A random variable x is uniformly distributed over the interval [4, 8]. Find the mean, variance, and standard deviation of x. (Note: Remember that standard deviation is the square root of variance

Exterior angles are outside the triangle. The measure of the ∠B in ΔABC is 92°

Given to us

\(& \angle B=2 x \\\)

\(& \angle A=x+2\)

We know that \($\angle B C D$\)is the exterior angle of the angel \($\angle C$\), therefore, \($\angle B C D+\angle C=180^{\circ}$\)

Substitute the value of the \($\angle B C D$\),

\(& 140^{\circ}+\angle C=180^{\circ} \\\)

\(& \angle C=180^{\circ}-140^{\circ} \\\)

\(& \angle C=40^{\circ}\)

thus, the measure of the\($\angle \mathrm{C}=40^{\circ}$\)

We know that the sum of all the angles of the triangle is equal to \($180^{\circ}$\), therefore,

\(& \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ} \\\)

\(& (x+2)+2 x+40^{\circ}=180^{\circ} \\\)

\(& x+2+2 x=180-40 \\\)

\(& 3 x+2=140 \\\)

\(& 3 x=140-2 \\\)

\(& x=46^{\circ}\)

As we know the value of x now, substitute the value of \($\mathbf{x}$\) in the\($\angle \mathbf{B}$\),

\(& \angle \mathrm{B}=2 \mathrm{x} \\\)

\(& \angle \mathrm{B}=2(46) \\\)

\(& \angle \mathrm{B}=92^{\circ}\)

hence, the measure of the \($\angle \mathbf{B}$\) in\($\mathbf{A A B C}$\) is\($\mathbf{9 2 ^ { \circ }}$\)

The complete question is,

In ABC, what is the measure of angle B? a.46 b.48 c.70 d.92

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The third-period class has a higher mean score than the first-period class.

The larger standard deviation of the third-period class compared to the first-period class indicates that the scores in the third-period class were more spread out.

We have,

We can make some general observations.

The third-period class has a higher mean score than the first-period class, indicating that, on average, the students in the third-period class scored higher on the midterm than the students in the first-period class.

The larger standard deviation of the third-period class compared to the first-period class indicates that the scores in the third-period class were more spread out, or more variable, than the scores in the first-period class.

This could be due to a variety of factors, such as differences in the difficulty of the test or differences in the academic abilities of the students.

Thus,

While we cannot draw any definitive conclusions without more information, we can use the mean and standard deviation to gain some insight into the performance of the two classes on the midterm.

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Answer:

Step-by-step explanation:

Circumference = 314

2*pi*r = 314

2*r = 314 / 3.14

2*r = 100

r = 50

Area = pi * r^2

Area = 3.14 * 50^2

Area = 3.14 * 2500

Area = 7850

===========

C = 2*pi * r

C = 2 * 3.14 * 10

C = 6.28 * 10

C = 62.80 cm

==========

C = 2*3.14*10.2

C = 64.056

==========

Area = pi * r^2

314 = 3.14 * r^2

314 / 3.14 = r^2

100 = r^2

sqrt(100) = sqrt(r^2)

r = 10

C = 2*pi *r

C = 2*3.14 * 10

C = 6.28 * 10

C = 62.8

Brody bought 2 drinks and 10 pretzels.  Let's use algebra to solve this problem. Let d be the number of drinks that Brody bought, and let p be the number of pretzels that he bought. We know that he bought a total of 12 drinks and pretzels, so:

d + p = 12

We also know that each drink costs $6 and each pretzel costs $3.25, and he spent a total of $44.10 on drinks and pretzels. So:

6d + 3.25p = 44.10

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:

p = 12 - d

Substituting this into the second equation, we get:

6d + 3.25(12 - d) = 44.10

Simplifying:

6d + 39 - 3.25d = 44.10

2.75d = 5.10

d = 1.85 (rounded to two decimal places)

Since d represents the number of drinks, we can't have a fractional value for it. However, we can round it to the nearest whole number and use that to solve for p:

d ≈ 2

p = 12 - d = 12 - 2 = 10

Therefore, Brody bought 2 drinks and 10 pretzels. We can check that this solution satisfies both equations:

2 + 10 = 12 (first equation)

6(2) + 3.25(10) = 44.10 (second equation)

Therefore, our solution is correct

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Brody and his children went into a movie theater and he bought $44.50 worth

of drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He

bought a total of 12 drinks and pretzels altogether. Determine the number of

drinks and the number of pretzels that Brody bought

Answer:

D

Step-by-step explanation:

If you draw a line in the middle of the w they will look the same

Answer:

it would be letter D

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

multiply both sides by 6 and get x=11x6=66

Answer:

Step-by-step explanation:

21(5m - 3) = 63*9

105m - 63 = 567

105m = 630

m = 6

Answer:

2/21

Step-by-step explanation:

5m=9/21+3/63

5m=27/63+3/63

5m=30/63

5m=10/21

m=10/21/5

m=10/21 x 1/5

m=2/21

sry if wrong

Answer:

1)The dependent is the number of cars produced. The independent is the amount of time

2)I know that the number of cars produced is the dependent because it will change whenever the amount of time changes

3)This relationship is linear because as you get more time, you will get more cars

4)I could create a graph because I could plot down these points and find the slope

5) I would need a couple more points to plot                        

Answer:

0

3

Step-by-step explanation:

Answer:

liked = 45 ; disliked = 18

Step-by-step explanation:

Let the number of songs he liked be x & disliked be y.

The ratio of x & y :-

\( \frac{x}{y} = \frac{5}{2} \\ = > 2x = 5y \: \: \: \: \)

And total number of songs he listened = 63

Then, x + y = 63...................eqn.1

=> x = 63 - y

Substituting the value of x in eqn. 2x = 5y gives :-

2(63 - y) = 5y

=> 126 - 2y = 5y

=> 7y = 126

=> y = 18

Substituting the value of y in eqn.1 gives

x = 63 - 18

= 45

Hence no. of songs he liked = 45 & disliked = 18

Step-by-step explanation:

answer criss-cross and divide by 5/8

Answer:

Least common denominator is the lowest number in similarity that a fraction can share and be divided into

Step-by-step explanation:

For example, in this example 1/5, and 1/2 the least common denominator would be 10 because when putting these fractions together you might want to find the total of what they equal. For example, think of this example as a pizza, to make one whole pizza in the first one would be 5 pieces but instead of all five pieces, all you have left is 1 piece of the five. so you only have 1/5. now just imagine you had another pizza the same size of the first one but instead of five pieces you it's only two pieces however, from this two piece pizza all you have left is 1/2. You want to find the in terms of what fraction would make them both equal each other in which you would eventually be able to find out how much pizza you would have left.  The denominator is the lower number under the fraction where that is the one most needed for a fraction to change. The least common denominator is a number that goes into both fractions that in reverse can be divided by against each other. our denominators are 5 and 2. Numbers that are divisible are 10, 20, 40 and so on since 5x2=10, 2x5=10; 5x4=20, 2x10=20; 5x8=40, 2x20=40. The least common denominator would be the lowest number which in this case would be 10.

Answer:

94

Step-by-step explanation:

The mean score is the sum of the test scores divided by the number of tests.

Let s = sum of the scores of the first 6 tests.

s/6 = 80

s = 80 × 6

s = 480

The sum of the scores of the first 6 tests is 480.

The next test is the 7th test.

Let x = score of the 7th test.

mean score of the first 7 tests = (s + x)/7

(s + x)/7 = 82

(480 + x)/7 = 82

480 + x = 574

x = 94

Answer: 94

To find the equation of the tangent plane to the surface z = ln(x - 7y) at the point (8, 1, 0), we need to determine the partial derivatives of z with respect to x and y at that point.

First, let's find the partial derivative ∂z/∂x:

∂z/∂x = 1/(x - 7y)

Next, let's find the partial derivative ∂z/∂y:

∂z/∂y = -7/(x - 7y)

Now, let's evaluate these partial derivatives at the point (8, 1, 0):

∂z/∂x = 1/(8 - 7(1)) = 1/(8 - 7) = 1

∂z/∂y = -7/(8 - 7(1)) = -7/(8 - 7) = -7

At the point (8, 1, 0), the partial derivatives are ∂z/∂x = 1 and ∂z/∂y = -7.

The equation of a plane can be expressed as:

z - z0 = (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)

Using the values we calculated:

z - 0 = 1(x - 8) + (-7)(y - 1)

Simplifying, we get:

z = x - 8 - 7y + 7

Rearranging terms, the equation of the tangent plane to the surface at the point (8, 1, 0) is:

z = x - 7y - 1

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Work Shown:

d = 3 = diameter

r = d/2 = 3/2 = 1.5 = radius

h = 12 = height or length of the pipe

pi = 3.14 approximately

V = volume of the cylinder pipe

V = pi*r^2*h

V = 3.14*(1.5)^2*12

V = 84.78

V = 85

The cylindrical pipe's volume is about 85 cubic feet.

: \(s = - \frac{2}{5} \)

: since | r | > 1 the series has no sum

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Answer:

c = 25.35

Step-by-step explanation:

Comment

Cost (c) = skate rental + time + miscellaneous

Givens

Answer

Cost = 6.35 + 18.00 + 1

Cost = 25.35 , but 24.35 is an hourly charge,

Answer:

1 9/10 = 1.9

Step-by-step explanation:

= 2 3/8 = 19/8

= 1 1/4 = 5/4

So

=19/8/5/4

=19/8 x 4/5

By simplification

=19/10=1 9/10=1.9

Answer:

See below

Step-by-step explanation:

The LHS and RHS are exactly the same, so the equality is true.

The associate property of addition says that

\(\boxed{a+(b+c)=(a+b)+c}\)

In order to make the addition of fractions, the denominators should be same. So we can write three fractions as one.

\(\dfrac{1}{2} +\left(\dfrac{2}{3}+\dfrac{3}{4} \right )\)

\(\dfrac{1}{2} +\dfrac{2}{3}+\dfrac{3}{4}\)

\(\dfrac{1\cdot 6 }{2\cdot 6} +\dfrac{2 \cdot 4}{3 \cdot 4}+\dfrac{3 \cdot 3 }{4 \cdot 3}\)

\(\dfrac{ 6 }{12} +\dfrac{8}{12}+\dfrac{9 }{12}\)

\(\dfrac{ 23 }{12}\)

Answer:

You gotta give me (us) more to work with homie.

Step-by-step explanation:

If I have more of a picture with it I could possibly help but all there is a barely readable and legible nonsense equation. Sorry :(

Answer:

758

Step-by-step explanation:

The largest number that can be made is 875 but it ends in 5 which makes it an odd number.

The only even number is 8 so we have to use it last.

7 is bigger than 5 so 7 goes first which means it's 758

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Hi there!

nearest percentage=64%

1.Subtract starting value and final value:

\(1599-579=1020\)

2.Divide it by the starting value:

\(1020*1599= 0.6378986866791744840525328330206378986\)

3.Multiply the term by 100:

\(0.6378986866791744840525328330206378986\)·\(100= 63.78986866791744840525328330206378986\)

4.Round the term:

\(63.78986866791744840525328330206378986=64\)

Therefore, the decrease of the total 8 years was 64%.

Answer:

64%

Step-by-step explanation:

579 is a 63.789868667917% decrease of 1599.

Percentage of decrease = |1599 - 579|/1599 = 1020/1599 = 0.63789868667917 = 63.789868667917%

The Volume V of balloon is 113.09 in³.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Capacity is another word for volume.

Given:

At t = 3 seconds

Diameter = t + 3 = 3 + 3 = 6 inches

                                        = 0.1524 meters

and radius of sphere = 1/2  x 0.1524 = 0.0762 meters

So, Volume of the sphere

= (4/3) x pi x (radius)³

= (4/3) x 3.14 x (0.0762)³

= 1.8533 x\(10^{-3\) m³

= 113.09 in³

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The ERD (Entity-Relationship Diagram) representing these relationships will include entities such as Book, Publisher, Author, and BookAuthor (associative entity). The relationships between these entities will be depicted using appropriate connectors and cardinality indicators. Please refer to the attached ERD screenshot for a visual representation of the relationships.

Based on the given description, we can identify the following relationships and their characteristics:

1. Book - Publisher Relationship:

  - Degree: 1-to-1 (One book has exactly one publisher)

  - Cardinalities: Each book is associated with one publisher, and one publisher can publish multiple books over time.

  - Graphical Representation: The Book entity will have a foreign key referencing the Publisher entity.

2. Book - Author Relationship:

  - Degree: Many-to-Many (One book can have multiple authors, and one author can write multiple books)

  - Cardinalities: Each book can have one or multiple authors, and each author can write one or multiple books.

  - Graphical Representation: To represent the many-to-many relationship between Book and Author, we will introduce a junction table or associative entity, commonly known as the "BookAuthor" entity. It will have foreign keys referencing both the Book and Author entities.

3. Author - Prospect Relationship:

  - Degree: 1-to-0 or 1 (One author can have either zero or one prospect status)

  - Cardinalities: Each author can either have no prospective status (if they have published books) or have a prospective status (if they haven't published any books yet).

  - Graphical Representation: The Author entity will have an attribute indicating the prospect status, such as a boolean flag.

Overall, the ERD (Entity-Relationship Diagram) representing these relationships will include entities such as Book, Publisher, Author, and BookAuthor (associative entity). The relationships between these entities will be depicted using appropriate connectors and cardinality indicators. Please refer to the attached ERD screenshot for a visual representation of the relationships.

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Answer:

1.176471

Step-by-step explanation:

that is in its simplest form!

Answer:

1 3/17

Step-by-step explanation:

the fraction would be 20 / 17

if you simplify it then it would be 1 3/17

Answer:

Translation:

1. Movement of furniture

2. Airplane positioning within a taxiway

3. The position of the mouse cursor on your computer

Reflection:

1. A mirror

2. A double-door exit at school

3. Chairs facing each other at school

Rotation:

1. The Earth's rotation

2. Hands on a clock

3. A carousel

Dilation/Stretch:

1. A balloon expanding

2. A balloon deflating

3. Biological growth

Transformation involves changing the position and/or size of a shape. Some real world examples of transformation are:

Translation: Mouse cursor

Reflection: Mirror

Rotation: The clock

Dilation: Magnifying lenses

Translation

When an object is moved away from its original position, then the object has been translated. Real world examples include:

Reflection

When an object is flipped from its original position, then the object has been reflected. Real world examples include:

Rotation

When an object is turned around a center, then the object has been rotated. Real world examples include:

Dilation

When the size of an object is changed in equivalent proportions, then the object has been dilated. Real world examples include:

See attachment for examples of each transformation

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The measure of angle A and angle B are 32° and 58° respectively.

The figures in the image are right-triangle.

To find the measure of angle A and B, we use the trigonometric ratio.

For angle A:

Angle θ = ?

Opposite to angle θ = 8

Hypotensue = 15

Note that: sine = opposite / hypotensue

sinθ = 8 / 15

Take th sine inverse

θ = sin⁻¹( 8/15 )

θ = 32°

Angle A = 32°

For angle B:

Angle B = ?

Adjacent to angle B = 8

Hypotensue = 15

Note that: cosine = adjacent / hypotensue

cosB = 8/15

Take th cosine inverse

B = cos⁻¹( 8/15 )

B = 58°

Therefore, angle B measures 58 degrees.

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The recursive formula for the sequence is aₙ = (-1/2) * aₙ₋₁

A geometric series is a set of numbers where each term increases or decreases by a predetermined ratio.

The common formula for geometric series is

Tₙ = a₁ rⁿ⁻¹

The nth term of the sequence can be found using the explicit formula shown above.

When the (n-1) th term is given, the nth term is found using the recursive formula.

The pattern in geometry is,

56, -28, 14, -7,.................

The sequence's initial term is 56.

By comparing the second term to the first term, the common ratio may be calculated.

r = -28/56 = -1/2

The recursive formula looks like this:

aₙ = r * aₙ₋₁

aₙ = (-1/2) * aₙ₋₁

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Answer:

It would be less than becuase 5/5=1 an 2/34= 17

Step-by-step explanation: