A bag contains 40 cards of five different colors. The probability of selecting each color is listed in the chart.

How many orange cards does the bag contain?

A. 1 orange card
B. 5 orange cards
C. 8 orange cards
D. 32 orange cards

Recall that to determine if a table represents a probability distribution, the sum of the probabilities must add up to 1, and all the probabilities have to be positive numbers less or equal to 1.

Now, notice that:

From the table, we notice that all the given probabilities are positive numbers between 0 and 1. Therefore, we can conclude that the given table represents a probability distribution.

Yes, it is a probability distribution.

Answer:

82 ft^2

Step-by-step explanation:

To find the amount of glass needed to cover the entire rectangular pyramid, we need to calculate the combined surface area of all its faces.

The rectangular base of the pyramid has an area of 5 feet by 4 feet, or 20 square feet. The two large triangular faces each have an area of (1/2) x base x height = (1/2) x 5 feet x 6.8 feet = 17 ft^2. The two small triangular faces each have an area of (1/2) x base x height = (1/2) x 4 feet x 7 feet = 14 ft^2.

Therefore, the total surface area of the pyramid is:

20 ft^2 (for the base) + 17 ft^2 + 17 ft^2 + 14 ft^2 + 14 ft^2 = 82 ft^2

So, the amount of glass needed to cover the entire pyramid is 82 square feet.

Therefore, the answer is 82 ft^2.

Answer:82  ft2

Step-by-step explanation:

i did it in class

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Answer:

Systematic

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

Every xth element, so systematic.

Answer:

Time taken by the ball to reach the maximum height = 5/32 seconds

Step-by-step explanation:

To find the time at which maximum height is reached , we will differentiate the given equation  with respect to t

\(\frac{db_{(t)}}{dt} = -32t + 5 = 0\\t = \frac{5}{32} \\\)

Substituting this value of t in formula of b(t), we get

\(-16 * (\frac{5}{32})^2 + 5 * \frac{5}{32} + 15 \\= 15.390\)

The probability that a simple random sample of 45 unemployed individuals will provide is 0.7372

Here, μ = 17.5, σ = 0.8944, x1 = 16.5 and x2 = 18.5.

We need to compute P(16.5<= X <= 18.5).

The corresponding z-value is calculated using Central Limit Theorem.

z = (x - μ)/σ

z1 ⇒ (16.5 - 17.5)/0.8944 = -1.12

z2 ⇒ (18.5 - 17.5)/0.8944 = 1.12

Therefore, we get

P(16.5 <= X <= 18.5) = P((18.5 - 17.5)/0.8944) <= z <= (18.5 - 17.5)/0.8944)

⇒ P(-1.12 <= z <= 1.12) = P(z <= 1.12) - P(z <= -1.12)

⇒ 0.8686 - 0.1314 = 0.7372

The principal limit theorem states that if you have a population with imply μ and trendy deviation σ and take sufficiently huge random samples from the populace with alternative, then the distribution of the pattern method may be about usually distributed.

The relevant limit theorem (CLT) states that the distribution of pattern manner approximates a normal distribution as the pattern size gets larger, regardless of the population's distribution. sample sizes identical to or extra than 30 are often considered enough for the CLT to preserve.

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Answer:

Rs 16,680

Step-by-step explanation:

Ok

let his income be 100%

he spends 60%

and saves 40%=11,120=Rs 27800=income answer

spend=60%

60÷40×11,120= Rs 16,680=expenditure answer

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

The sorted order of the impairs [3 7], [4 6], [3 4] using impair. compare to would be:
[C] [3 2], [4 6], [3 7]

When comparing in pairs using impair. compare to, the first element taking priority over the second element. So, in the list [3 7], [4 6], [3 4], the impair [3 2] would come first because 3 is smaller than both 4 and 3, and the second element (2) is also smaller than the second element of the other in pairs. Then, the impair [4 6] would come next as it has the second smallest first element, and finally, the impair [3 7] would come last as it has the largest first element. Therefore, the sorted order is [3 2], [4 6], [3 7], denoted as option C.

To sort the given list of in pairs ([3 7], [4 6], [3 4]) using impair. compared, follow these steps:

1. Compare the first elements of the in pairs (3, 4, and 3). If there is a tie, move to step 2.
2. Compare the second elements in pairs with the same first elements (7 and 4).
3. Arrange the impairs in ascending order based on the comparison results.

The sorted order is [3 4], [3 7], [4 6]. However, this order is not present in the given options. Please check the question for any discrepancies or provide the correct in pairs to sort.

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The sorted order of the impairs [3 7], [4 6], [3 4] using impair. compare to would be:

[C] [3 2], [4 6], [3 7]

When comparing in pairs using impair. compare to, the first element taking priority over the second element. So, in the list [3 7], [4 6], [3 4], the impair [3 2] would come first because 3 is smaller than both 4 and 3, and the second element (2) is also smaller than the second element of the other in pairs. Then, the impair [4 6] would come next as it has the second smallest first element, and finally, the impair [3 7] would come last as it has the largest first element. Therefore, the sorted order is [3 2], [4 6], [3 7], denoted as option C.

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

a) We have shown that if x is even, then \(x^2 = 0\) or 4 (mod 8).

b) We have shown that if x is odd, then \(x^2 = 1\) (mod 8).

a) To prove that if x is even, then\(x^2 = 0\) or 4 (mod 8), we can use the fact that any even integer can be written in the form 2k, where k is an integer. Then, we have:

\(x^2 = (2k)^2 = 4k^2\)

Since k^2 is also an integer, we can write \(4k^2\)as 8m or 8m + 4, where m is an integer. This can be simplified as:

\(4k^2 = 8m or 4k^2 = 8m + 4\\2k^2 = 4m or 2k^2 = 2m + 1\\k^2 = 2m or k^2 = (2m + 1)/2\)

In the first case, \(k^2\) is even and so\(x^2 = 0\) (mod 8). In the second case, \(k^2\)is odd and so \(x^2 = 4\) (mod 8).

b) To prove that if x is odd, then \(x^2 = 1\) (mod 8), we can again use the fact that any odd integer can be written in the form 2k + 1, where k is an integer. Then, we have:

\(x^2 = (2k + 1)^2 = 4k^2 + 4k + 1\)

Since \(k^2\)and k are integers, we can write \(4k^2 + 4k\) as 8m or 8m + 4, where m is an integer. This can be simplified as:

\(4k^2 + 4k = 8m or 4k^2 + 4k = 8m + 4\\2k^2 + 2k = 4m or 2k^2 + 2k = 2m + 1\)

k(k + 1) = 2m or k(k + 1) = (2m + 1)/2

In the first case, either k or k + 1 is even, so k(k + 1) is even and \(x^2 = 0\)(mod 8). In the second case, k and k + 1 are consecutive integers, so one of them must be even and the other odd. Therefore, k(k + 1) is even and x^2 ≡ 4 (mod 8).

Finally, we have:

\(x^2 = 4m + 1 or x^2 = 4m + 5\)

In either case, \(x^2 = 1\) (mod 8), since 4m + 1 and 4m + 5 are both congruent to 1 modulo 8.

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The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

what is triangle ?

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

Given, side length, a = 12 units.

the height of equilateral triangle, h = (a√3)/2.

Substituting the value of 'a',

h = (12√3)/2 = 6√3 =

10.39 units.

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

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The product of the terms   \((d - 9)\)  and  \((2d^{2} + 11d -4)\)  will be \((2d^{3} - 7d^{2} - 103d + 36)\).

We have to find the product of two terms.

First term = (d - 9)

Second term = \((2d^{2} + 11d -4)\)

To find the product of these two terms, we will be using the distributive property. According to the distributive property, when we multiply the sum of two or more addends by a number, it will give the same result as when we multiply each addend individually by the number and then add the products together.

We have to find :  \((d - 9) (2d^2 + 11d -4)\)

Using the distributive property,

\(d * 2d^{2} + d * 11 + d * (-4) - 9 * 2d^2 - 9 * 11d - 9 * (-4)\)

After further multiplication, we get

\(2d^{3} + 11d^2 - 4d - 18d^{2} - 99d + 36\)

Now, combine all the like terms.

\(2d^{3} + 11d^{2} - 18d^{2} - 4d - 99d + 36\)

\(2d^{3} - 7d^{2} - 103d + 36\)

Therefore, the product of d-9 and 2d^2 + 11d -4 is \(2d^{3} - 7d^{2} - 103d + 36\)

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Answer:

approx. 68%

Step-by-step explanation:

this is a normal distribution.

in a normal distribution, approximately 68% of the data is within one standard deviation of the mean (we also have 95% of data is within two standard deviations of the mean, and 99.7% of data is within three standard deviations of the mean).

one standard deviation in our question is 113.

315 is one standard deviation below the mean because 428 - 113 = 315.

541 is one standard deviation above the mean because 428 + 113 = 541.

so we expect approx. 68% of the data to be between 315 and 541.

The length of a wave does not directly determine its depth. The depth of a wave is influenced by various factors, including the shape and size of the seafloor,

The temperature and salinity of the water, and the strength and direction of the current. Therefore, without additional information about these factors, it is impossible to accurately determine the depth of a wave based solely on its length. I suggest seeking the advice of an expert in oceanography or physics for a more comprehensive explanation.

The length of a wave is the distance between two successive points in the same phase, such as from crest to crest or trough to trough. In your case, the wave length is given as 30 feet. However, without additional information about the wave, we cannot determine its depth solely based on its length.

Depth refers to the vertical distance from the surface to the lowest point of a wave (trough), and it's not directly related to the wave length. Therefore, we cannot accurately choose an option (a, b, c, or d) for the depth based on the provided information.

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The angle between \(\(\vec{a}\) and \(\vec{b}\) is \(60^\circ\).\)

To find the angle between two vectors\(\(\vec{a}\) and \(\vec{b}\)\), we can use the dot product formula:

\(\(\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos(\theta)\),\)

where \(\(|\vec{a}|\) and \(|\vec{b}|\)\) are the magnitudes of the vectors and\(\(\theta\)\)is the angle between them.

Given that \(\(\vec{a} \cdot \vec{b} = \sqrt{3}\),\) we can rewrite the equation as:

\(\(\sqrt{3} = |\vec{a}| |\vec{b}| \cos(\theta)\).\)

We are also given that \(\(\vec{a} \times \vec{b} = \langle 1, 2, 2 \rangle\),\)which represents the cross product of the vectors.

The magnitude of the cross product is given by:

\(\(|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(\theta)\).\)

Substituting the given values, we have:

\(\(|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(\theta) = |\langle 1, 2, 2 \rangle| = \sqrt{1^2 + 2^2 + 2^2} = \sqrt{9} = 3\).\)

We can rearrange the equation to solve for \(\(|\vec{a}| |\vec{b}| \sin(\theta)\):\(3 = |\vec{a}| |\vec{b}| \sin(\theta)\).\)

Now, we have two equations:

\(\(\sqrt{3} = |\vec{a}| |\vec{b}| \cos(\theta)\),\(3 = |\vec{a}| |\vec{b}| \sin(\theta)\).\)

To eliminate the magnitudes \(\(|\vec{a}|\) and \(|\vec{b}|\)\), we can square both equations and add them together:

\(\((\sqrt{3})^2 + 3^2 = (|\vec{a}| |\vec{b}|)^2 (\cos^2(\theta) + \sin^2(\theta))\)\).

Simplifying, we get:

\(\(3 + 9 = (|\vec{a}| |\vec{b}|)^2\).\(12 = (|\vec{a}| |\vec{b}|)^2\).\)

Taking the square root of both sides:

\(\(\sqrt{12} = |\vec{a}| |\vec{b}|\).\(\sqrt{12} = |\vec{a}| |\vec{b}| = |\vec{a}| |\vec{b}| \sqrt{\cos^2(\theta) + \sin^2(\theta)}\).\)

Since \(\(\cos^2(\theta) + \sin^2(\theta) = 1\)\), we have:

\(\(\sqrt{12} = |\vec{a}| |\vec{b}| \cdot 1\).\(\sqrt{12} = |\vec{a}| |\vec{b}|\).\)

Now, we can substitute this back into the first equation:

\(\(\sqrt{3} = \sqrt{12} \cos(\theta)\).\)

Simplifying, we get:

\(\(\cos(\theta) = \frac{\sqrt{3}}{\sqrt{12}} = \frac{\sqrt{3}}{2\sqrt{3}} = \frac{1}{2}\).\)

To find the angle \(\(\theta\)\), we take the inverse cosine (

arc cosine) of \(\(\frac{1}{2}\):\)

\(\(\theta = \cos^{-1}\left(\frac{1}{2}\right)\).\)

Using the unit circle or trigonometric identities, we find that\(\(\theta = \frac{\pi}{3}\) or \(60^\circ\).\)

Therefore, the angle between \(\(\vec{a}\) and \(\vec{b}\) is \(60^\circ\).\)

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Answer:

Perimeter = 56 m

Area = __ m^2

Step-by-step explanation:

Perimeter = ___ m

Area = __ m^2

To find Perimeter, you have to add up all the sides of the shape,

5 + 5 + 5 + 11 + 7 + 7 + 16

= 56 m

Perimeter = 56 m

To find area, you have to multiply length times width,

5 × 5 = 25

7 × 16 = 112

112 + 25 = 137

Area = 137 m^2

Therefore the perimeter of this shape is 56 m and the area of this shape is 137m^2.

Answer:

A total of 72 containers need to be set up. If 39 are already placed then there are 33 left. You multiple the number of rows by the number of containers per row to find your total and subtract what has already been done.

Answer:

96 chocolate bars

Step-by-step explanation:

If Brian sold 25% of his chocolate bars and now he's left with 72, let's subtract 25% from 100%.

100% - 25% = 75%

Now, let's set up the equation & solve:

1. Set up Equation

2. Cross-Multiply

3. Divide both sides by 75

Therefore, Brian started with 96 chocolate bars.

Answer:

96 bars

Step-by-step explanation:

100% - 25% = 75%

\(\frac{75}{100}\) = \(\frac{72}{x}\)

x = \(\frac{100*72}{75}\) = 96 bars

Using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.

According to the question,

For each correct question, you get 2 points, and there are 22 correct questions, so multiply 22 by 2

22 * 2 = 44 points.

For each question left blank, you get 0 points, and there are 7 questions left blank, so multiply 7 by 0

7 * 0 = 0 points

For each incorrect question, you get -1 point, and there are 5 incorrect questions, so multiply 5 by -1

5 * (-1) = -5 points.

The total number of score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points.

Hence, using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.

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Marsha must claim for itemized deductions.

Given,

Last year's gross income is $56,800.

Medical expenses = $4900

State and local income taxes paid = $3100

The mortgage interest paid = $1940

Charitable contributions = $530

Non-reimbursed work expenses = $1200

Standard deduction = $5700

The sum of all the expenses of last year = $4900 + $3100 + $1940 + $530 + $1200 = $11,670

And the Standard deduction is $5700.

Which is, $11,670 - $5700 = $5970 lesser.

Therefore, Marsha must claim for itemize deductions rather than the standard deductions.

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Answer:

You are correct :)

Step-by-step explanation:

Area of a circle = π * r2

R = 39

So 39 squared is 1521.

1521 times pi is 4775.94

Answer:

You are correct! The answer is 4775.94 in^2

Step-by-step explanation:

πr^2 or π(39)^2

In titration, the graph of qsp (solubility product) versus lead concentration is typically exponential due to the nature of the underlying chemical equilibrium involved.

During titration, a solution containing a known concentration of a reagent (known as the titrant) is slowly added to a solution containing an analyte of interest. In the case of lead titration, the analyte is a lead-containing compound.

As the titrant is added, a chemical reaction occurs between the titrant and the analyte, forming a precipitate of a sparingly soluble salt, typically represented as PbX2 (where X represents an anion). The solubility of this salt can be described by the solubility product (Ksp), which is the equilibrium constant for the dissolution of the salt into its constituent ions.

The solubility product (qsp) is defined as the product of the ion concentrations raised to the power of their stoichiometric coefficients in the balanced chemical equation describing the dissolution process.

In the case of lead titration, as the lead concentration increases, more of the sparingly soluble salt is formed until the point at which all the lead ions have reacted to form the precipitate. As a result, the solubility product (qsp) increases exponentially with increasing lead concentration.

The exponential nature of the qsp versus lead concentration graph arises from the mathematical relationship between the solubility product and the concentration of the ions involved in the precipitation reaction. This relationship reflects the equilibrium behavior of the system and the tendency of the precipitate to form as the concentration of lead ions increases.

It's important to note that the shape of the graph can be influenced by factors such as temperature, the nature of the analyte and titrant, and other conditions specific to the titration setup. The exponential trend is a general observation, but variations may occur depending on the specific titration system and experimental conditions.

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We Prοved that tanθ + cοtθ = secθcscθ using trigοnοmetry identified.

Trigοnοmetry is a branch οf mathematics that deals with the study οf angles, triangles, and their relatiοnships with each οther. It invοlves the study οf the prοperties and functiοns οf triangles, as well as the relatiοnships between angles and sides οf triangles.

Tο sοlve the equatiοn Tanθ + cοtθ = secθcscθ, we can start by expressing each term in terms οf sine and cοsine functiοns:

⇒ \($\mathrm{tan}\,\theta+\mathrm{cot}\,\theta\)

\($\Rightarrow\frac{\mathrm{sin}\ \theta}{\mathrm{cos}\,\theta}+\frac{\mathrm{cos}\,\theta}{\mathrm{sin}\,\theta}$\)

\($\Rightarrow{\frac{\sin^{2}\ \theta+\cos^{2}\!\theta}{\sin\theta.\cos\theta}}$\)

\($={\frac{1}{\sin\theta.\cos\theta}}$\)

= secθ·cscθ

Hence, Proved that tanθ + cotθ = secθcscθ

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Complete question:

Prove that tanθ + cotθ = secθcscθ.

Answer:

The slope is 3.5 it represents the amount of miles per hour

Step-by-step explanation:

I subtracted 6 from 13 and got 7miles every 2 hours, then I divided 7 by two to get 3.5 miles per hour.

Pls give me brainliest, hope this helped

Answer:

q = 3/4

Step-by-step explanation:

7+5(3q-4)=(q-1)

(5×3q)=15q (5×4)=20

7+15q-20=7

(7-20)= -13

-13+15q=7

The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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Answer:

The value of x=-8

Step-by-step explanation:

hope this helps.

Answer:

x = -8

Step-by-step explanation:

\(\frac{3}{4}(\frac{1}{4}x+8)-(\frac{1}{2}x+2) =\frac{3}{8}(4-x)-\frac{1}{4}x\\\\\frac{3}{4}*\frac{1}{4}x+\frac{3}{4}*8-\frac{1}{2}x-2 =\frac{3}{8}*4-\frac{3}{8}x-\frac{1}{4}x\\\\\frac{3}{16}x+3*2-\frac{1}{2}x-2 =\frac{3}{2}-\frac{3}{8}x-\frac{1}{4}x\\\\\\ \frac{3}{16}x+6-\frac{1}{2}x-2 =\frac{3}{2}-\frac{3}{8}x-\frac{1}{4}x\\\\\frac{3}{16}x-\frac{1}{2}x+\frac{3}{8}x+\frac{1}{4}x=\frac{3}{2}-4\\\\\\\frac{3}{16}x-\frac{1*8}{2*8}x+\frac{3*2}{8*2}x+\frac{1*4}{4*4}x=\frac{3}{2}-\frac{4*2}{1*2}\\\\\\\)

\(\frac{3}{16}x-\frac{8}{16}x+\frac{6}{16}x+\frac{4}{16}x = \frac{3}{2}-\frac{8}{2}\\\\\frac{3-8+6+4}{16}x = \frac{3-8}{2}\\\\\frac{5}{16}x = \frac{-5}{2}\\\\x = \frac{-5}{2}*\frac{16}{5}\\\\x = -8\)