With both the cold water and hot water faucets open it takes five minutes to fill a bathtub. The cold water facet alone takes 15 minutes to fill the tub. How long will it take to fill the tub with just the hot water faucet?

Answer:

a)  d = 4,712 cm

b) ∠ 108,52 ⁰

Step-by-step explanation:

The crcular path of the spider has radius = 3 cm

If the spider moves from the fa right side of the circle its start poin of the movement is P ( 3 , 0 ) (assuming the circle is at the center of the coordinate system. And the top of the web (going counterclockwise ) is the poin ( 0 , 3 )

So far the spider has traveled 1/4 of the circle

The lenght of the circle is

L = 2*π*r

The traveled distance for the spider (d) is

d = (1/4 )* 2*π*r       ⇒       d = (1/2)*3,1416*3      ⇒  d = 4,712 cm

And now spider go ahead a new distance of approximately 1 more cm

Therefore the spider went a total of 5.712 cm

Now we know that

πrad  =  180⁰    then   1 rad = 180/π         ⇒   1 rad  = 57⁰

rad = lenght of arc/radius  

so  5,712/3    =  1.904 rad

By rule of three

       1 rad           ⇒    57⁰

     1.904 rad     ⇒     ? x

x = 57 * 1.904      ⇒   108.52 ⁰

So the ∠ 108,52 ⁰

Explanation:

For the purpose of filling in the table, the BINOMPDF function is more appropriate. The table is asking for p(x)--not p(n≤x), which is what the CDF function gives you.

If you want to use the binomcdf function, the lower and upper limits should probably be the same: 0,0 or 1,1 or 2,2 and so on up to 5,5.

The binomcdf function on my TI-84 calculator only has the upper limit, so I would need to subtract the previous value to find the table entry for p(x).

Answer:

Minimum surface area =[tex]70.77 cm^2[/tex]

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container=[tex]54 cm^3[/tex]

We have to find the minimum surface areas that this container will have.

Volume of container=[tex]l\times b\times h[/tex]

[tex]x\times 2x\times h=54[/tex]

[tex]2x^2h=54[/tex]

[tex]h=\frac{54}{2x^2}=\frac{27}{x^2}[/tex]

Surface area of container=[tex]2(b+l)h+lb[/tex]

Because the container does not have lid

Surface area of container=[tex]S=2(2x+x)\times \frac{27}{x^2}+2x\times x[/tex]

[tex]S=\frac{162}{x}+2x^2[/tex]

Differentiate w.r.t x

[tex]\frac{dS}{dx}=-\frac{162}{x^2}+4x[/tex]

[tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]

Substitute [tex]\frac{dS}{dx}=0[/tex]

[tex]-\frac{162}{x^2}+4x=0[/tex]

[tex]4x=\frac{162}{x^2}[/tex]

[tex]x^3=\frac{162}{4}=40.5[/tex]

[tex]x^3=40.5[/tex]

[tex]x=(40.5)^{\frac{1}{3}}[/tex]

[tex]x=3.4[/tex]

Again differentiate w.r.t x

[tex]\frac{d^2S}{dx^2}=\frac{324}{x^3}+4[/tex]

Substitute x=3.4

[tex]\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0[/tex]

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area =[tex]\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2[/tex]

The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2

Given, two points are A(-5, 5) and B(3, -3)

We have to find the perpendicular bisector of segment AB.

Now, we know that perpendicular bisector passes through the midpoint of segment.

The formula for midpoint is:

[tex]\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

[tex]Here x_1 = -5 ; y_1 = 5 ; x_2 = 3 ; y_2 = -3[/tex]

[tex]\text { So, midpoint of } A B=\left(\frac{-5+3}{2}, \frac{5+(-3)}{2}\right)=\left(\frac{-2}{2}, \frac{2}{2}\right)=(-1,1)[/tex]

Finding slope of AB:

[tex]\text { Slope of } A B=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]\text { Slope } m=\frac{-3-5}{3-(-5)}=\frac{-8}{8}=-1[/tex]

We know that product of slopes of perpendicular lines = -1  

So, slope of AB [tex]\times[/tex] slope of perpendicular bisector = -1  

- 1 [tex]\times[/tex] slope of perpendicular bisector = -1  

Slope of perpendicular bisector = 1

We know its slope is 1 and it goes through the midpoint (-1, 1)

The slope intercept form is given as:

y = mx + c

where "m" is the slope of the line and "c" is the y-intercept

Plug in "m" = 1

y = x + c   ---- eqn 1

We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1

1 = -1 + c

c = 2

Now substitute c = 2 in eqn 1

y = x + 2

Thus y = x + 2 is the required equation in slope intercept form

The plot of land forms right triangle.

