The perimeter of rectangle is 25.13 feet
Solution:
Given that,
width of a rectangle = [tex]4\frac{1}{6} \text{ feet }[/tex]
Convert the mixed fraction to improper fraction
[tex]\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}[/tex]
Therefore,
[tex]\text{width of rectangle } = \frac{25}{6} \text{ feet }[/tex]
Area of rectangle = 35 feet
The area of rectangle is given by formula:
[tex]area = length \times width[/tex]
Substituting the given values, we get
[tex]35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}[/tex]
Thus we get,
[tex]\text{length of rectangle } = \frac{42}{5} \text{ feet }[/tex]
The perimeter of rectangle is given as:
perimeter = 2(length + width)
[tex]perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13[/tex]
Thus perimeter of rectangle is 25.13 feet
A, B, C? No explanation needed.
Answer: the answer is b
Step-by-step explanation: you said you needed none.
Solve the following systems of equations.
2= 2y + 5
| 3y - 3x = -12
Answer:
x=5/2, y=-3/2. (5/2, -3/2).
Step-by-step explanation:
2=2y+5
3y-3x=-12
--------------
2-5=2y
2y=-3
y=-3/2
3(-3/2)-3x=-12
-9/2-3x=-12
3x=-9/2-(-12)
3x=-9/2+12
3x=-9/2+24/2
3x=15/2
x=(15/2)/3
x=(15/2)(1/3)
x=15/6=5/2
The solution for the system of equations is x = -5/2 and y = -3/2.
To solve the system of equations given, one can use substitution or elimination methods. The first equation 2= 2y + 5 can be rearranged to solve for y:
2y = 2 - 5
2y = -3
y = -3/2
Using the second equation 3y - 3x = -12, we substitute y with -3/2 to solve for x:
3(-3/2) - 3x = -12
-9/2 - 3x = -12
3x = -12 + 9/2
3x = -15/2
x = -15/6
x = -5/2
Therefore, the solution for the system of equations is x = -5/2 and y = -3/2.
Find the sum of the whole numbers from 1 to 960
Step-by-step explanation:
A quick way to do this sort of question:
First add the last number and the first number:
1 + 960 = 961
Then divide the total amount of numbers by 2.
960 ÷2 = 480
Now multiply these two numbers together:
961 × 480 = 461280
The sum of the whole numbers from 1 to 960 can be found using the formula for the sum of an arithmetic series. By substituting the values into the formula, we find that the sum is 461280.
Explanation:The sum of the whole numbers from 1 to 960 can be found using a simple formula for the sum of an arithmetic series. The formula is S = n/2 * (a + l), where 'n' is the number of terms, 'a' is the first term, and 'l' is the last term.
In this case, 'n' is 960 (there are 960 terms from 1 to 960), 'a' is 1 (the first term), and 'l' is 960 (the last term).
Plug these values into the formula to get: S = 960/2 * (1 + 960) = 480 * 961 = 461280. So, the sum of the whole numbers from 1 to 960 is 461280.
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How do we express one-half of the
difference of a number cubed and one?
Answer:
Step-by-step explanation:
1/2 (n^3 - 1)
the difference means subtract
Step-by-step explanation:
1/2 (n^3 - 1)
Nia told Patrick that her new backpack only cost $14 because she used a 30% off coupon when she bought it. Patrick wants to buy a similar backpack. How much will it cost if he does not have a 30% coupon?
Please answer quick, and please show steps on how you did it, tysm.
Nia's backpack after 30% off represents 70% of the original backpack cost. Setting up a ratio of 70/100 = 14/X, we can solve for the original price, X. Patrick will pay $20 if he does not have a 30% off coupon.
Explanation:This problem can be solved using a bit of Percentage Calculations. We know that after a 30% discount, Nia's backpack cost $14. This means that $14 represents 70% of the original backpack cost (100% - 30%). So to find out the 100%, or the full price, we need to determine what number 70% is 14 of. We can set up a ratio to find the original cost (X).
The steps are:
We write the equation 70/100 = 14/X where X is the original price.Then we cross-multiply to solve for X: 70 * X = 100 * 14. Which simplifies to X = (100 * 14) / 70Calculate the value to get X = 20.So, the backpack would cost Patrick $20 without a 30% off coupon.
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a coffee shop used 30% more sugar this month than last month. if the coffee shop used 728 kilograms of the sugar this month, how much did it use last month
It used 560 kilograms of sugar last month
Step-by-step explanation:
The given is:
A coffee shop used 30% more sugar this month than last monthThe coffee shop used 728 kilograms of the sugar this monthWe need to find how much it used last month
Assume that the coffee shop used x kg sugar the last month
∵ The coffee shop used x kilogram of sugar last month
∵ It used 30% more sugar this month than last month
- Find the value of 30% of x and add it to x to find how many
kilograms it used for this month
∵ 30% of x = [tex]\frac{30}{100}[/tex] × x = 0.3 x
∴ It used this month = x + 0.3 x
∴ It used this month = 1.3 x kg
∴ The coffee shop used 1.3 x kilograms of sugar this month
∵ The coffee shop used 728 kilograms of the sugar this month
- Equate 1.3 x by 728 to find x
∴ 1.3 x = 728
- Divide both sides by 1.3
∴ x = 560
It used 560 kilograms of sugar last month
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I need help please and thank you
Answer:
∠3 = 114°
Step-by-step explanation:
Angle 3 is a corresponding angle to angle 7, since they are both in the southwest corner of the intersection of the transversal and the parallel lines. Corresponding angles have the same measure, so ...
∠3 = ∠7 = 114°
A triangle has a base of 4 units and a height of 3 units. Mark draws the triangle again but doubles the height. How does the area of the triangle change?
A. The area increases by 3 square units.
B. The area increases by 6 square units.
C. The area increases by 12 square units.
D. The area does not change.
Answer:the correct answer is b
Step-by-step explanation:
What two fractions are equivalent to 12/27
Step-by-step explanation:
I have no answer to choose...
[tex]\dfrac{12}{27}=\dfrac{12:3}{27:3}=\dfrac{4}{9}\\\\\dfrac{12}{27}=\dfrac{12\cdot2}{27\cdot2}=\dfrac{24}{54}\\\\\dfrac{12}{27}=\dfrac{4}{9}=\dfrac{4\cdot2}{9\cdot2}=\dfrac{8}{18}\\\vdots[/tex]
You can multiply (divide) the numerator and the denominator by the same number different from 0 then the value of the fraction will not change
(you will get a fraction equal to given)
What is y = 4 * (0.8) ^ t
The function y = 4 * (0.8)^t is an exponential decay function, representing the decrease of a quantity over time, with y being the value at time t. To find y at any given t, substitute t into the equation and calculate the result.
Explanation:The given function y = 4 * (0.8)^t is an exponential decay function, where y represents the value of the function at time t, the number 4 is the initial value of the function when t = 0, and 0.8 is the decay factor relevant for each time unit. This type of function is often used in contexts such as radioactive decay, depreciation of value over time, or population decrease in a closed environment, where some quantity decreases by a consistent percentage over equal time intervals.
To solve for y at a given time t, simply substitute the value of t into the function and evaluate the exponential expression. It is important to use a calculator or software tool to evaluate the exponential term accurately when t is not a round number.
$37.50 decreased by 4% =
Answer:
$36
Step-by-step explanation:
The original value is $37.50 so that is 100%.
A decrease of 4% from original value means that you are finding 96% of the value, since 100% -4%= 96%
So the new value is 37.50/100 ×96= $36
This is because:
100% ----- $37.50
1% --------- $0.375
96% ------- $36
or taking 96% of original value would be
96/100 × $37.50= $36
Which would give you the same answer
Consider the solution to the linear equation. 5 (x + 6) = 50. 5 x + 30 = 50. 5 x = 20. x = 4. Which describes the inverse operations used after the distributive property? addition then division subtraction then division multiplication then subtraction division then addition
Answer:b
Step-by-step explanation:
Answer:
Subtraction then Division
Step-by-step explanation:
Right on Edg
Which statements are true? Check all that apply.
KJ is a chord.
F is point of tangency for FE.
MH is a secant segment.
GN is a secant segment.
C is a point of tangency for DC.
The answer is:
the first, second, and fourth options.
KJ is a chord.
F is point of tangency for FE.
GN is a secant segment.
Answer:
1,2,4
Step-by-step explanation:
KJ is chord.
F is point of tangency.
GN is secant segment.
Answer:
1, 2, 4
Step-by-step explanation:
one for the team
What is a 1 killometers= ?
Answer:
0.62 miles
Step-by-step explanation:
ask google or siri
What is 7.5 divided by 8
Answer:
0.9375
Step-by-step explanation:
Answer:
I believe the answer to this question is: 0.94375.
Which ordered pair is a solution to the system of linear equations Negative 4 x + y = 8 and x minus 5 y = 17?
Answer:
(-3, -4).
Step-by-step explanation:
-4x + y = 8
x - 5y = 17 Multiply this by 4:
4x - 20y = 68 Add this to the first equation:
-19y = 76
y = 76/-19
y = -4.
Plug this into the second equation:
x - 5(-4) = 17
x = 17 - 20
x = -3.
CHECK this result in equation 1:
-4(-3) + -4 = 8
12 - 4 = 8
8 = 8 <------ OK.
The solution of the given system of equations is [tex]y=-4[/tex].
Important information:
[tex]-4x+y=8[/tex] ...(i)[tex]x-5y=17[/tex] ...(ii)System of equations:Multiply both sides by 5 in equation (i).
[tex]-20x+5y=40[/tex] ...(iii)
Add equation (ii) and (iii).
[tex]-19x=57[/tex]
[tex]x=\dfrac{57}{-19}[/tex]
[tex]x=-3[/tex]
Substitute [tex]x=-3[/tex] in (i).
[tex]-4(-3)+y=8[/tex]
[tex]12+y=8[/tex]
[tex]y=8-12[/tex]
[tex]y=-4[/tex]
Thus, the solution of the given system of equations is [tex]y=-4[/tex].
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Using the two-way table, what percentage of the students that do not like to travel out of state like camping? Round to the nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
32%
34%
38%
42%
The answer is B. 34%.
The percentage of the students that do not like to travel out of state like camping will be 41%. Then the correct option is D.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.
The two-way table is given below.
Likes Traveling Does Not Like Traveling Totals
Likes Camping 52 38 90
Do Not Like Camping 36 74 110
Column totals 88 112 200
Then the percentage of the students that do not like to travel out of state like camping will be
P = (36 / 88) x 100
P = 0.409090 x 100
P = 40.90%
P ≈ 41%
Thus, the percentage of the students that do not like to travel out of state like camping will be 41%.
Then the correct option is D.
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An apartment building currently has rented x apartments with two occupants and 16 apartments with one occupant. The apartment building has 92 total occupants.
2× + 16 =92
How many double-occupancy apartments are currently rented?
The currently rented double-occupancy apartments are 38 apartments.
Step-by-step explanation:
An apartment has rented x apartments with two occupants and 16 apartments with one occupant and the total occupants were 92, these can be written in the equation as
[tex]2x+16=92[/tex]
To find the number of double occupancy apartments that are rented, we need to solve the equation and find the value of x.
[tex]2x+16=92[/tex]
Subtracting 16 from both sides of the equation,
[tex]\begin{aligned}&2 x=92-16\\&2 x=76\end{aligned}[/tex]
Dividing both sides by 2, we get,
[tex]\begin{aligned}\frac{2 x}{2} &=\frac{76}{2} \\x &=38\end{aligned}[/tex]
Thus, there are 38 double-occupancy apartments are currently rented.
The correct answer is that there are 38 double-occupancy apartments currently rented.
To solve the problem, we start with the given equation that represents the total number of occupants in the apartment building:
[tex]\[ 2x + 16 = 92 \][/tex]
This equation takes into account that each double-occupancy apartment (x) houses two occupants, and there are also 16 single-occupancy apartments. We want to find the value of x, which represents the number of double-occupancy apartments.
First, we subtract 16 from both sides of the equation to isolate the term with x:
[tex]\[ 2x + 16 - 16 = 92 - 16 \][/tex]
[tex]\[ 2x = 76 \][/tex]
Next, we divide both sides of the equation by 2 to solve for x:
[tex]\[ \frac{2x}{2} = \frac{76}{2} \][/tex]
[tex]\[ x = 38 \][/tex]
Therefore, there are 38 double-occupancy apartments currently rented in the building. This matches the correct answer provided at the beginning.
y=x^2+8x+12 find the y-intercept for the parbola
Answer:
Y(x+2) (x+6)
Step-by-step explanation:
Ali has painting class every 20 days ria has a pottery class every 5 days they both met at the art building today. How many days will it be until they meet each other again
Answer:
4
Step-by-step explanation:
20 divided by 5 = 4
Answer:
20 days
Step-by-step explanation:
Since 20 is a multiple of 5 then the least common multiple of 5 and 20 is 20
therefore they will meet after 20 days
What is the formula for margin of error? ME = ME = ME = ME =
Answer:
the answer is C on edgen.
Step-by-step explanation:
Which is the solution of this system of equations? y=5x−83y=x+18
y+5(3)=15
Answer:
y=5x−83y=x+18 (the question is wrong; it has 2 equal signs)
y+5(3)=15
y+15=15 (multiply 5*3; you get 15)
y= 15-15
y= 0
Answer:
x=3, y=7
Step-by-step explanation:
how do u figure out the area of a rectangle
Answer:
Step-by-step explanation:
Hey there) We do it like this:
[tex]6\times 3\times 4+3\times 3\times 2=90[/tex]
Hope, this helps. Have a nice day :)
leah would like to earn at least $160 per month. She works at a restaurant for $5 an hour and works at an ice cream shop for $8 an hour. Leah wants to work at least 7 hours at the restaurant, and at least 10 hours at the ice cream shop.
Answer:
Leah can make more than $160 in a month if he works 7 hours for $35 and 10 hours for $80 daily or weekly.
Step-by-step explanation:
What is the slope of a line passing through (3, 4) and (5, 8)?
Answer:
The slope of the two points is 2.
Answer:
2 is teh answer
Step-by-step explanation:
What type of function is shown above?
A. Exponential
B. absolute value
C. Polynomial
D. Step
Answer:
that would be an exponential function
Step-by-step explanation:
a recipe for lemonade calls for 2 cups of sugar for every 1/2 cup of lemon juice. How many cups of sugar would be needed if you had 3 cups of lemon juice?
Answer: 12cups of sugar
Step-by-step explanation:
2cups of sugar = 1/2cup of memo
Xcups of sugar =3cups of lemon
X = 6÷ 1/2
= 12
Answer:
12 cups sugar
Step-by-step explanation:
there are a couple ways to do this...by unit rate or a proportion...
2 cups of sugar for every 1/2 cup of lemon juice
2 / (1/2) = 2 * 2 = 4.....the unit rate is 4/1....or 4 cups of sugar for every 1 cup of lemon.
so if u have 3 cups of lemon, and 1 cup of lemon = 4 cups of sugar, then 3 cups of lemon would equal (4 * 3) = 12 cups of sugar
or set it up as a proportion...
2 cups sugar to 1/2 cup lemon = x cups sugar to 3 cups lemon
2 / (1/2) = x / 3....cross multiply
(1/2)(x) = (3)(2)
1/2x = 6
x = 6 * 2
x = 12 cups sugar
either way u choose to do it will result in the same answer.
angle K and angle L are complementary angels. If the measurement of angle K =(3x+3) and the measurement of angle L =(10x-4).what is the measure of each angle
The measurement of two angles is 24° and 66°
Step-by-step explanation:
First of all, let us define complementary angles
The angles whose sum is 90° are called complementary angles
Given
∠K = (3x+3)
∠L = (10x-4)
According to the definition,
[tex]K+L = 90\\3x+3 + 10x-4 = 90\\13x -1 = 90\\13x-1+1 = 90+1\\13x = 91[/tex]
Dividing both sides by 13
[tex]\frac{13x}{13} = \frac{91}{13}\\x = 7[/tex]
So,
∠K = 3x + 3 = 3(7) + 3 = 21+3 = 24°
∠L = 10x - 4 = 10(7) -4 =70 -4 = 66°
Hence,
The measurement of two angles is 24° and 66°
Keywords: Complementary angles, Angles
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in a certain class,10 of 24 students play sports. what is the ratio of students who play sports to those who do not?
Answer:
Step-by-step explanation:
Student who don't play sports = 24 - 10 = 14
the ratio of students who play sports to those who do not = 10 : 14 = 5:7
Step-by-step explanation:
10:24
5:12
is can be you answer
What is the common difference of 80,60,45,33.75
Answer:
they are all less than 100