A) The matrix equation that represents the given information is;
[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]
B) The cost of a banana is; $0.05
The cost of an orange is; $0.12
How to create and solve a matrix equation?A matrix equation is defined as an equation where a variable stands for a matrix .
Let x represent cost of oranges
Let y represent cost of bananas
5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas
cost me $1.41. Thus, the equations are;
5x + 14y = 1.30 ----(1)
8x + 9y = 1.41 -----(2)
A) Now, the matrix form of the simultaneous equation above will be;
[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]
B) Multiply the first equation by 8 and the second one by 5 to get;
40x + 112y = 10.4
40x + 45y = 7.05 Subtract to get;
67y = 3.35
Divide both sides by 67 to get;
y = $0.05 per banana
Plug in 0.05 for y into eq 1 to get;
5x + 14(0.05) = 1.30
5x + 0.7 = 1.3
5x = 1.3 - 0.7
5x = 0.6
x = 0.6/5
x = $0.12
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Write 12.4% as a decimal and a simplified fraction.
O 1.24 and 124
1,000
31
O 0.124 and 250
O 1.24 and 31
250
O 0.124 and
124
1,000
Answers:
decimal form = 0.124
simplified fraction = 31/250
=========================================================
Explanation:
To convert from percent to decimal, we move the decimal point 2 spots to the left.
12.4% converts to the decimal form 0.124
Optionally you could use your calculator to say 12.4/100 = 0.124
--------
To convert from a terminating decimal to a fraction, we write the decimal digits over some power of 10. In this case, we write the "124" over 10^3 aka 1000. We write it over 1000 since the '4' is in the thousandths place value. Then reduce as much as possible.
124/1000 = (31*4)/(250*4) = 31/250 is the simplified fraction form
Use your calculator to see that 31/250 = 0.124 to confirm the answer.
work out
5/6 × 48
120 x 2/3
Answer:
1. 130/6
2. 240/3
Step-by-step explanation:
make the whole numbers into a fraction by putting 1 as the denominator.
48/1.
then multiply together.
48 x 5 = 130
6 x 1 = 6
130/6
do the same with the other
120 x 2 = 240
1 x 3 = 3
240/3
Answer:
40
80
Step-by-step explanation:
5/6 × 48
5 × 48 = 240
240/6
= 40
120 × 2/3
120 × 2 = 240
240/3
= 80
slope of the line passing through (3,-4), (-5,2)
Answer:
[tex]\boxed{\sf Slope( m)=-\cfrac{3}{4}}[/tex]
Step-by-step explanation:
To find the slope between two points we'll use the Slope formula:-
[tex]\boxed{\sf \mathrm{Slope(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]
______________
Given:-
(3,-4)(-5,2)Where,
[tex]\mathrm{\left(x_1,\:y_1\right)=\left(3,\:-4\right)}[/tex]
[tex]\mathrm{\left(x_2,\:y_2\right)=\left(-5,\:2\right)}[/tex]
[tex]\mathrm{m=\cfrac{2-\left(-4\right)}{-5-3}}[/tex] ← Subtract
[tex]\sf m=-\cfrac{6}{8}[/tex]
[tex]\sf m=-\cfrac{3}{4}[/tex]
Therefore, the slope of the line is m = - 3/4.
______________________
Hope this helps!
Have a great day!
Find x 96+2x+(x+12).
Answer:
bro u find it
Step-by-step explanation:
given three sets: a, b and c. a has 19 elements. b has 15. c has 14. the pair-wise intersections have 7 elements. the three sets share 2 elements. how many elements are there in total?
