A random sample of 18 adults, chosen from the 1500 adults in the town, took a survey asking their opinion on a recent property tax change. 25% of those who responded said they were in favor of the change. The company running the survey wants to construct a confidence interval estimating the proportion of all adults in the town who support the change. Which of the conditions for inference have been satisfied?

I. Random condition

II. Normal condition

III. 10% condition

A) I

B) II

C) I and III

D) II and III

E) I, II, and III

Answer:

factored is (x+1)(x+5)

Step-by-step explanation:

gradpoint

Step-by-step explanation:

sec(2x) − tan(2x)

Write in terms of sine and cosine:

1/cos(2x) − sin(2x)/cos(2x)

(1 − sin(2x)) / cos(2x)

Use double angle formulas:

[ 1 − 2 tan x / (1 + tan²x) ] / [ (1 − tan²x) / (1 + tan²x) ]

Multiply by reciprocal:

[ 1 − 2 tan x / (1 + tan²x) ] × [ (1 + tan²x) / (1 − tan²x) ]

Distribute 1 + tan²x:

(1 + tan²x − 2 tan x) / (1 − tan²x)

Factor:

(1 − tan x)² / ((1 − tan x) (1 + tan x))

Simplify:

(1 − tan x) / (1 + tan x)

Rewrite using 1 = tan(45°):

(tan(45°) − tan x) / (tan(45°) + tan x)

Use angle difference formula:

tan(45° − x)

Answer:

(5+7x)^2

Step-by-step explanation:

25+70x+49x^2

This is a perfect square trinomial

a^2 +2ab + b^2 = (a+b)^2

5^2 *2*5*7x+ (7x)^2 = (5+7x)^2

Answer:

c=15

Step-by-step explanation:

45=3c,divide

c=15

Answer:

5,10,15,20,25,30,25,40,45,50,55,

Step-by-step explanation:

Answer:

-4, 1

Step-by-step explanation:

A (-4, 1)

reflected over y-axis –> (4, 1)

reflected over x-axis –> (4, -1)

rotated 180º –> (-4, 1)

Answer:

3053.63 cu. inches

Step-by-step explanation

Volume = 4/3 pi r^3

Answer:

[tex]v \: \: ≈

3053.62 {in}^{3}

[/tex]

Step-by-step explanation:

[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times \pi \times {9}^{3} \\ ≈

3053.62806

[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

The multiplication property of 1

Step-by-step explanation:

Any number that multiplied by one gives the number

Answer:

Experimental.

Step-by-step explanation:

It is an independent measure design. Multiple experimental groups are used in an independent measures design, which is a research method and participants are only in one group. Each participant is only in one condition of the independent variable during the experiment.

Answer:

the equation used to determine the number of dimes in his pocket is an "algebraic equation" (3/4)x = 5.25

and the value of x = 7

Step-by-step explanation:

We are being told that:

Alex has 3 more quarters than dimes in his pocket, for a total of $5.25.

Let the value for the dimes in his pocket be x:

So he has 3 more quaters than x

We know that a quarter is 1/4

3 more quaters than x = (3/4) x

(3/4)x = 5.25

3x = 5.25 * 4

3x = 21

x = 21/3

x = 7

Thus, the equation used to determine the number of dimes in his pocket is an "algebraic equation" (3/4)x = 5.25

and the value of x = 7

Answer:

Step-by-step explanation:

Answer:

x = 9  or  x = -9

Step-by-step explanation:

x² - 4 = 77

then

x² - 4 + 4 = 77 + 4

then

x²  = 81

then

x² - 81 = 0

then

x² - 9² = 0

then

(x - 9)(x + 9) = 0

then

x - 9 = 0  or  x + 9 = 0

then

x = 9  or  x = -9

__________________________

:)

Answer:

Nancy's ambient locality might be having more suppliers, higher supply of Gasoline

Step-by-step explanation:

National average price of gasoline = $3.14

Stations near Nancy's home have an average price = $2.95

Gasoline price near Nancy's house is lesser than national average price level. Number of gasoline stations near her house might be more. It implies increase in its supply. This leads to competition among sellers & reduces the price level.

Step 1

Find the rate change at which the crickets are chirping.

Step 2

Find the function

Answer:

25%

Step-by-step explanation:

50% x 50%

Answer:

A. 1/5

Step-by-step explanation:

got on edge

Answer:

its true

Step-by-step explanation:

The answer is [tex]y^{4+6}[/tex] = [tex]y^{10}[/tex]

Answer:quadratic formula

Step-by-step explanation:

Answer:

Completing the square.

Step-by-step explanation:

x^2-8x+(-4)^2=22 can be rewritten as (x-4)^2=22. therefore, the best method would be completing the square.

