The values for the variables 'x' and 'y' are (3,7).
According to the question, to calculate the value of 'x' and 'y' then equate both the equations.
The given expressions are:
Equation (1): x + (1/7)y = 4 ⇒ 7x + y = 28
Equation (2): y = 3x - 2
Solving equation (1) and equation (2) by substituting the value of the 'y':
Therefore, 7x + 3x - 2 = 28 ⇒ 10x = 30 ⇒ x = 3
Now: y = 3(3) - 2 = 7
Hence, the values are: x = 3 and y = 7.
What is simplification?
Simplification of an expression can be defined as by making the complicated expression as less complicated. And through this method, it become easy to solve it and find the correct answer.
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Jackson asked a representative sample of 30 of his classmates about their favorite arctic animal for an upcoming science project.
Fill in the table to show reasonable predictions for the whole class.
His class has a total of 240 students.
Favorite Arctic Animal
Polar Bear 12
Reindeer 9
Seal 3
Walrus 6
Answer:
These are the estimates:
Polar Bear: 96
Reindeer: 72
Seal: 24
Walrus: 48
Step-by-step explanation:
240/30=8
Multiply the amount of people that like each animal by 8 to estimate how many out of 240 like that animal.
12*8=96
9*8=72
3*8=24
6*8=48
f(x)=6^x and g(x)=14^x labeled on graph
f(x)=6ˣ and g(x)=14ˣ on the graph are shown (refer to the graph given below).
What do we mean by the graph?While many people use the terms "graph" and "chart" interchangeably, they are not the same thing. Charts are tables, diagrams, or pictures that clearly and concisely organize large amounts of data. Charts are used to interpret current data and make predictions. Graphs, on the other hand, concentrate on raw data and show trends over time. A graph is defined as a diagram that depicts the relationships between two or more things. A pie chart is an example of a graph. Bar graphs, circle graphs, and line graphs are the three most common types of graphs. Each type of graph is appropriate for displaying a different type of data.So, f(x)=6ˣ and g(x)=14ˣ on graph as:
Refer to the graph given below.Therefore, f(x)=6ˣ and g(x)=14ˣ on the graph are shown (refer to the graph given below).
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Write the equation of the line that passes through the points (3, 5) and (6, 7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
HELP PLEASEEE
Answer:
We can use the point-slope form of the equation of a line to find the equation that passes through the points (3, 5) and (6, 7).
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is one of the points on the line and m is the slope of the line.
First, we need to find the slope of the line using the two given points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two points.
Plugging in the values we know, we get:
m = (7 - 5) / (6 - 3) = 2 / 3
So the slope of the line is 2/3.
Now we can use one of the given points and the slope to write the equation of the line in point-slope form. We'll use the first point, (3, 5).
y - 5 = (2/3)(x - 3)
This is the equation of the line in point-slope form.
If we want to write it in slope-intercept form (y = mx + b), we can simplify:
y - 5 = (2/3)x - 2
y = (2/3)x + 3
So the equation of the line that passes through the points (3, 5) and (6, 7) is y = (2/3)x + 3.
I need help with the problem 5/6 ÷ 3/4
Answer:
10/9 or 1 1/9
Explanation:
Multiply by the reciprocal
cancel out the greatest common factor
multiply the fractions
and you get 10/9 or 1 1/9
2. If lime juice has a pH of 1.7, what is the concentration of hydrogen
ions (in mol/L) in lime juice, to the nearest hundredth? Use the
formula pH = -log[H +].
Answer:0.02 mol/L
Step-by-step explanation:
Given: pH = 1.7
Required: [H+]
Equation: pH = -log [H+]
Solution:
Take the antilog of both sides
[H+] = antilog(-pH)
Antilog(-pH) is equal to 10^-pH. Therefore
[H+] = 10^-pH
Solve for [H+]
[H+] = 10^-1.7
Answer: [H+] = 0.02 mol/L
c. Choose two numbers other than 1 and 1 . Generate a Fibonaccilike sequence from them. Write the first ten terms of your sequence, find the sum, and divide the sum by 11. What do you notice?
The two numbers other than 1 and 1 are 2 and 3 finally get the 34 means 7 th term in the sequence.
What is Fibonacci sequence and what are the first ten terms?The Fibonacci numbers, sometimes known as Fn in mathematics, are a series of numbers. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.
from the question
Let take the first term as 2.
and second term as 3.
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
The Fibonacci sequence includes the numbers 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on.
Sum=2+3+ 5 + 8 +13 + 21+
34+55+89+144 = 374 is what we get when we add up the numbers in the series.
The first ten Fibonacci numbers sum is 374.
now divided the sum by 11.
374/11 = 34.
so,to get the 34 means 7 th term in the sequence.
Hence, the two numbers other than 1 and 1 are 2 and 3. finally get the 34 means 7 th term in the sequence.
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what is two and four nineths plus two thirds
Answer:
3 1/9
Change 2/3 to 6/9. Add 6/9 + 4/9 to get 10/9. Make a mixed number, 1 1/9. Add 2, 3 1/9.
Identify a pattern and find the next three numbers in the pattern. 8,16,24,32, . . .
The next three numbers are - 40, 48, 56,..
The pattern belongs to multiples of 8.
Complete pattern is - 8,16,24,32,40, 48, 56,..
What is pattern completing?Examine the pattern's initial three to four numbers. What connection exists between these numbers, you could ask. For instance, the first three to four numbers in this mathematical pattern are 1, 3, 6, and 10. As the numbers rise, it appears that you must add to obtain the subsequent number. You begin by adding 2, then 2, 3, and then 4. Therefore, if you put this on paper, you probably notice a pattern emerging.
To test whether your solution works, try the remaining pieces of the pattern that was provided.
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You stand on a street corner and record the gender of the first twelve people who pass by. if the city is half male and half female, what is the probability that you will record all females?
The probability is 6.
Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and one refers to an event with the highest possibility. The type of probability we will use to solve this problem is the geometric distribution.
The geometric distribution is defined as a discrete probability distribution representing the probability of consecutive failures before success in a Bernoulli trial. There could be only two possible outcomes; either True (1) or False (0).
Bernoulli's trial is an experiment in which we have only two possible outcomes, success or failure. In other words, the geometric distribution repeats Bernoulli trials until it succeeds, then stops. So, achieving success is the ultimate goal and is the point that stops Bernoulli's trials from happening further.
Geometric distribution, the class of probability distributions, is based on three key assumptions, and these assumptions are defined as:
The studies conducted are independent. Each event is independent of the other.Each attempt has only two outcomes: success or failure. If an event has any other possible outcome other than 0 and 1, it can not be classified as a Bernoulli trial.The probability of success, indicated by p, is the same for each trial.Now for our given problem, we stand on a street corner and record the gender of the first twelve people who pass by. The condition here is the city is half male and half female. Now to find the probability, we will consider the possibility of each of the twelve events. Since half of the population is Female, the probability of one single event is;
p = 1/2 (50 %)
The overall probability is the sum of all the individual probabilities:
P ( ALL FEMALE)
= 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2
= 6
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1) 28/z - z/4 + 1 1/8, when z = 4
A) 7 1/8
B) 4 7/8
C) 9 1/8
D) -5 7/8
2) n+23.1/ 3n - 8n, when n = 2.1
A) -12.8
B) -8.4
C) 20.8
D) -20.8
Answer:
Step-by-step explanation:
9 + 11 = 10 so 120=69 69-5 = 13 answer is 13
A rectangle has a perimeter of 15 inches. If the length is two times the sum of 3 and the width find the dimensions of the rectangle.
Answer:
See below
Step-by-step explanation:
Perimeter = 2( L + W ) L = 2 (3+W) <==== given
15 = 2 ( 2(3+W) + W)
15 = 2 ( 6 +3W)
15 = 12 + 6W
3 = 6W
W = 1/2 inch L = 2(3+W) = 7 inches
A random survey was conducted to determine where families vacationed. The results indicated that P(B)=0.6, P(B ^M)=0.2 , and the probability that a family did not vacation at either destination is 0.1 .
b. What is the probability that a family visiting the beach will also visit the mountains?
The probability that a family to visit the beach also will travel the mountains is 0.33.
What exactly is a Venn diagram?A Venn diagram is a graph that uses circles to represent relationships between objects or finite groups of objects. Circles that intersecting share properties, but circles that do not overlap do not.
Please see the Venn diagram.
P(B) [the entire blue circle] = 0.6 is the probability of such a family vacationing there at beach.
P(B∩M) [the red/blue intersecting intersection of two circles] = 0.2 is the possibility of a family taking a vacation in both locations.
Using the property of independent event: Two events are considered independent if the incidence of one does not affect the likelihood of occurrence of the other.
As, occurrence of family visiting the beach will also visit the mountains is an independent event. Thus,
The formula for the independent event is;
P(B | M) = P(B∩M)/P(B)
P(B | M) = 0.2/0.6
P(B | M) = 0.33
Therefore, the probability of the occurrence that family visiting the beach will also visit the mountains is 0.33.
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Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas and 4 neither degree nor diploma. How many of them have both.
Answer:
the answer is 6.
Step-by-step explanation:
solution is given in the photo
hi
let's rule ot first candidate with nothing :
as they are 4 , remains : 30 -4 = 26
Now let call X number of candidate with both degrees and diplomas
we have : 17+15 -X = 26
-X = 26 - 32
-X = -6
x = 6
We have to withdraw from categorie degree and diplomas 6 people who have both and then counted twice.
So figues goes as follow :
nothing : 4
degrees only : 11
diplomas only : 9
both degree and diplomas : 6
total : 4 +11 +9 +6 = 30
Write an equation in point-slope form of the line having the given slope that contains the given point.
m:-2,(-6,-7)
The equation in point-slope form of the line having the slope m=-2 and the given point (-6,-7) is y+7=-2(x+6)
Given,
The slope = -2
The point = (-6,-7)
We know the point slope form [tex]y-y_{1}=m(x-x_{1})[/tex]
Substitute the values in the equation
y-(-7)=-2(x-(-6))
y+7=-2(x+6)
Hence, the equation in point-slope form of the line having the slope m=-2 and the given point (-6,-7) is y+7=-2(x+6)
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HELP ME PLS PSL POPLSSLPPSLPSLPLSPSLPSLPLPLSPLPSLPSLPSLPSLPSLSPLSPLSPLPSLPSLPSLPSLPSLPSLPSLPSLPSLPSLPSLPSLPSLPLSPSLPSLPSLSP
Your answer would be the second one.
We know that adding [tex]\frac{1}{2}[/tex] to x gives us 4, as that's provided by the question.
So [tex]4=x+\frac{1}{2}[/tex]. Now, to find x, simply subtract [tex]\frac{1}{2}[/tex] from 4 to give us x, which gives us [tex]3\frac{1}{2}[/tex].
Which of the following is NOT an example of a situation in which an employee can apply the Family and Medical Leave Act of 1993?
O During birth and care of a newborn child
After placement of an adopted or foster care child
O When caring for a great-aunt or great-uncle with a serious medical condition
O When unable to work because of a serious medical condition.
Bonjour, je ne comprends pas mon exercice de Mathématiques.. Pouvez-vous m'aider à le résoudre ? Merci d'avance !
L'exercice en question :
" On donne f(x) = 6x² - 7x
Quelles sont les images de 2 et de -3 par la fonction f ? "
Answer:
Je vous souhaite le Bonjour dominical,
Step-by-step explanation:
Si tu veux une réponse:
soit tu postes ce devoir dans la matière French
soit tu postes le problème sur le site nosdevoirs.fr
f(2)=6*2²-7*2=24-14=10
f(-3)=6*(-3)²-7*(-3)=54+21=75
Explain the difference between a constant and a coefficient.
