Ethan's wallet contains 19 bills totaling to
$114. If Ethan's wallet only contains $20-
bills and $1-bills, how many $20 bills are in
Ethan's wallet?

Systems of linear equations applications

The 95% confidence interval for this population proportion is (0.10,0.23).

sample size n = 125

number of people planned to take an extended vacation = 21

sample proportion (p) = 21/125 = 0.168

Confidence level = 0.95

significance level (α) = 1-0.95 = 0.05

Z score = Z(0.05) = 1.96, from the Z table.

confidence interval for a population proportion is-

p±Zα/2 *[tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.168± 1.96[tex]* \sqrt{\frac{0.168(1-0.168)}{125} }[/tex]

                             = 0.168 ± 1.96*0.334

                             = 0.168 ± 0.0655

                              = (0.1025, 0.2335)

                              = (0.10,0.23)

Hence, the confidence interval is  (0.10,0.23).

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Answer:

20 sides

Step-by-step explanation:

The number of sides of a regular polygon, if each of its interior angles is 162° is 20.

The solution to the product is -18 and the property is negative factors

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

(4)(-0.5)(-3) (-3)

Using the property of negative factors, we have

(4)(-0.5)(3) (3)

Next, we remove the brackets

This gives

4 * -0.5 * 3 * 3

Evaluate the product

-18

Hence, the solution is -18

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The value of side BD of the kite is 12 units

In mathematics, kite is a quadrilateral which has two pairs of congruent adjacent sides.

A kite is a geometric shape which is symmetrical. It has two pairs of congruent adjacent sides, and two pairs of congruent opposite angles. The diagonals of a kite are perpendicular bisectors of each other.

Using Pythagoras theorem:

BC² = CE² + BE²

BE = √(BC² - CE²)

BE = √(10² - 8²) = 6 units

Since ΔCDE is identical to ΔBCE.

Thus, DE = BE

DE = 6 units

Since BD = BE + DE

Thus, BD = 6 + 6 = 12 units

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Answer:

x=6

Step-by-step explanation:

hope this helps you with your question

The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.

The graph of a function is a visual representation of the function's mathematical relationship between inputs and outputs. When a function is said to be "stretched", this means that the graph is being transformed in some way. In this case, the graph of function f is being stretched vertically by a factor of 3 to create the graph of function g. This means that the vertical distance between each point on the graph of function f will be 3 times as great on the graph of function g. For example, if the graph of function f has a point (1,2) then the corresponding point on the graph of function g would be (1, 6). This transformation will change the shape of the graph and the values of the inputs and outputs of the function. The graph of the transformed function g will be wider, taller, and have different values for the inputs and outputs.

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The resulting vector has the same dimensions as the original, 1 x 3.

A rectangular array of numbers, symbols, or expressions set up in rows and columns is known as a matrix. They are employed in a wide variety of mathematical disciplines and contexts, including calculus, statistics, physics, and engineering, as well as linear algebra. Matrices are an essential tool for solving systems of linear equations and representing linear transformations since they may be added, subtracted from, and multiplied by other matrices.

The matrix multiplication of [2 1 0] and [1 -1 2 -1 -2 1 0 1 1] is:

[2 1 0] x [1 -1 2 -1 -2 1 0 1 1] = [2(1) + 1(-1) + 0(2), 2(-1) + 1(-2) + 0(1), 2(0) + 1(1) + 0(1)]

= [2 -3 1]

Therefore, the product of the two matrices is a row vector [2 -3 1], which has the dimensions 1 x 3.

If we subtract 1 from each element of this row vector, we get:

[2 -3 1] - 1 = [1 -4 0]

So, the resulting vector has the same dimensions as the original, 1 x 3.

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{G} is the function of {t} and vice - versa is also true.

Given is a graph as shown in the image.

{ 1 } -

Yes, the given function G{t} is the function of {t}. It is a piecewise function.

{2} -

Let the given function is -

y = G{t}

We can find the inverse as -

t = G⁻¹{y}

Yes, {t] is also the function of {G}.

Therefore, it can be concluded that {G} is the function of {t} and vice - versa is also true.

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The elements of the set A'(B∩C)is  { r, t , v, x, y, z}

It is important to note that the universal set is the set containing all the elements for a given event.

From the information given, we have that;

The signs used to represent sets are;

To determine the set,

A'(B∩C)

A' = { r, t, v, x, z}

B∩C = { y, z}

Now, the set A'(B∩C)

A'(B∩C) = { r, t , v, x, y, z}

Hence, the set is { r, t , v, x, y, z}

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The probabilities are found to be 0.00196 in case- 1  and  

1 / 158753389900  in case - 2.

Note that there are a total of 52 cards in bridge, so by combinations that there are a total of

(13

52)    numbers to deal 13 cards. There are a total of 13 spades, hearts, diamonds and clubs, respectively, so there are

(13

6)   ways to get spades, etc., so that by multiplication principle the probability in we're looking for:

( a )  ( 13      (13      (13      (13

          6)       4)       2)        1)

                      (52

                       13)

      =  1716x715x78x13 / 635013559600

      =  0.00196.

( b)  there are a total of 4 drawings where all 13 cards are are of the same suit, corresponding to a choice of either spades, hearts, diamond, or clubs. Therefore the probability here is given by :

                4 / ( 52       =    4/ 635013559600

                        13)

                                   =    1 / 158753389900 .

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=======================================================

Explanation:

Every triangle has the rule where the inside angles add to 180.

(angle1)+(angle2)+(angle3) = 180

x + (x-4) + (x+16) = 180

3x+12 = 180

3x = 180-12

3x = 168

x = 168/3

x = 56

Then we can determine each angle.

As a check:

angle1+angle2+angle3 = 56+52+72 = 180

This confirms the answer is correct.

A logarithm is an operation used to determine the exponent of a given base number.

What is logarithm?

A logarithm is a mathematical function that describes the relationship between the power to which a number (called the base) must be raised, and the resulting value. The logarithm of a number is the power to which the base must be raised to produce that number.

Start by moving the logarithm to the left-hand side of the equation: log(x²-15) = log(2x)

Next, use the property of logarithms that log(a/b) = log(a) - log(b) to get x²-15 = 2x

then you can simplify the equation by subtracting 2x from both sides x²-2x-15=0

then factor the equation to get (x - 5)(x + 3) = 0

Finally, use the Zero Product Property to solve for x. The solutions will be x = 5 or x = -3

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Answer: The elimination method is a method for solving a system of equations by eliminating one of the variables. One way to do this is to multiply one equation by a constant and then add or subtract it from the other equation to cancel out one of the variables.

We will start by multiplying the first equation by -1:

x + 2y = 4 ----> -x - 2y = -4

Now we will add the second equation to the modified first equation:

-x - 2y = -4

(x + 3y = 10)

0x + 1y = 6

Now we can solve for y:

y = 6

Now that we know y = 6, we can substitute this back into one of the original equations, for example the first one:

x + 2y = 4

x + 2(6) = 4

x = -8

So the solution to the system of equations is x = -8 and y = 6

Therefore, the solution is (-8,6)

Step-by-step explanation:

The values of m and b on the linear equation:

2 + 3x + 5 - 2x = y

are

m = 1

b = 7

A general linear equation can be written as in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Here we have the linear equation

2 + 3x + 5 - 2x = y

Now we want to write this in the slope-intercept form, to do so, we just need to simplify the left side, then we will get:

2 + 3x + 5 - 2x = y

(2 + 5) + (3x - 2x)  =y

7 + x = y

Then the linear equation is:

y = 1*x + 7

So the values are:

a = 1

b = 7

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The parabola has a vertex at (7 , -1) has a p-value of -0.5 and it opens downwards.

The axis of symmetry of a parabola is basically perpendicular to the directrix and contains the focus and vertex.  

Thus, the axis of symmetry is the vertical line x = 7.  

The vertex lies halfway between the focus and directrix.  Thus, we can say that the vertex is (7, (6 - 8)/2) = (7, -1)

Due to the fact that the vertex lies above the focus and the directrix is horizontal, then it means that the parabola opens downward.  

Therefore, the focus is (7 - 8)/2 = -0.5 units below the vertex, so, p = -0.5

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Answer:

4 hrs

Step-by-step explanation:

let x = # of hours he rented the unicycle

$15 + ($2/hr)x = $23

($2/hr)x = $23 - $15 = $8

x = ($8) / ($2/hr) = 4 hours

The height of the pole used in the question is; 12.15 ft

The 3 main trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, since the guy wire makes an angle of 13 degrees with the ground, it means the guy wire will be the hypotenuse of the right angle triangle and the height of the pole which we will label as h will be the opposite side of the triangle. Thus;

height/54 = sin 13

height = 54 * sin 13

height = 54 * 0.225

Height = 12.15 ft

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The sum of the differences between sample observations and the sample mean is zero.

Statistics is a science that deals with methods of collecting data, processing data, presenting data, analyzing data, drawing conclusions, and making reasonable decisions based on existing facts.

There are some terms that are frequently used in statistics:

The sum of the differences between sample observations and the sample mean can be denoted as ∑(xi - mean), where n is the size of the sample and i = 1,2,3,...,n

∑(xi - mean) = ∑xi - n*mean,

                    = n*mean - n*mean

                    = 0

Thus the sum of the differences between sample observations and the sample mean is zero.

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The answer to this question is -12x+20

The values of IJ and JK in parallelogram HIJK are 52 and 80 respectively

Recall that in every parallelogram, the opposite sides are equal and parallel.

This implies that IJ ║ HK and HI ║ JK

⇒ 5s - 88 = 3s - 32

Collecting the like terms we have

5s-3s = -32 +88

2s = 56

This implies that s = 28

By substitution we have s as 3(28) -32

= 84-32 = 52 and and 4(28)-32 = 80

The sides of the parallelogram are 80 and 52 respectively

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Yes, the piecewise functions that coincide with the given function are [(x + 3)-1, when x is greater than or equal to 3, [(x-3)/2] -1, when x is less than 3, [(x+3)/2] -1, when x is greater than -3, and -(x+3)/2] -1, when x is greater than or equal to -3.

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Side AC of the similar triangle system has a length of 6 units. (Correct choice: C)

Two triangles are similar when both have congruent angles but sides are not congruent though proportional. In this problem we find the case of two similar right triangles, whose relationship is shown below:

AD / AC = CD / BC = AC / AB

If we know that AD = 4 and AB = 9, then the length of side AC is:

4 / AC = AC / 9

AC ² = 36

AC = 6

The length of side AC is equal to 6 units.

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Since the Fourier transform of a real value signal is the product of the even cosine transform and the odd sine transform, it is conjugate symmetric and consequently symmetric about the frequency 0.

A real-valued signal's Fourier transform is a conjugate symmetric function, which means it is symmetric about frequency 0. This is demonstrated by the fact that a real-valued signal's Fourier transform may be expressed as the product of its cosine and sine transforms:

F(w) = Fc(w) plus Fs (w)

Where the cosine and sine transforms, respectively, are denoted by Fc(w) and Fs(w). Both the sine and cosine transforms are symmetric about the frequency zero because the sine transform is an odd function and the cosine is an even function. As a result, a real-valued signal's Fourier transform also exhibits symmetry near frequency 0.

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The complete question is

g suppose that w(t) is a real-valued signal. prove that its fourier transform magnitude is symmetric around frequency 0.

The answer to question 1 is not a statistical question. The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

Question 1: e. secret statisticians code meaning that ohio state graduates are morons.

This is not a statistical question and does not have a correct answer.

Question 2: c. sigma, x-bar, sampling distribution, mu, s, ~, n

The notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape).

Question 3: b. the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

The notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

The answer to question 1 is that it does not have a correct answer as it is not a statistical question. The answer to question 2 is that the notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape). The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

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The ratio may be written if it is a component of a percentage.

6 is to 5 is 12 is to 10 .

Ratios can be expressed as a notation, like 1/2, or as a ratio, like 6:5. A ratio's value is determined by dividing the first and second numbers. Consider the ratio 12:10 as an example. "6 to 5" should be read as the ratio. Any fraction, like 6/5, can also be expressed as a ratio, which is written as 6:5.

A colon or a fraction bar are two typical symbols representing ratios. You can also use words.

6 : 5 = 6/5 = 6 to 5

The ratio may be written if it is a component of a percentage.

6 is to 5

as in ...

12 is to 10 what 6 is to 5, and vice versa.

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Answer:
Maria is able to spend less than $12.
C < 12

Step-by-step explanation:

If Maria has already spent 17 dollars, that means she has 12 dollars left. C cannot be greater than 12. It has to be less.

So think of this C < $12
So if we do the total on one side and the $17 and C on the other side of inequality we get
C + 17 < 29

It cannot be equal to 29 so that's why we don't use a less than or equal to symbol.

Simplify this to get C < 12

I hope this is able to help you :D

Answer:

(4x + 5)(4x + 5)

Step-by-step explanation:

4x * 4x = 4x^2, and 5 * 5 = 25. Thus being 4x^2 + 25