Answer: 17/22
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
3.68181818182=33409090909150000000000
Showing the work
Rewrite the decimal number as a fraction with 1 in the denominator
3.68181818182=3.681818181821
Multiply to remove 11 decimal places. Here, you multiply top and bottom by 1011 = 100000000000
3.681818181821×100000000000100000000000=368181818182100000000000
Find the Greatest Common Factor (GCF) of 368181818182 and 100000000000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 2,
368181818182÷2100000000000÷2=18409090909150000000000
Simplify the improper fraction,
=33409090909150000000000
In conclusion,
3.68181818182=33409090909150000000000
Find the equation of the line through (2,-4) and parallel to the line 5x-2y-4=0. Write your answer in general form.
We can find the equation of a line given one point and its slope.
Remember that two parallel lines have the same slope; therefore, the slope of 5x-2y-4=0 is equal to the slope of the line we are trying to find.
[tex]\begin{gathered} 5x-2y-4=0 \\ \Rightarrow2y=5x-4 \\ \Rightarrow y=\frac{5x}{2}-\frac{4}{2}=\frac{5x}{2}-2 \\ \Rightarrow y=\frac{5x}{2}-2 \\ \Rightarrow m=\frac{5}{2} \end{gathered}[/tex]Then, we have got everything we need, the slope is equal to 5/2 and a point in the line is (2,-4)
The equation is:
[tex]\begin{gathered} y-(-4)=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5x}{2}-5 \\ \Rightarrow y=\frac{5x}{2}-9 \\ \Rightarrow y+9=\frac{5}{2}x \\ \Rightarrow2y+18=5x \\ \Rightarrow5x-2y-18=0 \end{gathered}[/tex]The answer is 5x-2y-18=0
If the radius of the circle is 6cm, what is the length of arc BC? Round to the neare:thousandth (3 decimal places) and use the pi button on the calculator.
Given that:
Radius of the circle = 6 cm
Central angle of the arc = 120 degrees
The formula to find the arc length of a circle of radius is
[tex]Arc\text{ length=}\frac{\theta}{360^{\circ}}\cdot2\pi r[/tex]Substitute the given values into the formula.
[tex]\begin{gathered} Arc\text{ length=}\frac{120^{\circ}}{360^{\circ}}\cdot2\pi\cdot6 \\ =12.566\text{ cm} \end{gathered}[/tex]Fill in the missing number to complete the pattern.18, 12, ,0
using Ap formula,
[tex]\begin{gathered} a+(n-1)d \\ a=18 \\ d=12-18=-6 \\ 18+(3-1)-6 \\ 18-12=6 \end{gathered}[/tex]The missing term = 6
como se resuelve esto? 3x²+10x=O
3 x^2 + 10 x = 0
x ( 3 x + 10 ) = 0
x = 0 or 3 x+ 10 = 0
x = 0 or 3 x = -10
x = 0 or x = -10/3
i need help with math
The following basic properties and characteristics can be used to easily identify parallel lines:
They always are straight lines with equal spacing between them.They are parallel lines.They never cross, no matter how much farther you stretch them in just about any given direction.A transversal line intersecting two parallel lines at two separate positions will form four angles at each point.The statement are given as;
The measurement for the angles for the transversal are-
∠2 = 91° and ∠5 = 89°
Thus,
∠2 = ∠3 = 91° (vertically opposite angles)
The sum ∠3 + ∠5 = 180 (for the parallel lines)
91° + 89° = 180° (supplementary angles).
Thus, two lines are parallel.
The two lines are parallel; True.The measure of ∠7 = 89°; False,Correct; ∠7 = ∠3 = 91°(corresponding angles)
∠3 = ∠6 are same side of interior angles; FalseCorrect; They are opposite side of interior angles.
∠1 is congruent to angle ∠4 because they are vertical angles; True,Thus, the results for the given transversal lines are found.
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To make 6 cups of ramen, 2/3 cups of noodles is needed. How many cups of ramen can you make with 1 3/4 cups of noodles?
Explanation
The question calls for using the direct proportion concept. This can be seen below.
