There is such a positive integer: if it is divided by 5, the remainder is 3; if it is divided by 6, the remainder is 4; if it is divided by 7, the remainder is 1. Find the least possible value of such number.

Answers

Answer 1

Answer:

The least possible number is 148

---------------------------------------------------

Let the number be N.

If N is divided by 5 the remainder is 3:

N = 5k + 3,

Similarly:

N = 6p + 4,N = 7q + 1.

We can observe N + 2 is divisible by both 5 and 6, then it can be represented as:

N + 2 = 30m,

so

30m = 7q + 1 + 2 or30m - 3 = 7q

The left side is divisible by 3, then q = 3t:

30m - 3 = 7*3t10m - 1 = 7t

The least m and t would be m = 5 and t = 7.

Then:

N + 2 = 30*5 = 150 ⇒ N = 148 is the least possible number.

Proof:

148/5 = 29 (rem 3)148/6 = 24 (rem 4)148/7 = 21 (rem 1)


Related Questions

A train covers a dictance of 820KM in 8 hours. How much distance will ir cover in 1 hour?​

Answers

Answer:

102.5 km

Step-by-step explanation:

820km/8 hours=102.5 km

Rose has less than $30 to spend on decorations for the school dance. She has already spent $5. Which number line shows how much money she could still spend on decorations

Answers

The correct answer is number line A. Number Line A shows that Rose has $25 remaining to spend on decorations. The number line shows that she has already spent $5, as indicated by the arrow pointing from 0 to 5.

What is Number Line?

Number line is the  visual representation of numbers on a straight line. These are often used to represent linear equations, as well as to learn basic mathematical concepts such as addition, subtraction, multiplication, and division.

The number line shows that she has a total of $30 available for decorations, as indicated by the arrow pointing from 0 to 30. Between the two arrows, it is clear that Rose has $25 remaining to spend on decorations.

Number Line B does not accurately represent Rose’s situation because the arrow pointing from 0 to 20 does not indicate that Rose has already spent $5. Number Line C does not accurately represent Rose’s situation because the arrow pointing from 0 to 25 does not indicate that Rose has a total of $30 available to spend.

To solve this problem, Rose needs to identify the total amount of money she has available to spend on decorations and the amount of money she has already spent. Once she has identified these two values, she can use a number line to represent her situation.

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find the vertex of this quadratic??

find the vertex of this quadratic??

Answers

Answer:

(0,3)

Step-by-step explanation:

In this case the vertex is the maximum point of the parabola

vertex : (0,3)

What’s this ? I’ll mark up brainless .

Whats this ? Ill mark up brainless .

Answers

Answer: 0.7 i believe not sure

Step-by-step explanation:

Find the negative square root of
25
38

Answers

Answer: 33

Step-by-step explanation:

Answer:

-0.13157894736

Step-by-step explanation:

Parallel lines e and f are cut by transversal b.e=(2x+10) f=(3x-15)What is the value of x?A.1B.5C.25 D. 37

Answers

The value of x can be determined by solving the equations for e and f. To solve, subtract 3x from both sides of equation f, then add 10 to both sides of equation e. This will result in the equation -5=25, which when solved for x will result in a value of x=5.

In order to determine the value of x in the given problem, you must first solve the equations for e and f. Starting with equation e, add 10 to both sides of the equation to get 2x=20. Then, look to equation f and subtract 3x from both sides of the equation to get -15=3x. When both equations are combined, you get -5=25. Solving this equation for x will result in a value of x=5. Therefore, the value of x in this problem is 5. To summarize, when given two equations containing the same variable, you must solve them by adding or subtracting the same amount to both equations. This will result in an equation which can be solved for the desired variable. In this case, the value of x is 5.

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The volume of this cylinder is 4,939.22 cubic millimeters. What is the height? Use a 3.14 and round your answer to the nearest hundredth.​

The volume of this cylinder is 4,939.22 cubic millimeters. What is the height? Use a 3.14 and round your

Answers

Answer:

13 mm

Step-by-step explanation:

V = πr²h

4,939.22 mm³ = 3.14 × (11 mm)²h

4,939.22 mm³ = 3.14 × (11 mm)²h

h = 13 mm

Answer: 13 mm

PLEASE HELP!!
Solve the right triangle.
Round your answers to the nearest tenth.
A=
a=
c=

PLEASE HELP!! Solve the right triangle.Round your answers to the nearest tenth.A=a=c=

Answers

Answer:

Step-by-step explanation:

sum of ngles of triangle=180

90+39+A=180

129+a=180

A=180-129

A= 51

apply the some rule:

since 39 = opp/hyp

sin39=16/c

c= 16/sin39 = 25.42 ≅  25.4 rounded to the nearest tenth

sin 51 = opp/hyp

sin51=a/25.42415166

a=19.8 ( rounded to the nearest tenth)

create a conversion factor between grains of sand and mass based on the data you have collected. use this conversion factor to determine the grains of sand in your 50-ml beaker.

Answers

There are 0.001 grains of sand in your 50-ml beaker.

To create a conversion factor between grains of sand and mass, you need to determine the mass of one grain of sand. Once you have that information, you can create a conversion factor by dividing the mass of one grain of sand by the mass of the 50-ml beaker. This will give you the number of grains of sand per unit mass.

For example, if one grain of sand has a mass of 0.001 grams and the 50-ml beaker has a mass of 50 grams, the conversion factor would be 0.001 grams/grain of sand ÷ 50 grams = 0.00002 grains of sand/gram.

To determine the grains of sand in your 50-ml beaker, you can multiply the conversion factor by the mass of the beaker. In this case, 0.00002 grains of sand/gram x 50 grams = 0.001 grains of sand.

Therefore, there are 0.001 grains of sand in your 50-ml beaker.

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Determine if the following are True or False. If it is true, give a justification. If it's false, give an example showing why the statement is not always true.If v1,v2,v3,v4,v5 are in R5 and {v1,v2,v3,v4} is linearly dependent, then {v1,v2,v3,v4,v5} is also linearly dependent.If v1 and v2 are in R4 and v2 is not a scalar multiple of v1, then {v1,v2} is linearly independent.Must give justification/example for full points.\

Answers

{v1, v2, v3, v4, v5} is also linearly dependent. Therefore, the first statement is True. {v1, v2} is linearly independent. Therefore, the second statement is also True.

If {v1, v2, v3, v4} is linearly dependent, then there exists a non-zero scalar, say a1, a2, a3, and a4, such that a1v1 + a2v2 + a3v3 + a4v4 = 0. Now, if we add v5 to the set, we can simply take a5 = 0, and the equation a1v1 + a2v2 + a3v3 + a4v4 + a5v5 = 0 still holds. Therefore, {v1, v2, v3, v4, v5} is also linearly dependent.

For the second statement if v2 is not a scalar multiple of v1, then there are no scalars a1 and a2 such that a1v1 + a2v2 = 0, unless both a1 and a2 are zero. This means that {v1, v2} is linearly independent. A justification for this can be seen by considering the equation a1v1 + a2v2 = 0. If v2 is not a scalar multiple of v1, then the only solution to this equation is a1 = a2 = 0, which means that {v1, v2} is linearly independent.

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What do solar cells convert into electricity?
wind
water
sunlight
plants

Answers

Sunlight gives solar energy to solar panel to convert the sunlight into the electricity. Option C is correct.

What is solar cell?

A solar cell, is an electrical device that uses the photovoltaic effect, a physical and chemical phenomena, to convert light energy directly into electricity.

According to the Law of conservation of energy . Energy can not be created nor be destroyed, it can transfer from one to another form.

Sunlight gives solar energy to solar panel to convert the sunlight into the electricity.

Hence, option C is correct.

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One of the legs of a right triangle measures 1 cm and the other leg measures 7 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

Answers

Using the Pythagorean Theorem ( a^2 + b^2 = c^2, c is the length of the hypotenuse) and substituting values in, you get 1^2 + 7^2 = c^2. That can be simplified to the square root of 50 = c. The square root of 50 is not a whole number, so rounded to the nearest tenth it would be 7.1.

an event that increases the probability that a response will be repeated is called _____.

Answers

The term that describes an event that increases the likelihood of a response being repeated is known as reinforcement.

