If 1% of the phones were broken, then the number of good phones is 99% of 4,028:
99/100 x 4,028 = 3,987.72 (rounded to 3,988)
Out of the 3,988 good phones, 50% were sold to another city:
50/100 x 3,988 = 1,994
So, the remaining number of good phones that were sold locally is:
3,988 - 1,994 = 1,994
To find the percentage of phones sold locally, we need to divide the number of phones sold locally by the total number of phones:
1,994 / 4,028 = 0.494
Then, we can convert this decimal to a percentage and round to the nearest one percent:
0.494 x 100 ≈ 49%
Therefore, approximately 49% of the phones were sold locally.
If you go up to your attic on a summer day, which best explains why you may feel very hot?
A Conduction caused hot air to rise to the top of your house.
B Convection caused hot air to rise to the top of your house.
C The attic is insulated from the cooler temperatures below.
D None of the above
Answer:
Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.
Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.
Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.
Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.
ion:
A homeowner is building a patio with concrete blocks. The blocks are 11" x 10" x 6". The blocks are in a stack at the store that is 60" x 55" x 54". How many blocks are in a stack?
According to the question, if the blocks are 11" x 10" x 6" and the blocks are in a stack at the store that is 60" x 55" x 54" then there are 270 blocks in the store.
Given that dimensions of the blocks and the store :-
Block :- 11" x 10" x 6"
Store :- 60" x 55" x 54"
To find the number of blocks in a stack we need to first calculate the volume of the block as well as the store.
This, Volume of block = 11 x 10 x 6 = 660
and, Volume of the store = 60 x 55 x 54 = 178200
Therefore, the number of blocks would be = Volume of the store / Volume of block
No. of block = 178200/660
No. of block = 270
Hence Number of blocks stored in the stack at the storeroom is 270 blocks.
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Point P is plotted on the number line. What number is represented by point P? P 5 * 10 ^ - 3; 6 * 10 ^ - 3
For the plotted point P on the given number line, the number represented by point P is 5.80⁻³.
What is number line?A number line is a linear visual representation of numbers and integers. This line is used to compare equally spaced numbers on an infinite line that extends horizontally or vertically on either side. A number line shows point values and equal divisions on the line.
There are 10 points at equal intervals that falls between point 5.10⁻³ and point 6.10⁻³.
Counting from the very left the points are as follows:
5.10⁻³, 5.20⁻³, 5.30⁻³, 5.40⁻³, 5.50⁻³, 5.60⁻³, 5.70⁻³, 5.80⁻³, 5.90⁻³, 6.00⁻³, 6.10⁻³.
Point P falls on 5.80⁻³, therefore the value of point P is 5.80⁻³.
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The complete question is as follows:
it takes 8 minutes to fill up a tank to a depth of 2/5 meter. what is the unit rate for minutes per meter
Andy is a restaurant owner. He believes 72% of his customers are satisfied with the food quality of his restaurant. From a random sample of 78 customers, what are the following probabilities? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.)
(a) What is the probability that less than 57 customers are satisfied with the food quality?
(b) What is the probability that at least 57 customers are satisfied with the food quality?
(c) What is the probability that the sample proportion of customers who are satisfied with the food quality is between 70% and 77%?
The probability that the sample proportion of customers who are happy with the food quality is between 70% and 77% is 0.693
Andy is a restaurant owner who believes that 72% of his customers are happy with the food quality of his restaurant. What are the probabilities for the following questions, given a random sample of 78 customers? Probability that less than 57 customers are satisfied with the food quality:To find the probability that less than 57 customers are happy with the food quality, we'll first compute the z-score.Z = (x - µ) / σZ = (56.5 - 72.84) / 4.392 Z = -3.7 Using the table, we can find that the probability of a z-score less than -3.7 is 0.0001. Thus, the probability that less than 57 customers are happy with the food quality is 0.0001.
