15 minus the quotient of 50 and 10

The data given has: a) A strong correlation, b) A positive correlation

Correlation is a statistical measure that expresses the extent to which two variables are linearly related, meaning they change together at a constant rate.

We have ordered pairs in the data as:

x             y

1             2

2            3

3            8

4            10

5            26

6            38

7            46

8            50

9            68

Plotting the graph (attached)

Clearly, on plotting the scatter plot on the basis of table of values, we see that the relation is a strong correlation since we can find a relationship between variable x and y.

i.e. the points will lie above or below the curve  which is formed by connecting some points of the scatter plot and are not scattered away.

Hence, the data above has: A strong correlation.

Also, the graph is a positive correlation since with the increasing value of x the y-value also increases.

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The solution to the initial-value problem x' + 2y' + x = 0, x(0) = 0 and x' - y' + y = 0, y(0) = 2 using Laplace transforms is x(t) = -2t*sin(t) and y(t) = 2*cos(t).


1. Apply Laplace transform to both equations: L{x'} + 2L{y'} + L{x} = 0 and L{x'} - L{y'} + L{y} = 0.

2. Use properties of Laplace transforms: sX(s) - x(0) + 2[sY(s) - y(0)] + X(s) = 0 and sX(s) - x(0) - [sY(s) - y(0)] + Y(s) = 0.

3. Substitute initial conditions: sX(s) + 2[sY(s) - 2] + X(s) = 0 and sX(s) - [sY(s) - 2] + Y(s) = 0.

4. Rearrange and solve for X(s) and Y(s): X(s) = (4sY(s) - 4)/(s² + 1) and Y(s) = (s² + 2s + 2)/(s² + 1).

5. Apply inverse Laplace transform to find x(t) and y(t): x(t) = -2t*sin(t) and y(t) = 2*cos(t).

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The missing sides of the special right triangles are listed below:

Case 1: y = √2 · 13, x = 13

Case 2: x = y = 15√2

Case 3: x = 6, y = 3√3

Case 4: x = 17√3, y = 17

Case 5: x = y = 10

Case 6: x = 50, y = 25

Case 7: x = y = 4√7

Case 8: x = 16√3, y = 8√3

Case 9: x = 11√3, y = 33

Case 10: x = 3√2, y = 2√6

Case 11: x = √10, y = 2√5

Case 12: x = 4√7, y = 8√21

Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:

45 - 90 - 45 Right triangle

r = √2 · x = √2 · y

30 - 60 - 90 Right triangle

x = (1 / 2) · r

y = (√3 / 2) · r = √3 · x

Where:

Case 1

y = √2 · 13

x = 13

Case 2

x = y = 15√2

Case 3

x = 3 / (1 / 2)

x = 6

y = 3√3

Case 4

x = 34 · (√3 / 2)

x = 17√3

y = 34 · (1 / 2)

y = 17

Case 5

x = y = 10

Case 6

x = 25√3 / (√3 / 2)

x = 50

y = 25√3 / √3

y = 25

Case 7

x = y = 2√14 · √2 = 2√28 = 4√7

Case 8

x = 24 / (√3 / 2)

x = 48 / √3

x = 16√3

y = 24 / √3

y = 8√3

Case 9

x = 22√3 · (1 / 2)

x = 11√3

y = 22√3 · (√3 / 2)

y = 33

Case 10

x = √18

x = 3√2

y = √6 / (1 / 2)

y = 2√6

Case 11

x = √10

y = √20

y = 2√5

Case 12

x = 4√21 / √3

x = 4√7

y = 4√21 / (1 / 2)

y = 8√21

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Answer:  B. H(t) = -6.9(t - 2.3)² + 112

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k

where (h, k) is the vertex   ⇒    k is the maximum height

the distance traveled is when y = 0     ⇒    \(x=\sqrt{\dfrac{-k}{a}}+h\)

Given: H(t) = -7.1(t - 2.3)² + 98

maximum height (k) = 98 feet

distance traveled (x) = \(\sqrt{\dfrac{-98}{-7.1}}+2.3\)    = 6.02 seconds

A) H(t) = -7.5(t - 2.2)² + 112

maximum height (k) = 112 feet

distance traveled (x) = \(\sqrt{\dfrac{-112}{-7.5}}+2.2\)    = 6.06 seconds

B) H(t) = -6.9(t - 2.3)² + 112

maximum height (k) = 112 feet

distance traveled (x) = \(\sqrt{\dfrac{-112}{-6.9}}+2.3\)    = 6.33 seconds

C) H(t) = -6.9(t - 2.4)² + 95

maximum height (k) = 95 feet

This has a lower height than the given equation.

D) H(t) = -7.5(t - 2.3)² + 95

maximum height (k) = 95 feet

This has a lower height than the given equation.

Both options A and B travel higher and stay in the air longer than last year's winner, however option B stays in the air longer than option A.

Answer:

A coefficient is a number in front of a variable. For example, in the expression x 2-10x+25, the coefficient of the x 2 is 1 and the coefficient of the x is -10. The third term, 25, is called a constant.

Step-by-step explanation:

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Answer:

B)154

Step-by-step explanation:

98:7=x:11

x=154

The required  number of ways to elect four position is 5040.

Given that, a corporation has 10 members on its board of directors.

By using the concept of permutation , calculate the number of ways to elect each position.

There are 10 candidates available for president position. That implies, 10 choices to elect the president.

After the president is chosen, there are 9 candidates available for the vice-president position. That implies, 9 choices to elect the president.

After the president and vice-president are chosen, there are 8 candidates available for the secretary position. That implies, 8 choices to elect the secretary.

After the president, vice-president and secretary are chosen, there are 7 candidates available for the treasurer position. That implies, 7 choices to elect the treasurer.

The number of ways to elect president, vice-president , secretary and treasurer can be calculated by multiplying the number of choices for each position is 10 × 9 × 8 × 7 = 5040.

Hence, the number of ways to elect four position is 5040.

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Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

The domain of the relation as given in the task content; (x,y): y = x(x-3) / (x+4)(x-7) is the set of all real number values except; -4 and 7 and hence is represented as; { x : x R, x ≠ -4, x ≠ 7}.

It follows from the task content that the domain of the relation given in the task content be determined.

On this note, since the domain of a relation or function simply refers to the set of all possible input values of such function.

Since the relation in this scenario is a rational function, it follows that the domain is the set of all real number values except that which renders the relation undefined.

Therefore, since the values which render the relation undefined, render the denominator equal to 0; we have;

(x+4)(x-7) = 0.

x = -4 OR x = 7.

Ultimately, the domain of the relation is the set of all real numbers except; x = -4 and x = 7.

Therefore, when represented by set builder notation; we have; { x : x R, x ≠ -4, x ≠ 7}.

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The system of inequalities for the given situation is

x +y ≤ 70.

$4x +  $8x ≤ $400.

y ≤ 50.

And one possible solution is (40,30) and the graph of the inequality is attached below.

Inequality:

Inequality refers the non equal comparison of the expressions.

Given,

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 70 people. The drama club must make no less than $400 from ticket sales to cover the show's costs. Also, they can sell at most 50 adult tickets.

Here we need to find the system of inequalities graphically and also determine one possible solution for it.

Let us consider x represents the number of student tickets sold and y represents the number of adult tickets sold.

Therefore, in here we know that, they can sell at most 50 adult tickets.

Which means that the value of y can't be greater than 50.

So, in inequality it can be written as,

y ≤ 50.

And the total number of seats in the auditorium is 70.

Therefore,

x + y ≤ 70

And we also know that, they sells the ticket at the cost not less than $400.

So,

$4x +  $8x ≤ $400.

Now, we have to plot those inequality on the graph, the we get he following graph.

In the graph, the blue line represents the inequality x + y ≤ 70 and the red line represents the inequality $4x +  $8x ≤ $400.

While we looking into the graph we have identified that the solution of the graph is (40,30).

Which means there are 40 number of students and 30 number of adults.

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Answer:

10

Step-by-step explanation:

10x0 is 0

10x1 is 10

Answer:

10

Step-by-step explanation:

10 x 0 = 0

10 x 1 = 10

0 + 10 = 10

Answer:

  1 : 2

Step-by-step explanation:

The ratio is ...

  small dia : large dia = 1 : 2 = small circumference : large circumference

__

Further explanation

The diameter of the small circle is the radius of the large circle. Since the large circle's diameter is twice the length of its radius, the ratio of circle diameters is ...

  small : large = 1 : 2

We multiply the diameter by π to get the circumference. Multiplying both these numbers by π will give the ratio of the circumferences. In order to reduce the ratio to lowest terms we must divide by π again:

  dia ratio = circumference ratio = lowest terms ratio

  1 : 2 = π : 2π = 1 : 2

Answer: 1:2

Step-by-step explanation:

Answer:

m=0 and m=3

Step-by-step explanation:

there are two solutions

Answer:

125

Step-by-step explanation:

Angles on a straight line =180

180- (35+20) =125

The divergence theorem states that the surface integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface

we are given the vector field F = (11x, 2y, \(z^{2}\)) and the surface S defined by the equation \(x^2 + y^2 + z^2\)= 1, which represents a unit sphere.

To evaluate the surface integral ∬S F · ds using the divergence theorem, we first need to calculate the divergence of the vector field F. The divergence of F, denoted as ∇ · F, is given by the sum of the partial derivatives of the components of F with respect to their corresponding variables. Therefore, ∇ · F = ∂(11x)/∂x + ∂(2y)/∂y + ∂(z^2)/∂z = 11 + 2 + 2z.

Applying the divergence theorem, the surface integral ∬S F · ds is equal to the triple integral ∭V (∇ · F) dV, where V represents the volume enclosed by the surface S.

Since the surface S is a unit sphere centered at the origin, the triple integral ∭V (∇ · F) dV can be evaluated by integrating over the volume of the sphere.

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Answer:

y = -1/4x + 4

Step-by-step explanation:

x+4y=28

4y = -x + 28

y = -1/4x + 7

slope m = -1/4

Parallel lines have similar slope so we'll use -1/4 from above and given point (8,2) to find y-intercept.

y = mx +b

2 = -1/4(8) + b

2 = -2 + b

b = 4

Using m and b from above we can now form the new equation of line that is parallel to y = -1/4x + 7.

y = mx + b

y = -1/4x + 4

Answer:

Around 19 rows

Step-by-step explanation:603/31= 19.40 so I'm not too sure

Answer: (0, -7.2)

Step-by-step explanation:

Substituting into point-slope form, the equation is

\(y+6=4(x-0.3)\)

The y-intercept is when x=0, so substituting in x=0,

\(y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2\)

So, the y-intercept is (0, -7.2).

\(P=2L+2W\)

\(300=2L+2 \cdot 57\)

\(300=2L+114\)

\(2L=300 - 114\)

\(2L=186\)

\(L=\frac{186}{2} = 93\)

proof:

\(300=2\cdot 57+2 \cdot 93\)

\(300 = 114 + 186\)

\(300 = 300\)

I Hope I helped you!

Step-by-step explanation:

the perimeter of a rectangle : it is the distance when going around the whole rectangle once.

so, it is

2×length + 2×width

300 = 2×length + 2×57 = 2×length + 114

2×length = 300 - 114 = 186

length = 186/2 = 93 yards

Answer:

Step-by-step explanation:

Given

Perimeter of the shape is sum of two quarter circles:

The area is calculate as follows:

Half of the area of the shape is the difference of the quarter-sector of the circle and half-area of the square

The answer is

Perimeter = 8π

Area = 32π - 64

A one-way ANOVA is a statistical test used to compare the means of four populations in this case. Thus, the degrees of freedom for the F-statistic in this one-way ANOVA are (df1, df2) \(= (3, 78)\).

The degrees of freedom are essential for calculating the F-statistic, which helps determine whether there are significant differences among the population means.

To calculate the degrees of freedom for the F-statistic, we need to determine the numerator degrees of freedom (df1) and the denominator degrees of freedom (df2). For df1 (numerator degrees of freedom), it is equal to the number of populations (groups) minus 1.

In this case, there are four populations,

So: df1 \(= 4 - 1 = 3\)

For df2 (denominator degrees of freedom), it is equal to the total sample size (N) minus the number of populations (groups).

The total sample size is given as \(18 + 22 + 20 + 22 = 82\).

So: df2 \(= 82 - 4 = 78\)

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We have derivative of y = 6x^2 - 3x. Therefore, the correct option is c) 6x^2 - 3x

To determine the derivative d/dx (y) for the given function y = 2x^3 - 3x + 1, we need to take the derivative of each term with respect to x. The correct option for d/dx (y) is c) 6x^2 - 3x.

To find the derivative of y = 2x^3 - 3x + 1 with respect to x, we differentiate each term separately.

The derivative of 2x^3 is found using the power rule, which states that the derivative of x^n is n*x^(n-1). Applying the power rule, we get 6x^2.

The derivative of -3x is -3, as the derivative of a constant multiplied by x is simply the constant.

The derivative of 1 is 0 since it is a constant term.

Combining these derivatives, we have d/dx (y) = 6x^2 - 3x. Therefore, the correct option is c) 6x^2 - 3x


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The given expression is

The first option is correct.

The fourth option is correct.

Adding 8 and 15, we get

The second option is correct.

The length of the line is 5 feets

Taking the length of the line as L

According to the given information;

Height of kite = 12 ft

shadow of kite = 5 ft

We can set up a proportion between the lengths of the sides of the two similar triangles formed by the kite and its shadow:

Length of the kite / Length of the shadow = Height of the kite / Length of the line

Applying the given values:

12 ft / 5 ft = 12 ft / L

cross-multiply and then divide:

12L = 5 × 12

L = 60 / 12

L = 5

Therefore, the length of the line is 5 feets

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