a dot plot can easily show all the data.
Step-by-step explanation:
In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.
The left and right page numbers of an open book are two
consecutive integers whose sum is 67. Find these page
numbers. Show your work (the steps)! Show the original
equation. Write a short summary of the result. Hint: Let x be the
first consecutive integer.
The original equation will be x + x + 1 = 67 and the left page will have 33 page number and the right one will have 34 page number.
Let x be the first consecutive integer.
So, x + 1 is the first consecutive integer.
Sum of the two integers = 67
⇒ x + x + 1 = 67 (This is the original equation)
Combining the like terms:
⇒ 2x + 1 = 67
Subtract 1 from both the sides:
⇒ 2x = 67 - 1
⇒ 2x = 66
Divide both sides by 2:
⇒ x = 66/2 = 33
Therefore, the original equation will be x + x + 1 = 67 and the left page will have 33 page number and the right one will have 34 page number.
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|x-2|=|4+x|
How can I find the value of X?
Answer:
x = -1
Step-by-step explanation:
You want to find the value(s) of x that satisfy the equation |x-2| = |4+x|.
DomainsThe behavior of each absolute value function changes at the point where its argument is zero. For this equation, that will be two points:
x -2 = 0 ⇒ x = 2
x +4 = 0 ⇒ x = -4
These two points on the number line divide the domain of the equation into three parts:
x < -4-4 ≤ x < 22 ≤ x.The behavior of the equation will be different in those three domains.
x < -4In this domain, both absolute value functions negate their arguments. That means the equation is equivalent to ...
-(x -2) = -(4 +x)
2 = -4 . . . . . . . . . . add x to both sides
This has no solutions: there are no values of x that will make this true.
-4 ≤ x < 2In this domain, the absolute value function on the left negates its argument, so the equation is equivalent to ...
-(x -2) = (4 +x)
-2 = 2x . . . . . . . . . add x-4 to both sides
-1 = x . . . . . . . . . divide by 2
This value of x is in the domain, so represents a solution to the equation.
x = -1
2 ≤ xIn this domain, neither absolute value function negates its argument, so the equation is equivalent to ...
x -2 = 4 +x
-2 = 4 . . . . . . . subtract x
This has no solutions: there are no values of x that will make this true.
The given equation has one solution: x = -1.
__
Additional comment
When solving an equation like this graphically, it is often useful to put it in the form f(x) = 0. We can obtain that form by defining ...
f(x) = |x -2| -|4 +x|
The graph of this is attached. The only solution is where f(x) = 0, at x = -1.
Note that the function is parallel to the x-axis outside of the middle domain, so will not have any x-intercepts in those regions.
If the difference of a number and eight is tripled, the result is six more than the number. Find the number. Round your answer to the nearest integer, if necessary.
If the difference of a number and eight is tripled and the result is six more than the number, the number is 15
How to find the number using variable?The difference of a number and eight is tripled, then the result is six more than the number.
Therefore, the number will be represented by a variable
let the number = x
Hence,
3(x - 8) = x + 6
Therefore, let's open the bracket
3(x - 8) = x + 6
3x - 24 = x + 6
subtract x from both sides of the equation
3x - 24 = x + 6
3x - x - 24 = x - x + 6
2x - 24 = 6
add 24 to both sides of the equation
2x - 24 + 24 = 6 + 24
2x = 30
divide both sides by 2
x = 30 / 2
x = 15
Therefore, If the difference of a number and eight is tripled and the result is six more than the number, the number is 15
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Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
select all that apply
m - 4 = -7m - 8
-8 - 3m = 4 - m
-3m - 8 = 4 - m
-15m = -4m
-7m - 8 = m - 4
-8 - 7m = -4 + m
The equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4
How to determine the equations that are equivalent to the given equation?The equation is given as
-2m - 5m - 8 = 3 + (-7) + m
Remove the bracket
So, we have
-2m - 5m - 8 = 3 - 7 + m
Evaluate the like terms
So, we have
-7m - 8 = - 4 + m
The above expression can be written as follows
m - 4 = -7m - 8
-7m - 8 = m - 4
-8 - 7m = m - 4
Hence, the equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4
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-7(5x-70=-19-x i neeeeeeeeeeeeeeeeeeeeeeddddddd helppp
Answer:
hope this will help you
Step-by-step explanation:
-7(5x-70)=-19-x
-35x+490=-19-x
490+19=-x+35x
509=34x
x=509/34
x=14.97
The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.
