Find the circumference and area of a circle with a radius 9 cm.

Answer:

  500%

Step-by-step explanation:

The percentage change is given by ...

  percent change = ((new value)/(old value) -1) × 100% = (180/30 -1)×100%

  = (6 -1)×100% = 500%

Mobile device sales increased 500% from 1998 to 2007.

Answer:

Number of mobiles sold in the year 1998=30 million

Number of mobiles sold in the year 2007=180 million

Percentage increase in mobile sale from year 1998 to 2007 will be

           [tex]=\frac{\text{final}-\text{Initial}}{\text{Initial}}\\\\=\frac{180-30}{30}\times100\\\\=\frac{150}{30} \times 100\\\\=\frac{15000}{30}\\\\=500\text{Percent}[/tex]

 =500%

Final Answer:

To equal the triathlon record of 2 hours and 46 minutes, Mr. B must run at a speed of approximately 3.33 meters per second.

Explanation:

To find out how fast Mr. B must run in meters per second to equal the triathlon record, we first need to calculate the total time he spent on the swim and bike ride. Then, we can subtract that total time from the record time to find the remaining time available for the run. Finally, we can use this remaining time to calculate Mr. B's required running speed.

1.Total time spent on swim and bike ride:

  - Swim time: 25 minutes and 10 seconds

  - Bike ride time: 1 hour, 30 minutes, and 50 seconds

  Convert both times to seconds:

  - Swim time = 25 minutes * 60 seconds/minute + 10 seconds = 1510 seconds

  - Bike ride time = 1 hour * 60 minutes/hour * 60 seconds/minute + 30 minutes * 60 seconds/minute + 50 seconds = 5450 seconds

  Total time = Swim time + Bike ride time = 1510 seconds + 5450 seconds = 6960 seconds

2.Remaining time available for the run:

  Triathlon record time = 2 hours * 60 minutes/hour + 46 minutes = 2 hours * 60 minutes/hour + 46 * 60 seconds/minute = 7200 seconds + 2760 seconds = 9960 seconds

  Remaining time for the run = Triathlon record time - Total time spent on swim and bike ride = 9960 seconds - 6960 seconds = 3000 seconds

3.Calculating Mr. B's required running speed:

  Distance of the run = 10 km = 10000 meters

  Running speed = Distance / Time = 10000 meters / 3000 seconds ≈ 3.33 meters/second

So, Mr. B must run at a speed of approximately 3.33 meters per second to equal the triathlon record.

Answer:

Graph the two points (0,1) and (2,-1) then connect them with a straight edge.

Step-by-step explanation:

The transformed graph is still a line since the parent is a line.

[tex]g(x)=\frac{-1}{2}f(x+2)[/tex]

Identify two points that cross nicely on your curve for f:

(2,-2) and (4,2)

So I'm going to replace x in x+2 so that x+2 is 2 and then do it also for when x+2 is 4.

x+2=2 when x=0 since 0+2=2.

x+2=4 when x=2 since 2+2=4.

So plugging in x=0:

[tex]g(x)=\frac{-1}{2}f(x+2)[/tex]

[tex]g(0)=\frac{-1}{2}f(0+2)[/tex]

[tex]g(0)=\frac{-1}{2}f(2)[/tex]

[tex]g(0)=\frac{-1}{2}(-2)[/tex] since we had the point (2,-2) on line f.

[tex]g(0)=1[/tex] so g contains the point (0,1).

So plugging in the other value we had for x, x=2:

[tex]g(x)=\frac{-1}{2}f(x+2)[/tex]

[tex]g(2)=\frac{-1}{2}f(2+2)[/tex]

[tex]g(2)=\frac{-1}{2}f(4)[/tex]

[tex]g(2)=\frac{-1}{2}(2)[/tex] since we had the point (4,2) on the line f.

[tex]g(2)=-1[/tex] so g contains the point (2,-1).

Graph the two points (0,1) and (2,-1) then connect them with a straight edge.

Answer:

Step-by-step explanation:

The absolute value function graph is shifted to the right by some unknown amount. That is, the parent function p(x) = |x| has become f(x) = p(x-a) = |x-a|, a right-shift of "a" units.

The grid squares are not marked, so we cannot say exactly what the right-shift is. The only two answer choices having the correct form are ...

  f(x) = |x-7|

  f(x) = |x -23|

_____

Anything that looks like |x+a| will be left-shifted by "a" units.

Anything that looks like |x| +a will be shifted up by "a" units. If "a" is negative, the actual shift is downward.

Answer:

f(x) = |x – 23|

f(x) = |x – 7|

Step-by-step explanation:

Right on edge

For this case we have that by definition, it is called arcsine (arcsin) from a number to the angle that has that number as its sine.

We must find the [tex]arcsin (\frac {\sqrt {2}} {2})[/tex]. Then, we look for the angle whose sine is [tex]\frac {\sqrt {2}} {2}[/tex].

We have to, by definition:

[tex]Sin (45) = \frac {\sqrt {2}} {2}[/tex]

So, we have to:

[tex]arcsin (\frac {\sqrt {2}} {2}) = 45[/tex]

Answer:

Option B

Answer:

Choice B

Step-by-step explanation:

An option is to find the the square root of 2 in decimals is [tex]\frac{1.414213562}{2} ≈ 0.7071067812[/tex]

Now we can use the arc sine, which is the inverse of a sin.

To do this we must use a scientific calculator. By pressing the arc sin button and entering in 0.7071067812, we can find the arc sin, which is 45°.

To find the intervals on which a function is increasing or decreasing, analyze the sign of the derivative. The function is increasing on (-infinity, -1) and (2, infinity), and decreasing on (-1, 2).

To find the intervals on which a function is increasing or decreasing, we need to analyze the sign of the derivative of the function. In this case, the derivative of f(x) is f'(x) = 6x^2 + 6x - 12. We can find the critical points by setting the derivative equal to zero: 6x^2 + 6x - 12 = 0. Solving this equation gives us x = -1 and x = 2.

To determine the intervals of the function, we can create a sign chart:

x-2-1023f'(x)+0-0+

From the sign chart, we can see that the function is increasing on the intervals (-infinity, -1) and (2, infinity), and decreasing on the interval (-1, 2).

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(a) Intervals of Increase:

[tex]\[ (-\infty, -3) \cup (2, \infty) \][/tex]

Interval of Decrease:

[tex]\[ (-3, 2) \][/tex]

(b) Local Minimum and Maximum:

Local Maximum: [tex]\( x = -3 \)[/tex]

Local Minimum: [tex]\( x = 2 \)[/tex]

(c) Inflection Point:

[tex]\[ \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \][/tex]

(d) Concavity:

Concave Up: [tex]\( (-\infty, -\frac{1}{2}) \)[/tex]

Concave Down: [tex]\( (-\frac{1}{2}, \infty) \)[/tex]

(a) To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to examine the sign of its derivative, [tex]\( f'(x) \)[/tex].

[tex]\[ f(x) = 2x^3 + 3x^2 - 12x \][/tex]

First, let's find[tex]\( f'(x) \)[/tex]:

[tex]\[ f'(x) = 6x^2 + 6x - 12 \][/tex]

To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to find the critical points where [tex]\( f'(x) = 0 \)[/tex] or is undefined.

Setting [tex]\( f'(x) = 0 \)[/tex]:

[tex]\[ 6x^2 + 6x - 12 = 0 \][/tex]

[tex]\[ x^2 + x - 2 = 0 \][/tex]

This quadratic equation can be factored as:

[tex]\[ (x + 2)(x - 1) = 0 \][/tex]

So, the critical points are [tex]\( x = -3 \)[/tex] and [tex]\( x = 2 \)[/tex].

Now, let's test the intervals between and beyond these critical points:

For [tex]\( x < -3 \)[/tex]:

[tex]\[ f'(-4) = 6(-4)^2 + 6(-4) - 12 = 6(16) - 24 - 12 > 0 \][/tex]

Since [tex]\( f'(-4) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on[tex]\( (-\infty, -3) \)[/tex].

Between [tex]\( -3 \)[/tex] and [tex]\( 2 \)[/tex] :

[tex]\[ f'(0) = 6(0)^2 + 6(0) - 12 = -12 < 0 \][/tex]

Since [tex]\( f'(0) < 0 \)[/tex], [tex]\( f(x) \)[/tex] is decreasing on [tex]\( (-3, 2) \)[/tex].

For [tex]\( x > 2 \)[/tex]:

[tex]\[ f'(3) = 6(3)^2 + 6(3) - 12 = 6(9) + 18 - 12 > 0 \][/tex]

Since [tex]\( f'(3) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on [tex]\( (2, \infty) \)[/tex].

So, the interval on which [tex]\( f(x) \)[/tex] is increasing is [tex]\( (-\infty, -3) \cup (2, \infty) \)[/tex] , and the interval on which [tex]\( f(x) \)[/tex] is decreasing is [tex]\( (-3, 2) \)[/tex].

(b) To find the local minimum and maximum values of [tex]\( f(x) \)[/tex] :

we need to examine the critical points and the endpoints of the intervals we found.

Since [tex]\( f(x) \)[/tex] changes from increasing to decreasing at [tex]\( x = -3 \)[/tex], [tex]\( f(x) \)[/tex] has a local maximum at [tex]\( x = -3 \)[/tex] .

And since [tex]\( f(x) \)[/tex] changes from decreasing to increasing at [tex]\( x = 2 \)[/tex], [tex]\( f(x) \)[/tex] has a local minimum at [tex]\( x = 2 \)[/tex] .

(c) To find the inflection point:

we need to examine the concavity of [tex]\( f(x) \)[/tex], which is determined by the sign of the second derivative, [tex]\( f''(x) \)[/tex].

First, let's find [tex]\( f''(x) \)[/tex]:

[tex]\[ f''(x) = 12x + 6 \][/tex]

Setting [tex]\( f''(x) = 0 \)[/tex]:

[tex]\[ 12x + 6 = 0 \][/tex]

[tex]\[ x = -\frac{1}{2} \][/tex]

Since [tex]\( f''(x) \)[/tex] is positive for [tex]\( x < -\frac{1}{2} \)[/tex] and negative for [tex]\( x > -\frac{1}{2} \), \( f(x) \)[/tex] is concave up on [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and concave down on [tex]\( (-\frac{1}{2}, \infty) \)[/tex].

So, the inflection point is [tex]\( \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \)[/tex], and the intervals on which [tex]\( f(x) \)[/tex] is concave up and concave down are [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and [tex]\( (-\frac{1}{2}, \infty) \)[/tex] respectively.

Answer:

[tex]-10ms^{-1}[/tex]

Step-by-step explanation:

The position function is [tex]s(t)=1-10t[/tex].

The instantaneous velocity at t=10 is given by:

[tex]s'(10)[/tex].

We first of all find the derivative of the position function to get:

[tex]s'(t)=-10[/tex]

We now substitute t=10 to get:

[tex]s'(10)=-10[/tex]

Therefore the instantaneous velocity at t=10 is -10m/s

Transform M to the standard normally distributed random variable Z via

[tex]Z=\dfrac{M-\mu_M}{\sigma_M}[/tex]

where [tex]\mu_M[/tex] and [tex]\sigma_M[/tex] are the mean and standard deviation for [tex]M[/tex], respectively. Then

[tex]P(236.5<M<236.7)=P(-0.2308<Z<-0.0769)\approx\boxed{0.0606}[/tex]

Answer:

0.0606.                        .                

hope this helps

Answer:

The vehicle will get 25 mpg at speeds of approximately  22 mph and 101 mph.

Step-by-step explanation:

Given, the equation that is used to determine the gas mileage for a certain vehicle is,

[tex]m=-0.03x^2+3.7x-43----(1)[/tex]

If the mileage is 25 mpg.

That is, m = 25 mpg,

From equation (1),

[tex]-0.03x^2+3.7x-43=25[/tex]

By the quadratic formula,

[tex]x=\frac{-3.7\pm \sqrt{3.7^2-4\times -0.03\times -43}}{2\times -0.03}[/tex]

[tex]x=\frac{-3.7\pm \sqrt{8.53}}{-0.06}[/tex]

[tex]\implies x=\frac{-3.7+ \sqrt{8.53}}{-0.06}\text{ or }x=\frac{-3.7- \sqrt{8.53}}{-0.06}[/tex]

[tex]\implies x\approx 22\text{ or }x\approx 101[/tex]

Hence, the speed of the vehicle of the vehicle are approximately 22 mph and 101 mph.

To find the speed at which the car gets 25 mpg, the equation -0.03x^2 +3.7x-43 is set equal to 25 and then solved. Using the quadratic formula, the speeds are approximately 30 mph and 76 mph when rounded to the nearest whole number.

The question requires you to find the speed(s) at which the vehicle gets 25 miles per gallon (mpg). To do this, you'll need to equate the given quadratic equation (-0.03x^2 +3.7x-43) to 25 and then solve for x (representing speed in mph). So, the equation becomes:

-0.03x^2 +3.7x-43 = 25

This simplifies to:

-0.03x^2 +3.7x - 68 = 0

This quadratic equation can be solved by factoring, completing the square or using the quadratic formula. In this case, the quadratic formula is the best solution:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

By substituting a = -0.03, b = 3.7, and c = -68 into the formula, the calculated speeds are approximately 30 mph and 76 mph.

Please keep in mind that the answers were rounded to the nearest whole number (mph). Hence, the vehicle will get 25 mpg at speeds of approximately 30 mph and 76 mph.

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Substitute the given numbers for their letters in the equation:

N = NOe^kt

N - amount after t years

No = Original amount

K = 0.0001

t = number of years

Substitute the given numbers for their letters in the equation:

0.70 = 1 * e^-0.0001t

Take the logarithm of both sides:

log0.70 = loge^-0.0001t

-0.1549 = -0.0001t * 0.43429

t = -0.1549 / (-0.0001 * 0.43429)

t = 3566.74

Rounded to the nearest year = 3,567 years old.

The age of the mammal hide is  3,567 years old.

Given,

N = NOe^kt

Here

N - amount after t years

No = Original amount

K = 0.0001

t = number of years

Now

[tex]0.70 = 1 \times e^{-0.0001}t[/tex]

Now Take the logarithm of both sides:

[tex]log0.70 = loge^{-0.0001}t\\\\-0.1549 = -0.0001t \times 0.43429\\\\t = -0.1549 \div (-0.0001 \times 0.43429)[/tex]

t = 3566.74

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Answer:

  66°59'57.4379"

Step-by-step explanation:

A suitable calculator can find the angle whose sine is 0.9205 and convert that angle to degrees, minutes, and seconds

  θ = arcsin(0.9205) ≈ 66.999288° ≈ 66°59'57.4379"

___

Multiplying the fractional part of the degree measure by 60 minutes per degree gives the minutes measure:

  0.999288° ≈ 59.95730'

And multiplying the fractional part of that by 60 seconds per minute gives the seconds measure:

  0.95730' = 57.4379"

In total, we have 66°59'57.4379"

Answer:

Step-by-step explanation:

.

Answer:

  $3195

Step-by-step explanation:

The fraction remaining was ...