29 elements are there in total for sets A, B, and C
Since we are provided the values of pair-wise intersections which are: |A∩B|=|A∩C|=|B∩C|= 7 and the three sets have common is |A∩B∩C| = 2 and individual sets were having |A|=19 ,|B|=|15 and |C|=14. The formula we are referring to for calculating the total elememets altogether is A∪B∪C|=|A|+|B|+|C|−|A∩B|−|A∩C|−|B∩C|+|A∩B∩C|, where |A|,|B|,|C|quantity for individual sets,|A∩B|,|A∩C|,|B∩C| are the intersection subsets in a pairwise, and|A∩B∩C| is the intersection subset for the three sets altogether.
So substituting the know values in the above format, we get
=> |A∪B∪C|= 19+15+14-7-7-7+2
=>|A∪B∪C|=29
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which statements is true of the function f(x)= x2 + 6x3 - 4 + 2x5?
A. the function is positive for all values of x
B. the end behavior of the graph f(x) is similar to that of g(x) = -x
C.the graph has exactly one x-intercept
D. the function is increasing for all real numbers
The statements is true of the function f(x)= x^2 + 6x^3 - 4 + 2x^5 is C.the graph has exactly one x-intercept
How to show that the function has one interceptIt is shown that the function has one intercept in the x direction by plotting the graph of the polynomial
The graph showed one x intercept is at the coordinate (0.778, 0)
x intercept refers to the value of x when y is zero
The graph is plotted and attached
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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Two friends visited a taffy shop. Gordon bought 8 pounds of strawberry taffy and 3 pounds of banana taffy for $66. Next, Levi bought 10 pounds of strawberry taffy and 3 pounds of banana taffy for $78. How much does the candy cost?
I NEED AN ANSWER ASAP LIKE BEFORE TOMORROW
The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given,
Let's say the cost per pound of strawberry taffy is "s" and the cost per pound of banana taffy is "b".
Then, the cost of 8 pounds of strawberry taffy and 3 pounds of banana taffy will be,
8s + 3b = 66
And,
The cost of 10 pounds of strawberry taffy and 3 pounds of banana taffy will be,
10s + 3b = 78
By solving both above equations,
2s = 12
s = $6
3b = 78 - 10(6)
b = $6
Hence, "The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6".
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if f(x) = 2x - 4 find f(a^2)
Answer: [tex]f(a^2)=2a^2-4[/tex]
Step-by-step explanation:
Substituting [tex]a^2[/tex] for [tex]x[/tex], [tex]f(a^2)=2a^2-4[/tex].
Determine whether the relation is a function.
(0, 1) (5, 6) (7, 9) (8, 9)
A. Not a function, there is not a unique y-value for each x-value
B. Not a function, there is not a unique x-value for each y-value
C. Function, there is a unique x-value for each y-value
D. Function, there is a unique y-value for each x-value
Answer:
C. Function, there is a unique x-value for each y-value
9.
X
22
9. W
Y
36%
(4w+14)
R
36%
In the given figure, w= 27
What is the Side Angle Side theorem?The two triangles are congruent if the two sides of one triangle are equal to the two sides of another triangle and the angles formed by the two sides of each triangle are equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.The Side-Angle-Side theorem of congruency states that, if two sides and the angle formed by these two sides are equal to two sides and the included angle of another triangle, then these triangles are said to be congruent.Verification:
Let's perform an activity to show the proof of SAS. Given: AB=PQ, BC=QR, and ∠B=∠Q. To prove: ΔABC ≅ ΔPQRPlacing the triangle ABC over triangle QPR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because of AB=PQ.The side BC will fall along the side QR since B=Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ABC will therefore match QPR. Consequently, ABCPQR. This exemplifies the SAS congruence criterion.Solution
From SAS
XY=QP and YZ=QR
therefore ∠Y = ∠Q
since the interior angles of the triangle are supplementary
∠Y + ∠X +∠Z = 180
∠Y + 22 + 36 = 180
∠Y = 180 - 58 = 122
therefore, ∠Q is also equal to 122
and (4w+ 14) =122
122 - 14 = 4w
108 = 4w
w = 108/4 = 27
Hence, from the SAS criterion
w is equal to 27
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Cesium-137 has a half-life of about 30 years. if we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?
For 200mg of Cesium-137, it will be 229 years which is less than 230 years until only 1 milligram remains.
The amount of time a radioactive item takes to decay is known as the material's half-life.
The first-order kinetics for a half-life is given as 0.693 / k.
Given half-life = 30 years,
k = rate-constant =?
30 = 0.693 / k
k = 0.0231 years ⁻¹
The integrated rate law for first-order kinetics is given as follows:
A = A₀[tex]e^{-kt}[/tex]
k = rate constant of the reaction
A₀ = Concentration of reactant initially = 200 mg
A = t = 1 mg
Putting all values in the equation will give,
t = 229 years.
Thus, Cesium takes 229 years to decay to reach from 200milligram to 1 milligram in weight.
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D. 4. A Jamaican Airline plane flew 1,200 miles southeast from Freeport Bahamas to San Juan Puerto Rico. The plane then flew 800 miles west to Montego Bay, Jamaica. The plane then flew north back to Freeport. To the nearest whole mile, how far did the plane fly from Montego Bay to Freeport? Bermada 1,200 miles Hast Dominican Bers 800 miles CARII WorldA Atlantic Ocean TUK
The flight of plane from Montego bay to freeport is 894 miles.
To solve this we use Pythagoras theorem.
What is Pythagoras theorem?
The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem.
Main Body:
Formula for Pythagoras theorem = [tex]P^{2} +B^{2}[/tex]= [tex]H^{2}[/tex]
here H = 1200
B= 800
P =?
solving this equation
1200² = 800²+P²
P²= 800000
P=[tex]\sqrt{800000}[/tex]
P ≈ 894 miles
Hence the distance of flight from Montego Bay to Freeport is 894 miles.
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a question posted on the lycos web site on june 18, 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes. what is the most likely issue with the sample they collected?
The most likely problem with the sample they gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".
Defined the term biased survey?This phrase describes the different factors and biases that may affect survey results. Either biased responses are deliberate or unintentional, they make survey results less valuable because they are erroneous.With participant surveys that ask for self-reporting, this might become a specific problem.Any survey's bias response is crucial since it determines the validity of the data, so preventing bias is absolutely necessary if you want insightful survey responses.Among the most prevalent types is leading bias. As an illustration, consider the scenario in which your question concerns customer happiness and the response alternatives are Very Satisfied, Satisfied, and Dissatisfied. Results in this case may be affected by bias.Thus, the most likely problem with the sample lycos web site gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".
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Two families go to a zoo. The Smith family of two adults and three children pay £61. The Jones family of three adults and five children pay £96. Work out the cost of an adult ticket and the cost of a child ticket. In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.
The cost of an adult ticket is £17 and a child ticket is £9.
Let's assume 'a' for an adult ticket and 'c' for a child ticket
The cost of tickets for the Smith family of 2 adults and 3 children is £61
Equating, [tex]2a+3c=61[/tex]
[tex]2a=61-3c[/tex]
Dividing by 2, [tex]a=30.5-1.5c[/tex] (equation 1)
Now, the cost of tickets for the Jones family of three adults and five children is £96
Equating, [tex]3a+5c=96[/tex] (equation 2)
Using equation 1, [tex]3(30.5-1.5c)+5c=96[/tex]
[tex]91.5-4.5c+5c=96[/tex]
[tex]91.5+0.5c=96[/tex]
[tex]0.5c=96-91.5[/tex]
[tex]0.5c=4.5[/tex]
[tex]c = \frac{4.5}{0.5}[/tex]
[tex]c=9[/tex]
Similarly, putting the answer of equation 2 in equation 1
we get, [tex]a=30.5-1.5c[/tex]
[tex]a=30.5-1.5(9)[/tex]
[tex]a=17[/tex]
Therefore, adult tickets cost £17 and child tickets cost £9
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50 POINTS
You are looking at starting a summer business mowing lawns to get started. You already need to purchase some items investing in your business. You already have a lawnmower, but below are the items you still need to purchase.
what is the total amount you plan to invest in your lawn mowing business? [__]
1. You just determined how much you are willing to invest to get your summer job started. Write an inequality to represent when you start making a profit if you charge $15 to mow one lawn.
