Answers
Answer:
6
Step-by-step explanation:
This problem centers on recognizing the relationship between fractions and repeating decimals.
Note the following:
[tex]\frac{1}{3}=0.33333333333333333333333333333333333333333333333...[/tex]
or more simply [tex]\frac{1}{3}=0.\bar{3}[/tex]
This means that [tex]2\frac{1}{3}=2.\bar{3}[/tex]
Going back to the original expression, [tex]3\frac{2}{3}+2.\bar{3}[/tex] simplifies to [tex]3\frac{2}{3}+2\frac{1}{3}[/tex]
Next, adding mixed numbers. For adding mixed numbers, whole number parts and fractional parts can be added separately (this is because of the associative and commutative properties of addition)... because
[tex]3\frac{2}{3}+2\frac{1}{3}[/tex] means the same thing as
[tex](3+\frac{2}{3})+(2+\frac{1}{3})[/tex]
Changing the order, we can write it as
[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]
Adding the whole number parts, 3+2 is 5.
Next, adding the fraction parts:
For adding fractions, one must have a common denominator (the bottom part of the fraction must be the same). Once they are the same, the denominator just sort of "hangs out" until the end without changing, and the numerators (the tops) are added together.
Fortunately, the denominators are already the same. So, add the numerators, and the denominator will stay as a 3.
[tex]\frac{2}{3}+\frac{1}{3}[/tex]
[tex]\frac{1+2}{3}[/tex]
[tex]\frac{3}{3}[/tex]
It is important to recognize that any fraction* where the number on the top matches the number on the bottom, the fraction is equivalent to 1.
*(except if the number we're talking about is zero)
So, the fraction parts added together, are equivalent to 1, and the whole number parts added were equal to 5. Returning to our expression...
[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]
[tex]5+\frac{3}{3}[/tex]
[tex]5+1[/tex]
[tex]6[/tex]
Related Questions
1. Find the range for the given domain: {-2, -1, and 0} and the function is y = 3x^2
2. Find the range of the given function y = 8x + 1, where x > 2
3. Find the range of the given function y = 5x + 2, where x > -2
can someone explain how to do these?
Answers
1. The range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.
2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).
3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).
We know that the range of a function is the entire set of all possible values for the dependent variable (typically y), after substituting the domain.
1. For the function y = 3x²,
Here the domain is {- 2, - 1, and 0}. So, we have to find the y values for the x values - 2, - 1, and 0 to find the range of the function.
Now, at x = - 2,
y = 3(- 2)² = 3 × 4 = 12
At x = - 1,
y = 3(- 1)² = 3 × 1 = 3
At x = 0,
y = 3(0)² = 3 × 0 = 0
So, the range of this function is {12, 3, 0}.
2. Now, for the function y = 8x + 1,
At x = 2,
y = 8 × 2 + 1 = 16 + 1 = 17
Since the domain is x > 2, we can say that the range set will contain values greater than 17.
So, the range of this function is (17, ∞).
3. For the function y = 5x + 2,
Now, at x = - 2,
y = 5 × (- 2) + 2 = - 10 + 2 = - 8
Since the domain is x > - 2, we can say that the range set will contain values greater than - 8.
So, the range of this function is (-8, ∞).
1. Therefore, the range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.
2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).
3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).
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A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of `pi`.)
Answers
The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³
How to find volume?The volume of the air space surrounding the cone inside the cylinder is as follows:
volume of the air space = volume of cylinder - volume of a cone
volume of cylinder = πr²h
volume of cylinder = π16 × 5²
volume of cylinder = 400π
volume of the cone = 1 / 3 πr²h
volume of the cone = 1 / 3 × π × 12 × 4²
volume of the cone = 64π
Therefore,
volume of the air space = 400π - 64π
volume of the air space = 336π
volume of the air space = 1055.04 cm³
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The total pages a person reads in x days, if the person reads 6 pages a day
the cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
the total cost of x notebooks, if one notebook costs $6 and students receive a discount of $1 off their total bill
the total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
what are the corresponding functions for each situation?
Answers
The given expression will be written as follows:-
y = 6x
y = 6x + 6
y = 6x - 1
y = 6x +1
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
A) The total pages a person reads in x days, if the person reads 6 pages a day
y = 6x
B) The cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
y = 6x + 6
C) The total cost of x notebooks if one notebook costs $6 and students receive a discount of $1 off their total bill
y = 6x - 1
D) The total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
y = 6x + 1
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What is the distance between the points (4, 5) and (10, 13) on a coordinate
plane?
Answers
Answer:
10
Step-by-step explanation:
square root of 6^2 + 8^2
How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answers
Answer:
1
Step-by-step explanation:
the number of solutions corelatea with number of cross-points in the graphs, in our exame, 1 point, hence 1 solution
NEED HELP TODAY PLEASE solve 4(2/5x+7)=−8−4/5x show your work
Answers
Answer:
x = -15
Step-by-step explanation:
A passenger jet plane cruises at 550 knots. It enters a jet stream with
a tailwind speed of 120 knots. If the speed of sound is 661 knots,
will the jet travel faster or slower than sound during its journey?
Answers
Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.
What is the ground speed?The jet's speed, considering that there is a tailwind, is given by:
J = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 550 knots.Wind: 120 knots.Hence the jet's speed is given by:
J = 550 + 120 = 670 knots.
670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.
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Consider the quadratic function y = 1/5 (x – 2)2 + 5.
Which statements are true about the function and its graph? Select TWO options.
A) The vertex of the function is (–2, 5).
B) There are no real roots for the function.
C) The graph of the function opens down.
D) The graph contains the point (2, 5).
E) The graph intersects the x-axis at one unique point.
Answers
Answer:
B and D
Step-by-step explanation:
vertex(2,5) so D is correct
there are no real roots for the function B is correct
3. Angle r* = 2wº. What is the measure of angle rº1 Show your work. 125⁰ Thangle A wo Wo Triangle B 125⁰ 3. Angle r * = 2wº . What is the measure of angle rº1 Show your work . 125⁰ Thangle A wo Wo Triangle B 125⁰
Answers
Answer:
r = 290°
Step-by-step explanation:
Exterior angle property:In a triangle, exterior angles equals the sum of interior opposite angle.
In triangle A,
x + 90 = 125 {Exterior angle property}
x = 125 - 90
x = 35°
In triangle B,
y + 90 = 125
y = 125 - 90
y = 35°
x + y + r = 360 {Complete angle}
35 + 35 + r = 360
70 +r = 360
r = 360 - 70
r = 290°
There are some counters in a bag.
the counters are blue or green or red or yellow.
the table shows the probabilities that a counter taken at random from the bag
will be blue or will be green.
red
yellow
colour
blue
green
probability
0.32
0.20
the probability that a counter taken at random from the bag will be red is five times the
probability that the counter will be yellow.
there are 300 counters in the bag.
work out the number of yellow counters in the bag.
Answers
Answer:
187
Step-by-step explanation:
what are the roots of the polynomial below. x^3-3x^2+2
Answers
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The roots of the polynomial are 1, 2.7321, and -0.7321.
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The roots of the polynomial are:
x³ - 3x² + 2
If we divide the polynomial by (x-1), then
(x³ - 3x² + 2)/(x-1) = x² - 2x - 2
now, factorize the given polynomial,
x² - 2x - 2
x = 1 ± √3
x = 1, 2.7321, -0.7321
Hence, the roots of the polynomial are 1, 2.7321, and -0.7321.
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!!HELP PLS!! a triangle has side lengths measuring 3x cm 6xcm and h cm which expression describes the possible values of h in cm? 4x < h < 10x, 10x < h < 4x, h=4x, h=10x
Answers
Based on the triangle inequality theorem, the possible values of h in cm is: A. 4x < h < 10x
What is the Triangle Inequality Theorem?Based on the triangle inequality theorem, two sides of a triangle must be equal or more than the third sides.
Given a values of the side lengths of a triangle as, 3x, 6x, and h cm, the possible values would be determined as shown below:
h < 3x + 7x or 7x - 3x < h
h < 10x or 4x < h
The possible values of h would be: 4x < h < 10x.
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Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....
Note: the first term should be b(1).
b(n) =
Answers
Answer:
b(n) = -11 + (n-1)*8
Step-by-step explanation:
Let n be the sequence number, with n=1 the first number b(1) -11
The sequence changes by +8 each step.
b(1) -11 + 8 = -3
b(2) -3 + 8 = 5
b(3) 5 + 8 = 13
b(4) 13
b(1) = -11
b(2) = -3. or b(1) + 1*8
b(3) = 5, or b(1) + 2*8
b(4) = 13, or b(1) + 3*8
We note that each step adds a multiple of 8 to the initial value of -11. This can be stated as (n-1)*8
The formula for this sequence would be b(n) = b(1) + (n-1)*8
b(n) = -11 + (n-1)*8
Check: Does n=3 return the value of 5?
b(n) = -11 + (n-1)*8
b(3) = -11 + ((3)-1)*8
b(3) = -11 + (2)*8
b(3) = -11 + 16
b(3) = 5 YES
Solve by using Vertical Velocity model: h=-16t^2+vt+s
Where v = velocity
s = starting height
h = ending height
t = time
You can ignore the previous work, just solve B and C. Just there for context
USE VERTICAL VELOCITY MODEL FORMULA.
Answers
An equation that models the height of the ball as a function of time t is; h(t) = -16t² + 40t + 3. The maximum height that the ball will reach is 28 ft
How to Solve the Vertical velocity model?We are given the equation for the vertical velocity model as;
h = -16t² + vt + s
Where;
v = velocity
s = starting height
h = ending height
t = time
A) From the question, we have;
v = 40 ft/s
s = 3 ft
Thus, the equation is;
h = -16t² + 40t + 3
B) To find the time that the ball reaches its maximum height, we will equate the height equation to zero and find the roots. Thus;
-16t² + 40t + 3 = 0
Using an online quadratic equation calculator gives;
t = 2.573 s
C) The maximum height that the ball will reach is;
h'(t) = -32t + 40
At h'(t) = 0;
-32t + 40 = 0
32t = 40
Thus;
t = 1.25 s
Max height = -16(1.25)² + 40(1.25) + 3
Max height = 28 ft
D) The height of the ball after 2 seconds is;
h(2) = -16(2)² + 40(2) + 3
h(2) = 19 ft
E) Time for the ball to hit the ground is;
T = 2 * 2.573
T = 5.146 s
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(a+b)^2=10
and ab=1
then find a^2+b^2
Answers
[tex] \underline{\large \bf{Required \: Answer}} : - [/tex]
[tex] \dashrightarrow \: \red{\large8}[/tex]
[tex] \sf[/tex]
[tex] \underline{ \large{ \rm \pink{SolutioN}}} \: -[/tex]
[tex] \quad \qquad\sf \: {(a + b)}^{2} = 10[/tex]
[tex] \qquad \: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2ab = 10[/tex]
[tex] \qquad\: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2(1) = 10[/tex]
[tex] \qquad\: \: \to\: \: \sf \: {a}^{2} + {b}^{2} = 10 - 2[/tex]
[tex] \qquad\: \:\bf \to\: \: \: {a}^{2} + {b}^{2} = 8[/tex]
[tex] \sf[/tex]
[tex] \sf \therefore \: 8 \: \: is \: \: the \: \: required \: \: answer[/tex]
[tex] \rule{200pt}{2pt}[/tex]
The French club is sponsoring a bake sale to raise at least $305. How many pastries must they sell at $2.05 each in order to reach their goal?
Answers
Answer:
148.7804878
Step-by-step explanation:
All you have to do is divide!
Please help! Consider the following subset of the real number line. How can this set be expressed using inequalities?
Answers
Inequalities help us to compare two unequal expressions. The correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The set of numbers that the number line represents is -1, -2,-3, and -4. Thus, The inequalities that can express the given set are -4≤x≤-1.
Hence, the correct option is A.
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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answers
Answer:
The answer would be D 7mn+3m/2+5n/4
Step-by-step explanation:
A polynomial is a combination of terms separated by +
or − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.
If the inspection division of a county weights and measures department wants to estimate the mean amount of
Answers
If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.
Given 95% confidence level, standard deviation=0.05.
We know that margin of error is the range of values below and above the sample statistic in a confidence interval.
We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data near the mean are more frequent in occurence than data far from mean.
We know that margin of error for a confidence interval is given by:
Me=[tex]z/2* ST/\sqrt{N}[/tex]
α=1-0.95=0.05
α/2=0.025
z with α/2=1.96 (using normal distribution table)
Solving for n using formula of margin of error.
[tex]n=(z/2ST/Me)^{2}[/tex]
n=[tex](1.96*0.05)^{2} /(0.01)^{2}[/tex]
=96.4
By rounding off we will get 97.
Hence the sample size required will be 97.
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The given question is incomplete and the full question is as under:
If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?
55. The Cone Problem Begin with a circular piece of paper with
4-in. radius as shown in (a). Cut out a sector with an arc length o
x. Join the two edges of the remaining portion to form a cone
with radius r and height h, as shown in (b).
4 in.
4 in.
(a)
(b)
(a) Explain why the circumference of the base of the cone is
8T X
(b) Express the radius r as a function of x.
(c) Express the height has a function of x.
(d) Express the volume V of the cone as a function of x.
pls helpppp
Answers
The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.
How to calculate the values?The radius r as a function of x will be:
8π - x = 2πr
r = (8π - x)/2π
r = 4 - x/2π
The height has a function of x will be:
r² + h² = 16
h² = 16 - r²
where r = 4 - x/2π
h = √16 - ✓(4 - x/2π)²
h = 4✓(4 - x/2π)²
The volume V of the cone as a function of x will be:
= 1/3 πr²h
= π/3(4 - x/2π)² 4✓(4 - x/2π)²
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Please help! What is 4 yards 2 feet 7 inches + 2 yards 1 foot 6 inches?
Answers
Answer:
7 yds 1 ft 1 inch
Step-by-step explanation:
Quick Solve!
Side #1:
1 yard = 36 inches4 * 36 = 144 inches1 foot = 12 inches2 * 12 = 24 inches144 inches + 24 inches + 7 inches = 175 inches
Side #2:
2 yards = 2 * 36 = 72 inches1 foot = 12 inches + the 6 inches = 18 inches72 inches + 18 inches = 90 inches72 inches + 18 inches = 90 inches + 6 inches = 96 inches
Conclusion:
175 inches + 96 inches = 271 inches
Answer:
⇒ 7 yds 1 ft 1 inch
Answer:
7 yards 1 foot 1 inch
Step-by-step explanation:
Adding both of them together, you get:
6 yards 3 feet 13 inches
Since 1 foot = 12 inches, and 13 inches exceeds that, add a foot to the previous 3 feet and subtract 12 from the 13 inches
Therefore: 6 yards 4 feet 1 inch
Since 1 yard = 3 feet, and 4 feet exceeds that, add a yard to the previous 6 yards and subtract 3 feet from the remaining 4 feet
Hence:
7 yards 1 foot 1 inch
Which expression is equivalent to |8|+|-7|
Answers
Answer:
8 + 7.
Step-by-step explanation: It is absolute value.
*HELP**NEEDS IT RIGHT NOW*
Without using a calculator, match each expression to the correct point.
Answers
Answer:
a=-2π
b=-17/3
c=-sqrt18
Step-by-step explanation:
eyeball it.
-2π≈-6.28
-17/3 is less than -5 but more than -6, so it's between those 2
-sqrt 18 is between -sqrt 16 and -sqrt 25, so it's a little less than -4
what is equivalent to 7/5y
Answers
Answer:
1.4y
Step-by-step explanation:
Find the number of turns or bumps in the graph of the function f(x) = x² - 25
Answers
Answer:
1 turn
Step-by-step explanation:
this is what the graph would look like:
prove that Cos4x=8Cosx -8Cosx
Answers
I need the answer to
y = -x - 3
y=-x-5
Answers
Answer:
if you're supposed to be solving for x then the top one is x=-y+3 and the bottom is x=-y+5
can someone please help meee
Answers
Answer:
the y intercept is (0,2)
slope = -4
Step-by-step explanation:
from the graph the y intercept is (0,2) and we can consider it as p1
p2 (2,-6)
slope = y2-y1 / x2-x1
= -6 - 2/ 2 -0 = -8/2 = -4
(75 POINTS PLEASE RESPOND ASAP)
Explain how to solve 4x + ^3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answers
Answer:
1.596
Step-by-step explanation:
So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.
[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]
Answer:
x = -1.596
Explanation:
[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]
take log on both sides
[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]
[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]
[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]
[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]
calculate
[tex]\rightarrow \sf x= -1.596322539[/tex]
[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]
A group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet. Each ticket costs 32 dollars , so the debt for one ticket is-32 . The tour company adds a 15 dollar fee for the entire order. Including the fee, which number represents the total debt?
Answers
The number that represents the total debt is 303 if the group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet.
What is debt?
It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
We have:
Each ticket costs 32 dollars, so the debt for one ticket is -$32. The tour company adds a 15-dollar fee for the entire order.
A group of 9 pre-orders 9 tickets for a sightseeing tour.
Total cost of 9 tickets = 9×32 = $288
As this group doesn't have money
The debt for the tickets will be = $288
The tour company adds a $15 fee for the entire order.
The total debt for this tour = $15 + $288 = $303
Thus, the number that represents the total debt is 303 if the group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet.
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