(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even?
she needs to clean 15 uniforms to break even
Perimeter=8x-6 find the missing side of triangle
Answer:
Step-by-step explanation:
I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.
Need help in this question, with explanation please.
Answer:
a) (1/2)(5)(CD) = 20 cm^2
5CD = 40, so CD = 8 cm
b) (1/2)(12)(8) = 48 cm^2
Stan lawn mower had 1/8 of a gallon of gasoline in the tank he added 6/10 to the tank after he only had 1/4 of a gallon what was the total used
Stan used 19/40 of a gallon of gasoline.
Given that;
At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.
Hence, It means that the number of gallons of gasoline that he has already put in the tank is
1/8 + 6/10 = 29/40 of a gallon.
Now, After he mowed, 1/4 of a gallon was left in the tank.
Therefore, the total amount of gasoline Stan used is
29/40 - 1/4 = 19/40 of a gallon
Thus, the total amount of gasoline Stan used is, 19/40 of a gallon
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Use words to describe the relationship between the number of miles and each corresponding number of gallons.
10 gallons 300 miles.
The unit rate that relates the two quantities of distance and volume of gas is:
U = 30 miles per gallon.
How to describe this relation?To do so, we can find the unit rate.
This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.
Here we have the values:
10 gallons and 300 miles.
Then the unit rate is the quotient between these:
300miles/10 gallons = 30 miles per gallon
This says that with one gallon of gas you can travel 30 miles.
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Commutative property
Answer:
Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum
Select the correct answer from each drop-down menu.
Consider the expression below.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.
What is like term?In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).
The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.
Simplifying the expression we het 10 x + 5.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.
2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.
3. If the expression is set equal to -10x + 5, there would be only one solution.
10x + 5 = -10x + 5
20x = 0
x = 0
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The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
40 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A. Mean for both coffee shops because the data distribution is symmetric
B. Median for both coffee shops because the data distribution is not symmetric
C. Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
D. Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric
Why is the median better ?It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.
The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.
The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.
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Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
The logarithm expression can be simplified to:
In(6x^9)-In(x^2) =7·ln(6x)
How to write this as a single logarithm?There are some logarithm properties we can use here.
log(a) - log(b) = log(a/b)
log(a^n) = n*log(a)
(these obviously also apply to the natural logarithm)
Now let's look at our expression, it says that:
In(6x^9)-In(x^2)
Using the first rule, we can rewrite this as.
In(6x^9)-In(x^2) = ln(6x^9/x^2)
Now solving the quotient in the argument:
ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)
That is the expresison simplified.
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A small country emits 80,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 2.5% per year for the next 7 years. In the first year of the agreement, the country will keep its emissions at 80,000 kilotons and the emissions will decrease 2.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 7 year period, to the nearest whole number?
The total carbon dioxide emission over a period of 7 years will be 5,13,183 kilotons.
Considering the carbon emissions follow an exponential rate then
A(t)=A₀(1-r)^t
where A₀ is the initial value, and r is the decay rate as a decimal.
For the given problem A₀ =80000 kilotons and emissions will decrease at the rate of 2.5% per year therefore, r=0.025
The general equation for emission becomes
[tex]A(t)=80000(1-0.025)^t[/tex]
[tex]A(t)=80000(0.975)^t[/tex]
To calculate total emissions for 7 years it is calculated as follows
[tex]I=\int\limits^{7}_0 {A(t)} .dt=\int\limits^{7}_0 {80000(0.975)^tdt}[/tex]
[tex]I=80000(0.975)^t/ln (0.975)\left \{ {{t=7} \atop {t=0}} \right.[/tex]
I=5,13,183Kilotonnes
Hence, the total emission of 5,13,183 kilotons of carbon dioxide would be emitted over the course of the 7-year period.
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. Evaluate
11! 11!
24!
.
The evaluations are:
i. 11! = 39916800
ii. 24! = 2.045 x 10^37
What is expansion by factorial?Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;
5! = 5 x 4 x 3 x 2 x 1!
= 120
To evaluate the given expressions;
a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!
= 39916800
Also,
b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!
= 204484017332398 x 10 ^23
= 2.045 x 10^37
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ASAP PLEASE
The histogram shows data collected about the number of passengers using city bus transportation at a specific time of day.
A histogram titled City Bus Transportation. The x-axis is labeled Number Of Passengers and has intervals of 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 9. There is a shaded bar for 1 to 10 that stops at 2, for 11 to 20 that stops at 4, for 21 to 30 that stops at 5, for 31 to 40 that stops at 6, and for 42 to 50 that stops at 3.
Which of the following data sets best represents what is displayed in the histogram?
1 (4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42)
2 (4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
3 (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42)
4 (4, 6, 11, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42)
Answer:
Step-by-step explanation:
After organizing the data, the researcher must present them so they can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts and graphs. There are many different types of charts and graphs, and each one has a specific purpose.
This chapter explains how to organize data by constructing frequency distributions
and how to present the data by constructing charts and graphs. The charts and graphs
illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts,
and time series graphs. A graph that combines the characteristics of a frequency distribution and a histogram, called a stem and leaf plot, is also explained.
Section 2–2 Organizing Data 35
2–3
Objective
Organize data using
frequency
distributions.
1
2–2 Organizing Data
Suppose a researcher wished to do a study on the number of miles that the
employees of a large department store traveled to work each day. The researcher
first would have to collect the data by asking each employee the approximate distance the
store is from his or her home. When data are collected in original form, they are called
raw data. In this case, the data are
1 2 6 7 12 13 2 6 9 5
18 7 3 15 15 4 17 1 14 5
4 16 4 5 8 6 5 18 5 2
9 11 12 1 9 2 10 11 4 10
9 18 8 8 4 14 7 3 2 6
Since little information can be obtained from looking at raw data, the research
Answer:
c
Step-by-step explanation:
its ez
I need help on this I’m not to sure on it
Answer: your answer would be A.
Find f(−3), f(0) and f(1) for the following function.
f(x)=2x
Answer:
-6, 0, 2Step-by-step explanation:
f(x)=2x
note: putting anything in the f(x) parentheses replaces x in the function with that value
so,
f(-3) = 2(-3) = -6
f(0) = 2*0 = 0
f(2) = 2(2) = 4
An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink. If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink? Please help I have no clue how to do this at all. I listen in math class but this is hard!
The probability of drawing a pink case on the first draw is 30/80.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.
In the given question,
The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:
(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.
So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.
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natalie has $330mto send at the amusment park of this total amount 5% is soent on games, 5/11 is for food and drinks, and she spends $13 on parking. the rest of her budget is spent on buying a ticket for herself and a friend. what is the price of one ticket
Answer:
Step-by-step explanation:
This is a word problem involving percentages. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.
Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:
games+food and drinks+parking+tickets0.05×330+115×330+13+2x=total amount=330
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
16.5+150+13+2x2x2xxx=330=330−16.5−150−13=150.5=2150.5=75.25
Therefore, the price of one ticket is $75.25.
Me González designed a ramp for his caras shown in the picture below
what is the volume of the ramp in cubic feet
The ramp has a volume capacity of around 37.5 cubic feet.
How to solveCalculating the volume of a triangular prism shaped ramp follows a specific formula. First, identify the shape and refer to the equation:
Volume = (1/2) * Base Area * Height
To begin, the base is always in a right-angled triangle form, where its area depends on its width denoted as W, and height noted specifically as H.
Based on these computations, knowing that its triangular base measures 5 feet at its length while taking its height equates 3 feet therefore assessing how much it covers can be found using:
Triangle Area = (1/2) * Base * Height
Substituting values into solving areas leads us to have an answer of over 7 square feet.
Next is computing the volume of the said triangular prism. Placing all given data results in the same formula:
Volume = (1/2) * Base Area * Height
With one-half of the product of both areas which resulted in 7.5 square feet and then multiplying the figure by 10 ft, this yields us an approximate volume of 37.5 cubic feet.
In conclusion, we have determined that the ramp has a volume capacity of around 37.5 cubic feet.
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Length (L) = 10 feet
Width (W) = 5 feet
Height (H) = 3 feet
Mr. González designed a ramp for his car with a length of 10 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the ramp in cubic feet?
solution set of the following inequality 4x-1>15 is ........*
Answer:
4x - 1 > 15
4x > 16
x > 4
The solution set is all numbers greater than 4.
Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 15 square feet use 3.14 for pi
The distance from which the sprinkler can spread water is 4.37 feet
How to determine the valueTo determine the value, we need to know the area of the circle.
The formula for the area of a circle is expressed as;
A = πr²
Given that the parameters are;
A is the area of the circler is the radius of the circleSubstitute the values, we have;
15 = 3.14r²
Divide both sides by the coefficient, we get;
r² = 4. 77
find the square root of both sides, we get;
r = 2. 19 feet
But note that the formula for diameter is given as;
Diameter = 2radius
Diameter = 2(2.19)
multiply the values
Diameter = 4.37 feet
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HELPPPPPPPPPP... please help i don't get this whatsoever and my teacher doesn't really help. i dont get none of it at all. please help asap !
Answer:
I can tell
Step-by-step explanation:
Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)
Marisol is making bracelets and rings to sell at a craft fair She plans to sell each bracelet for $6 and each ring for $8. The craft fair committee charges a $25 fee to sell at the fair, and it costs Marisol $2 to make a bracelet and $4 to make a ring. If Marisol wants to sell at least $600 in jewelry and spend less than $300 for supplies and the fee, which system of inequalities represents the situation? Let b represent the number of bracelets and r represent the number of rings.
The equation that represent the number of bracelets b and the number of rings r is 6b + 8r > 600 and 2b + 4r < 275, hence, option A is correct.
Let b represent the number of bracelets and r represent the number of rings that Marisol makes. Marisol plans to sell each bracelet for $6 and each ring for $8. So the amount she earns from selling bracelets is 6b and the amount she earns from selling rings is 8r.
The craft fair committee charges a $25 fee to sell at the fair. So Marisol's total earnings after paying the fee is 6b + 8r - 25. It costs Marisol $2 to make a bracelet and $4 to make a ring. So the total cost of making b bracelets and r rings is 2b + 4r. To make a profit, Marisol's earnings must be greater than her costs,
6b + 8r - 25 > 2b + 4r
Simplifying this inequality, we get,
4b + 4r > 25
We also know that Marisol wants to sell at least $600 in jewelry. This can be expressed as,
6b + 8r > 600
Finally, Marisol wants to spend less than $300 for supplies and the fee. This can be expressed as,
2b + 4r + 25 < 300
Simplifying this inequality, we get,
2b + 4r < 275
Therefore, the system of inequalities that represents the situation is,
6b + 8r > 600
4b + 4r > 25
2b + 4r < 275
where b represents the number of bracelets and r represents the number of rings that Marisol makes.
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for the first question the answer choice is 35, 45, 145, 155,
the second question is a true or false answer
for the first question answer is 35 , which we can clearly see its pointing 35 degree in the protractor .second question is incomplete
what is protractor ?
To measure an angle using a protractor instrument, follow these steps:
Place the protractor on the angle: Place the flat side of the protractor on one of the angle's sides, making sure that the vertex (the point where the two sides of the angle meet) is at the center of the protractor.Align the protractor with the angle: Make sure the protractor is aligned with the angle you want to measure. The zero-degree mark on
In the given question,
for the first question answer is 35 , which we can clearly see in the protractor
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 4 feet and a height of 18 feet. Container B has a radius of 5 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.
What is volume of cylinder?[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.
To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.
The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.
Container A has a radius of [tex]4[/tex] feet and a height of 18 feet, so its volume is:
[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet
Container B has a radius of 5 feet and a height of 15 feet, so its volume is:
[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex] cubic feet
When the water from Container A is transferred to Container B, the volume of water in Container B will be:
V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet
The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:
V(empty in [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet
To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:
Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]
[tex]= (87\pi / 375\pi) \times 100[/tex]
[tex]= 23.2[/tex]%
Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.
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In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 40,000 dollars. Otherwise, they lose $1.
To find the probability of winning the lottery game, we can use the formula for combinations:
nCk = n! / (k! * (n - k)!)
where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).
So, the number of possible combinations of six numbers from 22 is:
22C6 = 22! / (6! * 16!) = 13,983,816
Therefore, the probability of winning the lottery game is 1 in 13,983,816.
The expected value of playing the lottery game can be calculated as follows:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)
Expected value = $0.5709
This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.
Which sequence below would best model the description? 50 points!
Please help me with this
There is higher variability of y with large values of x.
There is a non linear relation between x and y.
How to explain the variabilityWe observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.
Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.
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What is the answer to the equation?
-4(3/2x - 1/2)= -15
A. X= -19/6
B. X= - 29/4
C. X= 13/6
D. X= 17/6
Answer:
D
Step-by-step explanation:
- 4( [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ) = - 15 ← distribute parenthesis by - 4
- 6x + 2 = - 15 ( subtract 2 from both sides )
- 6x = - 17 ( divide both sides by - 6 )
x = [tex]\frac{-17}{6}[/tex] , that is
x = [tex]\frac{17}{6}[/tex]
a ups dispatcher sends a delivery truck to 10 different locations. if the truck stops at each location only once, how many different routes are possible
Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.
What is factorial notation?Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.
Here,
The number of different routes possible for the delivery truck can be calculated using factorial notation.
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
This simplifies to:
10! = 3,628,800
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A $162,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $14,650 annual income from the investments, how much should the bank invest in bonds? (It's okay to use your calculator to solve the system you set up on this problem.
The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
How to solve for the amount(162,000 - 2x) is invested in mortgages.
The annual income earned from the bond investment is:
0.09x
The annual income earned from the CD investment is:
0.07x
The annual income earned from the mortgage investment is:
0.10(162,000 - 2x) = 16,200 - 0.20x
The total annual income earned from the investments is:
0.09x + 0.07x + 16,200 - 0.20x = 14,650
Simplifying and solving for x, we get:
-0.04x + 16,200 = 14,650
-0.04x = -1,550
x = 38,750
Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
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