Ms. King wants to add a triangular deck in
the yard behind her house. Each side is to be
18 feet long. Find the length of the railing
that will fit completely around the deck.
Then find the area of the deck.
Answers
The length of the railing that will fit completely around the deck is 54 feet. The area of the triangular deck is approximately 164.25 square feet.
To find the length of the railing that will fit completely around the triangular deck, we need to calculate the perimeter of the triangle. The perimeter of a triangle is the sum of the lengths of all three sides.
Since each side of the triangular deck is 18 feet long, the perimeter (P) can be calculated as:
P = 18 feet + 18 feet + 18 feet
P = 54 feet
So, the length of the railing that will fit completely around the deck is 54 feet.
Next, let's find the area of the triangular deck. The area of a triangle can be calculated using the following formula:
Area (A) = (1/2) * base * height
Since the triangle is equilateral (all sides have the same length), any side can be considered as the base, and the height can be drawn from any vertex to the midpoint of the opposite side.
Let's consider one of the sides (18 feet) as the base. Now, to find the height, we can draw a perpendicular line from the vertex to the midpoint of the base, creating two right-angled triangles.
The height (h) of one right-angled triangle can be found using the Pythagorean theorem:
[tex]h^2 = (18 feet / 2)^2 + (18 feet)^2\\h^2 = 9 feet^2 + 324 feet^2\\h^2 = 333 feet^2\\[/tex]
h ≈ √333 feet
h ≈ 18.25 feet (rounded to two decimal places)
Now, we can find the area (A) of the triangular deck:
A = (1/2) * base * height
A = (1/2) * 18 feet * 18.25 feet
A ≈ 164.25 square feet (rounded to two decimal places)
So, the area of the triangular deck is approximately 164.25 square feet.
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Related Questions
The annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. hence the total number of burglaries increased by 40% over the two year period.
a. by what percent has the number of burglaries actually changed in the two-year period?
b. by what percent would the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase?
Answers
Answer:
a) 35%
b) 6.67%
Step-by-step explanation:
a) The annual number of burglaries in 2012 would be 150% and since in 2013, it fell by 10%:
10% of 150 is 15 so 150-15 = 135%.
The actual percentage increase of burglaries is 135% - 100% = 35% not 40%.
b) In the second year, the percentage would have to decrease by 10% of the initial 150% so [tex]\frac{10}{150}[/tex] = [tex]\frac{1}{15}[/tex] which as a percentage would be 6.66666....% or 6.67%.
The number of burglaries actually changed in the two-year period will be 35% and the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase will be 6.7%
BurglariesIt is act of breaking and entering a dwelling at night to commit a felony such as theft.
How to solve this problem?The steps are as follow:
Let us assume that the annual number of burglaries in 2011 are 100. After that there is 50% increase in 2012 so the number of burglaries will be: 100(1.50) = 150.Burglaries after the 10% reduction in 2013 would be: 150(.90) = 135So there will be change in burglaries over the two-year period = (135 / 100) - 1 = 35% To know how much burglaries would have to reduce in order to have a 40% change in burglaries we would be using the following formula:(x - 100) / 100 = 0.40
x - 100 = 40
x = 140
Change in burglaries over the two-year period to have 40% increase = (140 / 150) - 1 = 6.7%So, burglaries after the 10% reduction in 2013 would be 35% and change in burglaries over the two-year period to have 40% increase will be 6.7%.
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Leaf U. Allone needs to borrow $120,000 from his local bank for the home he is buying. The bank offers a 30 year mortgage at an APR of 6.5%.
A) How many monthly payments would it take to pay off the 30 year loan?
B) What is her monthly payment on the 30 year loan?
C) What is the total paid to the bank over 30 years?
D) How much of that is interest?
Answers
Answer:
A) It would take 360 monthly payment to pay of the 30-year loan.
B) Her monthly payment would be $650.
C) The total paid back to bank over 30 years would be $234,000
D) The total amount of interest was $114,000 (95% interest back to the bank after 30 years).
Step-by-step explanation:
6.5 percent *120000 =
(6.5:100)*120000 =
(6.5*120000):100 =
780000:100 = 7800
6.5% of 120,000 is 7,800.
Every year Leaf U. Allone has to pay $7,800 to the bank.
12 months in a year.
7,800 ÷ 12 = $650
Every month Leaf U. Allone has to pay $650 to the bank.
Over 30 years of paying 7,800
Multiply 7,800 * 30
= $234,000
To find the interest,
subtract 120,000 from 234,000
= $114,000 in interest.
Meaning the home value went up.
How can you use a
single measure to describe a data set?
Answers
Describing data Often we wish to describe a set of data with a single number, or a small set of numbers, in such a way that these values will yield enough information about the content of the data that we can produce a means of generating a similar set of data from this description.
Help! I got it wrong the first time
Answers
Answer:
The correct correspondence is B.
Zach's step counter tracked how many steps he took each day for a week. Number of steps 2,000 4,000 6,000 8,000 10,000 What was Zach's median number of steps?
Answers
Answer: 8,000
Step-by-step explanation: Did it on IXL
5(x - 20) = 1/2 (4x + 4)
Show your work
Help
Answers
Answer: 334
Step-by-step explanation: Find the steps in the file
Answer:
34
Step-by-step explanation:
1. Expand 5(x - 20):
Use the distributive property to distribute 5 to x and -205x - 100
2. Expand [tex]\frac{1}{2} (4x + 4)[/tex]:
Use the distributive property to distribute [tex]\frac{1}{2}[/tex] to 4x and 42x + 2
3. Add 100 to both sides:
5x - 100 = 2x + 2
5x - 100+100 = 2x + 2+100
5x = 2x + 102
4. Subtract 2x from both sides:
3x = 102
5. Divide both sides by 3:
x = 34
hope this helps!
HELP ME PLEASEEE URGENT I’ll mark the brainiest!!
Answers
216.66
169π-100π=69π
69*3.14= 216.66
What is the vertex of f(x)=x2−8x+15 ?
Answers
Answer:
(4,-1)
i strongly believe that is the answer, pls mark as brainlist
The exam scores in Bryan's class are Normally
distributed with a mean of 88 points and a standard
deviation of 1.5 points.
Exam Scores
83.5 85 86.5 88 89.5 91 92.5
Score
Which statements are true? Check all that apply.
□ About 16% of all exam scores are less than 86.5
points.
About 16% of all exam scores are greater than 89.5
points.
About 68% of the test scores fall between 85 and 91
points.
About 84% of all exam scores are less than 89.5
points.
About 84% of all exam scores are greater than 89.5
points.
0
Answers
Using the Empirical Rule, it is found that the correct statements are given by:
About 16% of all exam scores are less than 86.5 points.About 16% of all exam scores are greater than 89.5 points.About 84% of all exam scores are less than 89.5 points.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.We also have to consider that the normal distribution is symmetric. Then, alog with the mean of 88 and standard deviation of 1.5, the correct statements are given by:
About 16% of all exam scores are less than 86.5 points(more than 1 standard deviation below the mean, the percentage, considering the symmetry, is 0.5 x 32 = 16%).About 16% of all exam scores are greater than 89.5 points, due to the same explanation as above.About 84% of all exam scores are less than 89.5 points, as the percentage is 50%(all below the mean) + 50% x 68%(one standard deviation above the mean) = 84%.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Answer:
Step-by-step explanation:
Fill in the correct values in the statements.
About 68% of the observations will fall within
⇒ 1.5 points of the mean of
⇒ 88 points.
About
⇒ 95% of the observations will fall within 3 points of the mean.
About 99.7% of the observations will fall within
⇒ 4.5 points of the mean.
1. Jenna and Marcus want to calculate who got the better score on different math quizzes. Jenna got 4 out of
5 questions correct. Marcus got 8 out of 10 questions correct. Who did better? Explain.
Answers
Answer:
Jenna got a better score
Step-by-step explanation:
She got a better score because Marcus missed 2 but Jenna only missed one.
Christine exercises more than 40 minutes per day.
Use t to represent Christine's amount of exercise (in minutes per day).
Answers
Answer:
t=40+
Step-by-step explanation:
I couldn't really tell what you meant by that question
PLSSSSSSSSSSSSS HELPPPPPPPPPPPPPPP
Answers
number two is a
number three is d
You want to bake a 20" diameter pizza. Give exact answers.
a. What should be the circumference of the pan?
b. What is the area of the pizza?
c. If you cut the pizza into 8 congruent slices, what is the area of one slice?
d. What is the length of the crust of one slice?
Answers
Step-by-step explanation:
pizza = circle
the area of a circle is
pi×r²
r = radius (half of the diameter). in our case 20/2 = 10".
the circumference of a circle is
2×pi×r
again, r = radius.
in our case that gives us
a.
2×pi×r = 2×pi×10 = 20×pi = 62.83185307... "
b.
the area of the pizza is
pi×10² = 100×pi = 314.1592654... in²
c.
it is 1/8 of the whole area, of course.
314.1592654... / 8 = 39.26990817... in²
d.
it is 1/8 if the whole circumference, of course.
62.83185307... / 8 = 7.853981634... "
If P is the incenter of triangle JKL, find PJ
Answers
PN = PM = PO
To find PJ first we need to calculate the value of x
Since,
PN = 22
So,
PM = 22
Now, in ΔPJM we have,
PJ^2 = PM^2 + MJ^2
PJ^2= (22)^2 +(2x+3)^2...(1)
Also, In ΔPJO we have,
PJ^2 = PO^2 + OJ^2
PJ^2 = (22)^2 (5x - 45)^2...(2)
From equation (1) and (2) we obtain,
(5x - 45)^2+(22)^2=(2x+3)^2 +(22)^2
25x^2 — 450x + 2025 = 4x^2 + 12x + 9
25x^2 — 4x^2— 450x — 12x + 2025 — 9 = 0
21x^2 — 462x + 2016 = 0
x^2 - 22x+96 = 0
x^2 — 16x — 6x + 96 = 0
x(x - 16) -6(x - 16) = 0
(x - 6)(x - 16) = 0
Either x=6 or x=16
At x = 6
JO = 5 x 6 - 45
= 30 - 45
= -15
Which cannot be possible because edge length cannot be negative
So the value of x = 16
Hence, the length of PJ is
PJ^2 = 484 + (80 - 45)^2
PJ^2 = 484 + 1225
PJ^2 = 1709
PJ = √1709
PJ = 41.33
Therefore, the length of PJ is 41.3 units
the sides of a triangle are 54,31,and 69. use the phone ythagorean theorem to determine if the triangle is right acute or obtuse.
Answers
Answer:
obtuse
Step-by-step explanation:
a² + b² = c²
Let's use the two shorter sides as legs.
a² + b² = 31² + 54² = 961 + 2916 = 3877
c = √3877 = 62.2655...
For the triangle to be a right triangle, the third side would have to have a length of 62.2655. The actual length of the third side is 69. 69 is greater than 62.3, so the angle between the sides 31 and 54 must be greater than 90°. Therefore the triangle is an obtuse triangle.
A person with type O blood can donate red blood cells to anybody because type O blood is the universal blood type. About 44% of the US population has type O blood. University High held a blood drive where 50 students donated blood.
Part A: What is the probability that exactly 25 of the students had type O blood?
Part B: What is the probability that at least 25 of the students had type O blood?
Answers
Answer:
Part A.
k= 25
p= 44% = 0.44
n= 50
P(x = k) = (nk) p^k (1 - p) ^n - k
P(x = 25) = (50 25) (0.44)^25 (1 - 0.44) ^50 - 25
50!/25!(50 - 25)!
50!/25!(25)! = 1.264106 x 1014
P(x=25) = (1.264106 x 1014)(0.44)^25(0.56)^25
= 0.07812
= 7.8% probability that exactly 25 students have type O blood
Part B.
Do the same math you did above. Just replace 25 with 26 and 27 :)
25 = 7.8% probability
26 = 0.01851
= 1.8% probability
27 = 0.00405
= 0.4% probability
How many apples do you need to baked 3 apple pies if each pie need 5 apples?
Answers
Answer:
15
Step-by-step explanation:
Each pie requires 5 apples
5x3=15
Answer:
Step-by-step explanation:
1 apple pie = 5 apples
3 apple pies x 5 apples = 15 apples
can anyone help find the area pls ty
Answers
Answer:
53.72
Step-by-step explanation:
apply area of triangle and rectangle and add them
= 10 x 5.9
= 59 km2
4) Area of trapezoid = a+b/2 x h OR 1/2 (a+b)h
= 4.8 + 11/2 x 6.8
= 53.72 in2
find the mean, median and mode of the following data set: 8, 12, 15, 3, 7, 10, 15
Answers
8, 12, 15, 3, 7, 10, 15
to find:mean, median and mode.
solution:mean:to find mean you'll have to add all of the numbers and divide by the number of numbers in the data set.
[tex] \frac{(8 + 12 + 15 + 3 + 7 + 10 + 15)}{7} [/tex]
[tex] = \frac{70}{7} [/tex]
[tex] = 10[/tex]
median:to find median you'll have to order the numbers either in descending or ascending, and find the number in the middle.
[tex]3 \: 7 \: 8 \: 10 \: 12 \: 15 \: 15[/tex]
=10
mode:most frequently occurred number is the mode.
[tex] = 15[/tex]
HELP A marble paperweight shaped similar to a prism weighs 0.2 lb. How much does a similarly shaped marble paperweight weigh if its length, width, and height are tripled?
5.4 lb
0.6 lb
0.8 lb
1.8 lb
Answers
Answer:
0.6 lbs
0.2 ×3=0.6
explanation
Trust
The cost of a first-class postage stamp in 1962 was 4. In 1999 it is 33. The cost was (and is) growing exponentially. What was the growth rate? What will be the cost of a first-class postage stamp in 2010?
Answers
Answer:
The growth rate was 5.87%
Step-by-step explanation:
Time interval is t=1999−1962=37 yearsInitial cost in 1962 was a=4 unit Final cost in 1999 was y=33 unit Exponential growth function :y=a(1+r)t;a>0,r>0,ris rate of growth in decimal form.y=a(1+r)tor33=4(1+r)37 or(1+r)37=334or(1+r)37=8.25 , taking log on bothsides we get, 37log(1+r)=log(8.25) orlog(1+r)=log(8.25)37orlog(1+r)≈0.24769(1+r)=100.24769or1+r≈1.0587∴r=0.0587 orr%=0.0587⋅100≈5.87%The growth rate was 5.87% [Ans]
6. A circle has a circumference whose length is 25pi . Find the length of an arc whose
central angle is 90°.
Answers
Answer:
So, A 90° central angle cuts off an arc which has length 90/360 = 1/4 of the circumference. Therefore, length of arc = (1/4)(25π) = 25π/4.
Step-by-step explanation:
espero te sirva
Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answers
Answer:
18.852
Step-by-step explanation:
Formula to find the arc of semi circle is :
Arc length = π r
Given that,
diameter ⇒ 12
So, the radius will be,
Radius ⇒ 12 / 2
⇒ 6
Let us solve now.
Arc length = π r
= 3.142 × 6
= 18. 852
what is the area of the figure
Answers
Answer:
Explanation:
So you want to start by finding the area of the big square.
We know the width of the big square is 60cm. The length of the big square is
19
+
24
+
13
=
56
Big square
A
r
e
a
=
L
⋅
W
=
56
⋅
60
=
3360
Now let’s find the little square inside the bigger square. We see from the picture that the width is 34 and the length is 24cm. Using the same formula, we can find the area of the little square.
Little square
A
r
e
a
=
L
⋅
W
=
24
⋅
34
=
816
The area is enclosed in the area of the big square minus the area of the little square.
3360
−
816
=
2544
So the area enclosed is
2544
c
m
2
Step-by-step explanation:
What does "Y" equal? Answer ASAP and whoever gets it right can have brainliest
Answers
Answer:
Y = 21
To solve this, do the inverse of division, multiplication. Multiply 3 by the result, 7, and you get 21 as your answer to the missing digit.
Mr. Marsh plans to tile the floor in his 6-foot by 8-foot front hall. If each tile is an 8-inch square. what is the minimum number of tiles needed to cover the floor?
Answers
The division is one of the four fundamental arithmetic operations. The number of tiles that will be needed to cover the entire area of the hall is 864.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The area of the hall with dimensions 6 feet by 8 feet are:
[tex]\rm \text{Area of the hall} = 6 feet \times 8foot =48\ feet^2[/tex]
The area of the tile is 8 square inches, therefore, the area of tile in square feet can be written as,
[tex]\rm \text{Area of the tile} = \dfrac8{12 \times 12}\ feet^2[/tex]
Noe, the number of tiles needed to tile the complete area of the hall is,
[tex]\text{Number of tiles needed} = \dfrac{\text{Area of the hall}}{\text{Area of the tile}}\\\\\\\text{Number of tiles needed} = \dfrac{48}{\frac8{12 \times 12}} = \dfrac{48 \times 12 \times 12}{8} = 864[/tex]
Hence, the number of tiles that will be needed to cover the entire area of the hall is 864.
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a - 1 = 70; a = 71 solution or not a solution??
Answers
solution
hope it helps...!!!
What is the value of x? A=55 B=80
Answers
Answer:
x = 45°
Step-by-step explanation:
80° + 55° + x = 180°
135° + x = 180°
x = 45°
Pls pls pls pls help po
Answers
Here I did the working
Explanation:
Just use the formula of parallelogram
Parallelogram*
Consider the function
f(x) = x² ln(x)
Find the second derivative and use it to calculate f''(1). Type your answer in the space below.
Answers
Answer:
y'=(1/x^2-3/x^4)*(1+15x^2)+(-2/x^3+12/x^5)(x+5x^3)
Step-by-step explanation:
We know that (x2)′=2x and that (ln(x))′=1x, soOr, putting x in evidence