Angle θ is in standard position and

(

−

5

,

−

6

)

(−5,−6) is a point on the terminal side of θ. If

0

∘

≤

θ

<

36

0

∘

0

∘

≤θ<360

∘

, what is the measure of θ, to the nearest tenth of a degree (if necessary)?

Answer:

No

Step-by-step explanation:

"Looking" at our triangles

If Angle D is congruent to Angle G, and angle E is congruent to Angle H, lets call those the first and second vertices of each triangle.  If we're trying to prove the triangles congruent, we're trying to prove Triangle DEF is congruent to Triangle GHJ (in that order, since we're already given that the first and second angles correspond between triangles).

Could these triangle be congruent?  Yes!  As a quick example, imagine two Equilateral triangles with side lengths 5.  They are congruent, and they do have the first angle and second angle corresponding pairs congruent, and one of those sides from triangle 1 does match the length of one of the sides in triangle 2.  ...and they are congruent triangles.

The problem with the given scenario is that the side they give for triangle 1 (between vertex 1 and 2) is not the corresponding side of triangle 2 (between vertex 2 and 3).  This makes it so that we cannot guarantee that the triangles are congruent.

As can be seen in the attached image, I've made Side DE length 2, and put it on a coordinate plane so it's easy to see.  Side HJ is also definitely length 2.  Clearly, those triangles are not congruent.

When would triangles be congruent?

Going back to the definition of congruent triangles, three corresponding angles and three corresponding sides must be congruent.  That's 6 pairs of parts needed to be proven congruent to prove triangles congruent!

Fortunately, there are a number of theorems that can be proven to lessen the amount of pairs of parts needed to be proven congruent and still guarantee that the resulting triangles must be congruent.

There are exactly 5 cases:

It looks like a bunch of alphabet soup, but notice that all of them require 3 pieces of information (even HL, which is Hypotenuse-Leg... since there's a Hypotenuse, it must be a right triangle, so there are a pair of corresponding congruent right angles that are congruent that they don't talk about)

In order to remember which items work, remember that you MUST know 3 parts, and think about all of the way you could know 3 parts:

Scenario 1: Have all 3 side pairs (SSS)

There is only one way that all three sides can be equal, and yes, that is one of the triangle congruence shortcuts.

Scenario 2: Have 2 side pairs & 1 angle pair

There are two option here.  

Two sides with the angle between them is SAS (note the angle is between them).

Two sides with the angle not between them is ... (well, that can get you in trouble).  Conveniently, that is NOT one of the triangle congruence theorems.  So, stay out of trouble, and don't use this for triangle congruence.

Interestingly, HL, is a special case of this "trouble case".  Note that if you have the Hypotenuse and a leg, that's two Sides.  The right Angle is NOT the angle between those two sides (because the hypotenuse is always across from the right angle).  When that angle is 90 degrees, then the set of two sides and the angle not between them DOES work as sufficient to prove triangle congruence, and it's the only time that it's sufficient.

Scenario 3: Have 1 Side and 2 Angles

Again, there are two option here:

In either scenario, this is sufficient to prove the triangles are congruent.

Scenario 4: Have all 3 angles (AAA)

This definitely won't be enough to prove congruence.  Zoom in.  It's got the same angles, but not the same lengths.

So, only 5 short ways to prove triangles are congruent, and all of them require 3 parts of one triangle corresponding to 3 parts of another, each of the 3 pairs must be congruent.

The output of the function call doWork(30) is given as follows:

9.

The input of the function is given as follows:

n = 30.

Hence we apply the recursion as follows:

Now we apply the inverse procedure, as follows:

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The value of the integral for the given integral ∬ (\(x^2\)y) dA is:

∫∫ (\(x^2\)y) dA = (625/8) (\(sin^3\)π/3)

                   = (625/8) (0)

                   = 0

To evaluate the given integral ∬ (\(x^2\)y) dA, where d represents the top half of the disk with center at the origin and radius 5, we can change to polar coordinates.

In polar coordinates, we have the following transformations:

x = r cosθ

y = r sinθ

dA = r dr dθ

The limits of integration for r and θ can be determined based on the given region. Since we want the top half of the disk, we know that the angle θ will vary from 0 to π, and the radius r will vary from 0 to the radius of the disk, which is 5.

Now, let's evaluate the integral:

∬ (\(x^2\)y) dA = ∫∫ (\(r^2 cos^2\)θ) (r sinθ) r dr dθ

We can simplify the integrand:

∫∫ (\(r^3 cos^2\)θ sinθ) dr dθ

Now, we can integrate with respect to r first:

∫∫ (r^3 cos^2θ sinθ) dr dθ = ∫ [r^4/4 cos^2θ sinθ] |_\(0^5\) dθ

Substituting the limits of integration for r:

∫∫ (\(r^3 cos^2\)θ sinθ) dr dθ = ∫ [625/4 \(cos^2\)θ sinθ] dθ

Now, we can integrate with respect to θ:

∫ [625/4 \(cos^2\)θ sinθ] dθ = (625/4) ∫ [\(cos^2\)θ sinθ] dθ

We can use a trigonometric identity to simplify the integrand further:

\(cos^2\)θ sinθ = (1/2) sin2θ sinθ

                    = (1/2) \(sin^2\)θ cosθ

∫ [625/4 \(cos^2\)θ sinθ] dθ = (625/4) ∫ [(1/2) \(sin^2\)θ cosθ] dθ

Using a substitution u = sinθ:

du = cosθ dθ

The integral becomes:

(625/4) ∫ [(1/2) \(u^2\)] du = (625/4) (1/2) ∫ \(u^2\) du

                                  = (625/8) (\(u^3\)/3) + C

Substituting back u = sinθ:

(625/8) (\(sin^3\)θ/3) + C

Finally, we need to evaluate the integral over the limits of θ from 0 to π:

∫ [625/4 \(cos^2\)θ sinθ] dθ = [(625/8) (\(sin^3\)π/3) - (625/8) (\(sin^3\) 0/3)]

Since sin(π) = 0 and sin(0) = 0, the second term becomes 0. Therefore, the value of the integral is:

∫∫ (\(x^2\)y) dA = (625/8) (\(sin^3\)π/3)

                   = (625/8) (0)

                   = 0

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Step-by-step explanation:

ax+by+c=0 is the equation of a line

using y-y1=m(x-x1)

m=3+1/5+4=4/9

y+1=4/9(x+4) multiplying through 9

9y+9=4(x+4)

9y+9=4x+16

9y+9-4x-16=0

9y-7-4x=0

9y-4x-7=0

then you have your answer

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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2m = 28

Given the following parameter

Mai's savings = m

The product of Mai's savings and 2 is given as:

If 28 is equal to the product of Mai's savings and 2, the resulting expression will be given as:

28 = 2m

Hence the required equation is 2m = 28

As average animal has four legs, there were ten pigs and ten chickens, giving a total of 54 legs: 10 x 4 = 40 legs, 10 x 2 = 20 legs.

10 pigs and 10 chickens were present. 10 pigs have 4 legs each, for a total of 40 legs. 10 chickens have 2 legs each, for a total of 20 legs. 40 + 20 = 54 legs. Jill counted the animals in the farmyard and found twenty. The 20 animals had a total of 54 legs, according to Jack. We can perform a straightforward step-by-step computation to determine the number of pigs and chicks present. Since each pig has four legs, we may generate 40 legs by multiplying the number of pigs, 10, by 4. Similar to humans, chickens have two legs each, so multiplying 10 by 2 results in 20 legs. The sum of the two figures gives us 54 legs, which is the same as Jack's estimate. Hence, the farmyard contained 10 pigs and 10 hens.

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Factorial notation is used to represent the product of a series of descending positive integers, and is denoted by an exclamation mark.

For example, 5! represents 5 x 4 x 3 x 2 x 1, which equals 120. If the study involves counting the number of ways a certain group of items can be arranged, factorial notation may be used to express the total number of possible arrangements. However, without knowing the specifics of Dr. Elder's study, it is impossible to provide the correct factorial notation. Therefore, I would recommend providing more details about the study in order to receive a more accurate answer.

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Answer:

Step-by-step explanation:

-6+6=0 -3+3=0

This is because the signs are different so you count back starting with the negatives.

-6,-5,-4,-3,-2,-1,0

Answer:

B) 6 positive tiles

Step-by-step explanation:

Answer: $37.10.

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

you divide by one hundred multiply by the percent and ad the original cost

A function which has the same horizontal asymptote as the function graphed above include the following: A. f(x) = 4^{x + 2} - 3.

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 3, as shown in the image attached below.

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The general solution of the differential equation is y(x) = C₁x¹/² + 1/4 cos(x).

Given a differential equation:

4x²y" + y = x³/² sin(x)

and y(x) = x¹/²

We need to verify whether the given function is the solution of the differential equation or not.

Therefore, we will substitute the value of y(x) in the differential equation.

Let's start by finding the first and second derivatives of y(x) which will be used further.

y(x) = x¹/²y'(x)

= d/dx (x¹/²)y'(x)

= (1/2)x^(-1/2)y''(x)

= d/dx[(1/2)x^(-1/2)]y''(x)

= (-1/4)x^(-3/2)

Therefore, substituting y(x) and y" (x) in the differential equation:

4x² (-1/4)x^(-3/2) + x¹/² = x³/²sin(x)

Thus, the above equation simplifies as:-

x^(-1) + x¹/² = x³/²sin(x)

Here, we can see that the given function is not a solution of the differential equation.

However, we can find the particular solution of the differential equation by the method of variation of parameters.

Where we write the given equation in the standard form:

y'' + [1/4x⁴]y = [x¹/² sin(x)]/4x⁻²

On comparing with the standard form:

y'' + p(x) y' + q(x) y = g(x) where p(x) = 0, q(x) = 1/4x⁴ and g(x) = [x¹/² sin(x)]/4x⁻²

Now, let's calculate the Wronskian for the differential equation as:

W(y₁, y₂) = | y₁    y₂ |-1/4x²               1/4x²-1/2W(y₁, y₂)

= 1/4x³

The particular solution y₂(x) will be:

y₂(x) = -y₁(x) ∫[g(x) y₁(x)] / W(x) dx

Substituting the given value in the above equation, we get:

y₂(x) = -x¹/² ∫[x¹/² sin(x)] / (x³/² 4x⁻²) dx

y₂(x) = -1/4 ∫sin(x) dx

y₂(x) = -1/4 [-cos(x)] + C₁

y₂(x) = 1/4 cos(x) + C₁

Hence, the general solution of the differential equation is:

y(x) = C₁x¹/² + 1/4 cos(x)

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Answer:

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Step-by-step explanation:

The height of the ball after t seconds is given by the following equation:

\(h(t) = -4.9t^{2} + 5t + 1\)

How long will it take the ball to hit the ground if no other players touch it?

This is t when h(t) = 0. So

\(-4.9t^{2} + 5t + 1 = 0\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

\(-4.9t^{2} + 5t + 1 = 0\)

So \(a = -4.9, b = 5, c = 1\)

So

\(\bigtriangleup = 5^{2} - 4*4.9*1 = 44.6\)

\(t_{1} = \frac{-5 + \sqrt{44.6}}{2*(-4.9)} = -0.17\)

\(t_{2} = \frac{-5 - \sqrt{44.6}{2*(-4.9)}  = 1.19\)

Since we want a time measure, the answer cannot be negative.

It will take 1.19 seconds for the ball to hit the ground if no other players touch it

Answer:

a. (-2) (2)7

b. (-21) (2)2

Answer:

Therefore, the direction of the vector is 180° - 29.3° = 150.7° (measured counterclockwise from the positive x-axis).

Step-by-step explanation:

To find the direction of the vector, we need to calculate its angle with respect to the positive x-axis. We can use the inverse tangent function to do this. The formula for the angle θ is:

θ = tan⁻¹ (y/x)

where y is the vertical component and x is the horizontal component of the vector.

In this case, the x-component is -22.2 m and the y-component is 12.6 m. So, we have:

θ = tan⁻¹ (12.6 / (-22.2))

Using a calculator, we find:

θ ≈ -29.3°

Since the x-component is negative, the vector points towards the negative x-axis. Therefore, the direction of the vector is 180° - 29.3° = 150.7° (measured counterclockwise from the positive x-axis).

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Answer:

Definitely not the 2nd one. I think it is the first one, the 3rd one looks more like a 45, 45, 90

Answer: x=3

Step-by-step explanation:

6x + 3x - x + 9 = 33

Combine like terms:

6x+3x-x=8x

The equation is now 8x+9=33

Subtract 9 on both sides:

8x+9-9=33-9

8x=24

Divide 8 on both sides:

8x/8=24/8

x=3

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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The probability that the ball will fall into a red slot during the following spin is 0.14.

To calculate the probability of an occurrence, divide the total number of outcomes by the total number of possible outcomes. The concepts of probability and odds are distinct. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. When we toss the coin in the air, the probability that it will land with the heads side up is calculated. Here is a practical use of probability that you are probably already familiar with. We always check the weather forecast before a significant outing.

\(\frac{1}{7}=0.142857\)

The probability is 0.14

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The probability of the ball landing on a red slot in a single spin of a fair roulette wheel is 1/2, as there are an equal number of red and black slots.

The outcome of each spin is independent, meaning that the outcome of one spin does not affect the outcome of another. Therefore, the probability that the ball will land on a red slot in the next spin is still 1/2, regardless of the results of the previous seven spins.

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Given:

Length of a box is 9 inches, width is 2 inches and height is 1.5 inches.

The cost of silver coating is $2.50 per sq. inches.

To find:

The total cost of silver coating for the box.

Solution:

The total surface area of a cuboid is

\(A=2(lb+bh+hl)\)

Where, l is length, b is breadth and h is height.

Putting \(l=9,b=2,h=1.5\), we get

\(A=2(9\times 2+2\times 1.5+1.5\times 9)\)

\(A=2(18+3+13.5)\)

\(A=2(34.5)\)

\(A=69\)

So, the total surface area of the box is 69 square inches.

Cost of silver coating is $2.50 per sq. inches. So, the cost of silver coating for the box is

\(Cost=69\times 2.50\)

\(Cost=172.50\)

Therefore, the cost of silver coating for the box is $172.50.

That is ver very sad

yes,

abcdefghijklmnopqrstuvwxyz

Answer:

32n = 100 - 20

n = 2.5

he purchased 2 sweaters

Step-by-step explanation:

32n = 100 - 20

If Favian originally had $100 but spent $20 on a belt, he only had 80 left, meaning that 80 = 32n which means that he was able to but 2 sweaters and got $16 back. Therefore the formula would be 32n = 100 - 20

The formula for the number of sweaters will be 32n = 100 – 20.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Favian received a $100 gift card to a clothing store.

Using only the gift card, he was able to purchase n sweaters that cost $32 each and 1 belt for $20.

If there was no tax on the sweaters and belt,

Then the equation will be

32n + 1 x 20 = 100

    32n + 20 = 100

             32n = 80

                 n = 2.5 ≈ 2

If Favian originally had $100 but spent $20 on a belt, he only had 80 left, meaning that 80 = 32n, which means that he was able to but 2 sweaters and got $16 back.

Therefore, the formula would be 32n = 100 – 20.

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The answers of the following questions are provided below with full solution respectively.

Coordinate geometry is a branch of mathematics that combines algebra and geometry.

It involves using algebraic equations to describe the positions and relationships between points in a geometric plane.

It is also known as analytic geometry.

a) To find the midpoint of AB, we can use the midpoint formula:

Midpoint = ( (x1+x2)/2, (y1+y2)/2 )

So, the midpoint of AB is:

Midpoint = ( (1+6)/2, (4+(-8))/2 )

= ( 3.5, -2 )

Therefore, the midpoint of AB is (3.5, -2).

b) To find the slope of AB, we can use the slope formula:

Slope = (y2-y1)/(x2-x1)

So, the slope of AB is:

Slope = (-8-4)/(6-1)

= -12/5

Therefore, the slope of AB is -12/5.

c) To find the length of AB, we can use the distance formula:

Distance = √[(x2-x1)² + (y2-y1)²]

So, the length of AB is:

Distance = √[(6-1)² + (-8-4)²]

= √[5² + (-12)²]

= √(169)

= 13

Therefore, the length of AB is 13.

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Using coordinate geometry, we can find the following:

AB's midpoint is: (3.5, -2)

The slope of AB is -12/5.

The length of AB is 13.

Algebra and coordinate geometry are combined in the field of mathematics known as coordinate geometry.

It includes describing the locations and connections between points in a geometric plane using algebraic equations.

Another name for it is analytical geometry.

We can apply the midpoint formula to determine AB's midpoint as follows:

\(Midpoint=\frac{(x_1+x_2)}{2} ,\frac{(y_1+y_2)}{2}\)

Therefore, AB's midpoint is:

Midpoint = ((1+6)/2, (4+(-8))/2)

= (3.5, -2)

Hence, the midpoint of AB is (3.5, -2).

We may use the slope formula to determine the slope of AB:

\(slope=\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )}\)

So, the slope of AB is:

Slope = (-8-4)/ (6-1)

= -12/5

Hence, the slope of AB is -12/5.

We may use the distance formula to determine the length of AB:

\(Distance=\sqrt{[(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^2]}\)

So, the length of AB is:

Distance = √ [(6-1) ² + (-8-4) ²]

= √ [5² + (-12) ²]

= √ (169)

= 13

Therefore, the length of AB is 13.

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Answer:

a because it is the one that makes the most sense

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

To calculate the p-value, we need to perform a hypothesis test.

Let's assume the null hypothesis is that the proportion of defective systems produced by x-game is equal to or less than the industry standard of 0.02, while the alternative hypothesis is that the proportion is greater than 0.02.

We can use the normal approximation to the binomial distribution since we have a large sample size (n=120) and np and n(1-p) are both greater than or equal to 10.

The test statistic can be calculated as:

\(z = (p_hat - p) / \sqrt{(p*(1-p)/n)}\)

where \(p_hat\)  is the sample proportion of defective systems, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Using the values given in the question, we have:

\(p_hat = 6/120 = 0.05\)

p = 0.02

n = 120

Plugging these values into the formula, we get:

\(z = (0.05 - 0.02) / \sqrt{(0.02*(1-0.02)/120) = 2.041}\)

The p-value can be calculated as the probability of getting a test statistic as extreme or more extreme than 2.041 under the null hypothesis.

Since this is a one-tailed test (the alternative hypothesis is one-sided), we look up the area in the right tail of the standard normal distribution table.

Using a standard normal distribution table, we find that the area to the right of 2.041 is 0.0207.

Therefore, the p-value is 0.0207.

Therefore, we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

This means that there is strong evidence that the proportion of defective systems produced by x-game exceeds the industry standard of 0.02.

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Answer:

Below

Step-by-step explanation:

y ( 5.98x - 5.81) - 2.19 y =

5.98xy - 5.81y      - 2.19 y

5.98xy + ( - 5.81y - 2.19 y)

5.98xy + ( - 8y )

5.98xy - 8y       or   y ( 5.98x-8)

Given:

The system of equations is:

Line A: \(y=x-4\)

Line B: \(y=3x+4\)

To find:

The solution of given system of equations.

Solution:

We have,

\(y=x-4\)              ...(i)

\(y=3x+4\)           ...(ii)

Equating (i) and (ii), we get

\(x-4=3x+4\)

\(-4-4=3x-x\)

\(-8=2x\)

Divide both sides by 2.

\(-4=x\)

Substituting \(x=-4\) in (i), we get

\(y=-4-4\)

\(y=-8\)

The solution of system of equations is (-4,-8).

Now verify the solution by substituting \(x=-4, y=-8\) in the given equations.

\(-8=-4-4\)

\(-8=-8\)

This statement is true.

Similarly,

\(-8=3(-4)+4\)

\(-8=-12+4\)

\(-8=-8\)

This statement is also true.

Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.