The constant is the number that includes in the expression and the coefficient is the number that write along with the variable in the expression.
Here,
The constant is the number that includes in the expression. It is a fixed value that does not change over time
Example : 2x+5
Where 5 is the constant
The coefficient is the number that write along with the variable in the expression
Example : 2x+5
Where 2 is the coefficient.
Hence, the constant is the number that includes in the expression and the coefficient is the number that write along with the variable in the expression.
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Evaluate each expression for x=-2,0,1 , and 4.
(3/5)x-2
The value for x=-2,0,1 and 4 are -16/5, -2, -2/5, 2/5 respectively.
What does solving for x means?Find the value of x that would make the equation you see true is what it means to "solve for x." Consider the following formula: x + 1 Equals 3. If you were to attempt to solve it, you would need to identify a value for x such that it yields three when one is added.
Given expression is -
(3/5)x-2
For x = -2
The value of expression will be = (3/5)(-2) - 2
= -16/5
For x = 0
The value of expression will be = (3/5)(0) - 2
= -2
For x = 1
The value of expression will be = (3/5)(1) - 2
= -2/5
For x = 4
The value of expression will be = (3/5)(4) - 2
= 2/5
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A 138 inch pipe is cut into two pieces one piece is two times the length of the other. What is the lenfth of the shorter pipe?
Answer: 46 inches
Step-by-step explanation: the larger piece is 92 inches 92+46=138
A Dutch company built a submarine that can hold 10 passengers and 1 pilot. The submarine has a safety feature that will automatically raise the submarine if it goes below the certified depth of −650feet. To show this feature to a buyer the submarine dove to a depth of −872[tex]\frac{5}{12}[/tex]feet. The automatic feature then raised the submarine 50[tex]\frac{3}{5}[/tex]feet per minute. How much time, in minutes, does it take for the submarine to reach the certified depth? Round your answer to the nearest tenth of a minute.
The time, in minutes that it take for the submarine to reach the certified depth is 12.85 minutes.
How to illustrate the information?From the information, the submarine has a safety feature that will automatically raise the submarine if it goes below the certified depth of −650feet.
It should be noted that the automatic feature then raised the submarine 50 3/5 feet per minute.
Therefore, the time needed to reach the depth will be:
= 650 / 50 3/5
= 650 / 50.6
= 12.85 minutes
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Please help me out with this question
Thank you
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 45,90,180,360, .............
45,90,180,360, .... is a geometric sequence. The next two terms are 720, 1440.
In an arithmetic sequence, the difference between two subsequent terms is constant. This difference between two subsequent terms is usually called common difference (d), and its value is:
d = a(n) - a(n-1)
Where a(n) is the nth term and a(n-1) is the (n-1)-th term.
In a geometric sequence, the ratio (r) between two subsequent terms is constant.
r = a(n)/a(n-1)
The given sequence is: 45,90,180,360, .....
We can check that:
(90 - 45) is not equal to (180 - 90) and to (360 - 180)
So, there is no common difference in the given sequence.
Let us now check the ratio:
90/45 = 180/90 = 360/180 = 2
The ratio between two subsequent terms is constant, that is 2. Therefore, we can conclude that the given sequence is a geometric sequence with a(1) = 45 and r = 2.
In a geometric sequence, the next term is obtained by multiplying the current term by its ratio.
Hence, the next two terms are calculated as:
360 x 2 = 720
720 x 2 = 1440
or 720, 1440.
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In 2000, Jefferson High School had 1125 students. By 2006 , the student body had increased to 1425 students. When Fairview High School was built in 2001 , it had 1275 students. How many students did Fairview High School have in 2006 if the student body grew at the same rate as Jefferson High School?
The number of students that Fairview High School have in 2006 is 1615 students.
This is a question of percentages.
Given that:-
The number of students in Jefferson High School had in 2000 are 1125.
The number of students in Jefferson High School had in 2005 are 1425.
The number of students in Fairview High School had in 2000 are 1275.
It is given in the question that the student body of Fairview High school grew at the same rate as Jefferson High School.
We have to find the number of students in Fairview High School in 2006.
Rate at which the number of students grew at the Jefferson High School =
[(1425-1125)/1125]*100 = (300/1125)*100 = 26 (2/3) % or 80/3 %
Let the number of students in the Fairview High School in 2005 be x.
Hence,
80/3 = [(x-1275)/1275]*100
x = 1615
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Find the greatest common factor of the following terms. a^8b^6,-a^6b^3
Reason:
The 'a' terms are a^8 and a^6. We go for the smallest exponent when forming the GCF. Go for the largest exponent when finding the LCM.
The b terms are b^6 and b^3. The smaller exponent is b^3, which is also part of the GCF
We have a^6 and b^3 combine to form a^6b^3
Class is over! Mr. Shrager does not always let his
statistics class out on time. In fact, he seems to enc
class according to his own "internal clock." The
density curve models the distribution of the
amount of time after class ends (in minutes) when
Mr. Shrager dismisses the class. (A negative value
indicates he ended class early.)
Part (a)
The horizontal part of the rectangle goes from m = -1 to n = 4. This is a distance of 5 units because |m-n| = |-1-4| = 5
The height is some unknown variable h
It must multiply with the base (5) to get an area of 1
base*height = area
5h = 1
h = 1/5
h = 0.2
Answer: height = 1/5 = 0.2========================================================
Part (b)
x = dismissal time minutes after class
Something like x = 2 means he dismisses class 2 minutes after the bell, while x = -1 is him dismissing class 1 minute early before the bell.
The phrasing "within 1 minute" means that x is between p = -1 and q = 1. So we can say [tex]-1 \le x \le 1[/tex]
This is a span of 2 units because |p-q| = |-1-1| = 2. Divide this over the entire horizontal span: 2/5 = 0.4
Exactly 40% of the time the teacher lets his class out within one minute of the scheduled end time.
Answer: 0.4HELP: Write whether the ratio demonstrates a proportional relationship
Sandra swam 8 laps in 16 minutes. George swam 18 laps in 38 minutes.
Answer:
16/8 = 2
38/18 = 2.1
But 2.1 is approximately equal to 2, hence a proportional relationship.
Find the slope of the line through each pair of points. (-3,5) and (4,5)
The slope of the equation is 5 for the coordinates (-3,5) and (4,5).
What factors determine slope?Locate two points along the chosen line and find their coordinates.
Find the y-coordinate difference between these two sites (rise).
Find the x-coordinate difference between these two sites (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).
The slope calculation formula is -
m = y2 - y1 / x2 - x1
Given points are -
(-3,5) and (4,5)
Now, putting the values in equation,
m = 5-5 / 4+3
m = o
As slope is 0, this implies,
the equation of line is y = 5
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100 POINTS + BRAINLEIST ANSWER ASAP
Answer:
BC = 21
Step-by-step explanation:
AB + BC = AC
[tex]7x + 8 + 3x + 6 = 64[/tex]
[tex]10x + 14 = 64[/tex]
[tex]10x = 50[/tex]
[tex]x = 5[/tex]
BC = 3(5) + 6 = 21
A trapezoid has a height of 12 inches, a base length of 9 inches, and an area of 150 square inches. What is the length of the other base?
The length of other base is 16 inch.
The area of trapezoid is given by the formula -
Area = 1/2×(a+b)×height, where a and b represents the two different bases. Let a be the length of 9 inches and b be the length of other base.
150 = 1/2×(9 + b)×12
Shifting 2 to Left Hand Side and performing multiplication on both sides.
150×2 = (9 + b)×12
300 = 108 + 12b
12b = 300 - 108
12b = 192
Shifting 12 to Right Hand Side of equation to find the other base
b = 192 ÷ 12
Performing division
b = 16 inch
Hence, the length of other base is 16 inch.
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