Multiple choice: Select the best answer for Exercises 49 to 52. Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (a) 0.008. (b) 0.02. (c) 0.03. (d) 0.04. (e) 0.208.

The answers to all the parts are given below.

We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.

[A] -

For [x] = 1000ft, we can write -

1000 = -16t² + 1800

16t² = 800

t² = (800/16)

t² = 50

t = 7.07 seconds

[B] -

For [x] = 950ft, we can write -

950 = -16t² + 1800

16t² = 850

t² = 53.125

t² = √(53.125)

t = 7.29 seconds

[C] -

The domain of the function will be -

0 ≤ x ≤ 10

[D] -

The range of the function will be -

0 ≤ h ≤ 1800

Therefore, the answers to all the parts are given above.

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The correct answer is A.

500 is the size of the population at the moment of maximum growth.

Given data:

To find the size of the population at the moment when the population is growing most rapidly, we need to determine the maximum value of the derivative dP/dt.

Given the logistic differential equation [tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex], find the derivative by taking the derivative of each term separately:

[tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex]

To find the critical points where the derivative is zero or undefined, set dP/dt equal to zero:

[tex](\frac{1}{10})P - (\frac{1}{5000})P^2=0[/tex]

Simplifying:

[tex](\frac{1}{10})P= (\frac{1}{5000})P^2[/tex]

[tex]10P^2=5000P[/tex]

Dividing both sides by P and rearranging:

[tex]10P(P-500)=0[/tex]

This equation has two solutions: P = 0 and P = 500.

To determine which solution corresponds to the moment when the population is growing most rapidly, examine the second derivative. Taking the second derivative of the logistic differential equation, we have:

[tex]\frac{d^2P}{dt^2} = \frac{1}{10} - \frac{2}{5000}P[/tex]

Evaluating the second derivative at P = 0 and P = 500, we get:

[tex]\frac{d^2P}{dt^2}_{P=0} = \frac{1}{10} - \frac{2}{5000}(0)[/tex]

[tex]\frac{d^2P}{dt^2}_{P=0}= \frac{1}{10} > 0[/tex]

[tex]\frac{d^2P}{dt^2}_{P=500} = \frac{1}{10} - \frac{2}{5000}(500)[/tex]

[tex]\frac{d^2P}{dt^2}_{P=0}= -\frac{1}{10} < 0[/tex]

Since the second derivative is positive at P = 0 and negative at P = 500, the moment when the population is growing most rapidly occurs at P = 500.

Hence, the size of the population at the moment when the population is growing most rapidly is 500.

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Yosef's average weekly fuel cost is $24.35.

Yosef drove 11,190 miles last year.  His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon.

Yosef average weekly fuel cost can be computed as follows:

Yosef used 11190 / 19 = 588.95 gallons to drive 11190 miles.

Therefore, the average cost of gas last year was 2.15 dollars per gallon.

Therefore, Yosef's average weekly fuel cost would be as follows:

Yosef's average weekly fuel cost = 2.15 x 588.95 ÷ 52 = $1266.23684211 ÷ 52

Yosef's average weekly fuel cost = 24.350708502

Yosef's average weekly fuel cost = $24.35

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Answer: 33%

Step-by-step explanation: a third of the items in the bag are pretzels.

28 mph is  the average speed of the bus in mph.

What is speed?

The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.

                                 Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms-1, is the SI unit of velocity.

time = (1+ 1/2)hr = 3/2 hr = 1.5 hr

distance = 42 miles

average speed = total distance/total time

42/1.5 = 28 mph

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Answer: (x-5)²=8

Step-by-step explanation:

x²-10x+17=0

x²-2(x)(5)+5²-5²+17=0

(x²-2(x)(5)+5²)-25+17=0

(x-5)²-8=0

(x-5)²-8+8=0+8

(x-5)²=8

Answer:

(x - 5)² = 8

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

Given

Expression  x² - 10x +17.

Convert this to vertex form by completing the square.

Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:

x² - 10x + 17  =

x² - 2*5*x + 5² - 5² + 17  =

(x - 5)² - 25 + 17 = (x - 5)² - 8

(x - 5)² = 8

Answer:

Hypotenuse = 7.3 cm

Step-by-step explanation:

We can find the hypotenuse using the Pythagorean Theorem, which is:

[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the right triangle and c is the hypotenuse.

By plugging in 2 and 7 for a and b, we have:

[tex]2^2+7^2=c^2\\4+49=c^2\\53=c^2\\7.2801=7.3=c[/tex]

Answer:

X=1 Y=0

Step-by-step explanation:

Multiply the second equation (-2x + 8y = -2) by 2 in order to get -4x+16y=-4.
Using this equation, you can eliminate the x

4x - 8y = -4
-4x+16y=-4.
=
8y=0
y = 0

Now, knowing that y=0, plug y into the second equation:

-2x+8(0)=-2
simplify
-2x=-2
lastly, divide both sides by -2
x=1

Answer:

a=10

m=28

Step-by-step explanation:

2/3= 0.666666666666666

a/15=??????

try all numbers divided by 15 untill you found 0.666666666666666 which is =10/15

4/7=0.571428571428571

44/m=???????

do the same as the first one

it will be 44/28=0.571428571428571

Answer:

The 3rd statement is a lie and other two are truth.

Step-by-step explanation:

when two same numbers with power are divided their respective powers are subtracted.

1.

[tex] {b}^{a } \div {b}^{c} = {b}^{a - c} [/tex]

Using this formula for

[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]

[tex] {b}^{9 - 5} = {b}^{4} [/tex]

Here RHS =LHS

so the equation is true

2.

[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]

[tex] {b}^{7 - 2} = {b}^{2} [/tex]

Here RHS=LHS,

so the equation is true

[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]

[tex] {b}^{8 - 2} = {b}^{8}[/tex]

Here RHS is not equal to LHS

so the equation is false

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Answer:

- 7 < x < 6

Step-by-step explanation:

- 8 < x - 1 < 5 ( add 1 to each interval )

- 7 < x < 6

[tex]~~~~~~\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[/tex]

[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]

Answer:

The current price of sofa is $195.50.

Step by Step explanation:Cost price of the sofa for the store = $200

Now, the store marked it up 15%.

So, marked price of sofa = $200 + 15% of $200

=200 + 30

=$230

Now, it is given that the sofa could not sell at this price. So, the store reduces its price by 15% now.

So, current price of sofa = $230 - 15% of $230

= 230 - 34.5

=$195.5

So, the current price of the sofa is $195.50.

The given lines L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t and L2 ⇒ x = 3+8s, y = -6s, z = 7+2s  are parallel lines .

In the question ,

it is given that ,

the two lines are :

L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t

L2 ⇒ x = 3+8s, y = -6s, z = 7+2s

If the lines are intersecting then :

5 - 12t = 3 + 8s

8s + 12t = 2

4s + 6t = 1 ;   .....equation(1)

and 3 + 9t = -6s

3t + 2s + 1 = 0

multiplying both sides by 2 ,

we get ,

6t + 4s + 2 = 0  ....equation(2)

Solving equation(1) and equation(2) , we get

3 ≠ 0 .

So , the lines are not intersecting .

For lines to be parallel , the cross product of their directions must be 0 .

So , [tex]\left|\begin{array}{ccc}i&j&k\\-12&9&-3\\8&-6&2\end{array}\right|[/tex]

On simplifying further ,

we get ,

⇒ 0i - 0j + 0k

= 0

So , the cross product is 0 ,  lines will be parallel .

Therefore , the lines L1 and L2 are parallel .

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(p-124) / 9 min many liters of water are in the tank after 109 seconds.

for 4 min =  65 + (6.5x4) = 91 lit

for  109 sec = 65 + (9x 109/60) = 81.35 lit

for m min = 65 + (9m) lit

how long time

for 151 lit = (151 - 124)/9 = 3 min

for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec

for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec

for p lit = (p-124) / 9 min

What is liters ?

The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.

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The no. of cars that must drive by until a white one drives by is 40.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is

[tex]^nC_xp^Xq^{n-x}[/tex].

We know the expected value of a binomial distribution E(x) = np.

Given, Suppose that 40% of the cars in a certain town are white.

Therefore 50% of cars in the town are not which.

Let, The no. of cards in the town be 'n'.

So, p = 40/n and q = 60/n

Therefore from the formula E(x) = np we get,

E(x) = n×40/n

E(x) = 40.

So, The expected value of X is 40.

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Answer: We expect 2.5 cars to

The expected value of X is 2.5.

Step-by-step explanation:

In this case, it is a geometric distribution because we do not have a fixed number of trials.

We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.

In this case:

mu_x=1/0.4 = 2.5

In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).

Answer:

Step-by-step explanation:

17/5

Answer:

2 and 2/5

Step-by-step explanation:

A) The probability that the tyre wears out before 60000 miles is 0.4221

B) The probability that the tyre lasts more than 83000 miles is 0.49534

The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as

z = (x - u)/s

Where

x = the distance the tyres can run until wear-out

u = mean distance

s = standard deviation

From the information given,

u = 70000 miles

s = 7000 miles

A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as

P(x lesser than 60000)

For x = 60000,

z = (60000 - 70000)/7000 = - 1.42

Looking at the normal distribution table, the corresponding z score is 0.4221

B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as

P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)

For x = 83000,

z = (83000 - 70000)/5000 = 2.6

Looking at the normal distribution table, the corresponding z score is 0.49534

P(x greater than 83000)

= 1 - 0.49534  = 0.50466

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The possible value of other two angles will be 20 degree.

What are the types of triangle?

Basically, there are six different types of triangles in terms of lengths and measurements of triangle lines or angles. The sum of all interior angles of a triangle is always 180 degrees. This is called the angular summation of the triangle. Depending on the length of the sides, triangles can be divided into three types:

scale

Isosceles

equilateral

It is given that an isosceles triangle has an angle that measures 140°

We know that two sides of isosceles triangle are equal and by the property of triangle we know that angle opposite to equal sides are equal therefore remaning two angles of isosceles triangle will be equal.

Let the angles be x

By angle sum property of triangle

x + x + 140 = 180

2x = 180 - 140

2x = 40

x = 40/2 = 20

Therefore, the possible value of other two angles will be 20 degree.

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Answer:

y = x - 2

Step-by-step explanation:

Since m = 0, what we have so far is y=x+b

We have a point, which is (3,1)

Substitute the x and y with the x and y values in the coordinate point to solve for b (y-intercept).

1=3+b

1-3=3+b-3                  undo the 3 by subtracting

-2 = b

y = x + -2                   simplify

y = x - 2

Answer:

answer :J LOOK THE DIAGRAM CAREFULLY AND UNDERSTAND

Answer:

A <c - <b = 10

Step-by-step explanation:

The number of cups she can make is 2 cups

From the question, we have the following parameters that can be used in our computation:

Cups of sugar needed = 1/4

Cups of sugar available  = 1/2

Assume there exist a proportional relationship between the cups

The number of cups she needs can be calculated using the following equation

number of cups = (1/2)/(1/4)

Evaluate the quotient

number of cups = 2

Hence, the cups is 2 cups

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Answer:

i think the answer will be 6%

Answer:

below

Step-by-step explanation:

46 / 780  * 100% = 5.9 %

Answer:

........................

Answer:

8.8 minutes

Step-by-step explanation:

first we figure out how many liters are being lost

57 - 35 = 22

then divide that by 2.5

22 / 2.5 = 8.8

8.8 minutes

1. G is incompressible- True

2. F is irrotational- True

3. G is irrotational- False

4. F is incompressible- False

Divergence and Curl In Mathematics, divergence is a differential operator, which is applied to the 3D vector-valued function. Similarly, the curl is a vector operator which defines the infinitesimal circulation of a vector field in the 3D Euclidean space .

So if we calculate for F:

F has a divergence potentially

divF = df/dx + dg/fy + dh/dz

But curl(F )= 0(all cross derivatives df/dy df/dz, dg/dx etc = 0)

For G

G has zero divergence.

divG = df/dx + dg/fy + dh/dz = 0 + 0 + 0 = 0

But it may have a curl.

curl(G) = df/dy may be non-zero

df/dz, dg/dx etc may all be non-zero

Now, we also know that if the divergence is zero, the vector field is incompressible and if the curl is zero, the vector field is irrotational, that is,  

div = 0 = incompressible and

curl = 0= irrotational  

Thus,

1. G is incompressible- True

2. F is irrotational- True

3. G is irrotational- False

4. F is incompressible- False

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Answer:

7330.36

Step-by-step explanation:

A = P (1+i)^n

n  = 4×5 = 20

i = 0.03075

12.3% / 4 = 3.075  × 1/100

= 0.03075

A = 4000 ( 1+ 0.03075 ) ^20

= 7330.36

The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.

The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.

Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).

The slope of this line would be:

= ( Y2 - Y1 ) / ( X 2 - X1)

= ( 19 - 17 ) / (7 - 6 )

= 2.12

The y intercept would be:

y = mx + c

19 = 2.12 (7 ) + c

c = 4.42

The equation of the  line of best fit is then :
y = 2.12 x + 4.42

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