What is m /_ 2?

42
48
90
138

Answer:

a) 0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.

b) 0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.

c) 0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they are opposed to taxes on junk food and soda, or they are not. Each adult is independent of other adults, which means that the binomial probability distribution is used to solve the question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

63% of US adults opposed to taxes on junk food and soda.

This means that [tex]p = 0.63[/tex]

You randomly select 10 US adults.

This means that [tex]n = 10[/tex]

(a) exactly one

This is [tex]P(X = 1)[/tex]. So

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

[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]

0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.

(b) at least four

This is

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

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

[tex]P(X = 0) = C_{10,0}.(0.63)^{0}.(0.37)^{10} \approx 0[/tex]

[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]

[tex]P(X = 2) = C_{10,2}.(0.63)^{2}.(0.37)^{8} = 0.0063[/tex]

[tex]P(X = 3) = C_{10,3}.(0.63)^{3}.(0.37)^{7} = 0.0285[/tex]

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0008 + 0.0063 + 0.0285 = 0.0356[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0356 = 0.9644[/tex]

0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.

(c) less than eight

This is

[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]

In which

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

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

[tex]P(X = 8) = C_{10,8}.(0.63)^{8}.(0.37)^{2} = 0.1529[/tex]

[tex]P(X = 9) = C_{10,1}.(0.63)^{9}.(0.37)^{1} = 0.0578[/tex]

[tex]P(X = 10) = C_{10,2}.(0.63)^{10}.(0.37)^{0} = 0.0098[/tex]

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1529 + 0.0578 + 0.0098 = 0.2205[/tex]

[tex]P(X < 8) = 1 - P(X \geq 8) = 1 - 0.2205 = 0.7795[/tex]

0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.

Answer:

choices 2 and 5

Step-by-step explanation:

Answer:

52920cm

all you have to do is multiply all the numbers together.

sorry if its wrong.

but hope it helps.

have a great day.

Answer:

102

Step-by-step explanation:

area of the square (36) plus the area of the trapezoid (66)

Answer:

[tex]Total = \$7800[/tex]

Step-by-step explanation:

Given

[tex]Cost = \$32.50[/tex] per square yard

[tex]Length = 432.0ft[/tex]

[tex]Width = 5.0ft[/tex]

Required

Determine the cost of carpet and installation

First, calculate the area of the carpet

[tex]Area = Length * Width[/tex]

[tex]Area = 432.0ft * 5.0ft[/tex]

[tex]Area = 2160ft^2[/tex]

Convert to square yard

[tex]Area = \frac{2160yd^2}{9}[/tex]

[tex]Area = 240yd^2[/tex]

The cost is then calculated as:

[tex]Total= Area * Unit\ Cost[/tex]

[tex]Total = 240 * \$32.50[/tex]

[tex]Total = \$7800[/tex]

Answer:

Angle A- Obtuse angle

Angle B- Right angle

Angle C- Reflex angle

Angle D- Reflex angle

Angle E- Acute angle

Angle A is Obtuse angle, Angle B is  Right angle, Angle C is Reflex angle, Angle D is Reflex angle and Angle E is Acute angle

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Obtuse angle is any angle greater than 90°

A right angle is an angle measuring exactly 90°

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees.

Any angle that measures greater than 0° and less than 90° is called an acute angle.

By the definitions of these the angles are

Angle A- Obtuse angle

Angle B- Right angle

Angle C- Reflex angle

Angle D- Reflex angle

Angle E- Acute angle

Hence, Angle A is Obtuse angle, Angle B is  Right angle, Angle C is Reflex angle, Angle D is Reflex angle and Angle E is Acute angle

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Answer:

the estimated area of the fountain is 147.58 square yards and the estimated area of the path is 28.26 square yards

Step-by-step explanation:

#platolivesmatter

your welcome!!!

The area of the fountain is 147.58 square yards, and the area of the path is 28.25 square yards.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given

a circular fountain,

radius of fountain  = √47 yards

area of  fountain = πr²

area = π(√47)²

area = 147.58 square yards.

and fountain surrounded by a circular path,

which form a concentric circle with fountain,

the radius of the circular path from center of the fountain = √56 yards

area of the path = total area with radius √56 - an area of fountain

area of the path = π(√56)² - 147.58

area of the path = 175.84 - 147.58

area of the path = 28.26 square yards

Hence the area of the fountain is 147.58 square yards,

area of path = 28.25 square yards.

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Answer =

= (4x - 5)²

= 16x² - 40x + 25

Answer:

i think C

Step-by-step explanation:

Answer:

Good luck Dude

Step-by-step explanation:

Answer: 360>5.5+36.41d

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

Given

[tex]\frac{3}{500} \%[/tex]

Required

Represent as fraction

To do this, we simply multiply 3/500 by 100

[tex]\frac{3}{500} \% = \frac{3}{500} * 100[/tex]

[tex]\frac{3}{500} \% = \frac{3}{5}[/tex]

So, the fraction is 3/5

the answer to your question is C

Answer:

The height of the taller tree is 7.5 feet.

Step-by-step explanation:

I am going to say that:

The height of the shorter tree is x.

The height of the taller tree is y.

The height of shorter tree is 3/5 of the height of the taller tree.

This means that [tex]x = \frac{3y}{5}[/tex]

If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree? ​

This means that [tex]x = 4 + \frac{1}{2} = \frac{8+1}{2} = \frac{9}{2}[/tex]

We want to find y.

[tex]x = \frac{3y}{5}[/tex]

[tex]\frac{9}{2} = \frac{3y}{5}[/tex]

[tex]6y = 45[/tex]

[tex]y = \frac{45}{6}[/tex]

[tex]y = 7.5[/tex]

The height of the taller tree is 7.5 feet.

Answer:

Simple Interest (SI) = Amount (A) – Principal (P) = 6000 - 5400. = 600

Answer:

1. Robert deposits $ 3000 in State Bank of India for 3 year which earn him an interest of 8%.What is the amount he gets after 1 year, 2 years and 3 years?

Step-by-step explanation:

Solution:

In every $ 100, Robert gets $ 8.

(Since rate is 8% → 8 for every 100)

Therefore, for $ 1 he gets = $ 8/100

And for $ 2000 he gets = 3000 x 8/100 

= $ 240

Simple Interest for 1 year = $ 240.

Simple Interest for 2 year = $ 240 x 2 

= $ 480

Simple Interest for 3 year = $ 240 x 3

= $ 720

Therefore, Amount after 1 year = Principal (P) + Simple Interest (SI)

= 3000 + 240

= $ 3240

Amount after 2 years = Principal (P) + Simple Interest (SI)

= 3000 + 480

= $ 3480

Amount after 3 years = Principal (P) + Simple Interest (SI)

= 3000 + 720 = $ 3720

We observe from the above example that, the Interest cannot be calculated without Principal, Rate and Time.

Therefore, we can conclude that Simple Interest (S.I.) depends upon:

(i) Principal (P)

(ii) Rate (R)

(iii) Time (T)

And therefore, the formula for calculating the simple interest is

Simple Interest (SI) = {Principal (P) × Rate (R) × Time (T)}/100

Amount (A) = Principal (P) + Interest (I)

Principal (P) = Amount (A) – Interest (I)

Interest (I) = Amount (A) – Principal

Answer:

The estimated size of the population in 10 days is of 1372 mosquitos.

Step-by-step explanation:

Population after t days:

The population after t days is given by:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

P(0)=574.

So

[tex]P(t) = 574e^{rt}[/tex]

P'(0)=50

[tex]P^{\prime}(t) = 574re^{rt}[/tex]

Since P'(0)=50

[tex]574r = 50[/tex]

[tex]r = \frac{50}{574}[/tex]

[tex]r = 0.0871[/tex]

So

[tex]P(t) = 574e^{0.0871t}[/tex]

Estimate the size of the population in 10 days

This is P(10).

[tex]P(10) = 574e^{0.0871*10} = 1372[/tex]

The estimated size of the population in 10 days is of 1372 mosquitos.

The size of the population of mosquito follows an exponential model.

The size of the population in 10 days is 1370

The given parameters are:

[tex]\mathbf{P(0) = 574}[/tex]

[tex]\mathbf{P'(0) = 50}[/tex]

An exponential function is represented as:

[tex]\mathbf{P(t) = P(0) \times e^r^t}[/tex]

So, we have:

[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]

Differentiate

[tex]\mathbf{P'(t) = 574r}[/tex]

Substitute 0 for t

[tex]\mathbf{P'(0) = 574r}[/tex]

Substitute [tex]\mathbf{P'(0) = 50}[/tex]

[tex]\mathbf{50 = 574r}[/tex]

Divide both sides by 574

[tex]\mathbf{0.087 = r}[/tex]

So, we have:

[tex]\mathbf{r = 0.087 }[/tex]

The function becomes

[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]

[tex]\mathbf{P(t) = 574 \times e^{0.087t}}[/tex]

In 10 days, t = 10.

So, we have:

[tex]\mathbf{P(10) = 574 \times e^{0.087 \times 10}}[/tex]

[tex]\mathbf{P(10) = 574 \times e^{0.87}}[/tex]

Solve

[tex]\mathbf{P(10) = 1370}[/tex]

Hence, the size of the population in 10 days is 1370

Read more about exponential functions at:

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Answer:

39

Step-by-step explanation:

Answer:

78% = 78/100

= 0.78

78% of the 50 i equal 0.78 x 50 = 39

Macy has completed 39 questions

Answer:

follow me please and give thanks

[tex]2 \sqrt{13} [/tex]

that is your answer

Answer:

16

Step-by-step explanation:

[tex](\frac{2}{3} )*24=16[/tex]

Answer:

1.2 to 10 o->

2.8 to -10 <- with fully bubbled o

Answer:

I can not see the question

Step-by-step explanation:

Please post the question with the picture on your profile so I can attempt it

Answer:

180% is equivalent to the decimal 1.8

Answer:

answer is 1.8 hope it helps

Answer:

10 square units

Step-by-step explanation:

Base of triangle (b) = 4 units

Height of triangle (h) = 5 units

Therefore,

Area of triangle

[tex] = \frac{1}{2} bh \\ \\ = \frac{1}{2} \times 4 \times 5 \\ \\ = 2 \times 5 \\ \\ = 10 \: {units}^{2} [/tex]

Answer:

18

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We will solve this inequality by dividing both sides by -9.

Remember, whenever you multiply or divide both sides by a negative number, the sign must be switched.

So we get:

[tex]w>6[/tex]

The only answer that has possible solutions that are greater than 6 is A.