The length of the median of the trapezoid is 12 units.
What is trapezoid?
Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides. This article provides formulas for the area of the trapezium as well as its types, attributes, and other trapezoids.Let the parallel sides be x and x+4
The area of a trapezium is the average or the parallel sides multiplied by the height
Area = [(x + x+ 4)/2 ] *h
= [ (2x+4)/2] * 5
= [2(x+2)/2] * 5
Area = 5(x+2)
60 = 5(x+2)
60/5 = x+2
12 = x+2
x = 12 - 2
x = 10
The parallel sides are 10 and 14 units.
Now the median length is the average of the parallel side lengths
Length of median = (10+14)/2
Length of median = 12 units
Hence, the length of the median of the trapezoid is 12 units.
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Giselle’s father is 3 times as old as her. After 10 years his age will be 5 more than twice her age. Which equation can be used to find Giselle’s age?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equation that can be used to find Giselle's age is
3x + 10 = 5 + 2 (x + 10)
Giselle's age is 15 years.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Giselle's age = x
Father age = 3x
Now,
After 10 years his age will be 5 more than twice her age.
This can be written as,
3x + 10 = 5 + 2 (x + 10)
Solve for x.
3x + 10 = 5 + 2x + 20
3x - 2x = 5 + 20 - 10
x = 15
Thus,
The equation that can be used to find Giselle's age is
3x + 10 = 5 + 2 (x + 10)
Giselle's age is 15 years.
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Kimberly i hoting a movie marathon over the weekend. There will be p people at the party altogether. Kimberly etimate he'll need one bag of cheee popcorn and one pack of gummy worm per peron. A bag of cheee popcorn cot $2. 50, and a pack of gummy worm cot $1. 50. Pick all the expreion that repreent how much money Kimberly will pend on cheee popcorn and gummy worm
With the help of unitary method we can say that, $4 money Kimberly will pend on cheese popcorn and gummy worm.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
A bag of cheese popcorn cost= $2.50
A pack of gummy worm cost =$1. 50
2.50 * 1.50
4
Hence, $4 money Kimberly will pend on cheese popcorn and gummy worm.
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One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2 and + 12. Determine the other two degree measures for the missing angles.
The measure of missing angles is 48° and 36°.
Define angle sum property.The angle sum property of a triangle states that the sum of the three internal angles of a triangle equals 180 degrees. Three line segments combine to form a triangle, a closed shape having interior and exterior angles. When the values of the other two angles are known, one may utilize the angle sum property to determine the measure of an unknown interior angle.
Given Measure of one angle= 96, one angle= 2x, other angle= x + 12.
Using the angle sum property, we get
96 + 2x + x + 12 = 180
108 + 3x = 180
3x = 180 - 108
3x = 72
x = 72/3
x = 24
So, one angle = 2(24
= 48
The other angle is
x + 12 = 24 +12
= 36
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The complete question is:
One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2x and x + 12. Determine the other two degree measures for the missing angles."
question content area top part 1 in a fraternity with 36 members, 18 take mathematics, 5 take both mathematics and art history, and 8 take neither mathematics nor art history. how many take art history but not mathematics?
With the help of set relation and function the number of members taking art history but not mathematics is 12
what is set ?
Sets are collections of clearly defined objects, relations show the connections between the elements of two sets A and B, and functions are a special kind of relation where each element in A has exactly one relationship (or no more than one) with an element in B.
solution:
Total members (A + B + C + D)= 38
B + C = 18
C = 5
A = 8
Work from the end to the beginning:
A = 8
C = 5
B = 13 [from clues 3 and 2]
D = 12 [use clue 1 and above info]
Therefore, The member of taking art history but not mathematics D = 12
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which hypotheses can be used to perform the test in the following scenario? the mean startup time of two competing computers is to be compared to see if they are equal or not. eighteen startup times are randomly sampled from each computer. both populations have normal distributions with known standard deviation.
Hypothesis:
H0: The mean startup time for both computers is equal.
H1: The mean startup time for both computers is not equal.
A hypothesis is a potential explanation for a phenomenon.A hypothesis must be testable in order to be considered scientific according to the scientific method. Scientists typically base their scientific hypotheses on prior observations that cannot be adequately explained by the body of knowledge. Despite the fact that the terms "hypothesis" and "theory" are frequently used interchangeably, they are not the same thing. A working hypothesis is a theory that has been tentatively accepted and is put forth for further study after starting with an educated guess or idea.
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4.) numbers is a game in which you bet $1 on any 3-digit number from 000 to 999. if your number comes up, you get $500. find the expected payback.
As the probabilities of random variables are negative so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.
How did the math game function?
The rules of the "numbers" game are simple: a player selects a three-digit number between 000 and 999. Anyone who picks the winning number receives a payout equal to 600 times their original wager. The winning number is decided by a publicly disclosed source. The majority of bets were for $1 or less, and frequently.
What does a probability arrangement mean?
A permutation is an arrangement (or ordering) of a collection of items. (We can also arrange only some of the objects in the set.) The arrangement of the objects in a permutation depends on their order.
The random variable-0.499/1000
The random variable "winning" are $1 and $600.
and their probabilities are 999/1000 and 1/1000, respectively.
The expected "winnings" are calculated as follows:
=(999/1000)(-1)+(1/1000)(500)
=-0.499/1000
=-0.499 cents
so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.
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what is the rate of change for the equation y = 2x+ 40
Answer: 2
Step-by-step explanation: When we talk about rate change, we are talking about the slope!
The slope is 2x which means the rate change is rise 2 and run over 1.
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the manager of a store buys marine radios in lots of 48. suppose that, on the average, 2 out of each group of 48 are defective. the manager randomly selects 4 radios out of the group to test. assume independence. (round your answers to 4 decimal places.) (a) what is the probability that he will find 2 defective radios?
The probability that he will find 2 defective radios is 0.0350.
Given that,
The store's management purchases maritime radios in quantities of 48. Let's say that, on average, 4 people out of every 48 make up a faulty group. Out of the group, the manager chooses four radios at random for testing.
P = 4/48 = 0.083
n=4
P(X=x) = nCₓ Pˣ (1-P)ⁿ⁻ˣ
a) The probability that he will find 2 defective radios P(X=2)
P(X=x) = nCₓ Pˣ (1-P)ⁿ⁻ˣ
P(X=2) = 4C₂ (0.083)² (1-0.083)²
P(X=2) = 0.0350
Therefore, P(X=2) is 0.0350
Therefore, the probability that he will find 2 defective radios is 0.0350.
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pls help! picture is below. pls help by pst sunday december 4 , 2022 12:00 p.m.
Answer: August 12th
Step-by-step explanation: 4 and 6 have common multiples of 2, so you need to multiply 6 by 2 and 4 by 3. Both get you 12, so the earliest they have tennis practice is the 12th of August (12 days after July 31st).
Answer:
August 12
Step-by-step explanation:
To solve this question, we need to find the Least Common Multiple (LCM) of 4 and 6.
Since we know that Nick and Mark both had practice on July 31st, we can simply add {LCM of 4 and 6} days to that date to get when they will next both have practice.
To find the LCM of 4 and 6, find the prime factorization of both:
[tex]4 = 2 \times 2[/tex] [tex]6 = 2 \times 3[/tex]
Now, take the largest quantity of each distinct prime number and multiply them together:
The largest number of 2's is 2. The largest number of 3's is 1. So, we multiply
[tex](2 \times 2) \times (1 \times 3)[/tex]
[tex]= 4 \times 3[/tex]
[tex]= 12[/tex]
Therefore, the LCM of 4 and 6 is 12.
This means that Nick and Mark will have practice on the same day in 12 days.
The last step to solve this problem is to add 12 days to July 31.
[tex]\textrm{July } 31 + 12 \textrm{ days} = \textrm{August } 12[/tex]
Nick and Mark will next have practice on the same day on August 12.
Which pairs of triangles are similar? check all that apply. △abc ~ △def △def ~ △ghi △ghi ~ △abc △ghi ~ △jkl △jkl ~ △abc
The pairs of triangles that are similar are △jkl ~ △abc and their corresponding angles are congruent.
The fact that, When two triangles are comparable, their corresponding sides have a proportional ratio and their corresponding angles have a congruent relationship.
In this issue
△jkl ~ △abc
Because the proportion between its corresponding sides
Verify
CA/LJ=BC/KL
replace the specified values
14/7=20/10
2=2 >>>>> is correct
so
The proportion between the corresponding sides is linear.
therefore △jkl ~ △abc are similar.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
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Answer: b & e
Step-by-step explanation: cuz
For hi birthday Kameron received 18 toy car. He plan to tart collecting more car and i going to buy 2 more every month. Write the number of car to go with the month 0:18 in ratio form
The ratio of the number of cars to the month's 0:18 is 1:3.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
18 toy automobiles were given to Kameron.
And he intends to begin accumulating more automobiles, planning to purchase two more each month.
Month 0 finds him with 18 automobiles.
At the end of the 18th month, he will possess:
(18 + (218) vehicles = (18 + 36) cars = 54 cars
The ratio of month 0 to month 18 will therefore be as follows:
18:54 = 1:3
HENCE, the ratio form for the number of cars to accompany the month 0:18 is 1:3.
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now use the binomial probability formular, calculate the probability of observint 4 heads in 10 coin flips. (1pt) is the estimated probability from exercise 1 close to the true proability? (1pt)
By using Binomial distribution of probability, it can be calculated that
Probability of getting 4 heads in 10 coin flips = [tex]\frac{105}{512}[/tex]
What is Binomial distribution of probability?
Binomial distribution of probability is a discrete probability distribution where the probability mass function is given by
P(X = x) = [tex]{n \choose x}p^xq^{n - x}[/tex]
Where p is the probability of success and q is the probability of failure.
Here, Binomial distribution of probability is used
n = 10
Probability of getting a head = [tex]\frac{1}{2}[/tex]
Probability of getting a tail = [tex]\frac{1}{2}[/tex]
Probability of getting 4 heads in 10 coin flips = [tex]{10 \choose 4}(\frac{1}{2})^4(\frac{1}{2})^{10 - 4}[/tex]
= [tex]\frac{210}{1024}[/tex]
= [tex]\frac{105}{512}[/tex]
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11. If two million is the dividend and two hundred is the LE divisor, what is the quotient?
Answer:
bacon sotda
Step-by-step explanation:
I remember thejnwnenenenensenenenejee
In the figure below, points D, E, and F are the midpoints of the sides of ABC
Answer:
DF=28 AC=64 CF=32
Step-by-step explanation:
Nicholas bought 5 pens for $3. At this rate, how much will he spend on 10 pens?
$10
$6
$5
$3
The correct answer is $6
How did we figure out this?To solve this question, we need to multiply the numbers given.
Given:
[tex]10,5,3,2[/tex]
Therefore, the equation goes like this:
[tex]5*2\\3*2[/tex]
5 x 2 = 103 x 2 = 6Therefore, the correct answer is $6
If Z (4, 3) is translated to Z (2, 7), what is the translation?
Answer: Left 2, Up 4
Step-by-step explanation:
We see the x decrease by 2 from 4 to 2 so the translation is left 2, and the y increases by 4 from 3 to 7, so it is up 4!
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a rectangle has perimeter 52 km, and its area is 165 sq-km. find the dimensions of this rectangle. (for purposes of this problem only, the width is shorter than the length.)
The dimensions of the rectangle: length = 15 km and width = 11 km
Let l be the length of rectangle and w be the width of the rectangle.
A rectangle has perimeter 52 km
Using the formula of the perimeter of rectangle we get an equation,
2(l + w) = 52 ............(1)
And its area is 165 sq-km.
Using the formula of the area of rectangle we get an equation,
l * w = 165 ............(2)
From equation (1),
l = 26 - w
Subatitute above value of l in equation (2),
(26 - w) * w = 165
26w - w² = 165
w² - 26w + 165 = 0
(w - 15)(w - 11) = 0
w = 15 or w = 11
For w = 15,
l = 26 - 15
l = 11
For w = 11,
l = 26 - 11
l = 15
But as we know, the length of rectangle is always greater than the width,
l = 15 and w = 11 is true .
Therefore, the length of rectangle = 15 km and width of rectangle = 11 km
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.14 and the probability that the flight will be delayed is 0.06. The probability that it
will not rain and the flight will leave on time is 0.82. What is the probability that it is
raining and the flight is delayed? Round your answer to the nearest thousandth.
Pass please! next question
an inverted cylindrical cone, 44 ft deep and 22 ft across at the top, is being filled with water at a rate of 11 ft3/min. at what rate is the water rising in the tank when the depth of the water is:
The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
Explain the term rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.The rate of change of volume is-
dV/dt = 11 ft3/min.
Volume of cylindrical cone = (1/3)πr²h
As we're trying to find dh/dt, we need to calculate the volume within terms of just one variable, h.
Diameter = 22 ft
Thus, radius is 11 ft
By using height and radius of a water in the tank, we may calculate h using similar ratios.
11/44 = r/h
1/4 = r/h
r= h/4
Put into volume;
V = (1/3)π(h/4)h²
V = (1/3)(π)h³ / (16)
dV/dt = [(1/3)(3)(π)(h)² / 16](dh/dt)
V = [(π)(h)² / 16](dh/dt)
Solve for (dh/dt) ;
dh/dt = (dV/dt)(16) / [((π)(h)²]
Now, the change in volume is dV/dt = 11 ft³/min
dh/dt = (11 ft³/min)(16) / [((π)(h)²]
For h = 1 ft,
dh/dt = (11 ft³/min)(16) / [((π)(1 ft)²]
dh/dt ≈ 56.05 ft/min
Thus, the rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
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hannah claims that -3 is not a rational number because it is not written as a ratio of integers. is she correct? explain why or why not
Answer: -3 is a rational number
Step-by-step explanation:
-3 is a rational number because it can be written as a fraction -3/1 and have the same value of -3. Therefore -3 is a rational number and Hannah is correct.
Multiples of 3 and factors of 45??
Answer:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30
Factors of 45: 1, 3, 5, 9, 15, and 45
Step-by-step explanation:
please help me asap plssss
Answer: 9
Step-by-step explanation: The number of sides that a regular polygon has can be determined by the measure of one of its exterior angles. A regular polygon is a polygon with sides of equal length and angles of equal measure.
The measure of one exterior angle of a regular polygon is equal to 360° divided by the number of sides of the polygon. Therefore, if one exterior angle of a regular polygon measures 40°, we can use the following equation to find the number of sides of the polygon:
exterior angle measure = 360° / number of sides
40° = 360° / number of sides
number of sides = 360° / 40°
number of sides = 9
Therefore, a regular polygon with one exterior angle measuring 40° has 9 sides.
If x – y = 6 and x is twice the value of y, what is the value of x + y ?
Answer:
18
Step-by-step explanation:
x - y = 6
Given: 2x - x = 6 since x is twice the value of y.x = 6
2x = 6 · 2 = 12
12 + 6 = 18
x is twice the value of y can be written as:
x= 2y
then we replace x with 2y in the given equation
x - y = 6
2y - y = 6
y = 6
then to find x we replace y with 6 in either of the equations
x = 2y
x = 2(6) = 12
or
x - 6 = 6
x= 6 + 6 = 12
now find value if x + y
12 + 6 = 18
Evaluate the expression when x=3 and z=-6
Answer:wasd keys do be bussin
Step-by-step explanation:
cause it do be bussin
need help as quickly as possible
The measure of the unknown angles in the kite are as follows;
x = 66 degreesy = 158 degreesHow to find the measure of a kite?A kite has two pairs of adjacent equal sides.
In other words, a kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
One pair of opposite angles is equal. Diagonals are perpendicular to each other.
A kite has four interior angles and the sum of these interior angles is 360°
Therefore, the measures of the
x = 66 degrees.
Let's find y.
y = 360 - 70 - 66 - 66
y = 158 degrees.
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The length of a rectangle is 2 meters longer than the width. If the area is 22 square meters, find the rectangle's
dimensions. Round to the nearest tenth of a meter.
Answer:
5.8x3.8
Step-by-step explanation:
x times (x+2) = 22
A 24-inch board is to be cut into three pieces so that the second piece is twice as
long as the first piece and the third piece is 3 times as long as the first piece. If x
represents the length of the first piece, find the lengths of all three pieces.
Answer:
The answer to your question is: first piece = 4 in, second piece = 8 in, third piece = 12 in
Step-by-step explanation:
Data
total length = 24 inches
first piece = x in
second piece = 2x
third piece = 3x
Equation
x + 2x + 3x = 24
6x = 24
x = 24/6
x = 4 lengths of the first piece
second piece = 2(4) = 8 inches
third piece = 3(4) = 12 inches
The department of management science at Tech has sampled 250 of its majors and complied the following frequency distribution of grade point averages (on a 4.0 scale) for the previous semester:GPA Frequency0-0.5 1.5-1 41-1.5 201.5-2 352-2.5 672.5-3 583-3.5 473.5-4 181)Please calculate the probability of a student obtaining GPA at each range listed in the table above. You should calculate 8 probabilities, one for each GPA range. Please show your detailed calculation.2)What is the probability that a student’s GPA is higher than 1.5 (not include GPA = 1.5)?3)What is the probability that a student’s GPA between 2.5 (not include 2.5) and 3.5 (include 3.5)?
1) The probability table is calculated by the formula. 2) the probability that a student scores higher than 1.5 is 0.9, and 3) the probability a student scores between 2.5-3.5 is 0.47.
1)
We know that the probability of any event
= no. of observation for the event/total n. of observation
Here, the total no. of observations is 250
Hence we get the following probability table
GPA Frequency
0-0.5 1/250
0.5-1 4/250
1-1.5 20/250
1.5-2 35/250
2-2.5 67/250
2.5-3 58/250
3-3.5 47/250
3.5-4 18/250
2)
The probability that a student's GPA is higher than 1.5 is
P(1.5-2) + P(2-2.5) + P(2.5-3) + P(3-3.5) + P(3.5-4)
= (35 + 67 + 58 + 47 + 18)/250
= 225/250
= 0.9
3)
The probability that a student's GPA is between 2.5 and 3.5
= P(2.5-3) + P(3-3.5)
= (58 + 47)/250
= 105/250
= 0.42
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Complete Question
The department of management science at Tech has sampled 250 of its majors and compiled the following frequency distribution of grade point averages (on a 4.0 scale) for the previous semester:
Please calculate the probability of a student obtaining a GPA at each range listed in the table above. You should calculate 8 probabilities, one for each GPA range. Please show your detailed calculation.2)What is the probability that a student’s GPA is higher than 1.5 (not include GPA = 1.5)?3)What is the probability that a student’s GPA is between 2.5 (not include 2.5) and 3.5 (include 3.5)?
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Determine whether the pair of lines is parallel, perpendicular, or neither.
x-9y=-4
y = 5x-9
Answer: Perpendicular
given a collection of intervals, decide whether there is a subset of non-overlapping intervals of size at least k.
Non-overlapping intervals:
If the intervals(say interval a & interval b) doesn't overlap then the set of pairs form by [a. end, b. start] is the non-overlapping interval.
Interval:
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers {\displaystyle \mathbb {R} }\mathbb {R} , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Overlapping intervals:Let's take the below mentioned overlapping intervals example to explain the idea: If both ranges have at least one common point, then we say that they're overlapping. In other words, we say that two ranges and are overlapping if: On the other hand, non-overlapping ranges don't have any points in common.
Given N set of time intervals, the task is to find the intervals which don’t overlap with the given set of intervals.
Examples:
interval (a) = { {1, 3}, {2, 4}, {3, 5}, {7, 9} }
Output: [5, 7]
The only interval which doesn’t overlaps with the other intervals is [5, 7].
interval (a) = { {1, 3}, {9, 12}, {2, 4}, {6, 8} }
Output: [4, 6] and [8, 9]
There are two intervals which don’t overlap with other intervals are [4, 6], [8, 9].
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