What is the theoretical probability that an even number will be rolled on a number cube?

Answer:

A. ∆ABD ~ ∆CDE

B. x ≈ 5.3

Step-by-step explanation:

A. The Acute Angle Similarity Theorem states that when an acute angle in one right triangle is congruent to a corresponding acute angle in another, both right triangles are said to be similar to each other.

<B ≅ <D (both are right angles)

<A ≅ C,

Therefore, ∆ABD ~ ∆CDE

B. Since ∆ABD ~ ∆CDE, corresponding sides would be proportional to each other. This means that:

DE/BD = CD/AB

Substitute:

6/8 = 4/x

Cross multiply

6*x = 4*8

6x = 32

6x/6 = 32/6

x ≈ 5.3 (nearest tenth)

Answer:

What shape is it?

Please write the full question

Answer:

y ≤ [tex]\frac{1}{3}[/tex] x - 4

Step-by-step explanation:

the first step is to obtain the equation of the line.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (3, - 3) ← 2 points on the line

m = [tex]\frac{-3-(-4)}{3-0}[/tex] = [tex]\frac{-3+4}{3}[/tex] = [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y = [tex]\frac{1}{3}[/tex] x - 4 ← equation of the line

----------------------------------------------

the shaded region below the line indicates the values that are less than y

the solid line indicates that y can equal the values on the line (≤ )

the solution is then

y ≤ [tex]\frac{1}{3}[/tex] x - 4

The lowest ratio for 54 m in 2.5 hours will be:

= 54 / 2.5 is 21.6 : 1.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let USA say for instance, the ratio will be 3/10 if A is 5

3 and B is 10.

In this case, the lowest ratio for 54 m in 2.5 hours will be:

= 54 / 2.5.

= 21.6 / 1

= 21.6:1

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

Answer:

4

Step-by-step explanation:

7x+22=50

7x=50-22

7x = 28

x=4

Answer:

A

Step-by-step explanation:

Given

- 5x - 10 < 20 ( add 10 to both sides )

- 5x < 30

Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity

x > - 6 → A

Answer:

The height of Mrs. Marigold's roof is 10 feet.

Step-by-step explanation:

Given that,

Base of the given triangle = 48 ft

Hypotenuse = 26 ft

Half of the base = 24 ft

Using Pythagoras theorem,

[tex]h=\sqrt{26^2-24^2}\\\\h=10\ ft[/tex]

So, the height of Mrs. Marigold's roof is 10 feet.

Three true statements about the angles of the given figure are,

1. angle 1 and the 55 degree angle are adjacent.

5. angle 1 = 180 degree - 55 degree

6. angle 2 = 180 degree - 55 degree - 45 degree.

Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.

Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.

Analysing all the statements given in the question,the corrrect options are

Option 1, since angle 1 and 55 degree share the same vertex.

Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.

Option 6, since the sum of all the interior angles of a triangle is 180 degrees.

To learn more about angles visit:

https://brainly.com/question/28451077

#SPJ1

Answer:

quadrant 1

Step-by-step explanation:

b/c quadrant(+,+)

From the origin,

she is 22 units to the right and 1 unit upwards.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

Thalia is in the room located at (22,1).

From the origin to this point  (22,1).

In the first quadrant,

From the origin,

she is 22 units to the right and 1 unit upwards.

Therefore, she is 22 units to the right and 1 unit upwards.

To learn more about the coordinates;

https://brainly.com/question/27749090

#SPJ2

Answer:

-3

Step-by-step explanation:

y = -3x + b

-7 = -3(-3) + b

-7 = 9 + b

-16 = b

y = -3x - 16

The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).

The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

To learn more about discrete distribution refer to:

https://brainly.com/question/17145091

#SPJ4

a. E(B) = 9.5

b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

c. Standard variable shows how much deviation from mean variable.

In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

To learn more about discrete distribution refer to:

brainly.com/question/17145091

#SPJ4

Answer:

HM = 11

CD = 12.5

Step-by-step explanation:

[tex]A)[/tex]

[tex]1)\ NH*HM = JH * HK[/tex]

[tex]2)\ 33 * HM = 363[/tex]

[tex]3)\ HM = 11[/tex]

[tex]B)[/tex]

[tex]1)\ GV^2 = VC * (DC + AC)[/tex]

[tex]2)\ 15^2 = 10 * (CD + 10)\\[/tex]

[tex]3)\ 225 = 10CD + 100\\[/tex]

[tex]4)\ 125 = 10CD\\[/tex]

[tex]5)\ CD = 12.5[/tex]

Answer:

The slope of line r is -3/4

Step-by-step explanation:

First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Therefore, substitute in:

[tex]\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}[/tex]

Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is [tex]\displaystyle{m_1m_2=-1}[/tex].

Let [tex]m_1[/tex] be slope of the line q which is 4/3. Therefore, substitute in and solve for [tex]m_2[/tex] (slope of line r)

[tex]\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}[/tex]

Therefore, the slope of line r is -3/4

The relationship between the natural logarithm (ln) and the natural exponential (e) is given by the equation ln(x) = e^x. This equation is known as the exponential form of the natural logarithm.

To explain this relationship, let's start with a simple example. Suppose we have a number x, and we want to find its natural logarithm. To do this, we can use the following equation:

ln(x) = e^x

This equation states that the natural logarithm of x is equal to the natural exponential of x. In other words, we can calculate the natural logarithm of x by raising e to the power of x. To illustrate this with an example, suppose we want to calculate the natural logarithm of 10. We can do this using the equation above as follows:

ln(10) = e^10

Now, we can use a calculator to calculate e^10. If we do this, we get the result of 22,366.48. Therefore, the natural logarithm of 10 is equal to 22,366.48.

The relationship between the natural logarithm and the natural exponential is important because it allows us to easily calculate the natural logarithm of any number. All we have to do is raise e to the power of that number, and the result will be the natural logarithm of that number. This is a very useful tool in mathematics and can be used to solve many problems involving logarithms.

Learn more about natural logarithm here:

https://brainly.com/question/30085872

#SPJ4

Answer:

x = √35

Step-by-step explanation:

Please see attached photo for explanation.

We'll begin calculating the value of y. This can be obtained as follow:

10² = y² + 4²

100 = y² + 16

Collect like terms

100 – 16 = y²

84 = y²

Take the square root of both side

y = √84

Finally, we shall determine the value of x. This can be obtained as follow:

y² = x² + 7²

(√84)² = x² + 49

84 = x² + 49

Collect like terms

84 – 49 = x²

35 = x²

Take the square root of both side

x = √35

Answer:

√35

Step-by-step explanation:

10² = y² + 4²

100 = y² + 16

100 – 16 = y²

84 = y²

y = √84

y² = x² + 7²

(√84)² = x² + 49

84 = x² + 49

84 – 49 = x²

35 = x²

x = √35

Answer:

this is from my math teacher's notecards! :)

Step-by-step explanation:

The measure of angle is, 62°.

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

We have to given that;

⇒ Supplement of an angle is 6 more than 4 times of its complement.

Now,

Let measure of an angle = x

So, By given condition, we can formulate;

The supplement of an angle = 180 - x

And, The complement an angle = 90 - x

Hence, We get;

⇒ (180 - x) = 6 + 4 (90 - x)

Solve for x as;

⇒ 180 - x = 6 + 360 - 4x

⇒ 4x - x = 366 - 180

⇒ 3x = 186

⇒ x = 62°

Learn more about the complement angle visit:

https://brainly.com/question/16281260

#SPJ1

Answer:

x < -20

Step-by-step explanation:

To solve x/5 + 6 < 2,

First subtract 6 from both sides of the equation.

This makes x/5 < -4.

Then multiply both sides of the equation by 5.

This makes x < -20.

Therefore, the solution to the equation is x < -20.

Answer:

125

Step-by-step explanation:

The height of the right circular cylinder shown below is 12 feet and its base has a radius of 3 feet.

Answer:

314

Step-by-step explanation:

the formula to get the area of a circle is [tex]\pi r^{2}[/tex]

pi=3.14 and r=10

do you get 3.14 x [tex]10^{2}[/tex]

3.14 x 100

314

answer:

b+24

step-by-step explanation:

it’s just asking for the sum so add the two values. there are no other integers given other than 24 so the answer is in expression form. hope that helps!

No, Both will not have the same amount of comic books because they add the same number each month.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Adrian started with 12 comic books and buys 4 more each month.

Rory started with 8 comic books and buys 4 more each month.

let x be the number of books.

A(x) = 4x+12

Rory starts with 8 comic books and add 4 comic books each month.

R(x) = 4x+8

Hence, Both will not have the same amount of comic books because they add the same number each month. There will be 4 additional comic books for Adrian.

To learn more about equations visit:

brainly.com/question/2972832

#SPJ4

Answer:

3

Step-by-step explanation:

If I remember how to solve these questions correctly, if there is a triangle that is 45 degrees, the hypotenuse will be times the square root of 2 of the other two sides (which are equal to eachother). Hope this helped!

Answer:

[tex] \cos(45 \degree) = \frac{3 \sqrt{2} }{x} \\ x = \frac{3 \sqrt{2} }{ \cos(45 \degree) } \\ x = 6[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

Because the hypotenuse might not be a perfect square

Step-by-step explanation:

The requried inequality to determine the range of body temperature is given as 98.8 ≤ x ≤ 101.2.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
The normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees.
Let x be the average temperature of the horse,
100 - 1.2 ≤ x ≤ 100 + 1.2

98.8 ≤ x ≤ 101.2

Thus, the requried inequality determines the range of body temperature is given as 98.8 ≤ x ≤ 101.2.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ1

Answer: Reflection over the x-axis

Step-by-step explanation: This graph represents the transformation of a reflection over the x-axis because each x-coordinate stays the same but each y-coordinate becomes the positive version of the original negative y-coordinates. ABC and A'B'C' are symmetrical with the line of symmetry being the x-axis.

Answer:

english?

Step-by-step explanation: