What is the linear correlation coefficient and determine if there is a linear relationship between x and y

The value of x is 22.5

Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar , the corresponding angles of the triangle must be congruent.

Also, the ratio of corresponding sides of Similar triangles are equal.

Therefore;

6/9 = 15/x

6x = 15×9

6x = 135

divide both sides by 6

x = 135/6

x = 22.5

Therefore the value of x in the triangle is 22.5

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So the lengths of all four sides of ABCD are:

AB = BC = 15 cm

CD = DA = 31 cm

Let AB = x. Then AD = 2x + 1, since AD is 1 cm more than twice AB.

Since ABCD is a parallelogram, opposite sides are equal in length. So, BC = AB = x, and DC = AD = 2x + 1.

The perimeter of the parallelogram is the sum of the lengths of all four sides:

AB + BC + CD + DA = x + x + (2x + 1) + (2x + 1) = 6x + 2

We are given that the perimeter is 92 cm, so we can set this expression equal to 92 and solve for x:

6x + 2 = 92

6x = 90

x = 15

Therefore, AB = BC = 15 cm and AD = DC = 2(15) + 1 = 31 cm.

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Complete question:

The perimeter of parallelogram ABCD is 92 cm. AD is 1 cm more than twice AB. Find the lengths of all four sides of ABCD

Answer:  b

Step-by-step explanation:

[tex]\frac{h^{\frac{1}{3} } }{h^{\frac{1}{4} } }[/tex]             I started to subtract exponents than shortly realized that form is not an answer.  The  want you to covert the top and bottom to roots and that is your anser.

When you have a number to a fractional exponent that is your root

[tex]=\frac{\sqrt[3]{h} }{\sqrt[4]{h} }[/tex]

which is b

The solution to the inequality is -3 ≤ x ≤ -1/3

Given the inequality:

4|3x+5| ≤ 16

Let us simplify it by dividing both sides by 4 to get:

|3x+5| ≤ 4

Next, we can break the inequality into two cases, depending on whether 3x+5 is positive or negative:

First: 3x+5 ≥ 0

In this case, the inequality simplifies to:

3x+5 ≤ 4

Subtracting 5 from both sides, we get:

3x ≤ -1

Dividing by 3 (which is positive) gives:

x ≤ -1/3

Second: 3x+5 < 0

In this case, the inequality simplifies to:

-3x-5 ≤ 4

Adding 5 to both sides, we get:

-3x ≤ 9

Dividing by -3 (which is negative and requires us to flip the inequality), gives:

x ≥ -3

Therefore, the solution to the inequality is:

-3 ≤ x ≤ -1/3

The interval [-3,-1/3] is the solution set, and it includes all values of x between -3 and -1/3, including the endpoints.

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Answer:

The correct equation is A. y = (2/3)x - 2

The given radical in imaginary form as ±7i.

The given number is √-49.

Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.

Here, √-49 =±7i

Therefore, the given radical in imaginary form as ±7i.

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Answer:

2x - 2,000 = 28,000

Step-by-step explanation:

1. Define Variables

          Frank's Income = x

2. Write Equation

           2x - 2,000 = 28,000

3. Solve (if necessary)

           2x - 2,000 = 28,000

           2x = 30,000

           x = 15,000

The number 5 should be subtracted from the right side of the equation to make it a proportional equation.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The function in this problem is given as follows:

y = 6x + 5.

A proportional relationship is a special case of a linear function with an intercept of zero, hence we must subtract by 5 as follows:

y = 6x + 5 - y

y = 6x.

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The new quantity of firewood that is supplied at the price, would be A. 400 cords.

Use the formula for the slope of the supply curve to find the new quantity:

slope = ( Q2 - Q1 ) / ( P2 - P1 )

0.75 = ( Q2 - 300 ) / ( 348 - 255 )

0.75 = ( Q2 - 300 ) / 93

0.75 x 93 = Q2 - 300

69.75 = Q2 - 300

Q2 = 69.75 + 300

Q2 = 369. 75

Given that there are no options for 370 cords, we will pick the closest alternative of 400 cords.

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Answer: The value of c is 8

Step-by-step explanation:

On the thing it says the c=8

The price of the cost per quart of laundry detergent is A = $ 3.47

Given data ,

Let the unit cost rate be A

Now , There are 4 quarts in a gallon, so a 2-gallon container contains 8 quarts.

To find the price per quart, we can divide the total cost by the number of quarts:

Price per quart = Total cost / Number of quarts

Price per quart = $27.76 / 8 = $3.47

Hence , the price per quart of laundry detergent is $ 3.47

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With regard to the right triangles, the equations that expresses the relationship are:

a) 6² + 8² = 10²

b) (√5)² + (√3)² = (√8)²

c) √5)² + (√30)² = 5²

d) does not form a right triangle
e) (√2)² + (√7)² = 3²

In all the cases but the 4th, the sum of two sides are less than  the square of the hypotenuse.

The square of the hypotenuse of a right-angled triangle is always equal to the sum of the squares of the other two sides, according to the Pythagorean property.

This theorem is written as c2 = a2 + b2, where 'c' is the hypotenuse and 'a' and 'b' are the two triangle legs.

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We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

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Answer:

D).The complex numbers have opposite real numbers.

Step-by-step explanation:

I just test and kid above got it wrong eng2023

If the mass of each watermelon is 7 kilograms, there are 8 watermelons on the load.

To find the number of watermelons on the load, we need to divide the total mass of the load by the mass of each watermelon. We can set up an equation to represent this:

Number of watermelons = Total mass of load / Mass of each watermelon

Plugging in the given values, we get:

Number of watermelons = 56 kg / 7 kg per watermelon

Simplifying, we get:

Number of watermelons = 8

Therefore, there are 8 watermelons on the load.

It's important to note that this calculation assumes that all the watermelons have the same mass of 7 kg. In reality, there may be some variation in the mass of the individual watermelons, which could affect the total number of watermelons on the load. Additionally, other factors such as the size and shape of the watermelons may also affect how many can fit on the truck.

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The area of the trapezium is 30 square centimeters at the values of h = 4 cm, b = 10 cm, and b' = 5 cm.

We can use the formula for the area of a trapezoid:

A = 1/2 * h * (b + b')

Substituting the given values, we get:

A = 1/2 * 4 cm * (10 cm + 5 cm)

Simplifying the expression inside the parentheses:

A = 1/2 * 4 cm * 15 cm

Multiplying:

A = 30 cm²

Therefore, when h = 4 cm, b = 10 cm, and b' = 5 cm, the area of the trapezoid is 30 square centimeters.

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Answer:

Since the coefficients of the polynomial function h(x) have real values, if -3i is a zero of h(x), then its complex conjugate 3i must also be a zero of h(x). This is known as the Complex Conjugate Root Theorem.

Therefore, the remaining zeros of h(x) can be found by dividing the polynomial by the factors (x - (-3i)) and (x - 3i), using either polynomial long division or synthetic division. Here, we'll use synthetic division:

 3i  |  3   10   19   90   -72

     |      9i -63 -216 -294

     +-----------------------

     3  10+9i -44 -126 -366

Step-by-step explanation:

The quotient is 3x^3 + (10+9i)x^2 - 44x - 126, and the remainder is -366. This tells us that:

h(x) = (x - (-3i))(x - 3i)(3x^3 + (10+9i)x^2 - 44x - 126)

The remaining zeros of h(x) can now be found by solving the cubic polynomial 3x^3 + (10+9i)x^2 - 44x - 126. This can be done using various methods such as the Rational Root Theorem, factoring by grouping, or numerical methods. However, these methods can be quite involved and may not always lead to exact answers.

Answer: 112

Step-by-step explanation:

Take 144/9 to find how much he makes in a single hour. 144/9 is 16, 16*7=112. Which is how much he will make working 7 hours at the same rate.

The value of S₁₀ in the given geometric series is 699050.

Given that,

The formula to find the sum of a geometric series is,

Sₙ = (a - a rⁿ) / (1 - r)

Here a is the first term and r is the common ratio.

Given is a geometric series,

2 + 8 + 32 + 128 + ....

a = 2

r = 8/2 = 4

We have to find the sum of these terms up to 10 terms.

S₁₀ = (2 - 2 . 4¹⁰) / (1 - 4)

    = (2 - 2097152) / -3

    = -2097150 / -3

    = 699050

Hence the required value is 699050.

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The maximum value of the objective function z = 5x + 4y is 12

From the question, we have the following parameters that can be used in our computation:

z = 5x + 4y

2x + 4y ≤8

5x + y ≤8

x ≥ 0, y ²0

This means that the objective function is

Max z = 5x + 4y

And the constraints are

2x + 4y ≤8

5x + y ≤8

x, y ≥ 0

When solved graphically, we have

(x, y) = (4/3, 4/3)

Substitute (x, y) = (4/3, 4/3) in the objective function

So, we have

z = 5 * 4/3 + 4 * 4/3

Evaluate

z = 12

Hence, the maximum value of the objective function is 12

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a)

The system of equations that models the situation is:

p + m = 5

3p + m = 15

b)

None of the given options is a solution to the system of equations.

We have,

(a)

System of equations that models the situation:

Total weight equation

p + m = 5

Proportion equation:

0.6p + 0.2m = 0.6(5)

Simplifying the second equation:

0.6p + 0.2m = 3

3p + m = 15 (dividing both sides by 0.2)

The system of equations is:

p + m = 5

3p + m = 15

(b)

To check which of the given options is a solution to the system, we substitute the values of p and m from each option into the system of equations and check if both equations are true.

Option 1:

2 lb peanuts and 3 lb mixture

p = 2, m = 3

p + m = 5 (true)

3p + m = 15 (6 + 3 = 9 ≠ 15, not true)

Option 2:

2.5 lb peanuts and 2.5 lb mixture

p = 2.5, m = 2.5

p + m = 5 (true)

3p + m = 15 (7.5 + 2.5 = 10, not true)

Option 3:

4 lb peanuts and 1 lb mixture

p = 4, m = 1

p + m = 5 (true)

3p + m = 15 (12 + 1 = 13, not true)

We see that,

None of the given options is a solution to the system of equations,
This means that the exact values of p and m that satisfy the system are different from all the given options.

Thus,

The system of equations that models the situation is:

p + m = 5

3p + m = 15

None of the given options is a solution to the system of equations.

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The car that is opposite car Number 12 is given as follows:

Car of Number 26.

The trains are travelling in opposite directions, hence, if car Number 19 of one train is opposite car Number 19 of the other, we have that the pattern is given as follows:

An so on...

The difference between 19 and 12 is given as follows:

19 - 12 = 7.

Hence the number of the car opposite the car 12 is given as follows:

19 + 7 = 26.

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The given graph shows a system of equations with two solutions

From the question, we have the following parameters that can be used in our computation:

The graph

The solution to the system of equations is the point of intersection between the lines on the graph

Using the above as a guide, we have the following:

Intersection points = (-2, - 4) and (2, 3) (approximately)

This means that the solution to the system of equations are approximately (-2, - 4) and (2, 3)

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An equation of the line in slope-intercept form is y = 1/2(x) - 2.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about the graph of this line, it can be modeled by this linear equation:

y = mx + c

y = 1/2(x) + (-2)

y = 1/2(x) - 2

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