Reinforcement can be defined as any consequence that strengthens or increases the probability of a behavior occurring again in the future. This can include positive reinforcement, which involves adding a desirable consequence after a behavior, or negative reinforcement, which involves removing an aversive consequence after a behavior. Both types of reinforcement have been shown to be effective in increasing the likelihood of a behavior being repeated.

Overall, understanding the concept of reinforcement is essential in the field of psychology, particularly in the areas of behaviorism and behavior modification. By providing positive consequences after desired behaviors, individuals can be motivated to continue engaging in those behaviors, which can lead to long-term positive changes. Reinforcement can also be used to shape new behaviors or replace unwanted behaviors with more desirable ones.

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The demand function of blankets at COMESA is given by the equation P=60-2Q find the units of good Q ,when P=12 and use integration to calculate the consumer surplus

Answers

Answer:

a. 24

b. 864

Step-by-step explanation:

a. The demand function is:

P = 60 - 2Q

When P = 12:

12 = 60 - 2Q

2Q = 60 - 12

2Q = 48

Q = 48/2 = 24

b. Consumer surplus is given as the integral of Demand function:

\(CS = \int\limits {[P(Q) - (p)(Q)] \ dQ\\\)

This implies that:

\(CS = \int\limits {60 - 2Q} \, dQ\\\\CS = 60Q - Q^2\\\\CS = (60 * 24) - 24^2\\\\CS = 1440 - 576\\\\CS = 864\)

reverse percentage problem

Answers

answer: you're missing the problem

If a 12-foot-tall object casts a 9-foot shadow, how long a shadow would a 4-foot-tall object cast at the same time and place

Answers

Answer:

I think it is 3 feet

Step-by-step explanation:

12:9 is equal to 4:3

4:? should also be equal to 4:3, so ?=3

Hope this helps

let me know if it does and if it is right

is 19, and 40 a prime or composite number

Answers

Answer:

19 is a prime number. 40 is a composite number

Step-by-step explanation:

40 can be divided by number other than 1 and its self

19 can only be divided by 1 and itself

Answer:

19 is composition 40 is prime number

Convert -145 degrees to radians.

Answers

I got -2.53073 I don’t know if it’s right but I hope it helps

Answer:

\(\frac{-29}{36}\)π

Step-by-step explanation:

La edad de maria es el triple de la edad de juan. En 7 años mas la ssuma de sus edades sera de 46 años. La suma de las edades actuales de juan y maria es

Answers

Answer:

The sum  of the present age of Juan and Maria is 32 years.

Step-by-step explanation:

Maria's age is three times Juan's age. In 7 years the sum of their ages will be 46 years. The sum of the current ages of Juan and Maria is

Let the Juan's present age is p.

Maria's present age is 3 p.

After 7 years,

Juan's age = p + 7

Maria's age = 3 p + 7

According to the question

p + 7 + 3 p + 7 = 46

4 p + 14 = 46

4 p = 32

p = 8

So, the present age of Juan is 8 years and Maria is 24 years, the sum is 8 + 24 = 32.  

Tony planned to spend $100 for food this week. On Monday he spent $22 and on Thursday he spent $52. How much money dose he have left for the week

Answers

Answer:$26

Step-by-step explanation:

52+22=74

100-74=26

Tony has 26 dollars left.

Which type graph is the best choice for determining the change in the stock market over time?
a. Scatter Diagram
b. Time-series Plot
c. Box Plot
d. Pie Chart

Answers

Time-series Plot graph is the best choice for determining the change in the stock market over time.

The term stock exchange refers to several exchanges where shares of publicly traded companies are bought and sold. Such financial activities are conducted through formal stock exchanges and over-the-counter (OTC) markets that operate under a specific set of regulations.

Other major stock exchanges in the world are Tokyo Stock Exchange (Japan), Shanghai Stock Exchange (China) and London Stock Exchange (UK). Stock exchanges are considered capital markets as they provide long-term financing for companies.

A time series chart, also known as a time series chart or time series graph, is a data visualization tool that plots data points at successive time intervals. Each point on the chart corresponds to both time and quantity being measured.

