Help solve this question

Answer:     7 .

Step-by-step explanation:

The middle term is, +7x its coefficient is 7 . Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is

The toy has a volume of 200 cm³. The correct answer is Option d.

This is because when an object is submerged in water, it displaces an amount of water equal to its volume. In this case, the pool toy displaces 200 mL of water, which means it has a volume of 200 cm³ (since 1 mL is equal to 1 cm³). The correct answer is Option d.

It is not correct to say that the toy weighs 200 grams (option a), as the weight of the toy is not related to the amount of water it displaces. Similarly, it is not correct to say that the toy absorbed 200 mL of water (option b), as the toy is simply displacing the water, not absorbing it.

Finally, it is  correct to say that the toy has a surface area of 200 cm² (option c), as the amount of water displaced is related to the toy's volume, not its surface area.

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Answer:

The expression log3 2x + 3 log3 4x can be condensed to log3 8x + 3. This is because log3 4x = 2 log3 2x, so when we add the two logarithms together, the result is log3 8x + 3

Step-by-step explanation:

a) The graphic that illustrates the shape of the distribution of the data is shown below:



b) The Central Limit Theorem states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sample mean is 56.4645 and the sample standard deviation is 14.6052. Therefore, the standard deviation of the sample mean is 14.6052/sqrt(11) = 4.4016. Using a z-score of 1.645 for a 90% confidence interval, the interval is (56.4645 - (1.645*4.4016), 56.4645 + (1.645*4.4016)) = (50.2155, 62.7135). One reservation about this estimate is that the sample size is small and the distribution of the data is not normal, so the Central Limit Theorem may not be accurate.

c) The empirical bootstrap distribution (EBD) for the mean using 200 resamples is shown below:



The shape of the EBD is approximately normal, which is expected according to the Central Limit Theorem.

d) The 90% bootstrap confidence interval for the mean can be found by taking the 5th and 95th percentiles of the EBD. The 5th percentile is 52.7455 and the 95th percentile is 60.4818, so the interval is (52.7455, 60.4818). This interval is slightly wider than the one in (b), which is expected because the bootstrap method takes into account the variability of the sample.

e) The empirical bootstrap distribution (EBD) for the median using 200 resamples is shown below:



The EBD for the median is not as smooth as the EBD for the mean, and there are several spikes in the distribution. This occurs because the median is a more discrete measure than the mean, so there are fewer possible values for the median in the resamples.

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Fοr an equilateral triangle, sketch is drawn fοr side length = 5 cm.

Triangles are a particular sοrt οf pοlygοn in geοmetry that have three sides and three vertices. Three straight sides make up the twο-dimensiοnal figure shοwn here. An example οf a 3-sided pοlygοn is a triangle. The tοtal οf a triangle's three angles equals 180 degrees. One plane cοmpletely enclοses the triangle.

An equilateral triangle in geοmetry is a triangle with equal-length sides οn all three sides.

In the well-knοwn Euclidean geοmetry, an equilateral triangle is alsο equiangular, meaning that each οf its three internal angles is 60 degrees and cοngruent with the οthers.

The given triangle has a side length οf 5 cm.

Sο, each sire measures the same.

Therefοre, the sketch is drawn fοr the same.

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Precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

To make a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point, follow these steps:

1. Draw the given circle using a compass.
2. Mark the given point on the paper with a pencil.
3. Place the point of the compass at the given point and extend the compass until it touches the edge of the circle.
4. Draw a circle with the compass. This circle will intersect the given circle at two points.
5. Use a ruler to draw a line from the given point to each of the intersection points. These lines are the tangent lines to the given circle that pass through the given point.
6. Label the tangent lines and the given point for clarity.

By following these steps, you can create a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point. Remember to be precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

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The fact that the points are located along a straight path does not prove that the relationship is proportional.

A graph is a graphic representation of a collection of data or a mathematical function in mathematics. It consists of several nodes or vertices linked by arcs or edges. Graphs are frequently used to display data in a manner that is simple to comprehend and interpret. They can be used to demonstrate mathematical functions or equations as well as relationships between various variables and patterns or trends in data. Line graphs, bar graphs, scatter plots, pie charts, and other graphs come in a wide variety. Depending on the nature of the data being depicted and the insights that need to be communicated, each type of graph is used for a specific reason.

given

The fact that the points are located along a straight path does not prove that the relationship is proportional. The connection is proportional, though, if y rises by a constant multiple of x every time.

Since y does not have to increase by a fixed constant in order for a relationship to be proportional, the claim that "It must be proportional because each time y increases by 3, x remains the same" is untrue.

Since proportional relationships can have non-zero y-intercepts, the claim that it cannot be proportional because a straight line through the locations would not pass through the origin is false as well.

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The temperature on mountaintop was -10° and the temperature on the ground was 10°. The solution has been obtained by using the linear equation.

What is a linear equation?

One is the degree of the linear equation. It is obvious that there are no variables in linear equations with exponents greater than 1. The graph's equation results in a straight line.

We are given that the temperature on the mountaintop was 20° lower than temperature on the ground.

Let the temperature on the ground be 'x'.

So, temperature on the mountaintop = x - 20

Also, the temperature on a mountaintop and the temperature on the ground had opposite values.

So,

x = - (x - 20)

On solving this, we get

⇒x = -x + 20

⇒2x = 20

⇒x = 10°

So, x - 20 = 10 - 20 = -10°

Hence, the temperature on mountaintop was -10° and the temperature on the ground was 10°.

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Pythagorean theorem: Show that ⟨x, y⟩ = 0

Let V be an Euclidean space and let x, y ∈ V.(a) If ∥x + y∥ = ∥x − y∥ then determine ⟨x, y⟩.We know that ∥x + y∥² = ⟨x + y, x + y⟩ = ⟨x, x⟩ + ⟨x, y⟩ + ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ⟨x − y, x − y⟩ = ⟨x, x⟩ − ⟨x, y⟩ − ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x + y∥ = ∥x − y∥, we have ∥x∥² + 2⟨x, y⟩ + ∥y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²⟨x, y⟩ = 0(b) Show that 2⟨x, y⟩ ≤ ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x + y∥² ≥ 0So ∥x∥² + 2⟨x, y⟩ + ∥y∥² ≥ 0⟨x, y⟩ ≤ (∥x∥² + ∥y∥²)/2(c) If (z, y) = 0 for all z ∈ V then show that y = 0.Let z = y, then (y, y) = 0⟨y, y⟩ = ∥y∥² = 0∥y∥ = 0So y = 0(d) If ∥x∥ = ∥y∥ for some x, y ∈ V then ⟨x + y, x − y⟩ = 0.We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x∥ = ∥y∥, we have ∥x∥² = ∥y∥²So ∥x + y∥² − ∥x − y∥² = 4⟨x, y⟩ = 0⟨x, y⟩ = 0(e) Pythagorean theorem: Show that ⟨x, y⟩ = 0 if and only if ∥x + y∥² = ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²If ⟨x, y⟩ = 0, then ∥x + y∥² = ∥x∥² + ∥y∥²If ∥x + y∥² = ∥x∥² + ∥y∥², then 2⟨x, y⟩ = 0⟨x, y⟩ = 0

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the answer is x+10 i think bye

I is convergent.

The Comparison Theorem is an important tool in the study of Probability and Statistics, as it allows us to determine the convergence or divergence of improper integrals without directly evaluating them. In this case, we are asked to determine the convergence or divergence of the improper integral I=∫ 2 [infinity] ​ e −x 2 dx using the Comparison Theorem.

1. To justify the inequality e −2x ≥e −x 2 for all x≥2, we can take the natural logarithm of both sides of the inequality to get -2x ≥ -x^2. Since x≥2, we can divide both sides of the inequality by -x to get 2 ≤ x, which is true for all x≥2. Therefore, the inequality e −2x ≥e −x 2 is true for all x≥2.

2. To evaluate ∫ 2 [infinity] ​ e −2x dx, we can use the substitution u=-2x, du=-2dx. This gives us ∫ 2 [infinity] ​ e −2x dx = ∫ -4 [-infinity] ​ (1/2)e^u du = (1/2)(-e^u)|-4 [-infinity] = (1/2)(-e^-4 + e^[infinity]) = (1/2)(-e^-4 + 0) = (1/2)e^-4.

