To express the given ratio as a unit rate, divide the miles by the gallons to obtain 18.8 miles per gallon.
Explanation:To express the given ratio as a unit rate, divide the miles by the gallons. So, the unit rate would be:
325.4 miles ÷ 17.3 gallons = 18.8 miles per gallon
Therefore, the unit rate for the given ratio is 18.8 miles per gallon.
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Which expression represents the distance between 4.7 and −11.2 on the number line? Drag and drop the correct expression into the box.
Answer:
15.9Step-by-step explanation:
[tex]\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9[/tex]
The distance between 4.7 and -11.2 on the number line is 15.9.
Explanation:The distance between two points on a number line can be found by taking the positive difference between their coordinates. In this case, the distance between 4.7 and -11.2 is found by subtracting the smaller number from the larger number and taking the absolute value.
Distance = |-11.2 - 4.7| = |-15.9| = 15.9
Therefore, the correct expression is Distance = 15.9.
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Lane's arm span is 61 inches. If his height is 1⁄4 foot longer than his arm span, how tall is he?
1 foot = 12 inches
1/4 foot = 12/4 = 3 inches
61 +3 = 64 inches tall ( 5 ft 4 inches)
How do you take the limit of this
The limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) is DNE
To take the limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6), we proceed as follows
Since we have the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) and we want to take the limit, we proceed thus,.
First, we divide both the numerator and denominator by x⁴. So,
lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) = lim x → ∞(x⁴ - 9x² + x)/x⁴ ÷ (x³ - x + 6)/x⁴
= lim x → ∞(x⁴/x⁴ - 9x²/x⁴ + x/x⁴ ÷ (x³/x⁴ - x/x⁴ + 6/x⁴)
= lim x → ∞(1 - 9/x² + 1/x³ ÷ (1/x - 1/x³ + 6/x⁴)
Now, taking the limit as x tends to infinity, we have that
= lim x → ∞1 - lim x → ∞9/x² + lim x → ∞1/x³ ÷ lim x → ∞1/x - lim x → ∞1/x³ + lim x → ∞6/x⁴
= (0 - 9/∞² + 1/∞³)/(1/∞ - 1/∞³ + 6/∞⁴)
= (0 - 9/∞ + 1/∞)/(1/∞ - 1/∞ + 6/∞)
= (∞ - 0 + 0)/(0 - 0 + 0)
= (∞)/(0)
= DNE
the poster you are giving your friend is in a cardboard tube with a 2 in diameter and 26 in length. will a rectangular piece of wrapping paper that is 8 in by 28in completely cover the tube
If a = (8.4∠39°) and b = (5.2∠50.4°), find the product a·b and the quotient a/b
What is the probability of rolling a sum of 8 on a standard pair of six-sided dice? express your answer as a fraction or a decimal number rounded to three decimal places, if necessary?
The probability of rolling a sum of 8 on a pair of standard six-sided dice is 5 out of 36, or 0.139 rounded to three decimal places.
Explanation:The subject of your question is
probability
, a topic in Mathematics. To solve this, we want to know the total number of outcomes when two dice are rolled; which is 6*6 = 36. Then we determine how many of these outcomes result in a sum of 8. Upon careful examination, we find that there are 5 (2,6), (3,5), (4,4), (5,3), and (6,2). Therefore, the
probability of rolling a sum of 8
on a standard pair of six-sided dice is 5 out of 36, which can be expressed as
5/36 or 0.139
rounded to three decimal places.
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Expanded form 13,936
What is the value of x in the solution to the following system of equations?
x − 2y = 2
3x + y = 6
To find the value of x in a system of equations, you can use the substitution or elimination method. In this case, x = 2 is the solution.
To find the value of x in the system of equations x − 2y = 2 and 3x + y = 6, we can use the method of substitution or elimination.
Substitution method:
From the second equation, y = 6 - 3x.Substitute y = 6 - 3x into the first equation: x - 2(6 - 3x) = 2.Solve for x: x - 12 + 6x = 2, 7x = 14, x = 2.Therefore, the value of x in the solution to the system of equations is x = 2.
12<3b or 2b+14<4 please help
Find the inverse of each of the given functions.
f(x) = 4x − 12
f−1(x) = _x + _
f(x) = 4x − 12
f−1(x) =1/4 x + 3
The inverse of the function f(x) = 4x - 12 is f^-1(x) = (x + 12)/4.
Explanation:To find the inverse of the function f(x) = 4x - 12, we need to switch the roles of x and y and solve for y.
Step 1: Replace f(x) with y: y = 4x - 12.
Step 2: Swap x and y: x = 4y - 12.
Step 3: Solve for y: x + 12 = 4y.
Step 4: Divide both sides by 4: (x + 12)/4 = y.
Therefore, the inverse function is f-1(x) = (x + 12)/4.
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Which expression is equivalent to 6 – (–8)?
–6 + 8
–6 + –8
6 + –8
6 + 8
Answer:
A
Step-by-step explanation:
How many 1/4 cup portions can be served from 12 quarts of potato salad?
Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither
(A) 6x+4x-6=24+9x
(B)25-4x=15 -3x+10-x
(C) 4x+8=2x+7 +2x-20
what is the unit rate of 1/5 and 1/4
what is the circumference of a circle p PB=29m
Answer:
The circumference of the given circle = 182.12 meters
Step-by-step explanation:
The circle P is given to us in which length of PB = 29 meter
Now, Since P is the center of the circle so PB will be the radius of the circle
So, Radius of the circle = 29 meter
We need to find the circumference of this circle with radius 29 meter
So, Circumference of the circle = 2π × radius of the circle
⇒ Circumference of the circle = 2 × 3.14 × 29
= 182.12 meter
Hence, The circumference of the given circle = 182.12 meters
The length of each side of a square increases by 2.5 inches to form a new square with a perimeter of 70 inches. The length of each side of the original square was inches. NextReset
Answer:
The length of each side of the original square was [tex]15[/tex] inches
Step-by-step explanation:
Let
x------> the length side of the original square
we know that
The perimeter of a square is equal to
[tex]P=4b[/tex]
where
b is the length side of the square
In this problem
[tex]b=(x+2.5)\ in[/tex]
[tex]P=70\ in[/tex]
substitute
[tex]70=4(x+2.5)[/tex]
solve for x
[tex]70=4x+10[/tex]
[tex]4x=70-10[/tex]
[tex]x=60/4=15\ in[/tex]
Beth sold half of her comic books and then bought nine more. She now has 28. How many did she begin with?
2/3×5/12=reduce lowest form
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answer:
The required equation of line is y=-6x-57.
Step-by-step explanation:
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where m is slope of the line.
It is given that a line that passes through (–9, –3) and has a slope of –6.
Substitute m=-6, x₁=-9 and y₁=-3 in the above equation.
[tex]y-(-3)=-6(x-(-9))[/tex]
[tex]y+3=-6x-54[/tex]
Subtract 3 from both the sides.
[tex]y=-6x-54-3[/tex]
[tex]y=-6x-57[/tex]
Therefore the required equation of line is y=-6x-57.
Answer:
D).y+3=-6(x+9)
Step-by-step explanation:
took it on edge
The value of the 8 in 8.4 is 100 times greater than the 8 in?
Final answer:
The 8 in the number 8.4 has a value that is 100 times greater than the 8 in the number 0.084. The first 8 represents 8 ones, while the second represents 8 hundredths.
Explanation:
The value of the 8 in 8.4 is 100 times greater than the 8 in 0.084. To understand why, let's remember that each position in a decimal number has a place value that is 10 times less than the place value to its left. For instance, in the number 8.4, the 8 is in the ones place, meaning its value is 8 ones or '8'. However, in the number 0.084, the 8 is in the hundredths place, so its value is 8 hundredths or '0.08'.
Therefore, when comparing the two eights, we see that:
The 8 in 8.4 equals 8 ones (8 × 1 = 8).
The 8 in 0.084 equals 8 hundredths (8 × 0.01 = 0.08).
To find a number whose 8 is worth 100 times less than the 8 in 8.4, we need the 8 to be two places to the right of the decimal point, which is the hundredths place. The number 0.084 satisfies this because 8 ones (the value of the 8 in 8.4) are 100 times greater than 8 hundredths (the value of the 8 in 0.084).
A web server hosting company advertises 99.999 percent guaranteed network uptime. (a) how many independent network servers would be needed if each has 98 percent reliability? (round your answer up to the nearest whole number.) network servers (b) how many independent network servers would be needed if each has 89 percent reliability? (round your answer up to the nearest whole number.) network servers
a. The 50 independent network servers would be needed if each has 98% reliability.
b. Approximately 9 independent network servers would be needed if each has 89% reliability.
To calculate the number of independent network servers needed for a given level of reliability, we can use the following formula:
[tex][ \text{Number of servers} = \frac{1}{1 - \text{Reliability}} ][/tex]
a) For servers with 98% reliability:
[tex][ \text{Number of servers} = \frac{1}{1 - 0.98} = \frac{1}{0.02} = 50 ][/tex]
Therefore, 50 independent network servers would be needed if each has 98% reliability.
b) For servers with 89% reliability:
[tex][ \text{Number of servers} = \frac{1}{1 - 0.89} = \frac{1}{0.11} \approx 9 ][/tex]
Therefore, approximately 9 independent network servers would be needed if each has 89% reliability.
Solve this equation please !
−2 − (+7) = ?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='. The solution of the given equation,−2 − (+7) is −9.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
Given an equation, −2 − (+7) which is needed to be solved. Therefore, The given equation can be solved as shown below.
−2 − (+7)
Open the brackets,
= −2 − 7
Add the two terms,
= −9
Hence, the solution of the given equation,−2 − (+7) is −9.
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Assign point_dist with the distance between point (x1, y1) and point (x2, y2). the calculation is: distance = squarerootof( (x2 - x1)2 + (y2 - y1)2 ). sample output for the given program:
The program is an illustration of functions
Functions are collections of defined program statements, that are executed when evoked
The program in Python, where comments are used to explain each line is as follows:
#This imports the math module
import math
#This defines the function
def calculateDistance(x1,y1,x2,y2):
#This calculates the distance between the points
dist = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
#This returns the calculated distance
return dist distance
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Solve for n: a= p(1+nr)
Suppose the graph of a line has a negative slope and a positive y-intercept. Through which quadrants does the line pass?
A summer camp has divided its campers into 8 groups of 9 campers.How many campers are at the summer camp?
Which is another way to check the sum of 104 + 34 + 228 + 877? A. 877 – 104 + 34 + 228 B. 34 – 104 + 228 + 877 C. 877 + 228 + 34 + 104 D. 877 – 228 – 34 – 104
by adding the numbers in a different order would be a way to check so the answer is:
C. 877 + 228 + 34 + 104
what values make the inequality x+6/6-x<0 true?
It's C if you're taking the test
A submarine hovers at 240 meters below sea level.if it descends 160 meters and then ascends 390 meters,what is the new position
what percentage is 699 of 4736