Let the number of cups of ramen you can make with 1 3/4 cups of noodles be x. Therefore;
[tex]\frac{6}{x}=\frac{\frac{2}{3}}{1\frac{3}{4}}[/tex]We can them crossmultiply
[tex]\begin{gathered} \frac{2}{3}x=\frac{7}{4}\times6 \\ \frac{2}{3}x=21 \\ 2x=63 \\ x=\frac{63}{2} \\ x=31\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]31\frac{1}{2}\text{cups}[/tex]Answer:
31.5
Step-by-step explanation:
Which expression represents the area of the remainingpaper shape in square centimeters?O (x-7)(x-9)O (3x-2)(3x-8)O (3r-4)(3x +4)O (9x - 1)(x+16)
A square corner of 16 cm² is removed from a square paper with an area of 9X squared, square centimeters. which expression represents the area of the remaining paper shape in the square centimeters?
we have taht
Find out the difference
9x^2-16
apply difference of squares
9x^2-16=(3x-4)(3x+4)
answer is
(3x-4)(3x+4)
Write the given fraction in simplest form 25/27
Notice that:
[tex]\begin{gathered} 25=5\cdot5, \\ 27=3\cdot3\cdot3. \end{gathered}[/tex]Then 25 and 27 have no common factors.
Since the denominator and the numerator have no common factors, then the given fraction is in its simplest form.
Answer: 25/27.
[tex]\frac{25}{27}\text{.}[/tex]What is the area of a circle with a circumference of 31.4Area-
The circumference of a circle is give by:
[tex]C=2\pi r[/tex]Plugging the value we have for the circunference we can find the radius:
[tex]\begin{gathered} 31.4=2\pi r \\ r=\frac{31.4}{2\pi} \\ r=\frac{15.7}{\pi} \end{gathered}[/tex]Now that we have the radius we remember that the area of a circle is:
[tex]A=\pi r^2[/tex]Plugging the value of r we have that:
[tex]A=\pi(\frac{15.7}{\pi})^2=78.46[/tex]Therefore the area of the circle is 78.46
Anetha wants to eam at least $90 per month. She babysits for $8 per hour (x) and cleans houses for $5 per hour (y). She cannot work more than 15 hours per month. Which pairs (x,y) represent hours that Anetha could work to meet the given conditions?
ANSWER
(6, 9) and (7, 8)
EXPLANATION
We have that x represents the number of hours she spends babysitting and y represents the number of hours she spends cleaning houses.
She cannot work for more than 15 hours per week. This means that:
[tex]x\text{ + y }\leq\text{ 15 \_\_\_\_\_\_\_\_(1)}[/tex]She wants to earn at least $90 per month. This means that:
[tex]8(x)\text{ + 5(y) }\ge\text{ 90 \_\_\_\_\_\_\_\_\_\_(2)}[/tex]We can solve this by plotting the graphs of the inequalities. We have:
The solution of the inequalities is the region that the two shaded regions intersect.
Due to the fact that we are considering number of hours (x and y), we will only concern ourselves with the positive portion of the graph.
So, the pairs (x, y) that can represent the number of hours that Anetha can work are the pairs that fall in the positive x and y axis of the shaded part of the graph.
They are:
(6, 9) and (7, 8)
A car was valued at $32,000 in the year 1995. The value depreciated to $14,000 by the year 2001.A) What was the annual rate of change between 1995 and 2001?T =Round the rate of decrease to 4 decimal places.B) What is the correct answer to part A written in percentage form?T =%.C) Assume that the car value continues to drop by the same percentage. What will the value be in the year2005 ?value = $Round to the nearest 50 dollars.
Givn:
Value of the car in 1995 = $32,000
Value of the car in 2001 = $14,000
Let's solve for the following:
• (A). What was the annual rate of change between 1995 and 2001?
Apply the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]Where:
• t is the number of years between 2001 and 1995 = 2001 - 1995 = 6
,• a is the initial value = $32000
,• r is the rate of decay.
,• f(t) is the present value
Thus, we have
[tex]\begin{gathered} 14000=32000(1-r)^6 \\ \end{gathered}[/tex]Divide both sides by 32000:
[tex]\begin{gathered} \frac{14000}{32000}=\frac{32000(1-r)^6}{32000} \\ \\ 0.4375=(1-r)^6 \end{gathered}[/tex]Take the 6th root of both sides:
[tex]\begin{gathered} \sqrt[6]{0.4375}=\sqrt[6]{(1-r)^6} \\ \\ 0.87129=1-r \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} r=1-0.87129 \\ \\ r=0.1287 \\ \\ r=0.1287*100=12.87\text{ \%} \end{gathered}[/tex]Therefore, the rate of change between 1995 and 2001 is 0.1287
• (B). What is the correct answer to part A written in percentage form?
