Two customers spent the same total amount of money at a restaurant.
- The first customer bought 8 hot wings and left a $4 tip.
- The second customer bought 10 hot wings and left a $2.80 tip.
- Both customers paid the same amount per hot wing.
How much does one hot wing cost at this restaurant in dollars and cents?
One hot wing costs 60 cents at this restaurant.
What are unknown variables?A variable in an equation that has to be solved for is known as an unknown.
A polynomial or formal power series may contain an indeterminate symbol, often known as a variable. In the polynomial ring or the ring of formal power series, an indeterminate is a constant rather than a variable. Nonetheless, many writers view indeterminates as a distinct class of variables because of the close connection between polynomials or power series and the functions that they describe.
Let's us assume that the cost of one hot wing is x dollars.
Then,
Total amount spent by each customer:
8x + 4 = 10x + 2.8
8x - 10x = 2.8 - 4
-2x = -1.2
x = 0.6
Therefore, one hot wing costs 60 cents at this restaurant.
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Archimedes went to sleep beside a big rock. He wanted to get up at 7 77 AM, but the alarm clock was yet to be invented! He decided to sleep at the spot where the rock's shadow should end when it's 7 77 AM so as to be awakened by the direct sunlight. Archimedes knew that at 7 77 AM, the sunlight reaches the ground at an angle of 3 1 ∘ 31 ∘ 31, degrees. The rock beside which he slept was 5 55 meters tall. How far from the rock did Archimedes go to sleep? Round your final answer to the nearest hundredth.
Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.
Trigonometric ratios:Trigonometric ratios are ratios of the sides of a right triangle to its angles. The three primary trigonometric ratios are
Sine = opposite/hypotenuse.
Cosine = adjacent/hypotenuse.
Tangent = opposite/adjacent.
Here we have
Archimedes wanted to get up at 7. AM, but the alarm clock was yet to be invented. Archimedes knew that at 7.AM, the sunlight reaches the ground at an angle of 31°.
The rock beside which he slept was 5.55 meters tall.
Let's assume that the distance from the rock where Archimedes went to sleep is "x".
Form a right triangle where the height of the triangle is the height of the rock (5.55 meters) and the angle between the ground and the sunlight at 7 AM is 31° and the opposite side to that angle is x.
Using trigonometry, we can solve for x as follows
tan(31°) = 5.55 / x
x = 5.55 / tan(31°)
x = 5.55/0.60086
x = 9.24 meters
Therefore,
Archimedes went to sleep about 9.24 meters away from the rock where its shadow should end when it was 7 AM.
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Which of the following theorems verifies that ABC-DEF?
AA
63°
63
C
D
OA: AA
OB. HA
OC. LL
D. HL
The theorem that justifies the similarity of the two triangles is given as follows:
A: AA.
What is the Angle-Angle Similarity Theorem?The Angle-Angle (AA) Congruence Theorem states that if two pairs of corresponding angles are congruent, then the triangles are similar.
In other words, if two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle must also be equal in measure, and the two triangles are therefore congruent.
The two pairs of corresponding angles that are congruent in this problem are given as follows:
63º and 63º.90º and 90º. -> right angle.Hence the third angle will also have the same measure for both triangles.
Hence the AA theorem can be used and the correct option is given by option A.
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A 27-meter rope is cut into two pieces so that one piece is 2 meters longer than 4 times the shorter piece. Find the lengths of both pieces.
27-2=25
25:5=5
4(5)+2=20+2=22
the shorter piece = 5
the longer piece = 22
200 904/1000 as decimal
Answer:
200.904
Step-by-step explanation:
200904 is the same as 200904.0
On dividing by 1000, the point moves three steps to the left, 20090.4 , 2009.04 then finally 200.904.
A college professor randomly selects 10 of the 28 students in his statistics class and finds that
8 of them have part-time jobs in addition to being a full-time student.
He would like to construct a 90% confidence interval for the true proportion of students in his class who have part-time jobs in addition to being a full-time student.
Random condition:
✔ met
10% condition:
✔ not met
Large counts condition:
✔ not met
Are the conditions for inference met?
✔ no
(No one asked the question nor provided an answer, so here yous go FOR !!!!!EDGE2023!!!!!!!)
Answer:im confused
Step-by-step explanation:
Random condition:
✔ met
10% condition:
✔ not met
Large counts condition:
✔ not met
Are the conditions for inference met?
✔ no
common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and 95th percentile for men . In designing a work table the sitting knee height must be considered. Males have sitting knee heights that are normally distributed with a mean of 21.3 and s/d 1.2, Females have a mean of 19.9 in and a s/d of 1.1 . what is the minimum clearance required for safety of fitting 95% of men . True or False if 95% clearance for males ,there will certainly be clearance for all 5% of women. does the table fit anyone , what percentage. What percentage of womenfit the table.
The minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.
What is percentage ?
Percentage is a way of expressing a proportion or a ratio as a fraction of 100. It is often represented by the symbol % and is used to compare values, make comparisons, and analyze data. For example, if there are 25 red marbles and 75 green marbles in a jar, the percentage of red marbles is 25% (25/100), while the percentage of green marbles is 75% (75/100). Percentages are commonly used in many fields, including finance, business, statistics, and science.
To determine the minimum clearance required for safety of fitting 95% of men, we need to find the value of the sitting knee height at the 95th percentile for men.
Using the formula for a normal distribution, we can calculate that the sitting knee height at the 95th percentile for men is approximately 23.2 inches.
Therefore, the minimum clearance required for safety of fitting 95% of men would be the difference between the sitting knee height at the 95th percentile for men (23.2 inches) and the height of the work table.
Therefore, the minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.
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Can someone help me please? Thank you
Explain why m/NMO = 20°
Because of the isosceles triangle.
What is the isosceles triangle?The triangle whose two sides are equal length is called an isosceles triangle. The third side, known as the base, may or may not be a different length from the other two sides. An isosceles triangle also has two angles that are equal in measure, which are opposite the two equal sides.
Given that in ΔMQN: MQ=MN,
therefore, ∠MQP=60°=∠MNO (isosceles triangle )
also given in ΔMPO: MP=MO,
therefore, ∠MPO=80°=∠MOP (isosceles triangle )
For the straight line PON,
∠POM + ∠MON = 180° (straight line angle)
80° + ∠MON = 180°
∠MON = 100°
In ΔNMO,
∠NMO +∠MON + ∠MNO = 180° ()
∠NMO + 100° + 60° = 180°
∠NMO = 20°
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does inequality
2d+20<=120 explain?
The inequality 2d+20<=120 is a valid inequality. It means that some value of d can be substituted into the inequality to make it a true statement.
What is inequality?In mathematics, an inequality is a statement that compares two values and indicates how they are related in terms of magnitude or size. Inequalities use symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two values.
What is the types of inequality?Linear inequalities: These are inequalities in which the variables have a degree of one. For example, 2x + 3 < 7.Quadratic inequalities: These are inequalities in which the variables have a degree of two. For example, x^2 - 3x + 2 > 0.Rational inequalities: These are inequalities in which the variables appear in the denominator of a rational function. For example, (x + 3)/(x - 2) < 0.Absolute value inequalities: These are inequalities that contain absolute values. For example, |x + 2| < 5.In the given question,
Yes, the inequality 2d+20<=120 is a valid inequality. It means that some value of d can be substituted into the inequality to make it a true statement.
In this case, the inequality is saying that 2 times the value of d plus 20 is less than or equal to 120. To solve for d, we can subtract 20 from both sides to get:
2d <= 100
Then, we can divide both sides by 2 to isolate d:
d <= 50
So the solution to the inequality is that d must be less than or equal to 50 for the inequality to be true.
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O.5% as a fraction and decimal
Answer: As a fraction: 1/2
As a decimal: 0.005
Step-by-step explanation:
FRACTION:
To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.
DECIMAL:
0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.
Which retirement plan(s) is not managed by the U.S. government?
1. Fixed Annuity
II. Traditional IRA
III. Roth IRA
IV. Social Security
A. I, IV
B. II, III
C. I, III, IV
D. I, II, III
Answer:
I’m pretty sure 3
Step-by-step explanation:
Answer:
D. I, II, III
Step-by-step explanation:
Social security is the only plan managed by the government
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 1375 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week?
Answer:
Step-by-step explanation:
Let's call the number of gallons of gas consumed by the first car "x" and the number of gallons of gas consumed by the second car "y". We can set up a system of two equations to represent the information given in the problem:
x + y = 45 (equation 1: total gas consumption is 45 gallons)
35x + 25y = 1375 (equation 2: total distance traveled is 1375 miles)
To solve for x and y, we can use the first equation to solve for one variable in terms of the other. For example, we can solve for y as:
y = 45 - x
We can then substitute this expression for y into the second equation, and simplify:
35x + 25(45 - x) = 1375
35x + 1125 - 25x = 1375
10x = 250
x = 25
So the first car consumed 25 gallons of gas that week. We can substitute this value into equation 1 to find the number of gallons consumed by the second car:
25 + y = 45
y = 20
Therefore, the second car consumed 20 gallons of gas that week.
Determine what two whole numbers the radical is located between.
I tried 36 & 49 ?
The square root of 45 lies between the two whole numbers 36 and 49.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented in various forms, such as a numeral, a word, or an image. Numbers can be used to represent any quantity, such as a person's age, a distance, a temperature, or a length. They can also be used to represent abstract or intangible concepts, such as a feeling or a thought.
To determine this, we can use a process called the square root algorithm. The first step is to find the largest perfect square that is less than the number you are taking the square root of. In this case, that would be 36. Then, you subtract that perfect square from your number. In this case, you would subtract 36 from 45, leaving you with 9. The next step is to find the two whole numbers that the square root of this difference lies between. Since 9 is the square root of 81, the two numbers that the square root of 9 lies between are 3 and 4. Therefore, the square root of 45 lies between the two whole numbers 36 and 49.
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PLEASE HELP!! I do not understand how to try to solve this!!
Fractions
Barbara, Donna, Cindy and Nicole ran in a relay race. Their times are listed in the chart below
Barbara - 3 3/10
Donna- 2 4/5
Cindy- x
Nicole- 2 1/10
Question- The four girls ran in a relay race as a team. Each girl ran one part of the race. The teams total time was 11 3/5 minutes. What was Cindy's time?
Please help, I can't figure out how to solve this correctly.
Answer:
Cindy's time was 5 2/5 minutes, or 5.4 minutes to the nearest tenth.
Step-by-step explanation:
To find Cindy's time, we need to use the information given about the total time and the times of the other three runners.
Let's first convert all the times to fractions of a minute:
Barbara: 3 3/10 = 3 + 3/10 = 3.3 minutes
Donna: 2 4/5 = 2 + 4/5 = 2.8 minutes
Cindy: x minutes
Nicole: 2 1/10 = 2 + 1/10 = 2.1 minutes
Now, we can set up an equation to represent the total time of the team:
Barbara's time + Donna's time + Cindy's time + Nicole's time = 11 3/5 minutes
Substituting the values we know:
3.3 + 2.8 + x + 2.1 = 11 3/5
Simplifying and converting mixed numbers to fractions:
8/5 + 14/5 + x + 11/5 = 116/10 + 3/5
Multiplying both sides by 10 to eliminate the denominators:
16 + 28 + 10x + 22 = 116 + 6
Simplifying:
10x = 54
Dividing by 10:
x = 5.4
Therefore, Cindy's time was 5 2/5 minutes, or 5.4 minutes to the nearest tenth.
12a^4+ (-29a^4) simplify
Answer: -17a^4
Step-by-step explanation:
Combine like terms
12a^4 +(-29a^4)
(12a^4-12a^4) - (29a^4-12a^4) =
-17a^4
Hope this helps
You visit six randomly selected locations on campus and observe the number of people in the area using their cell phone. The data is as follows: 3, 4, 4, 5, 6, 8 1.
1. What scale of measurement was used by the researcher?
2. Calculate the mean, median, mode for the data set.
3. Calculate the range, variance and standard deviation for the data set (use the formula for sample).
4. Based on the sample, what is the number of people using their cell phone associated with +1 SD?
5. What number of people using their cell phone reflects 96% of the sample?
Answer:
The researcher used a ratio scale of measurement for the number of people using their cell phone.
Mean: (3+4+4+5+6+8)/6 = 30/6 = 5
Median: arrange the data in ascending order: 3, 4, 4, 5, 6, 8. The median is the middle value which is 5.
Mode: there is no mode as no value occurs more than once.
Range: 8-3 = 5
Variance:
s^2 = Σ(x-ȳ)^2 / (n-1)
s^2 = [(3-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (6-5)^2 + (8-5)^2] / (6-1)
s^2 = 5.6
Standard deviation: s = sqrt(s^2) = sqrt(5.6) ≈ 2.37
To find the number of people using their cell phone associated with +1 SD, we add one standard deviation to the mean:
Mean + 1 SD = 5 + 2.37 ≈ 7.37
Therefore, approximately 7 people using their cell phone are associated with +1 SD.
To find the number of people using their cell phone that reflects 96% of the sample, we need to find the z-score that corresponds to the 96th percentile. From a standard normal distribution table, we find that the z-score is approximately 1.75. We can use this z-score to find the corresponding value in our data set using the formula:
z = (x - ȳ) / s
Rearranging, we get:
x = z * s + ȳ
x = 1.75 * 2.37 + 5
x ≈ 9.3
Therefore, approximately 9 people using their cell phone reflect 96% of the sample.
Step-by-step explanation:
Solve the system of equations below graphically. Identify the graphs and the solution point on the Cartesian plane below.
x-y=0
5x+2y=7
A solution to the given system of linear equations is (2, 6).
How to graphically solve this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x - y = 0 ......equation 1.
5x + 2y = 7 ......equation 2.
In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (1, 1).
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A 5-yard roll of tape costs $0.30. What is the unit price?
Answer:
$0.06/yrd
Step-by-step explanation:
you want to divide the cost by the amount of units purchased.
.30/5=.06
this would mean your price per unit is 6 cents
Mr. Shaw is building a walkway from the corner of his house out to his vegetable garden in the corner of the yard. The dimensions of the yard and the garden are shown. What is the length of the walkway, w, to the nearest foot?
A. 24ft
B. 34ft
C. 46ft
D. 58ft
Ummi chose C as the correct answer. How might she have gotten that answer?
Find the circumference of the circle below which is 4 inches. use 3.14 for n. round your answer to the nearest tenth.
Show how you got your answer.
When the radius is 4 inches, the circle's circumference measures roughly 25.1 inches.
How was 3.14 determined?No matter what size circle you drew, you will obtain roughly 3.14 when you divide the circumference by the diameter. The ratio will never change even though a larger circle will have a higher radius and circumference. Circumference to diameter ratio (C/d) is always constant at. As a result, the diameter (D) and circumference (C) are always approximately 3.14 times each other (d).
C = 2r is the formula for calculating a circle's circumference.
C = 2π(4)
C = 8π
Using the approximation of π = 3.14, we can evaluate this expression:
C ≈ 8(3.14)
C ≈ 25.12
Rounding this answer to the nearest tenth gives:
C ≈ 25.1 inches.
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Find volume of triangular prism
I don’t know how to solve I know u use a b c base side and height but I don’t know which is each?
Explanation:
The front and back faces are triangles. They have a base of 10 ft and height of 4 ft.
area of triangular face = 0.5*base*height area = 0.5*10*4area = 20The front face has area 20 sq ft. The same applies for the back face as well.
Now imagine rotating the prism so that the front face is now laying on the floor. The floor and ceiling are triangles. Each wall is a rectangle.
volume of prism = (floor area)*(height)volume = (20 sq ft)*(5.5 ft)volume = 110 cubic feetAnswer: 110 ft^3
Step-by-step explanation:
Base is 10ft
Height is 4ft (distance from base to uppermost point)
0.5*10*4=20
20*5.5 (length)=110
what is P(less than 3)
Answer:-3p
Step-by-step explanation: less = subtract -3+p=-3p
The quotient of ten and a number
Answer: 10 / 5 = 2
Step-by-step explanation:
A baker weighs some pieces of chocolate before he begins making a recipe. He writes the following weights measured in ounces: 2.6, 2.796, 2.94, 2.29, 2.064. How many ounces did the heaviest piece of chocolate weigh?
Answer:
The heaviest piece of chocolate weighed 2.94 ounces.
Step-by-step explanation:
Given that cos Ø= 2/5 determine the exact value of csc Ø
Answer:
below
Step-by-step explanation:
Given cos, you will have to use this to calculate sin because csc is 1/ sin
Remember cos^2 + sin^2 = 1
(2/5)^2 + sin^2 = 1
sin^2 = 21/25
sin = sqrt (21) / 5 (ignoring negative root)
csc = 1/sin = 5 / sqrt(21)
NONE OF THE APPS WORK BRO
Answer:
1 term (monomial).
Step-by-step explanation:
A term includes at least either a number, a variable, or both together, and can have more than one.
In this case, there is 1 term, which denotes that a variable, has an exponent of 9.
[tex]b^9[/tex] is one term.
Examples of more than 1 term can include:
[tex]b^9 + 1[/tex] , which is two terms (Binomial).
[tex]a^2 + b + 3[/tex] is three terms (Trinomial).
* One thing to note is to always simplify when possible.
~
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The school parking lot has 6 rows of parking spaces.
There are also 35 parking spaces on the side of the
building for staff members. There is space for at
most 155 cars in these lots combined. Write an
inequality to represent the total number of cars
that will fit in the spaces at school. Then complete
the sentence.
The total number of cars that will fit in the spaces at school is less than or equal to 155, which means that the combined number of parking spaces in the parking lot and on the side of the building cannot exceed 155.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that represents a quantity or a relationship between quantities. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple variables and operations.
Let x be the number of parking spaces in each row of the school parking lot. Then, the total number of parking spaces in the parking lot is 6x.
The total number of parking spaces in the school is the sum of parking spaces in the parking lot and parking spaces on the side of the building, which is 6x + 35.
Since the total number of cars that will fit in the spaces at school is at most 155, we can write the inequality:
6x + 35 ≤ 155
Simplifying this inequality, we get:
6x ≤ 120
x ≤ 20
Therefore, the total number of cars that will fit in the spaces at school is less than or equal to 155, which means that the combined number of parking spaces in the parking lot and on the side of the building cannot exceed 155.
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Find the slope of the line shown below?
Find (f ∙ g)(2) when f(x) = and g(x) = x + 9.
Answer: We can start by evaluating g(2):
g(2) = 2 + 9 = 11
Now we can use the definition of function composition to evaluate (f ∙ g)(2):
(f ∙ g)(2) = f(g(2)) = f(11)
To find f(11), we need to substitute 11 for x in the expression for f(x):
f(11) = (11 - 3)^2 + 1 = 8^2 + 1 = 65
Therefore, (f ∙ g)(2) = f(g(2)) = f(11) = 65.
Step-by-step explanation: