The distance between -2 and 3 on a number line is 5 units.
What is a number line?
A horizontal line with evenly spaced numerical increments is referred to as a number line. The number on the line depends on how the number is contained.
The Distance Between Two Points on a number line.
The secret to finding the distance between two points is to remember that the geometric definition of subtraction is the distance between the two integers if we subtract the smaller number from the larger one.
Here, we have
the distance between -2 and 0 is 2 units
the distance between 0 and 3 is 3 units
2+3 = 5
OR
3- (-2) =
3+2 = 5
5 units
Hence, the distance between -2 and 3 on a number line is 5 units.
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divide and find quotient
(a⁴-b⁴) ÷ (a+b)
(step by step explanation)
Answer:
Step-by-step explanation:
(a⁴-b⁴)/(a-b)
using..(a+b²)=(a+b)(a-b)
=(a²+b²)(a²-b²)/(a-b)
=(a²+b²)(a+b)(a-b)/(a-b)
=(a²+b²)(a+b)
x/4 + 8 = 3
what does x equal
Answer:
x = -20
Step-by-step explanation:
x/4 + 8 = 3
subtract 8 from both sides:
x/4 + 8 - 8 = 3 - 8
x/4 = -5
multiply both sides by 4:
4(x/4) = 4(-5)
x = -20
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.
A: $69
B: $90
C: $420
D: $1,080
Oliver has to pay an amount of B: $90 with simple interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business.
The bank offered him an interest rate of 12% for 6 months.
P = $1500, r= 12% and t = 6 months or 1/2 or 0.5 years.
∴ SI = (1500×12×0.5)/100.
SI = 15×6.
SI = $90.
The amount of simple interest Oliver has to pay is $90.
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find the quotient of 67.98÷28 round your answer to the hundredths place
Answer:
2.43
Step-by-step explanation:
The quotient is the answer to a division problem.
67.98/28 = ~2.42785714286
To round to the nearest hundredth, leave 2 decimal digits remaining. If the thousandth place (3rd decimal digit) is greater they or equal to 5, add 1 to the hundredths digits.
7 [tex]\geq[/tex] 5
2.42+0.01
2.43
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located
1,-1), and Monique's desk is located at (-4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
O√7 feet
O√14 feet
√85 feet
O√61 feet
√14 feet, A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
What is coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of numbers, or coordinates, which are written as ((x,y)).
A coordinate can be expressed in one of three ways. a coordinate with an integer for degrees, a real number for minutes, and an integer for seconds (DMS). a coordinate that contains minutes (a real number) and degrees (an integer) (MinDec). a coordinate that merely contains degrees (real number).
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If p * q = 3p + 2q – 5, then 3 * 2 =
Work Shown:
p * q = 3p + 2q - 5
3 * 2 = 3(3) + 2(2) - 5
3 * 2 = 9 + 4 - 5
3 * 2 = 13 - 5
3 * 2 = 8
Carter is hooked on a new book series, The Galaxy. Each book in the series is the same
length and chronicles a different year in the Waka Waka Galaxy. Carter has cleared off the top
shelf of his bookcase to leave room for each of the books as they come out.
There is a proportional relationship between the number of books on the shelf, x, and how
much shelf space the books take up (in inches), y.
The proportional relationship between the number of books on shelf and how much shelf space the books takes up is 1 inch
What is proportionality?
The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.
When two or more parameters are directly or indirectly proportional to one another, the relationship is written as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables. The proportionality constant, k.
As we know [tex]\frac{y}{x}[/tex] = constant of proportionality
So, [tex]\frac{y}{x}[/tex] will be
[tex]\frac{2}{2} = \frac{11}{11} = \frac{13}{13} = \frac{16}{16}[/tex] = 1
∴ it is 1 inch per book
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sam rolls 3 standard fair dice. that probability that the three numbers rolled on the dice are the sides of a triangle is , where are relatively prime positive integers. what is the value of ?
The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.
Here,
When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).
Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.
As a result, 186 outcomes or triplets are possible and satisfy this property.
Hence, the required probability is 186/216=31/36.
The required probability is 31/36 for three dice rolls to produce triangle sides.
