Three divers kept track of the number of crabs they've seen this year.
Diver Crabs observed Dives
Scuba Sam 33 11
Wet Suit Willy 81 18
Deep Diving Dan 104 26
Which diver saw the most crabs per dive?
Choose 1 answer:

The four Quantities are a1 , r, n , [tex]S_{n}[/tex]

What is a Series:

A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.

Arithmetic progression

     an = a1 + ( n-1) d

     a1 is the first term

    d =common difference

    an is the nth term

   an can be found out if we know the a1 , d and n

b)  Arithmetic progression

         a1 is the first term

        an is the nth term

        sn is the sum of the n terms of the series

        Sn = n/2 ( a1 + an)

       we can calculate sn if we know a1 , an and n

c)Geometric progression

  an = a1rn-1

a1 is the first term

an is the nth term

r is the common ratio

we can calculate an if we know a1 , r and n

d)Geometric progression

  Sn = a1( 1- rn) / 1 - r

 a1 is the first term

r is the common ratio

sn is the sum of the n terms of the series

If we know a1 , r and n we can calculate [tex]S_{n}[/tex].

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By solving a linear equation we can see that:

Here we have two consecutive even integers, we can write these as x and x + 2

We know that half of the smaller of the two is equal to 2 more than the larger one, this can be writen as:

x/2 = (x + 2) + 2

Now we can solve that linear equation for x:

x/2 = x + 2 + 2

x/2 = x + 4

-4 = x - x/2

-4 = x/2

-4*2  = x = -8

The smaller number is -8

The larger number is -8 + 2 = -6

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Answer:

384, 576

Step-by-step explanation:

The surface area is

[tex]2(12 \cdot 6+12 \cdot 6+6\cdot 8)=384[/tex]

The volume is

[tex](12)(8)(6)=576[/tex]

The given sequence is not geometric.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: [tex]\frac{1}{2}, \frac{1}{4},\frac{1}{6},\frac{1}{8},...[/tex]

Here, [tex]\frac{\frac{1}{4}}{\frac{1}{2}}\neq \frac{\frac{1}{6}}{\frac{1}{4}}\neq \frac{\frac{1}{8}}{\frac{1}{6}}[/tex]

That is, the given sequence doesn't follow the only required condition for a sequence to be geometric.

Hence, The given sequence is not geometric.

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Answer:

If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.

Step-by-step explanation:

Answer: 6 and 27

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x+8= 4(x+2) and that should be the answer if not then i don't know what to do

Answer:

n – p

x= –––––

m

Hope that helps! Have a good day :)

The approximate circumference of the safety circle is 5026.54825 meters.

To find the circumference:

So,

Therefore, the approximate circumference of the safety circle is 5026.54825 meters.

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The expression can be simplified as follows:

a. (-4)(-2) -6(2 - 5) = 26

b. 12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = 43

c. 23 - (17 - 3.4)² +  6 = -155.96

The expressions can be solved using PEMDAS rule,

P = Parenthesis

E = Exponential

M = Multiplication

D = division

A = addition

S = Subtraction

Hence,

a.

(-4)(-2) -6(2 - 5) = (-4)(-2) - 6(-3) = 8 + 18 = 26

b.

12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = -5.8 + 15 + 6.3 - 1 + 28.5 = 9.2 + 6.3 - 1 + 28.5 = 15.5 - 1 + 28.5 = 14.5 + 28.5 = 43

c.

23 - (17 - 3.4)² +  6 = 23 - (13.6)² + 6 = 23 - 184.96 + 6 = -161.96 + 6 = -155.96

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Answer:

Statement is true

Step-by-step explanation:

  3m

----------  >  3;  m = 8

    6

  3(8)

----------  >  3

    6

  24

----------  >  3

    6

24 ÷ 6 = 4

4 > 3

or

  3m

----------  >  3;  m = 8

    6

  3m

----------  >  3 (6)

    6 (6)

3m > 18

÷3     ÷3

m > 6

8 > 6

Either way, the statement is true. I have no idea why it would be no. I'm sorry if I wasn't of any help.

The 8th term of the sequence 310 is closest to the term 300.

An arithmetic progression is a series of numbers that have a set common difference in between two consecutive numbers (A.P.).

Each term in an arithmetic sequence increases or decreases by adding or subtracting a constant term.

a = 30 for the first term

d = 40, common difference

We solve in what term is closest to 300 in this manner;

300 / 40 = 7.5

Thus, find the 7th and 8th term.

7th is solved by verifying for;

a₇ = a + ( n - 1 ) d

a₇ = 30 + ( 7 - 1 ) 40

a₇ = 30 + 240

a₇ = 270

The 8th term to certify the closest;

a₈ = T7 + d

a₈ = T7 + 40

a₈ = 270 + 40

a₈ = 310

As a result, the 8th term is the closest, with a value of 310.

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The complete question is-

The numbers in this sequence increase by 40 each time 30, 70, 110,The sequence is continued with the same rule. Which number in the sequence will be closest to 300?

The given infinite geometric series 150+30+6+ . . . is convergent and the sum is 187.5

The given geometric series is:

  150 + 30 + 6 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 150

a(2) = 30

a(3) = 6

Hence, the common ratio is

   r = a(2) / a(1) = 30/150 = 1/5

An infinite geometric series is convergent if 0 < | r | < 1.

Since r = 1/5, then the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 150 and r = 1/5 into the formula:

S = 150 / (1 - 1/5)

   = 150 / (4/5)

   =  187.5

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Answer:

4x + 7

Step-by-step explanation:

8x + 9 - 4x - 2 ← collect like terms

= (8x - 4x) + (9 - 2)

= 4x + 7

Answer:

32,14 minutes

Step-by-step explanation:

5.6 calories per hour = 5.6 x 60 = 336 calories per hour
So in 1 hour, that person will lose 336 calories

To lose only 180 calories time he should walk = 180/336 hour = 180/336 x 60 = 32,14 minutes

We can figure out our answer is in the ballpark by noting that 336/2 = 168

So to lose 168 calories, the person should walk for 1/2 hour so since 180 is slightly greater than 168, the person should walk for slightly more than half-hour

Answer:

x = 134°

Step-by-step explanation:

The angle labelled [tex]x^{\circ}[/tex] and the 46° add up to 180° as they are co-interior angles.

∴ [tex]x^{\circ} + 46^{\circ} = 180^{\circ}[/tex]

⇒ [tex]x^{\circ} = 180^{\circ} - 46^{\circ}[/tex]            [Subtracting 46° from both sides]

⇒ [tex]x = 134^{\circ}[/tex]

Therefore [tex]x[/tex] is equal to 134°.

Answer:

7 degrees

Step-by-step explanation:

Start with the temperature of -7 deg at 6:00 a.m.

The temperature increases 14 degrees in the next 6 hours.

6 hours after 6:00 a.m. is noon.

We are asked the temperature at noon.

At noon, the temperature is 14 degrees higher than -7 deg.

We add the increase, 14 deg, to the starting temperature, -7 deg.

-7 deg + 14 deg = 7 deg

Answer: 7 degrees

Two isosceles triangles are not necessarily similar triangles.

Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.

Analyzing each statements:

F. two right triangles with one angle measuring 30°

- these two triangles have angles measuring 90°, 30°, and 60°

- they both have equal angle measurements

∴ they are similar triangles

G. two right triangles with one angle measuring 45°

- these two triangles have angles measuring 90°, 45°, and 45°

- they both have equal angle measurements

∴ they are similar triangles

H. two isosceles triangles

- isosceles triangles are triangles that have two sides of equal lengths

- two isosceles triangles are similar if the angle of one is congruent to the corresponding angle of the other

∴ they are not necessarily similar, unless stated that their corresponding angles are equal

J. two equilateral triangles

- all equilateral triangles of any side lengths are considered similar triangles as each of its corresponding sides are proportional

∴ they are similar triangles

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Area of base:

3 * 9 = 27

So, 243 is the answer.

The slope of the line containing (-6,-11) and (-12,-10) is  (-1/6).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -10 , [tex]y_{1}[/tex] = -11 , [tex]x_{2}[/tex] = -12 , and [tex]x_{1}[/tex] = -6 .

On substituting the values of variables in equation1, we will get

m = ( (-10)-(-11) ) / ( (-12)-(-6) ) = (1/(-6)) = (-1/6).

As the slope of a line is (-1/6), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (-6,-11) and (-12,-10) is  (-1/6).

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=======================================================

Explanation:

Use the slope formula to find the slope of the line through A(-6,-1) and B(-5,2)

[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-5,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - (-1)}{-5 - (-6)}\\\\m = \frac{2 + 1}{-5 + 6}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]

The slope of segment AB is 3.

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

Repeat these set of steps for segment CD

C = (-1,-5)

D = (0,-2)

[tex](x_1,y_1) = (-1,-5) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-5)}{0 - (-1)}\\\\m = \frac{-2 + 5}{0 + 1}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]

The slope of segment CD is also 3

Parallel lines have equal slopes, but different y intercepts.

Since AB and CD have the same slope of 3, this shows AB is parallel to CD.

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

Now find the slope of segment BD

B = (-5,2)

D = (0,-2)

[tex](x_1,y_1) = (-5,2) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 2}{0 - (-5)}\\\\m = \frac{-2 - 2}{0 + 5}\\\\m = -\frac{4}{5}\\\\[/tex]

Segment BD has a slope of -4/5

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

Lastly, compute the slope of segment AC

A = (-6,-1)

C = (-1,-5)

[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-1,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - (-1)}{-1 - (-6)}\\\\m = \frac{-5 + 1}{-1 + 6}\\\\m = -\frac{4}{5}\\\\[/tex]

Segment AC has a slope of -4/5

Both segments BD and AC have the same slope of -4/5.

Therefore, segments BD and AC are parallel

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

We have two pairs of opposite parallel sides. Ultimately figure ABDC is a parallelogram

See the diagram below.  

Algebraic expression (C) p - 125 represents the reduced price.

So, if p is the mountain bike's original price.

Therefore, algebraic expression (C) p - 125 represents the reduced price.

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Answer:

add the like terms if there's no like the answer will be 3x+2y-3z=-1

The required number that is guessed  is 2x - 8 where inequality  2 < x < 6.

Given that,
Osslyn is thinking of a number, n.
Her first clue is that eight less than two times her number is between two and six (inclusive).
To write a compound inequality that shows the range of numbers that Josslyn might be thinking of.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number be x,
According to the question,
Gusset number = 2x - 8,   where x is between 2 and 8 implies
2 < x < 6

Thus, the required number that is guessed  is 2x - 8 where inequality  2 < x < 6.

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Answer:

y = 4x - 4

Step-by-step explanation:

Slope intercept follows the form y = mx + b

m represents the slope

b represents the y intercept

To find the slope of a table you can find the constant change in y over the constant change in x. The y values 0, 4, 8, 12 are increasing by 4 every point meaning the change in y is 4. The x values 1, 2, 3, 4 are increasing by 1 every point meaning the change in x is 1. Making the slope 4/1 or just 4.

Now use what you know: y = 4x + b to find b, we can use any of the coordinate points to substitute. I'm going to use point (1,0) where 1 is the x value and 0 is the y value.

y = 4x + b

0 = 4(1) + b

Solve for b

b = -4

:)

Super Gym employees sold 8,823 gym memberships this year, 70% more than the 5,190 gym memberships last year.

In mathematics, a percentage, usually denoted by %, is a number or ratio that represents a fraction of 100.

If the problem states that the gym's employees sold 70% (70 percent) more memberships than last year, and it's employees sold 5,190 gym memberships last year, then

memberships this year = 70% more than last year

memberships this year = 70%(5,190) + 5,190

memberships this year = 3,633 + 5,190

memberships this year = 8,823

Hence, the gym's employees sold 8,823 memberships this year.

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The sum of the given finite series is -1

The given series is:

     [tex]\sum\limits^9_{n=1} {(-1)^{n}}[/tex]

The summation notation tell us that we need to add each term (-1)ⁿ as n moves from 1 to 9.

Let us expand this summation notation:

n = 1  ⇒ a(1) = (-1)¹ = -1

n = 2  ⇒ a(2) = (-1)² = 1

n = 3  ⇒ a(3) = (-1)³ = -1

We can continue to expand until n = 9, but we can see the pattern. The series can be written as:

    [tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1[/tex]

We can see that a(1) and a(2) are cancelled out to each other. This applies to each pair of consecutive odd and even terms. Each term is cancelled out except a(9). Therefore:

    [tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1=-1[/tex]

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The simplification by combining like terms of 0.5g + g is 1.5g.

According to the given question.

We have an expression 0.5g + g .

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression 0.5g + g.

Here 0.5g, and g both are the like terms.

So, we add coeffcients of g to simplify the given expression.

Therefore, the simplification of 0.5g + g  is given by

0.5g + g

= 1.5g

Hence, the simplification by combining like terms of 0.5g + g is 1.5g.

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There must be pivot columns in the matrix. "A has a pivot place in every row" and "A's columns span an R5" seem to be logically equivalent.

When a matrix has been in row-echelon form, the first nonzero entry in each row is referred to as a pivot, as well as the columns wherein pivots appear are referred to as pivot columns.

The matrix must contain pivot columns. "A has a pivot position in each row" & "A's columns span an R5" appear rationally equivalent.

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The correct question is-

Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R⁵​? ​Why?

Answer:

Below in bold.

Step-by-step explanation:

The time you were driving = distance / average speed

= 1500/42

= 35.714 hours.

Required equation is

t = 42 - d/s          where t = time not driving, d = distance and s = average speed

Time not driving :

t = 42 - 35.714

 = 6.286 hours

That is about 6 hours 17 minutes.