Step-by-step explanation:

Let,

the three sides are a,b and c.

The sum of square of two sides equals to the square of third side. We will consider the larger side as c, therefore,

a= 2000 feet

b= 2100 feet

c= 2900 feet

Using Pythagoras theorem;

[tex]a^2+b^2=c^2\\(2000)^2+(2100)^2=(2900)^2\\4000000 + 4410000 = 8410000\\8410000 feet = 8410000 feet[/tex]

As the three sides satisfy pythagoras theorem, therefore, the plot of land form right triangle.

The plot of land forms right triangle.

Keywords: triangle, pythagoras theorem

Learn more about pythagoras theorem at:

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Answer:

Step-by-step explanation:

a) The probability that the hand contains exactly one ace

No of ways of selecting one ace and four non ace would be

=[tex]4C1 (48C4)\\\\= 778320[/tex]

i.e. α=778320

b) the probability that the hand is a flush

No of ways of getting a flush is either all 5 hearts or clubs of spades or dice

= [tex]4(13C5) = 5148[/tex]

ie. β=5148

c)  the probability that the hand is a straight flush

In each of the suit to get a straight flush we must have either A,2,3,4,5 or 2,3,4,5,6, or .... or 9,10, J, q, K

So total no of ways = [tex]=9(13C5) 4\\= 46332[/tex]

γ=46332

The probability of getting a hand with exactly one ace from a standard deck is 748,704/2,598,960. For a flush, the probability is 5,148/2,598,960. For a straight flush, the probability is 40/2,598,960.

The total number of possible five card hands from a standard deck is C(52,5)=2,598,960.

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Answer:

[tex]1117.01 \mathrm{ft}^{2} \text { is the watered are by the sprinkler. }[/tex]

Option: A

Step-by-step explanation:

A sprinkler sprays water over a distance of (r) = 40 feet

Rotates through an angle of (θ) =  80°

80° convert to radians

[tex]\text { Radians }=80^{\circ} \times\left(\frac{\pi}{180}\right)[/tex]

[tex]\text { Radians }=80^{\circ} \times 0.017453292[/tex]

θ in Radians = 1.396263402

We know that,

Area of sprinkler is [tex]\mathrm{A}=\frac{1}{2} \mathrm{r}^{2} \theta[/tex]

Substitute the given values,

[tex]A=\frac{1}{2} \times 40^{2} \times 1.396263402[/tex]

[tex]A=\frac{(1600 \times 1.396263402)}{2}[/tex]

[tex]\mathrm{A}=\frac{2234.021443}{2}[/tex]

[tex]\mathrm{A}=1117.01 \mathrm{ft}^{2}[/tex]

Area of sprinkler is [tex]1117.01 \mathrm{ft}^{2}[/tex]

Answer:

It take 12 hours for 2 lawnmowers to cut 6 acres of grass

Step-by-step explanation:

We are given that It takes 4 lawnmowers to cut 2 acres of grass in 2 hours.

Let [tex]T_1 , M_1 and W_1[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively in case 1 .

[tex]T_1=2 \\W_1=2\\M_1=4[/tex]

Now The amount of time varies directly with the amount of grass and inversely with the number of lawnmowers

Let [tex]T_2 , M_2 and W_2[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively i case 2

[tex]T_1=? \\W_1=6\\M_1=2[/tex]

So, [tex]\frac{M_1 \times T_1}{W_1}=\frac{M_2 \times T_2}{W_2}[/tex]

Substitute the values

[tex]\frac{4 \times 2}{2}=\frac{2 \times ?}{6}[/tex]

[tex]\frac{4 \times 2 \times 6}{2 \times 2}=?[/tex]

[tex]12=?[/tex]

Hence it take 12 hours for 2 lawnmowers to cut 6 acres of grass

Answer:

D. 12

Step-by-step explanation:

hope this helps :)

Answer:

(B) The correct interpretation of this interval is that 90% of the students in the population should have their scores improve by between 72.3 and 91.4 points.

Step-by-step explanation:

Confidence interval is the range the true values fall in under a given confidence level.

Confidence level states the probability that a random chosen sample performs the surveyed characteristic in the range of confidence interval. Thus,

90% confidence interval means that there is 90% probability that the statistic (in this case SAT score improvement) of a member of the population falls in the confidence interval.

Answer:

0.006

Step-by-step explanation:

This is joint probability and thus the probability of the given event is the product of:

(probability of drawing a 2 on the first draw)*(prob. of dring a 3 on the second draw), or

4         4          16

----- * ------ = ------------ = 0.006

52     52        (52)^2

Answer:

1/169

Step-by-step explanation:

if you mean a deck as in the 52 cards then the answer is the following.

there are 4 cards in a deck with the number 2 on it. 2 of spades, diamonds, hearts and clubs. so the probability would be 4/42 because there is 4 out of the 52 cards there are. next there is also 4 cards with three on it, so 4/52 again.you multiply these two to get the answer(but before you do i would recommend to simplify it to 1/13) to get 1/169

Answer:

56 and 57

Step-by-step explanation:

The numbers 56 and 57 are values that are very close it is better to estimate 56 and 57 then 6 and 56 and 57

The answer to the teacher's question is that approximately 95% of the sample lies within the range of 45 to 69. This conclusion is based on the features of the normal distribution

The study's results use elements of statistics, with the distribution in question being a normal distribution. A characteristic of a normal distribution is that approximately 95% of measurements will fall within two standard deviations, both above and below the mean. Given that the mean in this case is 57 and the standard deviation is 6, we can calculate the values between which approximately 95% of the sample falls.

Doing the math, we find that: 57 - (2*6) = 45 and 57 + (2*6) = 69. Thus, approximately 95% of the sample lies between the values of 45 and 69.

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Answer:

70 standard boxes, 40 deluxe boxes

Step-by-step explanation:

standard: x

deluxe: y

x + y = 110

7x + 11y = 930

Multiply the first equation by 7 and subtract.

7x + 7y = 770

-(7x + 11y = 930)

You get -4y = -160

y = 40

Substitute y into the first equation.

x + 40 = 110

x = 70

Answer: The price would be $80 at which supply and demand are equal.

Step-by-step explanation:

Since we have given that

Demand function is given by

[tex]\dfrac{9600}{p}[/tex]

where p is the price of a muffin in cents.

Supply function is given by

[tex]44p-200[/tex]

We need to find the price at which supply and demand are equal.

so, it becomes,

[tex]\dfrac{9600}{p}=44p-200\\\\9600=(4p-200)p\\\\9600=4p^2-200p\\\\2400=p^2-50p\\\\p^2-50p-2400=0\\\\p=80,-30[/tex]

We discarded p = -30 as price cannot be negative.

so, the price would be $80 at which supply and demand are equal.

Answer:

Step-by-step explanation:

The bakery found out that the demand is

D = 9600 / p

Where P is the price of muffins in cents

Daily supply is give as

S=4p — 200 ( I believe it is a typo error, and that is why I used 4p - 200, due to the experience I have with brainly site.)

We want to find the price at which the demand is equal to the supply

It is a very straight forward questions

Demand. = Supply

Then,

D = S

9600 / p = 4p - 200

Cross multiply

9600 = 4p² - 200p

Rearrange to form quadratic equation

4p² - 200p - 9600 = 0

Divide through by 4

p² - 50p - 2400 = 0

Check attachment for solution using formula method to solve quadratic equation

Using factorization

p² - 80p + 30p - 2400 = 0

p(p-80) + 30(p-80) = 0

(p+30)(p-80) = 0

So, it is either p+30 = 0. Or p-80=0

p = -30 or p = 80

Since the price can't be negative,

We are going to discard the negative price.

Then, the price is 80cents per muffins.

Answer:

The probability that the student selected will be one who both walks to school and has been late to school at least once is = 0.15 or 15%

Step-by-step explanation:

From the question given, we find the probability that the student selected will be one who both walks to school and has been late to school at least once

Let,

B = Event that student walk to school

C = Event that student have been late to school at least once.

So,

P(B) = 0.40 , P(C) = 0.32

P(C | B) = 0.375

We apply the  multiplication rule,

P(B and C) = P(C | B) * P(B)

= 0.375 * 0.40

= 0.15 or 15%

Answer:

  A:  x = 20

  C:  x = -9

Step-by-step explanation:

You can solve the inequality and compare that with the offered choices, or you can try the choices in the inequality to see if it is true. Either approach works, and they take about the same effort.

Solving it:

Unfold it ...

  -17 ≤ x -7.5 ≤ 17

Add 7.5 ...

  -9.5 ≤ x ≤ 24.5

The numbers 20 and -9 are in this range: answer choices A and C.

_____

Trying the choices:

A:  |20 -7.5| = 12.5 ≤ 17 . . . . this works

B:  |-10 -7.5| = 17.5 . . . doesn't work

C:  |-9 -7.5| = 16.5 ≤ 17 . . . . .this works

D:  |27-7.5| = 19.5 . . . doesn't work

The choices that work are answer choices A and C.

Answer:

Step-by-step explanation:

First we have to find the worth of 50 Ib of both mixtures, so we multiply 50 by 2.72 since the owner wants to sell the mixture at $2.72 per pound

50 Multiplied by $2.72 equals $135

Then we divide that amount by 2 since we are considering two types of products, raisins and nuts

$135 divided by 2 equals $67.5

So we find the amount of raisins that is worth $67.5 and we know a pound of raisins cost $3.2

We divide $67.5 by $3.2 which will give 21.09 Ib (Amount for the raisins)

We divide $67.5 by $2.4 which will give 28.13 Ib (Amount for the nuts)

Final answer:

The store owner should mix 20 lb of raisins with 30 lb of nuts to make a 50 lb mixture that can be sold for $2.72 per pound. This is determined by solving a system of linear equations.

Explanation:

The owner of the store wants to mix raisins and nuts to sell a 50 lb mixture for $2.72 per pound. To find out the quantities of raisins and nuts he should use, we can set up a system of equations. Let R represent the amount of raisins in pounds and N represent the amount of nuts in pounds. The two equations area:

We can solve this system using the substitution or elimination method. Assuming we choose elimination, we can multiply the first equation by 2.40 to make the coefficient of N the same in both equations:

Subtracting these equations gives us:

Dividing both sides by 0.80 gives us the amount of raisins:

Using the first equation (R + N = 50), we can find the amount of nuts:

So the owner should mix 20 lb of raisins with 30 lb of nuts to make the mixture.

Answer:

28. a) [tex]-7.3 + 7.4[/tex]

29. c) [tex]3n + 0.18[/tex]

Step-by-step explanation:

Question 28:

Given:

The equation is -9.6 + 9.5 + _________ = 0

In order to solve this, first let us simplify the terms -9.6 + 9.5.

-9.6 + 9.5 = -0.1

So, we are getting the sum of first 2 numbers as -0.1. Now, the result is 0. So, we know that,  -a + a = 0. Therefore, the number that should come in the blanks should be -(-0.1) = 0.1

Now, among all the 4 choices, only choice (a) gives the sum as 0.1 as shown below:

-7.3 + 7.4 = 0.1

The options (b) and (c) has a result of 0 and option (d) sum is -0.1.

Therefore, the correct option is option (a).

Question 29:

Given:

The expression to simplify is given as:

[tex]2n+n+0.18[/tex]

Using commutative property of addition, we add the like terms together. Here, the like terms are [tex]2n\ and\ n[/tex]. So, we add them as shown below:

[tex]2n+1n=(2+1)n=3n[/tex]

Therefore, the given expression is simplified to [tex]3n + 0.18[/tex]. Hence, the correct option is option (c).

Answer:

By definition, the derivative of f(x) is

[tex]lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]

Let's use the definition for [tex]f(x)=\frac{1}{x}[/tex]

[tex]lim_{h\rightarrow 0} \frac{\frac{1}{x+h}-\frac{1}{x}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{x-(x+h)}{x(x+h)}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{(-1)h}{x^2+xh}}{h}=\\lim_{h\rightarrow 0} \frac{(-1)h}{h(x^2+xh)}=\\lim_{h\rightarrow 0} \frac{-1}{x^2+xh)}=\frac{-1}{x^2+x*0}=\frac{-1}{x^2}[/tex]

Then, [tex]f'(x)=\frac{-1}{x^2}[/tex]

The Chinese exports of automobiles and parts reached a value of approximately $12.3 billion around the year 2004.

Let's first assume that the value of the function f(x) equals the targeted exports, $12.3 billion. Therefore, we have the equation 1.8208e⁽°³³⁵⁷ˣ⁾= 12.3. We can solve this equation for x, which represents the number of years since 1998.

First, divide both sides of the equation by 1.8208 to isolate e⁽°³³⁵⁷ˣ⁾. You will get e⁽°³³⁵⁷ˣ⁾  = 6.7475 approximately. To get rid of the base e, we take the natural logarithm (ln) of both sides. This gives us .3387x = ln(6.7475).

Divide this by .3387 to solve for x. The solution approximates to x = 5.9. This means the exports reach $12.3 billion approximately 6 years after 1998, which would be around the year 2004.

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The year with $12.3 billion in Chinese auto exports is found by setting the provided exponential function equal to it and solving for x, which represents years past 1998. We apply logarithms to solve the equation. The final value of x, when added to 1998, gives us the requested year.

The goal is to find the year when the value of China's exports (represented by f(x)) reaches $12.3 billion. This can be achieved by setting f ( x ) = 1.8208 e .3387 x equal to $12.3 billion and solving for x using logarithmic properties.

Here are the steps:

Once you find the value of x, add this value to the base year 1998 to get the year when the exports reached $12.3 billion.

Note: You require a calculator with the capability to calculate natural logs to solve for x.

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Answer:

  see below

Step-by-step explanation:

The next step in copying the angle is to copy the width of it (the length of its chord) to the new location. First, you have to set the compass to that chord length, GF.

The 95% confidence interval for the mean weight of all bags of oranges is calculated using the sample mean and the sample standard deviation. After calculation, we are 95% confident the mean weight is between 9.193 and 9.757 pounds.

To find the 95% confidence interval for the mean weight of all bags of oranges, we first need to calculate the sample mean and sample standard deviation. The sample mean, [tex]\overline{x}[/tex], is the sum of all sample weights divided by the number of samples. In this case, it is (9.3+9.7+9.2+9.7)/4 = 9.475 pounds.

The sample standard deviation, s, is the square root of the sum of the squared differences between each sample weight and the sample mean, divided by the number of samples minus one. The s value here is approximately 0.253 pounds.

For a 95% confidence interval with a sample size of 4, the z-score is 2.776 (obtained from a standard z-table). The margin of error is the z-score multiplied by the standard deviation divided by the square root of the sample size. This is approximately 0.282 pounds. So, the 95% confidence interval is (9.475-0.282, 9.475+0.282) = (9.193, 9.757) pounds.

So we can say that we are 95% confident that the mean weight of all bags of oranges is between 9.193 and 9.757 pounds.

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Answer: 3/13 is closer to 0 than 1/2 or 1.

- This is because 1/2 of 1/13 would be about 6.5/13.

- Since 3/13 is not close to 1/2, nor it will be to 1.

Step-by-step explanation:

Let [tex]f(x)[/tex] be the number of shares in [tex]x[/tex] days.

Let the function [tex]f(x)=ab^{x}[/tex].

It is given that each friend shares with three friends the next day.

So,[tex]f(x)=3\times f(x-1)[/tex]

substituting [tex]f(x)=ab^{x}[/tex]

[tex]ab^{x}=3\times ab^{x-1}[/tex]

So,[tex]b=3[/tex]

Given that at day [tex]0[/tex],there are [tex]2[/tex] shares.

So,[tex]f(0)=2[/tex]

[tex]a3^{0}=2[/tex]

[tex]a=2[/tex]

So,[tex]f(x)=2\times 3^{x}[/tex]

Answer:

- 0.2 cm/s

Step-by-step explanation:

Volume of a cylinder =  πr²l--------------------------------------------------------(1)

dV/dt =(dV /dr ) x (dr/dt) +  (dV /dl ) x (dl/dt) ---------------------------------(2)

dV/dr = 2 πrl

dV/dl  =  πr²

dr/dt   = Unknown

dl/dt   = 0.1 cm/s

dV/dt = 0

From equation (1), the length of the cylinder can be calculated when r = 5cm

V = πr²L

100 = π (5)²L

L =100/25π

  =4/π

To find the rate of radius change  (dr/dt) we substitute known values into equation (2):

0 = 2 π (5) (4/π) x  (dr/dt) + π(5)² x 0.1

0 =  40 (dr/dt)  + 2.5π

40 (dr/dt) = -2.5π

     dr/dt =   -2.5π/40

              =  -0.1963 cm/s

              ≈ - 0.2 cm/s

The negative sign shows that the radius of the cylinder of constant volume decrease at a rate twice the length.

Answer:

ΔDBE≅ΔQAP  (by RHS criteria)

Step-by-step explanation:

Given that, [tex]PQ=DE[/tex], [tex]PB=AE[/tex], [tex]QA[/tex]⊥[tex]PE[/tex]

and [tex]DB[/tex]⊥[tex]PE[/tex]

⇒∠PAQ=90° and ∠EBD=90°(definition of perpendicular lines)

Its given that PB=AE,

subtracting AB on both sides,

we get: PB-AE=AB-AE

         ⇒PA=EB (equals subtracted from equals, the remainders are equals)

Therefore, ΔDBE≅ΔQAP (by RHS criteria)

conditions for congruence:

So, ∡D=∡Q(as congruent parts of congruent triangles are equal)

Answer:

2,692 cans of tomato soup were sold in January and July

Step-by-step explanation:

The number of cans of soup sold in January = 1346

Store sold same number of soup cans in July.

⇒The number of cans of soup sold in July = 1346

So, the total soup cans sold in January and July

=  Sum of soup cans sold in both months

=  1346 +  1346

=2,692

Hence, 2,692 cans of tomato soup were sold in January and July.

Answer:

c) Sample parameters are usedto make inferences about population statistics

Step-by-step explanation:

In statistics we use samples to make inferences about population

That is the great advantage of the whole role of distribution. Once you know a particular situation or experiment, that you can associate to one specific distribution and compute parameters, you can obtain from a relative smaller quantity of dataand  with good approximation, inferences about the whole population (that can be conform by a very big numbers of elements)

Answer: D. Sample statistics are used to make inferences about population parameters.

Step-by-step explanation: got it right on edge 23  :)

Answer:

The probability is 0.74719

Step-by-step explanation:

Let's start defining the random variable X.

X : ''Number of children with hyperlipidemia out of 12 children''

X can be modeled as a binomial random variable.

X ~ Bi (n,p)

Where n is the sample size and p is the ''success probability''.

We defining as a success to find a child that has hyperlipidemia.

The probability function for X is :

[tex]P(X=x)=(nCx).p^{x}.(1-p)^{n-x}[/tex]

Where nCx is the combinatorial number define as :

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

We are looking for [tex]P(X\geq 3)[/tex]

[tex]P(X\geq 3)=1-P(X\leq 2)[/tex]

[tex]P(X\geq 3)=1-[P(X=0)+P(X=1)+P(X=2)][/tex]

[tex]P(X\geq 3)=1-[(12C0)0.3^{0}0.7^{12}+(12C1)0.3^{1}0.7^{11}+(12C2)0.3^{2}0.7^{10}][/tex]

[tex]P(X\geq 3)=1-(0.7^{12}+0.07118+0.16779)=1-0.25281=0.74719[/tex]

There is a probability of 0.74719 that at least 3 children are hyperlipidemic.

To find the probability that at least 3 out of the 12 children are hyperlipidemic, we can use the binomial probability formula. The probability is 36.21% or 0.3621.

To find the probability that at least 3 out of the 12 children are hyperlipidemic, we need to use the binomial probability formula. The probability of success is 30% or 0.3 (since 30% of children are hyperlipidemic), and the probability of failure is 1 - 0.3 = 0.7.

The formula for the binomial probability is P(X >= k) = 1 - P(X < k), where X follows a binomial distribution with n trials (12 children in this case) and probability of success p (0.3).

To find P(X < k), we need to calculate the probabilities for X = 0, 1, and 2 children being hyperlipidemic and then sum them up.

Summing up these probabilities, we get P(X < 3) = 0.0687 + 0.2332 + 0.3361 = 0.6379

Finally, the probability of at least 3 children being hyperlipidemic is P(X >= 3) = 1 - P(X < 3) = 1 - 0.6379 = 0.3621 or 36.21%.

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Answer:

C

Step-by-step explanation:

f"(x) < 0, which means the function is concave down at all values of x.

For any such function, within the domain of a ≤ x ≤ b, the secant line S(x) is below the curve of f(x), and the tangent line T(x) is above the curve of f(x).

Here's an example:

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Answer:

g=1

Step-by-step explanation:

Given equation is \[−3+5+6g=11−3g\]

Simplifying, \[2+6g=11−3g\]

Bringing all the terms containing g to the left hand side and the numeric terms to the right hand side,

\[6g + 3g=11−2\]

=> \[(6 + 3)g=9\]

In other words, \[g=\frac{9}{9}\]

Or, g = 1

The given equation is satisfied for g=1.

Validation:

Left hand side of the equation: -3+5+6 = 8

Right hand side of the equation: 11-3 = 8