Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. (a) How many sample points are possible?
(b) What is the probability of obtaining a value of 7?
(c) What is the probability of obtaining a value of 8 or greater?

The value of side DE of the triangle is 14.91 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

In triangle CDF,

tan 61° = DF/24

DF = 24 * tan 61°

DF = 43.30 units

In triangle DEF,

tan 19° = DE/43.30

DE = 43.30 * tan 19°

DE = 14.91 units

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

The probability that he teleports at least once per day is [tex]\frac{5}{9}[/tex].

the Marvin must select one of the three transportation alternatives at random.

The likelihood of selecting any one of the three alternatives is the same since the selection is random.

The likelihood of successful teleportation on the first try is:

[tex]P_t=\frac{1}{3}[/tex]

Consequently, the likelihood that you do not teleport is

q=1-p

q=1-[tex]\frac{1}{3}[/tex]

q=[tex]\frac{2}{3}[/tex]

The likelihood that the Marvin won't teleport when leaving for work and returning from work is as follows:

P=[tex]\frac{2}{3}[/tex]×[tex]\frac{2}{3}[/tex]

P=[tex]\frac{4}{9}[/tex]

As a result, the probability that someone will teleport at least once is:

P=1-[tex]\frac{4}{9}[/tex]

P=[tex]\frac{5}{9}[/tex]

Learn more about probability

brainly.com/question/30034780

#SPJ4

The numbers of flowers spaced every 4 feet, are needed

to surround a circular garden with a 70-foot radius, 105

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by:

C = 2πr,

To calculate the circumference of the circular garden, we can use the formula:

C = 2πr

where C is the circumference, π is the mathematical constant pi (approximated as 3 in this case), and r is the radius. Plugging in the given values, we have:

C = 2 x 3 x 70

  = 420 feet

Now, since the flowers are spaced every 4 feet, we can divide the circumference by 4 to find the number of flowers needed:

number of flowers = C / 4

                               = 420 / 4

                               = 105

Therefore, 105 flowers spaced every 4 feet are needed to surround a circular garden with a 70-foot radius.

To know more about circumference check:

https://brainly.com/question/4268218

#SPJ9

The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The integration equation is given below.

[tex]\begin{aligned} \rm I = \int _1^2 \sqrt{x^2 - 4} \ dx \end{aligned}[/tex]

We know that the formula is given as,

∫√(x² - a²) dx = (x/2)√(x² - a²) + (a² / 2) log [x + √(x² - a²)]

Then by the integration, we can write it as,

[tex]\begin{aligned} \rm I &= \int _1^2 \sqrt{x^2 - 4} \ dx \\\rm I &= \int _1^2 \sqrt{x^2 - 2^2} \dx\\\rm I &= \left [ \dfrac{x}{2}\sqrt{x^2-2^2} + \dfrac{2^2}{2} \log (x + \sqrt{x^2 - 2^2}) \right ]^2_1\\\end{aligned}[/tex]

Simplify the equation further, then we have

I = [(1/2) i√3 + 2 log (1 + 3i)]

The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].

More about the integration link is given below.

https://brainly.com/question/18651211

#SPJ9

Answer:

84

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve for 150% of 56, we can multiply 56 by 150%.

Therefore, 150% of 56 is 84.

The whole fraction of a pizza that shows 6 pieces is 6/1 or simply 6.
The whole fraction of a pizza that shows 6 pieces is 6/6 or 1.

In a fraction, the numerator represents the number of parts being considered, and the denominator represents the total number of parts. In this case, there are 6 pieces of pizza being considered out of a total of 6 pieces, which means the fraction is 6/6. This fraction can be simplified to 1, meaning the whole pizza is represented.

So, the whole fraction of a pizza that shows 6 pieces is 1.

Learn more about fraction of a pizza here: https://brainly.com/question/26254534

#SPJ11

Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

Learn more about linear equation here

https://brainly.com/question/11897796

#SPJ4

The solution for x is x ≤ -3/4.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

To solve for x in the inequalities:

5x - 4 ≥ 12 and 12x + 5 ≤ -4

We'll solve each inequality separately:

5x - 4 ≥ 12

Adding 4 to both sides, we get:

5x ≥ 16

x ≥ 16/5

So the first inequality is solved for x as x ≥ 16/5.

Now, 12x + 5 ≤ -4

Subtracting 5 from both sides, we get:

12x ≤ -9

x≤ -9/12

x≤ -3/4

The only values of x that satisfy both inequalities are those that are less than or equal to -3/4.

Therefore, the solution for x is x ≤ -3/4.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ9

The answer is 1.6!!!

How old are?

The height of the cylindrical tub of ice cream is 6.75 inches.

A cylinder is a 3 dimensional shape which has a curved side and two circular surfaces. The total surface area can be determined by the expression;

total surface area of a cylinder = 2πr^2 + 2πrh

where r is the radius of it circular surface, and h is its height.

Considering the given question, we have;

total surface area of a cylinder = 2πr^2 + 2πrh

But total surface area = 183.69 square inches

r = D/2

  = 6/ 2

r = 3 inches

Thus,

183.69 = 2*3.14*3^2 + 2*3.14*3*h

           = 56.52 + 18.84h

183.69 - 56.52 = 18.84h

127.17 = 18.84h

h = 127.17/ 18.84

  = 6.75

The height of the cylindrical tub of ice cream is 6.75 inches.

Learn more about surface area of cylinder at https://brainly.com/question/27440983

#SPJ1

Answer: The answer is (C) 6.75

Step-by-step explanation:

The formula for Surface Area is: SA = 2πr^2 + 2πrh

Let's do the first part: 2πr^2

So you need to find the radius, which is half the diameter. 6 is the diameter so half that, and you get 3.

Now, times 3 by itself

3 * 3 = 9

And then times 9 by 2

9 * 2 = 18

And times 18 by pi, 3.14

18 * 3.14 = 56.52

Now that we have our first value, lets move on to the second part of the formula: 2πrh

So we need the diameter, and the question gives us the value of the diameter.

6 is the diameter

so times 6 by pi, 3.14

6 * 3.14 = 18.84h  (leave h there because we don't know the height)

Now do this:

183.69 =  56.52 + 18.84h

You cannot add 56.52 and 18.84h because they are not like terms

So take away 56.52 from both sides

56.52 - 56.52 = 0

183.69 - 56.52 = 127.17

Now divide 127.17 by 18.84h

127.17/18.84  = 6.75 inches

Here is proof that my answer is correct. I have a photo of my results and it shows that 6.75 inches is correct. Here is the photo:

Have a an amazing day

The graph the depicts the solution set of the inequality is graph D. Option 4 is the correct answer.

There is a significant exception to the general rule that inequality manipulation is quite similar to equation manipulation.

An inequity still exists if the same amount is added to both sides.

The inequality still holds true if the same amount is subtracted from each side.

An inequality still holds true if both sides are multiplied or divided by the same positive value.

However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid.

The given inequality is x² + 10x + 16 / x-3 > 0.

Expand the quadratic equation:

x² + 8x + 2x + 16/ x-3 > 0

x(x + 8) + 2(x + 8) / x-3 > 0

(x + 2)(x + 8)/ x-3 > 0

x + 2 > 0 and (x + 8) < 0 and x - 3 > 0

x > -2 and x < -8 and x > 3

The intervals of x are:

-8 < x < -2 and x > 3

Hence, the graph the depicts the given interval is graph D. Option 4 is the correct answer.

Learn more about inequality here:

https://brainly.com/question/30231017

#SPJ1

The required number maximum number of copies can be afforded c < 13.33.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have $4.00 and you need to make copies of a flyer at a store that charges $0.30 per copy.

Here,

Let the number of copies be c,

According to the question,

0.30c < 4

c < 4/ 0.30

c < 13.33

Learn more about inequality here:

brainly.com/question/14098842

#SPJ9

Therefore, after answering the given query, we can state that the as we can multiply it as 7 multiply by 7 = 7*7 = 49.

Multiplication is one of the four matrix multiplication, along with arithmetic, addition, and subtraction. Multiplication in mathematics is the process of repeatedly combining subgroups of the same size. Multiplication is calculated using the formula multiplicand multiplier gives product. multiplicand: Starting number, to be more exact (factor). as a separator, use number two (factor). The result is what remains after splitting both the multiplicand and the multiplier. There are numerous additions necessary when adding numbers. similar to 5 x 4 = 5 x 5 x 5 x 5 = 20. What I did was multiply 5 by 4. Because to this, multiplication is frequently referred to as "doubling."

The standard form for seven squared is 49.

as we can multiply it as 7 multiply by 7 = 7*7 = 49.

To know more about multiply visit:

https://brainly.com/question/23536361

#SPJ1

One mile is equal to 5,280 feet. Therefore, to convert the altitude of Denver from miles to feet, we can multiply by 5,280:

1 mile × 5,280 feet/mile = 5,280 feet

So, Denver's altitude of 1 mile is equal to 5,280 feet.

The manager would expect 1000 defective players in the shipment.

A store receives a shipment of 5,000 mp3 players out of which 300 were found to be defective.

The clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players.

The results are given AS:

2,806 623 232 3,955 3,799 657 2,140 262 844 561

This means that out of the 10 samples 2 were found to be defective and 8 were in the working condition.

( Since the number 232 and 262 represent the defective mp3 players as they are the numbers which are less than or equal to 300 )

Hence, the Probability that the mp3 players were defective is:

P( defective)=2/10=1/5

Hence, out of 5000 mp3 players the number of players that clerk predict to be defective are:

P( defective)×5000

= 1/5 × 5000

= 1000.

Read more about defective samples at; https://brainly.com/question/30486439

#SPJ1

Answer: D (210.00)

Step-by-step explanation:

According to the formula of compound INTEREST this is correct

Step-by-step explanation:

We can find the other point using the axis of symmetry.

The axis of symmetry for a parabola passes through the x coordinate of the vertex.

So our axis of symmetry is x=4, which is a vertical line.

For any point on a parabola curve except the vertex, there will two points that share the same y value. The two x coordinates of those points midpoints should be the axis of symmetry.

So,

If we know (0,-6) and the vertex is 4, let's find the other point

[tex]( \frac{0 + b}{2} = 4[/tex]

[tex]b = 8[/tex]

So our other point is

(8,-6).

So the answer to #1 is we found point (8,-6) by using the axis of symmetry. By reflecting the point (0,-6) about the vertical line x=4, we end up getting the point (8,-6)

To find q, q(x) has the same vertex, so it is (4,10).

We know the axis of symmetry is x=4, we also know the y intercept is 18 so we have point (0,18)

Using the axis of symmetry we will get (8,18).

So the graphs above are the graphs of p and q

The graph facing upwards is q

The graph facing downwards is p.

For #2, you can say we know the vertex is (4,10) and using the y intercept and axis of symmetry we found the other point on the curve.

I don't fully see the table but if the other coordinates have a higher y value, the vertex is a minimum.

Else, of the other coordinates have a lower y value, the vertex is a maximum.

Answer:

Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era

Stoichiometry formula is founded on the basis that law of conservation of mass where the total mass of the reactants = total mass of the products.

This is referred to as the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers.

The stoichiometry of a balanced chemical equation identifies the maximum amount of product that can be obtained. The stoichiometry of a reaction describes the relative amounts of reactants and products in a balanced chemical equation.

Read more about Stoichiometry here https://brainly.com/question/14935523

#SPJ1

The values of 65 euros is 76.70 US dollars.

To convert 65 euros to dollars, you need to know the current exchange rate between the two currencies. As of September 2021, the exchange rate is 1 euro = 1.18 US dollars.

To calculate the conversion, you can simply multiply the amount of euros by the exchange rate.

65 euros x 1.18 US dollars = 76.70 US dollars

Therefore, 65 euros is equivalent to 76.70 US dollars.

It's important to note that exchange rates can fluctuate, so the conversion may not be the same in the future. It's always best to check the current exchange rate before making a conversion.

To know more about exchange rate click on below link:

brainly.com/question/29562028#

#SPJ11

The error in the solution is that the answer is written as 3000 instead of 30.

Percentage is defined as the parts of a number per fraction of 100 and it is denoted by the symbol '%'.

Percentage of a number is calculated as dividing the number with it's whole and then multiplying with 100.

We have to find the percentage of 40% of 75.

That is, the number which corresponds to the 40 parts per 100 of the number 75.

40% of 75 = 40% × 75

                 = (40 / 100) × 75

                 = 0.4 × 75

                 = 30

The correct percentage is 30, not 3000.

Hence the error is in the answer for which 30 is the correct answer.

To learn more about Percentage, click here :

https://brainly.com/question/30348137

#SPJ9

Answer:

205

Step-by-step explanation:

3hrs is 180 min

5/12 hours is just 25 min

180+25=205

Answer:

205 minutes

Step-by-step explanation:

*60 minutes = 1 hour

3 x 60 = 180

5/12 x 60 = 5/12 x 60/1 = 300/12 = 25

180 + 25 = 205 minutes

Answer: [tex](x+10)(x-10)[/tex]

Step-by-step explanation: Difference of squares is an important element in understanding square functions. In order to identify difference of squares, the equation should be given in the form a^2-b^2. You can factor it completely when b^2 can be square rooted perfectly and write the factored expression as (a-b)(a+b) as I have done above.

The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

Answer:  

4

Step-by-step explanation:

The radius of the circle is 21.92 feet

From the question, we have the following parameters that can be used in our computation:

A square lawn has an area of 1922 square feet

This means that

Area = 1922

Take the square root of both sides to determine the side length

side length = 43.84

This represents the circle diameter

So, we divide by 2

radius = 21.92

Hence, the radius is 21.92

Read more about radius at

https://brainly.com/question/24375372

#SPJ1

Step-by-step explanation:

so, for x = 0, y = 30.5

that means the first answer is out.

for x = 1, y = 21.35

so, only

y = 30.5(0.7)^x

can be right.

all other functions have an y-value of way over 30.5 (because the factor of 30.5 is larger than 1).

and to verify :

30.5 × 0.7¹ = 30.5 × 0.7 = 21.35

correct.