Step-by-step explanation:
7red marbles,3 blue marbles,4 green marbles
In the third month of a study, a sugar maple tree is 82 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month
The linear equation that gives the height on the x-th month is:
y = 2.5*x + 74.5
Which rule gives the height of the tree for the n-th month?
This will be modeled with a linear equation of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.
So the slope is:
[tex]a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5[/tex]
Then the linear equation is:
y = 2.5*x + b
To get the value of b, we use the fact that when x = 3, we have y = 82,
82 = 2.5*3 + b
82 = 7.5 + b
82 - 7.5 = b = 74.5
Then the linear equation is:
y = 2.5*x + 74.5
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what is an arithmetic pattern
2. Calculate the amount of compound interest paid on $7300 at the end of 3 years for each
rate. [2 marks each]
a) 10% compounded semi-annually
b) 8% compounded monthly
The compound interest when $7300 when interest is compounded semi annually is $2482.70.
The compound interest when $7300 when interest is compounded monthly is $1972.73.
What is the compound interest?An investment earns compound interest when both the amount invested and the interest accrued increases in value at predetermined time intervals.
The formula to represent compound interest is :
FV - amount invested
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsa. 7300 x [1 + (0.1/2)]^(3 x 2) = 9782.70
Compound interest = 9782.70 = 7300 = $2482.70
b. 7300 x [1 + (0.08/12)]^(12 x 3) = 9272.73
9272.73 - 7300 = $1972.73
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please help me with these questions????
An oblique cylinder has a radius of 9 centimeters and a volume of 486 cubic centimeters. Use Cavalieri’s Principle to calculate the height of the solid.
6 meters
5 meters
8 meters
7 meters
Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.
Option A) is the correct answer.
What is the height of the oblique cylinder?From Cavalieri's principle, the volume of an oblique cylinder is expressed as;
V = base area × h
V = πr² × h
Given that;
Radius r = 9cmVolume of the oblique cylinder V = 486πcm³Height of the oblique cylinder h = ?V = πr² × h
486πcm³ = π × ( 9cm )² × h
486πcm³ = π × 81cm² × h
486πcm³ = 81πcm² × h
h = 486πcm³ / 81πcm²
h = 6cm
Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.
Option A) is the correct answer.
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What is the equation of a line with a slope of -1 and a y-intercept of -5?
Answer:
y = -x - 5
Step-by-step explanation:
The general structure of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
Since you have been given the slope and y-intercept, you can substitute these values into the equation to find the answer.
m = -1
b = -5
y = mx + b
y = (-1)x + (-5)
y = -x - 5
Answer:
y = -x -5
Step-by-step explanation:
We can use y = mx + c to find the equation of the line.
Here,
m ⇒ slope of the line
c ⇒ y - intercept
They have already given that,
m ⇒ -1
c ⇒ -5
So, now we can write the equation of the line like this.
To write the equation of the line you can replace m and c with -1 & -5 respectively.
Let us write now.
y = m x + c
y = -1x - 5
PLEASE HELP 100 POINTS:
Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750m. What is the percentage change in volume from cylinde
A to cylinder B?
50% decrease
75% decrease
50% increase
200% increase
Answer:
The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
What is a cylinder?
In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the formula for the volume of the cylinder is given by:
We have r = 10 inches and h = 5 inches
V = 500π cubic inches
Percent change in volume from cylinder A to cylinder B:
= 50%
Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
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Step-by-step explanation:
Solve for x. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answer: 13.3
Step-by-step explanation:
Since angles in a triangle add to 180 degrees, we know that in triangle UWV, [tex]m\angle U=50^{\circ}[/tex]. Thus, the triangles are similar by AA.
Since corresponding sides of similar triangles are proportional,
[tex]\frac{x}{24}=\frac{20}{36}\\x=(20/36)(24)=\boxed{13.3}[/tex]
Freda waves a small flag pennant when her favorite player hits a grand slam. approximately how much fabric in square inches is used to make up the flag on her pennant
Answer: 15 inches
Step-by-step explanation:
Answer:
In a right triangle, the hypotenuse, 2x, is equal to twice the length of the shortest leg, x, and the longer leg is equal to the product of the length of the shortest leg, x, and the square root of 3.
Hypotenuse: 10 in.
Shortest Leg:2x=10 , so x=5 in,
Longer Leg: x sq rt 3 5 sq rt 3 in
area- 1/2 bh, 1/2 5*5 sq rt 3=
25t sq rt 3=21.65 sq inches
Your school has a massive gym. It is 16 feet by 24 feet. You
want to figure out how many stations for the fundraiser you
can have. All the tables are squares but come in different
styles. What is the greatest square table you can use?
The greatest square that the gym would be able to use is the one that is of 19.6sq/m
How to solve for the squareThe area of a triangle = L*W
= 24 * 16
= 384
To get the greatest square that can be gotten from the size of the gym would be
√384 = 19.6
Hence we can conclude that the greatest square table that can be used is 19.6 feet
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solve pls brainliest
Answer:
c = 22 (= -18)c = 23 (< -18 because - goes down).4 - c ≤ -18Step-by-step explanation:
Solve for 1st answer:
4 - c = -18= 4 - 22 = -18= 0 - 18 = -18 (Basically subtract 4 from 22)= -18c = 22Solve for 2nd answer:
4 - c < -18= 4 - 23 < -18= 0 - 19 < -18= -19c = 23Actual answer:
4 - c ≤ -18.The tree diagram represents an
experiment consisting of two trials.
Answer:
P(D) = 0.65
Step-by-step explanation:
it's like following a path on map
each line is like a street length
First, it's 0.5 to A and then 0.6 to D.
Then, it's 0.5 to B and 0.7 to D.
P(D) = (0.5 times 0.6) + (0.5 times 0.7) =
P(D) = 0.30 + 0.35 = 0.65
A tree diagram is simply a way of representing a sequence of events.
Tree diagrams are particularly useful in probability since they record all possible outcomes in a clear and uncomplicated manner.
like chance of getting heads or tails on coin flips
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nrich.maths.org
math is fun
will get brainliest if answered right. no smart remarks
Answer:
A.g, a.f ,a.b
Step-by-step explanation:
Which of the following shows the correct steps to find the value of 27 to the power of 1 over 3 ? (1 point)
A. 27 to the power of 1 over 3 equals 9 to the power of 3 to the power of 1 over 3 equals 9 to the power of 3 multiplied by 1 over 3 equals 9
B. 27 to the power of 1 over 3 equals 3 to the power of 9 to the power of 1 over 3 equals 3 to the power of 9 multiplied by 1 over 3 equals 3
C. 27 to the power of 1 over 3 equals 3 to the power of 4 to the power of 1 over 2 equals 3 to the power of 4 multiplied by 1 over 2 equals 9
D. 27 to the power of 1 over 3 equals 3 to the power of 3 to the power of 1 over 3 equals 3 to the power of 3 multiplied by 1 over 3 equals 3
Answer:
D
Step-by-step explanation:
it shows the correct one
Which of the following tables represent a function?
A.
X 3 3 4 4
Y 2 -2 3 -3
B.
X 5 -5 5 -5
Y 2 2 8 8
C.
3 3 5 5
Y 4 5 6 7
D.
X 4 -4 5 -5
Y 2 2 3 3
The 2 because I am goated
Step-by-step explanation:
Which segments are perpendicular?
Answer: B
Step-by-step explanation:
Angles that measure 90 degrees, angles that measure 90 degrees are right angles, and perpendicular lines form right angles.
Since angle EAB is a right angle, and it is formed by segments EA and AB, B is the answer.
Is 10h - 10 equal to10 - 10h
Answer:no
Step-by-step explanation:
it’s equal to -10 + 10h by the commutativity of addition and subtraction
Write the following ratio using two other notations. 7:6 Use only the numbers above (not any others).
[tex]\textbf{Notation one:}~~ \dfrac 76\\\\\textbf{Notation two:} ~ \text{7 to 6}[/tex]
find x in this two examples
The values of x in both figures are 45 and 34, respectively.
The value of x in (a)Start by calculating the angle CAB using:
CAB + ABC + BCA = 180 --- angles in a triangle
The triangle is an isosceles triangle.
So, we have:
CAB + ABC + CAB = 180
Evaluate
2CAB + 25 + 75 = 180
This gives
CAB = 40
Calculate angle BEA using:
BEA + CAB + ABE = 180 --- angles in a triangle
This gives
BEA + 40 + 25 = 180
Evaluate
BEA = 115
Vertical angles are equal.
So, we have:
CED = BEA = 115
Calculate angle EDC using:
EDC + CED + DCE = 180 --- angles in a triangle
This gives
EDC + 115 + 30 = 180
Evaluate
EDC = 35
Opposite angles of quadrilaterals add up to 180.
So, we have:
x + EDC + ABC = 180
This gives
x + 35 + 25 + 75 = 180
Evaluate
x = 45
Hence, the value of x is 45
The value of x in (b)Start by calculating the angle DEC using:
DEC + CDE + EED = 180 --- angles in a triangle
This gives
DEC + 18 + 30 = 180
Evaluate
DEC = 132
Vertical angles are equal.
So, we have:
AEB = DEC = 112
Calculate angle EAB using:
EAB + AEB + ABE = 180 --- angles in a triangle
This gives
EAB + 112 + 42 = 180
Evaluate
EAB = 26
Triangle ABC is an isosceles triangle.
So, we have:
BCE = EAB = 26
Calculate angle CBE using:
CBE + BCE + CEB = 180 --- angles in a triangle
Where CEB = 180 - DEC --- angle on a straight line
So, we have:
CBE + BCE + 180 - DEC = 180
This gives
CBE + 26 + 180 - 112 = 180
Evaluate
CBE = 86
Opposite angles of quadrilaterals add up to 180.
So, we have:
x + EDC + ABC = 180
This gives
x + 18 + 42 + 86 = 180
Evaluate
x = 34
Hence, the value of x is 34
Note that the figures are labeled to ease explanation (see attachment)
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divide $8 in the ratio 2:3
Answer:
3.2$ and 4.8$Step-by-step explanation:
divide $8 in the ratio 2:3
8 : (2 + 3) = 1.6 (unity)
1.6 * 2 = 3.2 (ratio2)
1.6 * 3 = 4.8 (ratio 3)
----------
3.2 + 4.8 = 8
the answer is good
The hour and minute hands of a clock form an angle that constantly changes. During each hour of the day, the clock hands will form right, acute, and obtuse angles. Assume the hour hand points directly at the hour.Write a time of day when the two clock hands form each type of angle
The each type of angle are discussed below
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
If the hours hand point to the hour 1 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 2 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 3 and minute hand at 12 then
angle will be right angle .
If the hours hand point to the hour 4 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 5 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 6 and minute hand at 12 then
angle will be straight angle .
If the hours hand point to the hour 7 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 8 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 9 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 10 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 11 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 12 and minute hand at 12 then
angle will be Complete angle.
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Need help with this
Answer:
y = 130
Step-by-step explanation:
given that y varies directly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
to find k use the condition y = 150 when x = 2.5 and z = 12 , then
150 = k × 2.5 × 12 = 30k ( divide both sides by 30 )
5 = k
y = 5xz ← equation of variation
when x = 4 and z = 6.5 , then
y = 5 × 4 × 6.5 = 20 × 6.5 = 130
What is the slope of the line graphed below ? (3, 5); (0, 1); m = A 1/3 B. 3 C. - 3; - 1/3
Answer:
4/3 = m
Step-by-step explanation:
Since you have been given the value of two points, you can use the point-slope formula to find the slope. This general structure of this formula is:
y₁ - y₂ = m(x₁ - x₂)
In this equation, "m" represents the slope, "y₁" and "x₁" represent the values in the first point, and "y₂" and "x₂" represent the values in the second point,
To find the slope, substitute the values of each point into the formula and simplify.
Point 1: (3, 5)
Point 2: (0, 1)
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
5 - y₂ = m(3 - x₂) <----- Plug values from Point 1 into equation
5 - 1 = m(3 - 0) <----- Plug values from Point 2 into equation
4 = m(3 - 0) <----- Simplify left side
4 = m(3) <----- Simplify inside the parentheses
4/3 = m <----- Divide both sides by 3
I am almost certain that my math is correct, yet my answer does not match any of the answers given. Perhaps I have been given the wrong points? For instance, the answer would be A.) if the value of Point 2 was (0,4).
please give me the answer to this
i beleive the answer is 2610.4109589
PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?
Answer:
$46.272
Step-by-step explanation:
The graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
The y-intercept is 3.75, and the equation of the line of best fit is
y = 1.5x + 3.75, and after 13 months, 23 matches could be won.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
Part A:
As we can see in the graph, the line crosses the y-axis at a certain point between 3 and 4.5.
So the y-intercept lies between 3 and 4.5
We can take the middle of these two values to get the approximate value of the y-intercept.
b = (3+4.5)/2 = 3.75
We know the line of the best fit is:
y = mx + b
y = mx + 3.75
b is the y-intercept and m is the slope of a line
Plug the point (9, 18) in the equation to get the value of m:
18 = 9m + 3.75
m = 1.5
y = 1.5x + 3.75
Plug x = 13 months in the above equation:
y = 1.5(13) + 3.75
y = 23.25 ≈ 23 number of matches that could be won
Thus, the y-intercept is 3.75, and the equation of the line of best fit is
y = 1.5x + 3.75, and after 13 months, 23 matches could be won.
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Combine like terms 2x - 5x
Answer:
-3x
Step-by-step explanation:
its just like regular subtraction, 2-5= -3, and just add an X at the end and you get -3x.
o. Find the domain and range of each of the three restricted functions.
Type your response here:
Domain
(restricted)
Function
Range
I
f(x)=sin(x)
f(x) = cos(x)
f(x) =tan(x)
The domain and range of the functions sin x, cos x, and tan x will be (-∞, ∞) and [-1, 1], (-∞, ∞) and [-1, 1], and R - (2n + 1)π/2 and (-∞, ∞) respectively.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The three restricted functions are given below.
f(x) = sin (x)
f(x) = cos (x)
f(x) = tan (x)
Then the domain of the three restricted functions will be
The domain of sin x will be (-∞, ∞).
The domain of cos x will be (-∞, ∞).
The domain of tan x will be R - (2n + 1)π/2.
Then the range of the three restricted functions will be
The range of sin x will be [-1, 1].
The range of cos x will be [-1, 1].
The range of tan x will be (-∞, ∞).
The graph is given below.
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Naomi's car exponentially depreciates at a rate of 8% per
year. If Nina bought the car when it was 4-years old for $16,500, what was
the approximate original price of the car?
The approximate original price of the car is $23032
How to determine the original price?The given parameters are:
Rate, r = 8%
Price at 4 years old = 16,500
An exponential function is represented as:
y = a(1 - r)^x
Where a represents the initial value
This gives
y = a(1 - 8%)^x
Evaluate
y = a(0.92)^x
At 4 years old, we have:
16500 = a(0.92)^4
Divide both sides by (0.92)^4
a = 23032
Hence, the approximate original price of the car is $23032
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x divided by the sum of x and 5
Answer:
1 + 1/5xStep-by-step explanation:
x divided by the sum of x and 5
x : (x + 5) =
x × (1/1x^-1 + 1/5) =
1 + 1/5x