Answers
D. 16
Cross multiply, to cancel the denominator; so if you multiple by 6 on one side, to cancel the division of 6 - you must also multiply the other side by 6 & vice versa.
You get:
8(x-4) = 6x
Expand bracket to get:
8x - 32
Now solve for x :
8x - 32 = 6x
- 8x
- 32. = - 2x
÷ - 2
16 = x
Or
8x - 32 = 6x
+ 32
8x. = 6x + 32
- 6x
2x. = 32
÷2
x =16
Check:
16 - 4 = 12, then ÷ 6 is 2
16/8 = 2
Hope this helps!
Related Questions
where should i place the points!!! help!!
Answers
Answer:
-7
Step-by-step explanation:
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
Question 4 (Essay Worth 10 points)
(05.07 HC)
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
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Answers
The correlation coefficient of r = 0.51 shows that it's an accurate value for this data.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm
There is a correlation between the number of hours of sunlight that a plant receives and the height to which it grows.
The function that best fits the data is y = 3x + 4.
The y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
What is a Scatter Plot?The association between two variables that are correlated can be shown by a scatter plot which has a trendline along which the data points are located.
A correlation coefficient of r = 0.51 is accurate based on the scatter plot given. If the trendline slopes upwards from the left to the right, it shows a positive correlation and vice versa.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.
There is a direct correlation between the number of hours of sunlight that a plant receives and the height to which it grows. This can be seen through the growth in the plant.
The function is y = 3x + 4
When x = 0, y = 3(0) + 4 = 4.
In conclusion, y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
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3² +4² = 5²,
6² + 8² = 10² and
9² + 12² = 15²
Can you prove,using algebraic method,that this relationship will be true for any multiple of the triple,
3, 4, 5?
Prove that the statement
5² +12² =13² will hold true for any multiple of this triple.
Answers
Answer:
They are all true
Step-by-step explanation:
1. 3² +4² = 5²
3x3 + 4x4 = 5x5
9 + 16 = 25
25 = 25
-----------------------
2. 6² + 8² = 10²
36 + 64 = 100
100 = 100
------------------
3. 9² + 12² = 15²
81 + 144 = 225
225 = 225
-------------------
4. 5² +12² =13²
25 + 144 = 169
169 =169
-------------------
What is the equation of the line that passes through the point (-6,2) and has a slope of 1?
Answers
Answer:
[tex]y = x + 8[/tex]
Step-by-step explanation:
The equation of a line is:
[tex]y = mx + c[/tex]
Where m is the gradient (or as you call it, the slope), and c is the y-intercept. We already know what the slope is, therefore we need to find the y-intercept. You have been given the coordinates (-6, 2), but to find the y-intercept, X must be equal to 0. Since the gradient is 1, we know that for every value we add to X, we must add the same to y. To get from -6 to 0, we must add 6, so we must do the same 2, leaving our y-intercept coordinates as (0, 8), and our y-intercept as 8. Plugging in our values, we are left with the following equation:
[tex]y = x + 8[/tex]
What type of polynomial is: 3x^4 - 2x^3 - 2
Answers
This polynomial has only 3 terms, so it is a trinomial. Hope it helps!
What is the domain of the following points? Group of answer choices {-4, 1, 4} {-4, -1, 1, 4} {-1, 4, 1} {1, 4}
Answers
The domain of the relation shown in the graph is -4 <= x <= 4
How to determine the domain of the relation shown in the graph?The complete question is added as an attachment
The relation on the graph is an ellipse function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -4 <= x <= 4
Hence, the domain of the relation shown in the graph is -4 <= x <= 4
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what is the area
please help me
Answers
The area and perimeter of the picture is 576 inches square and 96 inches respectively
How to determine the area
Given that each frame is a rectangle and four frames makes up the picture
Note that the picture takes the shape of a square
Let's find the total perimeter
Perimeter of the picture = sum of the four rectangular frame perimeters
Perimeter = 24 + 24 + 24 + 24
Perimeter = 96 inches
Formula for area of a square = a^2
Where 'a' is the length of the side = 24 inches
Substitute the value of 'a'
Area of the picture = 24^2
Area of the picture = 576 inches square
Thus, the area and perimeter of the picture is 576 inches square and 96 inches respectively.
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Talia buys a 6-ounce container of macadamia nuts for $5.94 what is the unit price per ounce?
Answers
Answer:
$0.99 or 99 cents
Step-by-step explanation:
Since 6 ounces is worth $5.94, divide 5.94 by 6 to get the unit price. This is $0.99 or 99 cents.
Boyle's law states that if the temperature of a gas remains constant, then PV=c, where P=pressure,V=volume , and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 10in^3/sec, at what rate is P increasing when P =60lb/in^2 and V=20in^3 in? (do not round your answer.)
a. 30 lb/in^2 per sec
b. 120lb/in^2 per sec
c. 9 lb/in^2 per sec
d. 10/3 lb/in^2 per sec
Answers
The pressure, P if V is decreasing at a rate of 10in^3/sec is 120lb/in^2 per sec.option B
Boyle's lawPV = c
where,
P=pressure,V=volume , and c is a constantwhen P =60lb/in^2 and V=20in^3
PV = c
60 × 20 = 1200 in
Find P if V is decreasing at a rate of 10in^3/sec
PV = c
P × 10 = 1200
10P = 1200
P = 1200 / 10
P = 120lb/in^2 per sec
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On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.
Which equation represents the parabola shown on the graph?
y2 = –2x
y2 = –8x
x2 = –2y
x2 = –8y
Answers
The equation represents the parabola shown on the graph is x^2 = - 8y . Option D
How to determine the equationWe were given the following parameters;
Vertex ( 0, 0 )Focus ( -2, 0)Directrix , at x = 2The standard for a parabola is given as;
y² = 4ax
It can also be written as;
x² = 4ay
Given the focus as ( -2, 0), we have the value of 'a' to be -2
Now, let's substitute the value into the standard equation of a parabola
x^2 = 4ay
x^2= 4 × -2 × y
Multiply through
x^2 = - 8y
The equation of the parabola is x^2 = - 8y
Thus, the equation represents the parabola shown on the graph is x^2 = - 8y . Option D
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Answer:
b
Step-by-step explanation:
trust
kelvin pumped 15.2 gallons of gas into his car. if he paid 59.13 for the total amount of gas, what was the rate per gallon that kelvin paid
Answers
Answer:
3.89
Step-by-step explanation:
if 15.2 gallons cost 59.13.What about 1
then we just divide 59.13 by 15.2 to get the cost of 1 gallon
Choose the division problem represented by this model.
Answers
Answer:
The answer is C
Step-by-step explanation:
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?
Answers
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
According to the question
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.
Assuming that the chance of rain is independent of the day
Probability is the chance that some event will happen.
It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.
Probability = Number of ways it can occur/Total number of outcomes
Probability of rain on first day = 1/2
Probability of rain on second day = 1/2
Then
Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4
Hence,
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
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13. The average of 15, 19, 23, 41, and x is 20. What is the value of x? (A) 2 (B) 20 (C) 23.6 (D) 31
Answers
Answer:
A
Step-by-step explanation:
(x + 15 + 19 + 23 + 41) / 5 = 20
x + 15 + 19 + 23 + 41 = 100
x + 98 = 100
x = 2
Answer: it’s 2 (A)
Step-by-step explanation:
20 * 5 = 100
15 + 19 + 23 + 41 = 98
100-98=2
A school club has 5 members. From these 5 members, a 2-person team must be chosen to represent the club at a school carnival. How many different 2-person teams can be made from the 5 club members?
A 10 teams
B 15 teams
C 20 teams
D 25 teams
Answers
Answer:
20 teams can be made
Answer:
A. 10 teams
Step-by-step explanation:
a 2-person team is a combination of two elements out of 5.
Then
The number of possible teams is :
[tex]C^{2}_5 = \frac{5!}{2! \times (5-2)!} = \frac{5!}{2! \times 3!}=10[/tex]
20 points please help
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 14, 13, 16, 12, 17, 21, 26
Answers
Answer:
3.71
Step-by-step explanation:
The mean absolute deviation(MAD) of a data set is given by the formula
[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]
[tex]n[/tex] = number of data set values. Here [tex]n = 7[/tex]
[tex]\bar{x}=[/tex] mean of the data set values; [tex]\bar{x}=[/tex] [tex](14+13+16+12+17+21+26)/7[/tex] = [tex]119/7=17[/tex]
[tex]x_{i}[/tex] are the n individual values
[tex]\frac{1}{7} |14-17| + |13-17| + |16-17| + |12-17| + |17-17| + |21-17| + |26-17|\\= (3 + 4 + 5 + 1+ 0 + 4 + 9)/7\\= 26/7 = 3.71428 \\[/tex]
= [tex]3.71 \textrm{ rounded to the nearest hundredth}[/tex] Answer
20. In the figure at right, ABDC lies in plane k and AD IDC.
AD is definitely perpendicular to k if which of the following is true?
(A) BDLDC (B) ADBC=AABC (C) ADBC is isosceles
(D) ADAB is similar to ADAC (E) none of these
Answers
The option that's true about the plane illustrated is E. None of these.
How to illustrate the plane?From the information given, it should be noted that DBC isn't an isosceles triangle.
Also, from the figure, one can see that DAB isn't similar to DAC.
Likewise, BD and DC aren't perpendicular.
In conclusion, the correct option is E.
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Please help !!! Need help !!!
Answers
Answer: B. alternate interior angles.
Step-by-step explanation:
Opposite angles are non-adjacent angles that are formed by two intersecting lines. They are congruent.
what is the decimal representation of 3/40
Answers
Answer:
0.075
Step-by-step explanation:
to convert a fraction to a decimal fraction
divide the numerator by the denominator, that is
[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075
Order the steps needed to factor - 12a^3b^2 + 18a^2b
Answers
Answer:
12a^3b^2+18a^2b
Step-by-step explanation:
12 3b2+182b
which of the tables represent a function??
please help me! asap!
Answers
For anything to be a function, it cannot have two pairs as my teacher taught me!
For example, let’s take the number 4
Let’s say 4 can take a friend to the fair!
4 decided to take 5 (4,5)
4 CANNOT take anyone else but 5
4 is allowed to take as many 5’s as they want but cannot take any other number
Let’s set up a table
X. Y
4. 5
4. 5
4. 5
This is a function
If the table changed:
X. Y.
4. 5
4. 5
4. 6
This will not be a function
I hope this helps!
A legend says that a tower of hanoi puzzle with 64 discs is being solved, one move per
second. how long will it take to solve this puzzle? explain how you know.
Answers
It will take 585 billion years to solve the puzzle tower of Hanoi puzzle.
What is hanoi of tower?
The Tower of Hanoi is a mathematical game or puzzle that uses three rods and a number of disks that can slide onto any rod. It is also known as The Problem of the Benares Temple, the Tower of Brahma, Lucas' Tower, or simply the pyramid puzzle. The disks are stacked on one rod at the start of the problem, the smallest at the top and roughly forming a conical shape.
Using the Tower of Hanoi as little as possible
In one version of the problem, 64 golden disks are being used by Brahmin priests to solve it.
Minimum moves required if you had 64 golden disks [tex]=2^{64}-1[/tex]
The problem would take around 585 billion years to solve if every move took a single second.
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BRAINLIEST !! Evaluate the following fractions giving your awnser in its simplest form.
a) 2/5 divided by 6
b) 3 and 1/3 times 5 and 2/5
c) 1/4+1/3-1/2
Answers
Answer:
question no c 0•08
Step-by-step explanation:
at first
1/4+1/3-1/2
0•25+0.33-0.50
0.58-0.50
0.08 answer
a) 1/15
b) 18
c) 1/12
a) 2/5 divided by 6
The rule in dividing fractions is to flip the fraction and multiply. Since “6” is 6/1, it becomes 1/6.
2/5 x 1/6 = 1/15
b) 3 1/3 times 5 2/5
Change the fractions into mixed fraction and multiply across.
10/3 x 27/5 = 270/15
Simplify by dividing numerator by denominator
270/15 = 18
c) 1/4 + 1/3 - 1/2
To add and subtract fractions the denominator has to be the same.
The lowest common denominator will be 12.
1/4 = 3/12
1/3 = 4/12
1/2 = 6/12
Now solve
3/12 + 4/12 - 6/12 = 1/12
The side length of each square is 6 units.
Answers
The area of the square A2 is 20 squared units
How to determine the area of A2?The complete question requires that we calculate the area of square A2
The side length of each square is 6 units.
So, the side length (L) of A2 is
L^2 = (2)^2 + (6 - 2)^2
This gives
L^2 = 20
The above represents the area of the square A2
Hence, the area of the square A2 is 20 squared units
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Answer:
Triangle Area = 4 units^2Step-by-step explanation:
assuming you are looking for the area of the triangles, there is no specific question, they are right-angled triangles congruent with the catheti of 2 and 4 units.
Triangle area = 1/2 base x height.
so 1/2 2 * 4 = 4 units^2
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answers
Answer:
334 in²
Step-by-step explanation:
The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.
Total cuboid areaThe area of a cuboid is given by the formula ...
A = 2(LW +H(L+W))
For the bottom cuboid, the area is ...
A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²
Lateral areaThe lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.
LA = Ph = (2(l +w))h
LA = 2(5 in +3 in)(3 in) = 48 in²
Total composite areaThe total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:
SA = (48 in²) +(286 in²) = 334 in²
The surface area of the composite figure is 334 square inches.
__
Additional comment
The exposed area of the bottom cuboid is its total area less the area of the very top face.
The exposed area of the top cuboid is its lateral area plus the area of the very top face.
When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.
Solve the compound inequality. 5x – 11 < –11 or 4x + 2 > 14
Answers
Answer:
5x-11<-11
group like terms
5x<11+11
5x<22
divide both sides by 5
Determine whether the following series converges conditionally, converges absolutely, or diverges. Be sure to state which test(s) you are using.
Answers
Answer:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Step-by-step explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Explanation:
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
PLEASE HELP ME QUICK!! I"M BEING TIMED
Carter and Ari had $240 altogether. Ari had twice as much as Carter after Carter gave him $16. How much more money did Ari have than Carter in the beginning?
Answers
Answer: $48 more
Step-by-step explanation: We use algebra. Let c = Carter and a = Ari. C+A = 240. A+16 = 2(C-16). 2C-32 + C-16 = 240. 3C - 48 is 240. 240+48 is 288. So, C is 96 and a is 144. 144- 96 = 48 more.
What is the slope of the line shown in the graph? Express your answer as an improper fraction or as an integer as appropriate. Show your work
Answers
Slope can be found between two points using the formula [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
If we substitute in your points (which is x and which is y does not matter as long as it is consistent), we will get
[tex]\frac{(4-1)}{(2-0)}[/tex].
Simplifying this further, your slope will be
[tex]\frac{3}{2}[/tex].
hope this helps!
Determine the number of different groups of 5 items that can be selected from 12 distinct items.
Answers
There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
According to the given question.
Total number of items, n = 12
Total numbers of items to be selected, r = 5
Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} P_{r}[/tex] is the total number of permutations.
n is the total number of objects.
r is teh total number of objects to be selected.
Therefore,
The number of different groups or permutaions of 5 items that can be selected from 12 distinct group
[tex]^{12} P_{5}[/tex]
[tex]= \frac{12!}{(12-5)!}[/tex]
[tex]= \frac{12!}{7!}[/tex]
[tex]= \frac{12\times11\times10\times9\times8\times7!}{7!}[/tex]
= 12 × 11 × 10 × 9 × 8
= 95040
Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
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