Evaluate Algebraic Expressions
The classroom is divided into four equal parts. The area of each part is 5.3 meters. What is the are of the classroom?​

Answer:

p = -14

Step-by-step explanation:

5/7p - 2/7p + 12 = 6

Combine like terms

3/7 p +12 = 6

Subtract 12 from each side

3/7p + 12-12 = 6-12

3/7p = -6

Multiply each side by 7/3

7/3 * 3/7p = -6*7/3

p = -14

Answer:

p = - 14

Step-by-step explanation:

5/7p - 2/7p + 12 = 6

subtract 12 both sides

5p/ 7 - 2p/7  + 12  = 6 - 12

simplify

5p/7 - 2p/7 = -6

multiply both side by 7

5p/7 * 7    -    2p/7 * 7     =  -6 * 7

simplify

5p - 2p = -42

p = -42 / 3

p = - 14

Hi there! Hopefully this helps!

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

[tex]\sqrt[]{2}[/tex] × [tex]\frac{8\sqrt{2} }{3}[/tex] ÷ 3 - 1

First, we express [tex]\sqrt{2}[/tex] × [tex](\frac{8\sqrt{2}}{3})[/tex] ≈ 5.333333333 as a single fraction.

[tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} } - 1[/tex]  ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now we express [tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{\frac{3}{3} }[/tex] ≈ 1.777777778 as a single fraction.

[tex]\frac{\sqrt{2 \times 8\sqrt{2} } }{3 \times 3} - 1[/tex]  ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply [tex]\sqrt{2}[/tex] ≈ 1.414213562 and [tex]\sqrt{2}[/tex] ≈ 1.414213562 to get 2.

[tex]\frac{2 \times 8}{3 \times 3} - 1[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply 2 and 8 to get 16.

[tex]\frac{16}{3 \times 3} - 1[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply 3 and 3 to get 9.

[tex]\frac{16}{9} - 1[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Convert 1 to fraction [tex]\frac{9}{9} = 1.[/tex]

[tex]\frac{16}{9} - \frac{9}{9}[/tex] ≈ 0.777777778

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since [tex]\frac{16}{9}[/tex] ≈ 1.777777778 and [tex]\frac{9}{9} = 1[/tex] have the same denominator, subtract them by subtracting their numerators.

[tex]\frac{16 - 9}{9}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Then you get................

[tex]\frac{7}{9}[/tex]

Answer:

r(t) and s(t) are parallel.

Step-by-step explanation:

Given that :

the  lines represented by the vector equations are:

r(t)=⟨1−t,3+2t,−3t⟩

s(t)=⟨2t,−3−4t,3+6t⟩

The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.

NOTE:

Two lines will be parallel if [tex]\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}[/tex]

here;

[tex]d_1 = (-1, \ 2, \ -3)[/tex]

Thus;

[tex]r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t[/tex]

[tex]d_2 =(2, \ -4, \ +6)[/tex]

[tex]s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t[/tex]

∴

[tex]\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}[/tex]

Hence, we can conclude that r(t) and s(t) are parallel.

Answer:

The correct option is four.

Step-by-step explanation:

The associative property implies that the values are added however we want, i.e. the numbers can be grouped in any way and the answer would still be the same.

The associative property of addition is:

[tex](a+b)+c=a+(b+c)[/tex]

The expression provided is:

(13 + 15 + 20) + (20 + 47 + 18)

The answer provided by four students are:

Jeremy : (20 + 13 + 15) + (20 + 47 + 18)

Layla : (20 + 47 + 18) + (13 + 15 + 20)

Keith : (13 + 20) + (20 + 47 + 18) + 15

Melinda : (13 + 15 + 20 + 20) + (47 + 18)

So, all the four students correctly applied only the associative property to rewrite the expression.

The correct option is four.

Answer: The answer is A or one lol

Step-by-step explanation:

Answer:

a) P [ Y ≤ -12 ]  =  0,32997      or        P [ Y ≤ -12 ]  = 32,99 %

b) P [ Y > -1 ]  =  0,3707          or   P [ Y > -1 ]  =  37,07 %

c) P [ 34 ≤  Y  ≤  44]    =  0,1585      or     P [ 34 ≤  Y  ≤  44]    =  15,85 %

d) P [ Y > -4 ]  = 0,59871         or        P [ Y > -4 ]  = 59,87 %

Step-by-step explanation:

Normal Distribution:   N ( -8 ; 9 )

a) P [ Y ≤ -12 ]  = ( - 12  - (-8))/9

P [ Y ≤ -12 ]  =  - 4/9  = - 0,44

From  z-table for the z score -0,44 we get:

