In a survey of 3475 ​adults, 1440 say they have started paying bills online in the last year. Construct a​ 99% confidence interval for the population proportion. Interpret the results. A​ 99% confidence interval for the population proportion is ( ), ( ). ​(Round to three decimal places as​ needed.) Interpret your results. Choose the correct answer below.

a. With​ 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
b. With​ 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Given:

Radius = 9 ft

Height = 52 ft

Volume of cylindrical (silo) is:

Nearst whole number is 13226

Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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the  parallelogram JKLM is a square.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

JM = -5² = 25

KL =  -5² = 25

JK = -4²=16

LM =-4²=16

So, the parallelogram JKLM is a square.

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Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To determine whether Atul's allowance is above or below the average, we need to calculate the average allowance for all the friends, including Atul.

To do his, we add up all the amounts and divide by the total number of friends:

Average allowance = (120+180+100+50+250+200+200+220+150+100+100+150+130+200+180+100+150+100+180+150+120+150+100+150+100+120+180+200+50) / 29

Average allowance = 162.07

So, the average allowance for Atul's friends, including himself, is Rs. 162.07 per day.

Since Atul's allowance is Rs. 120 per day, we can see that his allowance is actually less than the average.

Therefore, Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

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By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

c is correct

Step-by-step explanation:

The equation that represents this fraction is 1 ÷ 6 =1/6. Therefore, option C is the correct answer.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, a cake is cut into 6 equal-sized pieces. Each piece is one sixth of the whole.

The equation is 1 ÷ 6 =1/6

Therefore, option C is the correct answer.

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Solution :

If \(S_n\) is the total spending generated after n transactions, then \(a_n\) is the spending generated during the n-th transaction. Since the government spends D dollars, then \(a_1\) = D.

Then the second person will receive D dollars and spend \(D_c\) dollars. Therefore, \(a_2=D_c\). The next person will receive \(D_c\) dollars, which means they are spending \(a_3 = (D_c)c = Dc^2\) dollars. Therefore,

\(a_1 = D\)

\(a_2=D_c\)

\(a_3 = Dc^2\)

\(a_4 = (Dc^2)c= Dc^3\)

....

\(a_n=Dc^{n-1}\)

∴ \(S_n=a_1+a_2+a_3+....+a_n\)

  \(S_n = D+Dc+Dc^2+Dc^3+...+Dc^{n-1}\)

  \(S_n= D(1+c+c^2+...+c^{n-1})\)

  \(S-n=D . \frac{1-c^n}{1-c}\)

The angles are 42⁰ and 138⁰.

Alternate interior angles lie on the interior side of the parallel lines and are on the opposite side of the transversal.

Here, the given alternate interior angles are:

        (x+1)⁰ and (4x - 26)⁰

Sum of alternate interior angle is 180⁰.

     (x+1)⁰ + (4x - 26)⁰ = 180⁰

       x + 1 + 4x - 26 = 180

        5x - 25 = 180

         5x = 180 + 25

          5x = 205

           x = 205 / 5

          x = 41

then, (x+1)⁰ = (41+1)⁰ = 42⁰

and  (4x-26)⁰ = (4 X 41 - 26)⁰

                      = (164 - 26)⁰

                      = 138⁰

Thus, the angles are 42⁰ and 138⁰.

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Answer:

D and B

Step-by-step explanation:

The solution to 3+10p=5 is 0.20. The equation 10p=2 is just the equation after subtracting 3 from 5, and it also comes out as 0.20. I hope this helps!

The solution to 3+10p=5 is 0.20. The equation 10p=2 is just the equation Therefore, D and B are the correct option.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree

Jaime bought a notebook and a box of pencils for $5.00.

The notebook cost $3.00 and there are 10 pencils in a box.

The equation 3+10p=5 can be used to find the cost of one pencil. S

Let's represent notebooks with "N" and pencils with "P".

Then,

3+10p = 5

10 p = 5- 3

10 p = 2

Since 10p=2, we can substitute that directly into the equation:

p = 0.20

Therefore, D and B are the correct option.

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The numeric values of the function modeled by the proportional relationship d = 200t are given as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

d = 200t.

Hence the numeric values of the function are given as follows:

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Answer:

t = 1.2, -1.2

Answer: s squared.s2.sigma i think

Step-by-step explanation:

Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

Slope = 3

Step-by-step explanation:

The slope is m in the picture.