Answer:

Given:

n = 1003

[tex] p' = \frac{462}{1003} = 0.4606 [/tex]

q = 1 - 0.4606 = 0.5394

a) The sample size and count.

Here the sample size is the number that took part in the poll. It is denoted as n = 1003.

The count is the number that answered yes. Count = 462

b) The sample proportion.

The formula for sample proportion is: [tex] p' = \frac{x}{n} [/tex]

Therefore, sample proportion =

[tex] p' = \frac{462}{1003} = 0.4606 [/tex]

c) The relationship between population proportion and sample proportion.

Since the sample size is greater than 30 (n>30), the sample size is large. Hence, for a large sample, the population proportion is approximately equal to the sample proportion.

This means the population proportion, p = 0.4606

Answer:

A) Sample size n=1003

Count x=462

B) Sample proportion p=0.46

C) The population proportion can be estimated with a confidence interval, with the information given by the sample proportion.

The 95% confidence interval for the population proportion is (0.429, 0.491).

Step-by-step explanation:

A) The sample size include all the adult that answer the poll. The sample size is then n=1003.

The count is the number of adults that answer Yes in this case. The count is x=462.

B) The sample proportion can be calculated dividing the count by the sample size:

[tex]p=\dfrac{x}{n}=\dfrac{462}{1003}=0.46[/tex]

C) The population proportion is not known. It can only be estimated with the information given by samples of that population. The statistical inference is the tool by which the sample information can be used to estimate the population characteristics.

With the sample proportion p we can estimate a confidence interval for the population proportion.

We can calculate a 95% confidence interval.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.46*0.54}{1003}}\\\\\\ \sigma_p=\sqrt{0.00025}=0.0157[/tex]

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0157=0.031[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.46-0.031=0.429\\\\UL=p+z \cdot \sigma_p = 0.46+0.031=0.491[/tex]

The 95% confidence interval for the population proportion is (0.429, 0.491).

We have 95% that the population proportion is within this interval

Answer:

90%

Step-by-step explanation:

100%=120 pupils

           108pupils

 108 x 100= 10800/120=90 %

Answer:

[tex]8+i[/tex]

Step-by-step explanation:

We are given that an expression

[tex]6i^4+6i^3-2i^2+\sqrt{-49}[/tex]

We have to rewrite in the form of a+bi

[tex]6(i^2)^2+6i^3-2i^2+\sqrt{-49}[/tex]

We know that

[tex]i^2=-1[/tex]

[tex]i^3=-i[/tex]

[tex]\sqrt{-1}=i[/tex]

Using the identity

Then, we get

[tex]6-6i-2(-1)+7i[/tex]

[tex](6+2)+(7-6)i[/tex]

[tex]8+i[/tex]

This is required form of a+ib

Answer:

83.9357% increase for the buyer

Step-by-step explanation:

Answer:

Option 3.

Step-by-step explanation:

Let T=Total, B=Brother and S=Sister. By using given diagram, we get

[tex]n(B)=28+68=96[/tex]

[tex]n(S)=82+68=150[/tex]

[tex]n(T)=28+68+82+52=230[/tex]

[tex]n(B\cap S)=68[/tex]

Using this information, we get

[tex]P(B)=\dfrac{n(B)}{n(T)}=\dfrac{96}{230}\approx 0.42[/tex]

[tex]P(S)=\dfrac{n(S)}{n(T)}=\dfrac{150}{230}\approx 0.65[/tex]

[tex]P(S|B)=\dfrac{P(B\cap S)}{P(B)}=\dfrac{n(B\cap S)}{n(B)}=\dfrac{68}{96}\approx 0.71[/tex]

[tex]P(B|S)=\dfrac{P(B\cap S)}{P(S)}=\dfrac{n(B\cap S)}{n(S)}=\dfrac{68}{150}\approx 0.45[/tex]

The probability P(S|B) has the largest value.

Therefore, the correct option is 3.

Answer:5 and 4

Step-by-step explanation:

5*4=20

5+4=9 which is a square number

Answer:

P(either almond or cashew) = ⅔

Step-by-step explanation:

We are told that the bag contains a mixture of almonds walnuts and cashews of equal number.

Since the 3 nuts are equal in number, they will have a ratio of 1:1:1.

So, when a nut is chosen randomly,

Probability of choosing almond = 1/3

Probability of choosing cashew = 1/3

Thus,

Probability of choosing either almond or cashew in a random selection will be the sum of their individual probability.

So,

P(either almond or cashew) = ⅓ + ⅓ = ⅔

Answer:

Step-by-step explanation:

Hello!

For this study adult subjects were randomly assigned to three different exercise treatments establishing three different groups:

Group 1: Single long exercise period five days per week

Group 2: Several 10' exercise periods five days per week

Group 3: Several 10' exercise periods five days per week using a home treadmill

All subjects were weighed before and after 6 months of training and their weight loss was determined.