2. at the end of the summer, you have mowed a total of 16 lawns right in equation that represents your total earnings. How much did you earn? [Show your work]
with investment costs taken into account, did you:
a. lose money
b. make money
Regarding the situation described, it is found that:
The total amount invested is of $25.
1. You start making a profit when 15x - 25 > 0.
2. You earned $215 with this work.
With the investment, you made money (option b).
What is the total amount investment?The investment was as follows:
Pack of 50 lawn bags for $10.Eye protecting glasses for $15.Hence the total amount invested was of:
10 + 15 = $25.
What is the profit inequality?The profit is given by revenue subtracted by costs.
In the context of this problem, the revenue and the cost functions are given as follows:
Revenue: R(x) = 15x (as you charge $15 to mow one lawn).Cost: C(x) = 25. (investment).Hence the profit function is:
P(x) = R(x) - C(x)
P(x) = 15x - 25.
You start making a profit when:
P(x) > 0.
15x - 25 > 0.
The amount you earned mowing 16 lawns is of:
P(16) = 15(16) - 25 = $215.
(positive profit, hence you made money).
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find the area of the credit card width 3 1/3in length 2 1/4in
Answer:
Step-by-step explanation:
A=lw
= 21/4 in * 1/3in= 21/12 in.^2= 7/4in^2 or 7/4 inch squared
Find the value of x. 50 points
Answer:
x = 53°
Step-by-step explanation:
Forming the equation,
→ x + (2x + 21°) = 180°
Now the value of x will be,
→ x + (2x + 21°) = 180°
→ 3x = 180° - 21°
→ x = 159°/3
→ [ x = 53° ]
Hence, the value of x is 53°.
The altitude of a triangular sign is 18 inches less than 3 times its base. Define the functions that describe the altitude and base of the triangle, and then use these functions to build an area function of the triangle
Functions to build an area function of the triangle , A = b2 + 2b.
What Altitude of a Triangle?A perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude. A triangle can be drawn with three altitudes because it has three sides. There are various types of elevations in triangles. When computing the area of a triangle, the altitude, also known as its height, is indicated by the letter.The section of a perpendicular line traced from a triangle's vertex to the side directly across from it is the triangle's altitude. The base of the triangle that the altitude touches forms a straight angle. It is often referred to as a triangle's height and is represented by the letter "h." The distance between the vertex and its opposing side can be calculated to determine its size. It should be remembered that every triangle has three altitudes that can be drawn from each of the vertices. See the intersection of the triangle's three elevations by paying attention to the triangle in the illustration below. The "Orthocenter" is this location.According to our question-
Let b = the base
altitude = 2b + 4
A = b(2b+ 4)/2
A = b(b + 2)
A = b2 + 2b
Hence, Functions to build an area function of the triangle , A = b2 + 2b.
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth
Step-by-step explanation:
imagine a circle with the center at the vertex of the angle x, and the radius 72 ft.
cos(x) = 28/72 = 7/18 = 0.388888888...
x = 67.11461952...° ≈ 67.1°
A rectangle container with a base area of 200cm2 is filled with water to a height of 15cm. If the container has a height of 20cm, how much water ( in litres) should be added to it to fill it completely?
If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .
In the question ,
it is given that
the base area of the rectangular container is = 200 cm²
the total height of the container = 20 cm
the height at which the water if filled = 15 cm
the height of water that is needed to be filled = 20 - 15 = 5cm
So , the volume of water to be added is = base area × height
= 200 × 5
= 1000 cm³
= 1 Liter .... because 1000cm³ = 1 Liter
Therefore , If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .
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Find the value of the variables in the figure.
The value of the variables in figure x and y are 14 and 28.5 respectively.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
We have been given the following parameters;
The two lines a and b are parallel to each other.
Therefore, Angle (5x - 7) and Angle (3x + 17) are the same because of alternate interior angles.
Thus, (5x - 7) = (3x + 17)
Solving;
(5x - 7) = (3x + 17)
5x - 3x = 17 + 7
2x = 28
x = 14
Now, we can see that Angle (5x - 7) and Angle (4y + 3) makes linear pairs on line A.
Thus, (5x - 7) + (4y + 3) = 180
Substitute x = 14
(5(14) - 7) + (4y + 3) = 180
70 - 7 + 4y + 3 = 180
4y + 66 = 180
4y = 114
y = 28.5
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The sum of 12 and a number. Use n for the variable. Responses 12/n 12/n 12 x n 12 x n 12 - n 12 - n 12 + n
The expression for the sum is (12 + n).
We are given two terms to add. The first number is 12, which is an integer. The second number is unknown. An integer is a number that has no decimal or fractional portion and can be negative or positive, including zero.
The second number is represented by a variable "n". A variable is a mathematical object's symbol and placeholder. A variable can, for example, represent an integer, a vector, or other data.
We need to write the expression for the sum of these two numbers. Let S represent the sum of these two numbers.
S = 12 + n
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simplify by using order of operations 22 - (8 x 1) divided by (6 - 4) - 2
The value of the expression 22 - (8 x 1) divided by (6 - 4) - 2 is 0.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
The expression given is:
22 - (8 x 1) divided by (6 - 4) - 2
= 22 - (8 x 1) ÷ (6 - 4) - 2
= [22 - 8] ÷ [2 - 2]
= 14 ÷ 0
= 0
The value is 0.
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Evaluate the expression below without using a calculator
With the help of trignometric identities we can say that the answer is = 0.672355, nearly.
What is trignometric equation?A trigonometric equation is any equation that contains a trigonometric function. Up until now we have introduced trigonometric functions, but not fully explore them. In the lessons within this SparkNote on trigonometric equations, we'll learn exactly how to solve trigonometric equations.As mentioned in Trigonometric Identities, a trigonometric equation that holds true for any angle is called a trigonometric identity. There are other equations, though, that only are true for certain angles.They are generally known as conditional equations, but in this text we'll just call them equations. We'll learn some techniques for solving general equations, as well as how to derive an infinite number of solutions to an equation based on a single solution to that equation.acc to our question-
cos(75)= 2-√3tan(22/7)= 1+√2.sin 3π/6= √2-√√2/2Learn more about trignometric equation:
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Translation rule:
(x, y) (x + 2, y – 4)
Either draw in the translated image or write down the new coordinates for the translated image
Step-by-step explanation:
it is really simple :
every x is increased by 2, every y is decreased by 4.
C = (-4, 2) -> C' = (-2, -2)
R = (-5, -1) -> R' = (-3, -5)
T = (-1, 1) -> T' = (1, -3)
Write the converse, inverse, and contrapositive of the following conditional statement.
"If I eat too much candy, I will get sick."
Converse: If I get sick, I ate too much candy.
Inverse: If I don't eat too much candy, then I will not get sick
Contrapositive: If I do not get sick, I did not eat too much candy.
What is the conditional statement?
'If p, then q's statements are examples of conditional statements. In this case, "p" stands for "hypothesis" and "q" for "conclusion."
A converse statement is one that is produced by flipping a conditional statement's hypothesis and conclusion.
So, Converse: If I get sick, I ate too much candy.
An inverse assertion presupposes that each of the original claims is true.
So, Inverse: If I don't eat too much candy, then I will not get sick.
When you reverse the hypothesis and the conclusion in a statement, you have a contrapositive statement that refutes both propositions.
So, Contrapositive: If I do not get sick, I did not eat too much candy.
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write down the probability of getting an odd number when you roll a 6 sided die
The probability of getting an odd number when you roll a 6 sided die is 1/2
How does probability explain work?
Simple terms, probability is the probability that an event will occur. When we do not even understand how an event will come out, we can analyze the probability or likelihood from several outcomes. Statistical is the analysis of events which match a posterior distribution.
What is the likelihood that the result of a roll of a standard six-sided die will be an odd number?
A cube with six faces makes up a standard six-sided die. They have the following numbers: 1, 2, 3, 4, 5, and 6. Any integer that is not divisible by two is an odd number. The odd numbers in this situation are 1, 3, and 5. The number of successful outcomes divided by the total number of possible outcomes can be represented as a fraction to represent the likelihood that any event will occur.
There are three correct answers to this puzzle, or the three odd integers. Additionally, there are six potential outcomes, ranging from one to six. When using standard six-sided die, there is a three-sixths, or three from out six, chance that the outcome will be an odd number.
Three can be divided by both three and six. As a result, this fraction can be expressed as one-half. One is equal to three divided by three. Additionally, two is equal to six times three. One-half or one in two chances exist that the result is strange.
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a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 l/min, the well mixed solution is pumped out at a rate of 6 l/min. find the number a(t) of grams of salt in the tank at time t.
The number of grams of salt in the tank at time t is given by the differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
What is rate?The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.
An equation with a function and one or more of its derivatives is referred to as a differential equation:
At the start, the tank contains A(0) = 30 g of salt.
Salt flows in at a rate of
(1 g/L) * (4 L/min) = 4 g/min
and flows out at a rate of
(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min
so that the amount of salt in the tank at time t changes according to
A'(t) = 4 - A(t)/50
So,
[tex]A'(t) = 4 - \frac{A(t)}{50}[/tex]
The solution of linear differential equation y' + ay = g(x) is in the form,
[tex]e^{ax}y=\int {e^{ax}g(x)} \, dx +c[/tex]
Now, putting the values,
[tex]a=\frac{1}{50} \\g(x)=4[/tex]
[tex]e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\[/tex]
Now,
[tex]A(t)=200+Ce^{-\frac{1}{50}t}\\[/tex]
Putting the initial value,
[tex]30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170[/tex]
So, the function will be [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
Therefore, the number of grams of salt in tank at time t is given by differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
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gold miners in alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. assume the amount of gold found per 1,000 tons of dirt is normally distributed. if the miners excavated 1,000 tons of dirt, how little gold must they have found such that they find that amount or less only 15% of the time?
Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.
Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:
X ~ N (12, 3²)
Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:
P (X ≤ K) = 0.15
When we transform this into a typical normal variable, we get:
P [Z ≤ (K - 12) / 3] = 0.15
From the common normal tables, we can deduce:
P (Z ≤ -1.036) = 0.15
Comparing the two equations above, we obtain:
(K - 12) / 3 = -1.036
K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892
As a result, 8.892 ounces of gold are needed.
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In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 64 degrees, angle QPR is equal to x, angle PRD is equal to 110 degrees.
A) The value of the measure of angle x is; x = 55 degrees.
B) The way we got x is that the Internal angle between 2 parallel lines are equal and also that the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.
What is the measure of the missing angles?A) From the given image attached, we see that the angle RPB can be calculated as;
m∠RPB = 180 - 120 = 60 degrees.
This is because sum of angles on a straight line sums up to 180 degrees.
Now, by definition of alternate angles, we can say that angle BPR is equal to 60 degrees.
Thus, the value of angle x is;
x = 180 - 60 - 65
x = 55 degrees.
B) From the given diagram, we can say that;
m ∠RPB + m < PRD = 180 degrees
This is because Internal angle between 2 parallel lines are equal.
Secondly the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.
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