The price of one mug before the sale is $3.89.
What was the price of one mug before the sale?The first step is to form an equation that represents the information in the question.
Total amount paid for the 5 mugs = (initial cost of the mug - discount amount) x number of mugs
$28.20 = (x - $1.75) x 5
$28.20 = 5x - 8.75
In order to determine the value of x, take the following steps:
Combine similar terms: $28.20 - 8.75 = 5x
Add similar terms: $19.45 = 5x
Divide both sides of the equation by 5: x = $19.45 / 5
x = 3.89
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De un depósito se gasta primero la mitad del agua, y luego la cuarta parte de lo que quedaba. Al final,
quedan 12 litros. Hallar la capacidad del depósito.
Answer:5/8 fraction of the deposit has been spent, which is 20 liters
Let "a" be the initial amount of water, then first half the water is used: then a / 2 of water is used and the other half is left at / 2 * (1/4), then the fourth part is used: then 1/8 * a is used, so now it remains: a / 2 - a / 8 = 3/8 * a, so 5/8 * a has been used, then what remains are 12 liters:
3/8 * a = 12 L
a = 12 L * 8/3 = 32 L
Wasted: 32 L - 12 L = 20 L
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I need help asap pls.
Answer:
SSS I think
Step-by-step explanation:
SSS because It is side to side
5
Sarah want to buy shrimp at $10.99 a pound. How many pound can she
buy for $25? *Round to the nearest tenth, one decimal place
Answer:
2.3 (or 2.293)
Step-by-step explanation:
25/10.99
If a = (x-3) and b = (x+3), show that 2ab = 2x square - 18
Step-by-step explanation:
ab = (x - 3)(x + 3)
multiply
ab = x² + 3x - 3x - 9
Simplify
ab = x² - 9
---------------------------
2ab = 2(x² - 9)
Distribute
2ab = 2x² - 18
Part B
Write a numerical expression that represents the area Sabrina painted the second weekend. Using this numerical expression, find the area that Sabrina painted the second weekend.
Step-by-step explanation:
she painted half of the still to be painted area.
after the first weekend there were 800 of 1600 ft² painted, and therefore 1600 - 800 = 800 ft² left to be painted.
on the second weekend she then painted half of that :
800 / 2.
that means she painted 800/2 = 400 ft², and that left 800 - 400 = 400 ft² to be painted on the following weekends.
if we look in detail, we find the starting 800 ft² of the second weekend are already the result of the first weekend.
800 = 1600 / 2
so,
800 / 2 = 1600 / 2 / 2 = 1600 / 2² = 1600 / 4.
and the same principle goes on weekend after weekend.
therefore, the expression for the nth weekend could be
1600 × (1/2)^n ft²
that means, she painted
on the 1st weekend : 1600 × 1/2 = 800 ft²
on the 2nd weekend : 1600 × 1/4 = 400 ft²
on the 3rd weekend : 1600 × 1/8 = 200 ft²
on the 4th weekend : 1600 × 1/16 = 100 ft²
...
that also means : she will never be finished, as she always paints only half of what is still left open, and that leaves always some part open. it will be tinier and tinier over time, but never 0.
The function f(x) = –5x2 + 13x + 6 represents the height, in meters, of a coin x seconds after it is thrown into the air. What is the maximum height of the coin
The maximum height of the coin is approximately 14.825 meters.
To find the maximum height of the coin, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by:
x = -b/2a
where a = -5 and b = 13 are the coefficients of the quadratic function f(x) = -5x^2 + 13x + 6.
Plugging these values into the formula, we get:
x = -13/(2×(-5)) = 13/10
Now we can find the y-coordinate of the vertex by plugging in x = 13/10 into the function:
f(13/10) = -5(13/10)^2 + 13(13/10) + 6
Do the arithmetic operations
≈ 14.825 meters
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Line x is parallel to line y. Line z intersects lines x and y.
1/2
4/3
5/6
8/7
Determine whether each statement is Always True, Sometimes True, or Never True.
Always True Sometimes True Never True
m2 1 + m 24 = 180°
m2 5 - m2 7 = 0°
ZIY
22 28
m22-23= m_1-m24
ооооо
OOOOO
ооооо
The ∠1+∠4=180 degree is always true, ∠5-∠7=0 is always true , z⊥y is sometimes true, ∠2≅∠8 is always true and ∠2-∠3=∠1-∠4 be sometimes true.
