To calculate the change in volume of a box when cutout length increases from 0.3 inches to 1.2 inches using function notation, use the formula ΔV=f(l2)-f(l1), where f(l) represents the volume of the box given the length of the edge.
Explanation:The change in volume when the cutout length increases from 0.3 inches to 1.2 inches can be represented in function notation as ΔV=f(l2)-f(l1), where f(l) represents the volume of the box as a function of the length (l) of the edge. Here, l1=0.3 and l2=1.2.
Given the formula for the volume of the box V = Length x Width x Height. Let's assume Width and Height remain constant. If initially the volume was V1=f(l1) and finally it became V2=f(l2), the change in volume will be ΔV=V2-V1 which equals f(l2)-f(l1).
For example, if the width and height of the box are 6 inches and 3 inches respectively, then the initial volume is V1 = 0.3 x 6 x 3 cubic inches and the final volume is V2 = 1.2 x 6 x 3 cubic inches. Therefore, ΔV = (1.2 x 6 x 3) - (0.3 x 6 x 3) cubic inches.
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The change in the volume of the box when the cutout length increases from 0.3 inches to 1.2 inches can be calculated using the function ΔV = V(1.2) - V(0.3). Assuming the rest of the box's dimensions are constant, this results in a change in volume of 16.2 cubic inches.
To use function notation to represent how the volume of the box changes by if the cutout length increases from 0.3 inches to 1.2 inches, let us first define a function V(l) that represents the volume of the box as a function of the cutout length 'l'. If the initial cutout length is 0.3 inches and the final cutout is 1.2 inches, the change in length Δl would be 1.2 inches - 0.3 inches = 0.9 inches. We can express the change in volume, ΔV, as the function of the change in cutout length as follows: ΔV = V(1.2) - V(0.3).
Given that the volume of a rectangular box can be calculated by the formula volume = length × width × height, and assuming other dimensions of the box do not change, the function V(l) becomes:
V(l) = length × width × l
Let's consider an example where the dimensions of the box remain constant at 6 inches by 3 inches. The volume function would then be:
V(l) = 6 in. × 3 in. × l in.
The change in volume for an increase in cutout from 0.3 to 1.2 inches is then:
ΔV = V(1.2) - V(0.3) = (6 × 3 × 1.2) - (6 × 3 × 0.3) = 21.6 in.³ - 5.4 in.³ = 16.2 in.³.
A living room measures 24 feet by 15 feet. An adjacent square dining room measures 13 feet on each side. If carpet costs $6.98 per square foot, what is the total cost of putting carpet in both rooms?
Answer:
total cost of putting carpet in both rooms is $3692.42
Step-by-step explanation:
given data
living room length = 24 feet
living room width = 15 feet
dining room is square so length and width will be same
dining room length = 13 feet
dining room width = 13 feet
carpet costs = $6.98 per square foot
to find out
what is the total cost of putting carpet in both rooms
solution
first we find the total area of both room that is
area of living room = length × width .................1
area of living room = 24 × 15
area of living room = 360 feet² ...........................2
and
areas of dining room = length × width
area of dining room = 13 × 13
area of dining room = 169 feet² ...............................3
so total area = add equation 1 and 2
total area = 360 feet² + 169 feet²
total area = 529 feet²
and
total cost of putting carpet in both rooms are = total area × carpet costs .................4
put here value
total cost of putting carpet in both rooms = 529 × $6.98
total cost of putting carpet in both rooms =$3692.42
The calculated total square footage that needs carpeting is 529 square feet. At $6.98 per square foot, the total cost of carpeting both rooms would be $3,690.42.
Explanation:The subject of this problem is mathematics, specifically the topic of area calculations and cost analysis. First, calculate the area for both rooms. The area of a rectangle is given by the formula length x width, so the area of the living room is 24 feet x 15 feet which equals 360 square feet. As the dining room is a square, its area is side x side, thus 13 feet x 13 feet equals 169 square feet.
Then, add these to get the total square footage that will need carpeting, which is 360 + 169 = 529 square feet.
Lastly, multiply this total area by the cost per square foot for carpeting. This gives $6.98 x 529 square feet = $3,690.42. So, the total cost of carpeting both rooms would be $3,690.42.
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Seth traveled 1 mile in 57.1 seconds how many miles per hour does he drive
one hour has 60 minutes, each minute has 60 seconds, so then an hour has 60*60 seconds, namely 3600 seconds. How many miles does Seth travel in 3600 seconds?
[tex]\bf \begin{array}{ccll} miles&seconds\\ \cline{1-2} 1&57.1\\ x&3600 \end{array}\implies \cfrac{1}{x}=\cfrac{57.1}{3600}\implies 3600=57.1x \\\\\\ \cfrac{3600}{57.1}=x\implies 63.05 \approx x[/tex]
Answer:
In order to find miles per hour we must first change the time given to us (57.1 seconds) into hours. We will do this by first changing the seconds to minutes:
57.1 seconds / 60 = .952 minutes
Now we can change our minutes to hours:
.952 minutes / 60= .016 hours
Now to find miles per hour we divide the miles by our time:
1 mile / .016 hours = 63.04 mph
Solve the following system of equations graphically on the set of axes below. y=2x−5.
3x+4y=24
Answer:
all work is shown and pictured
3(3m - 2) -3 =36 step by step
Answer:
Step-by-step explanation: Alright so first you ditribute the 3 with 3m and - 2 so you will get 9m - 6 - 3 = 36 from there add all like terms like - 6 and - 3 so you will get 9m - 9 = 36 now we want variables in one side and normal numbers in the others so we add 9 to both sides so we get 9m = 45 now divide both by 9 so M = 5
If 7 ounces of cola costs $.59. How much should 19 ounces costs?
Answer:
$5.31
Step-by-step explanation:
If you times $.59 seven times you will get $4.13.
Then, you will have to add $.59 two times.
Finally, you will get $5.31 .
The cost will be $1.60 in the 19 ounces if the 7 ounces of cola costs $.59.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b, will be the denominator.
The proportion is a nature of a variable to another for example if we say x ∝ y then it will be a direct relation instant if we say x ∝ 1/y then it will be inverse relation.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given,
7 ounces ⇒ cost $0.59
Divide by 7 into both sides
7/7 ounces ⇒ cost $0.59/7
1 ounce ⇒ cost $0.084
Multiply both sides 19
19×1 ounce ⇒ cost $0.084 × 19
19 ounce ⇒ cost $1.60
Hence in 19 ounces of cola, it will cost $1.60.
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if r(x) = 3x - 1 and s(x) = 2x , which expression is equivalent to (r/s) (6)
Step-by-step explanation:
(r/s)(x)=3x-1
2x
(r/s)(6)=18-1/12
=17/12
Jose needs 6.2 lb of organic blueberries to make smoothies. Organic blueberries are on sale for $2.85 per pound. Jose estimates that he will need $12 to buy the 6.2 lb of blueberries. What is Jose’s error?
Jose did not make an error. His estimate of $12 is correct.
Jose incorrectly rounded $2.85 down to $2. The estimate should be $18.
Jose incorrectly rounded 6.2 up to 7.
Jose incorrectly multiplied 2 and 7. The estimate should be $14.
Answer:
Jose incorrectly rounded $2.85 down to $2. The estimate should be $18.
Step-by-step explanation:
When we round 6.2 lb to the nearest pound we round down, because the digit after point is less than 5 (2<5), so
[tex]6.2\ lb\approx 6\ lb[/tex]
When we round $2.85 to the nearest dollar we round up, because the digit after point is greater than 5 (8>5), so
[tex]\$2.85\approx \$3[/tex]
Now, 6.2 lb of blueberries will approximately cost
[tex]\$3\cdot 6=\$18[/tex]
Hence, Jose incorrectly rounded $2.85 down to $2. The estimate should be $18.
Answer:
answer is B Jose incorrectly rounded $2.85 down to $2. The estimate should be $18. have a great day.
Step-by-step explanation:
To convert a distance of 12,000 feet to miles, which ratio could you multiply
by?
5280 feet
1 mile
1 mile
5280 feet
O c. 52podle
1 foot
5280 miles
D
12 inches
1 foot
Answer:
1 mile = 5280 feet
Step-by-step explanation:
To convert a distance of 12,000 feet to miles, we use this ratio:
1 mile = 5280 feet
? = 12,000 feet
Cross multiplying gives;
[tex]\frac{12,000}{5,280}[/tex] × 1 mile = 2.272727273 miles.
Answer:
B.
Step-by-step explanation:
Simplify 3 1/2 x 1/14
Answer:
0.25 or 1/4
Step-by-step explanation:
3 1/2 x 1/14 = 0.25
Answer:
-9 /14
= -0.6428571
Step-by-step explanation:
so basically, you simplify it by turning the mixed number into an improper fraction and then multiplying it (=-9/14) then, divide numerator by denominator and you have your answer! -0.6428571!!!
What is 8 3/8 + 10 1/3 =
Answer:
18 17/24
Step-by-step explanation:
for further reasoning how i got the awnser ask in the comments
Answer:18.7
Step-by-step explanation:
In circle O, what is m? 50° 55° 125° 250°
Answer:
The measure of angle JAM is 55°
Step-by-step explanation:
The correct question is
Find the measure of angle JAM
See the attached figure to better understand the problem
step 1
Find the measure of angle JAK
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
m∠JAK=(1/2)[arc KJ+arc LM]
substitute the given values
m∠JAK=(1/2)[170°+80°]=125°
step 2
Find the measure of angle JAM
we know that
m∠JAK+m∠JAM=180° ------> by supplementary angles
we have
m∠JAK=125°
substitute
125°+m∠JAM=180°
m∠JAM=180°-125°=55°
Answer:
The answer is 55
Step-by-step explanation:
Solve for x and Y using the angles shown, please helppp
Answer:
x = 6
y = 24
Step-by-step explanation:
(14x + 4) + (16x - 4) <--- you add them because they are supplementary angles and are equal to 180°
(14x + 4) + (16x - 4) = 180
30x = 180
[tex]\frac{30x}{30} = \frac{180}{30}[/tex]
x = 6
Then you plug in 6 to (14x + 4)
(14(6) + 4) = 84 + 4 = 88
180 - 88 = 92
Now subtract 92 from 180 and make it equal to (4y - 8) to get y.
(4y - 8) = 180 - 92 ---> (4y - 8) = 88
+ 8 + 8
4y = 96
[tex]\frac{4y}{4} = \frac{96}{4}[/tex]
y = 24
Answer:
x = 6, y = 24Step-by-step explanation:
We have the vertical angles and supplementary angles.
Vertical angles are congruent. Therefore we have the equation:
[tex](1)\qquad14x+4=4y-8[/tex]
Supplementary angles add up to 180°. Therefore we have the equation:
[tex](2)\qquad(16x-4)+(14x+4)=180[/tex]
Solve (2):
[tex](16x-4)+(14x+4)=180\qquad\text{combine like terms}\\(16x+14x)+(-4+4)=180\\30x=180\qquad\text{divide both sides by 30}\\x=6[/tex]
Put the value of x to (1) and sole:
[tex]4y-8=14(6)+4\\4y-8=84+4\\4y-8=88\qquad\text{add 8 to both sides}\\4y=96\qquad\text{divide both sides by 4}\\y=24[/tex]
Julia asked to evaluate the expression four to the power of -3 before she can join her classmates outside. She decides to use the value of the expression to help choose which activity to do. If the value is greater on she’ll play basketball. Value is equal to one, she play soccer. If the value is less than 1to play tennis. Which activity is Julia going to do today?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value is less than 1.
She will play tennis today.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]4^{-3}[/tex]
We will evaluate this expression.
[tex]4^{-3}[/tex] can be written as [tex]\frac{1}{4^{3} }[/tex]
This means,
= 1/(4 x 4 x 4)
= 1/64
= 0.016
This is less than 1.
We have,
If the value is greater than 1, she’ll play basketball.
If the value is equal to 1, she plays soccer.
If the value is less than 1, she will play tennis.
The value is less than 1.
Thus,
The value is less than 1.
She will play tennis.
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The expression 'four to the power of -3' equals 0.015625. Since this value is less than 1, Julia will play tennis.
Explanation:To evaluate the expression four to the power of -3, we have to understand how negative exponents work. A negative exponent means to divide 1 by the base raised to the power of the absolute value of the exponent. So 4^-3 is equivalent to 1/(4^3).
Let's do the maths:
4^3 = 4 * 4 * 4 = 64.
Then, 1/64 = 0.015625.
Therefore, four to the power of negative three is 0.015625.
Julia will choose activities based on the value of the expression - since the value is less than 1, in this case, she would play tennis.
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What is the domain of the function on the graph?
Dall real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
Answer:
All real numbers greater than or equal to -3.
Step-by-step explanation:
The domain of a function is defined as the x values that are a part of the function. Therefore, looking at the graph, we see that the domain is all real numbers greater than or equal to -3, because the function doesn't contain x values less than -3.
A recipe requires 3 cups of sugar. You can only measure using 2/5 cups. how many 2/5 cups are needed for the recipe
To find how many 2/5 cups are needed for 3 cups of sugar, divide 3 by 2/5, resulting in 7.5. Therefore, 7.5 of the 2/5 cups are required.
To calculate how many 2/5 cups are needed for a recipe that requires 3 cups of sugar, you can follow these steps:
Determine the total amount required: The recipe requires 3 cups of sugar.
Determine the measurement of the cup you have: You can measure using only 2/5 cups.
Calculate the number of 2/5 cups needed: Divide the total amount needed by the measurement of the cup you have.
This gives you the equation: 3 cups \/ (2/5 cups) = 15/2 = 7.5. Therefore, you will need 7.5 of the 2/5 cups to measure out 3 cups of sugar.
How do you get 40y from the difference of 2 squares with the problem (5y+4+3x)(5y+4-3x)? I understand distribution method. I don't know where the 40y comes from using the special product method.
Answer:
Step-by-step explanation:
(5y+4+3x)(5y+4-3x) = (5y+4)² - (3x)²......(from the difference of 2 squares )
by identity : (a+b)(a-b) = a² - b²
in this exercice ; a = 5y+4 and b = 3x
What is the answer for this
Solve the formula for the specified variable.
S = ( 2 W + 2 H ) L + 2 W H
L = ???
Answer: [tex]\bold{L=\dfrac{S-2WH}{2W+2H}}[/tex]
Step-by-step explanation:
[tex]S=(2W+2H)L+2WH\\\\\\\underline{\text{Subtract 2WH from both sides:}}\\S-2WH=(2W+2H)L\\\\\\\underline{\text{Divide both sides by (2W + 2H):}}\\\\\dfrac{S-2WH}{2W+2H}=L[/tex]
Jackson is a 25 year old college student whose parents contribute to his support. His parents may claim him as a tax dependent in 2011 as long as They don't turn his bedroom into a home office. he makes under $500. he is under 30. they contribute more than half of his support for the year.
Answer:
Bot
Step-by-step explanation:
What is 5.5 divided by 3.5
5.5 divided by 3.5 is 1.57142857 when solved, but when rounded, you will get 1.6, or 1.57.
Hope this helped!
Nate
What is the remainder when 16,055 is divided by 16? (Input numeric values only)
Answer:
16055=16000+55
16000mod16=0
55mod16=7
(7+0)mod16=7
its 7
Put this in order 45.07 45.007 45.7 45.072 45.702
What is 2 19 over 20 terminating or repeating
Answer:
terminating
Step-by-step explanation:
20 is a factor of a 100
20 × 5 = 100
therefore 19 × 5= 95
So in decimal form it's 2.95
Chris has 2 pairs of black socks, 4 pairs of red socks, and 18 pairs of white socks in a dresser drawer. What is the probability that he will choose a pair of white socks, without looking in the drawer first?
75%
0.33
50%
Answer:
75%
Step-by-step explanat
Find the total pairs:
2 +4 +18 = 24 total pairs.
18 pairs are white.
The probability is the number of white over the total number of pairs:
18/24 = 0.75 = 75%
The answer is 75%
4π=w−6π???????????????????
537.05 is what percent of 467
Answer:
115%
Step-by-step explanation:
Set up the equation like this:
537.05 / 467 = x / 100
Cross multiply
467x = 53705
x = 115
a solid wooden cone with diameter 14cm and vertical length 24cm is vertically cut into two equal halves. one half is to be covered by paper at rate of rs 7per sq. cm find total cost of paper required?
Answer:
V = 392[tex]\pi[/tex]
Step-by-step explanation:
The volume of a cone is: V = [tex]\frac{1}{3} \pi r^{2} h[/tex]
diameter = 14 h = 24
diameter = 2r ---> r = 7
V = [tex]\frac{1}{3} \pi (7)^{2} (24)[/tex]
V = [tex]\frac{1}{3} \pi (49)(24)[/tex]
V = [tex]\frac{1}{3} \pi (1176)[/tex]
V = 392[tex]\pi[/tex]
In Alaska, the temperature can get cold really quickly. Yesterday, the temperature dropped 3 degrees for 9 hours straight. What is the total temperature change during the 9 hours?
Answer:
27
Step-by-step explanation:
3 x 9 = 27
you just multiply the two. (if it asks for temperature after the hours just subtract)
The temp dropped 27 degrees. 3 degrees times 9 nights is 27 degrees dropped. :)
4x-9= 3.5-9 please help!
Answer:
x = 7/8
Step-by-step explanation:
7/8 of 4 is 3.5
4x-9 = 3.5-9
PLEASE HELP ME FAST!! I NEED TO KNOW WHAT TO WRITE FOR THE RATIO!!
Answer:
100 kilometers per centimeter.
Step-by-step explanation: We are given that
Length of Mississippi River = 3,730 km.
The scale is required to find if the length of the river is given 37.3 cm.
Thus, the scale of the map is given by, = 100
Hence, the scale of the map is 100 kilometers per centimeter.