Probability that at least 57 customers are satisfied with the food quality:The probability that at least 57 customers are satisfied with the food quality is the complement of the probability that less than 57 customers are satisfied with the food quality. Hence, the answer is: 1 - 0.0001 = 0.9999 Probability that the sample proportion of customers who are satisfied with the food quality is between 70% and 77%:To calculate the probability that the sample proportion of customers who are happy with the food quality is between 70% and 77%, we'll need to compute the z-scores for both values.
The z-score is given by Z = (p - P) / sqrt(PQ/n), where P is the true proportion (0.72), Q is 1 - P (0.28), and n is the sample size (78).Z1 = (0.70 - 0.72) / sqrt(0.72*0.28/78) = -0.85Z2 = (0.77 - 0.72) / sqrt(0.72*0.28/78) = 1.24The probability is the difference between the two probabilities of the standard normal distribution, which is 0.8907 - 0.1977 = 0.693. Hence, the probability that the sample proportion of customers who are happy with the food quality is between 70% and 77% is 0.693.
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I NEED THIS DONE ASAP!!
Simplify a^-4/4a^6
Hence, in answering the stated question, we may say that Therefore, the simplified expression is [tex]1/(4a^6).[/tex]
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.
To simplify this expression, we can use the laws of exponents:
[tex]a^-4/4a^6 = 1/(4a^4 * a^2) = 1/(4a^6)[/tex]
Therefore, the simplified expression is [tex]1/(4a^6).[/tex]
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100 points please help
Answer:
(x² + 4) (x² + 6)
Step-by-step explanation:
Let's check
(x² + 4) (x² + 6)
[tex]x^{4}[/tex] + 6x² + 4x² + 24
[tex]x^{4}[/tex] + 10x² + 24
So, (x² + 4) (x² + 6) is the correct answer.
Ava is sewing a quilt. One of the fabric pieces is shaped like a triangle. One of the angles of the triangle measures 106°.
If the other two angles of the triangle have the same measure, what is the measure of each of them?
Enter your answer in the box.
°
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The three options of exterior angles are m∠5 + m∠6 =180°,
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is an exteriοr angle?The angles that are created οutside οf a triangle are its exteriοr angles. In οther wοrds, the angle fοrmed between οne οf a triangle's sides and its adjacent extended side is the triangle's exteriοr angle.
Given that the exteriοr angles are m∠1, m∠4, and m∠6.
The interiοr angles οf the triangle are angles m∠2, m∠3, and m∠5.
The sum οf all angles οf a triangle is 180°.
Thus m∠2 + m∠3 + m∠5 = 180°
The interiοr angle and the cοrrespοnding exteriοr angle in a triangle make up a linear pair. Exteriοr Angle plus Interiοr Angle equals 180°, sο.
The exteriοr angle at angle 5 is angle 6.
Thus m∠5 + m∠6 =180°
The interiοr and exteriοr angles that make up a triangle are always added tοgether tο fοrm the exteriοr angle. The term "exteriοr angle prοperty" refers tο this feature. If twο triangles' cοrrespοnding angles tend tο be cοngruent and their side lengths are prοpοrtiοnal, any twο triangles will be similar tο οne anοther.
The οppοsite interiοr angles οf m∠6 are m∠2, m∠3.
Thus m∠2 + m∠3 = m∠6
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Part I: Draw a line connecting each sphere to its volume in terms of me and rounded to the nearest tenth. (Not all of the values will be used. ) Pls help
Answer:
Step-by-step explanation:
Show transcribed data
Find the directions in which the function increases and decreases most rapidly at P_0. Then find the derivatives of the function in these directions. f(x, y) = x^2 + xy + y^2, P_0(-1, 4) The direction in which the given function f(x, y) = x^2 + xy + y^2 increases most rapidly at P_0 (-1, 4) is u = i + j. (Type exact answers, using radicals as needed.) The direction in which the given function f(x, y) = x^2 + xy + y^2 decreases most rapidly at P_0 (- 1, 4) is - u = i + j. (Type exact answers, using radicals as needed.) The derivative of the given function f(x, y) = x^2 + xy + y^2 in the direction in which the function increases most rapidly at P_0 (-1, 4) is D_u f = (Type an exact answer, using radicals as needed.) The derivative of the given function f(x, y) = x^2 + xy + y^2 in the direction in which the function decreases most rapidly at P_0 (-1, 4) is D_-u f = (Type an exact answer, using radicals as needed.)