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Given: p: 3x 7 = â€"5 q: 4x 12 = â€"4 which is the contrapositive of p → q? if 3x 7 = −5, then 4x 12 = â€"4. if 4x 12 = â€"4, then 3x 7 = −5. if 3x 7 ≠−5, then 4x 12 ≠â€"4. if 4x 12 ≠â€"4, then 3x 7 ≠−5.

Answers

The contrapositive of p → q is "if 3x + 7 ≠ -5, then 4x + 12 ≠ -4."

Given p: 3x + 7 = -5 and q: 4x + 12 = -4, the original implication is p → q.

As we know that the contrapositive of an implication statement flips the hypothesis and the conclusion of the original statement and negates them.

To find the contrapositive, we need to flip the hypothesis and conclusion and negate them.

The hypothesis of p is "3x + 7 = -5" and its negation is "3x + 7 ≠ -5."

The conclusion of q is "4x + 12 = -4" and its negation is "4x + 12 ≠ -4."

Therefore, the contrapositive of p → q is "if 3x + 7 ≠ -5, then 4x + 12 ≠ -4."

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The complete question is as follows:

Given: p: 3x + 7 = –5 q: 4x + 12 = –4

Which is the contrapositive of p → q?

Convert 6500 ounces to liters. We know There are 1.05 quarts in one liter

Answers

Answer:

192.22775 Liters

Step-by-step explanation:

Hector is flying a kite. He has let out 86 feet of string and is holding it 4 feet off the ground. If the string is at an angle of elevation of 42°15'30", how high is the kite?

Answers

Answer:

h = 61.83 feet

Step-by-step explanation:

length of string from Hector to kite = c = 86 feet.

and 4 feet off the ground.

angle A = 42° 15' 30"

req'd:  how high is the kite?

angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')

angle A = 42.26

to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp

Sin(A) = a / c

Sin(42.26) = a / 86

a = Sin(42.26) * 86

a = 57.83 feet

therefore, the height of the kite from the ground = h = 57.83 + 4

h = 61.83 feet

Hector is flying a kite. He has let out 86 feet of string and is holding it 4 feet off the ground. If

What is equivalent to 1/6

Answers

Answer:

0.16666...

6/36

2/12

3/18

4/24

5/30

There's a lot of things.

Please help asap thanks

Please help asap thanks

Answers

Shahs. Dickens icjcns a icjcns icjcns. Did d

£200 is invested for 10 years at 9 compound interest per annum

Answers

After 10 years at 9% compound interest per annum, The amount will be £393.57.

The amount of money you will have after 10 years can be calculated using the formula for compound interest:

\(A = P * (1 + r/n)^{nt}\)

where:

A is the final amount,

P is the initial amount (principal),

r is the interest rate as a decimal,

n is the number of times the interest is compounded per year,

t is the number of years the money is invested.

In this case:

P = £200

r = 9% = 0.09

n = 1 (because interest is compounded annually)

t = 10

So, plugging in the values, we get:

\(A = 200 * (1 + 0.09/1)^{1 * 10)} = 200 * (1.09)^{10}\)

\(A = 200 * 1.96787 = 393.57\)

So, after 10 years at 9% compound interest per annum, you will have £393.57.

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DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!

DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!

Answers

Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

Alexandra′s car can travel 85 miles on 5 gallons of fuel. How far can the car travle on 12 gallons of fuel? Responses​

Answers

204

You get 204 because first you divided 85 and 5 which equals 17.

Then you multiply 12 and 17 which equals 204.

I hope that this helps! :)

Answer:

204 miles

Step-by-step explanation:

So first we have to divide 85 by 5 which we get 17 then we multiply 17 by 12 which is 204. I hope this help but sorry I'm not that good at explaining thing

Each bag of trail mix weighs 3/8 pound. The combined weight of a set of bags is 3 3/4 pounds How many bags are there?

Answers

Answer:

10

Step-by-step explanation:

3/ 8 is 0.375 while 15/4 is 3.75

so I divide 3.75 by 0.375 which is now 10 the answer is 10 bags

Answer:

22

Step-by-step explanation:

(33/4)÷(3/8)

=8.25/.375

=22

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