a) What is the initial height of the object?
The initial height of the object is the height at t = 0. Substituting t = 0 in the equation for s(t), we get:
s(0) = -8.05(0)^2 + 35(0) = 0
Therefore, the initial height of the object is 0 feet, which means it is on the surface of the planet.
b) What is the maximum height reached by the object?
The maximum height reached by the object occurs at the vertex of the parabolic function s(t). The vertex of a parabola of the form ax^2 + bx + c is given by the formula:
t = -b/2a
In this case, a = -8.05 and b = 35. Substituting these values, we get:
t = -35/(2*(-8.05)) = 2.17 seconds (rounded to two decimal places)
To find the maximum height, we substitute t = 2.17 seconds in the equation for s(t):
s(2.17) = -8.05(2.17)^2 + 35(2.17) = 34.09 feet (rounded to two decimal places)
Therefore, the maximum height reached by the object is 34.09 feet.
c) When does the object hit the ground?
The object hits the ground when its height s(t) is equal to 0. We can solve the equation -8.05t^2 + 35t = 0 to find the times when s(t) = 0:
-8.05t^2 + 35t = 0
t(-8.05t + 35) = 0
t = 0 or t = 4.34 seconds (rounded to two decimal places)
The first solution, t = 0, corresponds to the initial position of the object, so we can discard it. Therefore, the object hits the ground after approximately 4.34 seconds.
7. Nkaiseng who is 25 years wants to invest some money for her retirement when she is 65 years. If she invest at a compound interest rate of 11.5% per annum. How much money should she invested if she wants to retire R500 300? Round up your answer to the nearest rand (10 Points).
Answer:
The formula for calculating the future value of a present amount with compound interest is:
FV = PV * (1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate (as a decimal), and n is the number of compounding periods.
In this case, Nkaiseng wants to invest some money now to retire with R500 300 in 40 years (from 25 to 65). The annual interest rate is 11.5%, which is equivalent to a monthly interest rate of 0.115/12 = 0.00958.
So we have:
FV = PV * (1 + 0.00958)^ (40*12)
500300 = PV * (1.00958)^480
Dividing both sides by (1.00958)^480, we get:
PV = 500300 / (1.00958)^480
PV = 500300 / 20.4524
PV = 24406.53
Therefore, Nkaiseng should invest R24406.53 (rounded up to the nearest rand) now to have R500 300 when she retires at 65 years with an interest rate of 11.5% per annum.
A Collection of books consists of six Math books and four English books. A book is chosen at random from the collection. Finc the probability of choosing: a) a Maths book b) an English book c) either a maths or an English book d) neither a maths nor an English book.
Answer:
A. 60%
B. 40%
C. Math because Math has higher chance of being chosen.
D. 0%
suface area of cuboid 9 5 4
The cuboid in question has a surface area of 202 square units.
We must sum together the areas of all six faces to determine a cuboid's surface area.
The dimensions of the given cuboid are:
length (l) = 9 units
width (w) = 5 units
height (h) = 4 units
The area of each face is given by:
Top and bottom faces:[tex]lw = 9 * 5 = 45[/tex] square units each
Front and back faces: [tex]lh = 9 *4 = 36[/tex] square units each
Left and right faces: [tex]wh = 5 * 4 = 20[/tex] square units each
Therefore, the total surface area of the cuboid is:
[tex]2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units[/tex]
Hence, the surface area of the given cuboid is 202 square units.
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The following question has two parts. First, answer part A. Then, answer part B.
Part A "If you share 7 apples equally with 3 people, then there are 2 1/3 ..."
First, complete the sentence. Then, briefly explain what the whole number 2, the denominator 3, and the numerator 1 mean in this problem.
Part B The expression 1 ÷ 1 4 is given. Give a real-life application to explain this expression and then simplify it.
"If you share 7 apples equally with 3 people, then there are 2 1/3 apples for each person."The whole number 2 represents the number of apples that each person will get when sharing 7 apples equally with 3 people.
The numerator 1 represents the remaining part of an apple that is left after sharing equally among 3 people. The denominator 3 represents the number of persons with whom the apples are being shared equally.