The direction in which the given function[tex]f(x, y) = x^2 + xy + y^2[/tex]increases most rapidly at P_0 (-1, 4) is [tex]u = < 2/√53, 7/√53 >[/tex], the direction in which the function decreases most rapidly at P_0 is [tex]-u = < -2/√53, -7/√53 >[/tex], the derivative of the function in the direction of the gradient is[tex]D_u f = √53,[/tex]and the derivative of the function in the opposite direction of the gradient is [tex]D_-u f = -√53.[/tex]
The direction in which a function increases most rapidly at a given point is the direction of the gradient of the function at that point. The gradient of the function [tex]f(x, y) = x^2 + xy + y^2[/tex] is given by:
[tex]∇f = < 2x + y, x + 2y >[/tex]
At the point P_0 (-1, 4), the gradient is:[tex]∇f(P_0) = < 2(-1) + 4, -1 + 2(4) > = < 2, 7 >[/tex]
The direction in which the function increases most rapidly at P_0 is the unit vector in the direction of the gradient:
[tex]u = ∇f(P_0)/||∇f(P_0)|| = < 2/√53, 7/√53 >[/tex]
The direction in which the function decreases most rapidly at P_0 is the opposite of the direction of the gradient:[tex]-u = < -2/√53, -7/√53 >[/tex]
The derivative of the function in the direction of the gradient is the dot product of the gradient and unit vector in the direction of the gradient:
[tex]D_u f = ∇f(P_0) · u = < 2, 7 > · < 2/√53, 7/√53 > = (4 + 49)/√53 = 53/√53 = √53[/tex]
The derivative of the function in the opposite direction of the gradient is the dot product of the gradient and the unit vector in the opposite direction of the gradient:
[tex]D_-u f = ∇f(P_0) · -u = < 2, 7 > · < -2/√53, -7/√53 > = (-4 - 49)/√53 = -53/√53 = -√53[/tex]
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You are in charge of ordering the food for a family party. There are 50 people attending the party. You have a budget of $1200. The catering company has three menus. You have coupon for 10% off the cost of the food. You are giving a 15% tip on the cost of the food. The sales tax is 8. 875%.
You must choose a menu, determine the total cost for the food including sales tax and tip and make sure that your work is presented in a manner that makes it easy to follow your thinking
In the following question, among the conditions given, Menu 1:Cost per person: $20, Total cost for 50 people: $20 x 50 = $1000, we can afford Menu 1 within our budget, and the total cost for the food, including sales tax and tip, is $1209.
First, we need to determine the total amount of the budget available after applying the 10% discount:
Budget after discount = $1200 - (10% x $1200) = $1080
Next, we need to consider the three menus offered by the catering company:
Menu 1:
Cost per person: $20
Total cost for 50 people: $20 x 50 = $1000
Menu 2:
Cost per person: $25
Total cost for 50 people: $25 x 50 = $1250
Menu 3:
Cost per person: $30
Total cost for 50 people: $30 x 50 = $1500
Since Menu 1 is the only option that fits within our budget, we will choose that menu.
Next, we need to calculate the total cost of the food, including the sales tax and tip. To do this, we'll need to add the sales tax and tip percentages to the original cost of the food:
Sales tax: 8.875%
Tip: 15%
Total cost per person after tax and tip = cost per person + (sales tax x cost per person) + (tip x cost per person)
Total cost per person after tax and tip = $20 + (8.875% x $20) + (15% x $20) = $24.18
Total cost for 50 people after tax and tip = $24.18 x 50 = $1209
Therefore, the total cost of the food, including sales tax and tip, for Menu 1 is $1209.
To summarize our calculations:
Budget after discount: $1080
Total cost for Menu 1: $1000
Total cost per person after tax and tip: $24.18
Total cost for 50 people after tax and tip: $1209
So, we can afford Menu 1 within our budget, and the total cost for the food, including sales tax and tip, is $1209.
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how do i find the center and radius of the given circle
There are multiple ways to find the center and radius of a circle, depending on what information your provided.
Method 1: Reading the standard equation of a circle
Equation of a circle: [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
where h is the center's x-coordinate, k is the center's y-coordinate, and r is the radius. Here's an example:
[tex](x-5)^{2} +(y+2)^{2} =25[/tex]
In this case, the center would be (5,-2) and the radius is 5
Method 2: Reading a graph
In the attached graph, there is a circle with a labeled center point. The radius can be found by finding the distance from the center to a different point on the circle.
Distance Formula:
[tex]D = \sqrt{ (x_{2}-x_{1}) ^{2} + (y_{2}-y_{1}) ^{2}}\\[/tex]
The first point we use will be the center ( 5 , -2 ), and the second point will be a point on the circle, (10,-2).
[tex]r = D = \sqrt{ ((10)-(5)) ^{2} + ((-2)-(-2) )^{2}}\\r = D = \sqrt{ (5 ^{2} + 0)^{2}}\\r = D = \sqrt{25}\\r = 5[/tex]
Next, plug in the values into the standard equation of a circle formula
[tex](x-5)^{2} +(y+2)^{2} =5^2[/tex]
Simplify
[tex](x-5)^{2} +(y+2)^{2} =25[/tex]
A wooden beam is (7y^2+7y+1) meters long. If a piece of length (y^2-10) meters is cut off, express the length of the remaining piece of beam as a polynomial in y.
The length of the remaining piece of beam as polynomial is 6y²⁺⁷⁺¹¹
Describe a polynomial.An algebraic expression with two or more algebraic terms is known as a polynomial.It has exponents, operators, coefficients, coefficients, variables, and constants. A polynomial is a mathematical expression that solely uses the operations addition, subtraction, multiplication, and non-negative integer powers of variables. It is made up of indeterminates (also known as variables) and coefficients.
The length of the wooden beam is (7y²⁺⁷⁺¹) meters long and a piece of length (y²⁻¹⁰) meters is cut off ¹.
Therefore, the length of the remaining piece of beam can be expressed as follows:
(7y²⁺⁷⁺¹)-(y²⁻¹⁰) = 6y²⁺⁷⁺¹¹
So, the length of the remaining piece of beam is 6y²⁺⁷⁺¹¹
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find m∠v given that p || q m∠u=75.8°, and m∠w=104.2°
Again, withοut a diagram οr mοre cοntext, it's difficult tο say fοr certain if cοοrdinates this is the cοrrect answer, but it is οne pοssible apprοach tο the prοblem based οn the infοrmatiοn prοvided.
what are cοοrdinate ?In mathematics, a cοοrdinate is a number οr permutatiοn οf integers that indicates the lοcatiοn οf a pοint οr οbject in space. Cοοrdinates are frequently used tο define a pοint οr οbject's pοsitiοn in a specific reference frame, such as the Euclidean οr antarctic cοοrdinate systems.
In the Cartesian cοοrdinate system, a pοint is lοcated by its distance frοm the οrigin alοng the x-axis and its distance first frοm οrigin alοng the y-axis. These distances are represented by twο numbers, its x-cοοrdinate and the y-cοοrdinate. The pοint's pοsitiοn in the plane is specified by the twο cοοrdinates.
If "p || q" means that lines p and q are parallel, then we can use the fact that alternate interiοr angles are cοngruent tο sοlve the prοblem. Angles οn οppοsite sides οf the transversal (in this case, line u) and within the twο parallel lines are equal.
Sο, if we knοw which angles are alternate interiοr angles, we can use that knοwledge tο calculate the measure οf angle v.
m∠u = m∠w
75.8° = 104.2° - m∠v
m∠v = 28.4°
Again, withοut a diagram οr mοre cοntext, it's difficult tο say fοr certain if this is the cοrrect answer, but it is οne pοssible apprοach tο the prοblem based οn the infοrmatiοn prοvided.
