Questio
Use the square roots property to solve the quadratic equation (6d + 1)2 + 12 = 13. If there are multiple answers, list
them separated by a comma, e.g. 1, 2. If there is no solution, enter Ø.​

Answer:

[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]    

[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]    

Step-by-step explanation:

Information given

90 34 41 106 84 53 55 48 41 75 49 97 92 73 74 80 94 102 56 83

In order to calculate the mean and the sample deviation we can use the following formulas:  

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

[tex]\bar X=71.35[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s=22.48 represent the sample standard deviation

n=20 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=20-1=19[/tex]

Since the Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.093[/tex]

And replacing we got:

[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]    

[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]    

Answer:

a) 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance = (0.498, 0.547)

This means we are 95% confident that the true proportion all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is within the range 49.8% and 54.7%.

b) The confidence interval from part (a) is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B because the interval obtained contains proportions that are greater than 50% indicating that there is significant evidence that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is more than half of the total population.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (820/1570) = 0.5223

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 95% confidence interval for sample size of 1570 is obtained from the z-tables.

Critical value = 1.960

Standard error of the mean = σₓ = √[p(1-p)/n]

p = sample proportion = 0.5223

n = sample size = 1570

σₓ = √(0.5223×0.4777/1570) = 0.0126063049 = 0.01261

95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.5223 ± (1.96 × 0.01261)

CI = 0.5223 ± 0.02471

95% CI = (0.4975916424, 0.5470083576)

95% Confidence interval = (0.4976, 0.5470)

We are 95% confident that the true proportion all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is within the range 49.8% and 54.7%.

b) The confidence interval from part (a) is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B because the interval obtained contains proportions that are greater than 50% indicating that there is significant evidence that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is more than half of the total population.

Hope this Helps!!!!

Answer:

Nothing can be further done to this equation. It has been simplified all the way.

Answer:

Should not be rejected.

Step-by-step explanation:

Answer:

[tex] \boxed{\sf Final \ velocity \ (v) = 26 \ m/s} [/tex]

Given:

[tex] \sf v = v_{0} + at[/tex]

[tex]\sf Initial \ velocity \ (v_{0}) = 20 \ m/s \\ \sf Acceleration \ (a) = 1.5 \ m/s^{2} \\ \sf Time \ (t) = 4 \ sec[/tex]

To Find:

Final velocity (v)

Step-by-step explanation:

[tex]\sf Substituting \ value \ of \ Initial \ velocity \\ \sf acceleration \ and \ time \ in \ given \ equation: \\ \\ \sf \implies v = v_{0} + at \\ \\ \sf \implies v = 20 + 1.5(4) \\ \\ \sf 1.5 \times 4 = 6 : \\ \sf \implies v = 20 + \boxed{6} \\ \\ \sf 20 + 6 = 26 : \\ \sf \implies v = 26 \: m/s[/tex]

Answer:

The answer is option A

Slope of the line using points

( 2,0) and (0, 3)

Slope = 3 - 0 / 0 - 2 = -3/2

Hope this helps

Start at the y-intercept of 3 on the coordinate system.

Remember, when choosing points, chose clear

cut points where the line crosses them.

The next put is on the x-intercept and it's 2.

To get from (0,3) to (2,0), we go down 3 units and run 2 units.

Since our slope is going down, it's negative.

So the slope is -3/2.

Answer:

He served as Assistant Secretary of the Navy under President William McKinley

hope i helped

-lvr

Answer:

The future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Consider the provided information:

It is provided that monthly payment is $175, interest is 7% and time is 11 years.

The formula for the future value of the annuity due is:

Now, substitute P = 175, r = 0.07 and t = 11 in above formula.

Hence, the future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Answer:

a.) 8x + 6y

b.) 4x + 2y

Step-by-step explanation:

Simply add like terms together (x with x and y with y).

Answer:

Function

Step-by-step explanation:

y = 1/3 x - 4

Is a function because for every x, we will get only one value of y.

Answer:

Yes,is a function

We can obtain the points (0,-4)(6,-2)

I hope this help you :)......  

Answer:

25/88

Step-by-step explanation:

25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles

P(red) = number of red/total

          = 25/88

Answer:

Dear user,

Answer to your query is provided below

Probability of choosing a red marble is 0.28 or (25/88)

Step-by-step explanation:

Total number of marbles = 88

Number of red marbles = 25

Probability = 25/88

Answer:

64/95

Step-by-step explanation:

Ok so unsimplified, you get 512 matchsticks to 760 penne pieces.