A possible real-life application for the expression 1 ÷ 1/4 is dividing a pizza into quarters and then sharing one slice of pizza equally among a group of people.
To simplify the expression for sharing, we need to remember that dividing by a fraction is the same as multiplying by its reciprocal. So, 1 ÷ 1/4 is equivalent to 1 × 4/1, which simplifies to 4.
Thus, 1 ÷ 1/4 is equal to 4.
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If you are given odds of 4 to 5 in favor of winning a bet, what is the probability of winning the bet?
Answer:
the probability of winning the bet is 4/9 or approximately 0.444 or 44.44%.
Step-by-step explanation:
To calculate the probability of winning a bet given odds in favor, we can use the following formula:
Probability of winning = Odds in favor / (Odds in favor + Odds against)
In this case, the odds in favor are given as 4 to 5. This means that for every 4 favorable outcomes, there are 5 unfavorable outcomes.
Plugging these values into the formula:
Probability of winning = 4 / (4 + 5)
Probability of winning = 4 / 9
So, the probability of winning the bet is 4/9 or approximately 0.444 or 44.44%.
Can some one solve this for me?
Options:
A - 24
B -21
C-18
D-6
The length of chord LM is determined as 24 inches.
option A.
What is the length of chord LM?The length of the chord LM is calculated by applying the following formula as shown below;
Based on intersecting chord theorem, when two chord intersect in a circle, the product of two segment of one chord is equal to the product of two segment of the second chord.
First we need to find the value of x;
3x(x) = 12 (9)
3x² = 108
x² = 108/3
x² = 36
x = √ 36
x = 6
The length of chord LM is calculated as follows;
LM = x + 3x
LM = 6 + 3(6)
LM = 24
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If Mrs. Hoover sells 50 books at the book fair on Friday, which prediction for Friday is
NOT supported by the data in the table?
The difference between the number of sports and trivia books sold and the
number of arts and crafts books sold on Friday will be 12.
The number of non-fiction books sold on Friday will be two-and-a-half times the
number of arts and crafts books sold on Friday.
The combined Friday sales for non-fiction books and novels will be 30 books.
The number of novels sold on Friday will be 10 times the number of non-fiction
books sold on Friday.
The prediction that is not supported by the data is option B: "The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday."
We can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.
On Thursday, 13 non-fiction books and 19 arts and crafts books were sold.
If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)×2.5 = 23.75 Which is not a whole number.
Therefore, this prediction is not supported by the data.
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from a hot air balloon the angles of depression to each end of the lake are 68º and and 32º. given that the balloon is 250 m above the ground, find the length of the lake.
The length of the lake is equivalent to 295 meters.
We can write that -
tan(32°) = 250/{x}
{x} = 250/tan(32°)
also
tan(68°) = 250/{y}
{y} = 250/tan(68°)
We can write the length of the lake as -
L = x - y
L = 250/tan(32°) - 250/tan(68°)
L = 250{1/tan(32°) - 1/tan(68°)}
L = 250{1/(0.63) - 1/(2.48)}
L = 250{1.58 - 0.40}
L = 250 x 1.18
L = 295 meters
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Need help now please! Thanks!
The simplest radical form of the sine of y/2 is:
sin(y/2) = ±√(2/5)
How to find the value of sin(y/2)?Here we know that:
cos(y) = 1/5.
We want to find sin(y/2), so we can use the identity:
sin(y/2) = ±√( ( 1 - cos(y))/2)
Replacing cos(y) there we will get.
sin(y/2) = ±√( ( 1 - 1/5)/2)
sin(y/2) = ±√( ( 4/5/2)
sin(y/2) = ±√(2/5)
That is the simplest radical form.
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Help me with this please
Answer:
29°
Step-by-step explanation:
since a right angle in 90° just subtract 61 out of 90
90°-61°=29°
2 tens + 23 ones=
Trying to help my daughter with homework
Use the graph to answer the question.
