Solve the system using substitution. Show your work and give your answers as an ordered pair.​

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:

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 =

= (4x - 5)²

= 16x² - 40x + 25

Answer:

josh

rabeesh

ronger

roger

roge

robert

Step-by-step explanation:

Answer:

1.2 to 10 o->

2.8 to -10 <- with fully bubbled o

Answer:

90

Step-by-step explanation:

77degrees is one half of the side if see the line is exactly straight aplogies if i'm wrong

Answer:

10.7%

Step-by-step explanation:

possibility to get a blue marker : 4/15

possibility to get a green marker: 6/15

possibility to get a blue then a green: 24/225

= 10.666666%

= 10.7%

[tex] \frac{95}{100} \times 420 = 399[/tex]

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:

https://brainly.com/question/11487261

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:

what is the question. the equation is invalid.

Answer:

18

Step-by-step explanation:

Answer:

follow me please and give thanks

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.

Answer:

5

Step-by-step explanation:

HOPE IT HELPS YOU .......

Answer:

180% is equivalent to the decimal 1.8

Answer:

answer is 1.8 hope it helps

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]

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

that is your answer

the answer to your question is C

Answer:

3/16 of her garden are red roses

she was not correct, 2/4 is not equal to 3/16

Step-by-step explanation:

3/4 garden are roses

1/4 of those are red  (1/4 of 3/4)

3/4 (1/4) = 3/16 of her garden are red roses

Answer:

Yes she is correct because if you have the 3/4 u still have 1/4 un planted an then she adds the 1/4 an that would make it 2/4.

Step-by-step explanation:

hope this helps

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:

1/3 = 0.3333 = 33.33% experimental probability of rolling a 9​.

Step-by-step explanation:

The experimental probability is given by the number of desired outcomes divided by the number of total outcomes, after a number of experiments is made.

In this question:

Cube rolled 78 times.

9 appeared 26 times

26/78 = 1/3 = 0.3333 = 33.33% experimental probability of rolling a 9​.

Answer:

Good luck Dude

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

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:

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: 360>5.5+36.41d

Step-by-step explanation: