A ladder leans against the side of a house. The angle of elevation of the ladder is 74° when the bottom of the ladder is 12 ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

?
12
74°

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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The answer to this question is -12x+20

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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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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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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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 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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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 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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{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 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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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 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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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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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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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 total surface area is 3994ft sq.

Suppose the base of the pyramid has length = l units, and width = w units.

Surface area of rectangular prism = 2lb +2lh+2bh

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given;

Length= 32ft

Breadth= 21ft

Height= 25ft

Now,

Surface area of rectangular prism = 2lb +2lh+2bh

=2*32*21+2*32*25+2*21*25

=1344+1600+1050

=3994

Therefore, the area will be 3994ft sq.

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Answer:

x=6

Step-by-step explanation:

hope this helps you with your question

For a positive angle, the rotation from the initial side to the terminal side takes place in a counter clockwise where as for a negative angle, the rotation takes place in a clockwise.

In math the term angle is defined as a figure in which two rays emerge from a common point and this is called the vertex of the angle and the two rays forming the angle are called its arms or sides.

Here we have to know that the angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.

Here we need to find the missing term in the given statement.

According to the definition of angle we have know that the rotation is measured from the initial side to the terminal side of the angle.

If it has Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.

Here we have know that the angle with its initial side on the x‐axis is said to be in standard position.

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If the terminal point determined by t is in the given quadrant.sin(t), cos(t);  sin(t)= -cos(t) in Quadrant II.

In Quadrant II, the sine function is positive and the cosine function is negative. The sine and cosine functions are related by the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1.

Since the sine is positive and the cosine is negative in Quadrant II, we can square the sine function and subtract it from 1 to get:

1 - sin^2(t) = cos^2(t)

We can then take the square root of both sides to get:

cos(t) = sqrt(1 - sin^2(t))

And since the cosine is negative in Quadrant II, we can then multiply the equation by -1 to get:

sin(t) = -cos(t)

This equation is only valid in Quadrant II.

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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.

The equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 is Y= 11/14 xz^2.

The concept that will be used here is variation.

since Y varies jointly with respect to z^2 and x  the we will introduce K which is the proportionality constant, then we have:

Y= Kxz^2.

The we can introduce Y, x and z  to solve for the single unknown and have the answer for the equation of variation.

231=K (6) (7^2)

231=6*49*K

231=(K*294)

231/294=K.

K = 11/14

We can  have Y= 11/14 xz^2 which is the equation of variation.

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complete question:

Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 the equation of varation is y

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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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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Answer:

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

Step-by-step explanation:

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

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 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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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