Graph of polygon ABCDE with vertices at negative 1 comma negative 4, negative 1 comma negative 1, 3 comma negative 1, 3 comma negative 4, 1 comma negative 6. A second polygon A prime B prime C prime D prime E prime with vertices at 13 comma negative 4, 13 comma negative 1, 9 comma negative 1, 9 comma negative 4, 11 comma negative 6.
Determine the line of reflection.
Reflection across the x-axis
Reflection across x = 6
Reflection across y = −3
Reflection across the y-axis
The line of reflection for the graph is Reflection across x = 6.
Given a graph of the polygon ABCDE.
Vertices of the polygon are :
A(-1, -4), B(-1, -1), C(3, -1), D(3, -4) and E(1, -6).
Also given a graph of the polygon A'B'C'D'E'.
A'(13, -4), B'(13, -1), C'(9, -1), D'(9, -4) and E'(11, -6).
Here the y coordinates has not been change. Only the x coordinates change.
So the line of reflection will be of the form x = c.
Mid point of each of the corresponding vertices are,
Mid point of AA' = (6, -4),
Midpoint of BB' = (6, -1)
Midpoint of CC' = (6, -1)
Midpoint of DD' = (6, -4)
Midpoint of EE' = (6, -6)
So all the x coordinates are same, x = 6
Hence the line of reflection is x = 6.
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Trigonometry. See attached image:
Show all work.
The expression sec θ / csc θ + 2sin θ / cos θ is equal to the expression 3tan θ is proven below.
Given that:
sec θ / csc θ + 2sin θ / cos θ = 3 tan θ
The properties are given as,
tan x = sin x / cos x
sec x = 1 / cos x
sin x = 1 / csc x
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Take the left-hand side, then
LHS = sec θ / csc θ + 2sin θ / cos θ
LHS = sin θ / cos θ + 2tan θ
LHS = tan θ + 2 tan θ
LHS = 3 tan θ
LHS = RHS
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if ABCD is the square. Find the value of x if BE = 3x + 5 and CA= 8x+2.
Answer:
x = 4----------------------
The diagonals of a square bisect each other.
It makes all half-diagonals of equal length. Therefore:
CA = 2BESubstitute and solve for x:
8x + 2 = 2(3x + 5)8x + 2 = 6x + 108x - 6x = 10 - 22x = 8x = 4Hence the value of x is 4.
Given f(x) = X-4 and g(x) = 9x + 4, find (g of (x).
A)9x+32
B) x-1
C) X
D) x + 8
Answer:
To find (g of f)(x), we need to first find f(x) and then substitute it into g(x).
f(x) = x - 4
Now we can substitute f(x) into g(x):
g(f(x)) = 9f(x) + 4
g(f(x)) = 9(x - 4) + 4
g(f(x)) = 9x - 36 + 4
g(f(x)) = 9x - 32
Therefore, the answer is (A) 9x+32.
Answer:
the answer is d- (x-5)
sylvia watched a movie that was 1 whole 3/4 hours long. then she went to a baseball game that lasted for 3 wholes 1/3 hours. how much longer was the baseball game than the movie?
The calculated time of is that the baseball game was 1 7/12 hour longer than the movie
How much longer was the baseball game than the movie?The given parametes in the question are
Movie = 1 3/4 hours
Baseball = 3 1/3 hours
To calculate how much longer was the baseball game than the movie, we subtract
So, we have
Longer = 3 1/3 - 1 3/4
Evaluate
Longer = 19/12
This gives
Longer = 1 7/12
Hence, the baseball game was 1 7/12 hour longer than the movie
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The volume of a right cone is 1824 � π units 3 3 . If its circumference measures 24 � π units, find its height.
The value of the height of the cone is 38 units
How to determine the height
The formula for calculating the circumference of a cone is represented as;
Circumference = 2πr
Now, substitute the value to determine the radius, we have;
24π = 2πr
Divide by the coefficient of r
r = 24π/2π
r = 12 units
The formula for the volume of a cone is;
Volume = πr²h/3
Substitute the values
1824 π = π × 144 ×h/3
Multiply the values
1824π = 144πh/3
Make h the subject
h = 38 units
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Solve please, see the picture
The area of the new shape is 74 squared cm
How to find the area of the new shape
The area of the new shape is solved by dividing the shape into three sections and then sum up all the areas
The area of the sections are as follows
Section 1: length x width
= 8 x 5
= 40 squared cm
Section 2: length x width
= 5 x 2
= 10 squared cm
Section 3: length x width
= 8 x 3
= 24 squared cm
Total area
= 24 + 10 + 40
= 74 squared cm
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The area of the new shape is 74cm²
What is area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
The shape is a combination of two rectangles. One of the rectangles cut out.
The area of the cut out is calculated as;
A = l × w
A = 3 × 2
A = 6cm²
The area of the cut out rectangle = area of the whole rectangle - area of cut out rectangle
= 8×5 -6
= 40-6
= 34cm²
The area of the second rectangle = l×w
= 8× 5
= 40cm²
Therefore area of the new shape = 40+34
= 74cm²
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The perimeter of the shape below is 44 feet. What is the area in square feet?
The area of the shape is 120 if the perimeter of the given shape is 44 feet.
The shape is given below.
It is in the shape of a rectangle.
Length = 6x and width = 4x + 2
Perimeter of a rectangle = 2 × (Length + Width)
So,
2 (6x + 4x + 2) = 44
2 (10x + 2) = 44
10x + 2 = 22
10x = 20
x = 2
So, length = 6x = 12
Width = 4x + 2 = 10
Area of the rectangle = Length × Width
= 12 × 10
= 120
Hence the area of the shape is 120.
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On a certain hot summer's day, 454 people used the public swimming pool. The daily prices are $1.50 for children and $2.50 for adults. The receipts for admission totaled $1,043.00. How many children and how many adults swam at the public pool that day?
Answer:
Let's assume that the number of children who used the public swimming pool is 'x' and the number of adults who used the pool is 'y'.
From the given information, we can form two equations:
x + y = 454 (equation 1) --> the total number of people who used the pool
1.5x + 2.5y = 1043 (equation 2) --> the total revenue collected from admission fees
We can use these equations to solve for 'x' and 'y'. Let's start by multiplying equation 1 by 1.5 to eliminate 'x':
1.5x + 1.5y = 681 (equation 1 multiplied by 1.5)
1.5x + 2.5y = 1043 (equation 2)
Now, we can subtract equation 1 from equation 2 to eliminate 'x' and solve for 'y':
2.5y - 1.5y = 1043 - 681
y = 224
So, there were 224 adults who used the pool. We can substitute this value into equation 1 to solve for 'x':
x + 224 = 454
x = 230
Therefore, there were 230 children who used the pool.
An elevator has a placard stating that the maximum capacity is 1944 lb-12 passengers. So, 12 adult male
passengers can have a mean weight of up to 1944/12 = 162 pounds. If the elevator is loaded with 12 adult
male passengers, find the probability that it is overloaded because they have a mean weight greater than 162
Ib. (Assume that weights of males are normally distributed with a mean of 169 lb and a standard deviation of 29 lb.)
Does this elevator appear to be safe?
The probability the elevator is overloaded is
(Round to four decimal places as needed.)
The probability 0.7977 that the sample mean weight of 12 adult male passengers is greater than 162 lb.
There is a 79.77% chance that the elevator is overloaded
What is Central Limit Theorem?We can use the Central Limit Theorem here, which states that the sample mean of a sufficiently large sample size (n≥30) will be approximately normally distributed with mean μ and standard deviation σ/√n, where μ is the population mean and σ is the population standard deviation.
In this case, n=12, μ=169 lb, and σ=29 lb. Therefore, the sample mean weight of 12 adult male passengers will be approximately normally distributed with mean 169 lb and standard deviation 29/√12 ≈ 8.38 lb.
Now we can standardize this distribution to find the probability that the sample mean weight is greater than 162 lb:
z = (162 - 169) / 8.38 ≈ -0.83
We determine that the probability of z being less than or equal to -0.83 is approximately 0.2023, which can be calculated using a standard normal distribution table or calculator.
Therefore, there is a probability of 1 - 0.2023 ≈ 0.7977 that the sample mean weight of 12 adult male passengers is greater than 162 lb.
This indicates that if the elevator is filled with 12 adult male passengers, there is a 79.77 percent chance that it will be overloaded. The elevator does not appear to be safe for this many passengers, and this is a very high probability
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A fitness expert was doing research on football teams. He randomly selected 10 players from a college team and 10 players from a professional team. The players were weighed and the statistics are shown below. First Quartile Second Quartile (Median) College Professional 190 205 235 255 232 Third Quartile 246 Based on these samples, what generalization can be made? O A. The median weight of the professional players is greater than the median weight of the college players. OB. Not enough information is provided to draw any of these conclusions. OC. The median weight of the college players is greater than the median weight of the professional players. OD. Out of the college and professional players, the professional players have the heaviest player. Reset Submit
Based on these samples, the generalization that can be made is The median weight of the professional players is greater than the median weight of the college players.
Therefore Option A is correct.
What is median weight?The median weight of the ordered data is found when the number that splits the data into two equal parts.
The median weight of the college players is
(215 + 232)/2 = 223.5 pounds.
The median weight of the professional players is
(235 + 255)/2 = 245 pounds.
In conclusion, the median weight of the professional players is greater than the median weight of the college players, so the generalization that can be made is The median weight of the professional players is greater than the median weight of the college players.
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Determine the area of the composite figure to the nearest whole number.
135cm²
117cm²
173cm²
74cm²
The area of the composite figure is A = 135 cm²
Given data ,
Let the figure consists of a rectangle and quarter circle
where the area of the rectangle is R and area of quarter circle is C
And , A = R + C
Area of rectangle A = 20 x 2 = 40 cm²
And , area of quarter circle C = ( 1/4 )π ( 11 )²
C = 95.033 cm²
So , A = 95 + 40
A = 135 cm²
Hence , the area of the figure is A = 135 cm²
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The complete question is attached below :
Determine the area of the composite figure to the nearest whole number.
135cm²
117cm²
173cm²
74cm²
2) 11 ft K-7 ft-K-8 ft- ·20 ft.
The area of the given figure is 192.5 ft².
Given is a figure we need to find its area,
By splitting the shape in 2, we can find the area.
Starting with the parallelogram (on the left), the area formula is A = b × h.
b (base) = 11 ft.
h (height) = 7 ft.
A (area) = (11 ft.)(7 ft.)
A = 77 ft.²
Then, the trapezoid's (on the right) area formula is A = [(a + b) ÷ 2] × h.
a (first base) = 8 ft.
b (second base) = (20 - 7) = 13 ft.
h (height) = 11 ft.
A = [(8 ft. + 13 ft.) ÷ 2] × 11 ft.
A = [(21 ft.) ÷ 2] × 11 ft.
A = (10.5 ft.) × 11 ft.
A = 115.5 ft.²
we can add them together to find the total area:
A = 77 ft.² + 115.5 ft.²
A = 192.5 ft.²
Hence, the area of the given figure is 192.5 ft².
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Cane somebody help me with this??
The values of the variables x, y and a in the circles are calculated below
Calculating the values of the variablesCircle 1
The measure of the angle x is calculated as
28 = 1/2(x - 61)
So, we have
x - 61 = 56
This gives
x = 117
For y, we have
y² = 4 * 18
So, we have
y = 6√2
Circle 2
The measure of the angle x is calculated as
x + 48 = 180
So, we have
x = 132
The length y is calculated as
tan(24) = 7/y
So, we have
y = 7/tan(24)
Evaluate
y = 15.7
Circle 3
This is calculated as
9 * (9 + a) = 8 * 21
So, we have
81 + 9a = 168
So, we have
a = 9.67
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Evaluate the expression
3(3a-1)+2, for a=2
Answer: 17
Step-by-step explanation:
Substitute the value of the variable into the equation and simplify.
3 ( 3 ( 2 ) - 1 ) + 2 = 17
NO LINKS!! URGENT HELP PLEASE!!
If a and h are real numbers, find the following values for the given function.
f(x) = 3 -2x
a. f(-a)=
b. -f(a)=
c. f(a + h)
d. f(a) + f(h)
e. (f(a + h) - f(a))/h if h ≠ 0
Answer:
Step-by-step explanation:
a. f(-a) = 3 - 2(-a) = 3 + 2a
b. -f(a) = -(3 - 2a) = -3 + 2a
c. f(a + h) = 3 - 2(a + h) = 3 - 2a - 2h
d. f(a) + f(h) = (3 - 2a) + (3 - 2h) = 6 - 2a - 2h
e. (f(a + h) - f(a))/h = [3 - 2(a + h) - (3 - 2a)]/h = [-2h]/h = -2, if h ≠ 0.
Answer:
a. To find f(-a), substitute -a for x in the given function:
f(-a) = 3 - 2(-a) = 3 + 2a
Therefore, f(-a) = 3 + 2a.
b. To find -f(a), evaluate f(a) and then multiply by -1:
f(a) = 3 - 2a
-f(a) = -(3 - 2a) = -3 + 2a
Therefore, -f(a) = -3 + 2a.
c. To find f(a + h), substitute a + h for x in the given function:
f(a + h) = 3 - 2(a + h) = 3 - 2a - 2h
Therefore, f(a + h) = 3 - 2a - 2h.
d. To find f(a) + f(h), evaluate f(a) and f(h), and then add them:
f(a) = 3 - 2a
f(h) = 3 - 2h
f(a) + f(h) = (3 - 2a) + (3 - 2h) = 6 - 2a - 2h
Therefore, f(a) + f(h) = 6 - 2a - 2h.
e. To find (f(a + h) - f(a))/h if h ≠ 0, substitute the expressions for f(a + h) and f(a) into the formula:
(f(a + h) - f(a))/h = ((3 - 2a - 2h) - (3 - 2a))/h = (-2h)/h = -2
Therefore, (f(a + h) - f(a))/h = -2 if h ≠ 0.
what is the factor form of the quadratic equation y=x^2-8x-9
Answer:
To factor the quadratic equation y = x^2 - 8x - 9, we need to find two numbers that multiply to give -9 and add to give -8 (the coefficient of the x term).
We can start by looking for two factors of -9 that add up to -8. The only pair of factors that works are -9 and 1. This is because (-9) + 1 = -8, and (-9) times 1 is -9.
Now we can use these factors to express the middle term of the quadratic in terms of two separate terms that can be factored by grouping. We can do this by splitting the -8x term into -9x + x:
y = x^2 - 9x + x - 9
Now we can group the first two terms together and the last two terms together:
y = (x^2 - 9x) + (x - 9)
We can factor out x from the first group, and factor out -9 from the second group:
y = x(x - 9) + (-9)(x - 9)
Finally, we can factor out the common factor of (x - 9):
y = (x - 9)(x - 1)
Therefore, the factor form of the quadratic equation y = x^2 - 8x - 9 is (x - 9)(x - 1).
What is the median in this boxplot?
000
900
700
500
400
300
200
100
O 154
O 345
420
O 484
0000000000000
O924
22%3
04.0
Ma
(154,000)
The median of the boxplot is 420.
In a boxplot, the median is the line in the Centre of the box.
Given that;
The upper horizontal line of the box is at 490
The Lower horizontal line of the box is at 350
Therefore the median of boxplot
= (upper point + lower point)/2
= (490 + 350)/2
= 420
Hence middle point be at 420.
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Marty has 6 gallons of orange juice. How many pints of orange juice does Marty have?
Answer:
Marty has 768 pints of orange juice.
Step-by-step explanation:
To convert gallons to pints, we need to remember that 1 gallon is equal to 128 fluid ounces, and 1 fluid ounce is equal to 1/8 pint.
Given that Marty has 6 gallons of orange juice, we can calculate the total amount in pints as follows:
6 gallons x 128 fluid ounces/gallon x 1/8 pint/fluid ounce = 768 pints
So, Marty has 768 pints of orange juice.
