Helpp pleasee i added an attachment

The area of the following circle is A ≈ 153.86 square units.

A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.

The circumference of a circle is the distance around the edge of the circle, and it is calculated using the formula C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The area of a circle is the region enclosed by the circle, and it is calculated using the formula A = πr².

The diameter of the circle is 14, so the radius is half of that, which is 7.

The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the values we get:

A = π(7)²

A = 49π

Therefore, the area of the circle is 49π square units. If you want to use an approximation, you can use 3.14 as an estimate for π and get:

A ≈ 153.86 square units.

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The complete question is -

The values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

The given functions are F(x)=−529, F(x)=x^2+33, h(x)=∣x∣−233, and g(x)=2x.

To find the value of F(x) when x=3, we can substitute x=3 into the equation F(x)=x^2+33 and solve for F(x):
F(x)=x^2+33
F(3)=3^2+33
F(3)=9+33
F(3)=42

Similarly, to find the value of h(x) when x=3, we can substitute x=3 into the equation h(x)=∣x∣−233 and solve for h(x):
h(x)=∣x∣−233
h(3)=∣3∣−233
h(3)=3−233
h(3)=-230

And to find the value of g(x) when x=3, we can substitute x=3 into the equation g(x)=2x and solve for g(x):
g(x)=2x
g(3)=2(3)
g(3)=6

Therefore, the values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

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A poset on [54] = {1, 2, ... ,54} with comparisons a < b if and only if a divides b is a partially ordered set where elements are related if one divides the other. The height of this poset is 6 (1, 2, 4, 8, 16, 32, 54), and the width is 10 (all the elements in the set).

A poset on [54] is a partially ordered set that is defined with the comparison a < b if and only if a divides b. In this poset, the elements are ordered based on the divisibility relation, meaning that an element a is considered to be less than another element b if and only if a divides b.

The height of this poset is the maximum number of elements in a chain, which is 6. This can be seen by considering the chain {1, 2, 4, 8, 16, 32}.

The width of this poset is the maximum number of elements in an antichain, which is 10. This can be seen by considering the antichain {3, 5, 6, 7, 10, 14, 15, 21, 22, 35}.

Therefore, the height and width of this poset are:
Height = 6
Width = 10

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Answer:

(a) The probability that all 4 calls are for medical help can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

n is the number of trials (in this case, 4)

k is the number of successes (in this case, 4)

p is the probability of success on a single trial (in this case, 0.81)

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.81^4 * (1 - 0.81)^(4 - 4)

P(X = 4) = 0.5314

Therefore, the probability that all 4 calls are for medical help is 0.5314, rounded to 4 decimal places.

(b) The probability that at least 1 of the calls is not for medical help can be calculated using the complement rule:

P(at least 1 call not for medical help) = 1 - P(all 4 calls for medical help)

We already calculated the probability of all 4 calls being for medical help in part (a), which is 0.5314. So, using the complement rule, we get:

P(at least 1 call not for medical help) = 1 - 0.5314

P(at least 1 call not for medical help) = 0.4686

Therefore, the probability that at least 1 of the calls is not for medical help is 0.4686, rounded to 4 decimal places.

(c) The calculation in part (a) may not be valid if we choose 4 consecutive calls to the station because the 4 consecutive calls being medical may not be independent events. For example, if a large accident or a natural disaster occurs in the area, there may be a higher probability of multiple consecutive medical calls due to the same incident or cause. In that case, the assumption of independence between the events would not hold, and the binomial probability formula would not be applicable.

Step-by-step explanation:

The equation of the midline of the sinusoidal function will be y = 4.

The most obvious representation of the amount that objects, in reality, modify their state is a sinusoidal waveform or sinusoidal wave. A sine wave depicts how the intensity of a variable varies over time. For example, the variable may be an audible sound.

The sinusoidal equation is written as,

y = A sin (ωt + ∅) + k

Here, 'A' is the amplitude, 'ω' is the frequency, and '∅' is the phase difference.

From the graph, it can be seen that the function is shifted upward by four units. Then the equation of the midline of the sine function is given as,

y = 4

The equation of the midline of the sinusoidal function will be y = 4.

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The height of the trapezoid is 23 cm.

What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height of a trapezoid is the perpendicular distance between the two bases.

To find the height of a trapezoid given its parallel sides and area, you can use the formula:

height = 2 * area / (sum of bases)

In this case, the sum of the bases is 12 cm + 18 cm = 30 cm, and the area is 345 cm². Substituting these values into the formula, we get:

height = 2 * 345 cm² / 30 cm

height = 23 cm

Therefore, the height of the trapezoid is 23 cm.

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The common tangent of the compound curve is parallel to its long chord. This means that the angle between the common tangent and the long chord is 0°. The long chord makes an angle of 18° with the shorter tangent and 12° with the longer tangent. We can use the law of sines to determine the length of the common tangent.

Let's call the length of the common tangent x, the length of the long chord L, the angle between the common tangent and the long chord θ, the angle between the long chord and the shorter tangent α, and the angle between the long chord and the longer tangent β.

Using the law of sines, we have:

x/sin(θ) = L/sin(α+β)

Substituting the given values, we have:

x/sin(0°) = 546/sin(18°+12°)

Simplifying the equation, we get:

x = 546*sin(0°)/sin(30°)

Since sin(0°) = 0 and sin(30°) = 0.5, we have:

x = 546*0/0.5

x = 0

Therefore, the length of the common tangent is 0m.

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The simplified expression is \(2 \cos x\).

The question is asking us to simplify the expression \( \frac{\sin x+\tan x \cos x}{\tan x} \) and show the steps to reach the final result.

First, we can use the identity \(\tan x = \frac{\sin x}{\cos x}\) to rewrite the expression:

\( \frac{\sin x+\tan x \cos x}{\tan x} = \frac{\sin x+\frac{\sin x}{\cos x} \cos x}{\frac{\sin x}{\cos x}} \)

Next, we can simplify the numerator by canceling out the \(\cos x\) terms:

\( \frac{\sin x+\frac{\sin x}{\cos x} \cos x}{\frac{\sin x}{\cos x}} = \frac{\sin x+\sin x}{\frac{\sin x}{\cos x}} \)

Now, we can combine the \(\sin x\) terms in the numerator:

\( \frac{\sin x+\sin x}{\frac{\sin x}{\cos x}} = \frac{2 \sin x}{\frac{\sin x}{\cos x}} \)

Finally, we can simplify the expression by canceling out the \(\sin x\) terms:

\( \frac{2 \sin x}{\frac{\sin x}{\cos x}} = \frac{2 \sin x}{\sin x} \cdot \frac{\cos x}{1} = 2 \cos x \)

So the final result is:

\( \frac{\sin x+\tan x \cos x}{\tan x} = 2 \cos x \)

Therefore, the simplified expression is \(2 \cos x\).

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The perimeter of the base is 32 cm.

The area of the base is 48 cm².

The total surface area of the triangular prism is 1184 cm².

The diagram above is a triangular prism. Therefore, let's find the perimeter of the base, area of the base and surface area of the triangular prism.

Hence,

perimeter of the base = 10 + 10 + 12

perimeter of the base = 20 + 12

perimeter of the base = 32 cm

Area of the base = 1 / 2 bh

where

Therefore,

Area of the base = 1 / 2 × 12 × 8

Area of the base = 48 cm²

Hence,

total surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)

total surface area of the triangular prism = 12(8) + 34(10 + 10 + 12)

total surface area of the triangular prism = 96 + 34(32)

total surface area of the triangular prism =96 + 1088

total surface area of the triangular prism = 1184 cm²

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The flare takes 10.7 seconds to hit the ground if a flare is shot from the top of a 120-foot building at a speed of 160 feet per second.

The given data is as follows:

Height of building = 120 feets

Speed =  160 feet per second

The given equation is h = −16t + 160t + 120

Time required to hit the ground =?

The flare hits the ground when h=0.

Substitute in the given equation we get,

-16t^2 + 160t + 120 = 0

By applying the Quadratic equation formula to find out the value of t,

Quadratic equation formula = ( -b± [tex]\sqrt{b^{2} - 4ac }[/tex] ) / 2a

x = (-160 ± [tex]\sqrt{160^{2} - 4(-16)(120) }[/tex] ) / 2(-16)

x = (-160 ± [tex]\sqrt{33280}[/tex] ) / -32

x = (-160 +[tex]\sqrt{33280}[/tex] ) / -32,  (-160 -[tex]\sqrt{33280}[/tex]  ) / -32

x = -10.70, 10.70

Neglecting the time in Negative values, x = 10.70 seconds

Therefore, we can conclude that the flare takes 10.7 seconds to hit the ground.

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The simplified form of the radical expressions are:
a) −12x2y6
b) 284x7t4y3

To simplify the following radical expressions, we need to factor the radicand and then use the properties of radicals to simplify.

For a) −72x4y122x8y2, we can factor the radicand as follows:

−72x4y12 = −(2*2*2*3*3)x4y12 = −(2*2*2*3*3)(x4)(y12)

Now we can use the properties of radicals to simplify:

√−(2*2*2*3*3)(x4)(y12) = √−(2*2)(2*2)(3*3)(x4)(y12) = −(2*2*3)(x2)(y6) = −12x2y6

For b) 7z21128x14t8y6, we can factor the radicand as follows:

1128x14t8y6 = (2*2*2*2*71)(x14)(t8)(y6)

Now we can use the properties of radicals to simplify:

√(2*2*2*2*71)(x14)(t8)(y6) = √(2*2)(2*2)(71)(x14)(t8)(y6) = (2*2*71)(x7)(t4)(y3) = 284x7t4y3

So the simplified form of the radical expressions are:

a) −12x2y6
b) 284x7t4y3

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The following are the values for the missing measures of x in the set of similar polygons:

1). x = 14

2). x = 9

3). x = 3

4). x = 2.

Given that each set of polygons are similar so:

1). 4/10 = 5.6/x

x = (5.6 × 10)/4 {cross multiplication}

x = 56/4

x = 14

2). x/18 = 6/12

x = (6 × 18)/12 {cross multiplication}

x = 9

3). x/4 = 4.5/6

x = (4.5 × 4)/6 {cross multiplication}

x = 18/6

x = 3

4). x/8 = 5/20

x = (8 × 5)/20 {cross multiplication}

x = 4/2

x = 2

The following are the values for the missing measures of x in the set of similar polygons:

1). x = 14

2). x = 9

3). x = 3

4). x = 2.

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The company deposited $1,487.88 at the end of each quarter during the first six years.

The amount deposited quarterly during the first six years can be calculated using the formula for the future value of an annuity:

[tex]PMT = (FV / ((1 + r)^{n-1}) * (1 + r)^{-n[/tex]

where PMT is the equal quarterly deposit, FV is the final value of the account, r is the quarterly interest rate (APR / 4), and n is the number of quarters (6 years * 4 quarters per year = 24 quarters).

Plugging in the given values, we get:

[tex]PMT = ($50,000 / ((1 + 0.068/4)^{28-1}) * (1 + 0.068/4)^{-28}[/tex]

PMT = $1,487.88 (rounded to the nearest cent)

Therefore, the company deposited $1,487.88 at the end of each quarter during the first six years.

The problem involves finding the amount deposited quarterly by a company for a period of six years, given the final value of the account four years after the company stopped making deposits. This can be solved using the formula for the future value of an annuity, which calculates the total value of a series of equal payments made at regular intervals over a specified period, taking into account compound interest.

By plugging in the given values into the formula, we can solve for the equal quarterly deposit made by the company during the first six years. The resulting amount is $1,487.88, which represents the total value of all the quarterly deposits made by the company during the six-year period. This answer assumes that the interest rate remained constant throughout the entire period and that the company made no withdrawals or additional deposits after the initial six years.

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Work Shown:

[tex]V = \text{Volume of a sphere}\\\\V = \frac{4}{3}\pi*r^3\\\\V = \frac{4}{3}\pi*6^3\\\\V = \frac{4}{3}\pi*216\\\\V = \frac{4}{3}*216\pi\\\\V = 288\pi\\\\[/tex]

Answer:

X = 1

Step-by-step explanation:

[tex]2x + 8 = 4x + 6 \\ collect \: the \: like \: terms \\ 8 - 6 = 4x - 2x \\ 2 = 2x \\ x = 1[/tex]

Answer:

x = 1

Step-by-step explanation:

first subtract 6 from both sides

2x + 8 = 4x + 6

     -6           -6

2x + 2 = 4x

Now get the variable on to one side by subtracting 2x from both sides

2x + 2 = 4x

-2x         -2x

2 = 2x

Now divide both sides by two to get the value of x

2 (÷ 2) = 2x (÷ 2)

1 = x

x = 1

to check your work, plug in one for x

2x + 8 = 4x + 6

2(1) + 8 = 4(1) + 6

2 + 8 = 4 + 6

10 = 10

this statement is true which means the solution is true

Hope this helps!

Answer:

  see attached

Step-by-step explanation:

Given some of the angles in a parallelogram with diagonals shown, you want the measures of missing angles.

The measures of missing angles are found by making use of triangle and parallelogram angle relations:

In the attached diagram, the given angles are shown in red. The requested angles are shown in blue.

  ∠BDC = 40°, congruent to alternate interior angle ABD

  ∠DEA = 78°, supplementary to adjacent angle AEB

  ∠BDA = 70°, congruent to alternate interior angle DBC

  ∠BCD = 70°, supplementary to adjacent angle ABC = 40°+70°.

We can see here that solving the parallelogram, we have:

A parallelogram is a quadrilateral (a polygon with four sides) in which opposite sides are parallel to each other. This means that the opposite sides of a parallelogram have the same slope and will never intersect, even if extended infinitely.

A parallelogram has four sides, four angles, and two pairs of opposite sides that are equal in length. The opposite angles of a parallelogram are also equal in measure.

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If Martina has already spent $22 and will spend more than $36 in total, then we can set up an inequality to represent the possible additional amounts she will spend:

$22 + c > $36

To solve for c, we can isolate it on one side of the inequality by subtracting $22 from both sides:

c > $36 - $22

c > $14

Therefore, the possible additional amounts Martina will spend (represented by c) must be greater than $14. The inequality solved for c is c > $14.

The solution set of the equation is {0}

A. The values of the variable that make a denominator zero are [tex]x = 3[/tex] and [tex]x = -3[/tex]. This is because when [tex]x = 3[/tex] or [tex]x = -3[/tex], the denominator of the fraction [tex]x^2 - 9[/tex] becomes zero, causing the entire equation to become undefined.

B. To find the solution of the equation, we can first multiply both sides by the common denominator, [tex]x^2 - 9[/tex]:

[tex](5/x+3-3/x-3)(x^2-9) = (5x/x^2-9)(x^2-9)[/tex]

Simplifying and combining like terms, we get:

[tex]5x - 9 - 3x + 9 = 5x[/tex]

[tex]2x = 5x[/tex]

Subtracting [tex]5x[/tex] from both sides, we get:

[tex]-3x = 0[/tex]

Dividing by -3, we find that the solution of the equation is x = 0.

Therefore, the solution set of the equation is {0}.

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The range οf P-values wοuld be 0.01 < P-value < 0.02

In statistics, a test statistic is a numerical value that is calculated frοm a sample οf data and is used tο determine whether οr nοt tο reject a null hypοthesis in a hypοthesis test.

The chοice οf test statistic depends οn the specific hypοthesis test being perfοrmed and the nature οf the data being analyzed. Fοr example, in a t-test fοr the mean οf a nοrmally distributed pοpulatiοn, the test statistic is the t-value, which is calculated as the difference between the sample mean and the hypοthesized pοpulatiοn mean divided by the standard errοr οf the mean.

Using Table A-3 with n = 38 and a left-tailed test statistic t = 2.714, we find the cοrrespοnding P-value tο be between 0.01 and 0.02. Therefοre, the range οf values fοr the P-value is:

0.01 < P-value < 0.02

Sο the cοrrect respοnse is:

0.01 < P-value < 0.02

Hence, the range οf P-values wοuld be 0.01 < P-value < 0.02

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Complete Question:

Yes, this is exponential growth. Exponential growth occurs when the rate of increase is proportional to the current amount. In this case, the retail revenue from shopping on the Internet is projected to grow at a rate of 56% per year, meaning that the amount of growth each year is 56% of the current amount. This is an example of exponential growth because the rate of growth is proportional to the current amount.

To further illustrate this point, let's say that the retail revenue from shopping on the Internet in year 1 is $100. In year 2, it would grow by 56% to $156 ($100 + ($100 * 0.56)). In year 3, it would grow by 56% again to $243.36 ($156 + ($156 * 0.56)). As you can see, the amount of growth each year is proportional to the current amount, which is the definition of exponential growth.

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The values of x, y, z, and w are 6, -13, -1, and 4, respectively. So, the answer is 6, -13, -1, 4.

To find a basis for the orthogonal complement of the subspace of R4 spanned by the given vectors, we need to find the null space of the matrix formed by the given vectors. The matrix is:
```
1 -1 7 5
2 -1 1 6
1 0 -6 1
```
We can use the reduced row echelon form to find the null space of this matrix. The reduced row echelon form of this matrix is:
```
1 0 -6 1
0 1 13 -4
0 0 0 0
```
The null space of this matrix is the set of all vectors (x, y, z, w) such that:
```
x - 6z + w = 0
y + 13z - 4w = 0
```
We can write the null space in parametric form as:
```
x = 6z - w
y = -13z + 4w
z = z
w = w
```
We can write the null space in the form {(x, y, 1, 0), (z, w, 0, 1)} by setting z = 1 and w = 0 in the first vector, and setting z = 0 and w = 1 in the second vector. This gives us:
```
x = 6(1) - 0 = 6
y = -13(1) + 4(0) = -13
z = 6(0) - 1 = -1
w = -13(0) + 4(1) = 4
```
Therefore, the basis for the orthogonal complement of the subspace of R4 spanned by the given vectors is {(6, -13, 1, 0), (-1, 4, 0, 1)}. The values of x, y, z, and w are 6, -13, -1, and 4, respectively. So, the answer is 6, -13, -1, 4.

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The number of hours one would spend doing homework now would be; 2.88 hours.

As evident in the task content; One spends 8% doing homework, if one adds 4% more.

The total percent of time spent doing homework is; 12%.

Since there are 24 hours in a day; it follows that the number of hours spent doing one's homework is;

= 12% of 24 = 0.12 × 24.

= 2.88 hours.

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Answer:

C

Step-by-step explanation:

Answer choice A implies that less than received an 80 or better, while according to the boxplot, at least 18 students did.

Answer choice B suggests that most students scored at least 90%, but that is false.

Answer choice C implies that the same number of students scored in the 70-80% range as in the 80-90% range, which is true according to the box plot.

Answer D says that more people scored 65-70% than 90-100%, but the opposite is true.

If there are 578 coyotes in 2003 with initial growth of 1.52, there will be approximately 336113 coyotes in 2028.

The number of coyotes in 2028 can be found by using the formula for exponential growth:

[tex]A = P(1 + r)^t[/tex]

Where:

A = final amount
P = initial amount
r = growth rate
t = time in years

Plugging in the given values:

[tex]A = 578(1 + 1.52)^25[/tex]

Using a calculator, we get:

[tex]A = 578(1.52)^25[/tex]
[tex]A = 578(581.68)[/tex]
[tex]A = 336112.64[/tex]

Therefore, there will be approximately 336113 coyotes in 2028.

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The derivative of u in terms of distributions.

Proof:

First, let's prove that u defines a distribution. To do this, we need to show that u is linear and continuous.
Linearity:

Let ɸ₁ and ɸ₂ be two test functions and let a and b be two scalars. Then:

u(aɸ₁ + bɸ₂) = ∫ 1/√x (aɸ₁(x) + bɸ₂(x)) dx

= a∫ 1/√x ɸ₁(x) dx + b∫ 1/√x ɸ₂(x) dx

= au(ɸ₁) + bu(ɸ₂)

Therefore, u is linear.
Continuity:

Let ɸₙ be a sequence of test functions converging to 0 in D(R). Then:

|u(ɸₙ)| = |∫ 1/√x ɸₙ(x) dx|

≤ ∫ |1/√x ɸₙ(x)| dx

≤ ∫ |1/√x| |ɸₙ(x)| dx

≤ ∫ |1/√x| ||ɸₙ||∞ dx

= ||ɸₙ||∞ ∫ |1/√x| dx

Since ɸₙ converges to 0 in D(R), ||ɸₙ||∞ → 0 as n → ∞. Also, ∫ |1/√x| dx is finite. Therefore, |u(ɸₙ)| → 0 as n → ∞, which means u is continuous.

Since u is linear and continuous, u defines a distribution.
Derivative:

Now, let's calculate the derivative of u in terms of distributions. By definition, the derivative of a distribution u is another distribution u' such that:

u'(ɸ) = -u(ɸ')

So, we need to find a distribution u' that satisfies this equation. Let's substitute the definition of u into the equation:

u'(ɸ) = -∫ 1/√x ɸ'(x) dx

Now, let's integrate by parts:

u'(ɸ) = -[1/√x ɸ(x)]∞₀ + ∫ ɸ(x) d(1/√x) dx

= -[1/√x ɸ(x)]∞₀ + ∫ ɸ(x) (-1/2x^(3/2)) dx

= ∫ (1/2x^(3/2)) ɸ(x) dx

Therefore, the derivative of u in terms of distributions is:

u'(ɸ) = ∫ (1/2x^(3/2)) ɸ(x) dx

This is the distribution that satisfies the equation u'(ɸ) = -u(ɸ').

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The solution to this linear programming problem is (x,y) = (3,4) and f = 22.

To solve this linear programming problem, we need to find the feasible region by graphing the constraints and then use the objective function to find the maximum value of f.

1. Graph the constraints:

x + y ≤ 7 can be rewritten as y ≤ -x + 7
2x + y ≤ 12 can be rewritten as y ≤ -2x + 12
y ≤ 4

2. Find the feasible region:

The feasible region is the area that satisfies all of the constraints. In this case, it is the area bounded by the three lines and the x and y axes.

3. Use the objective function to find the maximum value of f:

f = 2x + 4y

To find the maximum value of f, we need to find the corner points of the feasible region and plug them into the objective function. The corner points are (0,4), (3,4), and (4,3).

f(0,4) = 2(0) + 4(4) = 16
f(3,4) = 2(3) + 4(4) = 22
f(4,3) = 2(4) + 4(3) = 20

The maximum value of f is 22 at the point (3,4).

Therefore, the solution to this linear programming problem is (x,y) = (3,4) and f = 22.

Answer:

(x,y) = (3,4)

f = 22

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Answer: 10y - 3

Step-by-step explanation:

We just add the "+" sign between the two.

So we get:

8y - 6 + 2y + 3

The y terms are like, so we do :

(8y + 2y) - 6 + 3

Which is:

10y - 6 + 3

The integers are like (common), so we do:

10y (-6 + 3)

Which is :

10y - 3    

It is - 3 because -6 + 3 = -3, and we also add the "-" with the integer

So our final answer is=

10y - 3

The tangent trigonometry ratio can be used to determine the measure of m∠F using the length shown. Option C is correct

The given figure is a right triangle.

According to the question, we are to determine the trigonometry ratio that can be used to find m∠F.

Given the following sides

Hypotenuse = EF

Opposite to m∠F = DE

Adjacent = DF

Since tan m∠;F = opposite/adjacent = DE/DF

tan m∠F can be used to determine m∠F.

The same goes with tan and sine since we can determine the value of the hypotenuse but only tangent can be used to find the measure given the length shown.

Learn more on right triangles here;

https://brainly.com/question/2437195

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