Dean Field is a bookkeeper for a retail shop. He is super excited about his upcoming two-week vacation to Hawaii. His flight leaves to Honolulu at 7pm on Friday. At 4:45pm on Friday he realizes the company’s trial balance is a mess and it does not balance. He places random numbers in the General Ledger system to make it balance and leaves the office to catch his flight. He knows he can correct the situation when he returns from his vacation. What are your thoughts about this case?

The number of students that were absent is; 24

Let the total number of students be x .

The number of students which were absent = ¹/₃x.

Number of students which were present = ²/₃x

Thus;

Number of students who attended math's test = ¹/₂x

Number of students who attended physics test = ¹/₄x

No. of students who attended both tests = 6

A denotes number of students who attended math's test

B denotes number of students who attended physics test

Thus;

n(A) = ¹/₂x

n(B) = ¹/₄x

n(A ∩ B) = 6

n(A∪B) = number of students which were present

Thus;

n(A ∪ B) = n(A) + n(B) − n(A∩B)

²/₃x = ¹/₂x + ¹/₄x − 6

²/₃x = ³/₄x - 6

³/₄x - ²/₃x = 6

x = 72

Thus, number of students that were absent = ¹/₃ * 72

Number of students that were absent = 24

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Answer:

Exact form: -3/2

Decimal Form: -1.5

Step-by-step explanation:

Hello there!

We need to find out the slope of the given two coordinates/points, that are:

Solution:

We'll need to use the formulae that is used to find out the slope,that is:

[tex] \pink{\star}\boxed{\rm \: Slope = \cfrac{y_2 -y_1}{x_2 - x_1}} \pink{\star}[/tex]

According to this question,here:

So substitute them accordingly:

[tex] \rm \: m = \cfrac{ - 6 -( 6)}{8 - 0} [/tex]

Simplify using PEMDAS rule.

[tex] \rm \: m = \cfrac{ - 12}{8} [/tex]

-12/8 could be canceled.

[tex] \rm \: m = \cfrac{ - 6}{4} [/tex]

-6/4 could also be canceled.

[tex] \boxed{ \rm \: m = \cfrac{ - 3}{2} \: or \: - \cfrac{3}{2} }[/tex]

Or it could be represented as decimal:

[tex] \boxed{ \rm \: m = - 1.5}[/tex]

Hence , the slope m will be -3/2 or -1.5

[tex] \rule{225pt}{2pt}[/tex]

Answer:

X=60°

Step-by-step explanation:

Because the sum of angle of all side of a triangle is 180°

and

if that goes on

the equation become

x°+75°+45°=180°

x°+120°=180°

x°=180°-120°

x°=60° hence prove

Answer:

a negative linear association (C)

Re-Written Problem [Formatted]

Teams with varying numbers of players are playing a group card game. the time taken by each team to complete one game is given in the table. What is the relationship between the two variables?

Numbers of players on team are going to be 1, 2 , 3, 4, 5.

time taken to complete game (in minutes) 32, 26, 20, 14, 8

(Select the correct answer)

A. Positive linear association

B. Exponential relationship

C. Negative linear association

D. No relationship

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

Step-by-step explanation:

Lower x values (numbers of players on team) are correlated with higher y values (time taken to complete game)

[note: I know which values are x and y because of a cause-and-effect relationship. x causes y. number of players causes a change in minutes {it wouldn't make sense for the number of time it took to cause the number of players} ]

So, if we were to graph this relationship, we would see a downward-slope / negative slope of a line, because greater x-values are associated with lower y-values.

So, you would see a negative line, showing a negative linear association.

Answer:

4/7=12/21

18/20=9/10

6/5=30/25

81/90=9/10

Step-by-step explanation:

12 / 21  will be equal to 4/7 and is denoted in the simplest form.

A fraction that possesses the same value as another fraction regardless of how it's denominators and numeric components could be different is said to be equivalent.

12 / 21 can be simplified with the help of 3. This will result in 4/7.

18/20 can be simplified with the help of 2. This will result in a 9/10.

30/25 can be simplified with the help of 5. This will result in 6/5.

81/90 can be simplified with the help of 9. This will result in a 9/10.

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Answer:

33 blocks

Step-by-step explanation:

Given the length , breath and height for small block  6cm, 4cm, and 2cm an d for large 2m = 200cm, 4cm and 2cm.

volume is given by  

             V = Length x breath x height

Volume of small block = 6 x 4 x 2 = 48 cm^3

Volume of big block = 200 x 4 x 2 = 1600 cm^

No of blocks = Volume of big block/ volume of small block

                     = 1600/48

                     = 33.33

Therefore no of blocks formed = 33

Answer: $5.99 is the answer hope this helps!

Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

Using it's formula, it is found that the mean of the discrete random variable is given by:

B. 30.47.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence, considering the table, the mean of the discrete distribution is:

E(X) = 23 x 0.16 + 25 x 0.09 + 26 x 0.18 + 31 x 0.12 + 34 x 0.24 + 38 x 0.21 = 30.47.

Hence option B is correct.

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The other root is 1 and the value of the coefficient q is 12.

A quadratic equation is a second-order polynomial equation in a single variable x. ax²+bx+c=0. with a ≠ 0 .

Given:

x²-13x+q=0

when x= 12

So, 12²-13*12+q=0

144-156+q=0

-12+q=0

q=12

Now, x²-13x+12=0

x²-12x-x+12=0

x(x-12) - 1(x-12)=0

(x-1)(x-12)=0

x=1, 12

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Answer:

b

Step-by-step explanation:

because it is 4 dolls and x is the amount of dollars 1 doll is and 4x dolls are less then 102, the only answer that makes sense is b

The answer is B. I will choose to explain by process of elimination. It is not A because it is not less than or equal to, it is just less than. Therefore, we can also eliminate C. It is not D because it is four dolls that cost the same so it is 4x instead of 4+x. I hope I helped!

Answer: 2556

Step-by-step explanation:

Let the amount of the deposit be x dollars

The amount of simple interest earned can be represented by the formula PRT/100

Where,

P is the amount of deposit

R is the annual rate of interest

T is the time in years

Therefore,

P=x

R=6

T=150/360 = 15/36 = 5/12

So,

Simple interest = x(6)(5)/1200

63.90 = 30x/1200

63.90= x/40

x= 63.90×40

x=2556

Therefore, amount deposited = 2556

Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)

The greatest common factor is the value that will divide an expression without leaving a remainder.

Given the expression 21xy + 14y

Find the factors

21xy = 7 * 3 * x * y

14y = 7 * 2* y

Since 7y is common to both factors, hence the GCF of the expression is 7y. The factored form will be 7y(3x + 2)

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By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.

We know that the average temperature is given by the equation:

f(x)=31cos(0.0055πx)+88

And it is in Fahrenheit degrees.

To get the lowest average temperature, we just need to find the minimum of the above function.

Remember that the minimum of the cosine function is:

cos(x) = -1

Then the lowest value of the above function is:

f(x₀) = 31*(-1) + 88 = 57

From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.

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Answer:

2

Step-by-step explanation:

4 halves=2

1 half=0.5

2 halves=1

3 halves=1.5

4 halves=2

Answer:

Step-by-step explanation:

(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.

(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.

(3) By definition, all angles of a regular polygon are congruent.

(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.

(5) This is true. (See statement (1)).

Answer:

Options B, C, E

Step-by-step explanation:

Answer: 920.3 ft

Step-by-step explanation:

[tex]\tan 7^{\circ}=\frac{113}{x} \\ \\ x(\tan 7^{\circ})=113 \\ \\ x=\frac{113}{\tan 7^{\circ}} \approx \boxed{920.3 \text{ ft}}[/tex]

Answer:

(2,0)

Step-by-step explanation:

The intersecting points of the two lines is the solution for the two equations.

(2,0) is the solution.

Using the figure given, The one equation that matches with the diagram is 3x=30-6.  The diagram that matches the equation circled is given in the image attached.

From the above, we can see that the equation that matches with the diagram are:

Note that for 3(x+6)=30

3x +  18 = 30

3x = 30-18

3x = 12

x = 12/3

x = 4

Then fixing x into the equation =

3(x+6)=30

3(4+6)=30

Therefore , 12 + 18 will give us 30 and the answer is straight forward. The same applies for 30=3x+6 and 6+3x=30 as the answer is straight forward.

But the one equation that does not matches with the diagram is 3x=30-6 because its output is not straight forward.

3x =30-6

3x = 24

x = 24/3

x = 8

Fixing 8 into the equation

3x = 30-6

3(8) = 24

=24 is the  answer and not 30

Therefore, Using the figure given, The one equation that matches with the diagram is 3x=30-6.

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Answer:

it’s C, 5.2

hope i helped

ur wlcm :)

correct me if im wrong

Answer: [tex]a+b+\sqrt{a^{2}+b^{2}}[/tex]

Step-by-step explanation:

The distance from (0,b) to (0,0) is b.

The distance from (0,a) to (0,0) is a.

Using the Pythagorean theorem, the distance from (0,b) to (a,0) is [tex]\sqrt{a^{2}+b^{2}}[/tex]

So, the perimeter is [tex]\boxed{a+b+\sqrt{a^{2}+b^{2}}}[/tex]

Answer:

81

Step-by-step explanation:

for example log2 8=3 is the same as 2^3=8, so if you switch around the variables from your question, your able to do 3^4, which is 81

(f+g)(x)  

= f(x) + g(x)

= 4x^2 +5x -3 + 4x^3 -3x^2 +5

= 4x^3+x^2+5x+2

Answer:

135

Step-by-step explanation:

3b + B = 180

4b = 180. ÷4

b = 45

a = 135

Answer:

A. true

Step-by-step explanation:

"f(x) = ... " is the classic way of writing a function.