The most appropriate choice for Simultaneous linear equation will be given by -
8 packages of coffee and 4 packages of tea are sold.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288
So,
11x + 50y = 288 ...............(1)
The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248
So,
12x + 38y = 248
2(6x + 19y) = 248
6x + 19y = [tex]\frac{248}{2}[/tex]
6x + 19y = 124 ....................(2)
Multiplying (1) by 6 and (2) by 11,
66x + 300y = 1728
66x + 209 y = 1364
Subtracting above two equations,
91 y = 364
[tex]y = \frac{364}{91}[/tex]
y = 4
Putting the value of y in (2),
6x + 19[tex]\times[/tex]4 = 124
6x + 76 = 124
6x = 124 - 76
6x = 48
[tex]x = \frac{48}{6}\\x = 8[/tex]
8 packages of coffee and 4 packages of tea are sold.
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The most appropriate choice for Simultaneous linear equation will be given by -
8 packages of coffee and 4 packages of tea are sold.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288
So,
11x + 50y = 288 ...............(1)
The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248
So,
12x + 38y = 248
2(6x + 19y) = 248
6x + 19y =
6x + 19y = 124 ....................(2)
Multiplying (1) by 6 and (2) by 11,
66x + 300y = 1728
66x + 209 y = 1364
Subtracting above two equations,
91 y = 364
y = 4
Putting the value of y in (2),
6x + 194 = 124
6x + 76 = 124
6x = 124 - 76
6x = 48
8 packages of coffee and 4 packages of tea are sold.
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Point (2,11.9),(4,10.5)
(2,8) , (4,7.5)
(2,6) , (4,1.5)
(2,0.5) , (4.-1)
(2,-1) , (4,-1)
(-2.8,-5.0) , (-3.6,-5.9)
rise over run so what's the answer
The slopes formed by each of the pairs of points are given as follows:
(2,11.9),(4,10.5): -0.7.(2,8) , (4,7.5): -0.25.(2,6) , (4,1.5): -2.25.(2,0.5) , (4.-1): -0.75.(2,-1) , (4,-1): 0.(-2.8,-5.0) , (-3.6,-5.9): 0.89.SlopeThe slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.
For the first case, the points are:
(2, 11.9) and (4, 10.5)
Hence:
The change in x is of 4 - 2 = 2.The change in y is of 10.5 - 11.9 = -1.4.The slope is:
m = -1.4/2 = -0.7.
The other slopes are calculated as follows:
(2,8) , (4,7.5): m = (7.5 - 8)/(4 - 2) = -0.25.(2,6) , (4,1.5): m = (1.5 - 6)/(4 - 2) = -2.25.(2,0.5) , (4.-1): m = (-1 - 0.5)/(4 - 2) = -0.75.(2,-1) , (4,-1): m = (-1 - (-1))/(4 - 2) = 0. (no change in the output).(-2.8,-5.0) , (-3.6,-5.9): m = (-3.6 - (-2.8))/(-5.9 - (-5)) = 0.89.More can be learned about slopes at https://brainly.com/question/28954211
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This data can best be modeled withwhich type of function?ху018,250118,730a. Linearb. QuadraticC. Exponential219,210319,690420,170
A linear function is a function in which we add multiple of a constant.
Given data:
We have
[tex]\begin{gathered} y=18,250+480(1)\text{ at x=0} \\ y=18,730=18,250+480(1)\text{ at x=1} \\ y=19,210=18,250+480(2)\text{ at x=2} \\ y=19,690=18,250+480(3)\text{ at x=3} \\ y=20,170=18,250+480(4)\text{ at x=4} \end{gathered}[/tex]Clearly, we have add multiples of 480 to 18,250.
So, the given function represents a linear function.
So, the correct option is (a).
A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
Based on the lengths of the sides of the triangle, we can infer that this is NOT a right triangle.
How to find a right triangle?A right angled triangle would obey the Pythagoras Rule which is that the square of the hypotenuse (longest side) will be the sum of the squares of the other sides of the triangle.
This means that for this to be a right triangle, it needs to obey the function:
45 ² = 35 ² + 30 ²
Solving gives:
2,025 ≠ 2, 125
This shows that the triangle is not a right triangle.
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It is not a right-angle triangle since 2125 ≠ 2025 meant that it did not conform to Pythagoras' theorem's specifications.
This kind of query creates a right-angled triangle that Pythagoras' theorem can resolve.
What is Pythagoras' theorem?In a right-angled triangle, the square of the greatest side is equal to the sum of the squares of the smaller two sides.
Given, There are three sides to a triangle, each measuring 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
Due to the fact that it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
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Which expression is equivalent to 3 x − 2 − 5 2 − 4 x − 2 ? 2x-8/13-5x -5x-8/2x-8 -5x-4/x-2 13-5x/2x-8
The equivalent expression of the expression given as [tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex] is (13 - 5x)/(2x - 8)
How to determine the equivalent expression?From the question, the expression is given as
[tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex]
Take the LCM of the fractions in the above expression
So, we have
[tex]\frac{\frac{3 - 5x + 10}{x - 2}}{\frac{2x - 4 - 4}{x - 2}}[/tex]
Evaluate the like terms of the expressions
So, we have
[tex]\frac{\frac{13 - 5x}{x - 2}}{\frac{2x - 8}{x - 2}}[/tex]
Divide the common factor x -2 in the expression
So, we have
[tex]\frac{13 - 5x}{2x - 8}[/tex]
Rewrite as
(13 - 5x)/(2x - 8)
The expression cannot be further simplified
Hence, the solution is (13 - 5x)/(2x - 8)
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3. What is the probability of rolling a 5 on a fair die, if we know that the roll is odd? 4 Lamino dr
Let:
A = Rolling an odd number
B = Rolling a 5
N = Number of possible outcomes
so:
[tex]\begin{gathered} P(A)=\frac{3}{6}=\frac{1}{2} \\ P(B|A)=\frac{P(B\cap A)}{P(A)} \\ \text{Where:} \\ P(B\cap A)=P(A)\cdot P(B) \\ P(B)=\frac{1}{6} \\ so\colon \\ P(B|A)=\frac{\frac{1}{6}\cdot\frac{1}{2}}{\frac{1}{2}}=\frac{1}{6} \end{gathered}[/tex]How to solve Y=2x-1 2x+y=3 in solving systems using substitution
Answer:
x = 1, y = 1
Step-by-step explanation:
This Question involves the concept of Solving Simulteanous Equations.
Simulteanous EquationsSimulteanous Equations are 2 sets of equation with 2 unknownes to solve. Methods used are Substitution and Elimination methods, use either to solve unless question specify a method.
Example:
2x + 4y = 67
3x + 9y = 90
ApplicationWe are given the 2 equations:
y = 2x - 1 (Equation 1)
2x + y = 3 (Equation 2)
We are asked to use the Substitution Method.
We first substitute Equation 1 to Equation 2 to find the value of x.
2x + (2x - 1) = 3
2x + 2x - 1 = 3
4x - 1 = 3
4x = 3 + 1
4x = 4
x = 4 ÷ 4 = 1
Now we can substitute x into Equation 1 to find the value of y.
y = 2(1) - 1
y = 2 - 1 = 1
Students A and B have probabilities of failing an exam of 1/2 and 1/5 respectively. The probability of them both failing the examination is 1/10. Determine the probability that at least one of the two students fail.
Answer:
7/5
Step-by-step explanation:
1/2 + 1/5
probability that at least one of the two students fail is 7/5
consider the experiment of a worker assembling a product. a. define a random variable that represents the time in minutes required to assemble the product. b. what values may the random variable assume? c. is the random variable discrete or continuous?
(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.
(b) The random variable may assume the values in the interval (0, ∞).
(c) The random variable "X" is continuous in nature.
A random variable is a mathematical representation of a number or object that is affected by random occurrences. It is a mapping or function between probable outcomes in a sample space and a measured space, which is frequently real numbers.A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable might be discrete (with fixed values) or continuous (any value in a continuous range).To learn more about variables, visit :
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A political gathering in south america was attended by 8475 people. each south americas 12 3 territories was equally repesented.how many representatives atteded from each country
We will use simple division to solve the problem. The number of representatives attended from each country is 706.
In the given question we know that a political gathering in South America was attended by 8475 people and each 12 territories of South America were equally represented. We need to find out how many representatives attended from each country. Inorder to find the number of representatives we can divide 8475 by 12.
number of representatives= 8475/12 =706
Therefore number of representatives from each country is 706.
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in how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling?
Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.
There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.
There are 2 rows of 3 seats each.
We will try to find the number of ways each seat can be filled.
So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.
Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.
For the third seat remaining in the first row, one out of the remaining pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.
Now after filling the first row in this manner, the second row can be filled in only 2 ways.
So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways
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Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
Answer:
1,730
Step-by-step explanation:
173x10 (pieces)= 1730
on the number line drop box plot for data how many siblings does seventh grade have the number summaries below min:0,q1:1,medium:2,q3:3,max:10
Here, we want to drop a box plot on the number line given the listed numbers
We have the box plot as follows
The listing of the numbers is the actual way the numbers on the box plot will be listed from left to right
We have this as follows;
monty takes a cab to work and pays a fare of $12.75, he tips the diver 20% and the tax rate is 8%. how much does he spend on the trip
The cost of the fare based on the information is $16.32.
How to calculate the value?Amount for the fare = $12.75
Tip for the driver = 20% = 20% × $12.75 = $2.55
Tax rate = 8% = 8% × $12.75 = $1.02
Therefore the total amount will be:
= Cost of fare + Tip + Tax
= $12.75 + $2.55 + $1.02
= $16.32
The cost is $16.32. This illustrate the concept of addition.
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3. The following are the sizes in square feet of the seventeen new faculty office in the mathematics department at a college.102123142155104185159124154136113110107119120127155Find the mean square footage. Round your answer to the nearest tenth, if necessary. square feetFind the median square footage. square feet
Given a sample of the size, measured in square feet, of 17 faculty offices.
1) Mean
To calculate the mean of the sample you have to add all observations of the data set and divide it by the sample size:
[tex]\bar{x}=\frac{\Sigma x_i}{n}[/tex][tex]\begin{gathered} \bar{x}=\frac{102+123+142+155+104+185+159+124+154+136+113+110+107+119+120+127+155}{17} \\ \bar{x}=\frac{2235}{17} \\ \bar{x}=131.47\approx131.5ft^2 \end{gathered}[/tex]The mean square footage is 131.5 ft²
2) Median
To determine the median of the data set, first, you have to calculate the position of the median, following the formula:
[tex]\text{PosMe}=\frac{(n+1)}{2}[/tex]The sample size is n=17, then the position of the median is
[tex]\begin{gathered} \text{PosMe}=\frac{17+1}{2} \\ \text{PosMe}=\frac{18}{2} \\ \text{PosMe}=9 \end{gathered}[/tex]The median corresponds to the ninth observation of the data set.
Next, you have to order the data set from least to greatest:
102, 104, 107, 110, 113, 119, 120, 123, 124, 127, 136, 142, 154, 155, 155, 159, 185
Count the ninth observation from the left.
The median of the data set is Me= 124 ft²
6/15=3/x.
I'm going insane
Answer:
x = 7.5
Step-by-step explanation:
[tex] \frac{6}{15} = \frac{3}{x} [/tex]
cross multiply expressions
6x = 45 divide both sides by 6
x = 7.5
A girl scout troop hiked 6.8 miles southeast in 2 hours. What was the troop’s velocity?
Answer:
1.5 m/s
Step-by-step explanation:
Distance = 6.8×1609.344 = 10943.5392
time=2×60×60 = 7200
velocity= distance/time = 10943.5392/7200= 1.51 m/s
two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure
Answer:
60°Step-by-step explanation:
two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure
linear pair = 180°
180 : 3 = 60° (smaller angle)
60° x 2 = 120° (bigger angle)
120 is twice 60 and the sum is 180°
the answer is good
-3x – 10 = 32Help me I need the answer
Answer:
x = - 14
Step-by-step explanation:
-3x – 10 = 32 Help me I need the answer
-3x – 10 = 32
-3x = 32 + 10
-3x = 42
x = 42 :(-3)
x = - 14
-----------------
check
-3 × (-14) - 10 = 32 (remember pemdas)
42 - 10 = 32
32 = 32
the answer is good
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³ = 20b³
2. (3a²) ² x 2 (b ²) ³ = 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] 5d
3. 15d ³ divided by 3d ² = 5d
What is Operations?
An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's acuity is determined by the number of operands.
The given problems are:
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³
= 4 x 5b³
= 20b³
2. (3a²) ² x 2 (b ²) ³
By the exponent rule:
[tex](x^{n} )^m[/tex] = [tex]x^{n * m}[/tex]
= [tex]x^{nm}[/tex]
∴ 3[tex]a^{2*2}[/tex] x 2[tex]b^{2*3}[/tex]
= 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex]
3. 15d ³ divided by 3d ²
15d ³ ÷ 3d ²
By the exponent rule:
[tex]a^{m}[/tex]÷[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
∴ 5[tex]d^{3-2}[/tex] = 5[tex]d^{1}[/tex]
= 5d
Hence, The solutions are 20b³, 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] and 5d
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a newsletter publisher believes that more than 79y% of their readers own a laptop. is there sufficient evidence at the 0.020.02 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
The Null hypothesis will be expressed as u = 0.79 whereas the Alternative hypothesis will be expressed as. u > 0.79
The null hypothesis (H0) may be used to show that there exists no significant variation between variables or that a single variable is not different than its mean. While an alternative Hypothesis (Ha) is a theory that attempts to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean. According to the question we can say that the
Null hypothesis (H0): u = 0.79
Alternative hypothesis (Ha): u > 0.79
Where u may be called as the proportion of their reader that owns a personal computer.
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19. You have 15 pencils in your pencil case.1/5 of the pencils are green.
How many are not green?
Answer:
12
Step-by-step explanation:
You have 15 pencils in your pencil case.1/5 of the pencils are green. How many are not green?
= 1 - 1/5
= 5/5 - 1/5
= 4/5
This means that 4/5 of the 15 pencils are not green. So:
4/5 * 15 = 12 pencils are not green.
what is the rule for this pattern?
17, 20, 19, 22, 21
Answer:
+3, -1
Step-by-step explanation:
17 + 3 = 20
20 - 1 = 19
19 + 3 = 22
22 - 1 = 21
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Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answer:
x=-55Step-by-step explanation:
[tex]5(2-x)-10=25-2(3x+40)\\\\10-5x-10=25-6x-80\\\\-5x=-6x-55\\\\-5x+6x=-55\\\\x= -55 [/tex]
Answer:
x = -55
Step-by-step explanation:
Hello!
We can solve for x by isolating the variable.
Solve for x5(2 - x) - 10 = 25 - 2(3x + 40)5(2) - 5(x) - 10 = 25 - 2(3x) - 2(40)10 - 5x - 10 = 25 - 6x - 80-5x = -55 - 6xx = -55The value of x is -55.
The senior class sells hamburgers and hot dogs at a football game and makes a profit of $1.75 on each hamburger and $1.25 on each hot dog. The class would like a profit of at least $280. Let x represent the number of hamburgers and y represent the number of hot dogs sold
Answer:
1.75x + 1.25y >= 280
Step-by-step explanation:
1.75x + 1.25y >= 280
WILL GIVE BRAINLIEST PLS HELP
Passed exam | Did not pass exam | Row Totals
Completed exam review | 55% | 10% | 65%
Did not complete exam review | 20% | 15% | 35%
Column Totals | 75% | 25% | 100%
Part A: What is the percentage of students who failed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who failed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points)
Part C: Is there an association between failing the exam and completing the exam review? Justify your answer. (2 points)
Answer:
A: 15%
B: 43%
C: yes
Step-by-step explanation:
You want the percentages of students who failed the exam, given that they (A) did, or (B) did not complete the exam review. You also want to know if this indicates an association between failing and reviewing.
NotationLet F represent the event "failed the exam." Let R represent the event "completed the exam review." R' will be the event "did not complete the review."
A: P(F|R)The probability is ...
P(F|R) = P(F&R) / P(R)
P(F|R) = 0.10/0.65 = 2/13 ≈ 15%
About 15% failed who completed the review.
B: P(F|R')P(F|R') = P(F&R') / P(R')
P(F|R') = 0.15/0.35 = 3/7 ≈ 43%
About 43% failed who did not complete the review.
C: AssociationIf the events "Failed the exam" and "Completed the review" were independent, then the probability of one would not be conditional upon the other. Here, the probability of failing is clearly different for those who completed the review, so there is an association between failing the exam and completing the exam review.
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what is the answer to 20x + 35y
The greatest common factor is 5 .
If you factor it out, the expression becomes 5 (4x + 7y) .
Answer: 55x^1 y^1
Step-by-step explanation:
Add 20+35= 55
x & y can't stand by it's self, so x^1 and y^1
So you take those answers and you got 55x^1 y^1
You must keep it in letters in alphabetic order or it's considered wrong.
Cindy struck out 7, 14, 6, 4, 5, and 6 batters in softball games this season. In discussingher stats with a newspaper reporter, Cindy's coach mentions that the average number ofCindy's strikeouts is 7. Is the coach's statement misleading? Explain why or why not.O No; the mean of her strikeouts is 7.O None of the other answers are correctO Yes, she struck out 7 batters only one time.O No; she typically strikes out 7 batters in a game.O Yes; the median of her strikeouts is 7.
Given that the batters were 7, 14,6,4,5 and 6 then to find the average, you add the batters and divide by their number
[tex]\text{sum}=7+14+6+4+5+6=42[/tex][tex]\text{Average}=\frac{42}{6}=7[/tex]Here you notice that the average is 7, so the coach's statement is true.
Your answer is , No;the mean of her strikeouts is 7
What is 420÷60 hellllllllppp
Answer:7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
420÷60 is the same as 42÷6.
42 goes into 6, 7 times:
6, 12, 18, 24, 30, 36, 42.
Therefore, 420÷6 is 7.
Please use a calculator next time.
1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34
Solving those simple linear equations, by isolating the variable, and combining like terms.
1.3x-4=23
3x -4=23
3x=27
x=9
2) 9-4x=17
-4x =17-9
-4x=8
4x=-8
x=-2
3) 6(x-7)=36 Distributing the factor
6x -42=36
6x=36+42
6x=78
x=13
4) 2(x-5)-8=34 Distributing the factor
2x -10-8=34
2x -18=34
2x=52
x=26
A forest is decreasing in size by 60 hectares every 3 years. In how many years will the forest have decreased by 140 hectares?
A forest is decreasing in size by 60 hectares every 3 years. In 7 years, the forest will have decreased by 140 hectares.
Using the Unitary Method:
∵ In '3' years, a forest decreased in size by '60' hectares
∴ In '1' year, a forest will be decreased in size by '20' hectares
Every year 20 hectares is decreased. Considering a regular trend in the decrement of forest area, the time span of '7' years will diminish 'to 140' hectares.
The 'Unitary Method' is also known as the 'Mango Method'. It establishes a relation between given data. The relation is used to predict results in different conditions. The Unitary Method is always used for regular trends.
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