A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random
one after the other without replacement, then what is the probability that both the pencils
are purple?
5/182
10/91
2/91
9/182

please state reasoning as to why it is what ever answer you provide..

The correct statement regarding the unit circle is given as follows:

x = cos(θ) and y = sin(θ), and both functions have a period of 2π.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

These points are contained according to the following identity:

[tex]\cos^2{\theta} + sin^2{\theta} = 1[/tex]

(standard identity of trigonometry).

From the x-coordinate and the y-coordinate of each point on the unit circle, the function definitions are given as follows:

The period of both functions is of 2π, as the entire unit circle forms an angle of 360º = 2π.

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The area, lengths and dimensions of the plot of land and the situation picture are as follows;

a. 282.2 ft

b. 2330 ft²

c. 42.8 ft

Exercise 364

The true statements are;

The perimeter of ΔPQU is greater than 13 units

The perimeter of ΔPQR is 12 units

The area of ΔPST is 7.5 square units

The perimeter of a shape or figure is the length or distance of the edge boundary of the shape.

a. The perimeter of the plot of land, P, can be found as follows;

P = (70 - 0) + (60 - 0) + (80 - 0) + √((80 - 60)² + (0 - 70)²) ≈ 282.8

The perimeter of the fencing is approximately 282.8 feet

b. The shape of the plot of land is a trapezium

Area of the plot of land is therefore; A = 0.5 × (60 + 80) ×70 = 4900

The shape of the Parking Area is a trapezium, therefore;

Area of the Parking Area = 0.5 × ((49 - 8) + (60 - 8)) ×(70 - 50) = 930

The shape of the Warehouse is a square, therefore;

Area of the Warehouse = (49 - 8) × (50 - 10) = 1640

Area of the plot of land that does not include the warehouse and the parking area is therefore;

Required area = 4900 - (930 + 1640) = 2330

The area of the plot of land that does not include the warehouse and the parking area is 2330 ft²

c. The sum of the length of the legs of the parking area trapezoid, L, can be found as follows;

L = (70 - 50) + √((70 - 50)² + (60 - 49)²) ≈ 42.8

The total length of fence needed is about 42.8 ft

Exercise 364

The true statements are found as follows;

The perimeter of QRSTU = 3 + √(5² + 2²) + √(3² + 4²) + 4·√2 + √(5² + 2²) ≈ 24.43

The perimeter of QRSTU > 24

The area of ΔPRS  = 0.5 × 3 × 5 = 7.5

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Answer:

Below

Step-by-step explanation:

Area of square - area of circle = remnant               area of circle = pi r^2

(40 x 40) - pi (20^2) = 343 . 4 in^2  left over

( this assumes the circle touches the edges of the square)

The series of transformations that would map Figure T onto Figure U are:

What is rigid transformation?

Transformation is a process in which the dimensions of an object is resized, or its orientation is changed.

Rigid transformation is a topic that involves resizing an object, or changing its orientation. Some common methods used in transformation are: reflection, dilation, rotation and translation.

Reflection is the process in which a given object is turned about a reference point or line.Dilation involves changing the dimensions of a given object. Thus its size will be affected.

Rotation involves turning an object at a certain angle. Translation implies moving a whole object in a given direction and number of units.

In the given question, the required series of transformation are:

i. First rotating figure T at an angle of 90 degrees using its base as the reference line.

ii. Then translating the image some units.

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There are two groups of [tex]\dfrac{7}{4}[/tex], an integer which is equal to 1, and 0.75 which is decimal.

A fraction is a numeral that represents a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

The given fraction is,

[tex]\dfrac{7}{4}[/tex].

To find the groups of fraction,

Simplify the fraction,

[tex]\dfrac{7}{4} = 1 \dfrac{3}{4}\\\\ = 1.75[/tex]

There are two groups in the fraction of  [tex]\dfrac{7}{4}[/tex] ,

Integer part which is 1.

And decimal part which is 0.75.

Hence, there are two groups of fraction [tex]\dfrac{7}{4}[/tex].

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Answer:

64

Step-by-step explanation:

There are 4 prime digits: 2, 3, 5, and 7.

If the number is one digit, there are 4 possible numbers.

If the number is two digits, there are 4(3)=12 possible numbers.

If the number is three digits, there are (4)(3)(2)=24 possible numbers.

If the number is four digits, there are (4)(3)(2)(1)=24 possible numbers.

Taking the sum, the answer is 64.