In percentage form, the rate of change is 12.87 %
• (C),. Assume that the car value continues to drop by the same percentage. What will the value be in the year 2005?
We have the equation which represents this situation below:
[tex]f(t)=32000(1-0.1287)^t[/tex]Here, the value of t will be the number of years between 1995 and 2005.
t = 2005 - 1995 = 10
Now, substitute 10 for t and solve for f(10):
[tex]\begin{gathered} f(10)=32000(1-0.1287)^{10} \\ \\ f(10)=32000(0.8713)^{10} \\ \\ f(10)=32000(0.25216) \\ \\ f(10)=8069.14\approx8100 \end{gathered}[/tex]Therefore, the value in the year 2005 rounded to the nearest 50 dollars is $8100
ANSWER:
• (a). 0.1287
,• (b). 12.87%
,• (c). $8100
[tex] \sqrt[3]{80} [/tex]simplify in simplest radical form
Start by decomposing the number inside the root into primes
Then group the terms into cubes if possible
[tex]\begin{gathered} 80=2\cdot2\cdot2\cdot2\cdot5 \\ 80=2^3\cdot2\cdot5 \\ 80=10\cdot2^3 \end{gathered}[/tex]rewrite the root
[tex]\sqrt[3]{80}=\sqrt[3]{10\cdot2^3}[/tex]then cancel the terms that are cubes and bring them out of the root
[tex]\sqrt[3]{80}=2\sqrt[3]{10}[/tex]16) Select the sequence of transformations that will carry triangle A onto triangle A'Atranslate 6 units down, then reflect acrossA)'the y-axis5B) reflect over the y-axis, reflect over the x-axis,then 2 units upC)reflect over the x-axis, translate 2 units up,then 8 units left-5D)reflect over the x-axis, rotate 90° clockwise,then translate 4 units down
C
16) Let's first locate the points that make up the pre-image A, and the image A' picking them from each one of those three vertices.
A
(-3,5)
(-5, 5)
(-5,3)
A'
(5,-1)
(5,-3)
(3,-3)
16.2) Then let's pick just one point and apply the transformations, in this case, let's pick point (-3,5)
Counting on the graph
So if we reflect it over the x-axis, we'll get from (-3,5) to (3,-5) and translating up two units, we'll arrive at (-3,-3) and finally to (5,-3) one of the coordinates of the Image A'
16.3) Hence, the answer is C
Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)
Answer:
Explanations:
Given the limit of the function expressed as:
[tex]\begin{gathered} \lim _{n\to0}\frac{\sin8x}{x} \\ f(x)=\frac{\sin 8x}{x} \end{gathered}[/tex]First, we need to create a table for the given values in the table:
If x = -0.1
[tex]\begin{gathered} f(-0.1)=\frac{\sin8(-0.1)}{-0.1} \\ f(-0.1)=\frac{\sin(-0.8)}{-0.1} \\ f(-0.1)=0.1396 \end{gathered}[/tex]If x = -0.01
[tex]\begin{gathered} f(-0.01)=\frac{\sin8(-0.01)}{-0.01} \\ f(-0.01)=\frac{\sin(-0.08)}{-0.01} \\ f(-0.01)=0.1396 \end{gathered}[/tex]If x = -0.001
[tex]\begin{gathered} f(-0.001)=\frac{\sin8(-0.001)}{-0.001} \\ f(-0.001)=\frac{\sin(-0.008)}{-0.008} \\ f(-0.001)=0.1396 \end{gathered}[/tex]From the values above, we can conclude that the values of f(x) will all tend to be 0.1396 for the positives values of x
Therefore, we can conclude that as you approach the value 0 from the positive and negative directions, they approach the same value, hence the limit does exist.
The number of McDonald's restaurants worldwide in 2014 was 36.258. In 2009, there were 32,737 McDonald's restau- rants worldwide. Let y be the number of McDonald's res- taurants in the year, where r = O represents the year 2009 (Source: McDonald's Corporation) a. Write a linear equation that models the growth in the number of McDonald's restaurants worldwide in terms of the year x. [Hinr. The line must pass through the points (0.32.737) and (5.30,258).]b. use this equation to predict the number of McDonald's restaurants worldwide in 2016.
a) y = 704.2x + 32737
b) There are 37,666 McDonald's restaurants in 2016
Explanations:The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope, and is given by the formula: } \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]For the line passing through the points (0, 32737) and (5, 36258)
x₁ = 0, y₁ = 32737, x₂ = 5, y₂ = 36258
Substituting the values into the equations above:
[tex]\begin{gathered} \text{m = }\frac{36258-32737}{5-0} \\ \text{m = }\frac{3521}{5} \\ m\text{ = }704.2 \\ y\text{ - 32737 = 704.2}(x\text{ - 0)} \\ y\text{ - 32737 = 7}04.2x \\ y\text{ = 7}04.2x\text{ + 32737} \\ \end{gathered}[/tex]b) In 2016, x = 7
substitute x = 7 into the equation
[tex]\begin{gathered} y\text{ = 704.2(7) + 32737} \\ y\text{ = }4929.4+32737 \\ y\text{ = }37666.4 \end{gathered}[/tex]There are 37,666 McDonald's restaurants in 2016
Find the slope and y intercept of the line shown below question number 4
The image of the line provided seems to go through the following points:
(0, 4) , (-4, 5), and (4, 3)
Knowing at least two points is essential to calculate the slope via the formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]so, for example if we use the points (0, 4) and (-4, 5) to calculate the slope, we get:
[tex]\text{slope}=\frac{5-4}{-4-0}=-\frac{1}{4}[/tex]Therefore, the slope is -1/4 (negative one fourth)
Notice as well that one of the points we chose is (0, 4) which in fact is the y-intercept of the line (the point at which the line crosses the y-axis ).
so we have al the elements to built the equation of this line:
slope = -1/4
y intercept = 4 for the (0, 4) on the plane
Then the equation could be built using:
y = (-1/4) x + 4
Part A in. (a) For the following figure, the value of x is 45° 8 in. 459 B 45
Answer
The value of x = 8 in.
y = 8√2 = 11.31 in.
For the second question,
x = 8.3 units
Explanation
Isoscelles triangles have two of their sides being of the same lengths and those two sides are the ones whose base angles are the same.
From the image, we can see that two angles of the triangle have the same measures, hence, we can easily conclude that
x = 8 inches.
To find y, we will use pythagoras theorem.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this triangle,
hyp = y
a = 8 in
b = x = 8 in
a² + b² = (hyp)²
8² + 8² = y²
64 + 64 = y²
y² = 128
Take the square roots of both sides
√(y²) = √128
y = 8√2 = 11.31 in
For the other question.
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For that triangle,
Hyp = 11 units
Opp = ?
Adj = x
θ = 41°
We can then use trignometrical identities to solve this
CAH allows us to say
Cos 41° = (Adj/Hyp)
Cos 41° = (x/11)
x = 11 Cos 41°
x = 11 (0.7547)
x = 8.3 units
Hope this Helps!!!
(08.01 LC)Find the area of a circle with a diameter of 20 inches. Use 3.14 for pi.(1 point)
The area of a circle can be calculated using the following formula:
[tex]A=\pi r^2[/tex]Where
A represents the area
r represents the radius of the circle
π is the number pi, you have to use 3.14 for the calculatins
You have to calculate the area of a circle that has a diameter of 20 inches. The radius of a circle is half the diameter:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{20}{2} \\ r=10in \end{gathered}[/tex]The area of the circle can be determined as follows:
[tex]\begin{gathered} A=3.14\cdot10^2 \\ A=314in^2 \end{gathered}[/tex]The area of the circle is 314in²
Construct an obtuse angle called ABC. Bisect ABC and call the new angles ABP and PBC. Now bisect the ABP so that there are 3 angles. The measure of angle PBC is 66 degrees. Fe measures of the two smaller angles are equal to 11y and 3x respectively. What are the values of x and y in degrees?
Now,
3x + 11y + 66 = 66x2
3x + 11y + 66 = 132
3x + 11y = 132 - 66
3x + 11y = 66 ...............................(equ 1)
Find the slope of the line(Question in photo sorry) (Pre algebra)
Given that
There are two points and we have to find the slope of the line passing through these points.
Explanation -
The given two points are (19/2, -8/3) and (-7/2, -1/15)
The general formula to find the slope through two points is given as
[tex]\begin{gathered} If\text{ points are \lparen x}_1,y_1)\text{ and \lparen y}_1,y_2) \\ Then \\ slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]So on substituting the values we have
[tex]\begin{gathered} Slope=m=\frac{-\frac{1}{15}-(-\frac{8}{3})}{-\frac{7}{2}-\frac{19}{2}}=\frac{-\frac{1}{15}+\frac{8}{3}}{-\frac{7}{2}-\frac{19}{2}} \\ \\ m=\frac{\frac{-1\times1+5\times8}{15}}{\frac{-7-19}{2}}=\frac{\frac{-1+40}{15}}{\frac{-26}{2}}=\frac{\frac{39}{15}}{-\frac{13}{1}} \\ \\ m=\frac{39}{15}\times\frac{-1}{13}=-\frac{3}{15}=-\frac{1}{5} \end{gathered}[/tex]So the required slope passing through the given two points is -1/5.
Final answer -
Therefore the final answer is -1/5.Which of these is an exponential parent function?  A. f(x) = 2^x – 3  B. f(x) = 2^x + 2  C. f(x) = 2^x  D. f(x) = 2^x + 1/3
An exponential parent function is the option C. f(x)= [tex]2^{x}[/tex], from the given options.
What do you mean by exponential parent function?
The formula for their parent function is y = [tex]b^{x}[/tex], where b is any non zero constant. Below is a graph of the parent function, y = [tex]e^{x}[/tex], which demonstrates that it will never equal 0. And at y = 1 when x = 0, y crosses the y-axis.
According to options in the given question,
We have the option below in the given question:
A. f(x) = 2^x – 3 
B. f(x) = 2^x + 2 
C. f(x) = 2^x 
D. f(x) = 2^x + 1/3
We know from the above definition that the option C. is the right answer to the given question.
Therefore, the exponential parent function is f(x)= [tex]2^{x}[/tex].
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Number 11. Find a quadratic equation with (-2,3) and y intercept of 11
Answer:
[tex]y=2x^2+8x+11[/tex]Explanation:
A quadratic equation in vertex form is generally given as;
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the coordinate of the vertex.
Given the coordinate (-2, 3), we'll have that;
h = -2
k = 3
Given a y-intercept of 11 and we know that at the y-intercept x = 0.
Substituting the above values into the vertex form equation and solving for a, we'll have;
[tex]\begin{gathered} 11=a\lbrack0-(-2)\rbrack^2+3 \\ 11=4a+3 \\ 4a=8 \\ a=\frac{8}{4} \\ a=2 \end{gathered}[/tex]Substituting a = 2, h = -2 and k = 3 into the vertex form equation and taking it to standard form, we'll have;
[tex]\begin{gathered} y=2(x+2)^2+3 \\ y=2(x^2+4x+4)+3 \\ y=2x^2+8x+8+3 \\ y=2x^2+8x+11 \end{gathered}[/tex]factor each trinomial. if the trinomial cannot be factored write prime. show ALL work1.) 5x^2+17x+62.) 2x^2+5x-12
In order to determine the factors of the given trinomials, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial:
ax² + bx + c
Replace the values of the coefficients of the given trinomials into the quadratic formula.
1) 5x² + 17x + 6
a = 5, b = 17, c = 6
[tex]\begin{gathered} x=\frac{-17\pm\sqrt[]{17^{2}-4(5)(6)}}{2(5)} \\ x=\frac{-17\pm13}{10} \end{gathered}[/tex]the two solutions for x are:
x1 = (-17-13)/10 = -30/10 = -3
x2 = (-17+13)/10 = -4/10 = -2/5
The factors are given by the following expression:
(x - x1)(x - x2)
Then, you have:
5x² + 17x + 6 = (x - (-3))(x - (-2/5)) = (x + 3)(x + 2/5)
A cell phones was purchased for $400 and depreciates at a rate of 17% per year. How much is the cell phone worth after 4 years? Round to the nearest cent .
