m³ = 0.125

How do I break this down to get the answer

The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:

2

Step-by-step explanation:

Your slope is your change in y over your change in x.  The ordered pair is in the form of (x,y), so you subtract the y's and put that in your numerator (top)and subtract your x's and put that in your denominators (bottom).

2 - (-4) would be your top number.  To subtract a negative number is the same as adding a positive, so 2 - (-4) is the same as 2 +4, so your top number is 6.  

Now, to find the bottom number, you subtract the x's.

5-2 which is 3.

We now have the top and the bottom number

6/3 which is the same as 2.

The formula to calculate the remaining mass (m) of a decaying substance after time (t), with a given half-life (h) and initial mass (m0), is:

\(m = m0 * (1/2)^(t/h)\)

Here's a step-by-step explanation:

1. Start with the initial mass (m0) of the substance.
2. Divide the time elapsed (t) by the half-life (h). This will give you the number of half-life periods that have passed.
3. Raise the fraction 1/2 to the power of the number obtained in step 2.
4. Multiply the result from step 3 by the initial mass (m0).
5. The final result is the remaining mass (m) of the substance after time (t).

Remember to substitute the values of m0, t, and h into the formula to calculate the specific remaining mass.

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To calculate the remaining mass of a decaying substance after a certain time, you can use the formula \(m = m_0 \times (\frac{1}{2} )^{t/h}\), where m0 is the initial mass, t is the time elapsed, and h is the half-life.

The formula to calculate the remaining mass, m, of a decaying substance after time t is:

    \(m = m_0 \times (\frac{1}{2} )^{t/h}\)

    where:

    \(m_0\) is the initial mass,

    t is the time elapsed, and

    h is the half-life of the substance

To use this formula, you need to know the initial mass, the time elapsed, and the half-life of the substance. The half-life represents the time it takes for half of the substance to decay.

Let's take an example to understand the calculation. Suppose the initial mass, \(m_0\), is 100 grams, the time elapsed, t, is 4 hours, and the half-life, h, is 2 hours.

Using the formula, we can calculate the remaining mass, m:

    m = 100 * \((1/2)^{4/2}\)
=> m = 100 * \((1/2)^2\)
=> m = 100 * 1/4
=> m = 25 grams

In conclusion, to calculate the remaining mass of a decaying substance after a certain time, you can use the formula  \(m = m_0 \times (\frac{1}{2} )^{t/h}\), where \(m_0\) is the initial mass, t is the time elapsed, and h is the half-life.

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Answer:

A'

Step-by-step explanation:

it looks promising ngl ;))

Answer:

Hello there I would love to assist but could you give me a little more info I think I know the answer but I want to make sure I got it 100% correct unless you cant give me more info ill just tell you what I think it is but if u can give me more info before I give u the answer to make sure its correct would be appreciated

Step-by-step explanation:

Answer:

D, f(x)=5x

got it right

Answer:

8

Step-by-step explanation:

The following expression  →  |- 5| + |3| is equivalent to 8

The absolute value of a number is the magnitude of number. Absolute value describes the distance from zero that a number is on the number line, without considering direction.

We have the following expression -

|- 5| + |3|

For a number [x], such that [x] < 0, the absolute value would be -

v[a] = - x

and for [x] > 0

v[a] = x

So, for x = |- 5| + |3| , the equivalent expression would be -

5 + 3

8

Therefore, the following expression  →  |- 5| + |3| is equivalent to 8.

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Answer:

8/10 aka 4/5 chance

Step-by-step explanation:

if 8/10 batters have hit the ball that means that the chance that the next ball is hit is 8/10, reduced its 4/5 chance or 80%

Step-by-step explanation:

In given rt.angled triangle,

Sin thita =p/h

=26.1/28.7

=0.9094

So correct answer is option D.

0.9094 is the sine of angle θ

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have,

from the given figure,

In given rt.angled triangle,

Sin thita =p/h

=26.1/28.7

=0.9094

So correct answer is option D.

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Answer:

9/2 and mixed number: 4 1/2

Step-by-step explanation:

Answer:

I hope this helps!

The evolution of the function call (things '(11 -2 31)) is as follows:

(things '(11 -2 31)) -> (things '(-2 31)) -> (things '(31)) -> (things '()) -> '() the final result of the given call is '().

The given function is a recursive function called "things" that takes a list as input. It checks if the list is empty (null), and if so, it returns an empty list. Otherwise, it checks if the first element of the list (car x) is greater than 10. If it is, it adds 1 to the first element and recursively calls the "things" function on the rest of the list (cdr x). If the first element is not greater than 10, it subtracts 1 from the first element and recursively calls the "things" function on the rest of the list. The function then returns the result.

Now, let's see the evolution resulting from the call (things '(11 -2 31)):

1. (things '(11 -2 31))

  Since the list is not empty, we move to the next if statement.

  The first element (car x) is 11, which is greater than 10, so we add 1 to it and recursively call the "things" function on the rest of the list.

  The recursive call is (things '(-2 31)).

2. (things '(-2 31))

  Again, the list is not empty.

  The first element (car x) is -2, which is not greater than 10, so we subtract 1 from it and recursively call the "things" function on the rest of the list.

  The recursive call is (things '(31)).

3. (things '(31))

  The list is still not empty.

  The first element (car x) is 31, which is greater than 10, so we add 1 to it and recursively call the "things" function on the rest of the list.

  The recursive call is (things '()).

4. (things '())

  The list is now empty, so the function returns an empty list.

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Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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Step-by-step explanation:

if you're asking for distance then,

V = s / t

50 mph = s / 3 hrs

50 mph × 3 hrs = s

150 miles = s

The conclusion is that the expression \(\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}\) cannot be solved  without the l'hopital's rule,

The limit expression is given as:

\(\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}\)

The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞

i.e.

\(\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}\)

So, the best way is to apply the l'hopital's rule.

This is done as follows:

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}\)

When the numerator and the denominator are differentiated, we have:

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}\)

Further, differentiate

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}\)

Now, we can substitute \(\infty\) for x

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}\)

Evaluate the numerator

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}\)

Evaluate the quotient

\(\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty\)

Hence, the conclusion is that the expression \(\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}\) cannot be solved  without the l'hopital's rule

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The value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)] where E is bounded by the parabolic cylinder z=16−y2z=16−y2 and the planes z=0,x=4, and x=−4.

To evaluate the triple integral ∭E \(x^8 e^y\) dV, where E is bounded by the parabolic cylinder z=16−y² and the planes z = 0,x = 4, and x = −4, we can use the cylindrical coordinate system. Here are the steps to solve the integral:

Write down the limits of integration for each variable:

For ρ, the radial distance from the z-axis, the limits are 0 to 4.

For φ, the angle in the xy-plane, the limits are 0 to 2π.

For z, the height, the limits are 0 to 16 - y² for the parabolic cylinder, and 0 to the plane z = 0.

Write the integral using cylindrical coordinates:

∭E \(x^8 e^y\) dV = ∫\(0^4\) ∫0²π ∫\(0^{(16-y^2)\) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

Evaluate the integral:

∫0²π ∫\(0^4\)(16-y²) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) dφ ∫\(0^{(16-y^2)}\)(\(\rho^{10\) \(e^y\)) dρ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [\((16-y^2)^{11}\) / 11 \(e^y\)] dy dφ

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [(\(16^{11}\) / 11) \(e^y\) - (11/11) y² (\(16^{10}\)) \(e^y\) + (55/11) \(y^4\) (\(16^9\)) \(e^y\) - ...] dφ

= ∫\(0^4\) (\(16^{11}\) / 11) \(e^y\) [(\(cos^8\) φ) (2π)] dy

= (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)]

Therefore, the value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)].

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Answer: 4

Step-by-step explanation: if u want the slope it’s 4 since formula 2y-1y /2x-1x

Answer:

answer: 510 square feet

Step-by-step explanation:

Volume of a sphere is given by the formula

4/3 pi r^3       diameter = 6.3 cm  so radius, r = 3.15 cm

4/3 * pi * (3.15)^3 = 130.9 cm^3

Diego, this is the solution:

We have the following function:

g (x) = 4x - 7

In consequence,

g (3) = 4 * 3 - 7

g (3) = 12 - 7

g (3) = 5

Answer:

5

Step-by-step explanation:

Answer:

654321

Step-by-step explanation:

The value of function f(x) = 3x² + 8x-10 at f(2) is  18 .

We have given an function f(x) = 3x² + 8x-10

Putting x = 2 into this function , we get

 f(2) = 3(2)²+ 8x -10

        =3(4) + 8(2) -10

        = 12 + 16 -10

        = 18

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Domain ~

Range ~

Solution

Event 1: Probability is 8/16 = 1/2

Event 2: Probability is 1(certain to happen)

Event 3: Probability is 0(Impossible). There are no white slices in Spinner A

Event 4: Probability is 9/20

The equation which is equivalent to the given equation; 2/3 a - 7 = 1/3 as required to be determined is; 2a - 21 = 1.

It follows from the task content that the correct form of the given equation is; 2/3 a - 7 = 1/3.

Therefore, in a bid to find an equivalent equation; one must multiply both sides of the equation by 3 so that we have;

2a - 21 = 1.

On this note, it can be inferred that the equation which is equivalent to the given equation is; 2a - 21 = 1

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a. Correlation: This method measures the strength and direction of the relationship between two continuous variables.
b. Linear Regression: This method predicts the value of one continuous variable based on the value of another continuous variable.
c. Independent t-test: This method compares the means of two independent groups to determine if there is a significant difference between them.
d. Dependent t-test: This method compares the means of two related groups (e.g., pre-test and post-test) to determine if there is a significant difference between them.

a. Correlation - This statistical method is used when the research question involves examining the relationship between two continuous variables. For example, "Is there a correlation between hours spent studying and GPA?"

Research question type: "Is there a relationship between variable A and variable B?"
b. Linear Regression - This statistical method is used when the research question involves predicting a continuous dependent variable based on one or more continuous independent variables. For example, "Can we predict income based on years of education and work experience?"

Research question type: "Can we predict variable A based on variable B?"
c. Independent t-test - This statistical method is used when the research question involves comparing the means of two independent groups on a continuous variable. For example, "Is there a difference in salaries between male and female employees?"

Research question type: "Is there a significant difference in variable A between Group 1 and Group 2?"
d. Dependent t-test - This statistical method is used when the research question involves comparing the means of two related groups on a continuous variable. For example, "Is there a significant difference in test scores before and after a study intervention?"

Research question type: "Is there a significant difference in variable A between the pre-test and post-test results?"

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The equivalent of 0.85 hectogram (hg) is 850 decigram (dg)

The measure is given as:

0.85 hg

As a general rule:

1 hectogram (hg) = 1000 decigram (dg)

So, multiply both sides of the above equation by 0.85

So, we have:

0.85 * 1 hectogram (hg) = 0.85 * 1000 decigram (dg)

Evaluate the product

0.85 hectogram (hg) = 850 decigram (dg)

Hence, the equivalent of 0.85 hectogram (hg) is 850 decigram (dg)

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Answer:

A

Step-by-step explanation:

Answer choice a is correct because there is an open circle at 10 and it is shaded towards the right which represents greater! hope this helps:)

Answer:

B) 12

Step-by-step explanation:

(9y + 7)° + (7y - 19)° = 180° (interior angles in the same side of transversal)

(9y + 7 + 7y - 19)° = 180°

(16y - 12)° = 180°

16y - 12 = 180

16y = 180 + 12

16y = 192

y = 192/16

y = 12

Answer:

9y+7=7y-19

7+19=7y-9y

26=-2y

26/-2=-2y/-2

y=-13

I hope this helps: