6. Juan y Roberto son dos hermanos que juegan Piedra, Papel y Tijera para determinar quien hace el aseo de su cuarto. ¿Cuántos serán los posibles resultados que podemos tener?, ¿Cuál es la probabilidad de que Juan no haga el aseo? *​

Given:

Principal = $3000

Rate of interest = 4.7% = 0.047 compounded quarterly.

Time = 12 yeas

To find:

The value of John’s investment after 12 years.

Solution:

The formula for amount is

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

where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is number of years.

Substitute P=3000, r=0.047, n=4 and t=12 in the above formula.

\(A=3000\left(1+\dfrac{0.047}{4}\right)^{4(12)}\)

Therefore, the required equation is \(A=3000\left(1+\dfrac{0.047}{4}\right)^{4(12)}\).

We can further solve this.

\(A=3000\left(1+0.01175 \right)^{48}\)

\(A=3000\left(1.01175 \right)^{48}\)

\(A=5255.75947323\)

\(A\approx 5255.76\)

Therefore, the value of John’s investment after 12 years is $5255.76.

Answer:

A, there is a 50% chance of getting heads than tails.

Step-by-step explanation:

B would have a 12% chance of that.

C would have a 43% chance since it kind of still in the winter zone but near summer...

Answer: Population

Step-by-step explanation: Population is refers to the whole or entire members or of a given set. This is different from a sample which is used to refer to members of a subset (a subset is a certain portion or fraction of an entire set). In the scenario above, since the evaluation was based on the entire number of registered voters in the country, this means we are referring to a population. The inference about the percentage of democratic voters was drawn from a pool of all the entire number of registered voters available in the country and not from a certain subset or portion of registered voters. Hence, the evaluated group is a population.

Answer:

1.4

Step-by-step explanation:

The conversion rate for a gallon to quart is given as

This means that to get the number of quarts in a given measure in gallons, we multiply the number by 4.

The question asks us to convert 15 gallons to quarts.

This can be calculated as

Therefore,

Answer:

x = {2, 5 , -2}

Step-by-step explanation:

See photo for explanation:

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Answer:

We need a sample of at least 1937.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

For this problem, we have that:

\(\pi = 0.72\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

How large a sample should be if you want your estimate to be within 0.02 with 95% confidence.

We need a sample of at least n.

n is found when M = 0.02. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 1.96\sqrt{\frac{0.72*0.28}{n}}\)

\(0.02\sqrt{n} = 1.96\sqrt{0.72*0.28}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.72*0.28}}{0.02}\)

\((\sqrt{n})^{2} = (\frac{1.96\sqrt{0.72*0.28}}{0.02})^{2}\)

\(n = 1936.16\)

Rounding up to the nearest number.

We need a sample of at least 1937.

Answer:

125km

Step-by-step explanation:

50km ÷ 2in = 25km per 1 in.

5 in. × 25 km = 125km

Answer:

A

Step-by-step explanation:

The name of the point represented by V is an orthocenter. Option A

A triangle's point of concurrency is its orthocenter. It is the location where the triangle's three altitudes come together.

A line segment drawn perpendicular from a triangle's vertex to the other side or its extension represents the triangle's altitude.

Usually, the letter "H" is used to indicate the orthocenter. It is a crucial point in triangle geometry and has a variety of characteristics and connections to other triangle points like the circumcenter and centroid.

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Answer:

the answer is D

Step-by-step explanation:

The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

Answer:

20 cm

Step-by-step explanation:

just a guess since there isn't a pic

SOLUTION

We want to solve

Using the quadratic formula

We have

So, either

Or

Hence the answer is x = 0.5 or -2.3 to the nearest tenth

Answer:

20

Step-by-step explanation:

15+(-2)+7=13+7=20

\(\longrightarrow{\blue{20}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\(\:15 + ( - 2) + 7\)

➺ \( \: 15 - 2 + 7\)

➺ \( \: 22 - 2\)

➺ \( \: 20\)

\(\sf\pink{PEMDAS\: rule.}\)

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

Answer:

-3

Step-by-step explanation:

-3 + 7 = 4

2 x 4 = 8

Answer:

616

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

draw a small table with x and y

whenever x is 1 y becomes 14

using y=mx + c

y= 12(1) + 2

12×1=12

12+2=14

therefore x is 1

This question is incomplete, the complete question is;

For what value of a is the volume of the tetrahedron formed by the coordinate planes and the plane (x/a) + (y/10) + (z/6) = 1 equal to 10?

Answer: the value of a is 1

Step-by-step explanation:

Given that;

Volume of tetrahedron bounded by plane (x/a) + (y/10) + (z/6) = 1

and coordinate plane is; V = 1/6|abc|

(x/a) + (y/10) + (z/6) = 1

volume = 10

so

10 = 1/6 | a × 10 × 6 |

60 = a × 10 × 6

60 = 60a

a = 60 / 60

a = 1

Therefore the value of a is 1

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Step-by-step explanation:

y = 9x - 7

When x = 8

y = 9.8 - 7

y = 72 - 7

y = 65

When x = 6

y = 9.6 - 7

y = 54 - 7

y = 47

When x = 7

y = 9.7 - 7

y = 63 - 7

y = 56

When x = -8

y = 9.(-8) - 7

y = -72 - 7

y = -79

When x = 4

y = 9.4 - 7

y = 36 - 7

y = 29

As a result, option two (3.50) is correct.

Step-by-step explanation:                                                    
                                   
The code chunk that allows you to filter the data frame for chocolate bars with at least 70% cocoa and a rating of at least 3.5 pounds is as follows

∴ filter(Cocoa, percent>='70%'&Rating>=3.5)


Therefore, the code you write is facet wrap(Cocoa. Percent). Facet wrap() is a function in this code chunk that allows you to wrap a variable's facets. All of the ingredients are derived from cocoa beans. Cacao solids (the "brown" part, which contains health benefits and the unmistakable chocolatey flavor) and cacao butter (the "white" part, which contains the chocolate's fatty component) are split in proportion.


As a result, 3.5 appears in row 1 of your Tibble.

Other options I (iii), and (iv) are incorrect because the question states that any rating greater than or equal to 3.5 points can be considered a
high rating, and the rating here should be 3.5, not 3.75, 4.25, or 4

So, option (ii) is correct.  


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The freezing point of water in relation to the freezing point of acetone, is 169 °F

The difference between the freezing point of water (how much warmer the freezing point of water is) and the freezing point of acetone can be found by the formula:
= Freezing point of water - Freezing point of acetone

Freezing point of water = 32°F

Freezing point of Acetone = – 137°F

In relation to the freezing point of acetone, the degrees warmer that the freezing point of water is:

= 32 - (- 137)

= 32 + 137

= 169 °F

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Answer: -24

Step-by-step explanation:

\(\frac{x}{3}=-8\\\frac{x}{3}(3)=-8(3)\\ x=-24\)

The percent of data within the following interval from 28 to 82 is 99.73%

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

Mean = 55

Standard deviation = 9

Scores = from 28 to 82

So, we have

z = (28 - 55)/9 = -3

z = (82 - 55)/9 = 4

This means that it is between a z-score of -3 and a z-score of 3

This is represented as

Probability = (-3 < z < 3)

Using a graphing calculator, we have

Probability =  0.9973

Express as percentage

Probability =  99.73%

Hence, the probability is 99.73%

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The option A that is 2 days after being planted, the two plants will of the same height( Where the two lines intersect in a graph).

How to know if the lines intersect in the graph of a function?

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

And after solving both equations if the values of x and y satisfies both equations then they intersect at that values of x and y.

Now,

On Monday, Eric planted a 3-centimeter-high tomato plant and a 5-centimeter-high tomato plant in his garden.

The graph models the growth of each plant since the day they were planted.

The intersection of the two lines represents the days after being planted were the two plants the same height.

The answer is that 2 days after being planted, the two plants are the same height.

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The answer is that 2 days after being planted, the two plants are the same height.

How to know if a point lies in the graph of a function?

The answer is that 2 days after being planted, the two plants are the same height.

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