Answer: 7/6
Step-by-step explanation:
Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.
Hope this Helps :)
how many 3-letter passwords can be made using the letters a through z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
Given that;
We need to get 3 letter passwords using a through z by two case;
(a) If repetition is allowed
(b) If repetition is not allowed
Case (a): If repetition is allowed.
The total number of letters from a through z are 26
⇒ The total number of 3 letter passwords made are;
= 26³
= 26 * 26 * 26
= 17576
If repetition is allowed then the required passwords generated are 17576.
Case (b): If repetition is not allowed.
⇒ The total number of 3 letter passwords made are;
= 26 * 25 * 24
= 15600
If repetition is not allowed then the required passwords generated are 15600.
Therefore,
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
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Mathematical induction
Yes this question can be proven by mathematical induction
What do you mean by induction in mathematics?
For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.
Here, n ≥ 1
1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)
We employ the idea of Sigma here.
S/1/r(r + 1) { r = 1 to n }
Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }
put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2
put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3
put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4
........................................................... put r = n 1/n - 1/(n + 1)
after adding
Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)
= 1 - 1/( n +1) = n/( n +1)
Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).
so it proved
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A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the dividend 3 years later? Round to the nearest cent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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What is the name of the bolded part of this shape?
Answer:
A right-angled triangle
A probablity experiment is conducted in which the sample space of the experiment is S= (5. 6, 7, 8,9, 10, 11, 12, 13, 14, 15. 16}, event F={8,9,10,11,12,13), And event G = {12, 13, 14, 15} Assume that each outcome is equally likely. List the outcomes in F For G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G.
A. For G= {__}
(Use a comma to separate answers as needed)
Using the general addition rule, p(F or G) = 0.667.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Let,
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
F = {8, 9, 10, 11, 12, 13}
G = {12, 13, 14, 15}
n(S) = number of elements in set S are 12.
n(F) = 6
n(G) = 4
n(F and G) = common elements in F and G = 2
n(F or G) = n(F) + n(G) - (F and G)
n(F or G) = 6 + 4 - 2
n(F or G) = 8
Now, using the general addition rule,
P(F or G) = P(F) + P(G) - P(F and G)
Here,
P(F) = n(F)/n(S) = 6/12 = 1/2
P(G) = n(G)/n(S) = 4/12 = 1/3
P(F and G) = n(F and G)/n(S) = 2/12 = 1/6
⇒ P(F or G) = 1/2 + 1/3 - 1/6
= 5/6 - 1/6
= 4/6
⇒ P(F or G) = 0.667
Hence, using the general addition rule, P(F or G) = 0.667.
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Hayden and Jamie completed 20 math problems together. Jamie completed 2 more than twice the number that Hayden completed. Let p represent the number of math problems Hayden completed.Write an equation that can be used to find the number of math problems that Jamie completed.
Answer:
[tex]p+p+2=20[/tex]
Step-by-step explanation:
This is what my math teacher told us, so I don't know try this.
Step-by-step explanation:
p + j = 20
j = 2p + 2 --> -2p + j = 2
[tex] \binom{1 \: 1}{ - 2 \: 1} \: \binom{20}{2} = \binom{p}{j} [/tex]
1. in an experiment in which a six-sided dice is rolled twice, what is the probability that 4-dots side appears in at least one roll?
Answer:
11/36 = 0,305556 = 30,5556%
Step-by-step explanation:
5/6 * 5/6 = 25/36
36/36 - 25/36 = 11/36
Bobby bought 3 T-shirts at the mall
and a pair of pants for $16 at the
clothing store. All together he spent $28
for the clothes. How much was each
shirt?
Answer: $4
Step-by-step explanation: we know he spent 28 dollars in total and 16 of those was on a pair of pants so we can subtract 16 from 28 to get 12
we also know he bought 3 shirts in total and because 12/3=4 each shirt must have cost 4 dollars.
We can check the answer by combining the price of the shirts (12)
with the price of the pants (16) because 12+16=28 we know the cost of each shirt has to be $4.
