We need to convert the given information to meaningful mathematical equation.
Statement: "George is putting trim around his rectangular deck, including the gate. He will need 48 feet of trim to do the entire deck.", it means
[tex] Perimeter \; of\; the\; rectangle=48\; feet [/tex]
Assuming ' L ' as length of the rectangle & ' W ' as the width of the rectangle, the perimeter of rectangle is given by the below formula.
[tex] Perimeter \; of\; the\; rectangle\; =\; 2(L+W) [/tex]
We know "the deck is 14 feet long", which means...
[tex] L=14 \; feet [/tex]
Substituting 14 for L and 48 for Perimeter of rectangle in the formula above, we can set up and equation in terms of W.
[tex] 2(L+W)=Perimeter \; of\; the\; rectangle\\ 2(14+W)=48\\ Divide \; 2\; on\; both\; sides, \; we\; get...\\ \\ \frac{2(14+W)}{2}=\frac{48}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ 14+W=24\\ Subtracting\; 14\; on\; both\; sides\\ \\ 14+W-14=24-14\\ Combine\; like\; terms\\ \\ W=10 [/tex]
Conclusion:
The width of the deck is 10 Feet
Which choice below is a boxplot for the following distribution? 67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19
Answer:
Option E - Box plot E
Step-by-step explanation:
Given : Data,
67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19
To find : Which choice below is a boxplot for the following distribution?
Solution :
Step 1- Arranging the data from lowest to highest,
{19,21,35,38,40,40,41,42,46,50,54,56,60,62,64,66,67}
Step 2 - Find the median of the data
As the data is odd numbers so the median is [tex]\frac{n+1}{2}[/tex] th term.
[tex]\frac{n+1}{2}=\frac{17+1}{2}=9th[/tex] term.
9th term is 46
∴ [tex]Q_2=46[/tex]
Step 3 - To find Upper quartile and lower quartile
Lower quartile data set is the median of the upper terms from median
{19,21,35,38,40,40,41,42}
Median of the set is [tex]M=\frac{38+40}{2}=39[/tex]
∴ [tex]Q_1=39[/tex]
Upper quartile data set is the median of the lower terms from median
{ 50,54,56,60,62,64,66,67}
Median of the set is [tex]M=\frac{60+62}{2}=61[/tex]
∴ [tex]Q_3=61[/tex]
We have plot the box plot attached below.
Our box plot is matched with Box plot E.
Therefore, Option E is correct.
Answer: Box plot E
Step-by-step explanation:
A P E X
What is 1,289,845 rounded to the nearest ten thousand?
1,289,845 rounded to the nearest ten thousand is 1,290,000.
Explanation:To round 1,289,845 to the nearest ten thousand, we need to look at the digit in the ten thousandth place, which is the 8 in this case. If the digit is 5 or greater, we round up, and if it is less than 5, we round down. Since the 8 is greater than 5, we round up. To do this, we keep the digit in the ten thousandth place as it is and change all the digits to the right of it to zeros. Therefore, 1,289,845 rounded to the nearest ten thousand is 1,290,000.
Learn more about Rounding here:https://brainly.com/question/34045884
#SPJ12
3.25 tons converted to pounds
The answer is 6,500 pounds.
To convert tons to pounds, you can use the conversion factor that 1 ton is equal to 2,000 pounds. So, to convert 3.25 tons to pounds:
Multiply 3.25 tons by 2,000 pounds/ton to get the answer in pounds.3.25 tons * 2,000 pounds/ton = 6,500 pounds.Therefore, 3.25 tons is equal to 6,500 pounds.
The graph of the function f is shown. f(4) =
A) 0
B) 1
C) 4
D) 5
A monument in the shape of a right triangle sits on a rectangular pedestal that is 5 meters high by 11 meters long. The longest side of the triangular monument measures 61 meters. How high off the ground is the top of the monument?
Answer:
65 meters off the ground.
Step-by-step explanation:
The height of the monument is 9.80 m
Explanation:To find the height of the monument, we can use the Pythagorean theorem. The rectangle on the pedestal forms a right triangle with the longest side of the monument being the hypotenuse. Let's call the height of the monument 'h'. Using the Pythagorean theorem, we have:
[tex]h^2 = (11^2) - (5^2)[/tex]
[tex]h^2 = 121 - 25[/tex]
[tex]h^2 = 96[/tex]
[tex]h = \sqrt{96[/tex]
h ≈ 9.80 meters
In 2010, the estimated population of Chicago was 2.7×10^6 people. The population of Illinois that same year was about 4.76 times this number.
Which expression shows the approximate population of the state of Illinois in 2010?
Answer:
1.29 x 10^7 people
Step-by-step explanation:
1.29 x 10^7 people
1.Subtract
5/8 - 1/6
Express your answer in simplest form.
2.Subtract
6/7 - 3/5
A. 3/12
B. 9/35
C. 3/7
D. 3/35
3. Add
5 3/8 + 4 1/4
4. Add
2 5/6 + 3 3/4
Express your answer in simplest form
5. Subtract
3 1/4 - 1 5/8
Please Help ASAP I have to get the done before 10:00
A cylinder has a radius of 30 ft and a height of 19 ft. What is the exact surface area of the cylinder?
A.
1200π ft2
B.
1260π ft2
C.
1800π ft2
D.
2940π ft2
The exact surface area of the cylinder with a radius of 30 ft and height of 19 ft is calculated using the formula 2πr(h + r), resulting in an area of 2940π ft², which matches option D.
To find the exact surface area of a cylinder, we use the formula that states the surface area (SA) is SA = 2πr(h + r), where r is the radius and h is the height of the cylinder. Given that the radius (r) is 30 ft and the height (h) is 19 ft, we plug these values into the formula:
SA = 2π(30)(19 + 30)
SA = 2π30(49)
SA = 60π(49)
SA = 2940π ft²
Therefore, the exact surface area of the cylinder is 2940π square feet, which corresponds to option D.
Simplify the expression. 6g + 12 – 4g + 5
Alex is adding square-foot tiles on the floor in his laundry room. If the space he wants to fill is 7 feet long and 6 feet wide, how many square-foot tiles will he need to fill the area?
A) 12 tiles
B) 26 tiles
C) 36 tiles
D) 42 tiles
Solve the system of linear equations by substitution.
x=2y+7
3x−2y=3
Please help! How many inches is this?
Ryan and his friends flip 4 coins. What is the probability that they will flip 2 heads and 2 tails?
Wayne is solving a system of linear equations.
y= -3/4x+5
X= -2
To solve this system, he graphed the line y= - 3/4x+5
When Wayne graphs the line x= -2, at which point will he find the solution of this system of linear equations?
In m + 8, the variable m can have any value. Tell whether each statement is true or false. Then explsin your reasoning.
In algebra, the variable 'm' in the expression 'm + 8' can indeed take on any value; therefore, the statement is true because variables are meant to be placeholders for a wide range of numbers.
Explanation:In the expression m + 8, it is true that the variable m can have any value, which means that this expression does not impose any restrictions on the possible values of m. This type of statement involving a variable is common in mathematics, particularly in algebra where variables represent unknown quantities that can take on various values.
When evaluating statements for truth or false, the statement 'in m + 8, the variable m can have any value' is true. Variables, by their nature, are symbols that can represent any number, so unless specific limitations are given, we assume variables to have the full set of numbers (real numbers, integers, etc.) as potential values.
An artists builds a sculpture out of metal and wood that weighs 14.9 kilograms.3/4 of this weight is metal,and the rest is wood.How much does the wood part of the sculpture weigh?PLZZZ HELP!!!!!!!
Given is a sculpture that is built up of metal and wood, and the weight of this sculpture is 14.9 kilograms.
It says that three-fourth of the total weight is metal and says to find the weight of wooden part.
We can find the weight of metal part and then subtract it from the total weight to calculate the answer.
Total weight = 14.9 kilograms.
Metal part = three-fourth of total weight = [tex] \frac{3}{4} *14.9=\frac{44.7}{4} =11.175 \;kilograms [/tex]
Wooden part = 14.9 - 11.175 = 3.725 kilograms.
Hence, the wooden part is 3.725 kilograms.
3.725 kilograms or ¹/₄ part
Further explanationGiven:
An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms.
³/₄ of this weight is metal, and the rest is wood.Question:
How much does the wood part of the sculpture weighs?
The Process:
From the information above, we make a diagram that matches the composition of the sculpture material.
[tex]\boxed{metal}\boxed{metal}\boxed{metal}\boxed{wood} = 14.9 \ kilograms[/tex]
³/₄ of this weight is metal, and the rest is wood, which is [tex]\boxed{ \ 1 - \frac{3}{4} = \frac{1}{4} \ }[/tex].And now, let us calculate the wood part of the sculpture weighs.
[tex]\boxed{ \ = \frac{1}{4} \times 14.9 \ kilograms \ }[/tex]
Both 4 and 14.9 are multiplied by 10.
[tex]\boxed{ \ = \frac{1}{40} \times 149 \ kilograms \ }[/tex]
[tex]\boxed{ \ = \frac{149}{40} \ kilograms \ }[/tex]
Both the numerator and denominator are divided by 4.
[tex]\boxed{ \ = \frac{37.25}{10} \ kilograms \ }[/tex]
[tex]\boxed{ \ = \frac{3,725}{1,000} \ kilograms \ }[/tex]
[tex]\boxed{\boxed{ \ 3.725 \ kilograms \ }}[/tex]
Thus, the wood part of the sculpture weighs is 3.725 kilograms or ¹/₄ part.
Learn moreWhat is the area of the whole mosaic in square inches? brainly.com/question/982984How many students are wearing a shirt other than blue or white? https://brainly.com/question/895261What is the amount of apple juice in each bottle? brainly.com/question/5798698Keywords: an artist, builds a sculpture, out of metal and wood, that weighs 14.9 kilograms, 3/4, metal, the rest is wood, how much, the wood part, of the sculpture weighs
a number is added to 9. the result is then multiplied by 4 to give a new result of 120. what is the number ?
Answer:
n=21
Step-by-step explanation:
Ik im late but hopefully it can help other people :)
The equation is :
4(9+n)=120
n+9=120/4
n+9=30
n+9-9=30-9
n=21
Please rate... Thankyou :)
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?
f(x) = 20,000(0.85)x
f(x) = 20,000(0.15)x
f(x) = 20,000(1.15)x
f(x) = 20,000(1.85)x
The value of Terrence's car after x years is
A = 20,000 ( [tex]1-0.15)^x[/tex]
What is depreciation?Subtract the asset's salvage value (what you expect it to be worth at the end of its useful life) from its cost to calculate depreciation using the straight-line technique. The depreciable basis, or the amount that can be depreciated, is the result. Divide this figure by the number of years the asset will be useful.
Depreciation is the rate at which an object's value declines over time.
it is given by the formula,
A = P [tex](1-r)^t[/tex]
where A is the value of object after x period of time, P is the principal amount, r is the rate of depreciation, and t is the for the time period.
Given:
Terrence buys a new car for $20,000,
rate of depreciation = 15%,
We know the formula of the rate of depreciation,
A = P [tex](1-r)^t[/tex]
Here A= $20, 000
r = 15% = 0.15
So, the value of Terrence's car is A = 20,000 ( [tex]1-0.15)^x[/tex].
Learn more about Depreciation here:
brainly.com/question/3023490
#SPJ7
What is the value of 83?
Which expression shows 0.95 in expanded form?
Each cube in this rectangular prism is 1 cm3. What is the volume of the rectangular prism? A. 9 cm3 B. 20 cm3 C. 40 cm3 D. 48 cm3
9u^2^v and which term are like terms?
A.6u^2
B.9uv^2
C.15u^2^v
D.13u^2^v^2
jerry is 4 years older than hunter the sum of their ages is 24 how old is jerry
What’s twice the difference of a number and 8 is at least -20 using x as a variable into a inequality please help!!!
solve the linear system using substitution. SHOW WORK HELP ME PLEASE
help me please i dont understand
What is the area of this figure? Drag and drop the appropriate number into the box. A = cm² 108 135 189 318 A shape made up of a square with the length measuring 9 centimeters and a height measuring 9 centimeters. There are two equally sized right triangles attached to the square. The base of each triangle measures 9 centimeters. The height of each triangle measures 12 centimeters. The remaining side of each triangle measures 15 centimeters.
Answer:
the answer is 189
A local pizzeria sold 65 pizzas yesterday. Suppose the number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work.
help please really don't understand
Express 3/10 + 45/100 as a fraction with denominator 100