area = L x w
60 = 12 x w
w=60/12 = 5
300 = 12 x w
w = 300/12 = 25
so B is the correct answer
Answer:
Option B
[tex]5 \leq w \leq 25[/tex]
Step-by-step explanation:
Let
L------> the long of the cardboard piece
W-----> the width of the cardboard piece
The area of cardboard piece is equal to
[tex]A=L*W[/tex]
In this problem we have
[tex]L=12\ in[/tex]
so
[tex]A=12W[/tex]
[tex]f(W)=12W[/tex]------> equation A
[tex]f(W)\geq 60\ in^{2}[/tex] ------> inequality B
[tex]f(W)\leq 300\ in^{2}[/tex] ------> inequality C
Substitute equation A in the inequality B
[tex]12W\geq 60\ in^{2}[/tex]
[tex]W\geq 60/12[/tex]
[tex]W\geq 5\ in[/tex]
Substitute equation A in the inequality C
[tex]12W\leq 300\ in^{2}[/tex]
[tex]1W\leq 300/12[/tex]
[tex]1W\leq 25\ in[/tex]
The domain for the function f(W) is equal to the interval------> [tex][5,25][/tex]
Travis traveled 320 miles in 5 hours. What is his unit rate of speed in miles per hour? _____ miles per hour
The unit rate of speed in miles per hour is 64 miles per hour if Travis traveled 320 miles in 5 hours.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
Travis traveled 320 miles in 5 hours.
The distance d = 320 miles
Time is taken t = 5 hours
As we know, the change in values of a dependent variable with respect to the independent variables.
The unit rate of speed in miles per hour = 320/5
The unit rate of speed in miles per hour = 64 miles per hour
Thus, the unit rate of speed in miles per hour is 64 miles per hour if Travis traveled 320 miles in 5 hours.
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Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $14,500 in 1982 and $65,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S
Final answer:
To articulate the linear equation for yearly sales S, we calculate the slope from the two provided data points and use the slope-intercept form, ultimately deriving the equation S = 10200x + 14500.
Explanation:
To find the equation giving yearly sales S, we can use the two data points: sales were $14,500 in 1982 and $65,500 in 1987. With x = 0 representing 1982, the two points are (0, 14500) and (5, 65500). We can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which is the change in sales over the change in time.
So, m = (65500 - 14500) / (5 - 0) = 51000 / 5 = 10200. This means the sales are increasing at a rate of $10,200 per year.
Now, we can use the slope and one point to write the linear equation in the slope-intercept form, which is Y = mx + b, where b is the y-intercept. Since when x = 0, Y = 14500, we know that b = 14500. Therefore, our final equation for yearly sales S is S = 10200x + 14500.
I need help please!!
show six
ways to add 2,3,4
Answer and Explanation:
Given : Numbers 2,3,4.
To find : Show six ways to add the numbers?
Solution :
As there are three numbers so arrangement of these numbers are as follow by changing there positions,
[tex]2+3+4=9[/tex]
[tex]2+4+3=9[/tex]
[tex]3+2+4=9[/tex]
[tex]3+4+2=9[/tex]
[tex]4+2+3=9[/tex]
[tex]4+3+2=9[/tex]
Above are the ways.
What is the ratio of the circumferences for two circles with areas 6π m and 150π m?
The ratio of the circumferences equals the ratio of the radii.
so we need to find their radii
first circle's radius:
pir^2 = 6pi
r = √6
second circle's radius:
pir^2 = 150pi
r = √150
Their ratio is
√6 : √150 =
√6 : √6√25 =
√6 : 5√6 =
1 : 5
The ratio of the circumferences of two circles with areas of 6π m² and 150π m² is 5:1.
To find the ratio of the circumferences of two circles given their areas, we first recall the formula for the area of a circle, A = πr², where A is the area and r is the radius. Knowing the area, we can solve for the radius of each circle. The areas given are 6π m² and 150π m².
To find the radius for the first circle, we set up the equation:
6π = πr²
We solve for r, yielding:
r = √6.
Similarly, for the second circle:
150π = πr²
This gives us:
r = √150.
Next, we use the formula for the circumference C = 2πr. We calculate the circumferences of the circles using their respective radii:
First circle's circumference: C1 = 2π(√6)
Second circle's circumference: C2 = 2π(√150)
Finally, to find the ratio of the circumferences, we divide C2 by C1 and simplify:
Ratio = C2÷C1 = (2π(√150))÷(2π(√6)) = √(150÷6) = √25 = 5.
Therefore, the ratio of the circumferences of the two circles is 5:1.
The sum of the first natural number and 0 is 1, the sum of the first two natural numbers and 0 is 3, the sum of the first three natural numbers and 0 is 6, and the sum of the first four natural numbers and 0 is 10. Which explicit formula generates the sum of the first n natural numbers and 0?
A) n(n+1)/2
B) 2n-1
C) n(n+4)/4
D) 3n-2
a metallurgist has an alloy with 10% titanium and an alloy with 20% titanium. he needs 100 grams of an alloy with 17% titanium. how much of each alloy should be mixed to attain the 100 grams of alloy with 17% titanium?
Let us say that:
x = mass of 10% titanium alloy required
y = mass of 20% titanium alloy required
To solve this problem, we set-up two mass balances or equations.
Overall mass balance: x + y = 100
x = 100 – y ---> 1
Titanium mass balance: 0.10 x + 0.20 y = 0.17 (100)
0.10 x + 0.20 y = 17 ---> 2
Now we combine equations 1 and 2:
0.10 (100 – y) + 0.20 y = 17
10 – 0.10 y + 0.20 y = 17
0.10 y = 7
y = 70 g
Calculating for x using equation 1:
x = 100 – y
x = 100 – 70
x = 30 g
Answer:
x = 30 g of 10% titanium alloy required
y = 70 g of 20% titanium alloy required
Dan bought a truck for $29,800. The value of the truck depreciated at a constant rate per year. The table below shows the value of the truck after the first and second years: Year 1 2 Value (in dollars) 26,522 23,604.58 Which function best represents the value of the truck after t years?
A.F(T)=29,800(0.89)^t
B.F(T)=26,522(0.89)^t
C.F(T)=29,800(0.11)^t
D.F(T)=26,522(0.11)^t
Answer:
A
Step-by-step explanation:
did the test
If a four-sided figure has four congruent sides, then it has four right angles. Prove this wrong
A football player took forward and backward steps of equal length during the play.After taking 14 steps total , he was back at his starting position. How many steps did the football player take in the forward and backward directions? A.6steps forward and 8 backward B.7 forward 7 backward C.8 forward and 6 backward D.5 forward and 9 backward. I believe its B not sure
Answer:
7
Step-by-step explanation:
-7 + 7 = 0
7 steps forward 7 step backward
Suppose you are walking home from the skating ring , you have to walk 6 miles east and 9 miles north , use the Pythagorean theorem how far is the skating ring from where u are.
plzzzzz!!!!!help
this forms a right triangle where you need to calculate the length of the hypotenuse by using the Pythagorean theorem
a^ + b^2 = c^2
6^2 = 36
9^2 = 81
36+81 = 117
sqrt(117) = 10.816
10.8 miles
what is 12/20 as a percent?
Answer:
60%
Step-by-step explanation:
Identify the equation of the line that has a y-intercept of 7 and is parallel to the graph of y = 5x - 3
A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5), what are the coordinates of its image point?
(-5, -3)
(5, 3)
(-3, 5)
(-3, -5)
Answer:
(-5,-3)
Step-by-step explanation:
Robbie did a survey of four butterfly parks and wrote the following observations: Butterfly Park SurveyPark Number of White Butterflies Total Number of Butterflies A 24 86 B 43 92 C 12 68 D 32 52 Based on the survey, which park had the greatest percentage of white butterflies?
Answer:
A = 24 / 86 = 28%
B = 43 / 92 = 47%
C = 12 / 68 = 18 %
D = 32 / 52 = 62%
Answer D
Step-by-step explanation:
Avani went to the grocery store and bought home a cardboard box that was covered with a sealed top Two end face of the box are squares The area of the face on either end is 64 square inches what is the length of the side of a square face? Plz help me plz
Suppose that (x1, y1) and (x2, y2) are two points on a linear function. Write the formula to find the function’s rate of change for the interval [x1, x2].
Final answer:
The rate of change for a linear function on the interval [x1, x2] is the slope of the line m, calculated by dividing the difference in y-values by the difference in x-values: m = (y2 - y1) / (x2 - x1).
Explanation:
To find the rate of change of a linear function for the interval [x1, x2], we need to calculate the slope of the line connecting the points (x1, y1) and (x2, y2). This is done using the formula:
m = (y2 - y1) / (x2 - x1)
where m represents the slope, which is the ratio between the change in y-values (rise) and the change in x-values (run). When graphing the function, if you plotted these two points, you'd be able to draw a straight line between them, and by finding the slope, you determine how steep the line is. The slope, or rate of change, indicates how much y increases or decreases for each unit increase in x. This rate of change is constant along the entire length of a straight line.
Myles can ride his bike 24 miles in 6 hours. How many miles can he travel in 1 hour? (Unit rate)
How many miles can Myles travel in 5 hours?
Which is true? A 10.59 > 10.60 B 10.590 = 10.59 C 10.43 < 10.24 D 9.0005 = 9.0050
A) 10.59 > 10.60: True, because 10.59 is greater than 10.60.
B) 10.590 = 10.59: True, as they have the same value.
C) 10.43 < 10.24: False, as 10.43 is greater than 10.24.
D) 9.0005 = 9.0050: False, as they are not equal.
Use the concept of mathematical expression defined as:
Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
A) 10.59 > 10.60: This statement is true.
In decimal numbers, the higher the number, the greater its value.
Since 10.59 is greater than 10.60 (because 59 is greater than 60), this statement holds true.
B) 10.590 = 10.59: This statement is also true.
When two decimal numbers have the same digits after the decimal point, they are considered equal.
In this case, 10.590 and 10.59 have the same value.
C) 10.43 < 10.24: This statement is false.
Similar to the first option, the higher the number, the greater its value.
In this case, 10.43 is greater than 10.24,
So the statement is not true.
D) 9.0005 = 9.0050: This statement is also false.
Although the numbers are very close, they are not equal.
When comparing decimal numbers, each digit after the decimal point matters.
In this case, the numbers differ after the fourth decimal place, making them unequal.
Hence, the given expressions:
A) 10.59 > 10.60: True,
B) 10.590 = 10.59: True,
C) 10.43 < 10.24: False,
D) 9.0005 = 9.0050: False.
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The Lions won 35 out of 40 games this season what fraction of the games played did the Lions won? Write your answer in a simplest form
PLEASE HELP WITH THESE TWO IM VWRY CONFUSED AND SIPER DUMD !!
Which statement is true for the equation 4x − 4x − 5 = −5?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Meredith lives 24 blocks from her friends house. she travels 1 block per minute. What if she travels 2 blocks per minute? how many blocks would it take her to get to her friends house?
Answer:
12 block
Step-by-step explanation:
We are given that Meredith lives 24 blocks from her friends house if she travels 1 block per minute .
We have to find the number of blocks if she travel 2 blocks per minute .
In order to find the number of blocks from Meredith friend house
we will divide 24 by 2
Therefore, if she travels 2 block per minute then she travel
[tex]\frac{24}{2}=[/tex]12 block
Hence, Meredith lives 12 block from her friends house if she travel 2 block per minute .
I don't get how to do it i have tried but I can't I think that it might be 20 i think
A pizza is cut into six unequal slices (each cut starts at the center). The largest slice measures 90 degrees
If Larry eats the slices in order from the largest to the smallest, then the number of degrees spanned by a slice decreases at a constant rate. (So the second slice is smaller than the first by a certain number of degrees, then the third slice is smaller than the second slice by that same number of degrees, and so on.)
What is the degree measure of the fifth slice Larry eats?
Madison collage conducted a three-day orientation for incoming freshmen. Each day, an average of 110 students attend the morning session and an average of 160 students attend the afternoon session. write an expression that could be used to determine the total number of incoming freshmen who attended the orientation.
The land ares of Florida is 1×100,000+3×10,000+9×1,000+8×100+5×10+2×1 square kilometers. Write in standard form and word form
3 hours worked for$12;9 hours worked for $36
This answer explains the concept of Labor Economics and Wages by calculating the hourly rate from given total pay and total hours worked.
Explanation:The subject of this question involves Labor Economics and Wages.
In this scenario, the wage for working 3 hours is $12, while for working 9 hours, the pay is $36. To determine the hourly rate, we can use the formula: Hourly Rate = Total Pay / Total Hours Worked. Applying this formula, we find the hourly rate to be $4 per hour.
Example:
3 hours worked for $12 -> Hourly rate = $12 / 3 hours = $4 per hour9 hours worked for $36 -> Hourly rate = $36 / 9 hours = $4 per hour1. A package weighs 2.6 pounds. How much do 8 of some sized packages weigh?
It takes Maxine 0.3 hours to make a pat holder. How many pat holders can she make in 4.5 hours
3. A box of garss seed weighs 0.62 pounds. HOw much does a box containing 0.75times as grass seeds weigh?
4. A collection of nickels is worth 18.60$. how many nickels are in this collection?
5. Mrs.Anderson bought party flavors for the 24 studentsin ther class. Each flavor costs
$2.27. How much did all the party flavors cost.
6. Each prize for a carnival booth costs $0.32. How many prizes can you buy with $96?
7. Bob has a pack of 24 pencils, each pencil weighs 0.9 grams. How much does the pack of pencils weigh?
What is the ratio of 2.5 million to 1.5 million