A manufacturing plant is looking at units shipped for a 3-year period. In 2005, the plant shipped 12,500 units. In 2008, the
plant shipped 16,000 units. Find the rate of change of units shipped over the 3-year period.
A. 3,500/
2,008
B. 3,500/
2,005
C. 3,500/3
D. 9,500
Option C - 3500/3
Step-by-step explanation:
Step 1 :
Number of units shipped in the year 2005 = 12,500 units
Number of units shipped in the year 2008 = 16,000 units
Time period = 3 years
We have to determine the rate of change of units over the 3 year period. This is obtained by dividing the difference in units by the time period.
Step 2:
The difference in units over the 3 year period = 16000 - 12,500 = 3500 units.
Hence the required change rate over the 3 year period = 3500/3
Option C is the answer.
What is the algebraic way to solve 2000 (X -0.03)= 6000 by using the dividing each side first method
To solve the equation 2000 (X - 0.03) = 6000, divide both sides by 2000 to get X - 0.03 = 3, and then add 0.03 to each side to find X = 3.03.
Explanation:To solve the algebraic equation 2000 (X - 0.03) = 6000 using the divide each side method, we can follow these steps:
Divide both sides of the equation by 2000 to isolate the term with the variable X.This simplifies the equation to X - 0.03 = 3.Add 0.03 to both sides to solve for X.This gives us X = 3.03 as the solution.Now X has been isolated, and we have found the value that satisfies the equation.
Before lunch, Carol hiked 3 5/8 miles. After lunch, she hiked another 2 7/8 miles. How far did she hike altogether?
6 6/8 or 6 3/4 simplified
Step-by-step explanation:
First, add 5/8 and 7/8
Next, divide the sum of 5/8 and 7/8 (which is 1 4/8)
Lastly, add the wholes and 1 from 4/8
how many solutions does this system of Equations have x-2y=2 y=-2x+5
Answer:
One solution: x=2.4, y=0.2
Step-by-step explanation:
x-2y=2
y=-2x+5
x-2(-2x+5)=2
x+4x-10=2
5x=2+10=12
x=12:5=2.4
y=-2x+5=-2*2.4+5=-4.8+5=0.2
a value of 6000 is increased by 15% find the new value
Answer:
6900
Step-by-step explanation:
[tex] = 6000 \times \frac{115}{100} = 6900[/tex]
Alice has 800 MB of data. Bob has 1500 MB of data. Jack has 750 MB of data. Will it all fit on Alice's 4 GB thumb drive?
Answer:
Ill walk you through
Step-by-step explanation:
How many MBs are in a GB??
Remember that 1000 MB = 1 GB.
Start by adding together all the MB values.
800 MB + 1500 MB + 750 MB = 3050 MB.
Next, convert to GB by dividing by 1000.
3050 MB / 1000 = 3.05 GB
Since 3.05 < 4, YES. It will all fit in Alice's 4 GB thumb drive.
marvin has a standard deck of cards, what is the probability of 5?
Answer: 4/52
Step-by-step explanation:
Because thwre are 4, fives in a normal deck so the probability would be 4/52 not simplifyed
A data set consists of the following data points:
(2,4),(4,7), (5, 12)
The line of best fit has the equation y = 2.5x - 1.5. What does this equation
predict for a value of x = 7?
0
O A. 16
O B. 19
O C. 20.5
O D. 175
0 0 0
Answer: when x=7 the answer is 16
Step-by-step explanation:
9. Jady got a job at Yogurt land. She makes $17 per hour as a store manager. On Friday she worked 6 hours, on Sunday
she worked 4 hours and on Wednesday she worked 5 hours. When she picked up her paycheck her mom reminded her
that she owed her $65 for a pair of shoes she bought her. How much money did she have left after paying back her
mom (before taxes)?
steps ?
Answer:
190$
Step-by-step explanation:
6+4+5=15 (Hours per day she worked)
15*17=255 (The money Jady got from her paycheck)
255-65=190 (The money Jady owes her mom)
Suppose a population of 50 crickets doubles in size every 4 months. How many crickets will there be after 5 years?
1,500 crickets
1,600 crickets
2,000 crickets
1,638,400 crickets
Answer:
Starting population of crickets is 50. It doubles in size every 4 months.
5 years = 60 months
60 : 4 = 15
The equation is:
f ( x ) = 50 * 2^x ( an exponential function )
f ( 15 ) = 50 * 2^15 = 50 * 32,768
f ( 15 ) = 1,638,400
Answer: A ) 1,638,400
Find the area of this parallelogram. Be sure to include the correct unit in your answer
Area of the parallelogram = 96 yd²
Solution:
The formula to calculate area of the parallelogram = Base × Height
Base of the parallelogram = 8 yd
Height of the parallelogram = 12 yd
To find the area of the parallelogram:
Area of the parallelogram = Base × Height
= 8 yd × 12 yd
= 96 yd²
Area of the parallelogram = 96 yd²
Answerrrrrrrr nowwww
Answer:
a is equal to 22 because 11 times 2 is 22
Answer:
A is 22
Step-by-step explanation:
1/2 = 0.5
0.5×22=11
16k + 24, can you show work?
Answer:yes
Step-by-step explanation:
Answer:
k = -1.5
Step-by-step explanation:
Step 1: Solve for k
16k + 24 - 24 = 0 - 24
16k / 16 = -24 / 16
k = -3/2
k = -1.5
Answer: k = -1.5
(Two-Step Equations - Integers)
Sheet 3
1
The bartender of a poolside bar prepares 96 fluid Ounces of mocktail by blending
the juice of cranberries and oranges. He uses three times the amount of cranberry
juice than orange juice to prepare the mocktail. He also adds 24 ounces of lemon
extract. How many fluid Ounces of orange juice was used in all?
Cloubt 1tbe ofroncorn
Answer:
18
Step-by-step explanation:
cranberries, oranges and lemon extracts makes =96 fluid Ounces of mock-tail
i.e cranberries+oranges+lemon extracts=96 fluid Ounces of mock-tail....... (1)
let fluid ounces of orange=xthen fluid ounces of cranberry=3x; \\ because it is three times of orangeand lemon extract is given as 24 ounces.putting these values in (1), we get
[tex]3x+x+24=96[/tex]
[tex]4x+24=96\\4x=96-24\\4x=72\\x=\frac{72}{4}\\ x=18[/tex]
fluid Ounces of orange juice was used in all=18
Final answer:
To find the amount of orange juice used in the mocktail, we set up an equation and solve for 'x'. We find that the bartender used 18 fluid ounces of orange juice in the mocktail.
Explanation:
To find the number of fluid ounces of orange juice used, we need to set up an equation. Let's say the amount of orange juice used is represented by 'x'. According to the problem, the amount of cranberry juice used is three times the amount of orange juice, so it can be represented as '3x'.
We know that the total amount of mocktail prepared is 96 ounces, and the lemon extract added is 24 ounces. So, we can set up the equation: x + 3x + 24 = 96. Simplifying this equation, we get 4x + 24 = 96.
Next, we need to isolate 'x'. Subtracting 24 from both sides of the equation, we get 4x = 72. Dividing both sides by 4, we find that x = 18.
Therefore, the bartender used 18 fluid ounces of orange juice in the mocktail.
what value of x makes the equation true?
x+41=-90
i need help
Answer:
Step-by-step explanation:
x+41=-90 (original problem)
-41 -41 (you must get rid of the common factors by doing the opposite on both sides)
x= -132 (add -90 and -41 to get -132)
Determine the distance around a cherry pie crust with a 7 inch radius. Round to the nearest tenth.
Answer:
The circumference is 43.98
or 44 inches rounded, maybe
Step-by-step explanation:
Averi was trying to factor 4x2 + 20x - 16. She found
that the greatest common factor of these terms was 4
and made an area model:
What is the width of Averi's area model?
Answer:
The width will be [tex]x^{2} +5x-4[/tex]
Step-by-step explanation:
Thinking process:
Let the model be:
[tex]4x^{2} +20x-16[/tex]
factoring out 4 gives:
[tex]4(x^{2} +5x-4)[/tex]
Factorizing the expression in the parentheses gives:
[tex]4(x^{2} +5x-4)[/tex]
Therefore, since the expression in the parentheses cannot be factorized further, the expression is:
[tex]length = 4 units\\width = x^{2} +5x-4[/tex]
The width of the area model is x^2 + 5x - 4
How to determine the width?The area model is given as:
Area = 4x^2 + 20x - 16
Factor out 4 from the expression
Area = 4(x^2 + 5x - 4)
Express as product
Area = 4 * (x^2 + 5x - 4)
4 represents the length.
So, the width of the area model is x^2 + 5x - 4
Read more about areas at:
https://brainly.com/question/24487155
3.) Jada takes out a loan for $6000 to start a business after hig
8% interest for the loan. After 5 years how much interest will be added?
Answer:
$2,400
Step-by-step explanation:
1) lets use the i=prt formula
where i=interest
p=principal
r=rate
t=time
the principal here is $6000(starting amount)
rate is 0.08
and time is 5
so
I=0.08*5*6000
I=2400
you will gain an interest of $2400
If Sarah rents a washer and dryer for $52 per month for 13 months how much will she pay for 13 months?
Answer:
$676
Step-by-step explanation:
52x13= 676
Answer:
She would pay $676
Step-by-step explanation:
What points names the ordered -4 -2
-2x+y=5
-7x+9y=56
I don't know the answer, and I don't understand the material.
Answer:
what do you need to do plz give the question
Step-by-step explanation:
Machine 1 can complete a task in x hours while an upgraded machine (machine 2) needs 9 fewer hours. The plant mana
knows the two machines will take at least 6 hours, as represented by the inequality
Which answer choice includes all solutions to the inequality and identifies which interval(s) contain viable completion time
machine 12
(0.31 U 9.18] both contain viable times for machine 1
(0 3] U9,18]; only (9.18) contains viable times for machine 1
(-00U13,9 UL18,co), no interval contains viable times for machine 1
(-0,0) U(39) U (18,co), but only [18,00) contains viable times for machine 1
Answer:
its B
Step-by-step explanation:
after you find the intervals. you also need to consider that the plant manager knows the two machines will take at least 6 hours, so (0, 3] is taken out of the picture leaving you with B
The correct answer choice is:
(-0,0) U (3,9) U (18,∞), but only the interval [18,∞) contains viable times for machine 1.
Here, we have,
The given inequality represents the condition that the task should take at least 6 hours to complete.
Let's analyze the answer choices:
(0.31 U 9.18] both contain viable times for machine 1:
This answer choice includes the interval (0.31, 9.18], which contains values less than 6.
Therefore, it does not satisfy the condition of at least 6 hours.
(0, 3] U (9,18]; only (9, 18] contains viable times for machine 1:
This answer choice includes the intervals (0, 3] and (9, 18].
Both of these intervals contain values less than 6, so they do not satisfy the condition of at least 6 hours.
(-∞,0) U (13,9) U (18,∞), no interval contains viable times for machine 1:
This answer choice does not include the interval (0, 3] where viable times for machine 1 exist.
(-0,0) U (3,9) U (18,∞), but only [18,∞) contains viable times for machine 1:
This answer choice includes the intervals (0, 3] and (18,∞), which contain viable times for machine 1. However, the interval [18,∞) specifically represents viable completion times for machine 1.
Therefore, the correct answer is (-0,0) U (3,9) U (18,∞), but only the interval [18,∞) contains viable times for machine 1.
To learn more about the inequality visit:
brainly.com/question/24372553
#SPJ4
Order this fraction from largest to smallest
1/4, 1/2, 1/5, 2/3, 1/6
For the same numerator, bigger denominators mean smaller fractions (if everything's positive). 2/3 is bigger than all the other ones , which are 1/2 or less.
Answer: 2/3, 1/2, 1/4, 1/5, 1/6
1220000 scientific notation
Answer:
1.22 x [tex]10^{6}[/tex]
Step-by-step explanation:
1,220,000 would be...
1.22 x 10^6
Answer:
you could do this 1.22E+6 or 1.22 x 10⁶
Step-by-step explanation:
Simplest form of 7/10 and 2/10
Answer:
7/10 can't be simplified, 2/10->1/5
Step-by-step explanation:
7/10 cannot be simplified as 7 and 10 don't have any common factors other than 1
2/10 can be simplified by a factor of 2 to get 1/5
Answer:
Simplest form of 7/10=7/10
Simplest form of 2/10=1/5
Step-by-step explanation:
7/10 is 7/10 because it cannot be simply none has the same factors.
If A varies directly as b and A=6, when b=1/3, find the equation that relates A and b.
Answer:
A = 18b
Step-by-step explanation:
A = kb
6 = k(⅓)
k = 6×3
k = 18
A = 18b
Answer:
a = 18b
Step-by-step explanation:
Given that a varies directly as b then the equation relating them is
a = kb ← k is the constant of variation
To find k use the condition that a = 6 when b = [tex]\frac{1}{3}[/tex] , thus
k = [tex]\frac{a}{b}[/tex] = [tex]\frac{6}{\frac{1}{3} }[/tex] = 18
a = 18b ← equation of variation
The sum of Rodney and his sister is 31 his sister is five years less than three times Rodney’s age what is the difference in age between Ronnie and his sister
Answer: The difference in their ages is 13.
Step-by-step explanation: We shall start by assigning letters to represent the age of each one of them, that is the unknown variables. So, we shall call Rodney’s age r, and his sister’s age we shall call t. If the sum of Rodney and his sister’s age is 31, then we can write this as an expression,
r + t = 31
Also three times Rodney’s age can be written as 3 times r, or simply put, 3r. So five years less than three times Rodney’s age is equal to 3r - 5. Hence his sister’s age is equal to 3r - 5, or simply put,
t = 3r - 5
What we now have is a pair of simultaneous equations
r + t = 31 ————(1)
t = 3r - 5 ————(2)
We shall use the substitution method here. From equation (2), t = 3r - 5. So we shall substitute for the value of t into equation (1).
r + t = 31 now becomes
r + 3r - 5 = 31
4r - 5 = 31
Add 5 to both sides of the equation
4r -5 + 5 = 31 + 5
4r = 36
Divide both sides of the equation by 4
r = 9.
That means Rodney’s age is 9.
If from equation (1) r + t = 31, we can now insert the value of r in order to find t.
r + t = 31
9 + t = 31
Subtract 9 from both sides of the equation
t = 22.
That means his sister’s age is 22 while Rodney’s age is 9.
Therefore the difference in age between Rodney and his sister is
22 - 9 which equals 13.
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s?
units
Answer: Line s = 17 units
Step-by-step explanation: Please refer to the attached diagram.
The triangle ACD is drawn and labeled such that line BD extends from point D and forms a right angle at point D. A careful observation shows that we now have two right angled triangles. One is DAB and the other is DCB. The unknown side ‘s’ lies on triangle DAB, hence we shall use the available dimensions in DAB. Line AD or a, is the hypotenuse (side facing the right angle). We can now apply the Pythagoras theorem since we have been given the other two sides.
The theorem states that,
AD^2 = DB^2 + AB^2
AD^2 = 15^2 + 8^2
AD^2 = 225 + 64
AD^2 = 289
Add the square root sign to both sides of the equation
AD =17.
Therefore, s measures 17 units
The line BD drawn perpendicular to side AC forms two right triangles with
the side s being of the hypotenuse side.
The value of s is 17Reasons:
The given parameters are presented ;
The given triangle = ΔACD
The points on the line BD are; Point B on side AC and point D
Line BD forms a right angle
Line AD = s
Length AB = 8
Length BC = 5
Line BD = 15
According to Pythagorean theorem, we have;
[tex]\overline{AD}[/tex]² = [tex]\overline{BD}[/tex]² + [tex]\overline{AB}[/tex]²
Which gives;
[tex]\overline{AD}[/tex]² = 15² + 8² = 289
[tex]\overline{AD}[/tex] = √289 = 17
Therefore;
[tex]\overline{AD}[/tex] = s = 17
Learn more about Pythagorean Theorem here:
https://brainly.com/question/18929869
What is the perimeter of an isosceles trapezoid whose base 1 is 39ft, base 2 is 27ft and height is 12ft
Step-by-step explanation:
Given one is an isosceles trapezoid. Hence its non-parallel sides are equal.
In order to find the Perimeter of trapezoid, we need to find the length of non-parallel sides
Length of non-parallel sides can be obtained using Pythagoras theorem as given below:
[tex]Length \: of \: non-parallel \: sides \\ = \sqrt{ {(diff. \: of \: bases)}^{2} + ({height)}^{2} } \\ = \sqrt{ {(39 - 27)}^{2} + {(12)}^{2} } \\ = \sqrt{ {12}^{2} + {12}^{2} } \\ = \sqrt{2 \times {12}^{2} } \\ = 12 \sqrt{2} \\ = 12 \times 1.414 \\ = 16.968 \\ = 16.97 \: ft \\ \\ perimeter \: of \: trapezoid \\= 39 + 27 + 2 \times 16.97 \\ = 66 + 33.94 \\ = 99.94 \: ft[/tex]
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots
are located
x2 + 3x -4 = 0
Answer:
x = 1 and x = -4
Step-by-step explanation:
Step 1: Factor and find the roots
x^2 + 3x - 4 = 0
(x - 1)(x + 4)
x - 1 + 1 = 0 + 1 and x + 4 - 4 = 0 - 4
x = 1 and x = -4
Answer: x = 1 and x = -4
Graph Below: