the area of trapezoid $abcd$ is $60$. one base is $4$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.

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

The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.

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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Answer:wasd keys do be bussin

Step-by-step explanation:

cause it do be bussin

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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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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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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Pass please! next question

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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Answer:

5.8x3.8

Step-by-step explanation:

x times (x+2) = 22

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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The measure of the unknown angles in the kite are as follows;

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 correct answer is $6

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]

Therefore, the correct answer is $6

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.

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 ratio of the number of cars to the month's 0:18 is 1:3.

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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Answer:

18

Step-by-step explanation:

x - y = 6

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

As the probabilities of random variables are negative so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.

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.

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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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:

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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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.

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.

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).

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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The measure of missing angles is 48° and 36°.

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."

Answer:

bacon sotda

Step-by-step explanation:

I remember thejnwnenenenensenenenejee

With the help of unitary method we can say that, $4 money Kimberly will pend on cheese popcorn and gummy worm.

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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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.

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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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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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.

Answer:

DF=28 AC=64 CF=32

Step-by-step explanation:

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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Answer: Perpendicular