how many significant figures are in this number 6.01x10^3

Answer:

210

Step-by-step explanation:

[tex]512=2^9 \\[/tex] has 9 prime factors

Now, if you want to maximize the number of different prime factor, apply the following method: let [tex]p(n)[/tex]  be the nth prime number, in increasing order. Let [tex]v[/tex]  define as follow :  [tex]v(0)=1,v(n+1)=v(n)p(n+1)[/tex] , and find n  such that [tex]v(n) < 1000,v(n+1) > 1000[/tex]. n will be the number of factors and v(n) your integer.

[tex]v(1)=2v(0)=2v(2)=3v(1)=6v(3)=5v(2)=30v(4)=7v(3)=210v(5)=11v(4)=2310[/tex]

There you are,  210 , with only 4 different prime factors.

→Credits: Xavier Dectot←

Answer:

13

Step-by-step explanation:

This problem is a type of puzzle called a Number Pattern. Number patterns always follow a specific pattern. In this case, its +9, -3.

The first number in this pattern is 1.

The second number in this pattern is 10.

That is an increase of +9.

The third number in this pattern is 7

That is a decrease of -3.

The fourth number in this pattern is 16.

That is an increase of +9.

Therefore, we can conclude that the next number will have to be a decrease of -3.

16 - 3 = 13

That is your answer. I hope I helped. If you feel like this is the best answer, please rate brainliest.

a. The value of cos2θ = -119/169

b. The value of cosθ = -5/13

The question involves trigonometric identities

Trigonometric identities show the relationship between trigonometric ratios.

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cos2θ = 1 - 2sin²θ

Substituting sinθ = 12/13  into the equation, we have

cos2θ = 1 - 2sin²θ

cos2θ = 1 - 2(12/13)²

cos2θ = 1 - 2(144/169)

cos2θ = 1 - 288/169

cos2θ = (169 - 288)/169

cos2θ = -119/169

So, the value of cos2θ = -119/169

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cosθ = √(1 - sin²θ)

Substituting sinθ = 12/13  into the equation, we have

cosθ = √(1 - sin²θ)

cosθ = √[1 - (12/13)²]

cosθ = √[1 - (144/169)]

cosθ = ±√(169 - 144)/169

cosθ = ±√25/169

cosθ = ±5/13

θ is the quadrant II, it means that 90° ≤ θ ≤180° it means that cosθ is negative.

So, cosθ = -5/13

So, the value of cosθ = -5/13

Learn more about trigonometric identities here:

https://brainly.com/question/27990864

#SPJ1

Answer:

X is less than and equal to 4

Answer:

4.12 miles

Step-by-step explanation:

Use distance formula

d^2 = (-8- -4)^2 + ( -9 - -10)^2

d^2 =   16   +   1

d^2 = 17

d = sqrt 17 = 4.12 miles

Considering the vertex of the quadratic equation, the maximum height that the object will reach is of 80 feet.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

In this problem, the equation is:

f(t) = -16t² + 64t + 16.

Hence the coefficients are:

a = -16, b = 64, c = 16.

The maximum value is found as follows:

[tex]y_v = -\frac{64^2 - 4(-16)(16)}{4(-16)} = 80[/tex]

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

#SPJ1

Answer:

  x = 8

Step-by-step explanation:

Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.

The measure shown is equal to the angle measure of 90°.

  14x -22 = 90

We can solve this 2-step linear equation in the usual way.

  14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone

  x = 112/14 = 8 . . . step 2, divide by the coefficient of x

The value of x is 8.

Answer:$375

Step-by-step explanation: To find the average, we need to add all of the numbers up and divide by the number of numbers in the set. Since there are 4 deposits, to get an average of #365, Jen needs to have deposited 365x4 = $1460 in total. Now, it is pretty easy to find the answer. We add up her 3 deposits: 325+280+480 = $1085 and see that it is still $375(1460 - 1085) short. So, Jen needs to deposit $375 on her fourth deposit to have an average of $365.

The given function is quadratic. The quadratic term is -18x², the linear term is 39x, and the constant term is -20. So, first option is correct.

A function in which the highest degree of the variable is 2, then that function is said to be a quadratic function.

The general form of a quadratic function is ax² + bx + c. Where the terms are:

ax² - quadratic term;

bx - linear term;

c - constant term;

A function in which the highest degree of the variable is 1, then that function is said to be a linear function.

The general form of a linear function is ax + c. Where the terms are:

ax - linear term;

c - constant term;

The given function is f(x) = (3x - 4)(-6x + 5)

Expanding the given function,

f(x) = (3x)(-6x) + (3x)(5) + (-4)(-6x) + (-4)(5)

     = -18x² + 15x + 24x - 20

     = -18x² + 39x - 20

Since the highest degree of the variable x in the obtained function is 2, it is a quadratic function.

The terms in the obtained quadratic function are:

quadratic term: -18x²

linear term: 39x

constant term: -20

Therefore, the first option is correct.

Learn more about quadratic function here:

https://brainly.com/question/11631534

#SPJ1

Disclaimer: The question has a mistake in the function. The corrected question is here.

Question: Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

f(x)= (3x - 4)(-6x + 5)

Answer:

21%

Step-by-step explanation:

($63*100%) / $300 = 21%

Check the picture below.

[tex]sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}[/tex]

The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

According to the statement

we have given that the some values of the temperatures and we have to write it in the order from the coolest to the warmest means in increasing order.

So, For this purpose,

The given values of temperatures are:

3°C , -7°C , 2°F, 262 K

Firstly convert into one form

So, convert all values in Celsius form,

3°C = 3°C

-7°C = -7°C

2°F = -16.7°C

262 K = -11.15°C

Now arrange into the order from coolest to warmest

So, it will become

-16.7°C > -11.15°C > -7°C > 3°C

So, -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

Learn about the increasing order here

https://brainly.com/question/14662181

#SPJ1

                     _

Answer: 0.83

Step-by-step explanation:

5/6 = 0.8333...

                        _

0.8333... = 0.83

The polynomial equation x³ + 2x² + 4x+8 can be expressed as the method of factor polynomial exists (x² + 4)(x + 2).

The factoring process concerns removing factors from an experiment and then using them in the analytical method of factor analysis.

Polynomials exist as expressions with one or more terms with a non-zero coefficient. A polynomial can contain more than one term.

A mathematical expression of one or more additional algebraic terms each of which consists of a constant multiplied by one or more variables presented to a nonnegative integral power.

Given: x³ + 2x² + 4x+8

x³ + 2x² + 4x+8 = 0

simplifying the equation, we get

(x³+2x²)+(4x+8 )= 0

x²(x+2)+4(x+2)= 0

factorizing the above equation, we get

(x+2)(x²+4) = 0

Therefore, the polynomial equation x³ + 2x² + 4x+8 can be expressed as the method of factor polynomial exists (x² + 4)(x + 2).

To learn more about polynomial equation refer to:

https://brainly.com/question/10532996

#SPJ9

The best conclusion for Ashlee to make is (c) Ashlee determined that the box must be less than 15 feet by verifying the triangle inequality theorem.

The side lengths of the triangle are given as:

6 feet and 9 feet

Let the third side be x.

By triangle inequality theorem, we have:

a + b > c

So, we have

6 + 9 > x

6 + x > 9

9 + x > 6

Evaluate the inequalities

15 > x

x > 3

x > -3

Remove the negative inequality

15 > x

x > 3

Combine the inequalities

3 < x < 15

So, the maximum side is less than 15

Hence, the best conclusion for Ashlee to make is (c) Ashlee determined that the box must be less than 15 feet by verifying the triangle inequality theorem.

Read more about triangle inequality theorem at

https://brainly.com/question/309896

#SPJ1

The y factors of the given quadratic equation is -1 and 40/22.

According to the statement

we have given that the equation and we have to find the factors of those equation.

So, The given equation is:

[tex]Y =x^2-23x^2 + 18x+40[/tex]

where y is the factors of that equation.

So, we have to find the factors of the given quadratic equation.

[tex]x^2-23x^2 + 18x+40 = 0[/tex]

Then after solving it become

[tex]-22x^2 + 18x+40 = 0[/tex]

Then take negative sign common from it then

[tex]22x^2 - 18x - 40 = 0[/tex]

Make the factors of this quadratic equation

[tex]22x^2 + 22x -40x - 40 = 0[/tex]

Now take common values 22x and 40 from the equation then

[tex]22x (x + 1) -40 (x + 1) = 0[/tex]

Then it become

[tex](22x - 40) (x + 1) = 0[/tex]

Then the values of x become from the equation is

[tex]x = -1, x= 40/22[/tex]

The value of the factors y is -1 and 40/22.

So, The y factors of the given quadratic equation is -1 and 40/22.

Learn more about Quadratic equation here

https://brainly.com/question/24334139

#SPJ1

The length of the trip at a distance of 300 miles and the given times are

The distance is given as:

d = 300

The formula is represented as:

d = r * t

Make t the subject

t = d/r

Substitute 300 for d

t = 300/r

When r = 50 mph,

t = 300/50

Evaluate

t = 60

When r= 70 mph, we have

t = 300/70

Evaluate

t = 30/7

When r = x, we have

t = 300/x

When r = x + 10, we have

t = 300/x + 10

When r = x - 5, we have

t = 300/x - 5

Read more about rates and speed at:

https://brainly.com/question/4931057

#SPJ1

Complete question

A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of:

Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.