What is Coordinate System?Arrangement of reference lines or curves used to identify the location of points in space is called coordinate system.
Line x is parallel to line y.
Line z intersects lines x and y.
∠1+∠4=180 degree is always true.
∠5-∠7=0 is always true because the two angles are true.
z⊥y is sometimes true.
∠2≅∠8 is always true because the two angles are congruent.
∠2-∠3=∠1-∠4 will be sometimes true.
Hence, the ∠1+∠4=180 degree is always true, ∠5-∠7=0 is always true , z⊥y is sometimes true, ∠2≅∠8 is always true and ∠2-∠3=∠1-∠4 be sometimes true.
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the ratio of dividends to the average number of common shares outstanding is:
The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.
To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.
For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.
In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.
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Quentin agreed to pay 7% shipping and handling charge. If Quentin paid $9. 45 in shipping and handling, how much must the racquet have cost?
Answer:
The cost of the racquet is $135
Step-by-step explanation:
Let
x-----> the cost of the racquet
we know that
The racquet represent the 100%
so
using proportion
x/100%= $9.45/7%
x=100%*($9.45)/7
x=$135
My math teacher help me with it.
entering to par
C.
What is the unit rate, and what does it represent in the context of this situation.
C=50p to find the total cost,c, for the number of people p, entering a local amusement park. What is the unit rate, and what does it represent in this context
Answer: you would simple multiply the cost c which is fifty bucks times the number of p people
Step-by-step explanation: how much would it cost for 6 people to go to the fair to solve this you would just set up the equation 6 * 50 and solve from there
Write an equation of the line that passes through the points.
(0,1),(−2,−5)
Answer:
y=4/-2
Step-by-step explanation:
I think that is the answer
Answer:
\(y=3x+1\)
Step-by-step explanation:
Given the following question:
Point A = (0, 1) = (x1, y1)
Point B = (-2, -5) = (x2, y2)
In order to find the answer, we must first find the slope of the two given points by using rise over run.
\(m=\frac{y2-y1}{x2-x1}\)
\(m=\frac{-5-1}{-2-0}\)
\(m=\frac{-5-1}{-2-0} =\frac{-6}{-2}\)
\(=\frac{-6}{-2} =-6\div-2=3\)
\(m=3\)
Now that we know the slope, we can now write the equation in slope intercept form.
\(y=mx+b\)
\(m=3\)
\(y=1\)
\(x=0\)
Substitute:
\(1=3(0)+b\)
\(3\times0=0\)
\(1=b\)
\(b=1\)
\(y=3x+1\)
Hope this helps.
The lifetime of a camera costing $500 is exponentially distributed with mean 3 years. The manufacturer agrees to pay a full refund to a buyer if the camera fails during the first year following its purchase, and a one-half refund if it fails during the second year. If the manufacturer sells 100 cameras, how much should it expect to pay in refunds? Choose the correct answer below. A. $16,655 B. $21,409 C. $16,964 D. $14,969 E. $19,253
If the manufacturer sells 100 cameras, the expected refunds to be paid is $16,655(A).
To calculate the expected refund amount, we need to consider the probabilities of the camera failing during each year and the corresponding refund amounts.
The probability of the camera failing during the first year is given by P(X ≤ 1) = ∫[0, 1] f(x) dx = 1 - e^(-1/3) ≈ 0.2835.
The probability of the camera failing during the second year (but not the first year) is given by P(1 < X ≤ 2) = ∫[1, 2] f(x) dx = e^(-1/3) - e^(-2/3) ≈ 0.2027.
Since the manufacturer sells 100 cameras, the expected refund amount can be calculated as:
Expected refund amount = (100 cameras) × (0.2835 × $500 + 0.2027 × $250) = $16,944.50.
Hence, the correct answer is A. $16,655.
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Find the probability, expressed to the nearest percent, that a variable has a z-score less than 0.42. 65% 6690 6798 689
Explanation:
The probability that a variable has a z-score less than a number - let's call this number 'a'- is represented on a z-score table. Each number in the table represents the area under the curve on to the left of 'a':
In other words, the numbers in the table are the probability of the variable being less than a:
\(P(Z\(P(Z<0.42)=0.6628\)If we multiply by 100 we have the probability expressed as a percent: 66.28%.
Answer:
Rounded to the nearest percent, P( Z < 0.42) = 66%
g a simple undirected graph has 10 edges. 2 of the vertices are of degree 4, and the rest of the vertices are of degree 3. how many vertices are in this graph?
Therefore, there are 4 vertices in this graph.
Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.
We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.
If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:
3v + 2 * 4 = 20
3v = 12
v = 4
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Whare the vertex and range of y = |2x + 6| + 2?
The vertex of the absolute value function is (-3, 2) and the range is y ≥ 2
What is the vertex and range of the absolute value function?For a general absolute value function:
y = |a*x + b| + d
The vertex is at the value of x such that the argument of the absolute value part becomes zero, this is at:
a*x + b = 0
x = -b/a
And the y-value of the vertex is c
In our case:
y = |2x + 6| + 2
The vertex is at:
x = -6/2 = -3
y = 2
So we can write it as (-3, 2)
Finally, remember that the absolute value function opens upwards, then its range will be the set of all values larger than 2.
y ≥ 2
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IN DESPERATE NEED OF HELP
PLEASE HELP
NEED HELP WITH THE QUESTION IN THE PHOTO
NEED TO SHOW ALL MY WORK
THANKS
*15 Points* need help quickly plz
Answer:
Both of these statements are correct.
Step-by-step explanation:
Adjacent means next to each other, vertical angles are like angles 2 and 5, where they are right across from each other.
I hope this helps/ makes sense!!!
in the accompanying diagram of right triangle ABC , AB= 4 meters , and BC = 7. What is the approximate length of AC
The calculated approximate length of the segment AC is 8 meters
What is the approximate length of ACFrom the question, we have the following parameters that can be used in our computation:
AB = 4 meters
BC = 7 meters
Using the Pythagoras theorem, we have
AC^2 = AB^2 + BC^2
Substitute the known values in the above equation, so, we have the following representation
AC^2 = 4^2 + 7^2
So, we have
AC^2 = 65
Take the square roots
A = 8 (approximately)
Hence, the approximate length of AC is 8 meters
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4. There are major chords built on what three notes (with all white notes and no accidentals)? O CFG O ABC GEB OCDE
The three major chords built on white notes without accidentals are:
1. C major chord (C, E, G)
2. F major chord (F, A, C)
3. G major chord (G, B, D)
These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.
Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.
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Dec Average
July Aug Sept Oct Nov
740 800 650 820 820
120
880
3.
150 300 80
100
150
b.
200
240
320
300
280
220
C.
104
108
126 140 120 104
d.
80
90
60
80
100
88
Electricity
140
120
90 140
160
Water
52
58
62
48 48
62
9.
The Shahs decided they would not use the September amounts, when they were on vacation, nor the December amounts, when cousins stayed with them. Assume the chart
is a spreadsheet with row 1 as the month labels and column A as the expense categories.(Please put "=" sign if required in answers)
a. Write a spreadsheet formula to calculate the adjusted average for food.
b. What is the adjusted average for food?
Groceries (Food)
Dining Out
Fuel (car)
Cell Phone
Land Line Phone
160
c. Write a spreadsheet formula to calculate the adjusted average for electricity.
d. What is the adjusted average for electricity?
Answer:
a. The stem-and-leaf plot shows data for two different schools, but it does not give us information on which school is Bay Side and which school is Seaside. Assuming the first column is Bay Side and the second column is Seaside, the measures of center for each school are:
Bay Side: median = 6, mode = 5 and 6
Seaside: median = 5, mode = 5
b. The measures of variability for each school are:
Bay Side: range = 8 - 2 = 6, IQR = Q3 - Q1 = 8 - 5 = 3
Seaside: range = 8 - 0 = 8, IQR = Q3 - Q1 = 8 - 1 = 7
c. If you are interested in a smaller class size, Seaside School is a better choice as it has a smaller median and range compared to Bay Side School.
a. The adjusted average for food can be calculated using the following spreadsheet formula:
=SUM(B2:G2)-B2-E2-F2-G2-C7
This formula adds up all the food expenses for the months of July, August, October, and November, and subtracts the September and December expenses, which were not included.
b. Using the formula above, the adjusted average for food is $725.
c. The adjusted average for electricity can be calculated using the following spreadsheet formula:
=SUM(B11:F11)-C11
This formula adds up all the electricity expenses for the months of July, August, October, and November, and subtracts the September expenses, which were not included.
d. Using the formula above, the adjusted average for electricity is $132.
Step-by-step explanation:
The diameter of a pearl is about 4 x 10-3cm and the diameter of an atom is about10-11m. How much larger than an atom is a pearl?Show your work.
a)14x 10∧-14times b) 4 x 10 ∧-14timesc) 14x 10∧-11times d) 4 x 10∧6times
Answer:
D. 4 × 10⁶ timesStep-by-step explanation:
The diameter of a pearl is
4 × 10⁻³cm = 4 × 10⁻⁵ mThe diameter of an atom is
10⁻¹¹mHow much larger than an atom is a pearl?
4 × 10⁻⁵ ÷ 10⁻¹¹ = 4 × 10⁻⁵⁺¹¹ = 4 × 10⁶ timesCorrect option is D
What is debris flow? What are the characteristics of flow and
deposition of a debris flow? How to monitor and reduce the risk of
a stream with potential debris flow?
Debris flow refers to a type of fast-moving landslide or mass movement that involves a mixture of water, soil, rocks, and other debris. It typically occurs in mountainous or hilly regions, especially after heavy rainfall or during periods of intense snowmelt.
The characteristics of debris flow include high velocity, thick consistency, and destructive power. They often exhibit a turbulent, surging flow pattern and can transport large volumes of material downstream. Debris flows have the ability to erode and carry away sediment, rocks, and vegetation, causing significant damage to infrastructure, property, and natural environments.
To monitor and reduce the risk of a stream with potential debris flow, various measures can be implemented. Monitoring techniques may include the installation of gauges and sensors to measure rainfall, water levels, and ground movement. Early warning systems can be established to alert residents and authorities of potential debris flow events.
To reduce the risk, structural measures such as the construction of debris flow barriers or channels can be implemented to divert or contain the flow. Land-use planning and zoning regulations can help restrict development in high-risk areas.
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Solve the right triangle. If two sides are given, give angles in degrees and minutes.
Concept:
The diagram below represents the question given
The given dimensions from the question are
\(\begin{gathered} \angle A=10^038^{\prime} \\ c=271ft \end{gathered}\)Step 1:
We will convert the angle at A from degree minutes to degree decimal
\(\begin{gathered} \angle A=10^038^{\prime} \\ \angle A=10^0+\frac{38}{60} \\ \angle A=10^0+0.63^0 \\ \angle A=10.63^0 \end{gathered}\)Step 2: Calculate the value of b
To calculate the value of b, we will use the trigonometric ratio below
\(\begin{gathered} \cos A=\frac{Adjacent}{\text{hypotenus}} \\ \text{where,} \\ A=10.63^0 \\ \text{Adjacent}=b \\ \text{Hypotenus}=c=271ft \end{gathered}\)By substituting the values, we will have
\(\begin{gathered} \cos A=\frac{Adjacent}{\text{hypotenus}} \\ \cos 10.63^0=\frac{b}{271} \\ \cos 10.63=\frac{b}{271} \\ \text{cross multiply, we will have} \\ b=\cos 10.63\times271ft \\ b=266.35ft \end{gathered}\)Step 3: Calculate the value of c
To calculate the value of c, we will use the trigonometric ratio below
\(\begin{gathered} \sin A=\frac{opposite}{Hypotenus} \\ A=10.63^0 \\ \text{opposite}=a \\ \text{Hypotenus}=c=271ft \end{gathered}\)By substituting the values, we will have
\(\begin{gathered} \sin A=\frac{opposite}{Hypotenus} \\ \sin 10.63^0=\frac{a}{271} \\ \sin 10.63^0=\frac{a}{271ft} \\ \text{cross multiply, we will have} \\ a=\sin 10.63^0\times271 \\ a=49.99ft \end{gathered}\)Hence,
The final answers are
a= 49.99ft
b= 266.35ft
5. Which ordered pair, if any, is the solution to the system of linear equations here?
x-y=-4
–2x+2y=6
A. no solution
B. (-2,6)
C. (-6,-2)
D. (6,2)
Answer:
A. no solutionStep-by-step explanation:
Given:
Isolate the term of x and y from one side of the equation.
x-y=-4 and -2x+2y=6x-y=-4
First add by y from both sides.
x-y+y=-4+y
Solve.
x=-4+y
You have to substitute of x=-4+y.
