A plane has a cruising speed of miles per hour when there is no wind. At this speed, the plane flew miles with the wind in the same amount of time it flew miles against the wind. Find the speed of the wind.

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:

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:

9/14.

Step-by-step explanation:

The probability is given as a fraction or percentage.

9:5 odds in favour of a horse winning  means the horse will win 9 races for every 5 it does not win.

So the probability that this horse will win is 9/(9+5)

= 9/14.

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

Answer:

She used 9 tiles which are 3 cm long

Step-by-step explanation:

cuz 3x9=27 and yea

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!

❄

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 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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Answer: Divide the 4/4 then subtract that from 12.

Step-by-step explanation:

Use PEMDAS. The Division comes first, then the subtraction.

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: [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

Step-by-step explanation:

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

Answer:

Saturday

Step-by-step explanation:

2 days before (starting from Monday) is Saturday

Answer:

3, 7, 14

Step-by-step explanation:

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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The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]

The equation of the ellipse is given as:

4x^2 + 25y^2 – 8x + 100y + 4 = 0

Next, we plot the graph of the ellipse

See attachment for the graph of the ellipse

The domain

From the attached graph the minimum and the maximum values of x are:

Minimum = -4

Maximum = 6

So, the domain of the ellipse is [-4. 6]

The range

From the attached graph the minimum and the maximum values of y are:

Minimum = -4

Maximum = 0

So, the range of the ellipse is [-4. 0]

Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]

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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 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 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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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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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: (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]

The result is [tex]5x-2y=-2[/tex].

Answer:

1. e

Step-by-step explanation:

18/3 +2(12-5)

=6+2(7)

=6+14

=20

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]

Divide 18 by 3 to get 6.

Therefore, the correct option is "E".

================================================================

[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]

It seems that none of the options is correct.

The probability that the person is over 40 and prefers cola exists at 1.3725.

The probability of an event exists in the ratio of the size of the event space to the size of the sample space.

The size of the sample space exists the entire number of possible outcomes.

The event space exists the number of outcomes in the event you exists interested in.

So, P = size of the event space/size of the sample space

To estimate the probability that the person exists over 40 years.

Size of the sample size = 255

Size of the event space = 85

P = 85/255

P = 1/3

To estimate the probability that they drink cola.

Size of the sample size = 255

Size of the event space = 95

P = 95/255

P = 19/51

To estimate the probability that the person exists over 40 years of age or that they drink cola

So, P = (1/3) + (19/51)

[tex]$P = (51*3+3*19)/153[/tex]

P = 1.3725

Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.

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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 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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Split up the interval [0, 3] into 3 equally spaced subintervals of length [tex]\Delta x = \frac{3-0}3 = 1[/tex]. So we have the partition

[0, 1] U [1, 2] U [2, 3]

The left endpoint of the [tex]i[/tex]-th subinterval is

[tex]\ell_i = i - 1[/tex]

where [tex]i\in\{1,2,3\}[/tex].

Then the area is given by the definite integral and approximated by the left-hand Riemann sum

[tex]\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}[/tex]