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Complete Question;
The quotient of 30 and the sum of five and seven
Answer:
sum of 5 and 7
Step-by-step explanation:
5+7
sum means an adding equetion
Answer:
The answer is 2.5
Step-by-step explanation:
° The sum of 5 and 7 is 5 + 7 = 12
° The quotient of means "the result got from dividing one variable by another", so, 30/12 = 2.5
The function is defined by the following rule..
f(x)=-3x-3
Complete the function table.
X
-5
0
2
X
Explanation
0
0
0
0
0
5
Check
The value for f(-5), f(-1), f(0), f(2), f(4) are 12, 0, -3, -9, -15.
What is a function?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range) with the property that each input is related to exactly one output. A function is usually denoted by a symbol such as f(x), where x is the input variable and f(x) is the output variable. The value of the output variable depends on the value of the input variable and the rule that defines the function.
Given function:
f(x) = -3x -3
Now, we will substitute values of x in f(x) as follows:
when x =-5,
f(-5) = -3 (-5) - 3
= 15 -3 = 12.
when x =-1,
f(-5) = -3 (-1) - 3
= 3 -3 = 0.
when x = 0,
f(-5) = -3 (0) - 3
= 0 -3 = -3.
when x = 2,
f(-5) = -3 (2) - 3
= -6 -3 = -9.
when x = 4,
f(-5) = -3 (4) - 3
= -12 -3 = -15.
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Raymond’s class measures the masses of the books in their library. The mass of the dictionary is 2,702 grams. The dictionary’s mass is 1,429 grams greater than the mass of Raymond’s favorite book. What is the mass, in grams, of Raymond’s favorite book?
The mass of Raymond's favorite book is 1273 grams.
What is the linear function?
A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
Let x be the mass of Raymond's favorite book in grams. According to the problem, we have:
2702 = x + 1429
To solve for x, we can isolate it on one side of the equation by subtracting 1429 from both sides:
x = 2702 - 1429
x = 1273
Therefore, the mass of Raymond's favorite book is 1273 grams.
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PLEASE HELPPPP FAST In the picture below, find the value of a.
Answer:
A should be 180 - 68 which is 112 degrees
Step-by-step explanation:
Answer:a=108
Step-by-step explanation:
140+(180-60)+(180-84)+(180-68)=140+120+96+112=260+208=468
sum of angles are 540, so,
540-468=180-a
72=180-a
a=108
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
A) x = 13
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the opposite. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Additions
Subtractions
~
First, root both sides of the equation to eliminate the power:
[tex](x -7)^2 = (36)\\\sqrt{(x-7)^2} = \sqrt{36} \\x - 7 = 6[/tex]
Next, isolate the variable, x, by adding 7 to both sides of the equation:
[tex]x - 7 = 6\\x - 7 (+7) = 6 (+7)\\x = 6 + 7\\x = 13[/tex]
x = 13, or A) is your answer.
~
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averaged 462 raindrops over an area of 55 square meters. A nearby picnic table has an area of 1 square meter. Use the Poisson distribution to find the probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles. Do not round intermediate computations, and round your answer to three decimal places.
The probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles is 0.066, rounded to three decimal places.
We can model the number of raindrops that fall on the picnic table as a Poisson distribution with parameter a, where a is the expected number of raindrops that fall on a 1 square meter area during a rainstorm. Since 462 raindrops fell over an area of 55 square meters, the average number of raindrops per square meter is:
a = 462/55 ≈ 8.4
Therefore, the probability that exactly 11 raindrops fall on the picnic table during a rainstorm is:
P(X = 11) = (eᵃ * a¹¹) / 11!
= (e⁻⁸ ⁴ * 8.4¹¹) / 11!
≈ 0.066
Rounding to three decimal places, we get the probability that exactly 11 raindrops fall on the picnic table as 0.066.