  1 - 1/3 -1/5 = 15/15 -5/15 -3/15 = 7/15

The given amount is 7/15 of Tom' salary, ...

  $1491 = (7/15)×salary

  $1491×(15/7) = salary = $3195 . . . . . . . . . multiply by the inverse of the coefficient of salary

Tom's monthly salary was $3195.

[tex]\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=-2(x-\stackrel{h}{3})^2+\stackrel{k}{4}\qquad\qquad \stackrel{vertex}{(\underline{3},4)}\qquad \qquad \stackrel{\textit{axis of symmetry}}{x=\underline{3}}[/tex]

From the equation of the parabola in vertex-form, it's line of symmetry is given by:

[tex]l: x = 3[/tex]

The equation of a parabola of vertex (h,k) is given by:

[tex]y = a(x - h)^2 + k[/tex]

The line of symmetry is given by:

[tex]l: x = h[/tex]

In this problem, the parabola is modeled by the following equation:

[tex]y = -2(x - 3)^2 + 4[/tex]

Hence, the coefficients of the vertex are [tex]h = 3, k = 4[/tex], and the line of symmetry is:

[tex]l: x = 3[/tex]

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Answer:

  0.6 km

Step-by-step explanation:

(3 km)/(5 friends) = 0.6 km/friend

Each person should lead for 0.6 km.

Answer:

3/5

Step-by-step explanation:

3 divided by 5 equals to 3/5 or 0.6

Answer:

$9,220,000(0.888)^t

Step-by-step explanation:

Model this using the following formula:

Value = (Present Value)*(1 - rate of decay)^(number of years)

Here, Value after t years = $9,220,000(1 -0.112)^t

          Value after t years =  $9,220,000(0.888)^t

Answer:

see attached graph on the graph tool

Step-by-step explanation:

The equation of the parabola is

x²-6x-16y+25=0

vertex at (3,1) and focus at (3,5)

Answer:

  about 6.418 seconds

Step-by-step explanation:

You apparently want to find t when h=0:

  0 = -16t^2 +84t +120

  0 = 4t^2 -21t -30 . . . . . . divide by -4

  t = (-(-21 ±√((-21)² -4(4)(-30)))/(2(4)) = (21±√921)/8 . . . . only the positive time is of interest

  t = 2.625+√14.390625 ≈ 6.419 . . . . seconds

It takes about 6.42 seconds for the rock to hit the water.

Answer:

6.4

Step-by-step explanation:

Answer:

B. f(x) = x^2

Step-by-step explanation:

The only quadratic equation in the choices is the answer.

B. f(x) = x^2

Answer:

The third choice down

Step-by-step explanation:

Plotting the point (-2, 9) has us in QII.  We connect the point to the origin and then drop the altitude to the negative x-axis, creating a right triangle.  The side adjacent to the reference angle theta is |-2| and the alltitude (height) is 9.  The sin of the angle is found in the side opposite the angle (got it as 9) over the hypotenuse (don't have it).  We solve for the hypotenuse using Pythagorean's Theorem:

[tex]c^2=2^2+9^2[/tex] so

[tex]c^2=85[/tex] and

[tex]c=\sqrt{85}[/tex]

Now we can find the sin of theta:

[tex]sin\theta=\frac{9}{\sqrt{85} }[/tex]

We have to rationalize the denominator now.  Multiply the fraction by

[tex]\frac{\sqrt{85} }{\sqrt{85} }[/tex]

Doing that gives us the final

[tex]\frac{9\sqrt{85} }{85}[/tex]

third choice from the top

Answer:

Step-by-step explanation:

That a and b are actually h and k, the coordinates of the vertex of the parabola.  There is a formula to find h:

[tex]h=\frac{-b}{2a}[/tex]

then when you find h, sub it back into the original equation to find k.  For us, a = 1, b = -5, and c = 8:

[tex]h=\frac{-(-5)}{2(1)}=\frac{5}{2}[/tex]

so h (or a) = 5/2

Now we sub that value in for x to find k (or b):

[tex]k=1(\frac{5}{2})^2-5(\frac{5}{2})+8[/tex]

and k (or b) = 7/4.

Rewriting in vertex form:

[tex](x-\frac{5}{2})^2+\frac{7}{4}[/tex]

The expression x^2 - 5x + 8 can be written as (x - 5/2)^2 + 1.75 by the process of completing the square, where a = 5/2, and b = 1.75.

To express

x^2-5x+8

in the form

(x-a)^2+b

, we need to complete the square.

First, let's divide the coefficient of x, -5, by 2 to get -5/2 and square that to get 6.25. So, we add and subtract this inside the expression.

Therefore, x^2 - 5x + 8 becomes x^2 - 5x + 6.25 - 6.25 + 8.

This can be rewritten as (x - 5/2)^2 - 6.25 + 8 or (x - 5/2)^2 + 1.75.

Hence, the expression x^2 - 5x + 8 can be written in the form (x - a) ^2 + b where a = 5/2 and b = 1.75.

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Answer:

3,238

Step-by-step explanation:

1,685+1,356+197=3,238

Using the Central Limit Theorem, it is found that the standard deviation of the sampling distribution of this sample mean is of 96.6 hours.

The Central Limit Theorem states that for a sample of size n, from a population of standard deviation [tex]\sigma[/tex], the standard deviation of the sampling distribution is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that: [tex]\sigma = 1356, n = 197[/tex]

Then

[tex]s = \frac{1356}{\sqrt{197}} = 96.6[/tex]

The standard deviation of the sampling distribution of this sample mean is of 96.6 hours.

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Answer:

72

Step-by-step explanation:

If you find an interior angle, its supplement will be the exterior angle. That's one way to do the problem.

Another is to take 360 and divide it by the number of sides. That is the easier way to do it.

Exterior angle = 360 / divided by the number of sides

Exterior angle = 360 /5

Exterior angle = 72

---------------

The other way is done by

(n - 2) * 180 = 540

That's the total number of degrees in the interior of the pentagon.

1 interior angle = 540 / 5 = 108

The supplement of this angle is 180 - 108 = 72

Same answer 2 different ways.

Answer:

$ 1,965,334

Step-by-step explanation:

Annual sales of company in 1999 = $ 1,200,000

Geometric mean growth rate = 10.37 % = 0.1037

In order to forecast we have to use the concept of Geometric sequence. The annual sales of company in 1999 constitute the first term of the sequence, so:

[tex]a_{1}=1,200,000[/tex]

The growth rate is 10.37% more, this means compared to previous year the growth factor will be

r =1 + 0.1037 = 1.1037

We have to forecast the sales in 2004 which will be the 6th term of the sequence with 1999 being the first term. The general formula for n-th term of the sequence is given as:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

So, for 6th term or the year 2004, the forecast will be:

[tex]a_{6}=1,200,000(1.1037)^{6-1}\\\\ a_{6}=1,965,334[/tex]

Thus, the forecasted sales for 2004 are $ 1,965,334

Answer: Option D

[tex](9x^2+1)(3x+1)(3x-1)[/tex]

Step-by-step explanation:

We have the following expression

[tex]81x^4-1[/tex]

We can rewrite the expression in the following way:

[tex](9x^2)^2-1^2[/tex]

Remember the following property

[tex](a+b)(a-b) = a^2 -b^2[/tex]

Then in this case [tex]a=(9x^2)[/tex] and [tex]b=1[/tex]

So we have that

[tex](9x^2)^2-1^2[/tex]

[tex](9x^2+1)(9x^2-1)[/tex]

Now we can rewrite the expression  [tex]9x^2[/tex] as follows

[tex](3x)^2[/tex]

So

[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]

Then in this case [tex]a=(3x)[/tex] and [tex]b=1[/tex]

So we have that

[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]

[tex](9x^2+1)(9x^2-1) =(9x^2+1)(3x+1)(3x-1)[/tex]

finally the factored expression is:

[tex](9x^2+1)(3x+1)(3x-1)[/tex]

Answer:

  see below

Step-by-step explanation:

The sum is irrational, so can only be indicated or approximated.

[tex]\dfrac{1}{6}+\sqrt{6}=\dfrac{1+6\sqrt{6}}{6}\approx 2.61615\,64094\,49844\,76486\,39507\,4137\dots[/tex]

For this case we must find the sum of the following expression:

[tex]\frac {1} {6} + \sqrt {6}[/tex]

We have that when entering [tex]\sqrt {6}[/tex] in a calculator we obtain:

[tex]\sqrt {6} = 2.45[/tex]

On the other hand:

[tex]\frac {1} {6} = 0.16[/tex]periodic number

So, the expression is:

[tex]\frac {1} {6} + \sqrt {6} = 2.62[/tex]

Answer:

2.62

Answer:

Total length after 33 days will be 117 miles

Step-by-step explanation:

A construction crew is lengthening a road. The road started with a length of 51 miles.

Average addition of the road is = 2 miles per day

Let the number of days crew has worked are D and length of the road is L, then length of the road can represented by the equation

L = 2D + 51

If the number of days worked by the crew is = 33 days

Then total length of the road will be L = 2×33 + 51

L = 66 + 51

L = 117 miles

Total length of the road after 33 days of the construction will be 117 miles.

Answer:

Step-by-step explanation:

Adjacent angles are supplementary. If one of them is 90°, then they both are. Another name for a 90° angle is "right angle." In this geometry, all 8 of the angles are right angles, including interior, exterior, vertical, linear, adjacent, and any other pairing you might name.

Any statement restricting the congruent angles to "only" some subset will be incorrect. Any and every subset of the angles contains congruent angles.

Answer:

A. All the angles are congruent.

C. All the angles are right angles.

E. All the interior angles are congruent.

This should be right.

Step-by-step explanation:

Answer:

52 minutes and 30 seconds

Step-by-step explanation:

You know that Yuto has ridden for 5.25 miles when Riko left their house and you need to know and what time they will be together:

Then you can say that:

5.25 miles+(yutos speed)*t= (Rikos speed)*t

when t=Time in minutes when they will be together

5.25 miles+(0.25miles/min)*t= (0,35miles/min)*t

5.25miles=(0.35miles/min-0.25miles/min)*t

5.25miles/(0.35miles/min-0.25miles/min)=t

t=52.5 min =52 minutes and 30 seconds

Answer:

The solution means that Riko will be behind Yuto from the time she leaves the house, which corresponds to t = 0, until the time she catches up to Yuko after 52.5 minutes, which corresponds to t = 52.5. The reason that t cannot be less than zero is because it represents time, and time cannot be negative.

Hope this helps!!! :) Have a great day/night.

Answer:

1) 6 cm

2) 117°

Step-by-step explanation:

1) Draw a picture of the rhombus.  The distance between opposite sides is the height of the rhombus.  If we draw the height at the vertex, we get a right triangle.  Using trigonometry:

sin 30° = h / 12

h = 12 sin 30°

h = 6 cm

2) Draw a picture of the rectangle.

∠KML is the angle the diagonal makes with the shorter side ML.  This angle is 54°.  ∠NKM is the angle the diagonal makes with the shorter side NK.  ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.

The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P.  So m∠PKM = 27°.

KLMN is a rectangle, so it has right angles.  That means ∠KML and ∠KMN are complementary.  So m∠KMN = 36°.

We now know the measures of two angles of triangle KPM.  Since angles of a triangle add up to 180°, we can find the measure of the third angle:

m∠KPM + 36° + 27° = 180°

m∠KPM = 117°