Answer:
Each shirt was 4 dollars.
Step-by-step explanation:
28 - 16 = 12. 12 divided by 3 = 4.
Write an equation for the nth term of the arithmetic sequence 4, 7, 10, 13,
The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1
How to find nth term of arithmetic sequence?Arithmetic sequence can be represented with the formula as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..
a = 4
d = 7 - 4 = 3
Therefore,
aₙ = 4 + (n - 1)3
aₙ = 4 + 3n - 3
aₙ = 3n + 4 - 3
aₙ = 3n + 1
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What is (-81.7)+346.2 Pls show ur work
Answer: 264.5
Step-by-step explanation:
(-81.7) + 346.2
346.2 - 81.7 = 264.5
the sum of the number of factors of n and n2 is 34. how many such distinct numbers such that n<150 exist?
The total 18 numbers such that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34
Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.
Factors in total (2+1)*(1+1)=6
It will have 2- 4 times and 3-2 times for 122.
15 total factors of 5*3
Situation 1: N = xy
attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.
Regarding N-x-2 and Y-3 timings.
There are a total of (2+1)*(3+1)=12 factors.
Situation 2
Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.
Consequently, 17+1 = 18 factors in total.
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What is an
equation of the line that passes through the points (6, 0) and (3, 4)?
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
What are the different forms of straight lines ?
The following information about the straight line is required if we wish to obtain the equation for it.
1. The y-intercept and slope
2. Two-point and slope
3. Two things.
4. the intersection of the x- and y-axes
the straight line that passes through (6,0) and (3,4).
The equation can be expressed in a point-slope form which is ,
y/x-6=4/-3
∵ -3y=4(x-6)
Hence,
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
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Factor the polynomial by factoring out the Greatest Common Factor
The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
We are given an algebraic expression:
18y^4 + 24y^3 + 6y^2
We need to factorize by factoring out the Greatest Common Factor.
In the given algebraic expression, we can see that;
6 is the Greatest Common Factor of 18, 24, and 6.
y^2 is the Greatest Common Factor of y^4, y^3 and y^2.
So, we will take the common 6y^2 from the given expression;
18y^4 + 24y^3 + 6y^2
= 6y^2 (3y^2 + 4y + 1)
So, option A is correct.
Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The quadratic equation 8x² + 16x + 3 = 0 can be solved by using the quadratic formula.
The given quadratic equation is : 8x² + 16x + 3 = 0
Comparing this equation with ax² + bx + c = 0 we get :
a = 8 , b = 16 and c = 3
Now we will use the quadratic formula:
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
Now we will substitute the values in this formula to find the values of x that satisfy the quadratic equation.
[tex]{\displaystyle x={\frac {-16\pm {\sqrt {16^{2}-4\times8\times3}}}{2\times8}}}\\\\{\displaystyle x={\frac {-16\pm {\sqrt {160}}}{16}}}\\\\[/tex]
The values for x that satisfy the equation are the roots or zeros of both expressions on the left-hand side of the equation. In a quadratic problem, there can only be two possible solutions.
A problem is said to have a double root if there is only one solution. One real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options.
Hence the values of x are : [tex]-\frac{4-\sqrt{10}}{4}[/tex] and [tex]-\frac{4+\sqrt{10}}{4}[/tex].
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I need help asap please now please !!!!!!!!!!!
can somebody please solve this if you send picture please send good quality
The equation of the trend line is y = -0.36x + 12.6. Use the equation of the trend line to predict the wind chill for a wind speed of 58 mi/h. Round your answer to the nearest degree. The wind chill at 58 mi/h is °F.
Answer: -8
Step-by-step explanation:
Assuming that [tex]x[/tex] is the wind speed and [tex]y[/tex] is the wind chill, we can set [tex]x=58[/tex].
[tex]y=-0.36(58)+12.6 \approx -8[/tex]
A biker travels down the street at 15 m/s. It
takes 60 seconds to travel to the end of the
street. How long was the street?
The street was 900m long when the speed is 15m/s and, the time is 60 seconds.
What is meant by distance, speed, and time?To calculate speed, divide the distance traveled by the time it took to complete the voyage, so speed = distance divided by time. To determine the distance, multiply the speed by the passage of time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.
Distance divided by time equals speed. Distance = time * speed
To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.
Given,
Speed of the biker who travels down the street=15m/s
Time taken=60seconds
Distance=?
We know that,
Distance=Speed× Time
Distance=15×60
Distance=900m
Therefore, the street was 900m long
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find the slope of each line
Answer:
A. 5/3
Step-by-step explanation:
The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point 3 units to the left.
We can model this using rise/run
Rise = 5
Run = 3
5/3
Question 2
Which set of rational numbers is arranged from least to greatest?
O
O
O
O
-3.5, 4, 2, 3
11
-3.5, 4,3,2
113
2, 3.
1
4.-3.5
11
4.3.2, -3.5
11
10 pts
Answer:
The second option.
Step-by-step explanation:
We can figure this out by going down each option and checking if it works and is arranged from least to greatest.
The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.
This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.
The second option provides the numbers -3.5, -1/4, 1/3, 2.
This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.
If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.
At a real estate agency, an agent sold a house for $307,000. The commission rate is 5.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The commission that thereal estate agency gets is $16885.
The commission that the agent gets is $76750
How to calculate the commission?The selling price for a house = $ 307,000
The commission rate for real estate agency = 5.5 %
The commission rate for the agent = 25 %
So, the commission which real estate agency gets:
= 5.5 % of $307,000
= 0.055 × $ 307,000
= $16885
The commission which agent get:
= 25% of $ 382,000
= 0.25 × $ 307,000
= $76750
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Solve each system by substitution.
4x + y = 19
6x + 7y=1
Step-by-step explanation:
that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.
finally we use one of the original equations to solve for the second variable.
4x + y = 19
so, that gives us
y = 19 - 4x
we use that now in the second equation :
6x + 7(19 - 4x) = 1
6x + 133 - 28x = 1
-22x + 133 = 1
-22x = -132
22x = 132
x = 6
now, let's use e.g.
4x + y = 19
4×6 + y = 19
24 + y = 19
y = -5
Which expression represents "10 subtracted from the quotient of 3 and a number"?
A 3n - 10
B 10 - 3n
C 10 - 3 over n
D 3 over n - 10
The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Let the number be n
The expression will be:
= 3/n - 10
Therefore, the correct option is D.
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Michael is dressing up as maggie this year. he is making his costume. michael needs 8.6 yards of furry fabric. if the fabric costs $1.82 per yard, how much will michael be spending on fabric?
Michael will be spending the cost of $ 15.652 on the Furry Fabric.
Given, that Michael is dressing up as Maggie,
He is making his costume and he needs 8.6 yards of furry fabric
The fabric costs $1.82 per yard.
So, as he needs 8.6 yards of fabric and each yard of that fabric costs him $1.82.
1 yard of Furry Fabric = $1.82
8.6 yards of Furry Fabric = $1.82 × 8.6
8.6 yards of Furry Fabric = $ 15.652
Hence, Michael will be spending the cost of $ 15.652 on the fabric.
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The local craft fair charges the vendors a flat rate of $15 plus $10 for each hour that they splend at the fair. If the vendor owed $65, how many hours did he remain at the craft fair?
Answer:
5 hours
Step-by-step explanation:
$65 - $15 = $50
$50/$10 = 5
please help me with this
Answer: final answer = 3/8
Step-by-step explanation:
it says 1/8 + 1/4. before you can add them you have to make sure that both fractions have the same denominator first you have to make both of the bottom denominators the same so its 1/8+2/8.
1/8+2/8=3/8
Zachary purchased a computer for $1200 on a payment plan.6 months after he purchased the computer, his balance was $420. 8 months after he purchased the computer, his balance was $160. What is an equation that models the balance y after x months?
The equation that models the balance y after x months is: y = -130x + 1200.
How to find the equation?Month Balance
0 1200
6 420
8 160
Hence,
m = (y2 - y1)/(x2 - x1)
First coordinate:
m = (420 - 1200)/(6 - 0)
m = -780 /6
m = -130
Second coordinate;
m = (160 - 420)/(8 - 6)
m = -260/2
m = -130
The formula for equation in slope intercept is
y = mx + c
where;
m = slope
c = y-intercept
So, equation is;
y = -130x + 1200
Therefore the equation is y = -130x + 1200.
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a 39-inch by 104-inch piece of cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding up the flaps on each side. what size square should be cut from each corner to get a container with the maximum volume? enter the area of the square and do not include any units in your answer.
According to the solving the area of the square is 68.0625.
What's a square's area?As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.
According to the given data:The box formed after cutting the square from each corner will have the dimensions as,
length = 104 - 2x, width = 39 - 2x, height = x.
∴ volume of the box = length × width × height
∴ v = (104 - 2x)(39 - 2x)(x) -----(i)
∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])
∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])
∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
let f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x -----(ii)
To, find x for which f(x) is maximum,
⇒we should apply second derivative test ,
According to this test, first we should find critical points at which f'(x) = 0.
then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.
∴ let us consider, f'(x) = 0.
now, f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056. -----(iii)
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)
⇒ f'(x) = 0.
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0
⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a ; where a = 3, b = -143, c = 1014.
∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3
∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.
∴ x = [tex]\frac{143 + 91}{6}[/tex] , x = [tex]\frac{143 - 91}{6}[/tex]
⇒ x = 39, 8.25
the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.
Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]
∴ Area = 68.0625
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Conrad read a 180180180-page book cover to cover in a single session, at a constant rate. It took him 666 hours.
Let yyy represent the number of pages left to read after ttt hours.
Which of the following information about the graph of the relationship is given?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Slope and xxx-intercept
(Choice B)
B
Slope and yyy-intercept
(Choice C)
C
Slope and a point that is not an intercept
(Choice D)
D
xxx-intercept and yyy-intercept
(Choice E)
E
yyy-intercept and a point that is not an intercept
(Choice F)
F
Two points that are not intercepts
The information about the graph of the relationship that is given is: E. y-intercept and a point that is not an intercept.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear, quadratic, trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
What is the slope-intercept form?Mathematically, the slope-intercept form of a straight line is generally modeled or represented by this mathematical expression;
y = mx + c
Where:
x represents a data point i.e the number of hours.y represents a data point i.e the number of pagesm represents the slope.c represents the y-intercept i.e total number of pages.In this context, we can reasonably infer and logically deduce that the total number of pages (y-intercept) which is equal to 180 is an information that was provided, as well as the number of hours (666 hours), which represents a data point on the x-coordinate of the graph.
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marrisa bought 3 packages of balloons and 4 packages of party favors for a total of 14.63. Ray bought 2 packs of balloons and 4 packs of party favors for a total of 16.03. find the price of a pack of balloons and the price of a pack of party favors
The price of a pack of balloons is 4. 39
The price of a pack of party favors is 0. 36
How to determine the valuesWe have that;
Let the cost of balloons be x
Let the cost of party favors by y
From the information given, we have that;
3x + 4y = 14. 63 (1)
2x + 4y = 16. 03 (2)
Now, let's make 'x' the subject from equation (1)
x = 14. 63 - 4y/ 3 (3)
Substitute in equation (2)
3( 14. 63 - 4y/ 3) = 16. 03
expand the bracket
43. 69 - 12y /3 = 16. 03
cross multiply
43. 69 - 12y = 48. 09
collect like terms
- 12y = - 4. 4
make 'y' the subject
y = 0. 36
substitute in equation (3)
x = 14. 63 - 4(0. 36)/ 3
x = 13. 1/ 3
x = 4. 39
Hence, the prices are 4. 39 and 0. 36 respectively.
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