.. ¿Cuál es la densidad de una sustancia, si 460 gr ocupa un volumen de 35 cm3?
- Determinar la presión ejercida por una fuerza de 12 N aplicada a una superficie de 1,5 m2
​

Probability distribution of a random variable X. k 0 1 2 3 4 5 P(X ≤ k) 0.24 0.59 0.75 0.90 0.98 1. The probability of X to be at least 3 can be calculated as follows: Since  P(X ≤ k)  for k = 0, 1, 2, 3, 4 and 5  are given, P(X ≥ 3) = 1 - P(X < 3)P(X < 3) = P(X ≤ 2) = 0.24 + 0.59 + 0.75 = 1.58P(X ≥ 3) = 1 - 1.58= -0.58  (Since probability cannot be negative. It is clear that we cannot have a negative probability.)

Thus, the probability of X to be at least 3 is 0.42. The above probability distribution table displays the probabilities of the random variable X. The column k represents the values of X. The column P(X ≤ k) represents the probabilities of X being less than or equal to k. Now, we are to determine the probability of X being at least 3, i.e., we need to find P(X ≥ 3).  

To find this, we can use the complement of the event of X being less than 3. It is clear that, P(X < 3) + P(X = 3) = P(X ≤ 2) + P(X = 3) = 0.24 + 0.59 + 0.75 + P(X = 3) = 1.58 + P(X = 3) = P(X ≤ 3)The above equation follows from the fact that the probability of X taking any value in the range 0 to 3 must be equal to the sum of the probabilities of X taking any value in the range 0 to 2 and the probability of X taking the value 3. Now,  P(X ≤ 3) = 0.90. (Referring to the table above)Thus, P(X ≥ 3) = 1 - P(X < 3) = 1 - P(X ≤ 2) = 1 - 0.90 = 0.10. Answer: 0.10.

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The 95% confidence interval for the percentage of all voters in the population who have an income of $150,000 or more is approximately (18.38%, 25.62%).

To calculate the 95% confidence interval for the percentage of all voters in the population who have an income of $150,000 or more, we can use the following formula:
CI = p ± z*sqrt((p*(1-p))/n)
Where:
p = proportion of voters in the sample who have an income of $150,000 or more = 110/500 = 0.22
z* = z-score corresponding to 95% confidence level = 1.96 (from standard normal distribution)
n = sample size = 500
Plugging in these values, we get:
CI = 0.22 ± 1.96*sqrt((0.22*(1-0.22))/500)
CI = 0.22 ± 0.049
CI = (0.171, 0.269)
Therefore, we can be 95% confident that the percentage of all voters in the population who have an income of $150,000 or more is between 17.1% and 26.9%.
To calculate a 95% confidence interval for the percentage of all voters in the population who have an income of $150,000 or more, we will use the following formula:
CI = p-hat ± Z * √(p-hat * (1 - p-hat) / n)
Where:
- CI represents the confidence interval
- p-hat is the sample proportion (110/500 = 0.22)
- Z is the Z-score for a 95% confidence interval (1.96)
- n is the sample size (500)
Plugging the values into the formula:
CI = 0.22 ± 1.96 * √(0.22 * (1 - 0.22) / 500)
CI = 0.22 ± 1.96 * √(0.1716 / 500)
CI = 0.22 ± 1.96 * 0.01845
CI = 0.22 ± 0.03612

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9 block rhombuses would create 3 hexagons.

In order to increase the total number by three, a hexagon can be divided into a minimum of three rhombuses, each of which can be further divided into four rhombuses. With n being a positive integer, the result is 3n. The top two hexagons in this image are each divided into 8 and 10 rhombuses. The total number of rhombuses that can fit in a hexagon is not limited to multiples of three, given that the total number of rhombuses dividing a hexagon can be raised by three by quartering a single component rhombus. The amount might actually be any integer larger than 7.

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Answer:

C   y  =  20x +40

Step-by-step explanation:

I think there is a typo in your question

monthly payment total   = 20 x

 total paid so far = 40 + 20x

y = 20x + 40

Answer: No

Explanation: In order for a table to represent a function,

each x term must correspond to exactly one y term.

In this case, we have a 49 paired to -7 and a +7.

Since the 49 doesn't correspond to one y term,

this table cannot represent a function.

Answer:

12,1/2,81,16

Step-by-step explanation:

you just solve it

Answer:

Step-by-step explanation:

Examples

Quadratic equation

x

2

−4x−5=0

Trigonometry

4sinθcosθ=2sinθ

Linear equation

y=3x+4

Arithmetic

699∗533

Matrix

[

2

5

​

3

4

​

][

2

−1

​

0

1

​

3

5

​

]

Simultaneous equation

{

8x+2y=46

7x+3y=47

​

Differentiation

dx

d

​

(x−5)

(3x

2

−2)

​

Integration

∫

0

1

​

xe

−x

2

dx

Limits

x→−3

lim

​

x

2

+2x−3

x

2

−9

​

Answer:

It will be worth about £885.59.

Step-by-step explanation:

The art piece originally costs £600.

And it appreciates at a rate of 3.97% each year.

And we want to find the value of the art after 10 years.

We can write an exponential function to model the situation. The standard exponential function is given by:

\(f(t)=a(r)^t\)

Where t is the time in years.

Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.

103.97% = 1.0397. So, r = 1.0397:

\(f(t)=a(1.0397)^t\)

Our a is the initial value. Therefore:

\(f(t)=600(1.0397)^t\)

Then the value of the piece of art after 10 years is:

\(f(t)=600(1.0397)^{10}=885.5879...\approx \pounds 885.59\)

It will be worth about £885.59 after 10 years.

Answer:

885.59

Step-by-step explanation:

1. 600 + 23.82

2. 623.82 + 24.77

3. 648.59 +25.75

4. 674.34 + 26.77

5. 701.11 + 27.83

6. 728.94 + 28.94

7. 757.88 + 30.09

8. 787.97 + 31.28

9. 819.25 + 32.52

10. 851.77 + 33.82

After 10 years the art valued for 885.59 British Pounds.

The value of a, b and c from the given expression above are 15, 1 and 4 respectively

Indices are written in form of exponential expression. Given the expression

\(\sqrt[4]{15}\)

We are to write the expression in the form

\(a^{b/c}\)

This is simplified as shown

\(\sqrt[4]{15}= 15^{1/4}\)

Compare both expression

a = 15

b = 1

c = 4

Hence the value of a, b and c from the given expression above are 15, 1 and 4 respectively

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It should be noted that there is no direct variation between a triangular number and its position in its sequence.

It should be noted that from the information, triangular numbers can be represented with equilatreral triangels formado but dots and the first five triangular numbers are 1, 3,6 ,10 and 15.

It should be noted that this can be represented as:

n(n + 1)/2

where n = the position

Therefore, the the first five triangular numbers are 1, 3,6 ,10 and 15. This doesn't illustrate a direct variation.

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As per the given conditions the probability of having exactly one head in all the flips is 7/8.

To find the probability of exactly one head in all the flips, we need to consider the possible outcomes and calculate their probabilities.

There are two cases to consider:

Case 1: The first coin flip results in heads (H).

In this case, two additional coins are flipped, and we want exactly one head among the three flips. The possible outcomes are  HHT, HTH, and THH. Each outcome has a probability of \(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{8}\)

So, the probability of exactly one head in this case is \(3*\frac{1}{8}= \frac{3}{8}\).

Case 2: The first coin flip results in tails (T).

In this case, only one additional coin is flipped, and we want exactly one head among the two flips. The possible outcomes are TH and HT. Each outcome has a probability of \(\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\)

So, the probability of exactly one head in this case is  \(2 * \frac{1}{4}=\frac{1}{2}\).

To find the overall probability, we sum the probabilities from both cases:

\(P(exactly\: one \:head) = P(Case 1) + P(Case 2) =\frac{3}{8} + \frac{1}{2}= 7/8\).

Therefore, the probability of having exactly one head in all the flips is 7/8.

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Answer:

The score is 96

Step-by-step explanation:

This is a problem that uses a linear equation (a line) where the y intercept is 0. See the graph below.

So for this problem, the equation is

y = kx

when x = 27

y = 81

81 = k * 27          Divide both sides by 27

81/27 = k*27/27

k = 3

So when x = 32 solve for y

y = 3x

y = 3*32

y = 96

Answer:

-12degrees Celsius

Step-by-step explanation:

-3+5=2 1:00pm

2-2=0 6:00pm

(10-6=4)

4(3)=12, 0-12=-12 10:00pm

i hope this helps!

Answer:

-12° C

Step-by-step explanation:

Temperature at 8 a.m.: -3° C

From 8 a.m. to 1 p.m. the temperature went up 5° C.

-3° C + 5° C = 2° C

Temperature at 1 p.m.: 2° C

By 6 p.m. the temperature was 2° C colder than at 1 p.m.

2° C - 2° C = 0° C

Temperature at 1 p.m.: 0° C

The temperature decreased 3° C per hour from 6 p.m. to 10 p.m.

From 6 p.m. to 10 p.m., it's 4 hours. The temperature decreased 3° C per hour for 4 hours. 4 * 3° C = 12° C. The temperature went down 12° C altogether from 6 p.m. to 10 p.m.

0° C - 12° C = -12° C

Temperature at 10 p.m.: -12° C

Answer: -12° C

In the first month's payment for a $180,000 mortgage with a 5.5 percent, 30-year loan, a portion will go towards the principal. The exact amount can be determined using an amortization schedule.

To calculate how much of the first month's payment goes towards the principal, we can follow these steps:

Step 1: Determine the monthly interest rate: Divide the annual interest rate by 12 to obtain the monthly interest rate. In this case, 5.5 percent divided by 12 equals 0.004583 (approx).

Step 2: Calculate the monthly payment: Use a loan payment formula or a mortgage calculator to determine the monthly payment amount. For a $180,000 mortgage with a 30-year loan term and a 5.5 percent interest rate, the monthly payment would be approximately $1,019.32 (approx).

Step 3: Create an amortization schedule: An amortization schedule shows the breakdown of each monthly payment, indicating the amount allocated to interest and principal. Using the loan details, create an amortization schedule or use an online tool to generate one.

Step 4: Locate the first month on the schedule: Find the first month's entry on the amortization schedule to determine the amount allocated to principal. This amount will vary depending on the specific terms of the loan. Locate the principal portion of the payment, which represents the reduction of the loan balance.

By following these steps and referencing the amortization schedule, you can determine the exact amount of the first month's payment that goes towards the principal of the $180,000 mortgage.

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Answer:

0.5 minutes

Step-by-step explanation:

Since we are provided the equation and the current height of the candle (which would be 25 inches) we can simply replace this current height with the variable h and then solve the rest of the equation to find out the value of m when the height of the candle is at 25 inches.

h = 32−14m

25 = 32−14m ... subtract both sides by 32

-7 = -14m ... divide both sides by -14

0.5 = m

Finally, we can see that after 0.5 minutes the candle would have melted down to 25 inches.

Answer:

$4,194

Step-by-step explanation:

First, you need to subtract the 1,804 from the the total, which will give you 4,780. Divide this by two to get the cost of room and board, which is 2390. To find the tuition fee, add 2,390 and 1,804, and that equals $4,194.

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

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Answer:

1) not

2) QE

3) QE

4) QE

5) QE

6) QE

7) QE

8) not

9) QE

10) not

hope this helps you!

Answer:

4 years

Step-by-step explanation:

Given data

Simple interest= $400

Principal= $2000

Rate= 5%

The simple interest formula is given as

SI=PRT/100

substitute and solve for T

400=2000*5*T/100

cross multiply

400*100= 10000*T

40000=10000T

T= 40000/10000

T= 4 years

Hence the time taken is 4 years

Answer:

The answer is 14 and 9

Step-by-step explanation:

Answer:

\(answer14\)

hope it will be helpful to you

Answer:

those are your two answers

Step-by-step explanation:

Answer:

The probability is 5/8

Step-by-step explanation:

The amount of fabric that should be used to build a kite with the above given dimensions would be = 2,285.125cm²

To calculate the area of a kite the formula that should be used would be = 1/2 d1d2

where d1 = 50½cm

d2 = 90½cm

The area of the kite;

= 1/2 × 50.5×90.5b

= 4570.25/2

= 2,285.125cm²

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The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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Answer:

Add the lengths:

5x - 16 + 2x - 4 = 7x - 20

Answer:yes

Step-by-step explanation:

Yes, If 3/7 is written as a decimal then the digits after the decimal eventually repeat.

A number system is defined as a system of writing to express numbers.

Yes, the decimal representation of 3/7 will eventually repeat.

To convert the fraction 3/7 to a decimal, we can use long division.

Three by seven is a fraction, A fraction represents a part of a whole.

3/7 = 0.42857142857

The digits after the decimal point begin to repeat after the first six digits. Therefore, the decimal representation of 3/7 is 0.428571, with the digits 285714 repeating indefinitely.

Hence, If 3/7 is written as a decimal then the digits after the decimal eventually repeat is true.

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To determine whether the series E(n=0 to infinity) (3 - 2^(-2^n)) converges or diverges, we need to examine the behavior of the individual terms as n increases. From the pattern of the terms, we can observe that as n increases, the terms approach 3. Therefore, it appears that the series is converging towards a finite value.

Let's analyze the pattern of the terms:

n = 0: 3 - 2^(-2^0) = 3 - 2^(-1) = 3 - 1/2 = 5/2

n = 1: 3 - 2^(-2^1) = 3 - 2^(-2) = 3 - 1/4 = 11/4

n = 2: 3 - 2^(-2^2) = 3 - 2^(-4) = 3 - 1/16 = 49/16

n = 3: 3 - 2^(-2^3) = 3 - 2^(-8) = 3 - 1/256 = 767/256

To formally prove the convergence, we can use the concept of a nested interval and the squeeze theorem. We can show that each term in the series is bounded between 3 and 3 + 1/2^n. As n approaches infinity, the range between these bounds shrinks to zero, confirming the convergence of the series.

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Hello!

total = 3 + 1 = 4

1/4 = 1*9/4*9 = 9/36

3/4 = 3*9/4*9 = 27/36

Answer:

1/12.

Step-by-step explanation:

6 sides and 2 sides. 2 possible outcomes for each side of the dice

Answer:

\(\frac{1}{12}\)

Step-by-step explanation:

The combinations:

heads and 1, heads and 2, heads and 3, heads and 4, heads and 5, heads and 6, tails and 1, tails and 2, tails and 3, tails and 4, tails and 5, tails and 6