\(\sf{-2\left(-4+y\right)+2y=6}\)
Solve.
Use the distributive property.
Distributive property:
⇒ A(B+C)=AB+AC
-2(-4+y)
Multiply expand.
-2*-4=8
-2*y=-2y
Rewrite the expression down.
8-2y
8-2y+2y=6
-2y+2y=0
8=6
\(\Longrightarrow: \boxed{\sf{\text{\sf{NO solution}}}}\)
Therefore, the correct answer is "A. No solution".I hope this helps, let me know if you have any questions.
Santino tried to find the median from the following table, which shows the number of internet users in
2012
20122012 for the highest using countries. However, he made a mistake.
Country China United States Japan India Brazil
Number of internet users (in millions)
568
568568
254
254254
101
101101
152
152152
100
100100
Here is Santino's work:
"The numbers are
568
568568,
254
254254,
101
101101,
152
152152, and
100
100100.
There are
5
55 values, so the middle value is the
3
rd
3
rd
3, start superscript, start text, r, d, end text, end superscript value,
101
101101. The median is
101
101101 million internet users."
The correct Median from the given table is 152 million internet users, not 101 million internet users as Santino calculated.
Santino's work is incorrect in determining the median from the given table. Let's analyze the correct approach to finding the median.
the median, we need to arrange the values in ascending order. Let's rearrange the numbers:
100, 101, 152, 254, 568
Now, we have five values in total. The median is the middle value when the numbers are arranged in ascending order. Since we have an odd number of values, the median will be the third value.
Therefore, the correct median is 152 million internet users.
Santino mistakenly identified the third value as 101 million internet users. However, he failed to consider the correct ordering of the values and mistakenly identified the third value as the median.
the correct median from the given table is 152 million internet users, not 101 million internet users as Santino calculated.
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convert this equation into standard form
y=-0.25(x+0)(x-8)
Find an equation of the line that passes through the points (1,2) and (2,3).
es
A)
y=x-1
B)
y= x + 1
9
y=x-2
D)
y = 2x - 1
Answer:
Answer is B.) y= x+1
Step-by-step explanation:
hope this helps
a fair die has its faces numbered from 1 to 6. let random variable f represent the number landing face up when the die is tossed. the probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. for each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded.
The probability distribution for the random variable f, the number landing face up when the die is tossed, is a discrete uniform distribution. The mean and standard deviation of this distribution are given as 3.5 and 1.7078, respectively.
When the die is tossed 5 times and the mean of the 5 values landing face up is recorded, this is referred to as a sample mean. The sample mean of 5 tosses of a die is also a random variable and its distribution is called the sampling distribution of the sample mean.
The simulation with 400 trials that you described is designed to estimate the sampling distribution of the sample mean. This can be done by repeating the process of tossing the die 5 times, finding the mean of the 5 values, and recording the result, 400 times. By collecting the sample mean values over 400 trials, it will give an idea of the distribution of the sample mean.
It's worth noting that as the sample size increases, the sampling distribution of the sample mean becomes closer to a normal distribution, known as the central limit theorem. And the mean of the sampling distribution becomes equal to the mean of the original distribution and the standard deviation of the sampling distribution becomes smaller.
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You can use a table to find a constant rate of change a) The table shows the amount of money a booster club makes washing cars for a fundraiser. Use the information to find the constant rate of change in dollars per car
Answer: $8
From the table given, we obtained the below information
Number of cars Money ($)
5 40
10 80
15 120
20 160
Calculate the constant rate of change in dollars per car
For the first given data
The total number of cars washed is 5
The total money to washed the 5 cars is $40
Rate of change in dollars per car = Total amount of money / the total number of cars
Rate of change = 40 / 5
= $8
The same procedure applicable to the rest data
For 10 cars and $80
The rate of change in dollars per car =80/10
= $8
For 15 cars and $120
The rate of change in dollars = 120 / 15
= $8
For 20 cars and $160
The rate of change in dollars per car = 160 / 20
= $8
The constant rate of change in dollars per car is $8
The answer is $8
Simplify the equation
Answer:
2/3 or 0.6
Step-by-step explanation:
\((m)/(3)\times (n)/(2)-:(mn)/(4)\)=2/3
Hope it helped you brainiest plz and thank you!!!!!!!!