Answer:
35 miles
Step-by-step explanation:
The segment addition theorem tells you ...
DE + EF = DF
125 + EF = 160
EF = 35 . . . . . . . subtract 125
The distance from E to F is about 35 miles.
A box contains 3 plain pencils and 7 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected?
The first box has a total of 10 items ( 3 pencils + 7 pens = 10)
The probability of picking a pen would be 7/10
The second box has a total of 8 items ( 4 pencils + 4 crayons = 8)
The probability of picking a crayon would be 4/18, which reduces to 1/2
To find the probability of doing both, multiply each probability together:
7/10 x 1/2 = 7/20
The probability is 7/20
if f(x)=3x^2 and g(x)=4x^2+1, what is the degree of (f0g)(x)
Answer:
6⃣
Step-by-step explanation:
3 + 24x² + 48x⁶; take the highest degree term possible.
Answer:
degree 6
Step-by-step explanation:
To obtain (f ￮ g(x) substitute x = g(x) into f(x)
f(4x³ + 1)
= 3(4x³ + 1)²
= 3(16[tex]x^{6}[/tex] + 8x³ + 1)
= 48[tex]x^{6}[/tex] + 24x³ + 3
The degree is determined by the term with the largest exponent.
In this case 48[tex]x^{6}[/tex] ← with exponent 6
Hence the polynomial is of degree 6
NEED HELP WITH A MATH QUESTION
Answer:
14%
Step-by-step explanation:
If the selected student is a male, that reduces the population to consider, to 14 (4 + 6 + 2 + 2).
How many male juniors? 2
So, the chance for the random student to be a junior if he's a male, are 2 out of 14.
P = 2/ 14 = 1/ 7 = 14.29%
Rounded to the nearest whole percent: 14%
Can you use the Distributive Property to write the formula P = ( 2 x l ) + ( 2 x w ) another way? Explain.
Answer:
Step-by-step explanation:
Please avoid use of " x " to indicate multiplication; instead, use " * " or " · "
P = ( 2 x l ) + ( 2 x w ) comes out as P = ( 2 * l ) + ( 2 * w ).
This could be written in several different ways, e. g.,
P = ( 2 * l ) + ( 2 * w ),
P = ( 2 * w ) + ( 2 * l ),
P = ( l * 2 ) + ( w * 2), and so on.
The Distributive Property permits us to rewrite the formula P = (2 x l) + (2 x w) as P = 2(l + w). This factorization is an alternative mathematical representation of the same calculation.
Explanation:Yes, you can utilize the Distributive Property to rewrite the formula P = (2 x l) + (2 x w) in a different way. The Distributive Property in mathematics is a fundamental property that states a(b + c) = ab + ac, which means you can distribute multiplication over addition. Applying this property to the formula P = 2l + 2w, we can factor out a common factor of 2 from both terms. So the formula can be written equivalently as P = 2(l + w).
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Situation:
An archaelogist in Turkey discovers a
spear head that contains 54% of its
original amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
FIND THE AGE OF THE SPEAR HEAD TO THE NEAREST YEAR
Answer:
t = 6162 years
Step-by-step explanation:
This equation takes the form of
[tex]N=N_{0}e^{kt}[/tex]
We are given everything but the amount of C-14 at time t = 0. But we can figure it out from the info we ARE given. We are told that when the spear head is found it contains 54% of its original amount of C-14. Notice we are dealing in percents. If 54% remains when it is found, it started out with 100% of its amount. That's our N value. Filling in:
[tex]100=54e^{.0001t}[/tex]
Our goal is to get that t down from the exponential position that it is currently in. To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication. So we take the natural log of both sides. On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone. Before that, though, we will simplify by dividing both sides by 54. 100/54 = 1.851851852. So, altogether...
[tex]ln(1.851851852)=.0001t[/tex]
Simplifying by plugging the log of that number into our calculator, we get
.6161861395 = .0001t and
t = 6161.8613
Rounding to the nearest year, t = 6162 years
This question is really confusing me, it talks about unknown angle problems with Algebra.
Help, I need help!!
Answer:
20
Step-by-step explanation:
The two given and marked angles add up to 90.
A = x
B = 3x + 10
A + B = 90 Substitute for A and B. A and B are just letters I gave things.
x + 3x + 10 = 90 Combine the left
4x + 10 = 90 Subtract 10 from both sides.
4x +10-10 = 90-10 Combine
4x = 80 Divide by 4
4x/4=80/4
x = 20
Answer:
x=20
Step-by-step explanation:
The two angles are complementary angles. Complementary angles add to 90 degrees
x + 3x+10 = 90
Combine like terms
4x+10 = 90
Subtract 10 from each side
4x+10-10 = 90-10
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Doug's garden produces 5.8 times as many vegetables as Kelsey's garden. Together, the gardens produce 102 pounds of vegetables. How many pounds of vegetables does each garden produce?
Answer:
Doug's garden: 87 lbsKelsey's garden: 15 lbsStep-by-step explanation:
Let k represent the pounds of produce coming from Kelsey's garden. Then Doug's garden produces 5.8k pounds of produce, and the total weight of it is ...
k + 5.8k = 102
6.8k = 102 . . . . . . . . . . . simplify
k = 102/6.8 = 15 . . . . . . pounds of produce from Kelsey's garden
5.8k = 5.8·15 = 87 . . . . pounds of produce from Doug's garden
A birthday gift is wrapped in a cardboard box. The box measures 12 inches on each side. How many cubic inches will the box hold?
Answer:
1728 in³
Step-by-step explanation:
A 12-inch cube has a volume of (12 in)³ = 12³ in³ = 1728 in³.
The box will hold 1728 cubic inches.
To determine the volume of the box, which is the amount of space it can hold, one must calculate the product of its length, width, and height. Since the box measures 12 inches on each side, it is a cube. The volume ( V ) of a cube is given by the formula:
[tex]\[ V = a^3 \][/tex]
where a is the length of one side of the cube. In this case, a = 12 inches. Plugging this value into the formula, we get:
[tex]\[ V = 12^3 \] \[ V = 12 \times 12 \times 12 \] \[ V = 144 \times 12 \] \[ V = 1728 \][/tex]
Therefore, the volume of the box, or the number of cubic inches it will hold, is 1728 cubic inches.
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!!
Answer:
D
Step-by-step explanation:
The 3 angles on the right form a straight angle, thus they sum to 180°
Subtract the 2 given angles from 180 to find measure of third angle ( which is the angle inside the triangle )
third angle = 180° - (70 + 60)° = 180° - 130° = 50°
The sum of the 3 angles in a triangle = 180°
Subtract the 2 known angles from 180 for measure of x
x = 180° - (50 + 60)° = 180° - 110° = 70° → D
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If = 3.52895, then the time is about 3 years and how many days?
Answer:
193
Step-by-step explanation:
We need to convert the decimal part of that number from years to days. Do that like this:
.52895 × [tex]\frac{365days}{1year}[/tex].
The year label cancels and we are left to multiply .52895 by 365 to get 193.06675 days.
Final answer:
3.52895 years is approximately 3 years and 193 days when converted, using the average number of days in a year (365.2422) to calculate the days from the fractional part of the year.
Explanation:
To calculate the time in years and days when given a decimal of years, one must convert the fractional part of the year into days. Assuming that the initial figure 'If = 3.52895' represents 3.52895 years, we would have 3 complete years and a fraction of a year (0.52895). To find the number of days in this fractional year, we need to multiply it by the average number of days in a year. The average year contains 365.2422 days, accounting for the additional leap year day every four years.
To convert the 0.52895 of a year to days, the calculation would be:
0.52895 × 365.2422 = 193.215 (approximately).
Therefore, 3.52895 years is roughly 3 years and 193 days.
If θ is an angle in standard position and its terminal side passes through the point (5,6), find the exact value of
cot
Answer:
cot(θ) = 5/6
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you the tangent relationship is ...
Tan = Opposite/Adjacent
The cotangent function is the inverse of the tangent function, so ...
Cot = Adjacent/Opposite
For your angle, the adjacent side of the triangle is the x coordinate, 5; the opposite side is the y coordinate; 6. Then the cotangent is ...
cot(θ) = 5/6
A bike tire has a diameter of 14 inches. It runs over a piece of gum that sticks to the tire. Write a cosine function that describes the height of the gum above the ground as a function of angular distance.
a. y = -7 cos x + 7
b. y = 7 cos x + 14
c. y = -7 cos x + 14
d. y = 14 cos x + 28
Answer:
a. y = -7cos(x) +7
Step-by-step explanation:
The middle level of the gum is 7 inches above the ground, and it oscillates 7 inches either side of that. Thus the offset of the cosine function (average height) is 7 and the multiplier (amplitude of oscillation) is also 7. The -7 on the cosine multiplier means the height of the gum is zero at x=0.
The cosine function that describes the height of the gum above the ground as a function of the angular distance, considering the diameter of the bike tire is 14 inches, is y = -7 cos x + 14.
Explanation:The diameter of the bike tire is 14 inches which means that the radius is 7 inches. The maximum height the gum could reach would be the top of the wheel, or the diameter. The minimum height is when the gum is at the bottom of the wheel, touching the ground, or at 0. Thus, the range of the cosine function should be between 0 and 14. One pattern of the cosine function is that it starts from its maximum point, not from the middle of the range like the sine function. With this information, the correct answer is y = -7 cos x + 14. This starts at 14, dips to 0, and ranges back up to 14.
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Are independent events the same as mutually exclusive events? define your answer
Answer:
Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other. Two events are mutually exclusive when they cannot occur at the same time. For example, if we flip a coin it can only show a head OR a tail, not both. Independent event: The occurrence of one event does not affect the occurrence of the others.
Independent events do not affect each other's occurrence, while mutually exclusive events cannot occur at the same time. The concepts are distinct and significant in probability theory.
Independent vs Mutually Exclusive Events
Independent events and mutually exclusive events are not the same in probability theory. Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. The mathematical representation of this is P(A AND B) = P(A)P(B). On the other hand, two events are mutually exclusive if they cannot occur at the same time, meaning the events do not share any outcomes and the probability of both events occurring together, P(A AND B), is zero.
An example of independent events might be rolling a dice and flipping a coin. Whether the dice shows a six does not affect whether the coin shows heads. An example of mutually exclusive events would be drawing a heart or a club from a deck of cards as a single card cannot be both a heart and a club.
identify and equation in point-slope form for the line perpendicular to y=-1/2x-7 that passes through (-3,-2)
Answer:
y +2 = 2(x +3)
Step-by-step explanation:
The equation in point-slope form for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The slope of your given line is the coefficient of x, -1/2. The slope of a perpendicular line will be the negative reciprocal of that: -1/(-1/2) = 2. So, you have m = 2, (h, k) = (-3, -2), and your desired equation is ...
y -(-2) = 2(x -(-3)) . . . . . . which can be simplified to ...
y +2 = 2(x +3)
Martin flips a coin. What is the probability that the coin will land on heads? _______________________________________ 3. A spinner is divided into five equal sections labeled 1 to 5. What is the probability that the spinner will land on 3? _______________________________________ 5. Harriet rolls a number cube. What is the probability that the number cube will land on 3 or 4? _______________________________________ 7. A bag contains 6 red and 10 black marbles. If you pick a marble from the bag, what is the probability that the marble will be black? _______________________________________ 2. Martin flips the coin 64 times. How many times can Martin expect the coin to land on heads? ________________________________________ 4. If the spinner is spun 60 times, how many times can you expect the spinner to land on 3? ________________________________________ 6. If Harriet rolls the number cube 39 times, how many times can she expect to roll a 3 or 4? ________________________________________ 8. If you pick a marble, record its color, and return it to the bag 200 times, how many times can you expect to pick a black
Answer:
1/2 to land on heads
1/5 spinner
2/6=1/3 dice
10/16=5/3 marbles
32 out of 64
12/30
13 out of 39
125/200
PLZ HELP ASAP. What is the measure of B?
