Sum of an arithmetic sequence is defined by the formula,
[tex]T_n=\frac{n}{2}[2a+(n-1)d][/tex]
Total length of the wooden boards will be [tex]14\frac{1}{6}[/tex] feet.
It's given in the question,
Width of the bottom stair = [tex]3\frac{1}{2}[/tex] feetWidth of the top stair = [tex]2\frac{1}{6}[/tex] feetEach stair is 4 inch shorter than the one below.Since, 1 inch = [tex]\frac{1}{12}[/tex] feet
Therefore, [tex]4[/tex] inch = [tex]\frac{4}{12}[/tex] feet
= [tex]\frac{1}{3}[/tex] feet
So, each stair is [tex]\frac{1}{3}[/tex] feet shorter than one below.
Now the sequence formed will be,
[tex]\frac{7}{2},[\frac{7}{2}-\frac{1}{3}],[\frac{7}{2}-\frac{2}{3}],......\frac{13}{6}[/tex]
[tex]\frac{21}{6},\frac{19}{6},\frac{17}{6}....\frac{13}{6}[/tex]
It's an Arithmetic sequence with common difference 'd' = [tex]-\frac{1}{3}[/tex] and first term 'a' = [tex]\frac{7}{2}[/tex] and nth term [tex]T_n=\frac{13}{6}[/tex]
If there are 'n' stairs, expression for the for the top stair of the arithmetic sequence will be,
[tex]T_n=a+(n-1)d[/tex]
[tex]\frac{13}{6}=\frac{21}{6}+(n-1)(-\frac{1}{3})[/tex]
[tex]\frac{13}{6}-\frac{21}{6}=-(n-1)\frac{1}{3}[/tex]
[tex]\frac{8}{6}=(n-1)\frac{1}{3}[/tex]
[tex]\frac{4}{3}=(n-1)\frac{1}{3}[/tex]
[tex](n-1)=4[/tex]
[tex]n=5[/tex]
Therefore, there are 5 stairs.
Now total length of the wooden boards = Sum of 5 terms of the sequence
= [tex]\frac{n}{2}[2a+(n-1)(d)][/tex]
= [tex]\frac{5}{2}[2(\frac{21}{6})+(5-1)(-\frac{1}{3})][/tex]
= [tex]\frac{5}{2}[\frac{21}{3}-\frac{4}{3}][/tex]
= [tex]\frac{17}{3}\times \frac{5}{2}[/tex]
= [tex]\frac{85}{6}[/tex]
= [tex]14\frac{1}{6}[/tex] ft
Therefore, total length of the wooden boards will be [tex]14\frac{1}{6}[/tex] ft.
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Los vértices de un triángulo en el plano cartesiano son A(-3, 4), B(4, 4) y C(4, -3). ¿Cuál es el área en unidades cuadradas del triángulo?
rapido pllsssss
El área del triángulo es de 24.5 unidades cuadradas.
En este problema, procedemos a resumir el procedimiento como sigue:
1) Calculamos las longitudes de los segmentos de línea AB, BC y AC por medio de la ecuación de longitud del segmento de línea.
2) Determinamos el semiperímetro del triángulo.
3) Determinamos el área del triángulo mediante la fórmula de Herón.
Si tenemos que [tex]A(x,y) = (-3, 4)[/tex], [tex]B(x,y) = (4, 4)[/tex] and [tex]C(x,y) = (4, - 3)[/tex], entonces aplicamos el procedimiento como sigue:
Paso 1 - Longitudes de segmentos línea
Segmento AB
[tex]l_{AB} = \sqrt{[4-(-3)]^{2}+(4-4)^{2}}[/tex]
[tex]l_{AB} = 7[/tex]
Segmento BC
[tex]l_{BC} = \sqrt{(4-4)^{2}+[(-3)-4]^{2}}[/tex]
[tex]l_{BC} = 7[/tex]
Segmento AC
[tex]l_{AC} = \sqrt{[4-(-3)]^{2}+(-3-4)^{2}}[/tex]
[tex]l_{AC} = 7\sqrt{2}[/tex]
Paso 2 - Cálculo del semiparámetro
[tex]s = \frac{l_{AB}+l_{BC}+l_{AC}}{2}[/tex]
[tex]s = \frac{14+7\sqrt{2}}{2}[/tex]
[tex]s = 7 + \frac{7\sqrt{2}}{2}[/tex]
Paso 3 - Cálculo del área del triángulo
[tex]A = \sqrt{s\cdot (s-l_{AB})\cdot (s-l_{BC})\cdot (s-l_{AC})}[/tex]
[tex]A = 24.5[/tex]
El área del triángulo es de 24.5 unidades cuadradas.
Invitamos cordialmente a ver esta pregunta sobre áreas de triángulos: https://brainly.com/question/21677292
Help!! (Edgar's midterm have two screenshot's)
Answer:
Step-by-step explanation:
2)
80 +67 +97+ 98 +85 +72 = 499
499/6=83.1666666667
Average: 83.1666666667
3)
a) 97 93 92 90 90 90 86 =90
median of Edgars grades for his midterm is 90
99 93 93 89 88 88 86
median of Edgars grades for his trimester is 89
7)
(z+9+18)= z+27 (remember don't mix the numbers if they are attached to the x)
(z+18+9)= z+27 (because adding is both ways the same)
a) a + b =b + a
Geometry
1.
a) 6x^2
b)The surface area of a cube = 6a^2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, x is just the length of one side of a cube
c) The unit would be sq(squared) feet
I need help please. It’s due tomorrow! I’m confused
How would you classify the number -3 (NEGATIVE three) *
Natural Number, Whole Numer, Integer, Rational Number
Whole Number, Integer, Rational Number ONLY
Integer, Rational Number ONLY
Rational Number ONLY
Factoring trinomials: m^2 +13m-36
Answer:
[tex]m^2 +13m-36[/tex] does not factor.
Explanation:
[tex]m^2 +13m-36[/tex] is not factorable with rational numbers.
326-184=? umm sorry for asking but have homework and needs to be done by 9:30
Answer:
142 is the answer of this your homework
simplify this exponential expression
[tex]( \frac{1}{3} )^{2} [/tex]
Answer:
Answer: 3^-2
Step-by-step explanation:
[tex]( \frac{1}{3} ) {}^{2} \\ \\ = \frac{ {1}^{2} }{ {3}^{2} } \\ \\ = {3}^{ - 2} [/tex]
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Evaluate the power
[tex]\frac{1^2}{3^2}[/tex]
Divide
[tex]\frac{1}{9}[/tex]
The equation R=30A-50 represents the revenue R (in dollars) you make by spending A dollars on advertising. Your revenue totaled $160. How much did you spend on advertising?
Answer: $7
Step-by-step explanation:
R = Revenue = $160
$160 = 30A - 50
(+50) (+50)
210 = 30A
(÷30) (÷30)
$7 = A
13. Very hard for me
Answer:
A
Step-by-step explanation:
help me plz, 13 points! these questions are separate. help me work out both questions please
2x-7>3
Two step inequalities
I need the steps and answers please
Step-by-step explanation:
[tex]3(2x - 5) = 6(x + 3)[/tex]
[tex]6x - 15 = 6(x + 3)[/tex]
[tex]6x - 15 = 6x + 18[/tex]
[tex] - 15 = 18[/tex]
[tex] = x∈\O[/tex]
what does x=
please explain!
Answer:
x=37°
Step-by-step explanation:
2x°=74° (vertically opposite angles)
2x°/2=74°/2
x=37°
74° = 2x°
2x° = 74°
x° = 74° : 2
x° = 37°
find the equation of a line whose gradient is -¾ and y intercept is 2
Answer:y =-3x/4+2
Step-by-step explanation:
Slope= -3/4
The line is passing through (0,2).
y-2=(x-0)*-3/4
or
y =-3x/4+2
Wilbur Wright was born in 1867 his brother Orville was born in 1871 how old was each brother in 1903
Answer:
Wilbur Wright was 36 and his brother Orville was 32 in 1903
How to find the rate of change
Step-by-step explanation:
Rate of change = Slope
for Q11)
we take 2 points to find the slope P1 (0,-3)
P2 (1,1)
[tex]slope = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
= (1 - (-3))/(1-0)
= 4
Q12
P1 (0,1)
p2 (1 , -2)
-3/1 = -3
Q13
p1 ,(25 ,65)
p2 (26, 68)
slope = 3
ignore the computer lineslol
Answer:
2 acute and 1 right
Step-by-step explanation:
because in a right triangle theres two acute angle and 1 right
The sales of Horizon, a cell phone sales and service provider, were $127,693,100 last year. What is the value of the 6th digit in this number?
Answer:
600000
Step-by-step explanation:
Cuz it is in the 100000 spot
Answer:
600000
Step-by-step explanation:
Based on the place value system, the digits are ordered from the right to left. So the 6th digit is 6 located in the hundreds of thousands column. The value of the 6th digit is obtained by multiplying the digit by the value of it's place value column
i.e 6 * 100,000 = 600, 000
Ans: 600,000
1. a. In an examination, 60 candidates sat for either Mathematics or English language 20% passed in Mathematics only and 40% passed in English language only. If each candidate passed in at least one of the subjects, how many candidates passed in i. Mathematics ii. English language? b. Illustrate the information given in (a) on a Venn diagram c. Daddy had GH¢50.00 in his pocket. He gave half of the amount to Mama; he also gave GH€10 to the house boy later. What fraction of the amount was left on him? 2. a. i. Find the width of a cuboid with height 8m and length 12m, given that the volume is 480m ii. Calculate the total surface area of the cuboid b. Find the truth set of: 1 - m + m -3 = 6 5 4
A.)
Total Number of students = 60
Since each candidate passed in atleast one of English and Math ; the none of the students failed.
Percentage who passed :.
Mathematics only = 20%
English only = 40%
Since, no one failed ; percentage that passed both = 100% - (40+20)% = 40%
Number who passed Mathematics only :
20% × 60 = 12 students
Number that passed English only :
40% × 60 = 24 students.
Number that passed both = (40% × 60) = 24 students
Number that passed English = (Number that passed English only + Number that passed both) = 24 + 24 = 48
.Number that passed mathematics = (Number that passed Maths only + Number that passed both) = 12 + 24 = 36
2.)
Total daddy has = 50
Half given to mummy = 1/2 × 50 = 25
Amount given to houseboy = 10
Amount left = 50 - (25 + 10) = 15
Fraction of Amount left = 15/50 = 3/10
C.)
Length of cuboid = 12
Height = 8 cm
Volume of cuboid = 480
Width = w
Recall :
Volume = Length × width × height
480 = 12 × 8 × w
480 = 96w
w = 490 / 96
w = 5
Width of the cuboid = 5
The surface area of a cuboid : 2(lh + lw + hw)
Hence,
2([(12×8) + (12×5) + (8 ×5)]
2(96 + 60 + 40)
2(190)
380 m
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Find the ratio of triangles to circles in the diagram below
Answer:
Ratio should be equal so ratio is 3:3
PLEASE MARK ME BRAINLIEST.The ratio of the triangles to circles in the diagram below would be; 1: 1
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained.
Thus, there are three circles and three triangles shown in the figure.
Therefore, the ratio will be;
three circles: three triangle
3 : 3
1: 1
Hence, the ratio of the triangles to circles in the diagram below would be; 1: 1
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#SPJ2
Sketch the angle in standard position.
1. -450°
Answer:
When we draw the angle in what is known as standard position, we put its vertex at the origin, and we draw the initial side of the angle along the positive horizontal axis. ... The amount of that rotation corresponds to the measure of the angle.
Step-by-step explanation:
i think the answer _ 2/60
Please help but actually answer correctly
Find the complement of set B in-universe U.
U is the set of natural numbers less than or equal to 8
B is the set of even factors of 8
Answer:
B' = {1, 3, 5, 6, 7}
Step-by-step explanation:
U = {1, 2, 3, 4, 5, 6, 7, 8}
B = {2, 4, 8}
So the complement ( the set of elements in U but not in B) is:
B' = {1, 3, 5, 6, 7}
Jennifer is saving money to buy a bike. The bike costs $261. She has $107 saved, and each week she adds $14 to her savings.
How long will it take her to save enough money to buy the bike?
It will take her ____ weeks to save for the bike.
Answer:
It will take her 11 weeks to save for the bike
Step-by-step explanation:
261 -107 = 154
154 /14=11
In which of the following expressions is the coefficient of term "x" 1?
2x^2+x−9
3x^2−x−5
2x^2−3x+1
x^2+2x+7
Answer:
the answer of the following question is d
You are walking directly away from your house. You are 5 miles away from your house when you start walking, so you can determine your distance from your house by adding 5 to the number of miles you have walked. In the equation below, x represents the number of miles you have walked, and y represents your distance from home in miles.
The relationship between these two variables can be expressed by the following equation:
y=x+5
Identify the dependent and independent variables.
Answer:
y is the dependent variable and x is the independent variable
Step-by-step explanation
The number on the right of the equal sign is always the independent variable and the number on the left is always the dependent variable.
independent variable = dependent variable +5
14 less than f
what is it?
the proceeds from a car wash are directly proportional to the number of cars washed. the total after 9 cars was $180.
a. how much can be raised if 60 cars are washed? __
b. if $1,500 was earned from the car wash, how many cars were washed? __
Answer:
a) 1200
b) 75
Step-by-step explanation:
21 feet
You are standing 21 feet from a tree. You have a 25-inch stick you are holding 35 inches from your eye. You see that the top of the tree
exactly matches the top of the stick you are holding. The bottom of the stick exactly matches the bottom of the tree. How tall is the tree?
Step-by-step explanation:
don't know man I don't know it
PLEASE HELP!! What is the standard deviation of a data set whose values are all the same?
A. −1
B. 0
C. 1
D. −2
Answer:
zero
Step-by-step explanation:
Answer:
I got this same question on my quiz, so I added the other two questions as well, with their answers.
Step-by-step explanation:
1. What is the standard deviation of the data set? Round to the nearest tenth if needed.
2, 4, 7, 8, 9
Answer: 2.9
2. Data Set A has a mean of 215 and a standard deviation of 35. Data Set B has a mean of 400 and a standard deviation of 12. Which data set is more spread out?
Answer: Data Set A
3. What is the standard deviation of a data set whose values are all the same?
Answer: 0
Help me please!
Solve the equation
