what is a prime number

Answers

Answer 1

A number that can be divided exactly only by itself and 1.

For Eg:- 7, 10, 13.

Answer 2

Answer:

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic:


Related Questions

Which of the following statements is false?
a. A feasible solution satisfies all constraints.
b. In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.
c. It is possible to have exactly two optimal solutions to a linear programming problem.
d. An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Answers

Answer:

d. An optimal solution to linear programming problem can be found at an extreme point of the feasible region for the problem.

Step-by-step explanation:

A feasible solution satisfies all the constraints of the problem in linear programming. The constraints are the restrictions on decision variable. They limit the value of decision variable in linear programming. Optimal solutions occur when there is feasible problem in the programming.

What is the value of (-4)-3?

Answers

Answer:

Step-by-step explanation:

This is a bit ambiguous. I will answer it as (-4) - 3 = - 4 - 3 = - 7

However it could be (-4)(-3) = 12

Moral, with this editor use brackets.

Need help please! what is the total length of a 20 mm steel coiled like a spring with a 16 turns and an outer diameter of 600 mm. pitch is 300 mm. Show your solution please coz i don't really know how to do it! thanks

Answers

Answer:

L = 29,550 mm

Step-by-step explanation:

i think i've done this before.. but anyway Lets make it simple and easy.

Let A = 600mm

Let B = 300mm

Let C = 16 as number turns

Let d = 20mm

L = sqrt ((3.14 * (600 - 20))² + 300³)    * 16

L = 29,550 mm

What is the square root of -1

Answers

Answer:

the awnser is sqrt(-1) = i

One of two small classrooms is chosen at random with equally likely probability, and then a student is chosen at random from the chosen classroom. Classroom #1 has 5 boys and 11 girls. Classroom #2 has 15 boys and 9 girls. What is the probability that Classroom #2 was chosen at random, given that a girl was chosen? Your answers should be rounded to 4 digits after the decimal.

Answers

Answer:

0.1875

Step-by-step explanation:

Let A be the event that  class two has been chosen . So the probability of A would be P (A) = 1/2= 0.5

Now class two has 9 girls out of total 24 students . So the probability of chosing the girl would be= P (B=) 9/24= 0.375

So the probability that Classroom #2 was chosen at random, given that a girl was chosen is given by = P(A) . P(B)= 0.5 * 0.375= 0.1875

Another way of finding the probability that Classroom #2 was chosen at random, given that a girl was chosen is by drawing a tree diagram.

P (1/2) Class 1 ------------------------5 boys

                      -------------------------11 girls  (11/16)

P (1/2)  Class 2 -------------------------15 boys

                     -----------------------9 girls  P (9/24)   Class 2 was chosen (0.5) *9/24

the angle theta is in the second quadrant and cos theta = -2/√29 determine possible coordinates for point P on the terminal arm of theta a. (2,5) b. (-2,√29) c. (-5,2) d. (-2,5)

Answers

[tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex] and $\theta$ lies in $2^{\text{th}}$ quadrant.

where, $x-$ coordinate is negative, and $y-$ coordinate is positive

so it can't a.

now, cosine means, side adjacent over the hypotenuse, in Cartesian plane, that will be $x-$ coordinate over the distance from origin.

Assume the triangle , with base $2$ units and hypotenuse $\sqrt{29}$ and it's in second quadrant. (so [tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex])

now, the leftmost point on $x-$ axis is , obviously $(-2,0)$

and by Pythagoras theorem, we can find the perpendicular side, that will be $y^2=(\sqrt{29})^2-(2)^2\implies y=5$

so the coordinates of the upper vertex is $(-2,5)$, each point lying on this "ray" should have equal ratio of respective coordinates. i.e. $\frac25=\left|\frac xy\right| $

and it should lie on second quadrant, so $x<0 \, y>0$

Option d satisfies this.

Calculate, correct to one decimal plice
the acute angle between the lines
3x - 4y + 5 = 0 and 2x + 3y -1 = 0
A. 70.69
B. 50.2
C. 39.8
D. 19.4​

Answers

Answer:

A. 70.69 is the correct answer.

Step-by-step explanation:

Given:

Two lines:

[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]

To find:

Angle between the two lines = ?

Solution:

Acute Angle between two lines can be found by using the below formula:

[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]

Where [tex]\theta[/tex] is the acute angle between two lines.

[tex]m_1, m_2[/tex] are the slopes of two lines.

Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:

[tex]m = -\dfrac{a}{b }[/tex]

So,

[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]

[tex]m_2 = -\dfrac{2}{ 3}[/tex]

Putting the values in the formula:

[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]

So, correct answer is A. 70.69

If the half-life of cesium-137 is 30 years, find the decay constant, r. (Round your answer to nine decimal places.)

Answers

Answer:

r = 0.023104906

Step-by-step explanation:

Given half life = T = 30 yrs.

Decay constant = r.

Using the decay constant formula:

[tex]r=\frac{\ln2}{T}\\r=\frac{\ln2}{30}\\r=0.023104906[/tex]

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What does "C" represent and how do you evaluate this?

Answers

It represents 'combinations'.

It means that you have 9 items, and you want to count the combinations of 7 items.

The answer is:
9! / ((9-7)! * (7!))
= 9! / (2! * 7!)
= 9*8/2
= 36

[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]

Janet has 12 more cookies than Cody. If Janet has 60 cookies, write and solve to determine the number of cookies Cody has.

Answers

Answer: 48

Step-by-step explanation: 60-12=48

Cody has 48 cookies. In order to figure out how many cookies Cody has you have to subtract 12 from 60 or 60 - 12

Anita works a part-time job where she makes $9.45 per hour. Anita's gross pay for the current pay period is $238.61. Her deductions include $28.63 for federal taxes, Latex: \$14.79 for Social Security, $3.46 for Medicare, and $10.14 for state taxes.

Answers

Answer:

1. 181.59 is her net pay and she worked 25.25 hours.

Step-by-step explanation:

A store has clearance items that have been marked down about 30%. They are having a sale, advertising an additional 55% off clearance items. What percent of the original price do you end up paying

Answers

Answer:

60% discount given in total, so only 40% is paid.

Step-by-step explanation:

1/9, -0.1, -2/12 in order

Answers

Answer:

-2/12, -0.1, 1/9

Step-by-step explanation:

Answer:

Least to greatest: -2/12 , -0.1 , 1/9

Greatest to least: 1/9, -0.1, -2/12

Step-by-step explanation:

Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.

Divide:

1/9 = ~0.111 (rounded)

-0.1 = -0.1

-2/12 = - ~0.167 (rounded)

Put the numbers in number order:

-~0.167 , -0.1 , ~0.111

-2/12 , -0.1 , 1/9

~

What faction of a day is 5hrs 20 mine​

Answers

Answer:

16/3 hours  5 1/3

Step-by-step explanation:

Answer: 5 1/3

Step-by-step explanation:

Given the diagram below, where and mDE = 105^ and mGE = 125^ Find m

a. 65
b. 62.5
c. 55
d. 52.5

Answers

*Complete Question:

Given the diagram below, where and mDE = 105^ and mGE = 125^ Find m<DEG

Answer:

m<DEG = 65°

Step-by-step explanation:

Angle DEG is an inscribed angle that intercepts the DG. Based on the theorem of inscribed angles, angle DEG = ½ of the measure of arc DG.

To find the measure of angle DEG, find the measure of arc DG first.

Measure of arc DG = 360° - (105° + 125°) => a full circle measures 369°

Arc DG = 360° - 230 = 130°.

m<DEG = ½ of 130° = ½*130° = 65°

Which of the following is NOT a requirement of testing a claim about two population means when 1 and 2 are unknown and not assumed to be​ equal? Choose the correct answer below. A. The two samples are dependent. B. Both samples are simple random samples. C. Either the two sample sizes are large ​(30 and ​30) or both samples come from populations having normal​ distributions, or both of these conditions are satisfied. D. The two samples are independent.

Answers

Answer:

b

Step-by-step explanation:

Which table has a constant of proportionality between 7 and x of 1/4? Choices are in the image

Answers

Answer:

A. has a constant proportion of 1/4.

The x-intercept of the line y = 4x - 16 is the point (_,0)

Answers

Answer:

the point is (4,0)

Step-by-step explanation:

The x-intercept is the point on the x-axis where y=0.

Set y=0

0=4x-16

16=4x

x=4, y=0

So the notation for the point is (4,0).

Good luck!

Answer:

(4, 0)

Step-by-step explanation:

4x - 16 = 0

4x = 16

x = 4

What is 5/6 divided by 4

Answers

Answer:

[tex]\frac{5}{24}[/tex]

Step-by-step explanation:

If we have the division statement [tex]\frac{5}{6} \div \frac{4}{1}[/tex], we can multiply by the reciprocal and find the quotient.

[tex]\frac{5}{6} \cdot \frac{1}{4} = \frac{5}{24}[/tex].

Hope this helped!

Answer:

5/24

Step-by-step explanation:

Because the 5 is being divided by both the 6 and the 4, you just multiply these two and get 24. So it is 5 over 24.

if P(x)=1+6x-5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?

Answers

Answer:

600

Step-by-step explanation:

[tex]p(x) = 1 + 6x - 5x^2[/tex]

x max = [tex]-b/2a[/tex]

a = -5

b = 6

-6/2(-5) = 6/10 = 3/5 = .6

.6 thousand = 600

600 speakers should be sold.

Alternatively, you can check the vertex of the parabola formed.

Question 36 of 40
The distance of a line bound by two points is defined as
L?
O A. a line segment
B. a ray
O
c. a plane
O D. a vertex
SUBMI​

Answers

Answer:

A. a line segment

Step-by-step explanation:

a ray is directing in one dxn, and has no end pointa plane is a closed, so more than 2 points a vertex is a single point itself

Calculate how much 10% acid solution and how much pure acid must be mixed to end up with exactly 12 liters of 30% acid solution. Rounding to the nearest hundredth of a liter, you'll need ___ liters of the pure acid.

Answers

Answer:

  2.67 liters

Step-by-step explanation:

Let "a" represent the number of liters of pure acid needed to make the desired solution. Then the amount of acid in the mix is ...

  (100%)x +(10%)(12 -x) = (30%)(12)

  (90%)x = 12(20%) . . . . . subtract (10%)(12)

  x = 12(2/9) . . . . . divide by 90%

  x = 2 2/3 . . . liters

You'll need 2.67 liters of the pure acid.

Lee watches TV for 4 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?

Answers

Answer: Please Give me Brainliest, Thank You!

21.6$/month

Step-by-step explanation:

4*150=600watts = 0.6kW

12cents = 0.12$

0.12$*0.6=0.72$

0.72$ * 30days = 21.6$/month

The amount of the electricity cost for 30 days will be 2.16 dollars per month.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Lee watches TV for 4 hours per day.

During that time, the TV consumes 150 watts per hour.

The amount of electricity used in a day will be

⇒ 4 × 150

⇒ 600 watts per day

⇒ 0.60 kilowatts per day

Electricity costs (12 cents)/(1 kilowatt-hour). Then the amount of electricity cost in a day will be

⇒ 0.60 × 12 cents

⇒ 0.60 × 0.12 dollars

⇒ 0.072 dollars per day

Then the amount of the electricity cost for 30 days will be

⇒ 0.072 × 30

⇒ 2.16 dollars per month

The amount of the electricity cost for 30 days will be 2.16 dollars per month.

More about the Algebra link is given below.

https://brainly.com/question/953809

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A manufacturer knows that their items have a lengths that are skewed right, with a mean of 5.1 inches, and standard deviation of 1.1 inches. If 49 items are chosen at random, what is the probability that their mean length is greater than 4.8 inches? How do you answer this with the answer rounded 4 decimal places?

Answers

Answer:

0.9719

Step-by-step explanation:

Find the mean and standard deviation of the sampling distribution.

μ = 5.1

σ = 1.1 / √49 = 0.157

Find the z score.

z = (x − μ) / σ

z = (4.8 − 5.1) / 0.157

z = -1.909

Use a calculator to find the probability.

P(Z > -1.909)

= 1 − P(Z < -1.909)

= 1 − 0.0281

= 0.9719

The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

What is Probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

What is Standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.

What is Mean?

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given,

Mean = 5.1 inches

Standard deviation = 1.1 inches

Sample size = 49

New mean = 4.8

Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])

Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]

Z score = -1.909

Then the probability

P(Z>-1.909)

=1-P(Z>-1.909)

=1-0.0281

=0.9719

Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

Learn more about Probability, Standard deviation and Mean here

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‍The length of a jogging trail is 3528 m. A jogger wants to complete the trail within 30 min. How many meters must the jogger travel each minute? 1174/15 m 1173/10 m 1171/3 m 1173/5 m

Answers

Step-by-step explanation:

3528 ÷ 30 = 117.6

He should travel 117.6 m in one minute

Choose the point-slope form of the equation of
this line.
Oy - 8 = -5(x - 3)
Oy - 8 = -5(x + 3)
Oy + 8 = -5(x - 3)
O y + 8 = -5(x + 3)

Answers

Answer: C

Step-by-step explanation:

What number represents the same amount as 8 hundreds + 10 tens + 0 ones? i was told 810 is incorrect

Answers

Answer:

900

Step-by-step explanation:

You have 10 tens not 1 ten

8 * 100 + 10 * 10 + 0*1

800 + 100 + 0

900

Answer:

[tex]900[/tex]

Step-by-step explanation:

[tex]8 \times 100 + 10 \times 10 + 0 \times 1 \\ 800 + 100 + 0 \\ = 900[/tex]

y - 4= -2(x + 3)

Complete the missing value in
the solution to the equation.

(-3, _ )

Answers

Answer:

4

Step-by-step explanation:

i distributed the -2 to what's in the parentheses. that equal 0. I then moved the 4 to the zero so that it becomes positive. I just assumed that you were ask for Y

Step-by-step explanation:

y-4=-2(x+3)....eq(1)

y- 4= -2x-6

y=-2x-2...eq(2)

subtituting equation 2 in equation 1

(-2x-2)-4=-2x-6

-2x-6=-2x-6

=0

A salon and spa chain periodically analyzes its service times to check for variation in service processes using x-bar and R charts. Daily random samples, each containing service times observed with eight different customers are collected. The average mean and the average range of the service times for the past week were 27.2 and 3.76 minutes, respectively. The value of D4 for a sample size of eight is 1.864. What is the upper control limit (UCL) for the R-chart

Answers

Answer:

7.00864

Step-by-step explanation:

The upper control limit for R -chart can be computed by using following formula

UCL=Rbar*D4.

We are given that average range R bar is

Rbar=3.76.

The value of D4 for n=8 is also given that is

D4=1.864.

Thus, the required computed upper control limit is

UCL=3.76*1.864=7.00864.

F(x)=2x+6,g(x)=4x^2 find (f+g)(x)

Answers

Answer:  4x^2+2x+6

Work Shown:

(f+g)(x) = f(x) + g(x)

(f+g)(x) = 2x+6 + 4x^2

(f+g)(x) = 4x^2+2x+6

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