Mr. Maddox asked four students to create a number line to help find the sum of fractions 3 2/3 + 1 3/4 + 2/3
Answers
Answer with explanation:
Question asked by Mr.Maddox to find the sum of fractions with the help of number line :
[tex]\rightarrow 3 \frac{2}{3}+1 \frac{3}{4}+\frac{2}{3}\\\\ \text{Using Associative Property}\\\\\rightarrow a+(b+c)=(b+c)+a\\\\\rightarrow [\frac{2}{3}+ 1\frac{3}{4}]+3 \frac{2}{3}\\\\\rightarrow [\frac{2}{3}+\frac{7}{4}]+\frac{11}{3}\\\\\rightarrow \frac{21+8}{12}+ \frac{11}{3}\\\\\rightarrow\frac{29+44}{12}\\\\ \rightarrow\frac{73}{12}\\\\\rightarrow 6\frac{1}{12}[/tex]
Related Questions
A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be, to the nearest cent, after 12 years?
Answers
Answer:
y≈3508.16
Step-by-step explanation:
A line with a slope of 33 passes through (2,5)2,5. Which choice is an equation of this line? a)y+5=3x+2 b)y-5=3x-2 c) y-5=(x-2) d)y-2=3(x-5)
Answers
Answer:
y - 5 = 3 . (x - 2)
Step-by-step explanation:
A linear equation can be written in point-slope form.
y - y₁ = m. (x- x₁)
where
x is the independent variable
y is the dependent variable
(x₁, y₁) is an ordered pair representing a point through which the line passes
m is the slope
Given the slope is 3 (m = 3) and the line passes through the point (2, 5) (x₁ = 2, y₁ = 5), we can write the point-slope form of the linear equation.
y - 5 = 3 . (x - 2)
I think this might correspond to b, although it should have a parenthesis to be correct.
!!!!!!!!PLEASE HURRY !!!!!!!! The length of the base of a rectangular prism is 8 inches. The width of the prism is 4 1/2inches, and the height is 3 1/2
inches. What is the volume of the prism?
4 A) 84 in3
B) 921
C) 104 in3
D) 126 in3
Answers
Answer:
It is b
Step-by-step explanation:
LEon made 4 liters of lemonade for the party, but it was too strong, it was 14% lemon juice. How much 8% lemonade should he add to make a mixture that is 10% lemon juice?
can someone show me how to solve this using the table or bucket method? thanks
Answers
For a mixture of solutions to form a resulting solution, we know
V1 * N1 + v2 * N2 = V * N
where, V1 = Volume of mixture of 1 N1 = Concentration of mixture 1V2 = Volume of mixture of 2 N2 = Concentration of mixture 2
V = volume of mixture N = Concentration of mixture
So solving we get:
(4+x)*10 = 4*14 + x * 8or, 10x-8x = 4*14-4*10or, 2x = 16or x = 8
so 8 litres of the solution B must be added to the solution
The rectangular top of his table has an area of 3^7 square inches and a length of 3^4 inches. What is the width of the table top?
A. 9 inchesB. 27 inchesC. 2,187 inchesD. 59,049 inches
Answers
Answer:
27
Step-by-step explanation:
Because 3 plus 7 equals 12 plus another 9 equals 27
The width of the rectangular table top is 27 inches.
The correct answer is option (B).
What is the area of rectangle?A = l × w, where 'l' is the length and 'w' is the width of the rectangle
For given question,
The rectangular top of Karim's table has an area of [tex]3^7[/tex] square inches and a length of [tex]3^4[/tex] inches.
[tex]\Rightarrow A =3^7~sq.in.~,l=3^4~in.[/tex]
Using the formula for the area of the rectangle,
[tex]\Rightarrow A=l\times w\\\\\Rightarrow 3^7=3^4\times w\\\\\Rightarrow w=\frac{3^7}{3^4}\\\\ \Rightarrow w=3^7\times 3^{-4}\\\\\Rightarrow w=3^{7-4}\\\\\Rightarrow w=3^3\\\\\Rightarrow w=27~in.[/tex]
Therefore, the width of the rectangular table top is 27 inches.
The correct answer is option (B).
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What postulate is illustrated by the diagram above?
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which equation can be solved to find x, the measure of BD in the diagram below?
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Angle formed outside=1/2(difference of intercepted arcs)
∠ACE=1/2(AE-BD)
∠ACE=53°
AE=233°
BD=x
Hence the formula for obtaining BD will be:
53=1/2(233-x)
The correct answer is A
Answer:
A. [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]
Step-by-step explanation:
Let x be the measure of arc BD.
Since we know that an angle formed by two intersecting tangents equals one-half the difference of the measures of the intercepted arcs (the major arc-minus the minor arc).
[tex]\text{ Measure of tangent-tangent angle}=\frac{1}{2} (\text{measure of major arc-measure of minor arc})[/tex]
We can see from our given graph that the tangent-tangent angle's measure is 53 degree. The measure of its intercepting major arc equals 233 degrees and minor arc equals x.
Upon substituting our given values in above formula we will get,
[tex]53^{o}=\frac{1}{2} (233^{o}-x)[/tex]
[tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]
Therefore, the equation that can be solved to find x (the measure of arc BD) will be [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex] and option A is the correct choice.
(Extra points)
The lunch bill for Marty and Breanna add a dinner totaled $18.37. Tax on the meal was 6%, and they wanted to leave a 15% tip. How much was the meal including tax and tip?
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Add 6% of this as tax by either multiplying by dinner cost by 1.06 (to get dinner + tax)
For tip... If you calculate the 15% before, then you would add it together with the tax to get 21%, and then your answer would be calculated in the same way as just the tax.
If you tip the amount after tax, then take your answer for the (dinner + tax) part and use the same method, but with 15%.
(dinner + tax) x 1.15 = dinner, tax + tip
Final answer:
To calculate the total cost of Marty and Breanna's meal including tax and tip, add a 6% tax and a 15% tip to the original bill of $18.37 to get a total of $22.23.
Explanation:
To find the total cost of the meal for Marty and Breanna including tax and tip, we first calculate the tax. Since the tax rate is 6%, we convert that to a decimal (0.06) and multiply by the total cost of the meal ($18.37):
0.06 × $18.37 = $1.10 (rounded to the nearest cent).
Next, we calculate the tip, which is 15% of the pre-tax meal cost. We turn 15% into a decimal (0.15) and multiply by the meal cost:
0.15 × $18.37 = $2.76 (rounded to the nearest cent).
To find the total amount paid including tax and tip, we add all the amounts together:
$18.37 + $1.10 + $2.76 = $22.23
So, the total cost of the meal including tax and tip is $22.23.
Kersha has two jobs. During the day she works as an office clerk, and in the evening she works as a cashier. Her office job pays her $12.00 per hour. Her cashier job pays her $8.25 per hour. In one week, Kersha worked 55 hours. She earned a total of $585.
How many hours did Kersha work in each job?
Office clerk: 31 hours; cashier: 24 hours
Office clerk: 20 hours; cashier: 35 hours
Office clerk: 35 hours; cashier: 20 hours
Office clerk: 28 hours; cashier: 27 hours
Answers
Answer: c) Office clerk: 35 hours; cashier: 20 hours.
The correct answer is that Kersha worked as an office clerk for 35 hours and as a cashier for 20 hours.
To solve this problem, we can set up a system of equations based on the information given. Let's denote the number of hours Kersha worked as an office clerk as [tex]\( x \)[/tex] and the number of hours she worked as a cashier as [tex]\( y \).[/tex]
From the problem statement, we know the following:
1. Kersha earns $12.00 per hour at her office job.
2. Kersha earns $8.25 per hour at her cashier job.
3. Kersha worked a total of 55 hours in one week.
4. Kersha earned a total of $585 in one week.
Using this information, we can write two equations:
For the total number of hours worked:
[tex]\[ x + y = 55 \][/tex] (Equation 1)
For the total earnings:
[tex]\[ 12x + 8.25y = 585 \][/tex] (Equation 2)
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination. Let's use the substitution method.
First, we can solve Equation 1 for [tex]\( x \):[/tex]
[tex]\[ x = 55 - y \][/tex]
Now we substitute [tex]\( x \)[/tex] in Equation 2 with [tex]\( 55 - y \):[/tex]
[tex]\[ 12(55 - y) + 8.25y = 585 \][/tex]
Expanding the equation, we get:
[tex]\[ 660 - 12y + 8.25y = 585 \][/tex]
Combining like terms, we get:
[tex]\[ -3.75y = 585 - 660 \][/tex]
[tex]\[ -3.75y = -75 \][/tex]
Dividing both sides by -3.75 to solve for [tex]\( y \)[/tex], we get:
[tex]\[ y = \frac{-75}{-3.75} \][/tex]
[tex]\[ y = 20 \][/tex]
Now that we have the value of [tex]\( y \)[/tex], we can find [tex]\( x \)[/tex] using Equation 1:
[tex]\[ x = 55 - y \][/tex]
[tex]\[ x = 55 - 20 \][/tex]
[tex]\[ x = 35 \][/tex]
Therefore, Kersha worked 35 hours as an office clerk and 20 hours as a cashier. The correct option is:
Office clerk: 35 hours; cashier: 20 hours.
Approximately 50% of babies born are boys. Five coins are tossed 60 times and the coins showed two tails out of the five coins 40 times. Determine the experimental probability of a woman having 2 boys out of 5 children.
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Does the following represent growth or decay y=4x
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We can plug in numbers to see if it does.
y=4(1)
y=4
y=4(2)
y=8
This represents growth. When the input (x) increase, the output (y) increases.
I hope this helps!
~kaikers
two friends share 1/4 gallon of lemonade equally. What fraction of the gallon of lemonade does each friend get?
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1/4 / 2 = 1/8
Each friend gets 1/8 gallon of lemonade.
Hope this helps!
each week Samantha can pay as much $15 for her school at lunch. Write an inequality showing how much Samantha spends at lunch.
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Let us say Samantha spends $x for her school at lunch every week.
We are given that she can spend as much as $15 every week for her school at lunch every week.
As much as stands for maximum quantity that she can spend.
So $15 is the maximum she can spend.
Writing an inequality,
[tex] x \leq 15 [/tex]
On Monday, more than 500 people attended a county fair. Fourteen of the people who attended the fair that day were selected at random and asked how many rides they went on that day.
a.0
b. 2.8
c. 3
d.8
Answers
Hope this helps!:)
To make each costume, Rachel uses 6 yards of material and 3 yards of trim. Suppose she uses a total of 48 yards of material to make several costumes. How many yards of trim does she use? Write the rule you used to find the number of yards to trim
Answers
[tex]48 \div 6 = 8 \\ 8 \times 3 = 24[/tex]
(48/6)3=24
(f/6)3=t f= total fabric used t=total trim used
The area of a rectangle is 30 sq meters. The perimeter is 26 feet. What are the dimensions of the rectangle?
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Answer:
The given rectangle is not possible.
Step-by-step explanation:
The minimum perimeter of such a rectangle is 4√30 meters, about 21.9 meters. That is about 71.9 feet. The largest rectangle with a perimeter of 26 feet will have an area of about 3.93 square meters.
The rectangle described cannot exist.
a cafeteria table has a length of 8 feet and a width of 3 feet. If 3 tables are pushed together, what is the combined area of the tables?
Answers
According to m&ms web site, each package of the milk chocolate candies typically contain 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange m&ms. you go to the store and buy a standard-sized package. when you open it, you find that it contains 51 m&ms, distributed as follows: color brown red yellow green blue orange frequency 8 4 10 7 11 11 over the long run, you know that the probability of selecting a blue or an orange m&m will be 44% because these outcomes are: finite. disjoint. discrete. none of the answer choices is correct.
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Answer: Disjoint
Step-by-step explanation: Selecting specific colors in a m&m's pack is disjoint because the events cannot occur at the same time, i.e., when you take one m&m's, it can be blue and orange at the same time.
To determine the probability of disjoint or mutually exclusive events, you can find their probability by adding the probability of each event.
In the question, it is asked the probability of selecting a blue or an orange.
Probability of a blue:
P(b) = [tex]\frac{11}{51}[/tex]
Probability of an orange:
P(o) = [tex]\frac{11}{51}[/tex]
Probability of one OR the other:
P(b OR o) = P(b) + P(o)
P(b OR o) = [tex]\frac{11}{51} + \frac{11}{51}[/tex]
P(b OR o) = [tex]\frac{22}{51}[/tex]
P(b OR o) ≈ 0.44 or 44%
The probability of blue or orange m&m's is 44%, and the events are disjoint.
According to the provided probabilities on the M&M's website, the probability of choosing a blue or an orange M&M is a combined 44%. These outcomes are described as discrete, as they are distinct and countable events in the context of probabilities.
Explanation:The question is based on probabilities related to the distribution of M&M colors in a package, particularly focusing on the number of orange M&Ms and the number of yellow M&Ms. When analyzing the distribution of M&M colors, we utilize concepts from statistics such as uniform distribution and binomial distribution to assess the likelihood of pulling a particular color from a bag. If the M&Ms had a uniform distribution, we would expect each color to appear with equal probability; however, the provided probabilities for each color do not align with a uniform distribution.
In the long run, the probability of selecting a blue or an orange M&M is 44% combined, based on the provided percentages on the M&M's website (24% blue and 20% orange). These outcomes are discrete, as they represent distinct countable outcomes. The terms 'finite', 'disjoint', and 'discrete' are all descriptions of different characteristics of statistical outcomes. 'Finite' refers to a set that has a limited number of outcomes, 'disjoint' indicates that the events cannot happen at the same time, and 'discrete' encompasses outcomes that are countable and not continuous.
can somebody please show me how to find A? thanks
Answers
Answer C
Using Thales, 3/8=5/A==>A=5*8/3=40/3
Dwayne wants to buy a bowling ball that has a price of $120. As a member of a bowling league, he is entitled to a 15% discount off the price of the bowling ball. He will also have to pay 6% sales tax on the discounted price of the bowling ball. Dwayne thinks that the final price of the bowling ball can be determined by taking 9% off the original price. Is Dwayne correct? Support your answer with a detailed explanation.
Answers
$120-15%=$102
$102+%6=$108.12
so %6 represents tax
and 15% is his discount
if you were to take away %9 then you would get $109.20
$120-9%=109.20
so Dwayne is incorrect, because $108.12 ( his true final price) isn't equal to $109.20 (the price it would be if it was 9% off)
I hope this helps!
No, Dwayne is not correct.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Dwayne wants to buy a bowling ball that has a price of $120.
And, As a member of a bowling league, he is entitled to a 15% discount off the price of the bowling ball. He will also have to pay 6% sales tax on the discounted price of the bowling ball.
Now,
Here, Dwayne wants to buy a bowling ball that has a price of $120.
Hence, After 15% discount the price is,
⇒ 15% of 120
⇒ 15 x 120 / 100
⇒ $18
Hence, After discount the price is,
⇒ 120 - 18
⇒ $102
And, He will also have to pay 6% sales tax on the discounted price of the bowling ball.
Hence, The price of ball is,
⇒ $102 + 6% of 102
⇒ $102 + $6.12
⇒ $108.12
Since, Dwayne thinks that the final price of the bowling ball can be determined by taking 9% off the original price.
Hence, We can formulate;
⇒ $120 - 9% of 120
⇒ $120 - 10.8
⇒ $109.2
Thus, Dwayne is not correct.
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Explain how to find the surface are of a triangular prism using only the the dimensions of the figure.
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Given right triangle abc with altitude cd find ad ab and dc
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.. ab = √(ac^2 +bc^2)
Because all the triangles are similar,
.. cd/bc = ac/ab
.. cd = ac*bc/√(ac^2 +bc^2)
Likewise,
.. ad/ac = ac/ab
.. ad = ac^2/√(ac^2 +bc^2)
Your segments are
.. ad = ac^2/√(ac^2 +bc^2)
.. ab = √(ac^2 +bc^2)
.. dc = ac*bc/√(ac^2 +bc^2)
A CD which usually sells for $15.78 has a 15% discount. Estimate the amount of the discount.
Answers
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 15.78&100\\ a&15 \end{array}\implies \cfrac{15.78}{a}=\cfrac{100}{15}\implies \cfrac{15.78\cdot 15}{100}=a[/tex]
You need to round 15.78 to get 16. You then multiply 16 to 15 and divide by 100 to get your answer :
2.4
Which would also be $2.40
What is the sixth term of the sequence?
an= −3 ⋅ 2n+1
Enter your answer in the box.
a6=
Answers
-3*2(6)+1
-3*12+1
-36+1
-35=a6
Answer: its actually -384 and I TOOK THE TEST I promise !!!
Step-by-step explanation:
the figure is made of up of a cone and a cylinder, to the nearest whole number what is the approximate volume of this figure. PLEASE HELP FAST
Answers
Volume of cylinder = πr²h
π = 3.14
r = 4/2 = 2 mm
h = 2 mm
So, volume of cylinder equals:
[tex]3.14 *(2)^{2}*2 =25.12[/tex] mm³
Volume of cone = [tex] \frac{1}{3} \pi r^{2}h [/tex]
π = 3.14
r = 2 mm
h = 3 mm
So, volume of cylinder equals:
[tex] \frac{1}{3}*3.14* (2)^{2}*3=18.84 [/tex]mm³
Thus, total volume of the figure = 25.12 + 18.84 = 43.96 mm³
Complete the table of values for the linear equation -2x-5=30 brainly. Enter your answers in the boxes.
Answers
-2x=30+5
-2x/-2=35/-2
X=-17.5
The value of x is x = -17.5.
The linear equation in question is -2x - 5 = 30. To complete a table of values for this equation, solve for x first:
Add 5 to both sides of the equation to isolate the term with x: -2x = 35.
Divide both sides by -2 to solve for x: x = -17.5.
Now that you have the value of x, you can fill in the table with x = -17.5, since a table of values typically includes various values for x and the corresponding values for the equation. However, in this case, the equation is simply solved for a single value of x without needing different values for it.
a pieace of cheese is in the shape of a triangular prism.the dimensions of the cheese are shown below
what is the surface area of the piece of cheese
a)14.5
b)20.5
c)29
d)32
Answers
1) Two triangular faces
2) Three rectangular faces.
Surface area is the SUM of the areas of all of the faces.
Let us find these faces one by one:
1.
As you know, the area of the triangle is:
[tex] \frac{1}{2} * base * height [/tex]
Since, the base = 6 inches, and height = 4 inches;
Therefore, The area of ONE triangle = (1/2) * 6 * 4 = 12 inches squared.
In triangular prism, there are two triangles, therefore,
Two triangular faces = 2 * 12 inches = 24 inches squared --- (A)
2.
Now let us find the areas of three rectangular faces...
Since, two of the three rectangular faces are the same, therefore, we would find the area of one rectangular face, and multiple the result with two to get the total area of two rectangular faces.
Area of one rectangular face = base * height.
Since, base = 0.5 inches, height = 5 inches, therefore,
Area of one rectangular face = 0.5 * 5 = 2.5 inches squared.
Now that we have one rectangular face, therefore,
Area of two rectangular faces = 2 * 2.5 = 5 inches squared.
The area of the third rectangular base = 6 * 0.5 = 3 inches squared
Therefore,
The area of the three rectangular faces = 5 + 3 = 8 inches squared --- (B)
Now add both "area of two triangular faces(A)" and "area of three rectangular faces(B)" to get the final surface area of the triangular prism.
Surface Area of the triangular prism = Area of Two Triangular faces + Area of Three Rectangular faces
Surface Area = 24 + 8 = 32 inches squared
The surface area of the triangular prism = 32 inches squared.
The correct option is: d
-i
Answer:
Answer is d
Step-by-step explanation:
sorry that im 4 years late
find the equation of the circle with center at (-3,1) and through the point (2,13)
Answers
1. if centre of the circle is O(-3;1) and P(2;13), then OP=√(5²+12²)=13=r (radius);
2. in common view an equation of the circle is: (x-a)²+(y-b)²=r², where (a;b) is the centre.
Using this: (x+3)²+(y-1)²=13²
Find the first four terms of the sequence an=4-2n
Answers
Answer:
E2020
Step-by-step explanation:
The four successive terms of the given ap series by rule [tex]a_{n}[/tex] = 4 - 2n will be 2, 0, -2, and -4.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Now it has the same difference between any two consecutive terms d =2-1 = 3-2.
Given the rule for nth term of ap series
[tex]a_{n}[/tex] = 4 - 2n
Now,
First term (n = 1) ⇒ 4 - 2(1) = 2
Second term (n =2) ⇒ 4 - 2(2) = 0
Third term (n = 3) ⇒ 4 - 2(3) = -2
Fourth term (n = 4) ⇒4 - 2(4) = -4
Hence "The four successive terms of the given ap series by rule [tex]a_{n}[/tex] = 4 - 2n will be 2, 0, -2, and -4.".
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PLZ HELP ME, I AM ONLY IN LITTLE GRADE AND ITS EASY FOR YOU GUYS AND PLZ HELPPPPPPPPPPPP!!!!!!!!!!!
Q:Together, Xavier, Yolanda, and Zachary have $4.44. If each person has the same amount, how much money does each person have?
Answers
To figure out how much money each person has, we need to divide.
4.44 ÷ 3 = 1.48
So each person has $1.48
Hope this helps you!
Always remember, you are a Work Of Art!
- Nicole :) <3