statement and reason

Step-by-step explanation:

It is a square so all of the sides are = 3

Pythagorean theorem....looking for hypotenuse of right triangle with both  legs = 3 units

hypotenuse^2 = 3^2 + 3^2

hypot ^2 = 18

hypot = BD = sqrt (18) = 3 sqrt 2  = 4.24 UNITS

We can say with 95% confidence that the proportion of students in the school who prefer math is between 0.504 and 0.696.

What is Confidence Interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter, such as a mean or proportion.

To find a confidence interval for a population proportion, you can use the following formula:

CI = p ± z*(√(p*q/n))

Where:

CI represents the confidence interval

p is the sample proportion

q is the complement of the sample proportion (q = 1 - p)

n is the sample size

z is the z-score associated with the desired level of confidence

The z-score is determined based on the desired level of confidence and can be found in a standard normal distribution table or calculated using statistical software. For example, if you want a 95% confidence interval, the z-score would be 1.96.

It's important to note that this formula should only be used if the number of successes np' and the number of failures nq' are both greater than 5. If this condition is not met, the normal approximation may not be accurate and other methods should be used.

To use this formula, you would follow these steps:

Calculate the sample proportion (p) by dividing the number of successes by the sample size.

Calculate q by subtracting p from 1 (q = 1 - p).

Determine the z-score based on the desired level of confidence.

Calculate the confidence interval using the formula above.

For example, let's say you want to find a 95% confidence interval for the proportion of students in a school who prefer math over other subjects. You survey a random sample of 100 students and find that 60 prefer math.

Calculate the sample proportion: p = 60/100 = 0.6

Calculate q: q = 1 - 0.6 = 0.4

Determine the z-score for a 95% confidence interval: z = 1.96

Calculate the confidence interval: CI = 0.6 ± 1.96*(√(0.6*0.4/100)) = (0.504, 0.696)

Therefore, we can say with 95% confidence that the proportion of students in the school who prefer math is between 0.504 and 0.696.

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The correct statement is: The confidence interval does not contradict the statement because 0.75 is in the interval.

What is an Interval?

A collection of real numbers known as an interval in mathematics is defined by two values: a lower bound and an upper bound. The lower and upper boundaries themselves, as well as all the numbers between them, are included in the interval.

In statistical hypothesis testing, a confidence interval is a range of values ​​within which the true population parameter is estimated to lie with a certain level of confidence. In this case, a local newspaper conducted a study and obtained a 90% confidence interval (0.4332, 0.6168) for the proportion of the community supporting the proposed park expansion.

Since the politician's claim is that 75% of the community supports expanding the park, we can interpret this as saying that the true proportion lies at 0.75.

To determine whether a confidence interval supports or refutes a claim, we need to check whether the claimed proportion of 0.75 falls within the interval. In this case, 0.75 is within the range of the confidence interval (0.4332, 0.6168).

So we can conclude that the confidence interval does not contradict the statement of the politician because the value of 0.75 is inside the interval. This means that there is a high probability that the true proportion of the community supporting the expansion of the park falls within the range set by the confidence interval.

However, it should be noted that the interval does not provide conclusive evidence for the claim because it is not a point estimate, but rather a range of values ​​within which the true proportion is estimated to lie with a 90% confidence level.

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Answer:

1/2

Step-by-step explanation:

The diameter of the headlight's opening is 4 inches.

To find the diameter of the headlight's opening, we need to determine the distance between the two points on the paraboloid where the depth is 2 inches.

Using the formula for the paraboloid of revolution, we know that the equation for the shape of the headlight is:
\(y^2 = 4px\)

where p is the distance from the vertex to the focus. In this case, p = 1 inch.

To find the distance between two points on the paraboloid where the depth is 2 inches, we can set y = ±2 and solve for x:

\(4p^2 = 4x(\pm2)\\x = p^2/\pm1\)

Since we're interested in the distance between two points, we can subtract the two x-values:

\(x^2 - x^1 = p^{2/1} - p^{2/-1}\\x^2 - x^1 = 2p^2\)
Substituting in the value of p, we get:

x2 - x1 = 2(1^2) = 2

So the distance between the two points where the depth is 2 inches is 2 inches.

To find the diameter of the headlight's opening, we need to double this distance and then multiply by the focal length:

d = 2(2)(1) = 4 inches

Therefore, the diameter of the headlight's opening is 4 inches.

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The equation of the line in Slope-intercept form is y = -3x - 3.

The equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to solve for y.

Starting with the given equation:

9x + 3y = -9

We can isolate y by subtracting 9x from both sides:

3y = -9x - 9

Now we can simplify the equation by dividing both sides by 3:

y = (-9/3)x - 3

Simplifying the fraction, we get:

y = -3x - 3

Therefore, the equation of the line in slope-intercept form is y = -3x - 3.

The slope of the line is -3, which means that for every 1 unit increase in x, y decreases by 3 units. The y-intercept is -3, which means that the line crosses the y-axis at the point (0, -3).

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Answer:

The solution is n=1

Step-by-step explanation:

I hope you mean

4/5n-3/5=1/5n

if so then here's the solution

5n×4/5n-3/5×5n=1/5n×5n

4-3n=1

4-1=3n

3n=3

n=1

Answer:44

Step-by-step explanation:

Answer:

16 boys

Step-by-step explanation:

4/5 = ?/20 , multiply 20 and 4 then divide by 5

The value of 1/8 inches to 1 foot is,

⇒ 0.10375 foot

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

To find the value of 1/8 inches to 1 foot.

Since, We know that;

1 inch = 0.083 foot

Hence,

1/8 inches = 1/8 x 0.083

                = 0.10375 foot

Thus, The value of 1/8 inches to 1 foot is,

⇒ 0.10375 foot

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Step-by-step explanation:

8) Consider,

\( \frac{1}{1 + \sin(x) } \)

Multiplying And Dividing By 1-sinx

\( \frac{1}{1 + \sin(x) } \times \frac{1 - \sin(x) }{1 - \sin(x) } \)

\( \frac{1 - \sin(x) }{(1 + \sin(x) )(1 - \sin(x)) } \)

We know (a+b)(a-b)=a²-b²

\( \frac{1 - \sin(x) }{1 - \sin ^{2} (x) } \)

We know that sin²x+cos²x=1

cos²x=1-sin²x,

uisng this we get,

\( \frac{1 - \sin(x) }{ \cos ^{2} (x) } \)

\( \frac{1}{ \cos ^{2} (x) } - \frac{ \sin(x) }{cos ^{2} (x)} \)

We know that 1/cosx=secx and sinx/cosx=tanx

Using this we get,

\( \sec {}^{2} (x) - \frac{ \tan(x) }{ \cos(x) } \)

Hence Proved

The number of different arrangements that can be formed is 7920

From the question, we have the following parameters that can be used in our computation:

Pictures = 11

Arranged pictures = 6

These can be represented as

n = 11 and r = 6

The number of different arrangements that can be formed is

Number = nPr

So, we have

Number = 11P4

Evaluate

Number = 7920

Hence, the arrangements are 7920

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Answer:

1+1= 2

Step-by-step explanation:

or sometimes people say 11, but irl its 2

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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The power series you provided is Σ(22kx). To determine the radius of convergence (R), we can apply the Ratio Test. The Ratio Test states that if the limit as k approaches infinity of the absolute value of (a_(k+1)/a_k) exists, then the series converges. In this case, a_k = 22kx.

Now, let's find the limit:

lim (k→∞) |(22^(k+1)x) / (22^kx)|

We can rewrite this as:

lim (k→∞) |22x|

Since there's no k term remaining in the limit, the limit is dependent on x. Therefore, the series converges for all x. This means that the radius of convergence R is infinite.

To determine the interval of convergence, we can observe that the series converges for all x values due to the infinite radius of convergence. Therefore, the interval of convergence is (-∞, +∞). In summary, the radius of convergence R is infinite, and the interval of convergence is (-∞, +∞).

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A right pyramid with an equilateral triangular base has a lateral face with a surface area of 75 square meters. The side of the base of a slant with a height of 30 meters is 5 meters long.

Let’s call the side length of the equilateral triangular base “s”. We know that the area of one lateral face is 75 square meters, and that face is a triangle with base s and height 30 meters (the slant height). We can use the formula for the area of a triangle to solve for s:

Area = (1/2) * base * height

75 = (1/2) * s * 30

Simplifying the equation, we get:

75 = 15s

s = 75/15

s = 5

Therefore, the length of the side of the equilateral triangular base is 5 meters.

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Answer:

9 people

Step-by-step explanation:

100-50(flat fee)=50 left over for people.

50/5.50=9.090909 however, you can't have .0909 people, so the max is 9

Answer:

sorry

Step-by-step explanation:

Answer:

[0,-infinity[

Step-by-step explanation:

you look on the starting point and the ending point of the y-axis (♾ is always opened [ )

Answer:

10

Step-by-step explanation:

d =√[(-3+9)²+(6+2)²]

= √(6²+8²)

=√(36+64)

=√100

= 10

Answer:

\(\boxed {\boxed {\sf d=10}}\)

Step-by-step explanation:

The distance between two points can be calculated using the following formula.

\(d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

In this formula, (x₁, y₁) and (x₂, y₂) are the two points. We are given the points (-9, -2) and (-3,6). If we match the value with the corresponding variable we see that:

Substitute the values into the formula.

\(d= \sqrt {(-3 - -9)^2 + (6 - -2)^2\)

Solve inside the parentheses. Remember that 2 back to back negative signs become a plus sign.

\(d= \sqrt{ (6)^2 + (8)^2\)

Solve the exponents. Multiply the number by itself.

\(d= \sqrt{(36)+(64)\)

Add.

\(d= \sqrt{100\)

Take the square root of the number.

\(d= 10\)

The distance between the points (-9, -2) and (-3, 6) is 10.

Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

Answer:

y = 6

Step-by-step explanation:

Answer:

i helped

Step-by-step explanation:

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Answer:

Vertical stretch by a factor of 8

Answer:

send the graph and ill solve it

Step-by-step explanation:

The optimal solution for the primal LP is x1 = 0, x2 = 2, x3 = 2, with a maximum value of z = 16.

Let's start by writing down the dual LP. The dual LP is obtained by interchanging the roles of variables and constraints in the primal LP. The dual variables corresponding to the constraints are y1 and y2, representing the multipliers for the first and second constraint, respectively. The objective function of the dual LP is given by minimizing 4y1 + 9y2, and the dual LP subject to the dual constraints is as follows:

min 4y1 + 9y2 subject to:

2y1 + y2 ≥ 4

3y1 + 3y2 ≥ 3

y1, y2 ≥ 0

To graphically solve the dual LP, we can plot the feasible region defined by the dual constraints and find the point that minimizes the objective function. By solving the dual LP, we obtain y1 = 1/3 and y2 = 2/3, with a minimum value of 10/3. Now, using the complementary slackness conditions, we can find the set of optimal solutions for the primal LP. The conditions state that for any optimal solution, the product of the primal constraint and the dual variable must be zero. Since the primal constraints are inequalities, we consider them as equalities to check the conditions. For the first constraint, 2x1 + 2x2 + x3 = 4, we have y1(2x1 + 2x2 + x3 - 4) = 0, which gives y1 = 0. Similarly, for the second constraint, x1 + 3x2 + x3 = 9, we have y2(x1 + 3x2 + x3 - 9) = 0, which gives y2 = 0. Hence, the optimal solution for the primal LP is x1 = 0, x2 = 2, x3 = 2, with a maximum value of z = 16, satisfying the complementary slackness conditions.

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