The median number of pages of the 9 books that Mary read during the summer reading program is 195 pages .
To find the median number of pages of the 9 books that Mary read during the summer reading program, we first need to arrange the pages in ascending order:
112 pages, 138 pages, 138 pages, 159 pages, 195 pages, 210 pages, 217 pages, 270 pages, 356 pages
The median is the middle value in this ordered list. Since there are an odd number of values, the middle value is the fifth one, which is 195 pages.
The median is a measure of central tendency that divides a dataset into two equal halves. In this case, it represents the number of pages that is halfway between the smallest and largest values. It is a useful measure because it is less affected by outliers or extreme values than the mean.
In Mary's case, the median number of pages of the 9 books she read during the summer reading program is 195 pages. This means that half of the books she read had fewer than 195 pages and half had more than 195 pages. It gives us a good idea of what to expect in terms of the length of the books she read.
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What is that name of the shape
Answer:
trapezium
Step-by-step explanation:
it is a quadrilateral in which only one pair of opposite sides is parallel
Answer:
Trapezium
Step-by-step explanation:
That shape is a Trapezium as it is a quadrilateral having one pair of parallel sides.
Given: ABCD is a trapezoid.
CD
BA
Prove: BD
B
A
CA
D
C
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Angles Segments Triangles Statements Reasons
ZBAD
201
Statements
ZCDA
Reasons
Note that
1.BA~CD Given
2.ABCDis a trapezoid Given
3.ABCD is and isosceles trapezoid - Definition of of isosceles trapezoid
4. AD~AD - reflective property
5.6. Triangle BAD ~ triangle CDA - SAS Axiom
7.BD~ CA - CPCTC
What is an Isosceles Trapezoid?
The top and bottom sides of an isosceles trapezoid are parallel, but the other two non-parallel sides are the same length. A trapezoid is a quadrilateral having two parallel sides and two non-parallel sides, as we know.
The bases (top and bottom) are perpendicular to one other. The bases (top and bottom) are perpendicular to one other. Congruent angles can be found on either side of the base. Congruent angles can be found on either side of the base.
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Determine each segment length in right triangle ABC
The length of segment BD of the right triangle is 7 units.
The length of segment BC of the right triangle is 7√2.
What is the length of segment of the triangle?
The length of each segment of the triangle is calculated applying trig ratio as follows;
The length of segment BD is calculated as follows;
tan 45 = opposite side / adjacent side
The adjacent side of the right triangle is given as 7 units, the opposite side which is the height (BD) is calculated as follows;
tan 45 = BD/7
BD = 7 x tan 45
BD = 7 x 1
BD = 7
The segment BC is calculated as follows;
cos 45 = CD / BC
cos 45 = 7 / BC
BC = 7/ cos 45
BC = 7√2
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11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. How many rain jackets were sold
find the area of each triangle using the formula of A=L×W/2
The areas of the triangles are 5 square units and 35 square units
Calculating the areas of the trianglesFrom the question, we have the following parameters that can be used in our computation:
Area = Length * Width/2
Where
Length = L
Width = W
Triangle (a)
L = 2 and W = 5
When the given values are substituted, we have the following equation
Area = 2 * 5/2
Area = 5
Triangle (b)
L = 10 and W = 7
When the given values are substituted, we have the following equation
Area = 10 * 7/2
Area = 35
Hence, the areas of the triangles are 5 square units and 35 square units
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Complete question
Find the area of each triangle using the formula of A=L×W/2
(a) L = 2 and W = 5
(b) L = 10 and W = 7
write (-6, -3) slope = 1/2, in slope-intercept form
y=1/2x-3
"The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point."
Also, 1/2 (m= slope)
Also, rise⬆️/run↔️ is a good way to remember how to graph them. If the "Rise"(1) is positive it will go up. if it is negative it will go down. if the "Run" (2) is positive, youll go right, if it is negative youll go left.
Which graph shows the solution to the system of linear inequalities?
2x - 3y <12
y < =2
The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.
We have,
To find the solution to the system of linear inequalities:
2x - 3y < 12
y ≤ 2
We first graph the line 2x - 3y = 12:
To graph the line, we can find the x and y intercepts:
When x = 0, we have -3y = 12, then y = -4, so (0, -4) is a point on the line.
When y = 0, we have 2x = 12, then x = 6, so (6, 0) is a point on the line.
Plot these two points and draw the line passing through them:
Next, we shade the region that satisfies the inequality 2x - 3y < 12:
We can choose a test point not on the line, such as (0,0).
Substitute the coordinates into the inequality:
2(0) - 3(0) < 12, which is true.
Now,
We shade the region that satisfies the inequality y ≤ 2:
We shade the region below the horizontal line y = 2:
Therefore,
The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.
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Solve the system of equations.
3
�
−
11
�
=
−
1
2
�
−
5
�
=
−
3
3x−11y=−1
2x−5y=−3
�
=
x=x, equals
�
=
y=y, equals
The solution to the system is x = -4, y = -1.
How to solveOne can employ the techniques of substitution or elimination to obtain solutions for the given set of equations.
Let's apply the elimination approach in this scenario.
To ensure that the coefficients of x are equal, multiply the first equation by 2 and the second by 3.
6x - 22y = -2,
6x - 15y = -9.
Subtract the second equation from the first:
0x - 7y = 7.
So, y = -1.
Substitute y = -1 into the second equation:
2x - 5(-1) = -3,
2x + 5 = -3,
2x = -8.
So, x = -4.
The solution to the system is x = -4, y = -1.
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The Complete Question:
Solve the system of equations.
3x – 11y = -1
2x – 5y = -3
A baker used 33 3/4 cups of flour to make
4
15 batches of cookies. How many more cups
of flour does the baker need if she wants to
make 21 batches of cookies?
The baker would need 47. 25 cups of floor
How to determine the valueWe need to know that proportion is a form of mathematical comparison with two equations made equal to each other.
From the information given, we have that;
baker used 33 3/4 cups of flour to make 15 batches of cookies
This is represented as;
Convert to improper fractions
135/4 cups = 15 batches of cookies
Then, x cups = 21 batches of cookies
cross multiply the values
15x = 708. 75
Divide both sides by the coefficient of x, we have ;
x = 708. 75/15
x = 47. 25 cups of floor
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The auto parts department of an automotive dealership sends out a mean of 5 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 5? Round your answer to four decimal places.
17.55% is the probability for any day, the number of special orders sent out will be exactly 5
The given situation describes a Poisson distribution with a mean of 5 special orders per day. The probability of getting exactly 5 special orders in a day can be calculated using the Poisson probability formula, which is:
P(X = k) = (e^(-λ) * λ^k) / k!
where X is the random variable representing the number of special orders, λ is the mean number of special orders per day, and k is the number of special orders we want to find the probability for.
Plugging in the given values, we get:
P(X = 5) = (e^(-5) * 5^5) / 5!
Simplifying this expression, we get:
P(X = 5) = 0.1755
Therefore, the probability of getting exactly 5 special orders in a day is 0.1755 or 17.55%, rounded to four decimal places.
Intuitively, this means that out of many days, we can expect around 17.55% of them to have exactly 5 special orders sent out. The Poisson distribution is commonly used to model the number of events occurring in a fixed period of time, given a known average rate of occurrence. In this case, the Poisson distribution can be used to estimate the likelihood of a particular number of special orders being sent out in a day.
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a total of 584 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold??help please
Answer:
Tickets Sold: 146
Step-by-step explanation:
Let's assume that the number of adult tickets sold is "x".
According to the problem, the number of student tickets sold is three times the number of adult tickets sold. Therefore, the number of student tickets sold is 3x.
The total number of tickets sold is 584, so we can set up an equation:
x + 3x = 584
Simplifying the equation, we get:
4x = 584
Dividing both sides by 4, we get:
x = 146
Therefore, the number of adult tickets sold is 146.
Answer: 146
Step-by-step explanation:
let x = # of adult tickets sold
let y = # of student tickets sold
x + y = 584
this is because the sum of adult tickets and student tickets is 584.
3x = y
this equation is written because there is 3 times more students there than adults
using substitution, we can find the equation :
x + (3x) = 584
4x = 584
x = 146
since x is equal to the number of adult tickets sold, your answer is 146.
Trains to Aybrin leave the station every 35 minutes. Trains to Bleechtree leave the station every 40 minutes. Trains to both places leave at 7am. What is the next time trains to Aybrin and Bleechtree leave the station together?
The next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.
To find the next time trains to Aybrin and Bleechtree leave the station together, we need to determine the least common multiple (LCM) of 35 and 40, which represents the time interval at which both train schedules align.
The prime factorization of
35 = 5 x 7,
and 40 = 2 x 2 x 2 x 5
Now, the highest power of each prime factor that appears in either factorization.
So the LCM of 35 and 40 = 2 x 2 x 2 x 5 x 7 = 280.
Therefore, the next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.
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If the point A (5,4) is rotated 90 degrees clockwise about the point (0,1),what are the coordinates of the point A'?
Answer:
To rotate a point 90 degrees clockwise about another point, you can follow these steps:
1. Subtract the coordinates of the center of rotation from the coordinates of the point you want to rotate to translate the center of rotation to the origin.
A translated point A would be: (5 - 0, 4 - 1) = (5, 3)
2. Perform the rotation by swapping the x and y coordinates and negating the new x-coordinate.
The rotated point A' would be: (3, -5)
3. Add the coordinates of the original center of rotation to the rotated coordinates to translate the origin back to the center of rotation.
The final coordinates of point A' would be: (3 + 0, -5 + 1) = (3, -4)
Therefore, the coordinates of point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).The answer choices are:
A. 4
B. 2 radical 5
C. 4 radical 2
D. 2 radical 10
The calculated length of the segment WK is (b) 2√5
Calculating the length of the segment WKFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
W = (-6, -2)
K = (-2, 0)
The length of the segment WK is calculated as
WK = √[(x2 - x1)² + (y2 - y1)²]
Substitute the known values in the above equation, so, we have the following representation
WK = √[(-6 + 2)² + (-2 - 0)²]
Evaluate
WK = √20
This gives
WK = 2√5
Hence, the length of the segment WK is (b) 2√5
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After the party, a bag of ice weighs 7/8 pound. Before the party, the bag of ice weighed 3 times as much. How many pounds did the bac
party?
Drag the pointer to its correct location on the number line to show the weight of the bag of ice before the party.
3
4
Weight of Bag of Ice Before Party
2
4
Finish Late
The weight before the party could be any positive number
The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:
x - weight used at the party = 7/8
We know that the weight used at the party is the weight before the party minus the weight after the party.
So we can substitute 3x for the weight before the party:
3x - (7/8) = weight used at the party
We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.
So we can set up another inequality:
weight used at the party ≤ 3x
Putting it all together:
3x - (7/8) ≤ 3x
Simplifying:
-(7/8) ≤ 0
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Find the area of the shape.
4 m
17 m
18m
9 m
There are two ways to solve this problem: use the formula for the area of a trapezoid, or break the trapezoid up into 3 shapes.
Formula for the Area of a Trapezoid: A = 1/2(b1 + b2) x h
A = 1/2(17 + 9) x 8
A = 1/2(26) x 8
A = 13 x 8
A = 104 m^2
Trapezoid = 2 right triangles + 1 rectangle
Area of a triangle = 1/2 x base x height
A(triangle) = 1/2 x 4 x 8
A(triangle) = 16
A(both triangles in the trapezoid) = 32 m^2
A(rectangle) = 8 x 9
A(rectangle) = 72 m^2
Total area = 72 + 32 = 104 m^2
Answer: A = 104 m^2
Hope this helps!
20°
15
Solve for c.
125°
Length of c
C
c = [?]
Round your final answer
to the nearest tenth.
Enter
Answer:
We can use the law of cosines to solve for c:
c^2 = 20^2 + 15^2 - 2(20)(15)cos(125°)
c^2 = 400 + 225 + 600cos(125°)
c^2 = 625 + 600cos(125°)
c = sqrt(625 + 600cos(125°))
c ≈ 32.7
Therefore, the length of c is approximately 32.7 units.
A simulation for rolling two number cubes is run with 50 trials. The results are shown below.
(4,6)
(2,4)
(3, 1)
(1,6)
(6, 1)
(2, 2)
(2, 2)
(5, 1) (5,3)
(3,2)
(2,6)
(6,6)
(4,2)
(4,3)
(3,4)
(3,1)
(3,6)
(1,2)
(6,4)
(4,4)
(5,5)
(3,6)
(1,2)
(2,3)
(3, 3)
(4,4)
(4,4)
(1,5)
(6,-6)
(2,3)
(2,1)
(3,5) (4,1)
(4,4)
(4,5)
(4, 5)
(2,1) (4, 6)
(6, 6)
(5,2) (1,4)
(1,6)
(6,6)
(3,6)
(2,1)
What is the experimental probability a total of 9 will be rolled on two number cubes?
Use the paperclip button below to attach files.
(6,4)
(2,4)
(4,3)
(2,4)
(1, 1)
The experimental probability of rolling a total of 9 on two number cubes is 2/50, or 0.04.
How is this so ?To calculate the experimental probability,we divide the number of successful outcomes by the total number of trials.
In this case, there were 2 successful outcomes (the sum of the number cubes was 9) and 50 total trials.
Therefore, the experimental probability is
2/50 = 0.04.
It is important to note that this is just an experimental probability, and the actual probability of rolling a total of 9 may be different.
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A rectangular container is 25cm by 37cm by 21cm
The volume of this of rectangular container is equal to 19,425 cubic centimeter.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular container = 25 × 37 × 21
Volume of rectangular container = 19,425 cubic centimeter.
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Complete Question:
A rectangular container is 25cm by 37cm by 21cm. What is the volume of this rectangular container?
from the rope 8 m long, two pieces of length 15/7 m and 29/9m were cut.what is the length of remaining rope
The length of the remaining rope is 166/63 meters, or approximately 2.635 meters when rounded to three Decimal places.
To find the length of the remaining rope, we need to subtract the sum of the lengths of the two pieces that were cut from the original length of the rope.
Original length of the rope = 8 m
Length of the first piece cut = 15/7 m
Length of the second piece cut = 29/9 m
Therefore, the length of the remaining rope can be found as:
Remaining length = Original length - Length of first piece - Length of second piece
Remaining length = 8 - 15/7 - 29/9
To perform the subtraction, we need to find a common denominator for 7 and 9, which is 63.
Remaining length = 504/63 - 135/63 - 203/63
Remaining length = (504 - 135 - 203)/63
Remaining length = 166/63
To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1.
Remaining length = 166/63 meters
Therefore, the length of the remaining rope is 166/63 meters, or approximately 2.635 meters when rounded to three decimal places.
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What is m Please help answer
The value of x is 3 and angle Q is 39°
What is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A circle theorem states that : angles in thesame segment are equal.
With this theorem is means that angle 13x is equal to angle x +36 .
Therefore;
13x = x +36
collecting like terms
13x -x = 36
12x = 36
divide both sides by 12
x = 36/12
x = 3
therefore the value of angle Q = 13 × 3
= 39°
Therefore the value of angle Q is 39°
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URGENT please and thank you
The transformations that when applied to a triangle on a coordinate grid that would preserve congruence are
(x, y) -> (x + 7, y - 8)
A reflection of the triangle across the x-axis
What is rigid transformations?Rigid transformations refer to transformations in geometry that preserve shape and size
In other words when an object is transformed using a rigid transformation the object does not change its size or shape hence preserving congruence.
The types of rigid transformations translations rotations and reflections.
The first transformation: (x, y) -> (x + 7, y - 8)
is a translation of 7 units to the right and translation of 8 units down
While a reflection of the triangle across the x-axis also preserves congruence
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Convert 40 cups per minute to gallons per hour. Note: 1 pint is 2 cups, 1 quart is 2 pints and 1 gallons is 4 quarts.
Answer: 40 cups per min = 2.5 gallons per hour
Step-by-step explanation:
Find the quotient: 108m6+81m5−324m9m4. Simplify your answer completely.
please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The required dimensions are
22. x = 9.45
23. perimeter = 198.2
24. angle NSR = 110
25. x = 10
How to find the required dimensions22. The value of x is solved using Pythagoras theorem
x² = (7.4 + 4.6)² - 7.4²
x² = 144 - 54.76
x = √89.24 = 9.45
23. perimeter of tringle GHI
solving for x
7x + 4 = 12x - 20
x = 4.8
perimeter = 52 + (52 - 15 + 7x + 4) + 15 + 12x - 20
perimeter = 52 + (52 - 15 + 7(4.8) + 4) + 15 + 12(4.8) - 20
perimeter = 198.2
24. angle NSR = 1/2 (170 + 50 )
angle NSR = 1/2 (220) = 110
25.
angle V = 1/2 * 290 = 145
4x - 5 + 145 = 180
4x - 5 + 145 = 180
4x + 140 = 180
4x = 40
x = 10
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The graph models the value of a machine over a 10 -year period. Which equation best represents the relationship between x , the age of the machine in years, and y , the value of the machine in dollars over this 10-year period? A.y=500x+8,000 B.y=−500x+8,000 C.y=−0.002x+2,500 D.y=0.002x+2,500
Correct equation best represents the relationship between x , the age of the machine in years, and y , the value of the machine in dollars over this 10-year period is,
⇒ y = 500x + 8000
We have to given that;
The graph models the value of a machine over a 10 -year period.
Now, Let two points on graph are, (0, 8000) and (8, 4000)
Since, The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Hence, on substituting the values in above result, we get;
y - 8000 = (4000 - 0) / (8 - 0) (x - 0)
y - 8000 = 500x
y = 500x + 8000
Thus, The correct equation is,
y = 500x + 8000
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Which expression has the greatest quotient? (1 point) –20 ÷ –5 8 ÷ –4 –6 ÷ –3 12 ÷ –3
Answer:
-2
Step-by-step explanation:
The expression with the greatest quotient can be found by computing each expression and comparing the results.
-20 ÷ -5 = 4
8 ÷ -4 = -2
-6 ÷ -3 = 2
12 ÷ -3 = -4
Therefore, the expression with the greatest quotient is -2, since it has the largest absolute value.
What is 5x6 + (5x5-5) to the 2nd power
Answer: 2500
Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500
While visiting your friend in the city, you see two roads that intersect as shown. Your triend tells you that the angle between the roads on the west side is 78° and the angle between the roads on the east side is (3x)°. Find the value of x.
Answer:
Step-by-step explanation: 78 +3x+x=180 deg.
4x=180-78
4x=102/:4
x=25.5 deg
Step-by-step explanation:
180 = 78° + 3x°
78° + 3x° = 180°
3x°= 180° - 78°
3x = 102°
x = 102°/3
someone help please
sure the answer is c and a or b but the correct one is c