Answer:
C. 55°
Step-by-step explanation:
Note the total measurement of angles for a triangle. The total measurement of all angles in a triangle = 180°
Note that m∠C is a right angle (as shown through the square), and that right angles = 90°
Subtract to find the measurement of the unknown angle (∠B)
∠B = 180 - (∠A + ∠C)
∠B = 180 - (35 + 90)
Simplify. Combine like terms. First, add (solve parenthesis), then subtract.
∠B = 180 - (125)
∠B = 55
m∠B = C. 55°
~
Answer:D
Step-by-step explanation:
125
You rotate triangle ABC, with vertices A(-3, 1), B(-2, 2), and C(-3, 4), 90° counterclockwise about the origin to form triangle A?B?C?. Match each vertex of triangle A?B?C? to its coordinates. (2, 2) (-1, -3) (1, 3) (4, 3) (-2, -2) (-4, -3) A? arrowRight B? arrowRight C? arrowRight
Answer:
A'(-1,-3)
B'(-2,-2)
C'(-4,-3)
Step-by-step explanation:
The rotation by 90° counterclockwise about the origin has the rule
[tex](x,y)\rightarrow (-y,x)[/tex]
So, the vertices of the triangle ABC have the images:
[tex]A(-3,1)\rightarrow A'(-1,-3)\\ \\B(-2,2)\rightarrow B'(-2,-2)\\ \\C(-3,4)\rightarrow C'(-4,-3)[/tex]
see attached diagram for details.
Anyone knows the correct answer??
Answer:
The surface area of the composite figure = 1172.08 inches²
Step-by-step explanation:
* Lets explain the figure
- There is a cylinder with diameter 8 inches and height 9 inches
- Rectangular prism with dimensions 16 , 11 , 11 inches
- The surface area of the cylinder will be the curved area and the
top base
- The surface area of the prism will be the surface area of one base ,
four side faces and top face which is the remaining from the subtraction
of the rectangular base and the circular base
* Lets solve the problem
# The surface area of the cylinder
∵ The diameter of the base of the cylinder is 8 inches
∵ The diameter = twice the radius
∴ 8 = 2r ⇒ divide both sides by 2
∴ r = 4 inches
∵ The area of the circle = πr²
∴ The area of the base = π(4)² = 16π inches²
∵ π = 3.14
∴ The area of the base = 16(3.14) = 50.24 inches²
∵ The area of the curved surface = 2πrh
∵ r = 4 inches and h = 9 inches
∴ The area of the curved surface = 2(3.14)(4)(9) = 226.08 inches²
∴ The surface area of the cylinder = 226.08 + 50.24 = 276.32 inches²
# The surface area of the rectangular prism
∵ The dimensions of its base are 16 and 11 inches
∵ The area of the rectangle = length × width
∴ The area of the lower base = 16 × 11 = 176 inches²
∵ The area of the top face = area of the rectangle - area of the circle
∵ The area of the rectangle = 176 inches²
∵ The area of the circle = 50.24
∴ The area of the top face = 176 - 50.24 = 125.76 inches²
- There are two side faces with dimensions 16 and 11 inches
∴ The area of the two faces = 2 × 16 × 11 = 352 inches²
- There are two faces with dimensions 11 and 11 inches
∴ The area of the two faces = 2 × 11 × 11 = 242 inches²
∵ The surface area of the rectangular prism is the sum of the 6 faces
∴ The surface area of the prism = 176 + 125.76 + 352 + 242
∴ The surface area of the prism = 895.76 inches²
- The surface area of the composite figure is the sum of the surface
area of the cylinder and the surface area of the prism
∵ The surface area of the cylinder = 276.32 inches²
∵ The surface area of the prism = 895.76 inches²
∴ The surface area of the composite figure = 276.32 + 895.76
∴ The surface area of the composite figure = 1172.08 inches²
Joe is preparing 18 hot dogs for his party. However, Joe only has 12 hot dog buns. How many more hot dog buns does Joe need?* 2 buns 6 buns 8 buns 4 buns
Answer:
The answers 6
Step-by-step explanation:
haha buns
Victor is a mechanic who wants to ensure he has enough funds during his old age. Which account will be of benefit to Victor?
A.
checking account
B.
savings account
C.
money market account
D.
individual retirement account
Answer:
D.
individual retirement account
Step-by-step explanation:
The account that will be beneficial to Victor, to ensure he has enough funds during his old age, is the individual retirement account(IRA).
Answer:
The most appropriate answer option is D. Individual Retirement Account.
Step-by-step explanation:
We know that Victor is a mechanic and he wants to make sure that he has enough funds during his old age.
For this purpose, an Individual Retirement Account (IRA) would be the most suitable and beneficiary for him.
An Individual Retirement Account is a type of account that is tax advantaged and aims to help people save for their post retirement life.
At a high school,18% of the students play football and 6% of the students play afoot all and baseball. What is the probability that a student plays baseball given that he plays football
Answer:
1.08%
Step-by-step explanation:
When you solve problems like these you convert the percentages into fractions and multiply them together.
18%= 18/100 reduced------> 9/50
6% = 6/100 reduced------> 3/50
3/50 * 9/50 = 108/10000 reduced -------> 54/5000 reduced---->
27/2500. The probability is 27/2500, or 1.08%
Need help with a math question
Answer:
[tex]x =38.7\°[/tex]
Step-by-step explanation:
By definition, the tangent of a x-angle is defined as
[tex]tan(x) =\frac{opposite}{adjacent}[/tex]
For this case
[tex]opposite = 8[/tex]
[tex]adjacent = 10[/tex]
Therefore we have that
[tex]tan(x) =\frac{8}{10}[/tex]
[tex]x =arctan(\frac{8}{10})[/tex]
The answer is:
[tex]x =38.7\°[/tex]
The probability of success is 0.6 for each trial. Find the probability of each:
13 successes in 24 trials
9 successes in 20 trials
6 failures in 12 trials
Please help! Honestly clueless. Only have a few days of school left.
Answer:
1. 0.1367
2. 0.0709
3. 0.1766
Step-by-step explanation:
The probability of success is p=0.6, then the probability of a failure is q=1-0.6=0.4.
1. The probability that there are exactly 13 successes in 24 trials is
[tex]C^{24}_{13}p^{13}q^{24-13}=\dfrac{24!}{13!(24-13)!}\cdot (0.6)^{13}\cdot (0.4)^{11}\approx 0.1367[/tex]
2. The probability that there are exactly 9 successes in 20 trials is
[tex]C^{20}_{9}p^{9}q^{20-9}=\dfrac{20!}{9!(20-9)!}\cdot (0.6)^{9}\cdot (0.4)^{11}\approx 0.0709[/tex]
3. The probability that there are exactly 6 failures in 12 trials is
[tex]C^{12}_{6}q^{6}p^{12-6}=\dfrac{12!}{6!(12-6)!}\cdot (0.4)^{6}\cdot (0.6)^{6}\approx 0.1766[/tex]
Combine like terms to create an equivalent expression. 20(−1.5r+0.75)20(-1.5r+0.75)20(−1.5r+0.75)20, left parenthesis, minus, 1, point, 5, r, plus, 0, point, 75, right parenthesis
Answer:
The combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].
Step-by-step explanation:
Consider the provided expression:
[tex]20(-1.5r+0.75)[/tex]
Use the distributive property: [tex]a(b + c) = ab + bc[/tex]
[tex]-30r + 15[/tex]
After using distribution property there are no more like terms. Thus, [tex]-30r + 15[/tex] is the simplest form.
Hence, the combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].
Based on the information, the simplified expression is -30r + 15.
How to solve the expressionGiven expression:
20(-1.5r+0.75)
Applying the distributive property:
= 20(-1.5r) + 20(0.75)
= -30r + 15
Therefore, the simplified expression is -30r + 15.
Use the distributive property to distribute the 20 to each of the terms inside the parentheses.
Simplify the expression by combining the like terms.
The simplified expression is -30r + 15.
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Why is the metric system called a decimal system of measurement
Answer:
The metric system is a called a decimal-based system because it is based on multiples of ten.
Zoe payed $18.60 in sales tax and tips for her dinner. The sales tax is 11% and she tipped 20%. What was the price of Zoe's dinner, before sales tax and tip
Answer:
56.02 dollars
Step-by-step explanation:
Wanted x, the price before taxes and tip.
sales tax: x * 0.11
+
tip on sales tax: x * 0.11 * 0.2
+
tip on price: x * 0.2
= 0.332x
= 18.6 (presumption)
Therefore,
x = 18.6/0.332 = 56.02
Answer: $60
Step-by-step explanation:
Let the total price of Zoe dinner = x
According to question,
He paid 11 % sales tax 20% on tip.
Therefore, he paid total extra charge = 11 + 20 = 31 %
That is, he paid 31 % extra in sales tax and tips for dinner.
But again according to the question,
Zoe paid $18.60 in sales tax and tips for her dinner.
⇒ 31 % of x = 18.60
⇒
⇒
⇒
⇒ x = 60
Thus, The total cost of Zoe's dinner before tax = $60
The isosceles triangle has a perimeter of 7.5m. Which equation can be used to find the value of X if the shortest side,y, measures 2.1m? A. 2x-2.1=7.5 B. 4.2+y=7.5 C. y-4.2=7.5 D. 2.1+2x=7.5
Answer:
The equation can be used to find the value of x is 2.1 + 2x = 7.5 ⇒ D
Step-by-step explanation:
* Lets talk about the isosceles triangle
- The isosceles triangle has two equal sides
- The angle between the two equal sides is called the vertex angle
- The side opposite to the vertex angle is called the base of the triangle
- The end vertices of the base are called the base angles
- The two base angles are equal in measure
- The perimeter of any triangle is the sum of the length of its
three sides
* Lets solve the problem
∵ The triangle is isosceles triangle
- The shortest side is opposite to the shortest angle
∵ The two base angles are equal in measure
∴ The shortest angle is the vertex angle which opposite to the
base of the triangle
∴ The shortest side is the base of the triangle
∵ The length of the shortest side is y
∴ The length of the equal sides is x
∴ The lengths of the sides of the triangles are x , x , y
- The perimeter of the triangle is the sum of the length of its
three sides
∴ The perimeter of the triangle = x + x + y
∵ The perimeter of the triangle is 7.5 m
∴ x + x + y = 7.5 ⇒ add the like terms
∴ 2x + y = 7.5
∵ y = 2.1 ⇒ given
∴ 2x + 2.1 = 7.5
∴ 2.1 + 2x = 7.5
* The equation can be used to find the value of x is 2.1 + 2x = 7.5
Isabelle has $84.00 in her account on Sunday. Over the next week, she makes the following changes to her balance via deposits and purchases:On which day or days does Isabelle get charged an overdraft fee?
I. Thursday II. Friday III. Saturday
a. I only
b. I and III
c. II and III
d. III only
Hello There!
The answer would be "I and III"
If Isabelle makes these changes, she will get charged an overdraft fee on 2 days. The days will be Thursday and Saturday.
Answer:
B
Step-by-step explanation:
It snowed 5.5 inches on Sunday morning, and an additional 1 3/4 inches on Monday. On Tuesday, 3 1/8 melted during the afternoon. How much snow was there Tuesday evening?
Answer:
4 1/8 inches
Step-by-step explanation:
7 1/4 - 3 1/8
(7-3) + (1/4 -1/8)
4 + (1/4 - 1/8)
4 + 1/8
4 1/8 inches
Answer:
4 1/8 inches
Step-by-step explanation:
You apparently want to find the sum (in inches) ...
5.5 + (1 3/4) - (3 1/8)
This can be done a number of ways. One is to use an appropriate calculator.
__
Another way to do this is to add the integer parts and fraction parts separately:
= (5 +1 -3) +(1/2 +3/4 -1/8)
= 3 + (4/8 +6/8 -1/8) = 3 + (4+6-1)/8 = 3 9/8
= 4 1/8
__
Another way is to convert all the numbers to decimal, then add.
= 5.500 +1.750 -3.125
= 7.250 -3.125
= 4.125 = 4 1/8
__
There were 4 1/8 inches of snow remaining Tuesday evening.