Answer:

This is an example of correlation because there is an obvious relationship between the two scenarios

Step-by-step explanation:

This is not cause-and-effect therefore cannot be causation or "cause"

Answer:

See below

Step-by-step explanation:

Question is unclear

could be (11-2)^3  = 9^3 = 729

could be  11 - 2^3 = 11 - 8 = 3       Pick the one you want !

Answer:

m = -2

Step-by-step explanation:

to find the answer you must put rise over run

rise is (y2 - y1) and run is (x2 - x1)

lets use the bottom two points for thisd

y2 is 0 and y1 is 2

x2 is 1 and x1 is 0

0 - 2 = -2

1 - 0 = 1

-2/1 = -2

that is the slope

No the parents do not feel differently as they used to feel twenty years ago

Given :-

Po: p=0.46

Pa: p NE 0.46

alpha=0.01

Test statistic is one sample proportion [tex]z=(phat-p)/\sqrt{{ {0.46)(0.54)/800}}[/tex]

Critical value z> |2.576|

z=0.025/0.0176

=1.418

This is a p-value of 0.078

Fail to reject Po  and insufficient evidence to support the claim that parents feel differently.

Learn more about Statistics here :

https://brainly.com/question/23091366

#SPJ1

The estimated number of trout that is present in a random sample of 5,000 fish is 1429

The table of values is given as:

Type of Fish Piranha Catfish Trout

Number of fish 120 230 140

The proportion of fish that are trout is calculated as:

Trout = 140/(120 + 230 + 140)

Evaluate the sum

Trout = 140/490

Simplify the fraction

Trout = 2/7

The number of trout that is present in a random sample of 5,000 fish is calculated as:

Trout = 2/7 * 5000

Evaluate the product

Trout = 1429

Hence, the estimated number of trout that is present in a random sample of 5,000 fish is 1429

Read more about estimates at:

https://brainly.com/question/17203075

#SPJ1

1. The master budget variance for July was $3,900, and this variance was favorable.

2. The July sales volume variances in terms of contribution margin and operating income are $2,800 F and $3,900 F, respectively.

3. The July flexible-budget variances in terms of contribution margin and operating income are $5,550 F and $6,650 F, respectively.

4.  Flexible budgets for the following output levels are:

                                                     3,560 units        3,980 units

Sales revenue                           $53,400               $59,700

Variable manufacturing costs     14,240                  15,920

Fixed manufacturing costs         12,460                   13,930

Variable selling and

administrative expenses             7,120                    7,960

Fixed selling and

administrative expenses            9,100                     9,100

Operating Income                   $10,480                $12,790

                                             Actual Master      Budget   Per Unit  Variance

Units                                               3,500          4,000                          500 U

Sales revenue                          $ 54,300    $ 60,000       $15.00  $ 5,700 U

Variable manufacturing costs    10,000         16,000          4.00     6,000 F

Fixed manufacturing costs         13,000         14,000          3.50      1,000 F

Variable selling and

administrative expenses            6,500           8,000         2.00      1,500 F

Contribution margin               $24,800       $22,000                    $2,800 F

Fixed selling and

administrative expenses           8,000            9,100                        1,100 F

Total costs                              $37,500        $47,100

Operating income                  $16,800        $12,900                    $3,900 F

Sales volume variance:

Revenue per unit                   $15.51            $15.00         $0.51 F

                                             Actual Master      Budget    Variance

Units                                               3,500          3,500            U

Sales revenue                          $ 54,300    $ 52,500       $ 1,800 F

Variable manufacturing costs    10,000         14,000         4,000 F

Fixed manufacturing costs         13,000         12,250            750  U

Variable selling and

administrative expenses            6,500           7,000           500 F

Contribution margin               $24,800        $19,250      $5,550 F

Fixed selling and

administrative expenses           8,000            9,100          1,100 F

Operating income                  $16,800         $10,150      $6,650 F

Learn more about sales volume variance at https://brainly.com/question/4127264

#SPJ1

Answer:

3 :8

Step-by-step explanation:

12 : 32 = 3:8

I believe that is right.

(8) The algebraic expression representing the given phrase is 22x ≥ 350, where x is the number of units sold by Ms. Reed.

(9) The minimum number of shares needed to achieve the required profit is 1223, using the algebraic expression 2.25x ≥ 2750, where x is the number of shares.

(10) The number of books needed to be sold for the novelist to make a profit of $10,000 is 4350, using the algebraic expression 5000 + 1.1495x ≥ 10000, where x is the number of books sold,

(8) Weekly target for Ms. Reed is $350.

The cost of each unit she sells is $22.

We assume the number of units she sold to be x.

Thus, the total sales done by Ms. Reed is $22x.

For her to remain employed, her total sales should exceed her target, which can be shown as an algebraic expression: 22x ≥ 350.

Thus, the algebraic expression representing the given phrase is 22x ≥ 350, where x is the number of units sold by Ms. Reed.

(9) Profit on each share is $2.

The additional profit is $0.25.

Thus, the total profit on each share is $2 + $0.25 = $2.25.

The required profit by the customer is $2750.

We assume the number of shares needed to be x.

Thus, the total profit made by the customer is $2.25x.

For the customer to make the required profit, we can write the algebraic expression, 2.25x ≥ 2750.

To solve this, we divide both sides by 2.25 to get:

2.25x/2.25 ≥ 2750/2.25,

or, x ≥ 1222.22.

Thus, the minimum number of shares needed to achieve the required profit is 1223.

(10) Default contract of Book Maker publisher is $5000 and 5% royalty.

The cost of the book, for which the novelist has got the contract is $22.99.

We assume the number of books sold to be x.

The royalty share on each book given to the novelist is 5% of $22.99, or, $ 5/100 * 2299/100 = $ 11495/10000 = $1.1495.

Thus, the royalty received on x number of books = $1.1495*x = $1.1495x.

Thus, the total profit to the novelist = (5000 + 1.1495x).

Since the novelist wants to make a minimum profit of $10000, we can show it as the algebraic expression:

5000 + 1.1495x ≥ 10000.

To solve this, we go as follows:

5000 + 1.1495 ≥ 10000,

or, 1.1495x ≥ 10000 - 5000,

or, 1.1495x ≥ 5000,

or, x ≥ 5000/1.1495,

or, x ≥ 4349.717.

Approximating, we get x ≥ 4350.

Thus, 4350 books need to be sold to achieve the wanted profit.

Learn more about algebraic expressions at

https://brainly.com/question/4344214

#SPJ1

The minimum surface area that such a box can have is 380 square

Represent the base length with x and the bwith h.

So, the volume is

V = x^2h

This gives

x^2h = 500

Make h the subject

h = 500/x^2

The surface area is

S = 2(x^2 + 2xh)

Expand

S = 2x^2 + 4xh

Substitute h = 500/x^2

S = 2x^2 + 4x * 500/x^2

Evaluate

S = 2x^2 + 2000/x

Differentiate

S' = 4x - 2000/x^2

Set the equation to 0

4x - 2000/x^2 = 0

Multiply through by x^2

4x^3 - 2000 = 0

This gives

4x^3= 2000

Divide by 4

x^3 = 500

Take the cube root

x = 7.94

Substitute x = 7.94 in S = 2x^2 + 2000/x

S = 2 * 7.94^2 + 2000/7.94

Evaluate

S = 380

Hence, the minimum surface area that such a box can have is 380 square

Read more about surface area at

https://brainly.com/question/76387

#SPJ1

Answer: (x-2)

Step-by-step explanation:

This problem is a middle-term factorization, or factoring by splitting the middle term.

We have the equation

x^2 - 18x + 32

This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.

x^2 - 18x + 32

= x^2 - 16x - 2x + 32

= x(x-16) - 2(x - 16)

= (x-16) (x-2) -------> we get this through taking (x-16) common

We could also pretend that the length is x - y, where y is the number we need to finish the equation.

x^2 - 18x + 32

= (x-16) (x-y)

= x^2 -16x - xy + 16y

-16 minus 2 is -18, which is our middle term.

Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.

Our answer is that the length is (x-2).

Assuming that the company sells all that it produces, The profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.

Profit = R-C = -(x-100)^2/2 +5000 - 50x -100 =

-(x^2 -200x +10000)/2 -50x +4900 =

-x^2/2 +100x -5000 +5000 -50x +4900

Collect like terms

-x^/2+50x -100

Hence,

Profit function = P(x)=-0.5x²+50x -100

Maximum profit generating output  can be determine by taking the derivative and setting it equal to zero

R-C = -x^2/2 + 50x -100

R'-C' = -x + 50 =0

P(0)x = 50

Maximum profit  can be determine by substituting x=50 into the original profit equation, R-C

P(50) =-(1/2)(50)^2 +50(50) -100

P(50)= -1250 + 2500 -100

P(50) = $1150 profit

P(120) =-(1/2)(120)^2 +50(120) -100

P(120)= -3600 + 6000 -100

P(120) = $2300 profit

Therefore the profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.

Learn more about profit function here:https://brainly.com/question/4618859

#SPJ1