P [ Y ≤ -12 ]  =  0,32997      or        P [ Y ≤ -12 ]  = 32,99 %

b)  Normal Distribution:   N ( - 4 ; 9 )

P [ Y > -1 ]  =  1  - P [ Y ≤ -1 ]

P [ Y ≤ -1 ]  =  ( - 1 - ( - 4 ) ) / 9

P [ Y ≤ -1 ]  =  3 / 9  =  0,3333

From  z-table for the z score 0,33 we get:

P [ Y ≤ -1 ]  = 0,6293

P [ Y > -1 ]  =  1  - P [ Y ≤ -1 ]  =  1 - 0,6293

P [ Y > -1 ]  =  0,3707          or   P [ Y > -1 ]  =  37,07 %

c)  Normal Distribution:   N ( 40  ;  25  )

P [ 34 ≤  Y  ≤  44]

P [ 34 ≤  Y  ≤  44]    = P [  Y  ≤  44]  -  P [ Y ≤ 34 ]

 P [  Y  ≤  44]  = ( 44 - 40 ) / 25   = 0,16

From  z-table for the z score 0,16 we get:

P [  Y  ≤  44]  = 0,5636

P [ Y ≤ 34 ]  = ( 34  - 40 ) / 25   =  - 6 / 25   = -  0,24

From  z-table for the z score -0,24 we get:

P [ Y ≤ 34 ]  = 0,40517

Then

P [ 34 ≤  Y  ≤  44]    = P [  Y  ≤  44]  -  P [ Y ≤ 34 ]

P [ 34 ≤  Y  ≤  44]    =   0,5636 -  0,40517

P [ 34 ≤  Y  ≤  44]    =  0,1585      or     P [ 34 ≤  Y  ≤  44]    =  15,85 %

d)  Normal Distribution:   N ( -3  ;  4  )

P [ Y > -4 ]  =  1  -  P [ Y ≤ -4 ]

P [ Y ≤ -4 ]  =  ( - 4 - ( -3))/4  =  - 1/4  = - 0,25

From  z-table for the z score -0,25 we get:

P [ Y ≤ -4 ]  = 0,40129

P [ Y > -4 ]  =  1  -  0,40129

P [ Y > -4 ]  = 0,59871         or        P [ Y > -4 ]  = 59,87 %

Answer:

Step-by-step explanation:

Let the points be A and B

A ( 3 , -3 ) ⇒( x₁ , y₁ )

B ( 0 , 3 )⇒ ( x₂ , y₂ )

Finding the slope

Slope ( m ) = [tex] \sf{ \frac{y2 - y1}{x2 - x1} }[/tex]

plug the values

⇒[tex] \sf{ \frac{3 - ( - 3)}{0 - 3} }[/tex]

We know that , [tex] \sf{( - ) \times ( - ) = ( + )}[/tex]

⇒[tex] \sf{ \frac{3 + 3}{0 - 3} }[/tex]

Calculate

⇒[tex] \sf{ \frac{6}{ - 3} }[/tex]

⇒[tex] \sf{ - 2}[/tex]

Hope I helped!

Best regards!!

Answer:

-6/3=. -2

Step-by-step explanation:

Answer:

The calculated value Z=1.2413 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

An instructor in the English department at CBC believes rates at CBC may be equal to the state average

Step-by-step explanation:

Step(i):-

Given Population proportion

                                    P=68%= 0.68

Sample proportion

                            [tex]p^{-} =\frac{x}{n} = \frac{179}{250} = 0.716[/tex]

Null hypothesis : H₀ : p = 0.68

Alternative Hypothesis :H₁ : p > 0.68

Step(ii):-

Test statistic

                         [tex]Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }[/tex]

                        [tex]Z = \frac{0.716-0.68 }{\sqrt{\frac{0.68 X 0.32}{250} } }[/tex]

                       Z = 1.2413

Level of significance

             [tex]Z_{0.05} = 1.96[/tex]

The calculated value Z=1.2413 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

An instructor in the English department at CBC believes rates at CBC may be equal to the state average

Answer:

1012

Step-by-step explanation:

The ratio of student / applicant is 6 /11

So for 552 students, the applicants number is:

Number of applicants is 1012

Answer:

This is the answer

2/9=0.222222222.

Answer:

.2222 ( repeating)

Step-by-step explanation:

Hello, let's  note a the positive real number.

A positive real number is 4 less than another.

So, the other number is a - 4

When 8 times the larger is added to the square of the smaller, the result is 96.

So, we need to solve the following equation.

[tex]8a+(a-4)^2=96[/tex]

Let's do it!

