convert 472 base 8 to base 5 and base 4 ​

it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

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The  answer is:Karen would have $1000000 in the second account when she is 23 years old.

In order to calculate at what age Karen would have $1000000 in the second account, we need to calculate the future value of her investment in the first account, and then use that as the present value for the second account.Let us complete the tables given:

First Account PV: $0 FV: $0 Periods: 144 Rate: 5.75% Payment: $500 PMT/yr: 12 CMP/yr: 4Second Account PV: $163474.72 FV: $1000000 Periods: 23 Rate: 7% Payment: $0 PMT/yr: 1 CMP/yr: 1.

In the first account, Karen invested $500 a month for 12 years.

The total number of periods would be 12*4 = 48 (since it is compounded quarterly). The rate of interest per quarter would be (5.75/4)% = 1.4375%.

The PMT/yr is 12 (since she is investing $500 every month). Using these values, we can calculate the future value of her investment in the first account.FV of first account = (500*12)*(((1+(0.014375))^48 - 1)/(0.014375)) = $162975.15

Rounding off to the nearest cent, the future value of her investment in the first account is $162975.15.

This value is then used as the present value for the second account, and we need to find out at what age Karen would have $1000000 in this account. The rate of interest is 7% compounded annually.

The payment is 0 since she does not make any further investments in this account. The number of periods can be found by trial and error using the formula for future value, or by using the NPER function in Excel or a financial calculator.

Plugging in the values into the formula for future value, we get:FV of second account = 162975.15*(1.07^N) = $1000000Solving for N, we get N = 22.93. Rounding off to the nearest year, Karen would have $1000000 in the second account when she is 23 years old.

Therefore, the main answer is:Karen would have $1000000 in the second account when she is 23 years old.

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Given an LTI system that has an output y = 2te^-ul for the input x(t) = -(t). Here, e^-ul is the decay constant and is a real positive constant. The impulse response of the system can be found by considering the impulse input x(t) = δ(t).

The output of the system with an impulse input is given by y(t) = h(t), where h(t) is the impulse response of the system.We have,x(t) = -(t)..........(1)Applying derivative on both sides of the above equation, we get,y(t) = 2te^-ul, Applying derivative on both sides of the above equation, we get,

Plot of frequency response and Impulse response of the system Hence, the plot of frequency response and the impulse response of the LTI system is shown in the figure below:, the frequency response is given by H(jω) = (2/(-jω + ul)^2) where ω is the angular frequency. The impulse response of the system is given by h(t) = (2/ul^2)t.e^-ul.

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See solution below

Explanation:

a) 5x - 7 ≤ -2

collect like terms:

5x ≤ -2 + 7

5x ≤ 5

Divide through by 5:

x ≤ 1

From the graph above, the inequality has a solution.

b) 2/3b > -8

Cross multiply:

2 > -8(3b)

2 > -24b

Divide through by -24:

Note: when we divide an inequality by a negative number, the inequality sign changes.

2/-24 < b

-1/ 12 < b

Hence, b > -1/12

Note: To make it easier to graph, I represented b with x

From the graph above, the inequality has a solution.

c) 3w - 7 - w < 2w + 4

2w - 7 < 2w + 4

collect like terms:

2w - 2w < 4 + 7

0 < 11

Note: To make it easier to graph, I represented b with x

From the graph, the solution is for all real numbers.



Answer:

245/5 = 49 tickets per day

Answer:

245 / 5 = 49 so

49 tickets per day

Answer: you are dummy

Step-by-step explanation:dummy

The similarity statement that would be true for the given figure is;

A. ∆ DAB ~∆ DAC

Similar triangles are those triangles that have the same proportionate side lengths as well as related angle measurements.

here, we have,

Two triangles are said to be similar if their corresponding angles and sides have the same ratio. Similar triangles will possess the same form but may or may not have the same size.

The SAS similarity rule states that If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then it means that the two triangles are similar.

The Side-Side-Side (SSS) similarity rule states that If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

In this question, when we analyze the triangles well, it is clear that;

DA is congruent to itself by reflexive property of congruence.

Thus, we can say that ΔDAB is similar to ΔDAC,

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Answer:

360 miles

Step-by-step explanation:

45 miles=1 gallon

45x8=360

Answer:

360 miles

Step-by-step explanation:

8×45 ur just multiplying

Answer:

d = 3

Step-by-step explanation:

The sum to n terms of an AP is

\(S_{n}\) = \(\frac{n}{2}\) ( a + l)

where a is the first term and l the last term

Here a = 2, l = 59 and sum = 610 , then

\(\frac{n}{2}\) (2 + 59) = 610

\(\frac{n}{2}\) × 61 = 610 ( divide both sides by 61 )

\(\frac{n}{2}\) = 10 ( multiply both sides by 2 to clear the fraction )

n = 20

Then the sequence has 20 terms with a₂₀ = 59

The nth term of an AP is

\(a_{n}\) = a + (n - 1)d

where d is the common difference , then

2 + 19d = 59 ( subtract 2 from both sides )

19d = 57 ( divide both sides by 19 )

d = 3

To find the length of the curve defined by y =\(2x^(3/2)\) - 9, from x = 1 to x = 9, we use the arc length formula and integrate the square root of the sum of squares of the derivative of y with respect to x.

By evaluating this integral, we can determine the length of the curve.

To find the length of the curve defined by the equation y =\(2x^(3/2)\) - 9, from x = 1 to x = 9, we can use the arc length formula for a curve given by y = f(x) over the interval [a, b]:

L = ∫[a,b] √(1 + (f'\((x))^2\)) dx

First, we find the derivative of y with respect to x:

dy/dx = 3√(2x) / 2

Next, we substitute the derivative into the arc length formula and integrate over the interval [1, 9]:

L = ∫[1,9] √(1 + (3√(2x) / \(2)^2\)) dx

Simplifying the integrand, we have:

L = ∫[1,9] √(1 + 9x) dx

By evaluating this integral, we can determine the length of the curve.

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Answer:

90v - 80

Step-by-step explanation:

-10 ( -9v + 8 )

Distributive property (multiply what is in the parenthesis by -10)

-10 * -9v + -10 * 8

90v - 80

2 negatives become a positive

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:90v-80

Step-by-step explanation:

Answer:

Multiplication properly of equality

The fundamental set of solutions for the given differential equation is {e^(-2t), e^t}.

To find the fundamental set of solutions for the differential equation y'' + y' - 2y = 0 with the initial point t₀ = 0, we can follow the steps outlined in Theorem 3.2.5.

Find the characteristic equation:

The characteristic equation is obtained by substituting y = e^(rt) into the differential equation, where r is a constant:

r² + r - 2 = 0

Solve the characteristic equation:

Factoring the equation, we have:

(r + 2)(r - 1) = 0

Setting each factor equal to zero and solving for r, we get:

r₁ = -2

r₂ = 1

Determine the fundamental set of solutions:

The fundamental set of solutions is given by:

y₁(t) = e^(r₁t)

y₂(t) = e^(r₂t)

Substituting the values of r₁ and r₂, we have:

y₁(t) = e^(-2t)

y₂(t) = e^t

Therefore, the fundamental set of solutions for the given differential equation is {e^(-2t), e^t}.

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Answer:

51 mins were not ads

Step-by-step explanation:

1 video = 9 mins

6 videos = x

x = 9×6 = 54 mins

mins of ads = 3 mins

mins that were not ads = total mins of videos – total mins of ads

= 54 – 3 = 51 mins

if this helped pls give brainliest

Answer:

B. you can check the second one

Answer:

5/1

Step-by-step explanation:

Answer:

5/1

Step-by-step explanation:

On solving the provided question, we got to know that - distance she covered from her starting position is 2731 miles

If two things are equal, an equation declares it. A "=" equals sign will appear in the format: 7 + 2 = 10 − 1 What is on the left (7 + 2) equals what is on the right (10 1), according to that equation. The statement "this equals that" is analogous to an equation.

The flight's first leg is 1020 miles long and lasts (1.5 hours) at 680 mph. We'll refer to this as our triangle's side B.

The second leg of the journey is 1360 miles (2 hours x 680 mph) long. We'll refer to this as the triangle's side C.

The law of cosines allows us to determine the triangle's side a's length.A is a 170° angle between the two sides whose lengths we are aware of. (180° - 10° = 170°).

\(a^2 = b^2 + c^2 - (2)*(a)*(b)*cos(A)\)

\(a^2 = (1020 miles)^2 + (1360 miles)^2 - (2)*(1020 miles)(1360 miles)*cos(170)\\ a^2 = 1040400 miles^2 + 1849600 miles^2 - (2774400 miles2)*cos(170)\\ cos(170) = -0.9848\\ a^2 = 2890000 miles^2 + 2732251 miles^2 = 5622250.6 miles^2\\ a = (5622250.6 miles^2)^{\frac{1}{2} } = 2371 miles\)

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Answer:

p=1/27

Step-by-step explanation:

3p=1/9

when 9 goes to the left land side divide changes into multiplication so 3p and 9 gets multiplied

3p*9=1

27p=1

when 27 goes the right hand side multiplication changes to division .So

p=1/27

The value of P is 1/27 for equation 3P = 1/9​

Two or more expressions with an Equal sign is called as Equation.

Given,

Equation is  3P = 1/9​

Three times of P equal to one by nine

We need to find the value of P

3P = 1/9​

Divide both sides by nine

3P/3=1/9×1/3

P=1/27

Hence, the value of P is 1/27.

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Answer:

12.5 =x

Step-by-step explanation:

15 = 2x – 10

Add 10 to each side

15+10 = 2x – 10+10

25 = 2x

Divide by 2

25/2 = 2x/2

12.5 =x

Answer:

25/2

Step-by-step explanation:

2x-10=15

  +10 +10

2x=25

divide both sides by 2 to get 25/2

Answer:

1. 52.63% 2. 47.36%

Step-by-step explanation:

20 + 18 = 38 total people

20 divided by 38 = 0.5263 to 52.63%

18 divided by 38 = 0.4736 to 47.36%

Hope this helps!

Answer:

89.76 yd^2

Step-by-step explanation:

The area is given by

A = bh

A = 10.2 * 8.8

A =89.76 yd^2

a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Let's assume that the measure of angle BAC is less than or equal to the measure of angle ABC.

Since AB = AC, then angles BAC and BCA are also equal. Let's denote the measure of angle BAC as x, then the measure of angle ABC and angle BCA is also x.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. In our case, we have:

AB + BC > AC

AB + 24 > AC

2AB + BC > 2AC

2AB + 24 > 2AC

2AB > 2AC - 24

AB > AC - 12

Since AB = AC, then AC - 12 < AB = AC, which means AC < AC + 12. This is a contradiction, and therefore our assumption that the measure of angle BAC is less than or equal to the measure of angle ABC is false.

Therefore, we can conclude that Angle BAC > Angle ABC.

a) The average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. b) The estimated coefficients of REDS and TRAINS in the regression model are 1.3353 (REDS). c) The absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis.

a) To find the average estimated time in minutes for Bill to drive to work when he leaves on time at 6:30 and there are no red lights and no trains at the crossroad to wait, we substitute the values into the regression model:

TIME = -19.9166 + 0.3692(DEPART) + 1.3353(REDS) + 2.7548(TRAINS)

Given:

DEPART = 0 (as he leaves on time at 6:30)

REDS = 0 (no red lights)

TRAINS = 0 (no trains to wait for)

Substituting these values:

TIME = -19.9166 + 0.3692(0) + 1.3353(0) + 2.7548(0)

    = -19.9166

Therefore, the average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. However, it's important to note that negative values in this context may not make practical sense, so we should interpret this as Bill arriving approximately 19.92 minutes early to work.

b) The estimated coefficients of REDS and TRAINS in the regression model are:

1.3353 (REDS)

2.7548 (TRAINS)

Interpreting the coefficients:

- The coefficient of REDS (1.3353) suggests that for each additional red light, the estimated time to drive to work increases by approximately 1.3353 minutes, holding all other factors constant.

- The coefficient of TRAINS (2.7548) suggests that for each additional train Bill has to wait for at the crossing, the estimated time to drive to work increases by approximately 2.7548 minutes, holding all other factors constant.

c) To test the hypothesis that each train delays Bill by 3 minutes, we can conduct a hypothesis test.

Null hypothesis (H0): The coefficient of TRAINS is equal to 3 minutes.

Alternative hypothesis (Ha): The coefficient of TRAINS is not equal to 3 minutes.

We can use the t-test to test this hypothesis. The t-value is calculated as:

t-value = (coefficient of TRAINS - hypothesized value) / standard error of coefficient of TRAINS

Given:

Coefficient of TRAINS = 2.7548

Hypothesized value = 3

Standard error of coefficient of TRAINS = 0.1390

t-value = (2.7548 - 3) / 0.1390

       = -0.2465 / 0.1390

       ≈ -1.7733

Using a significance level of 5% (or alpha = 0.05) and looking up the critical value for a two-tailed test, the critical t-value for 230 degrees of freedom is approximately ±1.9719.

Since the absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that each train delays Bill by 3 minutes.

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Answer:

-18

Step-by-step explanation:

Every time you multiply a positive number to a negative number, it will always be negative.

9(-2) = 9 * -2 = -18

Best of Luck!

Answer:

The answer is C.

Step-by-step explanation:

You have to substitute the x-values into the equation to see whether it suits the y-value :

\(y = 2x\)

\(let \: x = 0 \\ y = 2(0) \\ y = 0 \: (incorrect)\)

\(let \: x = 2 \\ y = 2(2) \\ y = 4 \: (incorrect)\)

\(let \: x = 1 \\ y = 2(1) \\ y = 2 \: (correct)\)

\(let \: x = 2 \\ y = 2(2) \\ y = 4 \: (incorrect)\)

Answer: A. yes, closed and lines are straight B. No, curved lines C. no, curved lines D. yes, closed have lines are straight E. yes, closed have lines are straight  E. yes, closed and lines are straight F. No, curved lines G. yes, closed and lines are straight H. yes, closed and lines are straight

Step-by-step explanation:

Answer:

36 = 2h

Step-by-step explanation:

Here h represents the heigh

We know that the height of the door was twice the height of the window so that the equation will be

36 = 2h

Answer:

x=4

From the principles of isosceles triangles, two opposite sides are equal.

So,

4x+23=10x-1

solving the linear equation, we'd have x to be 4.

Answer:

x=4

Step-by-step explanation:

it is isosoles triangle so the value of x solve as follow

4x+23=10x-1

23+1=10x-4x

24=6x

x=4