You can write ratios like 512:760, but since you want simplified, I assume you want a fraction.

Both 512 and 760 can divide by 8, so 512/760 simplifies to 64/95.

Hope this helps!

The ratio of the match sticks to penne pieces is 64:95

The given parameters are:

Express as a ratio

Ratio = Matchsticks : Penne pieces

So, we have:

Ratio = 512 : 760

Simplify the ratio

Ratio = 64 : 95

Hence, the ratio of the match sticks to penne pieces is 64:95

Read more about ratios at:

https://brainly.com/question/2784798

Answer: The distance of the shortest route of return is 400

Step-by-step explanation:

The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

BC² = 320² + 240²

BC² = 160000

BC = √160000

BC = 400

Answer:

The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Step-by-step explanation:

Given first sample size n₁ = 677

First sample proportion

                             [tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]

Given second sample size n₂ = 3377

second sample proportion

                             [tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]

Null Hypothesis : H₀ :  p₁ = p₂.

Alternative Hypothesis : H₁ :  p₁ ≠ p₂.

      Test statistic

                [tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]

where

        [tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]

       P =  0.2036

      Q = 1 - P = 1 - 0.2036 = 0.7964

         [tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]

        Z =  3.775

Critical value ∝=0.05

Z- value = 1.96

The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Answer:

Step-by-step explanation:

Area of the circular zone = [tex]\pi[/tex]r^2

= 3.14 × 40^2 = 3.14 × 1600 = 5024 m^2

Area of the basketball court = l × b

= 30 × 15 = 450 m^2

Area of the trapezium shaped park =  ( 6 + 4 ) 3.5 / 2

= 35/2 = 17.5 m^2

∴ Area left in the circular zone = Area of the circular zone - ( Area of the basketball court + Area of the trapezium shaped park )

= 5024 - ( 450 + 17.5 )

= 5024 - 467.5

= 4556.5 m^2

hope this helps

plz mark it as brainliest!!!!!!!

Answer:

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Step-by-step explanation:

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

The success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b)

The formula to compute the expected value is:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]

Compute the expected number of available places when the limousine departs as follows:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

         [tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]

Thus, the expected number of available places when the limousine departs is 0.338.

Answer:

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

The probability would be 40 / 500 = 0.08.

Answer: The number of quarter inches in 23 inches is 4 × 23 = 92

None of the answers given is correct.

Step-by-step explanation:

The ÷ sign means divide.

There are 4 quarter inches in each inch, so you have to multiply 23 × 4

Dividing by 14 makes no sense.

23 ÷ 1/4 = 92 is also an equation that makes sense.

Answer:

P(33) = 0.0826

Step-by-step explanation:

The binomial distribution in this case has parameters n=55 and p=0.55.

The probability that k successes happen with these parameters can be calculated as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]

We have to calculate the probability fo X=33 succesess.

This can be calculated using the formula above as:

[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]

Answer:

216-343

Step-by-step explanation:

the number 312 lies between 125 and 330

Answer:

1/60

Step-by-step explanation:

Since there are 6 possible outcomes for the first event and 10 possible outcomes for the second event, and they are independent of each other, one outcome of the experiment would have a 1/(6*10)=1/60 chance of happening. Hope this helps!

Answer:

3/7 chance

Step-by-step explanation:

There are 3 numbers that are even out of the 7 numbers on the spinner.

This means that there is a 3/7 chance spinning an even number.

Answer:

US

World

Step-by-step explanation:

It depends on where you are. A "trapezium" outside the US is the same as a "trapezoid" in the US, and vice versa.

A trapezium (World; trapezoid in the US) is characterized by exactly one pair of parallel lines. One of the lines that are not parallel may be perpendicular to the parallel lines, but that will only be true for the specific case of a "right" trapezium.

__

A trapezium (US; trapezoid in the World) is characterized by no parallel lines. It may have one angle or opposite angles that are right angles (one or two sets of perpendicular lines), but neither diagonal may bisect the other.

In the US, "trapezium" is rarely used. The term "quadrilateral" is generally applied to a 4-sided figure with no sides parallel.

Answer: Her scores in one game may be 5 points and the other may be 4 points.

Step-by-step explanation:

You may think about dividing the 9 points into two to find how many points she made in each game. But after dividing you will have 4.5 which is not an accurate answer.In a basketball game you can't score have a point but you make whole points.

Answer:

C.

Step-by-step explanation:

The seats are counted by 1 for both tricycles and bicycles, so t + b has to equal 35. The only answer choice that has t + b = 35 is C.

Answer:

n-3

Step-by-step explanation:

Notice that the output is always 3 less than the input

output is input -3

f(n) = n-3

The result will be the probability that 17 or fewer out of the 50 sampled students are bilingual.

To determine the probability that 17 or fewer out of 50 sampled students are bilingual, we can use the binomial probability formula. Let's calculate it step by step:

First, we need to determine the probability of an individual student being bilingual. We can do this by dividing the number of bilingual students by the total number of students:

P(bilingual) = 466 / 1320

Next, we'll use this probability to calculate the probability of having 17 or fewer bilingual students out of a sample of 50. We'll sum up the probabilities for having 0, 1, 2, ..., 17 bilingual students using the binomial probability formula:

P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)

Where:

P(X = k) = (nCk) * (P(bilingual))^k * (1 - P(bilingual))^(n - k)

n = Sample size = 50

k = Number of bilingual students (0, 1, 2, ..., 17)

Now, let's use a calculator to compute these probabilities. Assuming you have access to a scientific calculator, you can follow these steps:

Convert the probability of an individual being bilingual to decimal form: P(bilingual) = 466 / 1320 = 0.353

Calculate the cumulative probabilities for having 0 to 17 bilingual students:

P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)

Using the binomial probability formula, we'll substitute the values:

P(X ≤ 17) = (50C0) * (0.353)^0 * (1 - 0.353)^(50 - 0) + (50C1) * (0.353)^1 * (1 - 0.353)^(50 - 1) + ... + (50C17) * (0.353)^17 * (1 - 0.353)^(50 - 17)

Evaluate this expression using your calculator to get the final probability. Make sure to use the combination (nCr) function on your calculator to calculate the binomial coefficients.

for such more question on probability

https://brainly.com/question/23417919

#SPJ8

Using the central limit theorem, the probability that 17 or fewer of them are bilingual.

The following information is given in the question:

Population size N = 1320

Number of bilingual students = 466

Sample size n = 50

number of bilingual students in the sample = 17

Population proportion:

[tex]P =\frac{466}{1320}[/tex]

P =0.3530

Q= 1-3530

Q = 0.647

Sample proportion:

[tex]p = \frac{17}{50}[/tex]

p = 0.34

q = 1-0.34

q = 0.66

Since,

[tex]X \sim B(n, p)[/tex]

E(x) = np and var(x) = npq

Here, the sample size (50) is large and the probability p is small.

So we can use the central limit theorem, which says that for large n and small p :

[tex]X \sim (nP, nPQ)[/tex]

Where, P =0.3530

nP = 50 x 0.3530 = 17.65

and nPQ = 50x0.3530x0.647 = 11.41

Now, we want to calculate P(X≤17)

[tex]P(X\leq 17) = P(\frac{x-nP}{\sqrt{nPQ}}\leq \frac{17-17.65}{\sqrt{11.41}})[/tex]

[tex]P(X\leq 17) = P(z}\leq \frac{-0.65}{3.78}})[/tex]

[tex]P(X\leq 17) = P(z}\leq -0.172)[/tex]

[tex]P(X\leq 17) = P(z}\geq 0.172)[/tex]

[tex]P(X\leq 17) =1- P(z}\leq 0.172)[/tex]

[tex]P(X\leq 17) =1-0.56[/tex]

[tex]P(X\leq 17) =0.44[/tex]

Hence, the probability that 17 or fewer of the students are bilingual is 0.44.

Learn more about central limit theorem here:

https://brainly.com/question/898534

#SPJ4

Answer:

[tex](x-3)^2=4[/tex]

Step-by-step explanation:

Tara's work is shown below:

[tex]\begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ &&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned}[/tex]

From the equation, we notice that in Step 1, Tara did:

[tex]2(x-3)^2+6=14\\2(x-3)^2=14-6\\2(x-3)^2=8[/tex]

She is trying to isolate the x-variable. Therefore, the next logical step will be to divide both sides by 2 and her Step 2 will therefore be:

[tex]\dfrac{2(x-3)^2}{2} =\dfrac{8}{2} \\\\(x-3)^2=4[/tex]

Tara could have written: [tex](x-3)^2=4[/tex] as her step 2 and we would then have her work as:

[tex]\begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ (x-3)^2&=4&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned}[/tex]

Answer:

Step 2

Step-by-step explanation:

I did the Khan Academy.