Answer:
S₂₀₀ = 121800
Step-by-step explanation:
the sum to n term of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 12 and d = a₂ - a₁ = 18 - 12 = 6 , then
S₂₀₀ = [tex]\frac{200}{2}[/tex] [ (2 × 12) + (199 × 6) ]
= 100(24 + 1194)
= 100 ×1218
= 121800
Keisha has two dogs. The larger dog weighs 1.2 pounds more than the smaller dog. The combined weight of the two dogs is 13.6 pounds. What is the weight, in pounds, of the smaller dog?
Answer:
x = 6.2
Step-by-step explanation:
let ‘x’ denotes the weight of a smaller dog.
“1.2″ + x” be the weight of the larger dog
combined weight = 13.6
smaller dog weight =
x+x+1.2 = 13.6
2x + 1.2 = 13.6
2x = 13.6–1.2
2x = 12.4
x = 12.4/2
x = 6.2 pounds.
Hope you understood it, Happy Learning.
What is the area of triangle ABC?
C
12
60°
60°
A
D
B
Answer:
Area of the triangle is 36√3
Step-by-step explanation: Hope this will help
The hypotenuse of each 30 - 60 - 90 triangle is 12
The base length is 6 + 6 = 12 because the triangle is equilateral and the
altitude of the triangle divides the base into two equal parts and the altitude (DC) is the height of the triangle.
Now you have two 30 - 60 - 90 triangles with the hypotenuse of 12, the short leg = 6 and you need to find the length of DC.
Finding DC .
a² + b² = c²
6² + b² = 12² 0r the long leg = short leg times √3
36 + b² = 144 6√3
b² = 108
b = 6√3
Area of a triangle = 1/2bh
= 1/2(12)(6√3)
= 6(6√3) = 36√3
All of the following are equivalent to 1.75 except _____. 14/8, 1 75/100, 1 3/4, 4/7
Solve -2x + 7 < -41 how do you solve this
Answer:
x>21
Step-by-step explanation:
-2x + 7 < -41 Subtract 7 from both sides
-2x<-48 Divide by negative 2
x>21 When you divide by a negative you have to flip the sign
Answer:
x<28
Step-by-step explanation:
-2x+7<-41
-2x<-48 subtract 7 from both sides
x>24 divide by -2 to both sides
Find the volume of the composite solid. Round your answer to the nearest tenth.
A composite solid is shown with a cone placed atop a cylinder. The height of the cone is 6 feet and the diameter of its base is 16 feet. The diameter of the circular bases of the cylinder are the same as the diameter of the cone. The height of the cylinder is 4 feet.
The volume is about
cubic feet.
Answer:
1206.4 ft³
Step-by-step explanation:
The volume of the composite figure is the sum of the volumes of its parts. Each part has its own volume formula.
__
formulasThe formula for the volume of a cone is ...
V = 1/3Bh . . . . where B is the area of the base, and h is the height
The formula for the volume of a cylinder is ...
V = Bh . . . . where B is the area of the base, and h is the height
The formula for the area of a circle is ...
A = πr² = π(d/2)² = (π/4)d²
Combining the volume formulas for a figure with the same base area, we have ...
V = B(cylinder height) + 1/3B(cone height)
V = B(cylinder height + 1/3×cone height) . . . . where B is the base area
composite volumeUsing 16 ft for the diameter, and 4 ft and 6 ft for the heights of the cylinder and cone, respectively, we have ...
V = (π/4)(16 ft)²(4 ft + 1/3×6 ft) = 64π(4 +2) ft³ = 384π ft³
The volume is about ...
384π ft³ ≈ 1206.4 ft³
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 97m long and 76m wide. Find the area of the training field. Use the value 3.14 for pie , and do not round your answer. Be sure to include the correct unit in your answer.
If the radius of the semi-circle is 38 m. Then the area of the training field will be 11,908.459 square meters.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 97 m long and 76 m wide.
Then the radius of the semi-circle will be
2r = 76
r = 38 m
Then the area of the training field will be
Area = area of rectangle + 2 x area of semi-circle
Area = 97 x 76 + 2 x (1/2) x π x 38²
Area = 7372 + 4536.459
Area = 11908.459 square m
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Honorable Quinn with 6 children earns 613 200 naira per month. Calculate:
a. tax allowance
b. taxable income
c. amount of tax paid
d. income after tax is paid
what least number should 27648 be divided so that the quotient will be a cube number
For this problem, a non-integer answer should be entered as a fraction in simplest form using / as the fraction bar. malik randomly picked two numbers from 1 to 9 (including 1 and 9). the same number could be picked more than once. the first of the two numbers he picks is odd and less than 5. what is the probability that the sum of the two numbers malik picks is less than 5, given that the first number is odd and less than 5?
Based on the numbers that Malik can pick and the condition of the sum being less than 5, the probability of this happening is 2/9.
What is the probability that Malik's number are less than 5 when added?The first number that Malik picked is an odd number less than 5 which makes it with 1 or 3.
In order for the two number to be less than 5 when added, the numbers to be picked have to be:
1 and 21 and 33 and 11 and 1These are 4 possibilities out of a total of 18 possibilities so the probability is:
= 4 / 18
= 2 / 9
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Answer:
See image
Step-by-step explanation:
Plato
Solve: 4+1.8x = 8 (1+0.1x)
A. There are infinitely many solutions.
B. x = -3
C. x = -4
D. x = 4
[tex]4+1.8x=8+0.8x\\\\4+1.0x=8\\\\1.0x=4\\\\x=4\\[/tex]
the answer is x = 4.
Juan bought 48 ounces of nuts at the store. How much is this in pounds?
3. The Wang family has a take-home income of $45 000 per year. If they budget 22% for rent, how much rent would they budget for the year? How much for each month?
Answer:
Step-by-step explanation:
45000 x %22 = 9900 per year
9900/12=825 per month
How many people out of 100,000 will survive until age 90?
Answer:
21,526 people
Step-by-step explanation:
Joe has 7/8 yards of string. What is the maximum number of 1/16 yards of string Joe can be cut from the string? 11 points
Answer:
14
Step-by-step explanation:
7/8 = 14/16
A swimming pool in a certain resort is enjoyed by people because it has a floor measurement of 8 ft by 12 ft and a depth of 9 ft. How much water can it contain?
Answer:
864 ft3
Step-by-step explanation:
length = 12 ft
width = 8 ft
depth = 9 ft
Volume = ? = length * width * depth
Triangle ABC represents a triangular garden with side lengths AB= 10cm ,BC= 8cm and AC=15cm .
What is the smallest and largest angle of the garden?
Answer:
Largest angle is "B" and smallest angle is "A".
Step-by-step explanation:
Given ∆ABC
AB = 10 cm , BC = 8 cm , AC = 15 cm
Angle opposite to side AB is "C"
Angle opposite to side BC is "A"
Angle opposite to side AC is "B"
we know that the angle opposite to largest side is largest angle and smallest side is smallest angle.
Here,∆ABC largest side is AC and smallest side is BC.
Hence,largest angle is "B" and smallest angle is "A".
What is the constant of proportionality shown in the table?
The constant of proportionality shown in the table that shows the cost and the number of books is 3.
What is the constant of proportionality ?When there is a direct proportional relationship, it means that as the value of one variable increases, the value of the other variable also increases. As the number of books increases, the cost increases.
Direct proportion: y = kx
Where:
y = dependent variable k = constant of proportionality x = independent variablek = y/x
6/2 = 3
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Answer:3
Step-by-step explanation:
Round to the nearest two decimal places
HELP PLEASE, I'LL GIVE BRAINLIEST.
if x + yi = (1 + i)⁴ , then x + y = ......
a) 4
b) - 4
c) 2
d) - 2
an explanation for future reference would be greatly appreciated <333
x + yi = (1 + i)⁴
then -4 + 4 = x
Can someone please find the coordinates for these shapes? pls I will mark them with Brainliest pls
Answer:
What shapes?!?! I can help you if you add an image of the shapes :)
Step-by-step explanation:
Distribute to create an equivalent expression with the fewest symbols possible.
(1 - 25 +4h) - 5 =
Answer:
4h - 29
Step-by-step explanation:
[tex](1-25+4h)-5\\=(-24+4h)-5\\=(4h-24)-5\\=4h-24-5\\=4h-29[/tex]
You could also write this solution as [tex]-29+4h[/tex], but I just think [tex]4h-29[/tex] looks nicer :)
a) What percentage of 5³ is 5?
b) What percentage of 5³ is 5²?
Step-by-step explanation:
a) 5³= 5*5*5 = 125
5/125*100%
4%
b) 5²=5*5=25
25/125*100%
20%
Question 39 of 40
The circle below has a radius of 8 centimeters. What is the area of the shaded
region?
X
120°
8 cm
OA. 32 square centimeters
B. 8 square centimeters
64
3
square centimeters
square centimeters
O C.
O D.
16
3
Convert angle to radians
120=2π/3So
Area
r²Ø/28²(2π/3)(1/2)64π/3cm²Answer:
[tex]\textsf{C.} \quad \dfrac{64 \pi}{3} \: \sf square\:centimeters[/tex]
Step-by-step explanation:
Formula
[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]
Given:
[tex]\theta[/tex] = 120°r = 8 cmSubstitute the given values into the formula and solve for Area:
[tex]\large \begin{aligned}\implies \textsf{Area} & =\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \pi (8)^2\\\\& =\left(\dfrac{1}{3}\right) \pi (64)\\\\& =\dfrac{64}{3} \pi \: \sf cm^2\end{aligned}[/tex]
Find the gradient of the graph shown
In Exercises 3–8, use the box-and-whisker plot to find the given measure.
Answer:
3. The least value is 3.
4. The greatest value is 14.
5. The third quartile is 11
6. The first quartile is 6
7. The median is 8.
8. The range is 3-14.
Step-by-step explanation:
Alice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to the nearest foot.
A.
40 feet
B.
80 feet
C.
117 feet
D.
160 feet
Answer:
C) 117 Feet
Step-by-step explanation:
The question is ultimately asking for the hypotenuse of the rectangle. We can calculate that with a^2 + b^2 = c^2.
100^2+60^2=c^2
10000+3600=c^2
c^2=13600
c=116.6190379
Round --> 117
Thus the answer, C).
Which sets of ordered pairs represent a function? Select all that apply.
A. (1,1), (1,2), (1,3), (1.4)
B. (1,1), (2,2), (3,3), (4,4)
C. (1,1), (2,1), (3,1), (4,1)
D. (1,4), (2,4), (1,3), (2,3)
E. (1,4), (2,2), (3,1), (4,3)
Answer:
B, C, and E
Step-by-step explanation:
In order for a function to be a function, an ordered pair cannot be on the same x coordinate
Which statement BEST describes the graph of f(x - 6)?
A. The graph of f(x) is shifted up 6 units.
6
B. The graph of f(x) is shifted left 6 units.
C. The graph of f(x) is shifted right 6 units.
D. The graph of f(x) is shifted down 6 units.
Answer:
B. f(x) is shifted left by 6 units
Step-by-step explanation:
when we talk about translations, we know they happen along the X axis, y axis or sometimes both, in this case we see that were subtracting x by six units, so we are moving left along the x axis
ways to remember this is:
-you count up x the RIGHT way going right
-you count UP y
and of cource by process of ellimination we know that decreasing X goes left and decreasing y goes down
ALSO NOTE: x always goes horizontally and y always goes vertically
6 cm
6 cm
What is the area?
Answer:
= 18 [tex]cm^{2}[/tex]
Step-by-step explanation:
As the triangle is right angled:
formula
= [tex]\frac{1}{2}[/tex] base x height
= [tex]\frac{1}{2}[/tex] 6 x 6
=[tex]\frac{1}{2}[/tex] x 36
=[tex]\frac{36}{2}[/tex]
= 18 [tex]cm^{2}[/tex]
Translate the following sentence into an equation: "Seven added to eight times a number is three less than
twice the number."
?
[tex]let\ x\ be\ the\ unknown\ number[/tex]
[tex]8x+7=2x-3[/tex]
first choose a variable to represent the number.
when something is "..." times a number, we are multiplying that number by that value.
"seven added to eight times a number" means that we are multiplying the number by eight (8x) and then adding seven to it (+7).
"is" usually means 'equals to' so we put an equal sign there.
"three less than twice the number" means that we are multiplying the number by two (2x) and then subtracting three from it (-3).
An equation form of given statement is, 7 + 8m = 3 - 2m where m is any real valued number.
What is an equation?"It is a mathematical statement which consists of equal symbol between two mathematical expressions."
For given question,
We have been given a statement.
We need to translate given statement into a equation.
Seven added to eight times a number is three less than twice the number.
Let 'm' be any real number.
We can rewrite above statement as,
Seven plus to eight times 'm' is three minus twice 'm'.
⇒ 7 + 8 × m = 3 - 2 × m
So, we get an equation,
⇒ 7 + 8m = 3 - 2m
Therefore, an equation form of given statement is, 7 + 8m = 3 - 2m where m is any real valued number.
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