Answer:
[tex] - \frac{2[1 - x]}{3} = g[f(x)] \\ \\ \frac{3x}{2 - x} = f[g(x)][/tex]
Step-by-step explanation:
They are not.
For the g[f(x)] function, you substitute ³/ₓ ₋ ₁ from the f(x) function in for x in the g(x) function to get this:
[tex] \frac{2}{ \frac{3}{x - 1}} [/tex]
Then, you bring x - 1 to the top while changing the expression to its conjugate [same expressions with opposite symbols]:
[tex] - \frac{2[1 - x]}{3}[/tex]
You could also do this [attaching another negative would make that positive].
For the f[g(x)] function, ²/ₓ from the g(x) function for x in the f(x) function to get this:
[tex] \frac{3}{ \frac{2}{x} - 1}[/tex]
Now, if you look closely, ²/ₓ is written as 2x⁻¹, and according to the Negative Exponential Rule, you bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM NEGATIVE TO POSITIVE:
[tex] \frac{3x}{2 - x} [/tex]
When this happens, x leaves the two and gets attached to the three, and 1 gets an x attached to it.
I am joyous to assist you anytime.
Elvira and Aletheia live 3.1 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira 12 hour and Aletheia 23 hour to walk to the coffee shop. Aletheia's speed is 0.6 miles per hour slower than Elvira's speed. Find both women's walking speeds.
Answer:
Elvira's speed: 3.0 mphAletheia's speed: 2.4 mphStep-by-step explanation:
Let "e" and "a" represent the speeds of Elvira and Aletheia, respectively. Then the total distance they cover is ...
distance = speed × time
(1/2)e + (2/3)a = 3.1
And the relationship between their speeds is ...
e - a = 0.6
__
To solve this system, we can double the first equation and subtract the second to get ...
2(1/2e +2/3a) -(e -a) = 2(3.1) -(0.6)
7/3a = 5.6 . . . . . . . . . . simplify
a = (3/7)(5.6) = 2.4 . . . multiply by 3/7
e = a +0.6 = 3.0 . . . . . Elvira's speed is 0.6 mph more than Aletheia's
Elvira's walking speed is 3.0 miles per hour; Aletheia's is 2.4 miles per hour.
Tomatoes are 5 for $2.keith spent $8 on tomatoes. How many tomatoes did he get
Answer:
20
Step-by-step explanation:
8/2 = 4
4 * 5 = 20
A map of a rectangular park has a length of 4 inches and a width olo and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. a. What is the actual area of the park? Show how you know.
Answer:
The actual area of the park is 21,600 miles square.
Step-by-step explanation:
Step 1: Calculate the area of the park
Area of rectangle = Length x width
Length = 4 inches
Width = 6 inches
Scale factor is given as, 1 inch = 30 miles.
So, converting the length and width in miles by using the scale factor, we get
Length = 4 * 30 = 120 miles
Width = 6 * 30 = 180 miles
The formula of finding the area of an rectangle is:
Area = length x width
By putting the values in equation, we get
Area = 120 x 180
Area = 21,600 miles square
Therefore, the actual area of the park is 21,600 miles square.
PLEASEEEE
In a school of 2000 students, the ratio of teachers to students is 3:80.
Some teachers join the school and the ratio changes to 1:20.
Find the number of teachers who joined the school.
Answer:
The answer to your questions is: 25 new teachers
Step-by-step explanation:
Data
# of students = 2000
ratio = 3:80 teachers to students
New teachers = ?
Process
I suggest to use rule of three to solve this problem
3 teachers ---------------- 80 students
x ---------------- 2000 students
x = (2000 x 3) / 80 = 75 teachers
Number of initial teachers = 75
The ratio change to 1:20
1 teacher ------------------- 20 students
x ------------------- 2000 students
x = (2000 x 1) / 20
x = 100 teachers
Number of new teachers = 100 - 75 = 25
Mr. Johnson has his newspaper delivered every day. He determines the probability the newspaper is on his front porch is 0.64. The rest of the time he finds the newspaper somewhere on his lawn. What is the probability that Mr. Johnson finds his newspaper on his lawn?
Answer:
Step-by-step explanation:
Probability of getting the newspaper on his front porch = P(A) = 0.64
Probability of finding the newspaper on his lawn = P(B) =? (We don't know, this is what we have to find.)
Total probability = 1
Formula, P(A) + P(B) = 1
Let's put all values in this formula,
0.64 + P(B) = 1
P(B) = 1 - 0.64
P(B) = 0.36
Thus, the probablity that Mr. Johnson finds his newspaper on his lawn is 0.36 or 36%.
Many states have programs for assessing the skills of students in various grades. The Indiana Statewide Testing for Educational Progress (ISTEP) is one such program. In a recent year, 76,531 tenth-grade Indiana students took the English/language arts exam. The mean score was 572 and the standard deviation was 51. Use the fact that the ISTEP scores are approximately Normal, N(572, 51). Find the proportion of students who have scores between 500 and 650.
Answer:
P ( 500<X<650 ) = 0.8577
Step-by-step explanation:
Since μ=572 and σ=51 we have:
P ( 500<X<650 ) = P ( 500−572< X−μ<650−572 )
[tex]\RightarrowP ( \frac{500-572}{51} < \frac{x-\mu}{\sigma} < \frac{650-572}{51})[/tex]
⇒ P ( 500<X<650 ) = P ( −1.41<Z<1.53 )
Now, Using the standard normal table to conclude that:
P ( −1.41< Z <1.53 ) = 0.8577
Final answer:
Approximately 85.77% of Indiana tenth-grade students scored between 500 and 650 on the English/language arts ISTEP exam, as calculated by converting the given scores to z-scores and finding the proportion within the standard normal distribution.
Explanation:
To find the proportion of Indiana tenth-grade students who scored between 500 and 650 on the English/language arts exam, given that the ISTEP scores are approximately normal with a mean (μ) of 572 and a standard deviation (σ) of 51, we can use the standard normal distribution.
First, we'll convert the scores to z-scores using the formula z = (X - μ) / σ where X is the score.
For X=500, the z-score would be (500 - 572) / 51 ≈ -1.41.For X=650, the z-score would be (650 - 572) / 51 ≈ 1.53.Then we'll look up these z-scores in a standard normal distribution table or use a calculator with normal distribution functions to find the proportion of students whose scores fall between these two z-scores. The table or calculator will provide us with the areas under the curve to the left of each z-score.
Let's assume the area to the left of z=-1.41 is approximately 0.0793 (7.93%) and to the left of z=1.53 is approximately 0.937 (93.7%). To find the proportion between 500 and 650, we'll subtract the smaller area from the larger one:
Proportion = Area to the left of z=1.53 - Area to the left of z=-1.41 = 0.937 - 0.0793 = 0.8577 or 85.77%
Therefore, approximately 85.77% of the students scored between 500 and 650 on the ISTEP English/language arts exam.
An automobile accelerates from rest at 1.7 m/s 2 for 22 s. The speed is then held constant for 29 s, after which there is an acceleration of −5.8 m/s 2 until the automobile stops. What total distance was traveled? Answer in units of km.
After 22 s, the car has velocity
[tex]v=\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)=36.4\dfrac{\rm m}{\rm s}[/tex]
In this time, it will have traveled a distance of
[tex]\dfrac12\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)^2=411.4\,\mathrm m[/tex]
Over the next 29 s, the car moves at a constant velocity of 36.4 m/s, so that it covers a distance of
[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(29\,\mathrm s)=1055.6\,\mathrm m[/tex]
so that after the first 51 s, the car will have moved 1467 m.
After the 29 s interval of constant speed, the car's negative acceleration kicks in, so that its velocity at time [tex]t[/tex] is
[tex]v(t)=36.4\dfrac{\rm m}{\rm s}+\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)t[/tex]
The car comes to rest when [tex]v(t)=0[/tex]:
[tex]36.4-5.8t=0\implies t=6.3[/tex]
That is, it comes to rest about 6.3 s after the first 51 s. In this interval, it will have traveled
[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(6.3\,\mathrm s)+\dfrac12\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)(6.3\,\mathrm s)^2=114.2\,\mathrm m[/tex]
so that after 57.3 s, the total distance traveled by the car is 1581.2 m, or about 1.6 km.
How do you solve this? 5/14 divided by 4/7??
Answer:
The answer to your question is: 5/8
Step-by-step explanation:
data
5/14 divided by 4/7
Process
[tex]\frac{5}{14\\}[/tex]
[tex]\frac{4}{7}[/tex]
multiply 5 and 7 and the result is the numerator
multiply 14 and 4 and the result is the denominator
(5 x 7) / ( 14 x 4)
35 / 56
5 / 8 simplify both numerator and denominator
Find the intersection of the three sets: A = {–4, 3, 10}, B = {3, 6, 10, 15}, C = {–4, 10, 20}. {–4, 10} {10} {–4, 3, 6, 10, 15, 20} {–4, 3, 10}
Answer:
The intersection is 10
Step-by-step explanation:
You just have to look at them and see what number is in all the sets.
Answer:
the answer is 10
A committee organizing a marathon has 14 jugs of water and 20 jugs of sports drink. The committee would like to set up a number of refreshment stations along the marathon course, with the same combination of jugs of water and jugs of sports drink at each station, with no beverages left over. What is the greatest number of refreshment stations that can be set up?
Answer:
2 stations with 7 of jugs of water and 10 of sports drink in each station
Step-by-step explanation:
Lets start with the jugs of water, to have the same amount in each station you need have a number of station that divide for 14 the remainder or "left over" equal to 0, or in other words multiple of 14 in the interval 1 to 14
multiples of 14 : 1, 2, 7 and 14
so you can have
1 station with 14 jugs of water
2 stations with 7 jugs of water each
7 stations with 2 jugs of water each
14 station with 1 jugs of water each
Now we need to do the same for the 20 jugs of sports drink
multiple of 20 in the interval 1 to 20: 1,2,4,5,10 and 20
so you can have:
1 station with 20 jugs of sports drink
2 stations with 10 jugs of sports drink
4 stations with 5 jugs of sports drink
5 station with 4 jugs of sports drink
10 station with 2 jugs of sports drink
20 stations with 1 jugs of sports drink
So we have that both cases, water and sport drinks have coincidence of 1 or 2 stations, and the maximum of both is 2 stations with 7 jugs of water and 10 of sports drink each
Final answer:
To determine the greatest number of refreshment stations that can be set up, we find the greatest common divisor (GCD) of 14 jugs of water and 20 jugs of sports drink, which is 2. Therefore, the committee can set up 7 refreshment stations with 1 jug of water and 2 jugs of sports drink at each.
Explanation:
The committee has 14 jugs of water and 20 jugs of sports drink and wants to set up the greatest number of refreshment stations along the marathon course without any beverages left over. To find this solution, we need to determine the greatest common divisor (GCD) of the two quantities of jugs because each station must have the same combination of jugs of water and sports drink.
First, list the factors of each number:
Factors of 14: 1, 2, 7, 14
Factors of 20: 1, 2, 4, 5, 10, 20
The largest common factor is 2, which means the refreshment stations can have a combination of 1 jug of water and 2 jugs of sports drink. So, the committee can set up 7 refreshment stations (14 jugs of water / 2 per station = 7 stations; and 20 jugs of sports drink / 2 per station = 10 stations, but limited by the smaller number of jugs of water).
Today a typical family of four spends $897.20/ month for food. If inflation occurs at the rate of 3%/ year over the next 6 years, how much should the typical family of four expect to spend for food 6 years from now?
Answer:
1071.30 per month
Step-by-step explanation:
The multiplier each year is 1 + .03 = 1.03. After 6 years, the cost has been multiplied by that factor 6 times, so has been multiplied by 1.03⁶ ≈ 1.194052.
$897.20 × 1.194052 ≈ $1071.30
The typical family of four should expect to spend $1,056.27 per month for food six years from now.
1. Calculate the inflation factor using the formula: [tex]\( (1 + \text{inflation rate})^{\text{number of years}} \).[/tex]
- Inflation rate = 3% or 0.03
- Number of years = 6
- Inflation factor = [tex]\( (1 + 0.03)^6 = 1.191016 \)[/tex]
2. Multiply the current monthly food expenditure by the inflation factor to find the expected expenditure six years from now.
- Current expenditure = $897.20/month
- Expected expenditure = $897.20 × 1.191016 = $1,056.27/month
Therefore, the typical family of four should expect to spend $1,056.27 per month for food six years from now if inflation occurs at a rate of 3% per year.
Can anyone help me with these two problems? I found the distance to one. Please, assignment is due tonight. Thank you.
Answer:
32 mi @ N77°E
Step-by-step explanation:
The route of travel forms legs of a right triangle, so the final distance (d) from harbor can be found using the Pythagorean theorem:
d² = 28² +16² = 784 +256 = 1040
d = √1040 ≈ 32.249 . . . miles
___
The angle (α) added to the original N47°E bearing can be found using the fact that opposite and adjacent sides are given. So, they can tell you the tangent of the angle:
tan(α) = 16/28
α = arctan(16/28) ≈ 29.74°
Then the bearing to the final position is ...
47° +29.74° = 76.74° . . . . . east of north
Rounded to whole numbers, the final position from harbor is ...
32 miles @ N 77° E
Consider the three functions below.
f(x) = Negative StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript x g(x) = StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript negative x h(x) = Negative StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript negative x
Which statement is true?
The range of h(x) is y > 0.
The domain of g(x) is y > 0.
The ranges of f(x) and h(x) are different from the range of g(x).
The domains of f(x) and g(x) are different from the domain of h(x).
Answer:
The range of g(x) is y > 0
The ranges of f(x) and h(x) are different from the range of g(x)
Step-by-step explanation:
we have
[tex]f(x)=-(\frac{6}{11})^{x}[/tex]
[tex]g(x)=(\frac{6}{11})^{-x}[/tex]
[tex]h(x)=-(\frac{6}{11})^{-x}[/tex]
Using a graphing tool
see the attached figure
Verify each statement
case A) The range of h(x) is y > 0.
The statement is false
The range of h(x) < 0
case B) The range of g(x) is y > 0. (Note the statement is The range of g(x) is y > 0 instead of The domain of g(x) is y > 0)
The statement is true (see the attached figure)
case C) The ranges of f(x) and h(x) are different from the range of g(x)
The statement is true (see the attached figure)
Because
The ranges of f(x) and h(x) are y < 0
and
The range of g(x) is y > 0
case D) The domains of f(x) and g(x) are different from the domain of h(x)
The statement is false
The domain of the three functions is the same
Answer:
OPTION C.The ranges of f(x) and h(x) are different from the range of g(x).
Step-by-step explanation:
If we have the curve y = sqrt(x), find the y value and the slope of the curve when x = 36. y = 6 Correct: Your answer is correct. slope = 1/12 Correct: Your answer is correct. Hence, find the equation of the tangent line to the curve at x = 36, writing your answer in the form y = mx + c. What are the values of m and c?
m =
c =
Answer:
Equation of tangent of curve at x = 36:
1)[tex]y = \frac{x}{12} + 3[/tex]
2[tex]y = \frac{-x}{12} - 3[/tex]
Step-by-step explanation:
We are given the following information:
[tex]y = \sqrt{x}[/tex]
Value of curve when x = 36:
[tex]y = \sqrt{36} = \pm 6[/tex]
Thus, [tex]y = \pm6[/tex], when x = 6.
Slope of curve, m =
[tex]\frac{dy}{dx} =\frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}[/tex]
At x = 36,
slope of curve =
[tex]\frac{1}{2\times \sqrt{36}}\\\\m=\frac{1}{12},\frac{-1}{12}[/tex]
Equation of tangent of curve at x = 36:
[tex](y-y_1) = m(x-x_1)[/tex]
[tex]= (y-(\pm 6)) = (\pm\frac{1}{12} )(x - 36)[/tex]
Thus, equation of tangents are:
1)
[tex](y-6) = \frac{1}{12}(x-36)\\12(y-6) = x-36\\y = \frac{x}{12} + 3[/tex]
Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{1}{12}[/tex] and [tex]c =3[/tex]
2)
[tex](y+6) = \frac{-1}{12}(x-36)\\12(y+6) = -x+36\\y = \frac{-x}{12} - 3[/tex]
Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{-1}{12}[/tex] and [tex]c =-3[/tex]
Final answer:
The equation of the tangent line at x = 36 for the curve y = sqrt(x) is y = 1/12x + 3, found by using the slope of 1/12 and solving for the y-intercept c, which is 3.
m = 1/12
c = 3
Explanation:
To find the equation of the tangent line at x = 36 for the curve y = sqrt(x), we first identified that y = 6 when x = 36 and computed the slope of the curve, which is 1/12 at x = 36.
Using the slope-intercept form of a line, y = mx + c, where m is the slope, and c is the y-intercept, we can substitute m = 1/12 and the point (36, 6) to solve for c.
Substituting into the slope-intercept equation gives us 6 = (1/12)\(36) + c.
Solving for c, we find that the y-intercept c = 3.
Thus, the equation of the tangent line is y = 1/12x + 3.
solve for m.
4+|7-m|=5
Answer:
m= 6 or m= 8. I'm not sure if its multiple choice, but that's what I got.
Answer:
m=6,8
Step-by-step explanation:
I am a number between 7 000 000 and 8 000 000 all my digits are odd all the digits in my thousands period are the same all the digits in my units period are the same the sum of my digits is 31 what number am i ?
Answer:
Any of 7,111,777 or 7,333,555 or 7,555,333 or 7,777,111.
Step-by-step explanation:
The first digit must be 7. The sum of the unknown digits is then 31-7 = 24. Since this represents 3 pairs of digits (a thousands period digit and a units period digit), each pair must total 24/3 = 8.
There are two ways that odd numbers can total 8: 1+7 = 3+5 = 8. Since there is no restriction on the digits other than they must be the same in any period and they must be odd, there are 4 ways the 2 pairs of digits can be arranged into a number:
7,111,7777,333,5557,555,3337,777,111The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take. A. Solve the equation for x.
Answer:
[tex]x=(c-60)/85[/tex]
Step-by-step explanation:
we have
[tex]c=85x+60[/tex]
Solve for x
That means -----> isolate the variable x
subtract 60 both sides
[tex]c-60=85x+60-60\\c-60=85x[/tex]
Divide by 85 both sides
[tex](c-60)/85=85x/85\\(c-60)/85=x[/tex]
Rewrite
[tex]x=(c-60)/85[/tex]
A salesperson obtained a systematic sample of size 25 from a list of 500 clients. To do so, he randomly selected a number from 1 to 20, obtaining the number 13. He included in the sample the 13th client on the list and every 20th client thereafter. List the numbers that correspond to the 25 clients selected.
A.. 25, 45.......500
B. 20, 33,.., 332
C. 13, 33, , 488
D. 13, 33, ..., 493
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
First term = 13
Increase each time = 20
Number of clients = 25
So, it forms an arithmetic progression:
So, 25 th term would be
[tex]a_{25}=a+(n-1)d\\\\a_{25}=13+(25-1)\times 20\\\\a_{25}=13+24\times 20\\\\a_{25}=13+480\\\\a_{25}=493[/tex]
Hence, list would look like 13,33,............493.
Therefore, Option 'D' is correct.
An equation of the secant line containing (4, h(4)) and (6, h(6)) is
Answer:
y= (h(6)-h(4))/2x +C
Where C=-2*h(6)+3*h(4)
Step-by-step explanation:
The secant line is the line that meets a function (in this case h(x) ) in two points, so we have to apply the ecuation of a straigt line that meets two points:
y-y1 = (y2-y1)/(x2-x1) * (x-x1)
In this case X1=4 , x2=6, y1 = h(4) and y2= h(6)
So
y-h(4)= 1/2 (h(6)-h(4)) * (x-4)
y-h(4)= 1/2 (h(6)-h(4)) x- 2 *(h(6)-h(4))
y-h(4)= 1/2 (h(6)-h(4)) x- 2 (h(6) + 2h(4))
y= 1/2 (h(6)-h(4)) x- 2 h(6) + 2h(4) + h(4)
y= 1/2 (h(6)-h(4)) x- 2 h(6) + 3h(4)
Good Luck!
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1.Solve for t.
3t + 35=6
Enter your answer in the box.
t =
Answer:
3t + 35 = 6
subtract 35 from both the sides of the equation
3t + 35 - 35 = 6-35
3t = -29
t = - 29/3
Step-by-step explanation:
Answer:
-29/3
Step-by-step explanation:
3t+35=6
3t=6-35
3t=-29
t=-29/3
PLEASE I BEG U NOW!!
£130 is divided between Henry, Gavin & Jim so that Henry gets twice as much as Gavin, and Gavin gets three times as much as Jim. How much does Henry get?
Answer:
The answer to your question is: Henry gets £ 78
Step-by-step explanation:
Data
Henry = H
Gavin = G
Jim = J
Henry + Gavin + Jim = £ 130
H = 2G
G = 3J
Process
Write an equation in terms of G
H + G + J = 130
2G + G + G/3 = 130
Solve it for G
3( 2G + G + G/3 = 130)
6G + 3G + G = 390
10G = 390
G = 390 / 10
G = £39
H = 2G = 2(39)
H = £78
J = G/3
J = 39/3
J = £13
Final answer:
By setting up and solving algebraic equations, we find that Henry receives £78, which is twice the amount that Gavin receives and six times the amount that Jim receives from the total sum of £130.
Explanation:
Let's solve the problem by denoting Jim's share of the money as x. According to the problem, Gavin gets triple the amount of money that Jim gets, which means Gavin gets 3x. Henry gets twice as much as Gavin, so he gets 2(3x) or 6x. The total amount of money is £130 and the sum of their shares is x + 3x + 6x = 10x. Setting up the equation:
10x = £130,
we find that x, Jim's share, is £130/10 = £13. Gavin's share is 3 times Jim's: 3 × £13 = £39, and Henry's share is 6 times Jim's: 6 × £13 = £78. So Henry gets £78.
a linear system in three variables has no solution. Your friend concludes that it is not possible for two of the three equations to have any points in common. is your friend correct? Explain your reasoning.
Answer:
He is correct.
Step-by-step explanation:
Because a linear system in three variables means that they have solutions if the all three have points in common in R3 space. But, in the case that they don't have any solution mean the opposite, they don't have points in common in R3 space.
In a linear system, variables must be related through common points. So, graphically, you should draw intersecting geometrical places in order to show the intersections, wich are the common results or points that are the solutions of the linear system.
A linear system of equation in three variables has no solution is the correct statement.
What is linear equation?" Linear equation is defined as the equation whose variables with highest degree one."
According to the question,
Given statement,
A linear system of equation in three variables has no solution.
Verification:
Consider a example of linear system of equation with three variables
[tex]2x-4y +z=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)[/tex]
[tex]8x-2y+ 4z=7 \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]
[tex]-4x+y -2z=-14\ \ \ \ \ \ \ \ \ \ (3)[/tex]
Solve linear equation to get the solution
Multiply [tex](3)[/tex] by [tex]2[/tex] and add it to [tex](2)[/tex],
[tex]\ \ 8x-2y+ 4z=7\\\\-8x+2y-4z =-28[/tex]
we get,
[tex]0x+0y + 0z = -21[/tex] which is not possible and has no solution.
Hence, linear system of equation has no solution is the correct statement.
Learn more about linear equation here
brainly.com/question/11897796
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Sarah has 2/3 gallon of blue paint and 7/12 gallon of red paint. If she has a total of 2 1/8 gallons of paint, how many gallons are neither red nor blue?
The Dulac Box plant produces 500 cypress packing boxes in two-10 hour shifts. Due to higher demand, Dulac has decided to operate three eight-hour shifts instead. Dulac is now able to produce 600 boxes per day. What has happened to production:a. It has increased by 50 sets/shiftb. It has increased by 20 percentc. It has increased by 37.5 sets/hrd. It has decreased by 8.3 percente. It has decreased by 9.1 percent.
Answer:
Production has increased 20/day
Step-by-step explanation:
In the first scenario production is 500/day and productivity 25 set/hour. After the changes, production is 600/day and 25 set/hour.
So productivity remains the same, nevertheless, as there are more productive hours per day, production raises, in this case the can be calculated as (New Production-Old Production)/Old Production=(600-500)/500=100/500=0.2=20%.
As productivity remains the same, you do not ge more sets/shift, as shifts are shorter (8 instead of hours, so you get 200/shift instead of 250/shift). The rest of the option is false as productivity remains constant
If the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets and the theater took in $584, how many of each ticket were sold?
Answer:
The number of child tickets sold was 43 and the number of adult tickets sold was 20
Step-by-step explanation:
Let
x ----> the number of child tickets sold
y ----> the number of adult tickets sold
we know that
[tex]x=3y-17[/tex] -----> equation A
[tex]8x+12y=584[/tex] ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (43,20)
see the attached figure
therefore
The number of child tickets sold was 43 and the number of adult tickets sold was 20
Answer:
Number of child tickets sold = 43
Number of adult tickets sold = 20
Step-by-step explanation:
Let the number of child ticket be c and number of adult ticket be a,
Given that the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets,
c = 3a - 17
3a - c = 17 ----------------------eqn 1
The theater received $584
That is
8 c + 12 a = 584 ----------------------eqn 2
eqn 2 /4
2 c + 3 a = 146 ----------------------eqn 3
eqn 3 - eqn 1 gives
2 c + 3 a - (3a - c) = 146 - 17
3 c = 129
c = 43
Substituting in eqn 1
3 x a - 43 = 17
3a = 60
a = 20
Number of child tickets sold = 43
Number of adult tickets sold = 20
Genghis Khan organized his men into groups of 10 soldiers under a "leader of 10." Ten "leaders of 10" were under a "leader of 100." Ten "leaders of 100" were under a "leader of 1000." *(a) If Khan had an army of 10,000 soldiers at the lowest level, how many men in total were under him in his organization? (b) If Khan had an army of 5763 soldiers at the lowest level, how many men in total were under him in his organization? Assume that the groups of 10 should contain 10 if possible, but that one group at each level may need to contain fewer.
Genghis Khan's army organizational structure can be used to calculate the total number of men under him: For an army of 10,000 soldiers, the total is 11,110 men; for an army of 5,763 soldiers, it is 6,404 men.
To solve both parts of the student's question, we use the military organizational structure implemented by Genghis Khan that is based on the 'decimal' system. We start with the lowest level groups of 10 soldiers and move up in orders of magnitude (10, 100, 1,000, and 10,000).
Part (a): Army of 10,000 soldiers
Groups of 10: There are 1,000 groups of 10 in an army of 10,000 soldiers.
Leaders of 10: Each group of 10 has 1 leader, resulting in 1,000 leaders of 10.
Groups of 100: 1,000 leaders of 10 make up 100 groups of 100 (because 1,000/10 = 100).
Leaders of 100: There are 100 leaders of 100.
Groups of 1,000: 100 leaders of 100 make up 10 groups of 1,000 (because 100/10 = 10).
Leaders of 1,000: There are 10 leaders of 1,000.
Adding it all together: 10,000 soldiers + 1,000 leaders of 10 + 100 leaders of 100 + 10 leaders of 1,000 = 11,110 total men under the command of Khan for an army of 10,000.
Part (b): Army of 5,763 soldiers
Groups of 10: There are 576 full groups of 10 and 1 incomplete group (with 3 soldiers), resulting in 577 groups.
Leaders of 10: There are 577 leaders of 10.
Groups of 100: 577 leaders of 10 make up 57 full groups of 100 and 1 incomplete group (with 7 leaders of 10), resulting in 58 groups.
Leaders of 100: There are 58 leaders of 100.
Groups of 1,000: 58 leaders of 100 make up 5 full groups of 1,000 and 1 incomplete group (with 8 leaders of 100), resulting in 6 groups.
Leaders of 1,000: There are 6 leaders of 1,000.
Adding it all together: 5,763 soldiers + 577 leaders of 10 + 58 leaders of 100 + 6 leaders of 1,000 = 6,404 total men under the command of Khan for an army of 5,763 soldiers.
Which is the graph of f(x) = Square root of x?
On a coordinate plane, a parabola opens up with a vertex at (0, 0).
On a coordinate plane, an absolute value graph starts at (0, 0) and goes up through (2, 4).
On a coordinate plane, a parabola opens to the right with a vertex at (0, 0).
On a coordinate plane, an absolute value graph starts at (0, 0) and goes up through (4, 2).
Answer:
Third option given
Step-by-step explanation:
On a coordinate plane, a parabola opens to the right with a vertex at (0, 0).
use the following x values to plot the associated y values on the x-y plane:
If x = 0, then [tex]y=\sqrt{0} =0[/tex]
If x = 1, then [tex]y=\sqrt{1} =1[/tex]
If x = 4, then [tex]y=\sqrt{4} =2[/tex]
If x = 9, then [tex]y=\sqrt{9} =3[/tex]
Join the points and you will find a branch of a parabola opening to the right.
Answer:
The Answer is D
Step-by-step explanation:
on e2020 its the last graph
Colton and Gage were building a castle together. Colton was 5 times as fast at building the castle than Gage. If it takes 120 blocks to build the castle, how many blocks did Colton build on the castle?
Answer:
100 blocks.
Step-by-step explanation:
Let x represent number of blocks built by Gage.
We have been given that Colton was 5 times as fast at building the castle than Gage, so number of blocks built by Colton would be [tex]5x[/tex].
We are also told that it takes 120 blocks to build the castle. Since Colton and Gage were building a castle together, so number of blocks built by both will be equal to 120.
[tex]x+5x=120[/tex]
[tex]6x=120[/tex]
[tex]\frac{6x}{6}=\frac{120}{6}[/tex]
[tex]x=20[/tex]
Number of blocks built by Colton: [tex]5x=5\cdot 20=100[/tex].
Therefore, Colton had build 100 blocks.
Select all of the following that are equivalent to 1/8. 0.125 0.18 12.5% 1.25%
Answer:
Hi, my friend! The answer to this questions are "0.125" and "12.5%"
Step-by-step explanation:
First, if you divide 1 by 8 using a calculator, you will see that the result will be 0.125. Also, the option 12,5% is correct because de symbol "%" means "divided by 100". If you check in the calculator, 12.5 divided by 100 will also be 0.125.
Hoping to be clear! Good luck!
Final answer:
Only 0.125 and 12.5% are equivalent to the fraction 1/8. This is because they both reflect a '125-like' number pattern which is crucial when identifying representations of 1/8 in decimal or percentage form.
Explanation:
The fraction 1/8 is equivalent to a few different representations in decimal and percentage forms.
To identify which options among 0.125, 0.18, 12.5%, and 1.25% are equivalent to 1/8, we should look for a number pattern resembling '125' as it indicates a connection to the fraction 1/8 or its reciprocal nature.
So, 0.125 is exactly 1/8 as a decimal, and 12.5% represents 1/8 in percentage form because 12.5% is 12.5 parts per 100, which can be equated to 125 parts per 1000, resembling the multiplication of 1000 by the reciprocal of 8, that is 0.125.
Therefore, the options 0.125 and 12.5% are equivalent to 1/8.
Jon’s picture frame is 6 inches high by 5 inches wide. He wants to know what other size frames he can use if he enlarges the photo by using the same relative proportions for length and width.
How can Jon find the sizes of other frames?
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and left 5 to find the next frame size, and then keep the same rate to find other points.
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.
Jon can plot the ratio of 6 to 5 on a graph (6, 5), then move right 6 and down 5 to find the next frame size, and then keep the same rate to find other points.
Jon can plot the ratio of 6 to 5 on a graph (6, 5), then move right 5 and up 6 to find the next frame size, and then keep the same rate to find other points.
Answer:
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.
Step-by-step explanation:
A line from the origin to the point (5, 6) has a slope of 6/5. To find other points on the same line, one would need to continue to rise 6 units for each run of 5 units to the right.
The only answer choice that appropriately matches (x, y) values to rise/run values is the one shown above.
_____
Comment on this answer
The slope of the line described in this answer is 6/5, which seems appropriate for a frame that is 6 inches high and 5 inches wide. However, I would call this a plot of the ratio 6 to 5, rather than the ratio 5 to 6.
Answer:
Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.
i hope this helps!