Answer:
No, the difference is -2.
Step-by-step explanation:
As the sequence progresses, the numbers get smaller(1, -1, -3, ...), and they get smaller by 2. Hence, the change in every number in the sequence as it progresses is -2.
PLEASE HELP QUICK WILL GIVE BRAINLIST !!!
How many times larger is 9 x 10^5 than 5 x 10^3?
1.8
18
180
1,800
Answer:
180.
Step-by-step explanation:
9/5 = 1.8 and 10^5/10^3 = 10^2
so tis 1.8 x 10^2 which is 180
pls give branliest
Answer: 180
Step-by-step explanation:
(9 x 10^5) / (5 x 10^3)=
(9 x 10^(2+3)) / (5 x 10^3)=
(9 x 10^2 x 10^3) / (5 x 10^3)=
(9 x 10^2)/5= ==> Divide each side by 10^3
900/5=180
A recent survey by the American Automobile Association showed that a family of two adults and two children on vacation in the United States will pay an average of $247 per day for food and lodging with a standard deviation of $60 per day. You can compute the mean food and lodging cost of a 10-day vacation by multiplying the per-day mean by 10. The standard deviation for the 10-day vacation can be found by multiplying by 10 also.
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).
a. What is the mean for food and lodging for a 10-day vacation? _______
b. What is the standard deviation of the distribution for the 10-day vacation? ______
c. What is the variance of the distribution for the 10-day vacation? ______
The statistical measures for the 10-day vacation are given as follows:
a) Mean: $2470.
b) Standard deviation: $189.74.
c) Variance: $²36,001.
What is the mean for the 10-day distribution?To find the mean for n days, we take the mean amount in a single day and multiply by n.
Hence:
247 x 10 = $2470.
What is the standard deviation for the 10-day distribution?To find the standard deviation for n days, we take the standard deviation for a single day and multiply by the square root n.
Hence:
60 x sqrt(10) = $189.74.
What is the variance for the 10-day distribution?The variance is the square of the standard deviation, hence:
($189.74) = $²36,001.
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10x-6-10x-2 simplified please show steps
Answer:
Step-by-step explanation:
1) group any number with an X together and rewrite answer (if there is a negative in front of a number always carry it with it when rearranging.)
10x-10x-6-2
2) lets solve the numbers with Xs together
10x+10x= 20x
3) now lets solve whole numbers
-6-2=-8
4) bring down the 20x and the -8/ rewrite problem with your solved numbers
20x-8
5) we have to have X alone so in order to get rid of the 20 in front of the X you must divide 20 by 20x,
20x/20 ( it cancel's out and now you're left with X)
X=-8
6) but whatever you do to one side of the equal sign you have to do to the other side so now you must divide -8/20 which will leave you with
Answer: X=-0.4 or -2/5
desperate need in help
Answer: 8x^10
Step-by-step explanation:i guessed but when you multiply exponents you just add them so the exponent is 10 and then 2 cubed is 8
The diameter
of the Earth is 1.3 × 10 km.
The diameter of the Moon is 3.5 × 10 km.
The diameter of the Sun is 400 times greater
than the diameter of the Moon.
How many times smaller is the diameter of
the Earth than the diameter of the Sun
Earth's diameter is 0.0092 times less than the sun's diameter.
Ratio, in math, is a time period this is used to examine or greater numbers. It is used to indicate how large or small a sum is in comparison to another.In a ratio, portions are as compared the use of division. Here the dividend is referred to as the `antecedent' and the divisor is referred to as the 'consequent'. For example, in a collection of 30 people, 17 of them opt for to stroll within side the morning and thirteen of them favor to cycle. We use the ratio formulation whilst evaluating the connection among numbers or portions. The popular shape of representing a ratio of among portions say 'a' and 'b' is a: b, that's examine as 'a is to b'.The Diameter of Earth = 1.3 * 10⁴ km
The Diameter of Moon = 3.5 * 10³ km
Let the diameter of sun be x km
According to the question
The diameter of the sun is 400 times that of the moon.
x = 400 * 3.5 * 10³ km
= 14 * 10⁵ km
The Diameter of earth / diameter of sun
= 1.3 * 10⁴ / 14 * 10⁵
= 0.0092
Hence, The diameter of the Earth is 0.0092 times that of the Sun.
