We conclude that there is zero (0) fraction of coal left in the bag with Tom.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
The numerator of a proper fraction is less than the denominator.
So, a fraction of coal left in the bag:
After 1 week the was 2/3 full. So, we have:
1 - 2/3 = 1/3
Next week, he used the remaining 1/3 coal. Now, we have:
1/3 - 1/3 = 0/0
Therefore, we conclude that there is zero (0) fraction of coal left in the bag with Tom.
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Correct question:
Tom bought a bag full of coal. After one week the bag was 2/3 full. During the next week, he used 1/3 of the remaining coal. What fraction was left in the bag?
Triangle PQR has the following measures: p= 16.2 m, q = 35.0 m, and m/R = 75°.
What is the area of triangle PQR?
After solving the area of the triangle PQR obtained will be equal to 273.6 m²
What is a triangle?
The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given information given in the question,
p= 16.2
q = 35.0 m and,
m ∠R = 75°
Find x by cosine rule,
cos 75° = (16.2² + 35² - x²)/(2 × 16.5 × 35)
x = 34.5 m
The value of r is 34.5 mm then the third side of the triangle pqr will be,
Use heron's formula,
s = (16.2 + 35 + 34.5)/2
s = 42.85
Area = [tex]\sqrt{s(s-p)(s-q)(s-r)}[/tex]
A = √42.85(42.85 - 16.2)(42.85 - 35)(42.85 - 34.5)
A = 273.6 m²
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Find the area of the composite figure. I got 78 but my teacher said that it is incorrect. WILL MARK BRAINLIEST! Thanks!
Answer:
44
Step-by-step explanation:
Essentially there are 3 triangles
The top left has a base of 5 and a height of 4
Its area is 1/2 x b x h = 1/2 x 5 x 4 = 10
Then there are two triangles with the same base of 2.5 + 6 = 8.5 and same height of 4 feet. So each of the triangles has the same area as the other.
Total area of both triangles = 2 (1/2 x b x h) = bh = 8.5 x 4 = 34
Total area = 10 + 34 = 44
Answer:
44 ft²
Step-by-step explanation:
Here's how I divided the parts of the composite figure:
1. There is a triangle at the left with the vertex pointing down and base above. The base is 5 ft. The height is 4 ft.
2. There are 4 triangles left. I divided them into two triangles like this:
An upper triangle which has a base of 2.5 ft + 6 ft, and a height of 4 ft with a horizontal base on the bottom and a vertex on the upper side.
A lower triangle that is a mirror image of the triangle just above. The dimensions are the same.
Triangle on upper left:
base = 5 ft
height = 4 ft
Triangles at right (2 triangles with the same dimensions)
base = 2.5 ft + 6 ft = 8.5 ft
height = 4 ft
area of triangle = base × height / 2
Total Area = (5 ft)(4 ft)/2 + 2 × (8.5 ft)(4 ft)/2
Total Area = 10 ft² + 34 ft²
Total Area = 44 ft²
Francisco is building a window seat below a bay window in the shape of an isosceles trapezoid. His blueprint for the window seat is shown below.
What is the area of the window seat?
Answer:
56
Step-by-step explanation:
the difference of vidya's age and 15 is 66 use the variable v to represent vidya's age
Answer:
[tex]\huge\boxed{\sf v = 81}[/tex]
Step-by-step explanation:
Let Vidya's age be v.
Given condition:v - 15 = 66
Add 15 to both sides
v = 66 + 15
v = 81[tex]\rule[225]{225}{2}[/tex]
Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)
The time taken for Bob take to run one lap of the track is 69 seconds
Akira is running around a circular track. Akira runs counterclockwise.
It takes him 95 seconds to run one complete lap
Bob starts running at the same time as Akira
Bob and Akira pass each other for the first time after 26 seconds
It takes him 95 seconds to run one complete lap
In 26 seconds he covers 26/95 laps
In this time Bob must have covered 69/95 laps
An inverse relationship
c/95 = 69/95
c = (69/95) x 95
c = 69
Therefore, time taken for Bob take to run one lap of the track is 69 seconds.
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9 2 8 7 6 5 1 4 3 show the contents of the array above each time an insertion sort changes it while sorting the array into ascending order.
The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.
A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.
Initial Pass: 2 9 8 7 6 5 1 4 3
The array's first two members are initially compared using an insertion sort.
Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.
Therefore, 2 is currently kept in a sorted sub-array.
Second Pass: Continue with the next two elements and compare them.
2 8 9 7 6 5 1 4 3
Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.
Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.
Moving on to the following two components, which are 9 & 7,
2 7 8 9 6 5 1 4 3
Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.
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two poles are connected by a wire that is also connected to the ground. the first pole is 30 ft tall and the second pole is 15 ft tall. there is a distance of 45 ft between the two poles. where should the wire be anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed?
At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x
The wire length from the top of the left pole to the anchor point is
[tex]L^{2} _l = 30^{2} + x^{2}[/tex]
= x² + 900
Similarly for the 2nd part of the wire
[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]
= 256 + 2025 - 45x + x²
= x² + 2281 - 45x
We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]
√x² + 900 + √ x² + 2281 - 45x
we can take the first derivative of this and set it to 0
[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]
x = 30
Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
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The average waiting time at a drive-in window of a local bank is 10. 3 minutes, with a standard deviation of 2. 7 minutes. Assume the variable is normally distributed. If a customer arrives at the bank, find the probability that the customer will have to wait between 4 and 9 minutes.
29.78% of customers will most likely probability be waiting between 4 and 9 minutes.
Explain the term z-score of the normal distribution?An observation's Z score indicates however many standard deviations it deviates from the mean. The standard normal distribution's mean is zero. Positive Z scores are those above the mean, while negative Z scores are those below the mean.The formula for the z score is-
z = (x - μ)/σ
In which,
μ = mean of 10. 3 minutes
σ = standard deviation of 2. 7 minutes.
z score for the x = 4 minutes.
z = (4 - 10.3)/2.7
z = -2.33
z score for the x = 9 minutes.
z = (9 - 10.3)/2.7
z = -0.48
Thus,
Probability that the customer will have to wait between 4 and 9 minutes.
P(4 < x < 9) = P(-0.48 < z < -2.33)
Use z score table-
P(4 < x < 9) = 0.3085 - 0.0107
P(4 < x < 9) = 0.2978
P(4 < x < 9) = 29.78%
Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.
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Olivia has has read 40 pages of a 70 page book, 60 pages of an 85 page book, and 43 pages. What is the percentage f pages that Olivia has not read?
Answer:
Below
Step-by-step explanation:
Total pages read = 40 + 60 +43 = 143 pages read
Total pages of all of the books = 70 + 85 + x
percentage READ = (143) / ( 70 + 85 + x) * 100% = ???
percentage NOT read = 100 - ???
(since 'x' was not given in the question post)
Read pages:
40+60+43=143
All pages:
70+85+43=198
198-143=55
55/198=0,2778
0,2778×100%=27.78%
Simplify: 8x62x4
A.6x2
B.4x2
C.8x10
D.10x10
a tower that is 106 feet tall casts a shadow 135 feet long. find the angle of elevation of the sun to the nearest degree.
The angle of elevation of the sun is [tex]tan^{-1}[/tex](106/ 135).
The angle of elevation:
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
Here we have to find the angle of elevation of the sun.
Data given:
length of the tower = 106 feet
shadow form by the tower = 135 feet
The formula for the angle of elevation = height/base
tanФ = height/base
= 106/ 135
Ф = [tex]tan^{-1}[/tex](106/135)
Therefore the angle of elevation is [tex]tan^{-1}[/tex]( 106/ 135).
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An initial population of 20 fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are 52 fish in the
lake after 7 years.
New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.
a) Create a probability model for this game.
b) Find the expected value and standard deviation of your prospective winnings.
c) You play this game five times. Find the expected value and standard deviation of your average winnings.
d) 100 people play this game. What's the probability the person running the game makes a profit?
a) Probability model
P(40) = 1/6
P(0) = 5/36
P(-10) = 25/36
b) E(X) = -5/18
standard deviation = 18.331
c) standard deviation = 91.65
d) Probability = 0.560
From the question, we have
a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:
P(40) = 1/6
P(0) = (5/6)(1/6) = 5/36
P(-10) = 1 - 1/6 - 5/36 = 25/36
b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9
Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324
standard deviation = sqrt [Var X] = 119043 / 6494 =18.331
c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
5 * E(X) = - 25/18
standard deviation = 5 * 18.331 = 91.65
d) Probability :
P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
Complete question:
From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?
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A pizza shop needs 5 ounces of cheese and 3 ounces of sauce to make one pizza. after 4 hours of being open one evening, the pizza shop has used 192 ounces combined of sauce and cheese. how many pizzas were made so far that evening?
The total number of pizzas were made in 4 hour in pizza shop is 24.
Describe the term unitary method?The unitary approach involves calculating the value of an individual unit, from which we can calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a separate unit.For the stated question-
For one pizza-
Ounce of cheese required = 5.
Ounces of sauce required = 3.
Total requirement = 8 ounces.
After 4 hours,
Total ounces combined of sauce and cheese used = 192.
Thus,
Number of pizza = 192 / 8
Number of pizza = 24
Thus, the total number of pizzas were made in 4 hour in pizza shop is 24.
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Graph the equation.
y = x
Answer:
Slope: 1
__________
y-intercept: (0,0)
Step-by-step explanation:
At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident. a) What is the probability that you will have to deal with no more than 4 incidents of identity theft in the next year (52 weeks)? b) When you have had 12 more incidents of identity theft, your company will send a detective to investigate. What are the expected value and variance of the time (in weeks) until a detective is sent to investigate? c) Use normal approximation to find the probability that the detective will be sent within 2 years.
Answer: At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.
Step-by-step explanation:
Find the indicated side of the
right triangle.
30°
X
60°
3
Answer:
6
Explanation:
x = 3 /cos(60) = 6
Can someone please help me
Answer:
6
Step-by-step explanation:
Perimeter = 2l + 2w
48 = 2(18) + 2(w)
48 = 36 + 2w
12 = 2w
w = 6
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Given AB, find C which is 1/3 of the distance from A to B. A(1,2) B(-5,8)
Answer: (2,0)
Step-by-step explanation:
PLS HELP ASAP!!!! 50 PTS
Answer: x=4
Step-by-step explanation:
6x + 10 = 5x + 14
x + 10 = 14
x = 4
The equation of a line is 2y = 8x + 10
find the SLOPE of a line that is
a) parallel to the line
b) perpendicular to the line
c) neither parallel or perpendicular
State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial. Give an example proving your answer is correct.
Grading: 2 points: Correct Answer; 2 points: Explanation; 1 point: Example
The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.
A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.
An example of an unary expression is: 12
A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7
A trinomial is always of higher degree than a monomial is false statement .
A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.
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3x + 4x +5x = 4(x + 2) Please write as the actual answer and a decimal
Answer: 1
Step-by-step explanation:
We can rewrite the equation as
12x = 4x +8
8x= 8
x=1
can someone please help me?
The value of x in the given function, f(x) = 3/2x - 4 when f(x) = 5, is x = 6
Determining the value of x in a functionFrom the question, we are to determine the value of x in the given function for the given value of f(x).
The given function is
f(x) = 3/2x - 4
and
f(x) = 5
Now, to determine the value of x, put f(x) = 5 in the given function
f(x) = 3/2x - 4
5 = 3/2x - 4
Add 4 to both sides of the equation
5 + 4 = 3/2x - 4 + 4
9 = 3/2x
Multiply both sides by 2
2 × 9 = 2 × 3/2x
18 = 3x
Divide both sides by 3
18/3 = 3x/3
6 = x
Therefore,
x = 6
Hence, the value of x is 6
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Terry has a goal of making $300 in commission for the week. If her commission is based on 18% of sales how much does she need to sell to make her goal? I need an answer ASAP pls
The amount of sales Terry must make is $1667
How to determine the amount in sales?From the question, we have the following parameters that can be used in our computation:
Commission = 18% of sales
Commission = $300
These parameters mean that
Commission = 18% of sales
Substitute the known values in the above equation, so, we have the following representation
18% of sales = 300
Divide both sides by 18%
Sales = 1667
Hence, the amount is $1667
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I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $96 for the project. What are the dimensions of the vegetable patch with the largest area i can enclose?.
The dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
Given, a rectangular vegetable patch.
The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot.
We have a budget of $96 for the project.
Let the length of the rectangle be, l
and breadth of the rectangle be, b
according to the ques,
4l + 8b = 96
l + 2b = 24
l = 24 - 2b
Now, area of the rectangle be,
Area = length×breadth
Area = l×b
A = (24 - 2b)b
A = 24b - 2b²
On differentiating both sides, we get
A' = 24 - 4b
b = 6
l = 24 - 12 = 12
So, the dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
Hence, The dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
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Danni placed $5700 in a savings account which compounds interest continuously at a rate of 2. 1%. How much will she have in the account after 4 years? round your answer to the nearest whole number. Do not include a $ in your answer.
Using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Compound interest works by periodically adding collected interest to your main, which is the sum you first deposited into the savings account so that interest can then be earned on both.
In essence, your interest begins to generate interest of its own.
Compound interest formula: [tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]
Now, calculate the amount Danni will have after 4 years:
[tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]
A = 5700(1+0.021)⁴
A = 5700(1.0210⁴
A = $6,194.09
Therefore, using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.
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Answer:
A=6199.48
Step-by-step explanation:
Use the formula for calculating compound interest A=P0ert where A is the unknown, P0=5700, r=0.021, and t=4. Substitute the values into the formula and simplify.
A=5700e0.021⋅4
A=5700e0.084
A=5700(1.0876...)
A=6199.48
The amount in the account after four years is A≈6199, to the nearest dollar.
What is the average rate of change of the function f(x)=2(3)xfrom x = 2 to x = 4?.
The average rate of change of the function f(x)=2(3)x from x = 2 to x = 4 = 72
How do functions work?The term "function" refers to the relationship between a collection of inputs and outputs with one each. Simply described, a function is an association of inputs where each input is coupled with exactly one output. Every function has an associated domain, codomain, or range. The most common way to represent a function is as f(x), where x represents the input.
To calculate the average rate of change, use the slope formula:
y2−y1/x2−x1=m
f(4)−f(2)/4−2=m
Finding the values of f(4) and f(2) will help us to simplify this.
f(4)=2(3)4=2(81)=162
f(2)=2(3)2=2(9)=18
m=162−18/2
m=144/2
m=72
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.
What is an expression that represents the total amount that Zoe paid?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.
From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.
The expression will be:
= x + (5% × x) + (15% × 1.05x)
= x + 0.05x + 0.1575x
= 1.2075x
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Which set of ordered pairs (x, y) could represent a linear function
A = \{(1, - 2), (3, 1), (5, 4), (8, 7)\}
B = \{(- 6, 6), (- 3, 3), (0, 0), (3, - 4)\}
C = \{(- 2, 8), (- 1, 6), (0, 4), (2, 1)\}
D = \{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)\}
{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Linear function is a function whose graph is a straight line
Slope of a line tells us how steep the line is . Slope of a line is same at all the points.
For option A:
m=1+2/3-1=3/2
m=3/2
m=7-4/8-5=3/3=1
Slopes are not same
For option B:
m=3-6/-3+6=-3/3=-1
m=0-3/0+3=-1
m=-4/3
Slopes are not same
For option C:
m=6-8/-1+2=-2
m=4-6/1=-2
m=-3/2
Slopes are not same
For option D:
m=3-6/-4+8=-3/4
m=-3/4
m=-3/4
Slopes are same at every point, so this set of ordered pairs could represent a linear function
Hence, {(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function
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