Use the laplace transform to solve the given system of differential equations. dx dt + 3x + dy dt = 1 dx dt − x + dy dt − y = et x(0) = 0, y(0) = 0

The difference of the means of the two data sets is = 4.57

The mean absolute deviation of the roller coaster speeds in North America is 13.3

The mean absolute deviation of the roller coaster speeds in Asia is 16.8

First we have to start with the data for North America

128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77

To get the mean you have to sum up the values and divide through by the total number 10

937.8/10

Mean = 93.78

Mean Absolute Deviation  = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10

133.32/10 = 13.3

For Asia, we have the data as

149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4

Mean for Asia = 892.1/10

= 89.21

Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10

= 168.32/10

16.8

The difference in the means = 93.78 -89.21

=  4.57

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Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(6,~-7)[/tex]

[tex](x_2,~y_2)=(4,~3)[/tex]

Given the midpoint formula

[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]

Substitute values into the given formula

[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]

Simplify values on the numerator

[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]

Simplify the fractions

[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound

From the question given above, the following data were obtained:

F = Ke

Divide both sides by e

K = F/ e

K = 3 / 0.6

K = 5 pound/foot

Thus, the spring constant of the spring is 5 pound/foot

Wd = ½Ke²

Wd = ½ × 5 × 0.7²

Wd = 2.5 × 0.49

Wd = 1.23 foot-pound

Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound

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The correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875

The given figure is a right triangle with legs 12.0 and 22.5cm and the hypotenuse 25.5cm

For sinA, <A is the reference angle, hence the opposite side will be 22.5cm

sin A = opp/hyp

sinA = 22.5/25.5

For cos C, the adjacent side will be 22.5cm, hence the measure of cos C is 22.5/25.5

cosC = 22.5/25.5

Similarly, sinC = 12/25.5 = 24/51

<A = 180-(90 +38)

<A =180 - 128
<A = 62 degrees

tan A = opp/adj

tan A = 22.5/12 = 1.875

tan C = 12/22.5

tan C = 0.533

Hence the correct expressions are sinC = 12/25.5 = 24/51, <A = 62 degrees and tan A = 1.875

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x + 7 = -8

(x + 7) - (7) = -8 - (7)

x = -8 - 7 = -15

The correct answer is -15

❄ Hi there,

let us first consider this: What should we do to get x all alone, on one side of the equation?

Since

we should

[tex]\ \sf{x=-8-7}[/tex]

[tex]\triangleright \ \sf{x=-15}[/tex]

That's it!

❄

Step-by-step explanation:

Because the two sides have been shown to be equivalent, the equation is an identity.

The factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).

The given expression is 20m²/n²- 30n²/m² +1.

We need to factorise the given expression.

To factor, a trinomial in the form x²+ bx + c, find two integers, r and s, whose product is c and whose sum is b.

Rewrite the trinomial as x²+ rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).

Now, we can rewrite 20m²/n² +1 - 30n²/m² as 20m²/n² +25mn/mn- 24mn/mn- 30n²/m².

=(20m²/n² +25mn/mn)- (24mn/mn- 30n²/m²)

=5m/n(4m/n + 5m/n)-6n/m(4m/n+5n/m)

=(4m/n + 5m/n)(5m/n-6n/m)

Therefore, the factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).

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5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.

A number is a perfect square if the following property is satisfied:

a = b², where is a natural number.

Please notice that b can be either a prime number or a product of prime numbers.

Initially, we proceed to factorize 35280 by factorial decomposition, that is, as a product of prime numbers:

35280 = 2⁴ × 3² × 5 × 7²

35280 = (2²)² × 3² × 5 × 7²

35280 = 4² × 3² × 5 × 7²

Then, we must add a 5 to find a product that is a perfect square:

4² × 3² × 5² × 7² = 176400

5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.

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Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)

----------------------------------------------------------------------------------------------------------
Explanation Section:

It is false

If f(x) is a function , then for each value of x there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

Bye! - SunnyBunny <3

Answer:

3, 7, 14

Step-by-step explanation:

Answer:

Saturday

Step-by-step explanation:

2 days before (starting from Monday) is Saturday

The value of the product expression 6 * 330 is 1980

The product expression is given as:

6 * 330

Express 330 as the product of 33 and 10

6 * 330 = 6 * 33 * 10

Express 33 as the product of 3 and 11

6 * 330 = 6 * 3 * 11 * 10

Evaluate the product of 6 and 3

6 * 330 = 18 * 11 * 10

Evaluate the product of 11 and 10

6 * 330 = 18 * 110

Evaluate the product of 18 and 110

6 * 330 = 1980

Hence, the value of the product expression 6 * 330 is 1980

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When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

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2r + t + r

3r + t

The correct answer is C - None of the Above.

When we combine like terms, we combine terms that have the same variables but different coefficients. We cannot add 2r and t because r and t are not the same variables.

Hope this helps!

Answer:

None of the above

Step-by-step explanation:

Because the answer is 3r + t

The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard equation of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the circle center and r is the radius of the circle.

The diameter of the circle DE is at D(-3, 3) and E(13, 11). Hence the coordinate of point center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7)

[tex]Diameter = \sqrt{(3-11)^2+(-3-13)^2} = 8\sqrt{5}[/tex]

Radius = diameter / 2 = 8√5 ÷ 2 = 4√5

The equation of the circle is:

(x - 5)² + (y - 7)² = (4√5)²

(x - 5)² + (y - 7)² = 80

The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80

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The smaller number that we can take is x = 14, and in that case, the value of the other number is y = 34

First, we have two numbers, x and y, such that:

y = 6 + 2*x

"the first number is 6 more than 2 times another number".

Now we know that the sum of these two numbers is smaller than 50, then we can write:

x + y < 50

Replacing y by the above equation we get:

x + 6 + 2x <  50

3x + 6 < 50

Now we can solve that inequality for x:

3x < 50 - 6 = 44

x < 44/3 = 14.6

And x can only be a whole number, then:

x ≤ 14

The smaller number that we can take is x = 14, and in that case, the value of the other number is:

y = 6 + 2*14 = 34

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The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the length and y represent the width. Hence:

x + 2y = 50

x = 50 - 2y

Also:

xy = 288

(50 - 2y)y = 288

y = 9; and y = 16

x = 32; and x = 18

The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

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The correct graph is in the attached image.

Answer:

  B.  A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)

Step-by-step explanation:

The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.

When the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.

When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.

The given inequality

  y ≤ 2x -4

includes the "or equal to" case, so the boundary line is solid.

The equation of the boundary line is written in slope-intercept form:

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.

This tells you that the boundary line intercepts the y-axis at the point (0, -4).

Answer:

g(x) = (x + 1)² + 1

Step-by-step explanation:

the original function

f(x) = x²

for the new function g(x)

it is shifted 1 unit to the left and 1 unit up.

the shift to the left is done by adding these units to the input variable x :

g(x) = f(x+1) = (x+1)²

that way we get the function value for x+1 already at x :

1 unit "earlier" than in the original.

and the shift up is easy.

whatever the function calculates, we simply add 1 to everything.

the whole curve stays as it is, just one unit higher. g

so, the final g(x) = f(x+1) + 1 = (x + 1)² + 1

Answer:

5x^2+22x-12         x cannot be -5, -4, -2

(x+5)(x+4)(x+2)

Step-by-step explanation:

In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:

x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)

x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)

Now that you have factored out the two quadratics, plug them into the equation.

    5x        -       3

(x+4)(x+2)      (x+5)(x+2)

Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.

5x (x+5)             -           3(x+4)  

(x+5)(x+4)(x+2)      (x+5)(x+4)(x+2)

Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:

5x^2+25x - (3x+12)     =    5x^2+22x-12         x cannot be -5, -4, -2

 (x+5)(x+4)(x+2)               (x+5)(x+4)(x+2)

Answer: (f+g)(x)=2(x-2)(x+1).

Step-by-step explanation:

[tex]f(x)=x^2-3x-4\ \ \ \ \ g(x)=x^2+x\\(f+g)(x)=(x^2-3x-4)+(x^2+x)\\(f+g)(x)=x^2-3x-4+x^2+x\\(f+g)(x)=2x^2-2x-4\\(f+g)(x)=2*(x^2-x-2)\\(f+g)(x)=2*(x^2-2x+x-2)\\(f+g)(x)=2*(x*(x-2)+(x-2))\\(f+g)(x)=2*(x-2)*(x+1).[/tex]

Answer: [tex]\Large\boxed{x=40^\circ}[/tex]

Step-by-step explanation:

Given information

∡ 1 = 90°

∡ 2 = 50°

∡ 3 = x°

Total Angle = 180° (Triangle angle sum theorem)

Given formula

∡ 1 + ∡ 2 + ∡ 3 = Total Angle

Substitute values into the formula

(90) + (50) + (x) = (180)

Combine like terms

140 + x = 180

Subtract 140 on both sides

140 + x - 140 = 180 - 140

[tex]\Large\boxed{x=40^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4/7

Step-by-step explanation:

[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12

7x3=21

[tex]\frac{12}{21} = \frac{4}{7}[/tex]

Answer:

She used 9 tiles which are 3 cm long

Step-by-step explanation:

cuz 3x9=27 and yea

Answer:

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Step-by-step explanation:

Tossing a coin has two possible outcomes, heads (H) and tails (T).

Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.

Table:

First spin                   H     H     H     H     H    T     T     T     T     T

Second spin              1      2      3     4      5     1     2     3     4     5

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Answer:The number of pennies on square 64 is greater than the pennies on 63 squares  since 64 is already greater 63 that when 63 gets bigger 64 will also get bigger so it will always be greater than 63

Step-by-step explanation:

Answer:

Step-by-step explanation:

greater than

The probability that the red die shows a 2 and the green die shows a 5 is 1/36

The sample space of a die is

S = {1, 2, 3, 4, 5, 6}

This means that

Red die = {1, 2, 3, 4, 5, 6}

Green die = {1, 2, 3, 4, 5, 6}

On the dice, we have

P(Red = 2) = 1/6

P(Green = 5) = 1/6

The probability that the red die shows a 2 and the green die shows a 5 is

P = P(Red = 2) * P(Green = 5)

Substitute the known values in the above equation

P = 1/6 *1/6

Evaluate the product

P = 1/36

Hence, the probability that the red die shows a 2 and the green die shows a 5 is 1/36

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The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.

In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.

We are asked to find the total number of students that plotted the number of books they read using the dot plot.

The dot plot is attached to the solution.

The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.

Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

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The line that is not another name for Q is RL

For a line to represent the point Q, the following must be true:

Using the above highlights,

Hence, the line that is not another name for Q is RL

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The answer is B.

If the terminal point of θ is at (0, -1), then tanθ is equal to :

The tangent of the given angle is undefined, so the correct option is B.

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

Given that on a unit circle, the terminal point of θ is (0, - 1) we need to determine tan θ,

We know that the terminal point of θ is (0, -1).

Now, the tangent of an angle is equal to the quotient between the y-component and the x-component of the terminal point, then we have:

tan(θ) = =1/0

And we can't divide by zero, so it is undefined, then the correct option is B.

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