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Please stop with the trolls
Answer:
6
scale factor b to A = 4
Step-by-step explanation:
scale factor
We multiply the scale factor times the original figure length to get the new figure length
x * scale factor = 1.5
The scale factor is 1/4
x * 1/4 = 1.5
Multiply each side by 4 to get rid of the fraction
x * 1/4 *4 = 1.5 * 4
x = 6
The scale factor from figure B to figure A
1.5 * scale factor = 6
scale factor = 6/ 1.5
scale factor = 4
Can you please help me
Jack is building a wall.
He uses 300 bricks to build part of the wall.
This part of the wall is 5 metres long and 1.5 metres high.
The complete wall will be 8 metres long and 1.5 metres high.
How many more bricks does Jack need to complete the wall?
The amount of bricks that Jack would need to complete the wall is 180.
How many more bricks does he need?The first step is to determine the total amount of bricks he would need to build the wall. In order to determine this value, ratio analysis would be used.
Total bricks needed = (area of wall x number of blocks already used) / (area of wall already built)
Area of wall = 8 x 1.5 = 12
Area of wall already built = 5 x 1.5 = 7.5
Total bricks needed = (12 x 300) / 7.5 = 400 bricks
Number of bricks needed to complete the wall = 400 - 300 = 180 bricks
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Can someone help me I will mark u brilliant
Answer: R'=(-4, -3)
S'=(-4, -10)
T'=(-8, -10)
U'=(-8, -3)
Step-by-step explanation:
When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.
R=(4,3) ==> R'=(-4, -3)
S=(4,10) ==> S'=(-4, -10)
T=(8,10) ==> T'=(-8, -10)
U=(8,3) ==> U'=(-8, -3)
Write the decimal as a fraction.
8.33 = 10F
- 0.83 = -F
[?]
=
Hint: Subtract the first equation from this new
equation to eliminate the repeating decimal.
Enter the decimal value
the fraction form of the number will be 5 / 18.
We are given the decimal number as:
0.83(bar on 3) = F ...(1)
Now, we need to convert this into fraction.
For this, we will first multiply both the sides by 10
Do, we get that:
8.33 ( bar on 3) = 10 F ...(2)
Now, we will Subract (1) from (2), we get that:
9 F = 8.33 (bar on 3) - 0.83 (bar on 3)
9 F = 7.5
F = 7.5 / 9
F = 2.5 / 9
F = 25 / 90
Reducing the fraction into simplest form:
F = 5 / 18.
Therefore, we get that the fraction form of the number will be 5 / 18.
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What is that converted to Celcius?
degrees Celcius
Answer:
32° degree Fahrenheit is converted to celcius
Answer:
use 273k that is if is changing from celcius to Kelvin
Which is the following in an irrational number?
A. -8.264264264...
B. -5/9
C. 17.47
D. 4.28192489...
*
Answer:
D
Step-by-step explanation:
Irrational numbers are those which cannot be expressed by the ratio of two integers.
A is rational because it is a recurring decimal. Recurring decimals can be represented by the ratio of two integers (this one can be represented by the fraction -2752/333, which is a ratio of two integers).
B is a fraction with two integers, therefore it is rational. -5/9 is a ratio of two integers.
C can be represented by 1747/100.
D is an infinite decimal but isn't recurring like A, meaning it cannot be represented by the ratio of two integers, and is therefore it is irrational, unless you are shown further digits of the decimal which prove it to be recurring, which is not the case here.
A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
Answer:
40 students
Step-by-step explanation:
I think it is 40 students because 60 + 40= 100 then 100 x 40 = 4,000
then the SCHOOL has to pay a $30 cleaning fee so that will add up to $4,030! I hope this helps everybody!
40 students will be going on the trip
How to calculate the number of students that will be going on the trip ?Each student will pay $60 for food and lodging
Each student will also pay $40 for the bus
Total amount of fee that will be paid by each student is
= 60 +40
= 100
The school will pay $30 cleaning fee for the bus, it's only the school that will be paying this fee, the students are not included. This will will be subtracted from the total cost which is $4,030 leaving us with $4,000
Therefore the number of students going on the trip can be calculated as follows
= 4,000/100
= 40
Hence 40 students will be going on the trip
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Okay what about 124.35$ and the sales tax is 6.75%
Answer:
$132.74
Step-by-step explanation:
First: divide the sales price by 100
6.75 ÷ 100 = 0.0675
Second: multiply the answer from the first step by the original price
0.0675 x 124.35 = 8.393625
round to the hundredths place
8.393625
8.39
Third: add the original price with the answer from the second step
124.35 + 8.39 = 132.74
Pls help me with thisss
Answer:
A
Step-by-step explanation:
Each hash mark between "School" and "Declan's house" is one-eighth of a mile. Starting at "School" count 5 hash marks to the left to get where Harper lives.
The variables and y vary inversely. Use the given values to write an equation relating and y. Then find y when x = 3.
x = 5, y = -4
An equation is y =
When x = 3, y =
Answer:
x=5$
$y=-4
Step-by-step explanation:
the solution is easy no more you have to put the first numbers and put it in order
What value of x makes this proportion true?
25/20 = x/4
A. 6
B. 9
C. 20
D. 5
A textile artist is asked
to make a wall-hanging that measures at most
3.75 feet wide by 6.5 feet tall. When finished,
the wall hanging measures 3 3/8 feet wide by
6 3/4 feet tall. Does the wall hanging meet the
specifications?
He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values. The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle. A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other. The greater than sign is an approximation of a closing square bracket.Maximum width of the wall hanging can be 3.75 feet and maximum height can be 6.5 feet.
After completing the work it was found that the width measures 3 3/5 feet and height was 3 3/4 tall.
If the height and width after completing the work is less than or equal to the maximum height and width then he will be able to meet the specifications .
Width
3 3/4
= (12+3)/4
= 15/4
= 3.75
Height
6 3/4
= (24+3)/4
= 27/4
= 6.75
He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height .
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3 1/5 ÷ 3 4/5 answer plsss
Answer: oh ofc! here is the answer it is 0.84210526315
but im not 100% sure it is the right answer
Step-by-step explanation: i really hope this helps have a good day/night (: <3
Find the remainder when 2x^10 - 3ix^8 + (1 + i)x^2 - (3 + 2i)x + 1 is divided by (x - i)
Be sure to show your work.
Use the polynomial remainder theorem. The remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x-c[/tex] is exactly [tex]p(c)[/tex].
In this case,
[tex]p(x) = 2x^{10} - 3ix^8 + (1+i)x^2 - (3+2i)x + 1[/tex]
and [tex]c=i[/tex]. Then the remainder is
[tex]p(i) = 2i^{10} - 3i^9 + (1+i)i^2 - (3+2i)i + 1[/tex]
Since [tex]i^2=-1[/tex] and [tex]i^4=1[/tex],
[tex]p(i) = -2 - 3i - 1 - i - 3i + 2 + 1 = \boxed{-7i}[/tex]
Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training.
Week Time (s)
28.8
27.6
27.1
How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent
Randy's percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.
The percentage change will be calculated by the relation -
Percentage change = change in timing ÷ original time × 100
Calculating percentage change between Week 1 and Week 2
Change = 28.8 - 27.6
Change = 1.2 seconds
Percentage = (1.2 ÷ 28.8) × 100
Percentage = 4.17%
Calculating percentage change between Week 2 and Week 3
Change = 27.6 - 27.1
Change = 0.5 seconds
Percentage = (0.5 ÷ 27.6) × 100
Percentage = 1.8%
So, percent of change from Week 1 to Week 2 than from Week 2 to Week 3 was = 4.17 - 1.8
Percentage change = 2.37%
Therefore, the percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.
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Solving Advanced Linear Equations: Mastery Test
Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 3:
Step 4:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
-2 to 5x and 8.
6.x
✓16.
-2(5z + 8) = 14 + 6z
-16.
-10z <- 16
-16z
Reset
-
16 = 14
-16z =
30
= 14 + 6z
H
=
H =
Next
30656
-18
Submit T
The solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8
How to complete the steps to solve the equation?The equation is given as
-2(5z + 8) = 14 + 6z
Open the bracket
So, we have
-10z - 16 = 14 + 6z
Collect the like terms
So, we have
-10z - 6z = 14 + 16
Evaluate the like terms
So, we have
-16z = 30
Divide both sides of the equation by 16
So, we have
z = -15/8
Hence, the solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8
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Frind the sale price if 15% discount is allowed off market price of 25.00. fly
Is x = -14 a solution to 9x - 7 = -7?
Answer:
since x=-14
9(-14)-7
-126-7=-133.