What is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9

Answers

Answer 1

Answer:

  2519

Step-by-step explanation:

In each case, the remainder is 1 less than the divisor. This means the number of interest will be 1 less than the least common multiple of 5, 6, 7, 8, 9, 10.

The prime factors of these numbers are ...

  5 = 5

  6 = 2·3

  7 = 7

  8 = 2³

  9 = 3²

  10 = 2·5

The unique factors are 2, 3, 5, 7. When they are used to their highest powers, the resulting product is ...

  2³·3²·5·7 = 2520

The number of interest is 1 less than this, so is 2519.

2519 is the least positive integer that will give the required remainders.


Related Questions


Please help due tmrw

Please help due tmrw

Answers

Answer:

B

Step-by-step explanation:

less than equal to circle is filled

Answer:

the answer that you are looking for would be A.

QETJHSN. XGKDXBFX N.CCBX ..BDBZVDB.NDWHDSWGVB

Answers

Answer:

Wut WUt Wut oof :.

Step-by-step explanation:

During a sale, the price of a lounge suite dropped from $1600 to $1250. What was the percentage decrease in price?

Answers

Answer:

subtract 1600 by 1250 which is 350 then divide 350 by 1600 to get 0.218 simplify it to 0.22 and turn it into decimal form which is 22%

LAnswer:

Step-by-step explanation:

359/1600 = 21.88 % = 22%

When you multiply a mixed number by___________ the product is equal to the mixed number fill in the blank

Answers

Answer:

A whole number

Step-by-step explanation:

Answer: 1

Step-by-step explanation: If it was anything more than 1 it would not equal the same number.

Btw I didn't understand well if you have more questions put it into the comments. I hope I helped :)

what equation relates surface tension γ to the radius of a bubble?

Answers

The equation that relates surface tension (γ) to the radius of a bubble (r) is the Laplace-Young equation, which is given as ΔP = 2γ/r.

How we get the radium of a bubble?

The equation that relates surface tension γ to the radius of a bubble is:

γ = (2T)/r

γ is the surface tension

T is the surface tension of the liquid surrounding the bubble

r is the radius of the bubble

This equation is known as the Laplace pressure equation and it relates the surface tension of a liquid to the radius of a bubble. It states that the pressure inside a bubble is higher than the pressure outside the bubble, and the difference in pressure is directly proportional to the surface tension of the liquid and inversely proportional to the radius of the bubble.

In other words, the smaller the radius of the bubble, the greater the surface tension required to maintain the bubble. This is because as the radius decreases, the Laplace pressure increases, requiring a stronger surface tension to balance the pressure difference and maintain the bubble.

Conversely, a larger bubble requires less surface tension to maintain, since the pressure difference is smaller.

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What is the conversion of 3000 m to miles ?

Answers

The converted value of the units 3000 meters to the required miles is given by 1. 8641 miles ( round up to four decimal places ) .

Meters and Miles are related to each other as both are units which are used to measure the distance /length between any two or more endpoints.

Standard form to Convert meters and miles is equal to :

1 meter = 0.000621371 miles

Now,  the value of 3000 meters in miles we get by multiplying it by 0.000621371 we get,

3000 meters = ( 3000 ) × ( 0.000621371 ) miles

                      = ( 1.864113 ) miles

                      = ( 1.8641 ) miles ( round up to four decimals places )

Therefore, the value of 3000 meters to miles is equal to ( 1.8641 ) miles ( round up to four decimals places ) .

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8. Given P = {vowels) and Q= {consonants), what is PU Q?
(a) PUQ = 0
(b) PU Q = {a, e, i, o, u}
(c) PU Q = {consonants}
(d) PU Q = {The English alphabet}​




please answer urgent I'm timed please.....

Answers

Answer:

d) PU Q = {The English alphabet}​

Step-by-step explanation:

because U means Union of all P and Q

Sam spends exactly £20 on petrol. The petrol costs £1.45 per litre. Work out the number of litres of petrol she buys.

Answers

Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= \(\frac{20 *1}{1.45} = 13,79310345 L\) = 13,8 L

Ramundo is shopping for a new pair of rollerblades. Roller World sells a pair of rollerblades for $94 regular price. Currently, the rollerblades are on sale for 15% off. Outdoor Adventures sells the same pair of rollerblades for $81.50 with no discount. The sales tax rate in Ramundo's city is 6%.



Part A



To get the better deal, Ramundo should buy the rollerblades from , 1 of 2.
Select Choice
.



Part B



In doing so, he will save , 2 of 2.
Select Choice
(after tax) over the other store.

Answers

Ramundo will get a better deal at Roller worlds.

This is a question of percentages.

Given that:-

Regular price of rollerblades at roller world = $ 94

Discount at rollerworld = 15 %

Price of rollerblades at Outdoor adventures = $ 81.50

Sales tax = 6 %

Price of rollerblades at roller world after discount = 94 - (15/100)*94 = 94 - 14.1 = $79.9

Price of rollerblades at roller world after sales tax = 79.9 + (6/100)*79.9 = 79.9 + 4.794 = $ 84.694

Price of rollerblades at outdoor adventures = $81.50

Price of rollerblades at roller world after sales tax = 81.50 + (6/100)*81.50 = 81.50 + 4.89 = $ 87.39

As,

$ 84.694 <  $ 87.39

Ramundo will get a better deal at Roller worlds.

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This table shows outcomes of a spinner with 3 equal sections colored blue, yellow, and red. Section Outcomes Blue 22 Yellow 32 Red 46 Based on the outcomes, enter the estimated probability of the spinner landing on blue.

This table shows outcomes of a spinner with 3 equal sections colored blue, yellow, and red. Section Outcomes

Answers

Based on the outcomes, the estimated probability of the spinner landing on blue which has equal sections colored blue, yellow, and red is 0.22 or 22%.

What do you mean by probability?

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

This table shows outcomes of a spinner with 3 equal sections colored blue, yellow, and red.

Section      Outcomes Blue                22 Yellow            32 Red                 46 Total               100

The total number of outcome is 100. The total number of favorable outcome to land blue is 22.

Thus, the estimated probability of the spinner landing on blue has to be found out is,

\(P=\dfrac{22}{100}\\P=0.22\\P=22\%\)

Hence, based on the outcomes, the estimated probability of the spinner landing on blue which has equal sections colored blue, yellow, and red is 0.22 or 22%.

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13.4 x 0.05 x 1.8 =?

Answers

Answer:

1.206

Step-by-step explanation:

13.4 × 0.05 × 1.8

= 67/5 × 5/100 × 9/5

= 603/500

= 1.206

suppose you toss two dice at the same time. if at least one of them is 5 or 6 you win. then, you toss them 8 times; what is your expected number of wins?

Answers

Step-by-step explanation:

The probability of winning on a single toss of two dice is equal to the probability of getting at least one 5 or 6, which is 11/36. The probability of losing on a single toss is 1 - 11/36 = 25/36.

Let X be the number of wins in 8 tosses. Then X follows a binomial distribution with n=8 and p=11/36. The expected number of wins is given by:

E(X) = n * p = 8 * 11/36 = 2.44

Therefore, the expected number of wins in 8 tosses is approximately 2.44.

Wow...I forgot how to do this please help

Wow...I forgot how to do this please help

Answers

Answer:

B. y = -6x+7

Step-by-step explanation:

change in x is positive 6 change in y is negative 1

6/-1 is the slope

-6 is the slope

(b) Problem 15: Find the rate of change for this two-variable equation. y-x = 10 ​

Answers

The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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What can we conclude if the omnibus null hypothesis is rejected in a one-factor anova?

Answers

Answer:

Not all the means are equal.

Step-by-step explanation:

In an ANOVA table, a sum of squares for the independent variable divided by its respective degrees of freedom.

So if the omnibus null hypothesis is rejected it means that there is sufficient evidence to conclude that not all the means are equal.

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If the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

ANOVA table gives us the total sum of squares ( TSS ), the residual sum of squares ( RSS ) and the estimated sum of squares ( ESS ).

It establishes the relation that:

ESS + RSS = TSS.

If we reject the omnibus null hypothesis, then it means that:

at least one of the population means is different from at least one other population mean.

Therefore, we get that, if the omnibus null hypothesis is rejected in a one-factor ANOVA, then, we can conclude that at least one of the population means is different from at least one other population mean.

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Sandy and Tom went for a run. Sandy started running 12 seconds before Tom. Sandy runs 7 meter per second. Tom runs 9 meters per second. How long did it take for both Sandy and Tom to cover the same distance?

Answers

It took both Sandy and Tom 54 seconds to cover the same distance.

To solve this problem

We can set up an equation based on their relative speed

Take the supposition that Tom needs "t" seconds to travel the distance. Sandy started jogging 12 seconds before Tom, so it will take her "t + 12" seconds longer to complete the same distance.

To determine the distance traveled by Sandy, multiply her speed (7 meters per second) by her time (t + 12) seconds. Tom's distance traveled may be determined by dividing his speed (9 meters per second) by his time (t) seconds.

Equating the distances covered by Sandy and Tom:

7(t + 12) = 9t

Expanding the equation:

7t + 84 = 9t

Subtracting 7t from both sides:

84 = 2t

Dividing both sides by 2:

t = 42

Tom traveled the distance in 42 seconds as a result. We add the 12-second lead Sandy had to determine the time it took for both Sandy and Tom to travel the same distance:

t + 12 = 42 + 12 = 54

So, it took both Sandy and Tom 54 seconds to cover the same distance.

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Give your answer in index form

Give your answer in index form

Answers

Answer:

1/4

Step-by-step explanation:

\(2^{4}\) x \(2^{3}\) = 16 x 8 = 128 = numerator

\(2^{5}\) x \(2^{4}\) = 32 x 16 = 512 = denominator

128/512 = 1/4 if you divide both numbers by 128 then you get 1 over 4 = 1/4

How many bricks each 25 cm by 15 cm by 8 cm, are required for a wall 32 m long, 3 m high and 40 cm thick?

Answers

Answer:

8

Step-by-step explanation:

81. Volume of a cone: 1. V = (1/3)πr2h 2. Slant height of a cone: 1. s = √(r2 + h2) 3. Lateral surface area of a cone: 1. L = πrs = πr√(r2 + h2) 4. Base surface area of a cone (a circle): 1. B = πr2 5. Total surface area of a cone: 1. A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

hope this helps

What is the answer to 5+ b = -b-2(1 - b)

Answers

Answer:

No solutions

Step-by-step explanation:

\(5+b=-b-2(1-b) \\ \\ 5+b=-b-2+2b \\ \\ 5+b=b-2 \\ \\ 5=-2\)

This is a false statement, so the equation has no solutions.

Which of the following lines would be the best fit for the data points plotted in the scatter plot below?

Which of the following lines would be the best fit for the data points plotted in the scatter plot below?

Answers

The line of the  best fit for the data points plotted in the scatter plot is y = -0.88x + 8

How to determine the line of the  best fit for the data points plotted in the scatter plot?

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

The graph

Using the line of the best fit, we have"

(x, y) = (8, 1) and (0, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 8

Using the points, we have

1 = 8m + 8

This gives

m = -0.88

So, we have

y = -0.88x + 8

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using a protractor and a ruler draw a right triangle with a side length of 5cm that is beetween the right angle and a 30 degree angle

Answers

The Triangle will look in this way (Attached image)-

How do you draw a 30 degree angle with a protractor?

Step 1: Draw a line segment OQ.

Step 2: Place the center tip of the protractor at point O such that the protractor perfectly aligns with line AQ.

Step 3: Start from 'Q' on the protractor in the anti - clockwise direction and stop at 30. Mark it as point 'P'. If point 'Q' lies to the right of 'O', then start measuring clockwise and stop at 30.

Step 4: Now, place the protector at point Q, mark the point 'P' at 90, such that ∠OQP = 90.

Step 5: Join point 'P' with 'O'. ∠QOP=30° is the required 30 degree angle.

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using a protractor and a ruler draw a right triangle with a side length of 5cm that is beetween the right

What's the slope of the line

What's the slope of the line

Answers

y= 2/3x+3

i’m sure this is right

Answer:

\(y=-\frac{3}{2} +3\)

Step-by-step explanation:

Start at the y-intercept, and go down until you see an even intersection (down 3 over 2).

Fill in the blank. A trapezoid (not isosceles) has ___ lines of symmetry.

Answers

A trapezoid (not isosceles) has zero lines of symmetry. A line of symmetry is a line that divides a figure into two congruent halves that are mirror images of each other.

Since a non-isosceles trapezoid has no congruent sides or angles, it cannot be divided into two congruent halves by any line. Therefore, it has no lines of symmetry.To see this, imagine drawing a trapezoid with unequal length sides and base. Now, try to draw a line of symmetry that divides the trapezoid into two congruent halves.

We will not be able to find such a line, no matter where you draw it. This is because the trapezoid is not symmetric in any way.On the other hand, an isosceles trapezoid has one line of symmetry. This is because it can be divided into two congruent halves by a line that passes through the midpoints of the non-parallel sides.

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HELP PLEASE!!!!
Write the first five terms of two different sequences that have 10 as the second term Describe the pattern (in words) in each of your sequences

Answers

Answer:

eh..you probaly shouldnt trust me

Step-by-step explanation:

8, and (8+2) = 10 Therefore the second term is 10. Another arithmetic sequence of common difference-5 and first term 15. The firs two terms of this sequence are: 15, and (15 - 5) = 10. Therefore again a 10 as second term.

Which expression shows the product of 1.5 x 106 and 12,000?
A. 1.8 x 1018
B. 1.8 x 1010
C 1.8 x 10°
D 1.8 x 1024

Answers

Answer:

d

Step-by-step explanation:

help me please i will give brainlyest

help me please i will give brainlyest

Answers

Answer:

Answer: 1645.

Step-by-step explanation:

Given data:

No. Of days of rental = 11 days.

Solution:

= 325 + 120d

Input the data for (d) into the equation

= 325 + 120(11)

= 325 + 1320

= 1645.

Step-by-step explanation:

A swimming coach needs to choose a team for a relay race. The coach must select 444 of 666 available swimmers and put them in a strategic sequence. How many unique ways are there to arrange 444 of the 666 swimmers?.

Answers

When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×\(10^{1735}\)

There are a total of 444\(C_{444}\) (or 6.64 x \(10^{847}\)) ways to select 444 swimmers from the pool of 666.

Once the swimmers have been chosen, they need to be arranged in a strategic sequence.

This can be done in 444! (or 5.34 x \(10^{906}\)) ways.

Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is

6.64 x \(10^{847}\) x 5.34 x \(10^{906}\)

3.53 x \(10^{1735}\)

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How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used to calculate your answer. Please don't link me any answers, I am unable to open them.

Answers

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

\(\displaystyle\sum_{n=1}^N a(n) = 2332\)

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

\(\displaystyle\sum_{n=1}^N (21n-20) = 2332\)

Expand the sum on the left as

\(\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332\)

and recall the formulas,

\(\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n\)

\(\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2\)

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

What is the value of x in the figure below? In this diagram, ABD ~ CAD.

A. 16/5
B. 16
C. √160
D. √5
E. 8
F. 25/4

What is the value of x in the figure below? In this diagram, ABD ~ CAD.A. 16/5B. 16C. 160D. 5E. 8F. 25/4

Answers

Answer:

F an amazing result.

Step-by-step explanation:

I'm sure I didn't do this the way it was intended, but I think I got it right.

First of all, we have to agree that CAB is marked as a right angle. If you do not agree, leave a note.

Step One

Find the length of AC

BC = 16

AB = 10

AC^2 = BC^2 - AB^2

AC^2 = 16^2 - 10^2

AC^2 = 256 - 100

AC^2 = 156

AC = SQRT(156)

AC = SQRT(4*13 * 3)

AC = 2 SQRT(13)

Step Two

Find the height (AD)

There are two ways to find the area of the large triangle ABC

Area = 1/2 * 16 * AD          and

Area = 1/2 AC * 10            The two legs.

Since these areas must be equal, equate them. You are looking for AD

16 * AD = 2*sqrt(39) * 10   Divide by 16

AD =  20* sqrt(39)/16

AD = 5 * sqrt(39) / 4

Step 3

Find x or DB

DB^2 = 10^2 - [(5 *sqrt(39)/4]^2

DB^2 = 100 - 25*39/16

DB^2 = 100 - 60.9375

DB^2 = 39.0625

DB = SQRT(39.0625)

DB = 6 1/4

6 1/4 is the same thing as 25/6 which is F

Answer:

F. 25/4

Step-by-step explanation:

just took the quiz

what is the length of CD
Find the ratio of the area of the triange abp & bpd

what is the length of CDFind the ratio of the area of the triange abp &amp; bpd

Answers

Answer:

if aman wieght 900N an earth what is his weight on jupiter where the acceleration due to gravity is25m/s?

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