A 12 foot board is cut so that one piece is 5 times as long as the other. Find the length of each piece.

Complete Question

The complete question is shown on uploaded image

Answer:

The  correct option is  B  

Step-by-step explanation:

The reason the correct answers is [tex]NumCyl \ and\ HPMax[/tex]  is because from the table  we see that the 95% confidence interval for [tex]NumCyl \ and\ HPMax[/tex]  does not contain zero

Which means the [tex]NumCyl \ and\ HPMax[/tex]   differ form zero in a two-tailed  test

Answer:

c is the square of half of b

Step-by-step explanation:

A quadratic equation can be written in the following form:

[tex]ax^2+bx+c[/tex].

Based off of the information provided, we can test to see if which answer choice is correct.

OPTION A IS INCORRECT:

Although, for [tex]x^2+6x+9[/tex], c is 1.5 times b, we do not see that relationship reflected in other equations, such as [tex]x^2+10x+25[/tex] and [tex]x^2+12x+36[/tex].  There must be a different relationship.

OPTION B IS INCORRECT:

Although c is double b for x^2+8x+16, this rule is not applicable for the rest of the equations. C is double b for the  is 1.5 times that of b for x^2+6x+9, and for and for x^2+10x+25, c is 2.5 times b, and for x^2+12x+36, c is 3 times of b.

OPTION C IS CORRECT:

We can test this relationship based off of the information given.

for x^2+6x+9, c equals (6/2)^2 which is 9

for x^2+8x+16, c equals (8/2)^2 which is 16

for x^2+10x+25 c equals (10/2)^2 which is 25

and finally, for x^2+12x+36 c equals (12/2)^2 which is 36.

OPTION D IS INCORRECT:

C is not the square of B.

for x^2+6x+9, b^2 which is 36 (c here is 9)

for x^2+8x+16, b^2 is 64 (c here is 16)

for x^2+10x+25 b^2 is 100 (c here is 25)

and finally, for x^2+12x+36 b^2 is 144 (c here is 36).

Hello, please consider the following.

We will multiply the numerator and denominator by

[tex]4+\sqrt{6x}[/tex]

to get rid of the root in the denominator.

First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.

[tex]4-\sqrt{6x} =0<=>\sqrt{6x}=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=\dfrac{16}{6}=\dfrac{8}{3}[/tex]

We need to take any x real number different from 8/3 then and simplify the expression.

Let's do it!

[tex]\begin{aligned}\dfrac{4}{4-\sqrt{6x}}&=\dfrac{4(4+\sqrt{6x})}{(4+\sqrt{6x})(4-\sqrt{6x})}\\\\&=\dfrac{4(4+\sqrt{6x})}{(4^2-\sqrt{6x}^2)}\\\\&=\dfrac{4(4+\sqrt{6x})}{(16-6x)}\\\\&=\dfrac{2(4+\sqrt{6x})}{(8-3x)}\\\\&\large \boxed{=\dfrac{8+2\sqrt{6x}}{8-3x}}\end{aligned}[/tex]

Thank you

Answer:

YES

Step-by-step explanation:

$157+$210+$377+$145=$889

$695+$95=$790

Leftover

$889-$790 =$99

he would have $99 leftover

The amount left over with Jean is given by the equation A = $ 99

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount left over be represented as A

Now , the equation will be

The cost of basic computer is = $ 695.00

The cost of printer is = $ 95.00

The amount saved in month of May = $ 157.00

The amount saved in month of June = $ 210.00

The amount saved in month of July = $ 377.00

The amount saved in month of August = $ 145.00

The total amount saved = $ 157.00 + $ 210.00 + $ 377.00 + $ 145.00

The total amount saved = $ 889

The total cost of computer and printer = $ 695 + $ 95

The total cost of computer and printer = $ 790

The amount of money left over with Jean A = total amount saved - total cost of computer and printer

Substituting the values in the equation , we get

The amount of money left over with Jean A = $ 889 - $ 790

The amount of money left over with Jean A = $ 99

Therefore , the value of A is $ 99

Hence , the amount left over is $ 99

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Answer:

10

Step-by-step explanation:

The most number of questions answered correctly are 10 and 11.

The typical number of questions a student answered correctly can be represented by the middle most value that is common to the data set.

If the data set is distributed evenly, the median, or the middle most value will fall on the 15th and 16th dots, which represents 10 correct correct challenge questions answered.

The typical number is 10.

Answer:

[tex]10[/tex]

Answer:

D.)22

Step-by-step explanation:

D. 22 people has an average of 4000 or more than 4000 steps each day.

To find an average sum up the weights of each individuals and divide by no. of individuals.

From the given diagram

2 people has an average of 0 to 1999 steps.

5 people has an average of 2000 to 3999 steps.

12 people has an average of 4000 to 5999 steps.

7 people has an average of 6000 to 7999 steps.

3 people has an average of 8000 to 9999 steps.

We have been asked how many people has an average of 4000 or more steps.

∴ ( 12 + 7 + 3) people has 4000 or more average steps each day.

= 22 people.

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Answer:

4

Step-by-step explanation:

y = 4x + 12

In y = mx+b

The coefficient of x (m) is the slope.

So the slope is 4

Answer:

The slope is 4

Step-by-step explanation:

y = 4x +12

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 4 and the y intercept is 12

The translation of the given graph has done in two steps.

1. Horizontal shift of 5 units to the left

2. Vertical shift of 4 units in the downwards direction.

"The translation of a graph is its rigid movement, vertically or horizontally."

The given translation of graph is:

[tex]y = (x - 6)^{2} + 7[/tex] to [tex]y = (x - 1)^{2} + 3[/tex]

Here, two types of translation has done to the first graph.

1. First of all, there is a horizontal shift of 5 units to the left has done.

[tex]y = (x - 6)^{2}[/tex] ⇒ [tex]y = [(x - 1) - 5)]^{2}[/tex]

2.After that, there is a vertical shift of 4 units in the downwards direction.

[tex]y = (x - 6)^{2} + 7[/tex]  ⇒ [tex]y = (x - 1)^{2} + 3[/tex]

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Answer:

1. 40 % is 40 / 100

by cancelling it the output is 2 /5

2. 35% is 35 / 100

7 / 20 is your answer

plz brainlist me and follow me

Answer:

C. -2

Step-by-step explanation:

You have to look at the factor in front of the x after normalizing the equation in to y = ax + b. In other words, find a.

y+2 = -2(x-3) =>

y = -2x + 6 - 2

y = -2x + 4

a = -2

b = 4

Answer:

C. -2

Step-by-step explanation:

Bringing the equation to slope-intercept form of y = mx + b, where m is a slope:

Correct answer choice: C. -2

Answer:

$7.80

Step-by-step explanation:

Find the cost to download 1 song. Divide 6 from 4.68

4.68/6 = 0.78

Each song costs $0.78.

Find the amount 10 songs cost. Multiply 0.78 with 10:

10 x 0.78 = 7.80

$7.80 is your answer.

~

Hi

6 = 4.68

10 = X

X = 10*4.68 /6

X = 46.8/6

X = 7.8

Answer:

[tex]\huge \boxed{\mathrm{12}}[/tex]

Step-by-step explanation:

R is a point on the line segment QS.

QR = 2

RS = 10

QS = 2 + 10

QS = 12

The length of the line segment QS is 12 units.

Given that, point R is on the line segment QS. Given QR =2 and RS = 10.

We need to determine the length of QS.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Here, since R is in between QS, QS=QR+RS

=2+10=12 units

Therefore, the length of the line segment QS is 12 units.

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Answer:

ASA

SSA

Step-by-step explanation:

The law of sines states that;

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

Where a,b,c are sides of the triangle and A,B,C are sides corresponding to those angles.

Hence we can use the sine rule when;

I) two angles and one side are given

2) two sides and an angle are given

Not that sine rule applies to triangles that are not right angled triangles.

Answer: B

Step-by-step explanation:

a is negtive  bcs grph opens down. h value is -1 and k is +2

Answer:

50

Step-by-step explanation:

Ratio is

Total number is

Since F type pencils number is known:

Then total number is:

Answer:

V = 150π units^3

Step-by-step explanation:

The volume of this cylinder is V = πr²h = π(5 units)^2·(6 units), or

V = 150π units^3

The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.

The volume of a solid is the total space it contains in the three-dimensional space.

The volume of a cylinder can be given by the formula,

V = πr²h cube units,

where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

In the question, we are asked to find the volume of the cylinder shown in the figure.

The cylinder has a base radius (r) of 5 units, and height (h) of 6 units.

So, we can find its volume using the formula,

V = πr²h cube units,

where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

∴ The volume of the cylinder = π(5²)6 cube units

or, the volume of the cylinder = π*25*6 cube units

or, the volume of the cylinder = 150π cube units

or, the volume of the cylinder = 150*3.14 cube units = 471 cube units.

∴ The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.

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Answer:

x = 57

Step-by-step explanation:

x−53 = 4

Add 53 to each side

x-53+53 = 4+53

x = 57

Answer:

x = 57

Step-by-step explanation:

x−53 = 4

x (- 53 + 53) = 4 + 53

x = 57

Answer:

So Jeff is faster with 7 km per hour

Step-by-step explanation:

Jeff says I can run 7 kilometers per hour!

Cameron says "I can run 100 meters per minute!!

To actually know which one of them is the fastest we will convert their speed to be in the same unit

Let's convert meters per minute to kilometers per hour

100 meters per minute= 100 M/m

100 meters per minute= 100 *60/1000

100 meters per minute= 6000/1000

100 meters per minute= 6 km /h

100 meters per minute= 6 kilometers per hour

So Jeff is faster with 7 km per hour

Answer:

Jeff is faster than Cameron. Khan Academy

Step-by-step explanation:

Answer:

7p + 4

Step-by-step explanation:

7p - (-5) + (-1)

7p + 5 -1

7p + 4

Hey There!!

STEP 1:

1

Simplify ——————————

(4x + 3y)2

Equation at the end of step

(4x-3y) 1

——————————————————————————— ÷ ————————

(((16•(x2))+24xy)+(9•(y2))) (4x+3y)2

STEP 2:

Equation at the end of step

2

:

(4x-3y) 1

——————————————————————— ÷ ————————

(((16•(x2))+24xy)+32y2) (4x+3y)2

STEP 3:

Equation at the end of step

(4x - 3y) 1

—————————————————————— ÷ ——————————

((24x2 + 24xy) + 32y2) (4x + 3y)2

STEP 4:

4x - 3y

Simplify —————————————————

16x2 + 24xy + 9y2

Trying to factor a multi variable polynomial :

4.1 Factoring 16x2 + 24xy + 9y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (4x + 3y)•(4x + 3y)

Detecting a perfect square :

4.2 16x2 +24xy +9y2 is a perfect square

It factors into (4x+3y)•(4x+3y)

which is another way of writing (4x+3y)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Equation at the end of step

4:

(4x - 3y) 1

—————————— ÷ ——————————

(4x + 3y)2 (4x + 3y)2

STEP 5:

4x-3y 1

Divide ———————— by ————————

(4x+3y)2 (4x+3y)2

5.1 Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

4x - 3y 1 4x - 3y (4x + 3y)2

—————————— ÷ —————————— = —————————— • ——————————

(4x + 3y)2 (4x + 3y)2 (4x + 3y)2 1

Canceling Out :

5.2 Cancel out (4x + 3y)2 which appears on both sides of the fraction line.

Final result :

4x - 3y

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

a). converges

b). diverges

c). converges

Step-by-step explanation:

{ [tex]$ a_n $[/tex] } = { [tex]$ nr^n $[/tex] }

Using radio test,

L = [tex]$ \lim_{n \rightarrow \infty} |\frac{a_n + 1}{a_n}| $[/tex]

   = [tex]$ \lim_{n \rightarrow \infty} |\frac{(n+1)r^{n+1}}{nr^n}| $[/tex]

   = [tex]$ \lim_{n \rightarrow \infty} |(1+\frac{1}{n})^r| $[/tex]

   = [tex]$ \lim_{n \rightarrow \infty} |r| $[/tex]

   = |r|

Therefore, [tex]$a_n$[/tex] converges in |r| < 1

a). r = 1/5

    [tex]$\{ a_n \}= \{\frac{1}{5}, n \}$[/tex]

This sequence is monotonically decreasing and bounded.

0 < [tex]$ a_n $[/tex] < 1

Hence, { [tex]$ a_n $[/tex] } converges.

b). r = 1

    { [tex]$ a_n $[/tex] } = { n }

This sequence is monotonically increasing sequence which is not bounded.

Hence, { [tex]$ a_n $[/tex] } diverges.

c). r = 1/6

[tex]$\{ a_n \}= \{\frac{1}{6}, n \}$[/tex]

This sequence is monotonically decreasing and bounded.

0 < [tex]$ a_n $[/tex] < 1

Hence, { [tex]$ a_n $[/tex] } converges.

For  |r| < 1, the [tex]$a_n$[/tex] converges.

Answer:

D) 89.6 %

Average  or mean of the given data = 89.6 %

Step-by-step explanation:

Step(i):-

Given data

        X      :     82        100        84

P(X=x)       :    0.40      0.40     0.20

Step(ii)

Let 'X' be the discrete distribution

Mean of the discrete distribution = ∑ x P( x=x)

                                                       = 82 ×0.40 +100 ×0.40 +84 ×0.20

                                                       = 89.6

Final answer:-

Average of the given data = 89.6 %

Answer:

Step-by-step explanation:

For

The number 30 / 15 belongs to the whole, integer, and rational numbers. the correct option is C.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.

The number set from 0 to infinity are called whole numbers. The number set from negative infinity to positive infinity are called integers.

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

The given number 30 / 15 is in the form of a rational number that can also be written as 2. Then the number 30 / 15 can be the whole, integer, and rational number.

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Answer:

Divisor

Step-by-step explanation:

Given

[tex]a\ mod\ n[/tex]

Required

What does n represents

In arithmetic, the number that divides another is referred to as divisor;

Take for instance;

[tex]5\ mod\ 3 = 2[/tex]

This implies that when 5 is divided by 3, the remainder is 2

The bold text (divided by 3) means that 3 is the divisor of 5;

When compared to [tex]a\ mod\ n[/tex]

We have that

n = 3

Reason being that, n and 3 are in the same position base on order of appearance;

Hence, n represents the divisor

Answer:

C

Step-by-step explanation:

The definition of a limit is the value a function it is approaching as the limit approaches a certain point.

We have the limit:

[tex]\lim_{x\to3} f(x)=5[/tex]

In other words, the value of f(x) as x approaches 3 approaches 5.

We do not care what happens at x=3. Rather, the limit tells us that as x approaches or gets closer to x=3, the function f(x) gets closer to 5.

Thus, the correct answer is C.

Answer:

87 women

Step-by-step explanation:

4x+3x=203

7x=203

x=29

29*3=87 :D

Answer:

0

Step-by-step explanation:

Hello!

To solve this we put in the values given to us for x and go till we get one this is true.

The values given for x are -0.5, 0, and 1

                 1                  

5 + 1 - 12 = 2(1) - 7

Combine like terms

-6 = -5

Since -6 does equal -5 the answer is not 1

                 0                  

5 + 0 - 12 = 2(0) - 7

Combine like terms

-7 = -7

Since -7 equals -7 the answer is 0

Hope this Helps!

Step-by-step explanation:

Range = highest value - lowest value

=25 – 12

= 13

First Quartile = 15

Third Quartile = 22

Interquartile = 7

Answer:

a) 7

b) 15

c) 13

d) 22

Answer:

the 2 is in the hundreds and hundredths place