1) Gathering the data
Cell phone
$400
Depreciates at -17% yearly
Period: 4 yrs
2) Let's write an exponential function to calculate that depreciation:
y = The brand new price x (depreciation rate)^time
17%= 0.17
[tex]\begin{gathered} y=400(1-0.17)^4 \\ y=400(0.83)^4 \\ y=189.83 \end{gathered}[/tex]3) So 4 years from the data of the purchase, the cell phone worths $189.83
Choose a natural number between 1 and 36, inclusive. What is the probability that the number is a multiple of 3 (enter the probability as a fraction.)
List of multiples of 3 in the interval:
3,6,9,12,15,18,21,24,27,30,33,36. (12 numbers)
The probability of choosing a number multiple of 3 is:
Number of multiples of 3 in the interval / Total number of values in the interval
12/36 (Replacing)
1/3 ( Simplifying the fraction)
The answer is 1/3.
Which shows another way to write 6*3? A.3 + 3 + 3 + 3 + 3 + 3 B.3 × 3 × 3 × 3 × 3 × 3 C.6 × 6 × 6 D.6 + 6 + 6
Another way to write the given expression 6×3 is by use of addition operator 6+6+6 .
We know that multiplying a number by another number is another way of adding the number that many times.
If we multiply a with n it can be written as
a × n = a + a + a + a +.... n terms
Similarly we can use the same formula for 6×3.
6×3 = 6+6+6
Addition can be defined and carried out using abstractions known as numbers, such as integers, real numbers, and complex numbers, in addition to counting things.
Addition is a part of the arithmetic branch of mathematics. In algebra, a different area of mathematics, addition can also be performed on abstract objects like vectors, matrices, subspaces, and subgroups.
The words, addends, or summands collectively refer to the quantities or components that must be combined to make a whole number; this terminology also includes the summing of multiple terms. This needs to be differentiated from multiple factors.
Hence the given expression can be written as 6+6+6 .
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suppose the odds against winning the lottery are 59,000,000 to 1. What is the probability of the event of winning the lottery given those odds? P(E) = __________
The odds against winning the lottery is 59,000,000 : 1
Thus,
Not winning bets = 59,000,000
Winning bets = 1
Total bets = 59,000,000 + 1 = 59,000,001
Thus,
The probability of winning = 1/59,000,001
Answer[tex]P(E)=\frac{1}{59,000,001}[/tex]Consider the figure below.MGiven:PM 2PN, LM I MN,MNI ONLN bisects ZMNO, OM bisects LMNAMPL XANPO?Which of the following statements is enough to prove
Since PM=PN
And
[tex]LM\perp MN[/tex]While
[tex]MN\perp ON[/tex]We can assume that
[tex]\begin{gathered} LN=OM\text{ and bisect each other} \\ \text{Therefore,} \\ PM=OP\text{ and }PN=LP \end{gathered}[/tex]Then we can conclude that
[tex]\begin{gathered} LP=PO\text{ ( Isosceles triangle theorem)} \\ \angle\text{MPL}=\angle NPO(\text{ Vertically opposite angles)} \\ \text{hence,} \\ \Delta MPL=\Delta NPO(By\text{ sides angle side)} \end{gathered}[/tex]Therefore,
The correct answer IS OPTION C
tell whether the red line segment is the height or Stan height.
The slant height is the height that can be found using the height of the pyramid and the half length from the center of one of the sides to the center of the pyramid, this would be the hypotenuse.
The red line in this case represents the height of the pyramid.
A rare manuscript increased in value 400% over the past 4 years. This was an increase of $1,000. What was the value of the manuscript 4 years ago? What is the value of the manuscript now?The value of the manuscript 4 years ago was $.The manuscript is now worth $
Given
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
To find:
a) What was the value of the manuscript 4 years ago?
b) What is the value of the manuscript now?
Explanation:
It is given that,
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
Then, let x be the value of manuscript 4 years ago.
That implies,
[tex]\begin{gathered} 400\%\times4x=1000+x \\ \frac{400}{100}\times4x=1000+x \\ 16x=1000+x \\ 16x-x=1000 \\ 15x=1000 \\ x=\frac{1000}{15} \\ x=\text{ \$}66.67 \end{gathered}[/tex]And, the value of the manuscript now is,
[tex]\begin{gathered} 4x=4(66.67) \\ =\text{ \$}266.67 \end{gathered}[/tex]Hence, the value of the manuscript is $66.67, and the value off the manuscript now is $266.67.