3. To determine if I is convergent or divergent, we can use the Comparison Theorem. Since e −2x ≥e −x 2 for all x≥2, and ∫ 2 [infinity] ​ e −2x dx is convergent, then ∫ 2 [infinity] ​ e −x 2 dx is also convergent by the Comparison Theorem. Therefore, I is convergent.

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The solution to the all six equations is that they have infinite many real solutions

Expression (a)

We have:

√(x^2-14x+49)=x-7

Squaring both sides we get:

x^2 - 14x + 49 = x^2 - 14x + 49

Evaluate the like terms

0 = 0

This means that the equation has infinite many solutions

Expression (b)

Here, we have:

√(4x^2-20x+25)=5-2x

Squaring both sides we get:

4x^2-20x+25 = 25 - 20x + 4x^2

Evaluate the like terms

0 = 0

This means that the equation has infinite many solutions

For the remaining expressions, we have the following (using the above steps)

Expression (c)

√(y^4+2y^2+1) = y^2 + 1

y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1

0 = 0

Expression (d)

√(x^2+2x+1)=x+1

x^2 + 2x + 1 = x^2 + 2x + 1

0 = 0

Expression (e)

√(y^2-20y+100)=y-10

y^2 - 20y + 100 = y^2 - 20y + 100

0 = 0

Expression (f)

√(y^6-2y^3+1)=y^3-1

y^6-2y^3+1 = y^6-2y^3+1

0 = 0

Hence, the equations have infinite solutions

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The profit function is obtained by subtracting the cost function from the revenue function. In other words, Profit = Revenue - Cost.

In the given question, the profit function is already given as P(x) = -x^(2) + 1230x - 36000. This means that the profit is a function of x, which could represent the number of units sold or produced.

To find the profit for a specific value of x, simply substitute the value of x into the profit function and simplify. For example, if x = 100, then the profit would be:

P(100) = -(100)^(2) + 1230(100) - 36000
P(100) = -10000 + 123000 - 36000
P(100) = 77000

Therefore, the profit when x = 100 is $77,000.

Similarly, you can find the profit for any value of x by substituting the value into the profit function and simplifying.

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The expression which uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16) is (-3/4)x(-16)x1/5) which is therefore denoted as option A.

This states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

In the expression (-3/4)x1/5x(-16) , there is the need to arrange them so as to make it easier for them to be reduced to their lowest factor which is why -16 was put close to the  (-3/4).

(-3/4)x(-16)x1/5 = 12 × 1/5 =  12/5

This is therefore the reason why option A was chosen as the correct choice.

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Answer:

Step-by-step explanation:

A= 5(x+3)=17

B= 5x+3=17

C= 3x+5=17 A girl decides to buy 5 pens for 3 of her friends. The total cost of the pens was 17$. She then decides to make her friends guess the cost of each pen.

The x-coordinate of point P is approximately -5.33.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

To find the x-coordinate of point P, we can use the formula:

x-coordinate of P = (4x-coordinate of A + 2x-coordinate of B) / (4+2)

We are given the coordinates of points A and B:

A(-8, -9) and B(0, -2)

Using the formula, we can substitute the x- and y-coordinates of A and B into the formula and simplify:

x-coordinate of P = (4(-8) + 2(0)) / (4+2)

= (-32) / 6

= -5.33 (rounded to 2 decimal places)

Therefore, the x-coordinate of point P is approximately -5.33.

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To find the total distance Henri hiked, we can multiply the distance he hiked each day (7/10 mile) by the number of days he hiked (9 days):

Total distance = (7/10) mile/day * 9 days

We can simplify this expression by multiplying the fractions and then multiplying by 9:

Total distance = (7/10) * 9 mile

Total distance = 63/10 mile

Therefore, the equation equivalent to the total amount hiked is:

Total distance = 63/10 mile

or, if we prefer to write the distance in decimal form:

Total distance = 6.3 miles

From  the function φ(x)=31​x3−21​x,  0 is a fixed point of φ(x) it shows in calculation below.  The iteration xk+1 = φ(xk) converges locally to 0 shows below. The iteration diverges as k increases.

(a) To show that 0 is a fixed point of φ(x), we need to show that φ(0) = 0. Substituting x = 0 into the function gives us:

φ(0) = (3/1)(0)3 - (2/1)(0) = 0 - 0 = 0

Therefore, 0 is a fixed point of φ(x).

(b) To show that the iteration xk+1 = φ(xk) converges locally to 0, we need to show that |φ'(x)| < 1 for x near 0. Taking the derivative of φ(x) gives us:

φ'(x) = (9/1)x2 - (2/1)

At x = 0, φ'(0) = 0 - 2 = -2. Since |φ'(0)| > 1, the iteration does not converge locally to 0.

(c) By numerical tests, we can find an initial guess x0 such that the iteration converges to 0 and an initial guess x0 such that the iteration diverges. For example, if we choose x0 = 0.5, the iteration converges to 0:

x1 = φ(0.5) = (3/1)(0.5)3 - (2/1)(0.5) = -0.625

x2 = φ(-0.625) = (3/1)(-0.625)3 - (2/1)(-0.625) = 0.8203125

x3 = φ(0.8203125) = (3/1)(0.8203125)3 - (2/1)(0.8203125) = -0.4625244140625

And so on. The iteration converges to 0 as k increases.

On the other hand, if we choose x0 = 2, the iteration diverges:

x1 = φ(2) = (3/1)(2)3 - (2/1)(2) = 20

x2 = φ(20) = (3/1)(20)3 - (2/1)(20) = 23980

x3 = φ(23980) = (3/1)(23980)3 - (2/1)(23980) = 3.47119332792e+13

And so on. The iteration diverges as k increases.

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The lengths of the sides of the of the right triangles are found using the Pythagorean Theorem as follows;

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the lengths of the legs of the right triangle.

1) The location of the angles and the congruent 90° angle and a second congruent angle indicates;

ΔABN ~ ΔTBA ~ ΔTAN

The missing values of x can be obtained using Pythagorean Theorem as follows;

2) AB = √(10² + 5²) = √(125) = 5·√5

[tex]\overline{AB}[/tex]² = (5 + x)² - [tex]\overline{AN}[/tex]²

[tex]\overline{AN}[/tex]² = (5 + x)² - [tex]\overline{AB}[/tex]²

[tex]\overline{AN}[/tex]² = 10² - x²

10² + x² = (5 + x)² - [tex]\overline{AB}[/tex]²

10² + x² = (5 + x)² - 125

[tex]\overline{AB}[/tex]² = (5 + x)² - (10² + x²) = 10·x - 75

10·x - 75 = (5·√5)² = 125

10·x - 75 = 125

10·x = 125 + 75 = 200

x = 200/10 = 20

x = 20

3) The hypotenuse side of the right triangle with sides 8 and 4 can be found as follows;

Length of the hypotenuse = √(8² + 4²) = 4·√5

Length of the leg of the larger right triangle is, length = √(8² + x²)

Therefore;

(x + 4)² = (8² + x²) + (4·√5)²

(x + 4)² - (8² + x²) = (4·√5)²

8·x - 48 = 80

8·x = 80 + 48 = 128

x = 128/8 = 16

x = 16

4) The leg of the larger right triangle = (12 + 2)² - x² = 14² - x²

14² - x² - 12² = x² - 2²

2·x² = 14² - 12² + 2² = 56

x² = 56/2 = 28

x = √(28) = 2·√7

x = 2·√7

5) The length of the shorter leg of the larger right triangle can be found as follows;

Length of the shorter leg = (20 + 25)²- x²

x² - 25² = (20 + 25)²- x² - 20²

2·x² = (20 + 25)² + 25² - 20² = 2250

x² = 2250/2 = 1125

x = √(1125) = 15·√5

x = 15·√5

6) x² - 4² = (32 + 4)² - x² - 32²

2·x² = (32 + 4)² + 4² - 32² = 288

x² = 288/2 = 144

x = √(144) = 12

x = 12

7) Let x represent the length of the right tringle and let h represent the altitude of the right triangle

(PR)² = 16² - x²

16² - x² - 12² = x² - 4²

2·x² = 16² - 12² + 4² = 128

x² = 128/2 = 64

x = √(64) = 8

The length of the short leg is; x = 8

Length of the longer leg, PR = √(16² - x²)

PR = √(16² - 8²) = 8·√3

Length of the longer leg = 8·√3

The square of the altitude = 16² - x² - 12²

Length of the altitude = √(16² - 64 - 12²) = 4·√3

8) Let x represent the length of the shorter leg, we get;

(PR)² = 18² - x²

The square of the altitude, (PS)² = 18² - x² - 15² = x² - 3²

2·x² = 18² - 15²+ 3² = 108

x² = 108/2 = 54

x = √(54) = 3·√6

Length of the shorter leg, x = 3·√6

PR = √(18² - 54) = 3·√(30)

Length of the longer leg, PR = 3·√(30)

Length of the altitude, PS = √(54 - 3²) = 3·√(15)

9) Let PQ = x, we get;

(QR)² = 30² - x²

30² - x² - (30 - 6)² = x² - 6²

2·x² = 30² - (30 - 6)² + 6² = 360

x² = 360/2 = 180

x = √(180) = 6·√5

PQ = x = 6·√5

(QR)² = 30² - 180 = 720

QR = √(720) = 12·√5

QS = √(720 - (30 - 6)²) = 12

The altitude, QS = 12

The geometric mean of 2 numbers is the square root of the product of the numbers;

10) The geometric mean of 5 and 8 = √(5 × 8) = 4·√10

11) 7 and 11

The geometric mean = √(7 × 11) = √(77)

12) 4 and 5

The geometric mean is; √(4 × 5) = 2·√5

13) 2 and 25

The geometric mean is; √(2 × 25) = √(50) = 5·√2

14) 6 and 8

The geometric mean is; √(6 × 8) = √(48) = 16·√3

15) 8 and 32

The geometric mean is; √(8 × 32) = 16

16) (15 + 5)² - y² = z²

15² + x² = y²

x² + 5² = z²

Therefore;

(15 + 5)² - 15² - x² = x² + 5²

2·x² = (15 + 5)² - 15² - 5² = 150

x² = 150/2 = 75

x = √(75) = 5·√3

x = 5·√3

z² = x² + 5²

z² = 75 + 25 = 100

z = √(100) = 10

z = 10

15² + x² = y²

15² + 75 = 300 = y²

y = √(300) = 10·√3

y = 10·√3

17) 12² - y² = z²

z² - 9² = x²

z² = 9² + x²

x² + 3² = y²

12² - x² - 3²  = z²

12² - x² - 3²  = 9² + x²

2·x² = 12² - 3² - 9² = 54

x² = 54/2 = 27

x = √(27) = 3·√3

x = 3·√3

z² = 9² + x²

z² = 9² + 27 = 108

z = 6·√3

x² + 3² = y²

y² = x² + 3²

y² = 27 + 3² = 36

y = √(36) = 6

y = 6

18) x² - 6² = y²

z² - 24² = y²

(6 + 24)² - x² = z²

Therefore; x² - 6² = z² - 24² = (6 + 24)² - x² - 24²

x² - 6² = (6 + 24)² - x² - 24² = 30² - x² - 24²

x² - 6² = 30² - x² - 24²

2·x² = 30² + 6² - 24² = 360

x² = 360/2 = 180

x = √(180) = 6·√(5)

x = 6·√(5)

z² = (6 + 24)² - x²

z² = (6 + 24)² - 180 = 720

z² = 720

z = √(720) = 12·√5

z = 12·√5

z² - 24² = y²

y² = 720 - 24² = 144

y² = 144

y = 12

19) Let x represent GH, we get;

32² - x² = (HK)²

32² - x² - (32 - 8)² = x² + 8²

2·x² = 32² - (32 - 8)² - 8² = 384

x² = 184

x = √(184) = 2·√(46)

GH = x = 2·√(46)

GH = 2·√(46)

(HK)² = (32 - 8)² + (x² - 8²)²

(HK)² = (32 - 8)² + (184 - 8²) = 696

HK = √(696) = 2·√(174)

HK = 2·√(174)

20) Let x represent the length of the lake, we get;

x² + 6² = (x + 4)² - (4² + 6²) = x² + 8·x - 36

x² + 6² = x² + 8·x - 36

8·x = 6² + 36 = 72

x = 72/8 = 9

The length of the lake, x = 9 km

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Answer:

25, 27

Step-by-step explanation:

maybe ,,,,,,,,,hhy2u2u

Answer: Sum: 28 + 26 = 54

Difference: 28 - 26 = 2

Step-by-step explanation:

x + y = 54

x + 26 = 54

X = 28

Step-by-step explanation:

cost1(t) = 100.25t + 6500

cost2(t) = 225.5t + 4496

both companies charge the same for the amount of t (tons), when both functions deliver the same result :

100.25t + 6500 = 225.5t + 4496

2004 = 125.25t

t = 2004/125.25 = 16

1. for the transport of 16 tons of sugar they both charge the same.

2. that charge is

100.25×16 + 6500 = $8,104

The formula that expresses R as a function of M and S is R = (M - 2S)/2.

To write a formula that expresses R as a function of M and S, we will need to rearrange the equation M=2R+2S to solve for R.

First, we will subtract 2S from both sides of the equation to isolate the term with R on one side:
M - 2S = 2R

Next, we will divide both sides of the equation by 2 to solve for R:
(M - 2S)/2 = R

Finally, we can write the equation in function form, with R as the dependent variable and M and S as the independent variables:
R = (M - 2S)/2

Therefore, the formula that expresses R as a function of M and S is R = (M - 2S)/2.

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The angle measures, considering the linear pair formed by angles 1 and 2, are given as follows:

When a parallel line is cut by a transversal, a linear pair is formed when two adjacent angles add up to 180 degrees. A linear pair of angles is always formed by two adjacent angles that are supplementary, which means that they add up to 180 degrees.

In this case, a linear pair is formed by two adjacent angles that are formed by the intersection of the transversal with each of the parallel lines.

Hence, angles 1 and 2 are supplementary, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

3x + 5 + 2x + 10 = 180

5x + 15 = 180

5x = 165

x = 33.

Then the measures are given as follows:

The diagram that represents the situation is given by the image presented at the end of the answer.

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The solutions to the cosine functions are x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer and x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.

1. 2 cos x - 1 = 0

Adding 1 to both sides and dividing by 2, we get:

cos x = 1/2

This equation has solutions for x of π/3 and 5π/3 (plus any integer multiple of 2π, since the cosine function is periodic with period 2π).

Therefore, the solutions are:

x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer.

2. 5 cos x + 3√2 = 3 cos x + 2√2

Subtracting 3 cos x and 2√2 from both sides, we get:

2 cos x = -√2

Dividing by 2, we get:

cos x = -√2/2

This equation has solutions for x of 3π/4 and 5π/4 (plus any integer multiple of 2π).

Therefore, the solutions are:

x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.

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Answer: 2783 minutes

Step-by-step explanation:

Answer:

2783

Step-by-step explanation:

Since there is 11 episodes in each season and there is 23 seasons we multiply and get 253 so 253 episodes and each one has 11 minutes so 11 x 253 which is 2783

The slope-intercept form of the equation of the line that passes through the point P (5, 4) and makes an angle, θ = 30°, with the x-axis is the option A.

A. y = ((sqrt(3))/3)·x - ((5·sqrt(3))/3 - 4)

The slope-intercept form of linear equation is an equation of the form; y = m·x + c, where;

m = The slope of the graph of the equation

c = The y-intercept of the graph of the equation.

The point through which the line passes, P = (5, 4)

The angle θ the line makes with the positive x-axis = 30°

The slope of the line = The tangent of the angle the line makes with the positive x-axis, therefore;

(y - 4)/(x - 5) = tan(30°) = 1/√3

y - 4 = (x - 5)/√3 = (x - 5)/√3 × (√3/√3) = (x - 5)·√3/3

y = (x - 5)·√3/3 + 4

The above equation can be converted into the slope-intercept form of a linear equation; y = m·x + c by simplifying the equation and rearranging the equation, into the required form;

y = (x - 5)·√3/3 + 4

y = (√3/3)·x - 5·√3/3 + 4 = (√3/3)·x - (5·√3/3 - 4)

y = (√3/3)·x - (5·√3/3 - 4)

The equation in slope-intercept form, is therefore;

A. y = (sqrt(3))/3)·x - (5·sqrt(3))/3 - 4)

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We can be 90% confident that the true population variance of unemployed workers' math test scores falls between 65.61 and 197.57.

The first step in finding a 90% confidence interval for the population variance is to find the degrees of freedom for the sample. In this case, the degrees of freedom is 18 - 1 = 17.

Next, we need to find the critical value for a 90% confidence interval with 17 degrees of freedom. We can do this using a chi-squared distribution table. The critical values for a 90% confidence interval with 17 degrees of freedom are 8.671 and 27.488.

Now we can use the formula for a confidence interval for the population variance:

CI = [(n-1) * s²] / X²

Where n is the sample size, s is the sample standard deviation, and X^2 is the critical value from the chi-squared distribution table.

Plugging in the values we have:

CI = [(17) * (10.4)²] / X²

For the lower bound of the confidence interval, we use the smaller critical value:

CI = [(17) * (10.4)²] / 8.671

CI = 197.57

For the upper bound of the confidence interval, we use the larger critical value:

CI = [(17) * (10.4)²] / 27.488

CI = 65.61

So the 90% confidence interval for the population variance is (65.61, 197.57).

In conclusion, we can be 90% confident that the true population variance of unemployed workers' math test scores falls between 65.61 and 197.57.

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The investor should invest $32,500 in the lowest-yielding, least-risky account, $20,000 in the medium-yielding, medium-risk account, and $17,500 in the highest-yielding, highest-risk account.

To solve this problem, we can use a system of linear equations.

We have three equations and three unknowns: x, y, and z.

The equations are: x + y + z = 50,0000.03x + 0.055y + 0.09z = 2540

We can use substitution or elimination to solve for one of the variables and then plug that value back into the other equations to find the remaining variables.

For example, we can solve for x in the first equation:

x = 50,000 - y - z

Then we can substitute this value of x into the second equation:

0.03(50,000 - y - z) + 0.055y + 0.09z = 2540

Simplifying this equation gives us:

1500 - 0.03y - 0.03z + 0.055y + 0.09z = 25400.025y + 0.06z = 1040

Now we can solve for one of the remaining variables, such as y:

y = (1040 - 0.06z) / 0.025

And we can substitute this value of y back into the first equation to find z:

50,000 - (1040 - 0.06z) / 0.025 - z = 50,000

Solving for z gives us:

z = 17,500

Finally, we can plug this value of z back into the equations for x and y to find the remaining variables:

x = 50,000 - y - 17,500 = 32,500 - y

y = (1040 - 0.06(17,500)) / 0.025 = 20,000

So the solution is x = 32,500, y = 20,000, and z = 17,500.

This means that the investor should invest $32,500 in the lowest-yielding, least-risky account, $20,000 in the medium-yielding, medium-risk account, and $17,500 in the highest-yielding, highest-risk account.

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The inverse of f(x)=−8x+9 is y = (-x + 9)/8.

The inverse of a function is found by switching the x and y variables and solving for y. This is done to find the function that will undo the original function.

To find the inverse of f(x)=−8x+9, we will follow these steps:

1. Switch the x and y variables: x = -8y + 9
2. Solve for y by isolating the y variable on one side of the equation:
x - 9 = -8y
(x - 9)/-8 = y
3. Simplify the equation by dividing the numerator and denominator by -1:
y = (-x + 9)/8

Therefore, the inverse of f(x)=−8x+9 is y = (-x + 9)/8.

Note that we do not need to use parentheses around the denominator since it is a single term. We also do not need to use the term "inverse" in our answer since we are simply finding the inverse of the function. The terms "denominator" and "parentheses" are also not needed in our answer since they do not apply to this specific problem.

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Answer:

Step-by-step explanatio