for 251 units:
A(251) = 12(251) + 1250/251 ≈ 3012 + 4.98 ≈ 3016.98 dollars.

Now, find the change in average cost:
Change = A(251) - A(250) ≈ 3016.98 - 3005 = 11.98 dollars.

The change in average cost is approximately 11.98 dollars.

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A 94.6 L gasoline with a density of 0.680 g/cm^3 has a mass of 64328 g.

Density is defined as the ratio between the mass of a substance and the volume it occupies. Denoted by ρ, density is mass per unit volume and the formula is given below:

ρ =  mass / volume

Converting first the volume from L to cm^3.

1 L = 1000 cm^3

94.6 L = 94.6(1000 cm^3)

94.6 L = 94,600 cm^3

Given the density of the gasoline and its volume, solve for the mass of the gasoline using the formula for the density.

ρ =  mass / volume

0.680 g/cm^3 = mass / 94,600 cm^3

mass = 0.680 g/cm^3 (94,600 cm^3)

mass = 64328 g

mass = 64.328 kg

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The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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89 /3

frogs = 29.6

fish =  29.6

dragonflies =  29.6

all of them equal 89

Answer:

15 and 270

Step-by-step explanation:

using the property of radicals

(\(\sqrt{x}\) )² = x and (\(\sqrt[3]{x}\) )³ = x

then

(\(\sqrt{5}\) )² × (\(\sqrt{3}\) )² = 5 × 3 = 15

(\(\sqrt[3]{9}\) )³ × (\(\sqrt{30}\) )² = 9 × 30 = 270

The same formula as used in part (b) with r = 7%/12 = 0.005833 and the answers are: a) $171,900 b) $1,031.62 c) $1,145.80

a) The amount of the loan is going to be $171,900.

We can use the following formula to calculate the loan amount:

Loan Amount = Total Cost - Down Payment

$191,000 - (0.1 × $191,000) = $171,900b)

If the interest rate is 6%, the monthly payments will be $1,031.62.

We can use the following formula to calculate the monthly payments:

Monthly Payment = P × (r/n) × [1 + (r/n)]nt / [(1 + (r/n))nt - 1]

Where,

P = Loan amountr = Interest rate per year (as a decimal)

n = Number of payments per year

12t  = Number of years

P = $171,900r

= 6%/12

= 0.005t

= 30

Plug these values in the above formula, we get:

Monthly Payment = $1,031.62 (approx)c)

If the interest rate is 7%, the monthly payments will be $1,145.80.

We can use the same formula as used in part (b) with r = 7%/12 = 0.005833. We get:

Monthly Payment = $1,145.80 (approx)

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The measure of the numbered angle in a triangle is as follows:

∠1 = ∠3 = 50°

∠2 = ∠4  = 130°

∠5 = 40°

∠7 = 90°

∠8 = 140°

The measure of the angles can be found as follows:

The sum of angles in a triangle is 180 degrees. We have two right triangles in the diagram. A right triangle has one of its angles as 90 degrees.

Therefore,

90 + 40 + ∠1 = 180

∠1 = 180 - 130

∠1 = 50 degrees

Hence,

∠1 = ∠3 = 50 degrees(vertically opposite angles)

∠2 = ∠4 = 360 - 100 ÷ 2 = 260 ÷ 2 = 130 degrees

∠5 = 180 - 50 - 90 = 40 degrees

∠7 = 90 degrees(angles on a straight line)

∠8 = 180 - 40 = 140 degrees

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The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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