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the international average salary income database provides a comparison of average salaries for various professions. the data are gathered from publications and reports obtained directly from government agencies (such as the us bureau of labor statistics) or from the international labour organization. suppose an industrial/organizational psychologist is interested in the relationships between job satisfaction, job performance, and job compensation. she has data from five different countries on the average monthly salaries paid to accountants. she begins her analysis by converting all of the salary data into us dollars:
To convert the salary data from different countries into US dollars, the industrial/organizational psychologist would need to use the exchange rates between each country's currency and the US dollar. Exchange rates are the value of one currency in terms of another currency.
For example, if the exchange rate between the US dollar and the British pound is 1.38, this means that one US dollar is worth 1.38 British pounds. So, to convert the average monthly salary of an accountant in the UK into US dollars, the psychologist would divide the salary in pounds by the exchange rate.
Once the psychologist has converted all of the salary data into US dollars, she can then compare the average monthly salaries of accountants across the five different countries and analyze the relationships between job satisfaction, job performance, and job compensation.
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20 Points
...................................
Answer:
Its the 3rd one
Step-by-step explanation:
I had this question twice
Answer:
number 3 i did this 2 days ago
Step-by-step explanation:
3.-3y ≤-18 (1 point)
y2
Answer 3 - 3y (< with the line under) -18
1
y^2
Step-by-step explanation:
Chucky grabbed 12 items in the grocery store that each had a different price and had a mean cost of about $7. 41 $7. 41dollar sign, 7, point, 41. One of the items was an entire wheel of cheese that cost $39. 99\$39. 99 $39. 99 dollar sign, 39, point, 99
B. Both the mean and median will decrease, but the mean will decrease by more than the median.
Since the wheel of cheese has a much higher cost than the other 11 items, removing it will decrease the overall mean cost of the items purchased. However, the median, which is the middle value when the items are arranged in order, will also decrease but not by as much as the mean since it is not as affected by outliers like the wheel of cheese.
The mean is calculated by taking the sum of all the prices and dividing it by the number of items, so removing the most expensive item (the wheel of cheese) will decrease the sum of prices and thus decrease the mean.
The median is the middle value when all the prices are arranged in order. Since the wheel of cheese is the most expensive item, it will be the last item on the ordered list. Removing it will not change the position of any other items, so the median will simply be the middle value of the remaining 11 items. The value of the median is not affected by the price of the wheel of cheese, so the median will also decrease but only by a small amount. T
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The correct question should be:
Chucky grabbed 12 items in the grocery store that each had a different price and had a mean cost of about $7.41. One of the items was an entire wheel of cheese that cost $39.99. Chucky then decided to put the wheel of cheese back and only buy the other 11 items. How will removing the wheel of cheese affect the mean and median?
A. Both the mean and median will decrease, but the median will decrease by more than the mean.
B. Both the mean and median will decrease, but the mean will decrease by more than the median.
C. Both the mean and median will increase, but the median will increase by more than the mean.
D. Both the mean and median will increase, but the mean will increase by more than the median.
y
8
X
Solve for y.
Start by finding the side
lengths of the smallest triangle.
Fill in the green blank.
2
[?] X
Enter
The equation given is an instance of a linear equation in two variables, which can be solved by using the process of substitution to find the value of one of the variables.Therefore, the solution to the given equation is y = 4√(3).
What is equation?Equation is a mathematical statement that states the equality of two expressions. It is usually expressed as a numerical equation with an equal sign (=) between the two expressions. Equations are used to express relationships between various quantities and can be used to solve problems in many areas of mathematics, science, and engineering. In addition, equations are often used to describe physical laws and chemical reactions.
In this case, the equation is y = 8/x, and we want to solve for y.
To do this, we need to first find the value of x. We can do this by using the side lengths of the triangle given, which are 2 and x. We can use the Pythagorean theorem to calculate the value of x. The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. So, we can use this equation to find the value of x: 2²+ x²= (8/x)². Solving for x, we get x = 2√(3).
Now that we have the value of x, we can substitute it into the original equation and solve for y. So, y = 8/2√(3), which simplifies to y = 4√(3). Therefore, the solution to the given equation is y = 4√(3).
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A father's age is four times the age of his daughter. After 5 years his age would be three times his daughters age. After 5 more years , how many times of his daughter age his age would be
If a father's age is four times the age of his daughter.. After 5 more years , his age would be 5 times his daughter's age at that time.
Let's use D to represent the daughter's current age and F to represent the father's current age.
We know that the father's age is four times the age of his daughter, so we can write an equation to represent this relationship:
F = 4D
We also know that after 5 years, the father's age would be three times his daughter's age, so we can write another equation to represent this:
F + 5 = 3(D + 5)
Now we can substitute the first equation into the second equation to get an equation with only one variable:
4D + 5 = 3(D + 5)
Simplifying the equation, we get:
4D + 5 = 3D + 15
Subtracting 3D and 5 from both sides, we get:
D = 10
Therefore, the daughter's current age is 10 years old. We can use the first equation to find out the father's current age:
F = 4D = 4(10) = 40
After 5 more years, the father's age would be:
F + 5 + 5 = 40 + 10 = 50
In summary, after 5 more years, the father's age would be 50 and his daughter's age would be 10, which is 5 times younger than the father.
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Graph the linear equation find three points that solve the equation then plot on the graph -x-3y=-6
I’m stuck on this question, may someone help?
Use operation signs, -,x,+,/ once each to fill in the blanks so that the value of the expression is 5.
3 _ 2 _ (8 _ 7) _ 1 = 5
Answer:
3 + 2 × (8 - 7) ÷ 1
Step-by-step explanation:
You want to fill in math operations to make the expression 3 _ 2 _ (8 _ 7) _ 1 equal to 5, using +, -, ×, and ÷ once each.
AnalysisIt is unlikely that ÷ will go between 3 and 2, because that would give a fraction not easily modified to give a value of 5.
It is likely that + or - goes inside the parentheses, as there would be no need for parentheses if that operation were × or ÷. The minus sign seems more appropriate, since adding 8 and 7 would give 15, a value not easily modified to make 5.
Using - inside parentheses reduces the problem to ...
3 _ 2 _ 1 _ 1 = 5 . . . . . with available remaining operators: +, ×, ÷
It seems appropriate to make this be ...
3 + 2 = 5 . . . . . . uses the + operation in the first blank
which requires that 2 _ 1 _ 1 = 2 using × and ÷. We can only use them in that order if we want the value 2: 2 × 1 ÷ 1 = 2
The desired expression is ...
3 + 2 × (8 - 7) ÷ 1 = 5
Answer:
3 + 2 ÷ (8 - 7) × 1 = 5
Step-by-step explanation:
There is likely more than one way to do this problem.
Here's one way:
3 + 2 ÷ (8 - 7) × 1 = 5
Do parenthesis first.
3 + 2 ÷ (1) × 1 = 5
Multiply or divide in order from left to right.
3 + 2 × 1 = 5
3 + 2 = 5
Lastly, add.
5 = 5
So, this checks out.
One possible answer is:
3 + 2 ÷ (8 - 7) × 1 = 5
A store began selling its line of fall sweaters. On the first day, 6 cotton, 4 orlon, and 5 wool sweaters were sold. On the second day, 3 cotton, 5 orlon, and 8 wool sweaters were sold. On the third day, 4 cotton, 1 orlon and 4 wool sweaters were sold. Total sales for the three days were $395, $505, and $260, respectively. What was the sale price for each sweater?
The given data in this problem allows for the creation of a system with three variables, that represent the earnings from the sales in the three days, by solving this system we can obtain these following sale prices:
Cotton: $15.Orlon: $20.Wool: $45.How to obtain the sale price for each sweater?The sale price for each sweater is obtained solving a system of equations.
The variables of the system of equations are given as follows:
Variable x: cost of a cotton sweater.Variable y: cost of an orlon sweater.Variable z: cost of a wool sweater.Considering the profits for each day, along with the amounts of each sweater sold, the equations that compose the system are given as follows:
6x + 4y + 5z = 395.3x + 5y + 8z = 505.4x + y + 4z = 260.Inserting these three equations into a calculator, the solution to the system of equations is given as follows:
x = 15, y = 20, z = 45.
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