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The two Consecutive number is 16 and 17.

What is consecutive number?

Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference. The mean and median of a sequence of numbers are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.

Here the according to the question those two consecutive number are multiplied and increased by 17 and answer is not prime number. Now,

=> 1× 2+17 = 2+17 = 19(prime number)

=> 2×3+17=6+17=23(prime number)

=> 3×4 +17 = 12+17 = 29(prime number)

=> 4×5+17 = 20+17 = 37(prime number)

=> 5×6+17 = 30+17 = 47(Prime number)

=> 6×7+17 = 42+17 = 59(prime number)

=> 7×8+17 = 56+17 = 73(prime number)

=> 8×9+17 =72+17 = 89(prime number)

=> 9×10+17 = 90+17= 107(prime number)

=> 10×11+17=110+17 = 127(prime number)

=> 11×12+17=132+17 =149(prime number)

=> 12×13+17=156+17 = 173(prime number)

=> 13×14+17=182+17 = 199(prime number)

=> 14×15+17=210+17 = 227(prime number)

=> 15×16+17 = 240+17=257 (prime number)

=> 16×17+ 17= 272+17 = 289( not prime number)

Hence the two consecutive number is 16 and 17.

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Answer:

For 35 its C

Step-by-step explanation:

1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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Answer:

9/1 x 3/1

Step-by-step explanation:

Answer:

57.9

Step-by-step explanation:

11/19×100=57.894 to one decimal place =57.9

Answer:

b < 3

Step-by-step explanation:

3 ( b - 5 ) < - 2b

3 ( b ) - 3 ( 5 ) < - 2b

3b - 15 < - 2b

3b + 2b < 15

5b < 15

b < 15/5

b < 3

Answer:(f/g)(x)=(1+2x)/(1-3x) where x<>0

Step-by-step explanation:

f(x)= 1/x+2= (1+2x)/x  ,   x<>0

g(x)=1/x-3=(1-3x)/x    , x<>0

=>f(x)/g(x)= (1+2x)/(1-3x)    ,  x<>0

Answer:

Step-by-step explanation:

No figure supplied, so lots of assumptions needed.

Assume side length of triangle is 4 cm.  

( If = 4 cm  means ??)

Assume ABC is equiangular, all three angles are 60 degrees.

(This is a cross-sectional view, but don't see any)

Side length = 4

altitude of triangle = 4 sin(60) = 2sqrt(3)

radius of circumscribed circle of equilateral triangle

R = (2/3) altitude

= (2/3)*2sqrt(3)

= (4/3)sqrt(3)

Diameter

D = 2R

= (8/3) sqrt(3)

Answer: 8 cm

Step-by-step explanation:

The figure in the image attached below shows that there are two specific angles that are congruent to each other, angles AD and CD.

We are given the length of one of these angles:

AD= 4 cm so we must multiply 4 by 2, since there are TWO angles measuring 4 cm.

4 cm x 2 angles (AD and CD) =8 cm.

Proof of answer is shown below!

The solution to the triangle is: a ≈ 22.4, b = 4 , c ≈ 77.2 ,A = 27° ,B ≈ 42.5°

C ≈ 110.5°  we got the answer by using law of sine

what is  law of sine?

The Law of Sines, also known as the Sine Rule, is a mathematical formula used in trigonometry to relate the sides and angles of a non-right-angled triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

In the given question,

Using the law of sines and the fact that the angles of a triangle sum up to 180 degrees, we can solve for the missing parts of the triangle:

sin(A)/a = sin(B)/b = sin(C)/c

sin(27)/a = sin(B)/42 = sin(C)/72

We can use the first equation to solve for a:

a = b(sin(A)/sin(B)) = 42(sin(27)/sin(B)) ≈ 22.4161

Next, we can use the second equation to solve for sin(B):

sin(B) = b(sin(A)/a) = 42(sin(27)/a) ≈ 0.6822

Taking the inverse sine, we find that B ≈ 42.4827 degrees.

Now we can use the fact that the angles of a triangle sum up to 180 degrees to solve for C:

C = 180 - A - B ≈ 110.5173 degrees.

Finally, we can use the law of sines again to solve for the remaining side, c:

c = a(sin(C)/sin(A)) = 22.4161(sin(110.5173)/sin(27)) ≈ 77.2352

Therefore, the solution to the triangle is:

a ≈ 22.4

b = 42

c ≈ 77.2

A = 27°

B ≈ 42.5°

C ≈ 110.5°

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The simultaneous equations 2x + y = 6 and x + y/2 = 3 are dependent because both equations are the same and they have an infinite number of solutions that satisfy both equations.

A system of simultaneous equations is called dependent if it has infinitely many solutions. In other words, one equation in the system can be obtained by adding or subtracting multiples of the other equation(s), or if all the equations represent the same line or plane in higher dimension.

We can write the equations as:

2x + y = 6...(1)

x + y/2 = 3...(2)

equation (2) can be rewritten as follows:

(2x + y)/2 = 3 {simplifying the left hand side to a single denominator}

2x + y = 2 × 3 {cross multiplication}

2x + y = 6

We can observe that equations (1) and (2) are the same. Any value of x and y that satisfies the equation 2x + y = 6 will also satisfy the second equation, x + y/2 = 3.

In conclusion, the simultaneous equations 2x + y = 6 and x + y/2 = 3 are dependent because both equations are the same, hence they have an infinite number of solutions that satisfy both equations.

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The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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Answer:

Step-by-step explanation:To find the outer measure of B, denoted as µ*(B), we need to take the infimum of the sums of the lengths of the intervals that cover B.

We start by considering a cover of B by intervals. Since B is a set of four points, we can construct a cover of B with four intervals, each containing one of the points. Specifically, we define:

I1 = (8 - ε, 8 + ε)

I2 = (145 - ε, 145 + ε)

I3 = (287 - ε, 287 + ε)

I4 = (7005 - ε, 7005 + ε)

where ε is a small positive number.

Then, the lengths of these intervals are:

|I1| = 2ε

|I2| = 2ε

|I3| = 2ε

|I4| = 2ε

The sum of the lengths of these intervals is:

|I1| + |I2| + |I3| + |I4| = 8ε

Since ε can be made arbitrarily small, we can take the infimum of the sum of the lengths of the intervals over all covers of B by intervals. Therefore, we have:

µ*(B) = inf{|I1| + |I2| + |I3| + |I4|} = inf{8ε} = 0

Hence, the outer measure of B is 0.

Answer:

They dig 42.5 meters in 5 hours

Step-by-step explanation:

The following information was given:

Time (hours)        Distance (meters)

1                             8.5

2                            17

3                            25.5

4                            34

5                            x

Finding x when the rate of meters per hour remains the same

Let us first find the rate in meters per hour

rate = change in distance ÷ change in time

Between 1 and 2 hours

\(rate = \frac{d_2 - d_1}{t_2 - t_1} \\where:\\d_2 = 17 m\\d_1 = 8.5m\\t_2 = 2\ hours\\t_1 = 1\ hour\\\therefore\ rate = \frac{17 - 8.5}{2-1} \\rate =\frac{8.5}{1} \\rate = 8.5\ m/hr\)

This means that for every additional 1 hour, 8.5 meters is dug

Finding the meters dug in 5 hours

4 hours = 34 meters

4 hours to 5 hours = 1 hour

for every additional 1 hour, 8.5 meters are dug

∴ 4 hours to 5 hours = 34 + 8.5

4 hours to 5 hours = 42.5 meters

Answer:

it's A

Step-by-step explanation:

if you go to the fair they also tell you the price for one ticket then you have to add all that up to see how much money you need for that much people that you bring so it would make more since

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

the function y=5x+5

plug in the hours 4.5 for x

y=5(4.5)+5

=27.5kilometers

Answer:

in fraction form is 6/20 in decimal form its 0.3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

(-6 - 4) ÷ -5 = 2

9514 1404 393

Answer:

  g(x) = 4x -2

Step-by-step explanation:

The translation of f(x) up by k units is accomplished by adding k to each function value:

  g(x) = f(x) +k

For your function, translation up 3 units gives the function ...

  g(x) = f(x) +3 = 4x -5 +3

  g(x) = 4x -2

Answer:

Step-by-step explanation:

no.

The probability that Belle will select two hearts is 2/15.

To find the probability of Belle selecting two hearts, we need to calculate the probability of selecting a heart on the first draw and then, given that the first card was a heart, the probability of selecting another heart on the second draw.

Total number of cards = 3 (star cards) + 4 (hearts cards) + 3 (spade cards) = 10 cards

Probability of selecting a heart on the first draw = 4 (hearts cards) / 10 (total cards) = 2/5

After selecting a heart on the first draw, there will be 9 cards remaining, with 3 hearts cards left.

Probability of selecting a heart on the second draw, given that the first card was a heart = 3 (hearts cards) / 9 (remaining cards) = 1/3

To find the probability of both events happening (selecting two hearts), we multiply the probabilities:

Probability of selecting two hearts = (2/5) x (1/3) = 2/15

Therefore, the probability that Belle will select two hearts is 2/15.

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Once a die has the numbers 1,2,3,4,5 and 6, it means the numbers that are less than 3 are just the numbers 1 and 2. Now the probability can be built as follows:

As we can see above, once there are just two possibilities of numbers that are less than 3, the probability that the number rolled is less than 3 is equal to 2/6.

Answer:

44 minutes

Step-by-step explanation:

It takes him 4 minutes to read one page, so you multiple 4 by 11 and get the amount of time it takes him to read 11 pages

Answer:

takes 44 minutes to read 11 pages

Step-by-step explanation:

We know that

Solving for x,

x is aproximately 33.56

Answer:

Step-by-step explanation:

Solution by substitution method

3x+5y=7

and 4x-y=5

Suppose,

3x+5y=7→(1)

and 4x-y=5→(2)

Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

→(4)

Now, Putting x=32/23

in equation (3), we get

y=4x-5

⇒y=4(32/23)-5

⇒y=(128-115)/23

⇒y=13/23

∴y=13/23   and x=32/23

Answer:

all real numbers

only the range value is with a minimum of -1 and a maximum of 1 unless there's a vertical shift.

The domain of the sine and cosine functions are all real numbers

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the domain of the function be represented as D

Now , the functions are

f ( x ) = sin x

g ( x ) = cos x

where the trigonometric functions have the range as [ -1 , 1 ]

And , sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle

Therefore , the value of D is all real numbers

Hence , the domain is all real numbers

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Answer:

(5y)x

Step-by-step explanation:

the commutative law of multiplication=ab=ba, a(bc)=c(ab)

(5x)y=(5y)x=5(xy)