Answer:
a) 1/5 bucket = 1 gallon
b) 8.4 buckets = 1 barrel
c) 5376 fl oz per barrel
Step-by-step explanation:
a) From the given information, 1 bucket = 5 gallons. This means 1/5 of a bucket is 1 gallon.
b) From the given information, 8.4 buckets = 1 barrel. This seems to be in the form that the question is asking for. If the question was asking how many barrels were in a bucket the answer would be 1/8.4 barrels = 1 bucket.
c) From the previously determined conversion factors, we can take ounces to barrels by converting barrels down to gallons.
1/8.4 barrels = 1 bucket; 1/5 bucket = 1 gallon; 1 gallon = 128 fluid ounces
We need to set up a series of fractions that use these factors:
[tex]\frac{128 fl oz}{1 gallon}*\frac{1 gallon}{1/5 buckets}*\frac{1 bucket}{1/8.4 barrels}[/tex]
These fractions can be simplified to [tex]\frac{128 fl oz}{1 gallon}*\frac{5 gallon}{1 bucket}*\frac{8.4 buckets}{1 barrel}[/tex]
Multiply the fractions: 5376 fl oz per barrel
(Note that the units cancel out in the fractions so that only fluid ounces per barrel are left.)
What property states that changing the order of two or more terms does what to the value of the sum
Answer: Commutative property
Max w = 5y1 + 3y2
s. a.
y1 + y2 ≤ 50
2y1 + 3y2 ≤ 60
y1
, y2 ≥ 0
The maximum value of the objective function is 330
How to maximize the objective function?The given parameters are:
Max w = 5y₁ + 3y₂
Subject to
y₁ + y₂ ≤ 50
2y₁ + 3y₂ ≤ 60
y₁ , y₂ ≥ 0
Start by plotting the graph of the constraints (see attachment)
From the attached graph, we have:
(y₁ , y₂) = (90, -40)
Substitute (y₁ , y₂) = (90, -40) in w = 5y₁ + 3y₂
w = 5 * 90 - 3 * 40
Evaluate
w = 330
Hence, the maximum value of the function is 330
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During the basketball season, Morgan made 3 times as many 2-point baskets as she made 3-point baskets and free throws combined. If she made 14 free throws and eight 3-point baskets, How many 2-point baskets did she make. And simplify your answer.
Answer:
123 save some for me
Step-by-step explanation:
:0
Answer: 123
Step-by-step explanation: I did the math- lol-
Evaluate the expression shown below and write your answer as a fraction in simplest form. 16/11 − 12/1
Answer:
-10 6/11
Step-by-step explanation:
16/11−12/1=16/11+−12/1=16/11+−132/11=16+−132/11=−116/11
-116/11 = −10 6/11
Ryan is on a game show. He will choose a box to see if he wins a prize. The odds in favor of Ryan winning a prize are 5/7.
Find the probability of Ryan winning a prize.
The probability of Ryan winning a prize would be 0.71.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Ryan is on a game show. He will choose a box to see if he wins a prize.
The odds in favor of Ryan winning a prize are 5/7.
P(Ryan wins a prize) = 5/7 = 0.71
Thus, the probability of Ryan winning a prize would be 0.71.
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The drama club meets in the school auditorium every 8 days, and the choir meets there every 6 days. If the groups are both meeting in the auditorium today, then how many days from now will they next have to share the auditorium?
You need to find the least common multiple of 8 and 6.
[tex]8=2^3\\6=2\cdot3\\\\\text{lcm}(8,6)=2^3\cdot3=24[/tex]
Therefore, the answer is 24 days.
Distance (km)
a.
b.
c.
d.
400
300
200
100
Travel Rate
(3, 318)
(1, 106)
(0, 0)
1
(2,212)
111 km/h
106 km/h
102 km/h
97 km/h
2 3
Time (h)
Answer:
good and right and keep trying your best
The product of three consecutive integers is 30 times the smallest of the three
integers. Find the two possible sets of integers that will satisfy this condition.
AnswEr :
Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .
⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]
⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.
[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]
Therefore ,
When , x = 2 ,
First Integer : x , 2 ,Second Integer : ( x +1 ) , 3 & Third Integer : ( x +2 ) = 4 .When , x = –7 ,
First Integer : x , – 7 ,Second Integer : ( x +1 ) , – 6 & Third Integer : ( x +2 ) = – 5 .Answer:
Hi,
Step-by-step explanation:
If the "is" means is equal to
Let's say a-1, a, a+1 the 3 consecutive integers.
[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]
[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]
The two sets are : (0,1,2) and (4,5,6).
Place the indicated product in the proper location on the grid. (4a + x)(a-x)
Step-by-step explanation:
4a(a-x)+x(a-x)
[4a]2-4ax+ax-(x)2
(4a)2-3ax-(x)2
I need this asap plsss help me!!!!!
If the diameter is d = 8, then we divide that in half to get the radius of r = 4.
If the radius is r = 9, then we double it to get the diameter of d = 18
The formulas are:
radius = diameter/2diameter = 2*radiusI'll let you determine the others.
Answer:
Step-by-step explanation:
Diameter is twice the radius. d = 2*r
Radius is half the diameter r = d÷2
1) d = 8
r = 8÷ 2
r = 4
2) r = 9
d = 2*r
= 2*9
d = 18
3) r = 24
d = 24*2 =48
4) d = 36
r = 36 ÷2 = 18
5) d = 52
r = 52÷2 = 26
if f(x)=2x-1 and g(x)=x^2-4, what is g(f(x))
Answer:
4x^2 - 4x - 3
Step-by-step explanation:
f(x) = 2x - 1
g(x) = x^2 - 4
g(f(x)) = ?
[substitute the x of g(x) with f(x)]
g(x) = x^2 - 4
g(f(x)) = (2x - 1)^2 - 4
[solve]
[binomial * binomial = quadratic equation]
[use FOIL method (first, outer, inner, last)]
g(f(x)) = (2x - 1)(2x - 1) - 4
g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4
[combine like terms]
g(f(x)) = 4x^2 - 2x - 2x + 1 - 4
g(f(x)) = 4x^2 - 4x - 3
Five times the sum of a number and -23.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We need to translate "five times the sum of a number and -23" into an algebraic expression.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Can you see the word "sum" there? It tells us to add.So in this case we should add a number (let it be x) and -23:
[tex]\star~\large\pmb{x+-23}[/tex]
Which is the same thing as
[tex]\star~\large\pmb{x-23}[/tex]
Now we multiply this little expression by 5, which gives us
[tex]\star~\large\pmb{5(x-23)}[/tex]
The parentheses around the expression indicate that we multiply 5 by the entire expression, and not just one term.
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
D = {f, g, k}
L = {a,f,j}
Find the intersection of D and L.
Find the union of D and I.
Answer:
Step-by-step explanation:
D∩L={f}
D∪L={a,f,g,j,k}
The line segment located in the circle below is the circle’s ____________
Pi
Area
Radius
Diameter
Circumference
Find the present value, using the future value formula and a calculator. Future value is $6,000 in two years at 9.5% simple interest. Round your answer to the nearest cent (two decimal places). Enter only the number without $ sign.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6000\\ P=\textit{original amount deposited}\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ t=years\dotfill &2 \end{cases} \\\\\\ 6000=P[1+(0.095)(2)]\implies \cfrac{6000}{1.19}=P\implies 5042.02\approx P[/tex]
Sine is opposite divided by hypotenuse. So the sine of an angle times the hypotenuse is the length of the opposite side. What is the length of the side opposite a 30 degree angle for a right triangle with a hypotenuse of 20 meters?
Answer:
10 m
Step-by-step explanation:
opposite = sin30° × 20 = [tex]\frac{1}{2}[/tex] × 20 = 10 m
Find the missing angle
120 & 30
y = [???]
Answer:
z = 30
Step-by-step explanation:
All angles of a triangle add up to 180:
z + 120 + 30 = 180
z + 150 = 180
z = 180 - 150
z = 30
Is the graph increasing, decreasing, or constant?
Answer:
increasing to the certain point
Step-by-step explanation:
Potato head
Which best tells how heavy a dog might be?
A dog is shown.
A.
100 g
B.
25 kg
C.
25 g
D.
100 kg
Answer:
B
Step-by-step explanation:
A dog might be around
b) 25 kgs
CAN SOMEONE PLEASE PLEASE HELP ME?? I’LL GIVE YOU FREE EASY POINTS AND IT’S ONLY 4 QUESTIONS. JUST MAKE SURE YOU GIVE THE RIGHT ANSWERS PLSS. THE PICTURE IS ABOVE IF ANYBODY NEEDS TO SEE IT!
Answer:
Step-by-step explanation:
1. To find f(0.5), substitute the x value in the function f(x) with 0.5
f(x) = 30x + 5
f(0.5) = 30*0.5 + 5
= 15 + 5
= 20
At 0.5 gigabytes of data used, the cost is $20
2) g(x) = 10x + 20
g(0.5) = 10*0.5 + 20
= 5 + 20
= 25
At 0.5 gigabytes of data used, the cost is $ 25.
3) f(x) = 50
30x + 5 = 50
Subtract 5 from both sides
30x = 50 - 5
30x = 45
Divide both sides by 30
x = 45/30
x = 1.5
If she chooses plan 'f', she could use 1.5 gigabytes.
g(x) = 50
10x + 20 = 50
10x =50- 20
10x = 30
x = 30/10
x = 3
If she chooses plan 'g', she could use 3 gigabytes.
4) Function 'g' would be better for a $50 monthly budget as she could get more gigabytes than function 'f'
how many different sample size of n=3 can be drawn from the population
I'll focus on question 10 only. Let me know if you need me to answer the others.
We have the population with this set of numbers: {2,4,6,8,10}
There are 5 values in that set.
Now consider having slots labeled A,B and C to represent the three placeholders for the numbers.
For slot A, we have 5 choicesSlot B has 5-1 = 4 choicesSlot C has 5-2 = 3 choicesThere are 5*4*3 = 20*3 = 60 permutations and 60/(3*2*1) = 60/6 = 10 combinations.
Therefore, we have 10 different subsamples of 3 items.
Answer: Choice C) 10One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know that the perimeter of the rectangle is 58 meters
Answer:
22 meters
Step-by-step explanation:
Let x = width of the rectangle
Let y = length of the rectangle
Equation 1
If the length of the rectangle is 6 meters shorter than four times the width then:
⇒ y = 4x - 6
Equation 2
Perimeter of a rectangle = 2(width + length)
If the perimeter is 58 inches, then:
⇒ 58 = 2(x + y)
Solve by substitution
Substitute Equation 1 into Equation 2 and solve for x:
⇒ 58 = 2(x + 4x - 6)
⇒ 58 = 2(5x - 6)
⇒ 58 = 2 · 5x - 2 · 6
⇒ 58 = 10x - 12
⇒ 58 + 12 = 10x -12 + 12
⇒ 10x = 70
⇒ 10x ÷ 10 = 70 ÷ 10
⇒ x = 7
Substitute found value of x into Equation 1 and solve for y:
⇒ y = 4(7) - 6
⇒ y = 28 - 6
⇒ y = 22
Conclusion
The dimensions of the rectangle are:
width = 7 meterslength = 22 metersTherefore, the length of the longer side is 22 meters
The length of the longer side is 22 meters.
Let, one side of the rectangle is x meters.
According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is 58 meters:
58 = 2 * (x + 4x - 6)
Now, let's solve for x:
58 = 2 * (5x - 6)
58 = 10x - 12
Add 12 to both sides:
58 + 12 = 10x
70 = 10x
Now, divide both sides by 10 to isolate x:
x = 70 / 10
x = 7
So, one side of the rectangle is 7 meters.
Now, we can find the length of the longer side:
Length of the longer side = 4x - 6
Length of the longer side = 4 * 7 - 6
Length of the longer side = 28 - 6
Length of the longer side = 22 meters
Therefore, the length of the longer side is 22 meters.
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Find the domain and range of the function:
--√√5-x-3
The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]
How to determine the domain and the range?The function is given as:
[tex]f(x) = \sqrt{5 - x} - 3[/tex]
The radicand must be at least 0.
So, we have:
[tex]\sqrt{5 - x} \ge 0[/tex]
Square both sides
[tex]5 - x \ge 0[/tex]
Rewrite as:
[tex]5 \ge x[/tex]
Solve for x
[tex]x \le 5[/tex]
This means that the domain is [tex]x \le 5[/tex]
For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]
This means that:
[tex]f(x) \ge 0 - 3[/tex]
[tex]f(x) \ge - 3[/tex]
Hence, the range of the function is [tex]f(x) \ge - 3[/tex]
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Solve this for me please
Answer:
a=11,b=7 Is the correct answer
Please mark me as brainliest
Answer:
a = 11 and b = 7
Step-by-step explanation:
Multiply numerical values 5 x (-4) then add exponents of like terms x⁷(x⁴) = x¹¹ then y²(y⁵) = y⁷
I need it done asap please help before 12:00
Which of these steps will eliminate a variable in this system?
4x - 9y = 8
2x + 3y = 24
A. Multiply the first equation by 3. Then subtract the second equation from the first.
B. Multiply the second equation by 2. Then add the equations.
C. Multiply the second equation by 2. Then subtract the second equation from the first.
D. Multiply the second equation by 3. Then subtract the second equation from the first.
Answer:
option c is correctStep-by-step explanation:
for any variable to be eliminated in a simultaneous equation, the one of the coefficients must be the same in the two equations. and:
FOR OPTION A
if the first equation is multiplied by 3 , we will be having 12x-27y= 24 as the new equation 1 and since the cofficient of y or x are different in equation 1 and 2, no variable can be eliminated.
FOR OPTION B
if the second equation is multiplied by 2, our new equation 2 will be 4x+6y= 48. here, the cofficient of x in the two equations are now the same but since we're going to add, 4x+4x = 8x which does not eliminate x
FOR OPTION C if the second equation is multiplied by 2, our new equation 2 becomes 4x + 6y= 48 and if we subtract, 4X-4x= 0 so we have eliminated X ( option C is correct)FOR OPTION D
if the second equation is multiplied by three, our new equation 2 becomes 6x+9y= 72 and subtracting,-9y -9y= -18y which does not eliminate y
Work out the coordinate of R
Answer:
The problem is with the arrangement of the ratios
PQ is the whole line but PR is a part of it only so you need QR to the ratio of PR
Answer:
[tex]\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]
Step-by-step explanation:
Coordinates of the extreme points of the segment are P(-4, -1) and Q (6, 11)[tex]\implies x_1= -4,\:y_1=-1,\:x_2=6,\:y_2=11[/tex]PQ = 4PR (Given)......(1)PQ = PR + RQ.....(2)-> 4PR = PR + RQ [From (1) and (2)]-> 4PR - PR = RQ-> 3PR = RQ-> PR/RQ = 1/3-> PR : RQ = 1 : 3This means point R divides segment PQ in the ratio 1 : 3.-> m : n = 1 : 3Now, coordinates of point R can be obtained by the section formula for internal division, which is given below:[tex]R=\bigg(\frac{mx_2+nx_1}{m+n},\:\frac{my_2+ny_1}{m+n}\bigg)[/tex][tex]\implies R=\bigg(\frac{1(6)+3(-4)}{1+3},\:\frac{1(11)+3(-1)}{1+3}\bigg)[/tex][tex]\implies R=\bigg(\frac{6-12}{4},\:\frac{11-3}{4}\bigg)[/tex][tex]\implies R=\bigg(\frac{-6}{4},\:\frac{8}{4}\bigg)[/tex][tex]\implies\huge{\red{ R=\bigg(-1.5,\: 2\bigg)}}[/tex]
In the arithmetic sequence {13, 6,-1,-8,...}, what is the common difference?
Explanation:
Pick any term. Subtract off the previous one to find the common difference.
term2 - term1 = 6-13 = -7term3 - term2 = -1-6 = -7term4 - term3 = -8-(-1) = -8+1 = -7And so on. You only need to pick one of those to show as your steps to your teacher. However, doing all three subtractions is a good way to get practice in seeing how we have an arithmetic sequence. The common difference must be the same each time.
We subtract 7 from each term to get the next term, i.e. we add -7 to each term to get the next one.
how many solutions does 9x+5=9x+7
Answer:
There are 0 solutions to this problem because it cannot be re-arranged logically enough to come to a new conclusion.
Answer:
0
Step-by-step explanation:
If we try to solve this question, we get no solutions:
First we subtract 5 from both sides :
9x = 9x + 2
Now we subtract 9x from both sides :
0 = 0 +2
0 = 2 ❌
This is why this equation has no solutions
Hope this helped and have a good day
SOMEONE
HELP MEE
What are the y-intercept and the asymptote of g(x) = 2x – 3?
The y-intercept of g(x) is (0, -3) and there are no asymptotes for g(x).
The function is given as g(x) = 2x - 3 and we need to find the y-intercept and the asymptote of this function g(x).
What are the y-intercept and asymptotes of a given function?Y-intercepts of a given function are the points on the y-axis that the given function passes through.
In y-intercept points we always have x=0.
Asymptotes are straight lines on the graph that meets the given function as it moves towards infinity.
Asymptotes occur only when the given function is a rational function or when one term of the function approaches zero as one term approaches infinity.
Find the y-intercept of g(x).
We have,
g(x) = 2x - 3
Since x = 0.
we get,
g(x) = 0 - 3
g(x) = -3 or y = -3
Thus the y-intercept of g(x) is (0, -3)
Find the asymptotes of g(x).
We see that g(x) is not a rational function and when x approaches infinity g(x) does not approach zero.
Hence we can say that g(x) has no asymptotes.
The y-intercept and asymptotes of g(x) are (0, -3) and no asymptotes.
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To find the y-intercept of g(x), we set x = 0 and solve for y:g(0) = 2^0 - 3 = -2Therefore, the y-intercept of g(x) is (0, -2).To find the asymptote of g(x), we take the limit of g) as x approaches negative or positive infinity:lim x→-∞ 2^x - 3 = -3 (the asymptote is y = -3 as x approaches negative infinity)lim x→+∞ 2^x - 3 = +∞ (the graph of g(x) goes arbitrarily high as x approaches positive infinity, so there is no horizontal asymptote)Therefore, the asymptote of g(x) is y = -3.