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-5(x + 1) - 9 = 2
help me this is algebra and i dont not look like dream *half moon emoji*
Answer:
-3.2
Step-by-step explanation:
-5(x+1)-9=2
first simplify by distributiom
-5(x)-5(1)-9=2
simplify the multiplication
-5x-5-9=2
add the numbers
-5x-14=2
now to get x by itself on one side we undo in reverse order and move the -14 over to the other side so add 14 to both sides to cancel the -14
-5x=2+14
simplify
-5x=16
now divide both sides by -5 to get x by itself
-5x/-5=16/-5
simplify
x=-3.2 or as a fraction, [tex]-\frac{16}{5}[/tex]
What is the inverse of
f(x) = (2x + 1)² for
x ≥ − 1/2?
Answer: [tex]f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]
Step-by-step explanation:
Let [tex]f(y)=x[/tex].
[tex]x=(2y+1)^2\\\\\pm \sqrt{x}=2y+1\\\\-1 \pm \sqrt{x}=2y\\\\y=-\frac{1}{2} \pm \frac{\sqrt{x}}{2}[/tex]
Since the domain of the original function is the same as the range of the inverse, the rate of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x) \geq -1/2[/tex]. This means we consider the positive case.
[tex]\therefore f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]
Mr. solo invested in the certificate of deposit that pays 8% interest investment was $325 how much interest will she receive in one year
Using the simple interest formula, Mr. Solo received $26 interest.
In the given question we have to find how much interest Mr. Solo received.
The investment(P) = $325.
Interest rate(R) = 8%
Time(T) = 1 year
Finding the interest using the simple interest formula.
I = PRT/100
where I = interest
P = Principal Amount
T = Time
R = Interest Rate
Putting the value
I = 325*8*1/100
I = 26
Hence, Mr. Solo received $26 interest.
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eight people are sitting around a circular table, each holding a fair coin. all eight people flip their coins and those who flip heads stand while those who flip tails remain seated. what is the probability that no two adjacent people will stand?
The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.
What is combination?A combination is a grouping of items where order does not matter. The formula of combination is
[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]
Where
C = number of combinationsn = number of total itemsr = number of choosing itemsGiven the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.
What is the probability that no two adjacent people will stand?
First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.
The number of arrangements according to the number of people standing.
Case 1: 0 people standing = 1 arrangement.
Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.
Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.
Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.
Case 5: 4 people standing but no two adjacent people = 2 arrangements.
The number of arrangements that no two adjacent people will stand.
n(A) = 1 + 8 + 20 + 16 + 2 = 47
The probability that no two adjacent people will stand is
P(A) = n(A)/n(S)
P(A) = 47/256
Hence, the probability that no two adjacent people will stand is 47/256.
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when the repeating decimal $0.\overline{12}$ is expressed as a common fraction in lowest terms, what is the sum of its numerator and denominator?
The sum of the numerator and denominator of the decimal is found as 111.
Define the term common fraction?A fraction with an integer for both the numerator and denominator is referred to as a common fraction or vulgar fraction.A fraction with an integer for both the numerator and denominator is described to as a common fraction or vulgar fraction.A ratio can be named with a common fraction.Boys outnumber females in a class 4:3, or 4/3. 4/3 is a popular proportion.As for the given question;
The decimal number is given as;
0.12 bar
Decimal to fraction conversion
100(0.12 bar) = 12(0.12 bar)
99.(0.12bar) = 100(0.12bar) - (0.12 bar)
99.(0.12bar) = 12 × 0.12bar - 0.12bar
99.(0.12bar) = 12
0.12 bar = 12/99 (lowest fraction)
Thus, in the result the numerator is found as 12 and the denominator is found as 99.
Add = 12 + 99
Add = 111
Thus, the sum of the numerator and denominator of the decimal is found as 111.
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A prize is divided in the ratio
10: 1. If the difference
between the shares is £270
what is the larger share?
a student cycles for x hours at 12km/h and y hours at 16km/h.altogether, tge student cycles 66km in 5 hours. find x and y
Answer:
x = 3.5 hours
y = 1.5 hours
Step-by-step explanation:
There are two unknowns, x and y, both in umits of hours. We need at least two equations before we start trying to solve this with substitution. Looking at the information, this should be possible.
First, we know that Speed x Time = Distance.
The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster. Together, the student travels 66 km.
The total distance of 66 km would be comprised of the two distances 12x and 16y:
12x + 16y = 66 km
For the second equation, we know that the total time is 5 hours. That would be the sum of x and y:
x + y = 5 hours
We now have 2 equations, so we stand a good chance of finding the answer. Pick one of the equations and isolate one of the variables to one side. Let's choose x + y = 5 hours, since that is easy to rearrange:
x = 5-y
Now take the first equation and substitute the definition of x from above (5-y):
12x + 16y = 66
12(5-y) + 16y = 66
60-12y + 16y = 66
4y = 66-60
4y = 6
y = (6/4) or 1.5 h
The time spent at 16 km/h was 1.5 hours.
Use this value of y in either equation to find x. Let's use x+y=5, since that will be easier:
x+y = 5 for y = 1.5
x+1.5 = 5
x = 3.5h
The time spent at 12 km/h was 3.5 hours
Graph this line using the slope and y-intercept: y= 1/5x + 8
The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
According to the given information line using the slope and y-intercept is; y= 1/5x + 8
thus, the slope of this line is:
m = 1/5
And its y-intercept is: c= 8
The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.
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what is 398+8967 i need help with this
Which capital letters in the word TRANSFORMATION produce the same letter after being rotated 180°?
The capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter are I, N, O and S.
Define the term rotation?Geometry can be used to determine the meaning of rotation in mathematics. As a result, it is described as the movement of an object round the center or an axis.The point of rotation is the point where the object is rotated.An angle of rotation is the degree of rotation calculated in degrees.It is possible to rotate clockwise or counterclockwise. If an item needs to be rotated, there are several methods for doing so:
90 degrees counterclockwise90° counterclockwise180 degrees counterclockwiseanticlockwise 180 degreesWhen the capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter: I, N, O and S.
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Julio is running in a 13.1 mile race. There are water stops every 2.75 miles along the route from the beginning of the race. What is the distance between the last water stop and the end of the race?
There is 2.1 miles distance between the last water stop and the end of the race.
Total miles Julio will run = 13.1 miles
Distance at which water stops are location = 2.75
Total number of water stops in full race of 13.1 miles = 13.1 / 2.75
=4.764
so , there are 4 stops in the runs for drinking water every 2.75 miles
Distance from starting point of race and last water stops = 4 × 2.75 = 11 miles
Distance between the last water stop and the end of the race = 13.1 - 11
= 2.1 miles
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time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:
Z = (x - )/ ( / sqrt(n)
where,
x=11, sample score.10 is the sample mean.Standard deviation equals 2
sample size, n With n = 5, calculating the z and p values:
z =(11 - 10) / (2 / sqrt(5))z = 1.12The tables show that p(5) = 0.8686.
For n = 6, calculate the z and p values as follows:
z =(11 - 10) / (2 / sqrt(6))z = 1.22The tables show that p(6) = 0.8888.
If both days to occur, the probability that each day will last no more than 11 minutes is as follows:
p total = p(5) * p(6)p total = 0.8686 * 0.8888p total = 0.772learn more about probability click here:
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$12000 into an investment account for 5 years. The investment earns 6% interest per
annum, compounding quarterly.
What is the interest rate per quarter?
Answer:
We may use the logarithm formula,
N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.
EV is end value, SV is start value.
EV is 20000, SV is 12000, interest is 5.6% semi annual
(1+r) is obtained as,
Step-by-step explanation:
Please help me I am stuck on this
Step-by-step explanation:
when we say "a/b of c", we mean mathematically :
a/b × c
so,
a)
x = 1/5 × 15 = 15/5 = 3
b)
x = 3/4 × 48 = 3×48/4 = 3×12 = 36
Answer:
a) 3 b) 36Step-by-step explanation:
a) 1/5 of 15 = ?
→ 1/5 of 15
→ (1/5) × 15
→ 15/5 = 3
So, answer is 3.
b) 3/4 of 48 = ?
→ 3/4 of 48
→ (3/4) × 48
→ 144/4 = 36
So, answer is 36.
Pls answer
Use the complete the method to solve
2y²+2y-5=0
The required solutions to the given quadratic function are below as:
[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The quadratic function is given in the question:
2y² + 2y - 5 = 0
Compare the given function to the standard quadratic function f(x) = ax² + b x + c.
We get a = 2, b = 2 and c = -5
Using the quadratic formula to solve the above quadratic function
[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a = 2, b = 2 and c = -5 in the above formula
[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]
[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]
Separate the solutions as:
[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]
[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]
Therefore, the required solutions to the given quadratic function are below as:
[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]
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Find the value of x and 3x
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
now let's consider the white, "cut-out" triangle on the left side.
the purple one angles at the top and bottom corner are 45°.
the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.
so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).
and that means that the third white angle is
180 - 45 - 45 = 90°.
and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.
360 = 90 + 3x
270 = 3x
x = 90°
3x = 270°
If you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually? Is there anything you could change in the problem that would make you change your answer?
a. I would rather compound annually at 5 % interest
b. I would increase the simple interest rate if i were to change my answer
a. How to determine which option to choose?Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.
Since you have $200 to invest for 10 years at 7% simple interest, using the simple interest formula for the amount, we have
A = P(1 + rt) where
P = principal amount = $ 200, r = rate = 7% = 0.07 and t = time = 10 yearsSubstituting the values of the variables into the equation, we have
A = P(1 + rt)
A = 200(1 + 0.07 × 10)
A = 200(1 + 0.7)
A = 200(1.7)
A = 340
Also, since you have $200 to invest for 10 years at 5% interest compounded annually, using the compound interest formula for the amount, we have
A' = P(1 + r)ⁿ where
P = principal amount = $ 200, r = rate = 7% = 0.07 and n = time = 10 yearsSubstituting the values of the variables into the equation, we have
A' = P(1 + r)ⁿ
A' = 200(1 + 0.07)¹⁰
A' = 200(1.07)¹⁰
A' = 200(1.9672)
A' = 393.43
Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest
b. Is there anything you could change in the problem that would make you change your answer?To change my answer, I would increase the simple interest rate if i were to change my answer
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i have an idea on how to solve but i need to see if im right. please help me
⇒Note this is a fraction.
⇒For a fraction to be undefined that is of when the denominator is equal to 0
⇒Now equate what is in the denominator with 0
⇒ [tex]k+3=0\\k=-3[/tex]
⇒So that the denominator is 0 that is of when k is equal to -3..it is then that the whole expression will be undefined.
⇒The expression is undefined when k=-3
When y=9, the value of y² - 1 is
One year, the population of a city was 325,000. Several years later it was 263,250. Find the percent decrease.
The percentage decrease of the population of a city is 19%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the population of a city was 325,000 and several years later it was 263,250.
The percentage decrease will be:
= Decrease in population / Original population × 100
= (325000 - 263250) / 325000 × 100
= 61750 / 325000 × 100
= 19%
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Please finish the sentences in the picture below
The completed statement with regards to Chang and Carlotta's methods used for solving the word problem is presented as follows;
Chang's and Carlotta's method use different operations to simplify the expressions in the same order.Chang's method uses variables, but Carlotta's method does not.What is a word problem in mathematics?A word problem in mathematics and science is the verbal presentation of the information in a scenario required to mathematically solve a problem.
The steps to solve the problem is presented as follows;
The amount in the bank account = $50
Amount made per hour by mowing lawns = $8
The number of hours put into mowing lawns in order to have a total of $130 in the account can be found by using the equation;
The amount in the account increases based on the number of hours used for mowing lawns, therefore;
130 = 50 + 8 × h
8·h = 130 - 50 = 80
h = 80/8 = 10
Ten hours of lawn mowing is required to have a total of $130 in the bank.
Chang's method involve the use of expressing the situation mathematically, by use of variables.
Carlotta's method involves the use of verbal expressions to outline the relationship between the variables, simplifying them to arrive at the determining variable that indicates the number of hours require.
Therefore;
The operations used by Chang and Carlotta are differentThe order in which the expressions is simplified is the same in both Chang and Carlotta's assignmentsThere is a variable, h, for the hour in Chang's method, but Carlotta's method does not make use of a variable for the hours that must be used for mowing lawns.Learn more about word problems in mathematics here:
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A youth group is planning a trip to a local amusement park. They are taking a van which holds 10 people. It will cost $25 for parking and tickets to enter the park are $18 per person. Create a table to represent the situation, showing the possible total costs for the various numbers of people who could go?