The problem is in the pictures, please show step by step how to do it. Thanks! :)

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:

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.

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:

  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:

  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:E 83[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

50% of the apartment in a certain building have windows and hardwood floors.

25% of the remaining 50% apartment without window have hardwood floors.

40% of the apartment do not have hardwood floors i.e. 60 % have hardwood floor

Therefore percent of the apartments with windows have hardwood floors is

[tex]=\frac{50 percent of total\ apartment }{60\ percent\ of\ apartment}[/tex]

=83[tex]\frac{1}{3}[/tex]%

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 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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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

Answer:

609

Step-by-step explanation:

Standard deviation = [tex]\sigma[/tex] = $30

Margin of error = E = $2

Confidence level = 90%

Since the distribution is said to be normal, we will use z scores to solve this problem.

The z score for 90% confidence level = z = 1.645

Sample size= n = ?

The formula to calculate the margin of error is:

[tex]E=z\frac{\sigma}{\sqrt{n}}\\\\\sqrt{n}=z\frac{\sigma}{E}\\\\n=(\frac{z\sigma}{E} )^{2}[/tex]

Using the values in above equation, we get:

[tex]n=(\frac{1.645 \times 30}{2} )^{2}\\\\ n = 608.9[/tex]

This means, the minimum number of observations required is 609

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°

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.

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:

8793

Step-by-step explanation:

Multiply and divide first, making the equation 8811-17-1. Now subtract. This leaves 8793

Answer:

8793

Step-by-step explanation:

99×89-34÷2-1 = 8793

Multiply: 99 x 89 = 8811

Divide: 32 ÷ 2 = 17

Add: 17 + 1 = 18

Subtract: 8811 - 18 = 8793

Answer:

Probability of missing two passes in a row is 0.08.

Step-by-step explanation:

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

Answer:

Probability of missing two passes in a row is 0.08.

Step-by-step explanation:

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

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:

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:

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

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:

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.

A similar problem is given at https://brainly.com/question/15122730

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"

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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[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]

A similar problem is given at https://brainly.com/question/24737967

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%

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: the answer would be -4

Step-by-step explanation: it is going down 4 units

Answer:

The height of the red prism must be twice the height of the blue prism

Step-by-step explanation:

The height of the red prism must be twice the height of the blue prism.

Since the height of the blue prism is twice that of the red prism, the height of the red prism must be twice as much as that of the blue prism to make the volumes equal.Volume of a prism can be calculated as the area of the base multiplied by the height.

V= b*h....

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.

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