Answer:  

The slope is 3

Step-by-step explanation:

we use the equation :  \(m=\frac{y2 - y1}{x2 - x1} = \frac{?}{?} =(simplify)\frac{?}{?}\)   to find the slope so when we use the equation it should look like this:   \(m=\frac{8-2}{(-2)-(-4)} =\frac{6}{2} =(simplify) 3\)

Based on the given parameters, the length of c is 8.0 units

The given parameters are

Angle c = 76 degrees

Side a = 20

Side b = 13

The length of c is then calculated using the following law of sines

c^2 = a^2 + b^2 - 2absin(C)

Substitute the known values in the above equation

So, we have

c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)

Express 20^2 as 400

c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)

Express 13^2 as 169

c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)

Evaluate the product and sin(76)

c^2 = 400 + 169 - 520 * 0.9703

Evaluate the product

c^2 = 400 + 169 - 504.55

Evaluate the exponents

c^2 = 400 + 169 - 504.55

So, we have

c^2 = 64.45

Evaluate the square root

c = 8.0

Hence, the length of c is 8.0 units

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In order to have a linear equation, you have to write an equation like

\(y=mx+q\)

The sequence has to start with 3, so we must choose \(q=3\), because this guarantees that when \(x=0\) we have

\(y=0\cdot m + 3 =3\)

Now, \(m\) must be even. In fact, if \(m\) is even, \(mx\) will always be even for every possible \(x\), and \(mx+3\) will be odd.

So, for example, you might choose

\(y=2x+3\)

Which will produce the following sequence:

\(\begin{array}{c|c}x&f(x)\\0&3\\1&5\\2&7\\3&9\end{array}\)

and so on

(∀x)P(x) can be written as p ∧ q, (Ǝx)P(x) can be written as ¬p ∨ ¬q, and the universal and existential negation rules of predicate logic correspond to the DeMorgan's law of propositional logic, which states that ¬(p ∨ q) = ¬p ∧ ¬q.

a) The statement (∀x)P(x) states that P(x) is true for all x in the domain, which consists of just 0 and 1. So, if P(0) is true, represented by p, and P(1) is true, represented by q, then (∀x)P(x) is true. Therefore, (∀x)P(x) can be written as p ∧ q.

b) The statement (Ǝx)P(x) states that P(x) is true for at least one x in the domain, which consists of just 0 and 1. So, if either P(0) is true, represented by p, or P(1) is true, represented by q, then (Ǝx)P(x) is true. Therefore, (Ǝx)P(x) can be written as p ∨ q.

c) The negation of (∀x)P(x), represented as ¬(∀x)P(x), is equivalent to the negation of (∀x)P(x) in predicate logic, represented as (Ǝx)¬P(x). This corresponds to DeMorgan's law of propositional logic, which states that ¬(p ∧ q) = ¬p ∨ ¬q.

Similarly, the negation of (Ǝx)P(x), represented as ¬(Ǝx)P(x), is equivalent to the negation of (Ǝx)P(x) in predicate logic, represented as (∀x)¬P(x). This corresponds to DeMorgan's law of propositional logic, which states that ¬(p ∨ q) = ¬p ∧ ¬q.

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Answer:

The value is  \(E(X) = 4 \ days\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 36^oC\)

    The standard deviation \(\sigma = 3^oC\)

Generally the probability that in June , the midday  temperature is between  

39°C and 42°C is mathematically represented as

      \(P(39 < X < 42) = P(\frac{39 - 36}{3} < \frac{X - \mu }{\sigma} < (\frac{42 - 36}{3} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

      \(P(39 < X < 42) = P(1 < Z <2 )\)

=>   \(P(39 < X < 42) = P(Z < 2) - P( Z <1 )\)

From the z table  the area under the normal curve to the left corresponding to  1 and  2  is

     P(Z   < 2)  = 0.97725

and

    P(Z   < 1)  = 0.84134

    \(P(39 < X < 42) = 0.97725 - 0.84134\)

=>  \(P(39 < X < 42) = 0.13591\)

Generally number of days in June would you expect the midday temperature to be between 39°C and 42°C

      \(E(X) = n * P(39 < X 42 )\)

Here n is the number of days in June which is  n = 30

       \(E(X) = 30 * 0.13591\)

=>    \(E(X) = 4 \ days\)

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

6

Step-by-step explanation:

Answer:

Use the A = p(1 + r/100)^t.  A is the amount after appreciation, p is the principal or starting value, r is the interest rate, and t is the time in years.

Step-by-step explanation:

Answer: -59

Step-by-step explanation: https://byjus.com/discriminant-calculator/

The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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Answer:

10. x ≈ 15,9

11. x ≈ 17,5

Step-by-step explanation:

10. Use the Pythagorean theorem:

\( {x}^{2} = {17}^{2} - {6}^{2} = 289 - 36 = 253\)

\(x > 0\)

\(x = \sqrt{253} ≈15.9\)

11.

\( {x}^{2} = {9}^{2} + {15}^{2} = 81 + 225 = 306\)

\(x > 0\)

\(x = \sqrt{306} ≈17.5\)

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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