Don't drink and drive: A highway safety council reported that there were 3972 fatalities among drivers in auto accidents in a particular year. Following is a frequency distribution of their ages. Approximate the mean age. Round your answer to one decimal place. Age Number of Fatalities 11-20 340 21-30 1527 31-40 866 41-50 693 51-60 423 61-70 123 Send data to Excel The mean is approximately .

Answer:

1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.

Square the equality √2 + √3 = r − √5 to obtain 5 + 2

√6 = r2 + 5 − 2r

√5. It follows

that 2√6 + 2r

√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r

√30

is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is

irrational can now be applied to show that this is not true. Write √30 = m

n in lowest

terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because

2( m

2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest

terms, a contradiction. We conclude that the initial assumption was false, and therefore

√2 + √3 + √5 is irrational.

Step-by-step explanation:

Answer:

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Answer:

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Step-by-step explanation:

Answer:

Commutative Property

Step-by-step explanation:

It looks like Associative property which is when you change the GROUP, but actually it’s commutative because it didn’t change any numbers in the group, just the order of where they were.

Associative: (25 + 19) + 15 = (15 + 19) + 25

Commutative: (25 + 19) + 15 = (19 + 25) + 15

It didn’t change the numbers, only the order. Therefore, it would be commutative property

Answer:

25+19=44

44+15=59

19+25=44

44+15=59

Answer:

[tex] 84 \: {cm}^{2} [/tex]

Step-by-step explanation:

Area of the figure = Area of rectangle + Area of trapezoid

[tex] = 18 \times 3 + \frac{1}{2} \{(18 - 11) + 3) \}(9 - 3) \\ \\ = 54 + \frac{1}{2} \{7 + 3 \}6\\ \\ = 54 + 10 \times 3\\ \\ = 54 + 30 \\ \\ = 84 \: {cm}^{2} [/tex]

Answer:

Step-by-step explanation:

A(10,6), M(5, -4), B(x,y)

5 = (10+x)/2

x = 0

-4 = (6+y)/2

-8 = 6+y

y = -14

B(0, -14)

The required coordinate of B is given as (0, -2 ).

Given that,

To determine the coordinates of B, If the midpoint of AB Is (5,-4) and the coordinates of A are (10,-6).

The midpoint is that point the line whose length from both the ends of the line is equal.

Here,

We have given two coordinates one of the endpoints A of AB and the other is midpoint M i.e. A(10, -6) and M(5, -4).

Definition of midpoint says,

x = [x₁ +  x₂] / 2 ; y = [y₁ + y₂] / 2

x₁ = 10, x = 5 , y₁ = -6 , y = -4

now,
5 = [10 + x₂] / 2 ; -4 = [-6 + y₂] / 2

x₂ = 10 - 10 ; y₂ = -8 + 6

x₂ = 0 : y₂ = -2

Thus, the required coordinate of B is given as (0, -2 ).

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Answer:

It would land on the first quadrant.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

This is a 5 sided shape, aka a pentagon, and we know that five sided shape's angles add up to 540, so our equation is:

(9x-6)+(3x+23)+95+(7x-4)+90=540.

Combine like terms:

We get 25x+90=540

x = 18

Answer:

b

Step-by-step explanation:

cause a negative number is to the left of zero and a positive to the right

Answer:

The slope is 9 3/4 or 9.75

Step-by-step explanation:

slope= rise/run or y/x

29.25/3=9.75 or 9 3/4

Answer:

y = -3x - 1

Step-by-step explanation:

First find the slope then the Y-intercept

Answer:

[tex]x = 2.5[/tex]

Step-by-step explanation:

Given

[tex]AC = 2x - 1[/tex]

[tex]AB = 2x + 1[/tex]

[tex]BC = 2\sqrt{7[/tex]

[tex]\angle A = 60^{\circ}[/tex]

Required

Find x

To find x, we make use of cosine formula which states:

[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]

In this case:

[tex]BC^2 = AB^2 + AC^2 - 2*AB*BC*CosA[/tex]

Substitute values

[tex](2\sqrt{7})^2 = (2x + 1)^2 + (2x-1)^2 - 2*(2x + 1)*(2x - 1)*Cos(60^{\circ})[/tex]

Evaluate all exponents

[tex]4*7 = (4x^2 + 4x + 1)+(4x^2 - 4x + 1) - 2(4x^2 - 1)*cos(60^{\circ})[/tex]

Open brackets

[tex]28 = 4x^2 + 4x + 1+4x^2 - 4x + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]

Collect Like Terms

[tex]28 = 4x^2 +4x^2+ 4x - 4x+ 1 + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]

[tex]28 = 8x^2+ 2 - (8x^2 - 2)*cos(60^{\circ})[/tex]

Substitute 0.5 for cos(60)

[tex]28 = 8x^2+ 2 - (8x^2 - 2)*0.5[/tex]

Open bracket

[tex]28 = 8x^2+ 2 - 4x^2 + 1[/tex]

Collect Like Terms

[tex]8x^2- 4x^2 + 2 + 1 - 28 = 0[/tex]

[tex]4x^2 -25 = 0[/tex]

Collect Like Terms

[tex]4x^2 =25[/tex]

Divide both sides by 4

[tex]x^2 =\frac{25}{4}[/tex]

[tex]x^2 =6.25[/tex]

Take positive square root of both sides

[tex]x = \sqrt{6.25[/tex]

[tex]x = 2.5[/tex]

Answer:48ft

Step-by-step explanation:

9514 1404 393

Answer:

  x = 18

Step-by-step explanation:

The parallel lines cut the transversals proportionally.

  (2x -1)/40 = 21/24

  2x -1 = 35 . . . . . . . multiply by 40

  2x = 36 . . . . . . . . add 1

  x = 18  . . . . . . . . . divide by 2

Answer:

ti 5

Step-by-step explanation:

its 5

Answer:

the answer is one solution (70)

Step-by-step explanation:

2(a+11)=-3(16-a)

distribute

2a+22=-48+3a

subtract 2a from both sides

22=-48+a

add 48 to both sides

70=a

the answer is one solution (70)

Answer:

I. -9 + y = 18

Step-by-step explanation:

Double-check to see if I was correct

The equations I. and III. satisfies the condition when y = 27

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The value of y = 27

So , substituting the value of y in all of the given equations , we get

I.  

-9 + y = 18

when y = 27

Substituting the value of y , we get

-9 + 27 = 18

18 = 18

So , I. satisfies the condition and the equation is TRUE

II.

-18 + y = 45

when y = 27

Substituting the value of y , we get

-18 + 27 = 45

9 ≠ 45

So , II. does not satisfy the condition and the equation is FALSE

III.

5y = 135

when y = 27

Substituting the value of y , we get

5 x 27 = 135

135 = 135

So , III. satisfies the condition and the equation is TRUE

IV.

2y = 49

when y = 27

Substituting the value of y , we get

2 x 27 = 29

54 ≠ 29

So , IV. does not satisfy the condition and the equation is FALSE

Hence , the equations I. and III. are TRUE

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Answer:

5/9

Step-by-step explanation:

Answer:

158 m²

Step-by-step explanation:

I made this into 3 rectangles.

Figure 1:

9•8=72

The 9 is from the 13 m side, but I've taken 4 m off from the overlapping square.

Figure 2:

6•7=42

The 7 is from the 10 m side, but I've taken 4m off from the overlapping square again.

Remaining Area:

If you extend the lines into figures 1 and 2 from the top left corner and bottom right corner vertically, you will get a rectangle that is (11 m) x (4 m). This is not yet accounted for.

11•4=44

Add together: 72 + 42 + 44 = 158

*Note: You could also find the area of the squares a much easier way by subtracting the overlapping part after finding the area of both figures , but this is how I did it*

Answer:

Step-by-step explanation:

[tex] step - 1 : define[/tex]

[tex] \sin( {30}^{o} ) = \frac{a}{12} [/tex]

[tex] step - 2 : solve[/tex]

Answer:

166 years older.

Step-by-step explanation: Subtract 1751 from 1917

Answer:

ABC

Step-by-step explanation:

Answer:

YZX ~ ABC

Step-by-step explanation:

For Angle Y, there is one curved line, so you must go to the other triangle and find which angle has one curved line too, in this case that is angle A. Then, Angle Z has three curved lines, and in the other triangle, Angle B has three curved lines, so you now have AB, which only leaves C left. So your final answer is ABC.

Answer:

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]

Step-by-step explanation:

Given

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx[/tex]

Required

Solve

Let

[tex]u = \frac{x^2}{4}[/tex]

Differentiate

[tex]du = 2 * \frac{x^{2-1}}{4}\ dx[/tex]

[tex]du = 2 * \frac{x}{4}\ dx[/tex]

[tex]du = \frac{x}{2}\ dx[/tex]

Make dx the subject

[tex]dx = \frac{2}{x}\ du[/tex]

The given integral becomes:

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]

Recall that: [tex]u = \frac{x^2}{4}[/tex]

Make [tex]x^2[/tex] the subject

[tex]x^2= 4u[/tex]

Square both sides

[tex]x^4= (4u)^2[/tex]

[tex]x^4= 16u^2[/tex]

Substitute [tex]16u^2[/tex] for [tex]x^4[/tex] in [tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du[/tex]

Simplify

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]

In standard integration

[tex]\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)[/tex]

So, the expression becomes:

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)[/tex]

Recall that: [tex]u = \frac{x^2}{4}[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]

Answer:

Since a blogger has 400 subscribers to her blog in January, and the number of subscribers has grown by a factor of 1.5 every month since the, to write a sequence to represent the number of subscribers in the 3 months that followed, the following reasoning has to be made:

January: 400 subscribers

February: 400 x 1.5 = 600 subscribers

March: 600 x 1.5 = 900 subscribers

April: 900 x 1.5 = 1,350 subscribers

The sequence to represent the number of subscribers in the 3 months that followed are :

First month = 600 subscribers

Second month = 900 subscribers

Third month = 1350 subscribers

The blogger has 400 subscriber to her blog in January.

The number of subscriber has grown by a factor of 1.5 every month since then.

Therefore, the sequence to represent the number of subscribers in the 3 months that followed can be calculated below

January Subscribers = 400

February Subscribers = 1.5 × 400 = 600

March Subscribers = 1.5 × 600 = 900

April subscribers = 1.5 × 900 = 1350

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Answer:

They multiplied by 100

Step-by-step explanation:

1 x 1.5 = 1.5

10 x 1.5 = 15

100 x 1.5 = 150

Answer:

the one on the bottom and Lewis made one less of whatever Bryan made

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

bryan- 7x4=28

lewis- 6x4=24

28+24=52

Answer:

The top right one 3(x+4)=30

Step-by-step explanation:

Answer:

The answer should be the one on the top right.

Step-by-step explanation:

So we know that the whole entire model equals 30, and each of the three sections are s+4. So, in order to get 30, the equation has to have something to do with three times s+4. We can eliminate the one on the top left because the model does not have a 12 involved. We can also eliminate the bottom left because it only represents one of the three s+4s. The bottom right can be taken off because the 3 in that equation is only multiplied to s, and not s+4. The top right works because it is saying that s+4 multiplied by 3 times is equal to 30. There you go! I hope this helps❤️

Answer:

9%

Step-by-step explanation:

Peace and love

Peace

9514 1404 393

Answer:

  x -3y -7 = 0

Step-by-step explanation:

The general form of the equation for a line is ...

  ax +by +c = 0

where a, b, c are mutually prime and the leading coefficient is greater than zero.

__

The general form equation for a line with slope m = rise/run through point (h, k) can be found by simplifying ...

  rise(x -h) -run(y -k) = 0 . . . . where run has the sign of the slope

For the given point and slope, we have ...

  1(x -1) -3(y -(-2)) = 0

  x -3y -7 = 0