Answer:

D

Step-by-step explanation:

Looking at the graph, when x <= 1, the line is x + 6. Only one answer has this option.

Answer:

Step-by-step explanation:

So your first point has x=325.0 and y=1.10, your second point has x=348.9 and y=1.40, and so on.

The graph should look something like this:

The conclusion that you would draw from your plot is that the power seems to vary linearly with the speed. The data points are almost in a straight line. They are not perfectly aligned, of course. There is always some variability in real data, but you can see a trend.

A stable sorting algorithm is one that keeps the relative order of two equal elements. Quicksort is a sorting algorithm that has a high degree of instability, which means that it may alter the relative order of two equal components.

The Merge Sort, Timsort, Counting Sort, Insertion Sort, and Bubble Sort are just a few examples of popular sorting algorithms that are by their very nature stable. Others, like Quicksort, Heapsort, and Selection Sort, are erratic. Stable sorting algorithms can be modified to be more efficient.

Because we swap elements according on the location of the pivot, QuickSort is an unstable algorithm (without considering their original positions). A sorting algorithm is said to sort in-place if it never stores more than a fixed number of input array members outside of the array. If the order of elements with the same value is not altered by a sorting technique, it is stable. Binary insertion sort is the only stable algorithm available from the options offered.

Therefore the correct answer is false.

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The statement supported by the plot is that the IQR of the distribution is roughly 10. It is possible to estimate the median from the plot, and the distribution appears to be unimodal, with the mean being smaller than the median. There are no outliers shown in the plot.

The relative frequency histogram provides a visual representation of the distribution of the data. From the plot, it is possible to estimate the median, which is the middle value of the distribution, as well as the interquartile range (IQR), which is the difference between the upper and lower quartiles. The IQR of the distribution is roughly 10, which can be seen by the distance between the upper and lower quartiles in the plot. Additionally, the distribution appears to be unimodal, which means that it has only one mode or peak. It is also apparent that the mean of the distribution is smaller than its median, as the peak is shifted to the left of the median. Finally, there are no outliers shown in the plot, as all of the values appear to be within the range of the distribution.

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Answer:

The function g(x) = log(-3x - 9) - 1 is obtained from the parent function f(x) = log(x) through two transformations: a shift to the right and a shift downward. The shift to the right is achieved by multiplying x by -3 and subtracting 9, which results in a rightward shift in the function's graph. The shift downward is achieved by subtracting 1 from the final result, which results in a downward shift in the function's graph. These transformations result in a graph that is shifted to the right and downward compared to the graph of the parent function.

[tex]log( - 3x - 9) = log( 3( - x - 3)) \\ = log( 3) + log( - (x + 3))[/tex]

A vertical shift by 1 unit downwards

A vertical shift by log(3) units upwards

A horizontal shift by 3 units to the left

A reflection along the line x=-3

Answer:

GCF: 50

Step-by-step explanation:

Let's test

50 ( 5 + 6)

= 250 + 300

So, my answer is correct!

The value of the trigonometric expression will be 1. Then the correct option is C.

Mathematical capabilities inspect the collaboration between the aspects and points of a three-sided structure.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

⇒ tan²x / sec²x + cot²x / cosec²x

Simplify the expression, then the value of the expression is given as,

⇒ tan²x / sec²x + cot²x / cosec²x

⇒ (sin²x × cos²x) / cos²x + (cos²x × sin²x) / sin²x

⇒ sin²x + cos²x

⇒ 1

The worth of the mathematical articulation will be 1. Then, at that point, the right choice is C.

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1) Nominal GDP = Current year price* Current year quantity

= 500*3000 + 400,000*20

= 1,500,000 + 8,000,000

= $9,500,000

2) Real GDP = Base year price* Current year quantity

= 500*2000 + 400,000*10

=1,000,000 + 4,000,000

= $5,000,000

3) GDP Deflator = Nominal GDP/Real GDP

=9,500,000/5,000,000

Answer:

76 [tex]ft^{2}[/tex]

Step-by-step explanation:

We are looking for the area of the walkway.

Area = length times width.

We know the length, we need to find the width.

Perimeter is the distance around the rectangle.  It is two length and two widths.

p = 2l + 2w

80 = 2(38) + 2W

80 = 76 + 2W  Subtract 76 from both sides.

80 - 76 = 76 - 76 + 2w

4 = 2w Divide both sides by 2

[tex]\frac{4}{2}[/tex] = [tex]\frac{2w}{2}[/tex]

2 = w

Now that we know the width we can find the area

a = 38 x 2

a = 76 [tex]ft^{2}[/tex]

Answer:

Length=38 ft

breadth=?

Perimeter=80 ft

we know,

Perimeter= 2(length+breadth)

or,80ft=2(38 ft + breadth)

or,40 ft=38ft + breadth

or,breadth=40 ft-38 ft

:. breadth=2 ft

Now,

Area of walkway= length ×breadth

=38 ft×2 ft=76 ft²

Hence,72 square feet of gravel is required to cover the entire walkway.

The expression that is equivalent to 5.8 ÷ 1.15 is 580 ÷ 115

Equivalent expressions are expressions that have equal values when compared

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

5.8 ÷ 1.15

Divide both sides of the equation by 1/10

So, we have the following representation

5.8 ÷ 1.15 = 5.8/(1/10) ÷ 1.15/(1/10)

Evaluate the quotients

So, we have the following representation

5.8 ÷ 1.15 = 58 ÷ 11.5

Multiply both sides of the equation by 10

So, we have the following representation

5.8 ÷ 1.15 = 580 ÷ 115

Hence, the equivalent equation is 580 ÷ 115

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We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

Given that,

With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.

We have to find which of the following best describes the significance of this growth factor.

We know that,

The required expression for y with respect to x is

y=(1.8)ˣ------>equation(1)

1.8=1- unit growth factor.

Whenever x changes by 1.

x=x-1----->equation(2)

Putting equation (2) in (1)

y'=1.8ˣ⁺¹

y'=1.8ˣ×1.8----->equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ

y'=(1.8)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.

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y=(1.8)ˣ               equation(1)

1.8=1- unit growth factor.

Whenever x changes by 1.

x=x-1                     equation(2)

y'=1.8ˣ⁺¹

y'=1.8ˣ×1.8              equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ

y'=(1.8)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.

Answer: D

Step-by-step explanation:

The slope equation is:  [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

The slope of the points (0, 2) and (1, -3) is: -5

The slope of the points (-5, -8) and (10, 12): 4/3

First graph: m = 1

Second graph: m = -2/3.

The slope of a line is calculated using the formula below:

Slope (m) = rise/run = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Therefore, the equation of the slope is expressed as:  [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Find the slope of the points (0, 2) and (1, -3):

m = change in y / change in x = (-3 - 2) / (1 - 0)

m = -5/1

Slope (m) = -5

Find the slope of the points (-5, -8) and (10, 12):

Slope (m) = (12 -(-8)) / (10 - (-5))

m = 20/15

m = 4/3

Find the slope of the first graph:

Slope (m) = rise/run = 1/1

m = 1

The slope of the second graph = rise/run = -2/3.

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x = 6 is the value of x does f(x) = 2.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Here, we have

Given function:  f(x) = −1 + 0.5x

We have to find the value of x does f(x) = 2.

For this, we put the different values of x and see what value satisfies the given function.

For x = -6

f(x) = −1 + 0.5(-6)

f(x) = -4

For x = 5

f(x) = −1 + 0.5(5)

f(x) = 1.5

For x = 6

f(x) = −1 + 0.5(6)

f(x) = 2

Hence, x = 6 is the value of x does f(x) = 2.

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The equation of a line is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To find the equation of the line that passes through the points (3, 4) and (5, 8), we need to first calculate the slope of the line.

The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we have:

m = (8 - 4) / (5 - 3) = 4/2 = 2

Now that we know the slope of the line, we can use one of the given points to find the y-intercept. Let's use the point (3, 4). If we plug the values of x and y into the equation y = mx + b, we get:

4 = 2 * 3 + b

4 = 6 + b

-2 = b

Therefore, the equation of the line that passes through the points (3, 4) and (5, 8) is:

y = 2x - 2

Measure of angle VTK is 90°.

Angles come in many different varieties in geometry. Angle is among the most crucial and fundamental units. Two rays or lines are linked at their shared terminus when they create an angle. We use angles in many facets of our daily lives, starting with the construction of buildings, dams, and monuments, not only in mathematics. The study of angles is essential to civil engineering. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Given

∠VTK = 90°

∠VMK = 90°

∠VTK is given

∠VTK = 90°

Measure of angle VTK is 90°.

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The Solution for the given problem is 6x² +4x

What is Polynomial?

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Solution:

We are given with the values of the following terms f(x), g(x), and m(x)

f(x) = 3x² + 5x - z

g(x) = 5x² - 3x + z

m(x) = 2x² - 2x

To find: f(x) + [g(x) - m(x)]

so, we need to put the respective values in the equation and simplify it

3x² + 5x - z + [5x² - 3x + z - 2x² + 2x]

3x² + 5x - z + [3x² - x + z]

6x² +4x

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Answer:

45

Step-by-step explanation:

15(3) = 45

Answer:

[tex]\ln (y) = 0.210x-2.601[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Length & \sf Diameter \\x & y\\\cline{1-2} \vphantom{\dfrac12} 2 & 0.113\\\cline{1-2} \vphantom{\dfrac12} 3& 0.151\\\cline{1-2} \vphantom{\dfrac12} 4& 0.192\\\cline{1-2} \vphantom{\dfrac12} 5& 0.222\\\cline{1-2} \vphantom{\dfrac12} 6& 0.262\\\cline{1-2} \end{array}[/tex]

To convert  y = abˣ  to linear form, take natural logs of both sides and rearrange:

[tex]\begin{aligned}y=ab^x \implies \ln y &= \ln ab^x\\\implies \ln y &= \ln a + \ln b^x\\\implies \ln y &= \ln a + x \ln b\\\implies \ln y &=x \ln b+ \ln a\end{aligned}[/tex]

This is in the straight-line form y = mx + c.

Substitute the first and last values of x and y from the table into the natural log formula:

Subtract the first equation from the second equation to eliminate ln(a);

[tex]\implies \ln 0.262 - \ln 0.113 = 6 \ln b - 2 \ln b[/tex]

[tex]\implies \ln 0.262 - \ln 0.113 = 4 \ln b[/tex]

Apply the quotient log law:

[tex]\implies \ln \dfrac{0.262}{0.113} = 4\ln b[/tex]

Rearrange and solve for ln(b):

[tex]\implies \ln b = \dfrac{1}{4}\ln \dfrac{0.262}{0.113}[/tex]

[tex]\implies \ln b = 0.210\; \sf (3\;d.p.)[/tex]

Substitute the found value of ln(b) into one of the equations and solve for ln(a):

[tex]\implies \ln 0.262 = 6 \cdot \dfrac{1}{4}\ln \dfrac{0.262}{0.113}+\ln a[/tex]

[tex]\implies \ln a=\ln 0.262 -\dfrac{6}{4}\ln \dfrac{0.262}{0.113}[/tex]

[tex]\implies \ln a = -2.601\; \sf (3\;d.p.)[/tex]

Substitute the found values of ln(a) and ln(b) into the formula to create an equation for ln(y):

[tex]\boxed{\ln (y) = 0.210x-2.601}[/tex]

Answer:

61 degrees

Step-by-step explanation:

sum of all angles of a triangle is 180 degrees

82+37+x=180

119+x=180

-119.  -119

x=61

hopes this helps

180 Degrees

[tex]37+82+x=180[/tex]

[tex]119+x=180[/tex]

[tex]x+119=180[/tex]

Subtract 119 from both sides:

[tex]x+119-119=180-119[/tex]

[tex]\fbox{x = 61}[/tex]

Answer:

6 marbles per bag

Step-by-step explanation:

42 marbles * 1 bag / 7 bags =

42 * 1/7 =

42/7 = 6 marbles per bag

1 bag represents each bag of the 7 total bags.

Multiply 1 bag / 7 bags with 42 marbles(total amount of marbles) to get the marbles in EACH bag.

Answer:

let x = marbles in a bag

x = 42/7

x = 6

(6) + (6) + (6) + (6) + (6) + (6) + (6)

This is 7 bags, total of 42 marbles

this is my own explanation moderator, please dont delete just because its almost the same with previous answer. well its because its the only way to solve it hehe but i add another explanation, i really dont want to get warnings for this kind of questions you knoww..

Step-by-step explanation:

Answer:

15 stairs would be needed

Step-by-step explanation:

10x12= 120

15 x 8 = 120

The megabytes that have been downloaded will be 48 megabytes.

Based on the information, percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since 273 megabytes is being download if the download is 17.7%, the megabytes that have been downloaded will be:

= 17.7% × 273

= 48 megabytes.

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The study of data collection, analysis, presentation, and interpretation is known as statistics.

Given,

What is statistics?

Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activity and census data.

Types of statistics;

Based on the characteristics, the various statistical kinds are divided: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as using pie charts, bar graphs, or tables.

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