[tex]8a+(a-4)^2=96\\\\8a+a^2-8a+16=96\\\\a^2=96-16=80=4^2*5\\\\a=\pm4\sqrt{5}[/tex]

As a is positive, there is only one solution which is.

[tex]\Large \boxed{\sf \bf \ \ a=4\sqrt{5} \ \ }[/tex]

Thank you.

The amount given by the sum of numbers can be presented in an equation

form from which the value of each number can be obtained.

The large number is 4·√5, the smaller number is 4·(√5 - 1)

Reason:

Let x represent the large number, we have;

The smaller number = x - 4

8 × x + (x - 4)² = 96

8·x + (x - 4)² = 96

Required:

The values of the numbers

Solution:

8·x + (x - 4)² = 8·x + x² - 8·x + 16 = 96

8·x - 8·x + x² + 16 = 96

x² + 16 = 96

x² = 96 - 16 = 80

x = ±√(80) = ±4·√5

Given that the numbers are positive, we have;

The large number, x = 4·√5

The smaller number = x - 4 = 4·√5 - 4

The smaller number = 4·√5 - 4 = 4·(√5 - 1)

Learn more here:

https://brainly.com/question/24676383

Answer:

He will eat 0.233 of one slice

Step-by-step explanation:

If Landon eats only two slices of pizza from a 12 inch pizza cut into 6

It means each slice has 2 inch pizza and Landon eats 2 of these

So Landon eats 2*2 = 4 inch pizza

So a rectangular pizza of 10 by 15

= 10*15

= 150 inch pizza

Cut into 8 slices

= 150/8

.= 18.75 inch per slice

4/18.75 = 0.233

He will eat 0.233 of one slice

Answer:

[tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]

Step-by-step explanation:

Given the function [tex]\dfrac{37}{x(x-6)}[/tex], to write the form of its partial fraction on decomposition, we will separate the two functions separated by an addition sign. The numerator of each function will be constants A and b and the denominator will be the individual factors of each function at the denominator. The partial fraction of the rational function is as shown below.

[tex]= \dfrac{37}{x(x-6)}\\\\= \dfrac{A}{x}+\dfrac{B}{x-6}[/tex]

Since we are not to solve for the constants, hence the partial fraction is [tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]

Answer:

56

Step-by-step explanation:

Keep the order of opperations in mind when doing this (PEMDAS). First, solve what is inside the parentheses (6-1). Then, solve the exponent and the multiplication (6² and 5×5). Finally, finish adding and subtracting to get the answer.

Answer:

56

Step-by-step explanation:

Hello!

We have to follow the order of PEMDAS

Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction

5 x 5 - (6 - 1) + [tex]6^{2}[/tex]

Parenthesis First

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

Exponents next

[tex]5x5 - (5) + 36[/tex]

Multiplication and Divsion from left to right

25 - (5) + 36

Addition and Subtraction from left to right

20 + 36

56

The answer is 56

Hope this Helps!

Use the Pythagorean theorem.

Distance = sqrt(16^2 + 5^2)

Distance = sqrt(256 + 25)

Distance = sqrt(281)

Distance = 16.763

Rounded to the nearest tenth = 16.8 miles

Answer:

( 2x - 1 ) ( x + 3) / ( 2x - 3 ) ( x + 1 )

Step-by-step explanation:

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

{ ( x - 2 ) ( 2x - 3) - 3 ( 1- 4x) } / ( 2x - 3 ) ( x + 1 )

{ 2x^2 - 7x - 3 + 12x} / ( 2x - 3 ) ( x + 1 )

{ 2x^2 + 5x - 3 } / ( 2x - 3 ) ( x + 1 )

( 2x - 1 ) ( x + 3 ) / ( 2x - 3 ) ( x + 1 )

Answer:

Hey there!

We can write the proportion:

[tex]88/4840 = x/1155[/tex]

101640=4840x

x=21

The car would need 21 gallons of gas to travel 1155 miles.

Let me know if this helps :)

Answer:

21 gallons

Step-by-step explanation:

4,840 miles = 88 gallons

=> 1155 miles = x gallons

=> Cross-multiply

=> 4840 * x = 1155 * 88

=> 4840x = 101640

=> 4840x/4840 = 101640/4840

=> x = 21

The car can travel 1,155 miles using 21 gallons.

Answer:

12i

Step-by-step explanation:

Step 1: Write it out

√-144

Step 2: Factor

√144(√-1)

Step 3: Evaluate

12i

Answer:

A)5/8

Step-by-step explanation:

Given data set:

Rewriting the data set in the same denominator to compare:

As we see the smallest value is 5/8 and the highest value is 10/8, so the difference:

So, the range of the given data set is 5/8

Correct choice is: A)5/8

The relation {(3, 4), (-3, 8), (6, 8)}, is a function, because

all the x–coordinates are different.

It's important to understand that even though two of the y-coordinates

are the same, this relation is still a function.

The y-coordinates do not have any affect

on whether the relation is a function.

Answer:

A) No solution

Step-by-step explanation:

The absolute value of a quantity is either zero or positive. It cannot be negative.

For the absolute value of a quantity to be less than or equal to -1, it means the absolute value of the quantity is negative. This cannot be, so there is no solution.

Answer: A) No solution

Answer:

no solutions

Step-by-step explanation:

An absolute value is non negative

The smallest value of an absolute value is 0

0 ≤ -1

This is never true so there is no solution

Answer:

The colony of bats will take 1.612 hours to cover an area of 80,000 square miles.

Step-by-step explanation:

As the colony of bats emerges from a cave and spreads out in a circular pattern, the area covered ([tex]A[/tex]) by the colony, measured in square miles, is represented by the following geometrical formula:

[tex]A = \pi\cdot r^{2}[/tex]

Where:

[tex]r[/tex] - Distance of the bat regarding the cave, measured in miles.

In addition, each bat moves at constant speed and distance is represented by this kinematic formula:

[tex]r = r_{o}+\dot r \cdot \Delta t[/tex]

Where:

[tex]r_{o}[/tex] - Initial distance of the bat regarding the cave, measured in miles.

[tex]\dot r[/tex] - Speed of the bat, measured in miles per hour.

[tex]\Delta t[/tex] - Time, measured in hours.

The distance of the bat regarding the cave is now substituted and time is therefore cleared:

[tex]A = \pi \cdot (r_{o}+\dot r \cdot \Delta t)^{2}[/tex]

[tex]\sqrt{\frac{A}{\pi} }-r_{o} = \dot r \cdot \Delta t[/tex]

[tex]\Delta t = \frac{1}{\dot r} \cdot \left(\sqrt{\frac{A}{\pi} }-r_{o} \right)[/tex]

Given that [tex]\dot r = 99\,\frac{mi}{h}[/tex], [tex]A = 80,000\,mi^{2}[/tex], [tex]\pi = 3.14[/tex] and [tex]r_{o} = 0\,mi[/tex], the time spent by the colony of bats is:

[tex]\Delta t = \left(\frac{1}{99\,\frac{mi}{h} } \right)\cdot \left(\sqrt{\frac{80,000\,mi^{2}}{3.14} }-0\,mi \right)[/tex]

[tex]\Delta t \approx 1.612\,hours[/tex]

The colony of bats will take 1.612 hours to cover an area of 80,000 square miles.

Answer:

B:  1.6 hours

Step-by-step explanation:

Answer:

170

Step-by-step explanation:

17 dogs per 30 students or 17/30

Same ratio for 300 students:

So 170 students have a dog

Answer:

the answer would be G.12

Step-by-step explanation:

Answer: 700 billion

Step-by-step explanation:

Answer:

A. {e, h}

Step-by-step explanation:

In a Venn diagram, the set of elements in any intersection can simply be visualised. The elements contained in the region where the circles representing different sets overlap, are the set of elements of intersection.

In the Venn diagram given, the set of elements contained in the region where the circles representing A and B overlap are {e, h}.

{e, h} is common to both set A and set B.

Answer:

3

Step-by-step explanation:

16+5f=31

5f=31-16

5f=15

f=3

CHECK:

16+5(3)=31

16+15=31

31=31

since e=-14 in the first equation, the last one is

-14-3=-17, which is correct

Answer:

x and y is 115 exterior angle property

Answer:

[tex]\boxed{x = 65, y=50}[/tex]

Step-by-step explanation:

→ We know that angles on a straight line add up to 180° so we can use that to work out angle x

x + 115° = 180°

⇒ Minus 115° from both sides to isolate x

x = 65°

→ We can see that there are 2 angles labelled x so we can use that to find the value of y

65° × 2 = 130°

→ We utilise the angle fact that angles in a triangle add up to 180°

130° + y = 180°

⇒ Minus 130° from both sides to isolate y

y = 50°

Answer:

2 2/3 hours

Step-by-step explanation:

Before it was 5 hours for 1 guitar, or 5 hours/guitar

Now it is 7 guitars in 3 hours or 7/3 hours/guitar

7/3 = 2 1/3

5 hours - 2 1/3 hours = 15/3 hours - 7/3 hours = 8/3 hours = 2 2/3 hours

The reduced the time it takes to build 1 guitar by 2 2/3 hours.