The objective of this study is to determine if there is any difference between the treatments, meaning, if the weight loss is the same regarding the type of exercise or if the type of exercise has some influence over it.

To test this you have to conduct an ANOVA, with the hypothesis:

H₀: μ₁= μ₂= μ₃

H₁: At least one μi differs from the others. ∀ i=1, 2, 3

α: 0.05

The statistic is:

[tex]F= \frac{MS_{Tr}}{MS_{Er}} ~~F_{k-1; n-k}[/tex]

Normally it is better to have the raw data to conduct the analysis using statistical software, but it is not impossible to calculate the statistic using the descriptive statistics for each group.

As you know the statistic is calculated as the ratio between the mean square of the treatments (between groups) and the mean squares of errors.

Each means square is calculated as the sum of squares by the degrees of freedom of the category: SS/Df

So first you need to determine the SS and Df of treatments and errors, then the MS and finally the value of F.

Treatments:

> The degrees of freedom between treatments are k-1 (k represents the number of treatments):

DfTr: 3-1= 2

>The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean is the mean that results of all the groups together.

So the Sum of squares of treatments (SSTr) is the sum of the square of the difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ k = (10.2+9.3+10.2)/3= 29.7/3= 9.9

SSTr= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (10.2 - 9.9)² + (9.3 - 9.9)² + (10.2 - 9.9)²= 0.54

> The Means Squares is:

MSTr= SSTr/DFTr= 0.54/2= 0.27

Errors

>Degrees of freedom of error DfEr= N-k Where N is the total of observations of the experiment (N= n₁+n₂+n₃) and k is the number of treatments.

DfEr= N-k= 30-3= 27

>The mean square error (MSEr) is the estimation of the variance error (σ[tex]_{e}^2[/tex] → S[tex]_{e}^2[/tex]), you have to use the following formula:

[tex]S_{e}^2= \frac{(n_1-1)S^2_1+(n_2-1)S_2^2+(n_3-1)S^2_3}{N-k}= \frac{(9*17.64)+(9*20.25)+(9*27.04)}{27}= \frac{584.37}{27}= 21.643[/tex]

Finally you calculate the statistic:

[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Er}}= \frac{0.27}{21.643}= 0.012[/tex]

This test is One-tailed right, meaning that you'll reject to high values of the statistic and there is one critical value:

[tex]F_{k-1;N-k;1-\alpha }= F_{2;27;0.95}= 3.35[/tex]

Using the critical value approach, the decision rule is:

If [tex]F_{H_0}[/tex] ≥ 3.35, reject the null hypothesis.

If [tex]F_{H_0}[/tex] < 3.35, do not reject the null hypothesis.

The calculated value is less than the critical value, the decision is to not reject the null hypothesis.

So at a 5% significance level, there is not enough evidence to conclude that the treatments influence significantly in weight loss. The population mean weight loss is the same for the treatments "Single long exercise period five days per week", "Several 10' exercise periods five days per week" and "Several 10' exercise periods five days per week using a home treadmill"

I hope this helps!

Answer:

It is 18

Step-by-step explanation:

Hope this helps have a wonderful day

The possible outcomes of ordering be 18.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Drink = 3 choice

Entree= 3 choices

Dessert = 2 choice

So, Using tree method

drink              1                                      2                            3

Entree         1      2      3                   1      2      3                 1      2     3  

Dessert    1  2   1  2   1  2              1  2  1  2  1  2              1  2  1  2  1  2

So, the possible outcomes of ordering be 18.

Learn more about combination here:

https://brainly.com/question/26852614

#SPJ2

Answer:

The volume of the cup is of 142.2 cubic centimeters.

Step-by-step explanation:

The cone volume is given by the following equation:

[tex]V = \frac{\pi r^{2}h}{3}[/tex]

In which r is the radius, which is half the diameter, and h is the height.

In this question:

Dimensions in cm, so the volume will be in cubic centimers.

Height of 10 cm, so [tex]h = 10[/tex]

Diameter of [tex]7 + \frac{3}{8} = \frac{7*8 + 3}{8} = \frac{59}{8} = 7.375[/tex]

So the radius is [tex]r = \frac{7.375}{2} = 3.6875[/tex]

Volume of the cup:

[tex]V = \frac{\pi*(3.6875)^{2}*10}{3} = 142.4[/tex]

The volume of the cup is of 142.2 cubic centimeters.

Answer:

1/18

Step-by-step explanation:

There are 36 different possible combinations. There are only two ways of rolling a sum of 11.

2/36 = 1/18

Answer:

A. 2/300=1/150

B.1/315,000

Step-by-step explanation:

B. 1/150*2100=1/315000