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exis [7]
3 years ago
10

The yoga instructor at Universe Fitness spent $1,925 on 200 items for the upcoming yoga seminar. He purchased yoga mats for $12.

50 each, yoga towels for $8.00 each, and carrying cases for $10.00 each*. He purchased twice as many towels as mats.
Part A: Define variables and write a system of equations to represent the situation.

Part B: The instructor’s bookkeeper was auditing books. She noticed that in this transaction, the instructor purchased 200 items: 25 mats, 50 towels, and 125 carrying cases. Are the records accurate? Justify your answer.
Mathematics
1 answer:
Alex17521 [72]3 years ago
4 0

Answer:

The auditing book is not accurate

Step-by-step explanation:

25($12.5)+50($8)+125($10)+= $1,925

$312.5 + $400 + $1,250 = $1,925

$1,962.5 not= to $1,925

You might be interested in
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Salsk061 [2.6K]

When two lines intersect at 90° degrees angle, the lines are perpendicular to each other. Two perpendicular lines, their slope will give a product of -1

i.e. if the first's line slope is 5, then the second line's will be -1 ÷ 5 = -¹/₅

To find the slope of a line, we divide the vertical distance by the horizontal distance. 

We'll use the trial and error method to find the right pairing

Let's start with A(3, 3) and B(12, 6)

Vertical distance = 

Horizontal distance = 

The slope AB = ³/₉ = ¹/₃

We want BC to have a slope -1 ÷ ¹/₃ = -3

Try C(16, -6); check the slope with B(12, 6)

Vertical distance = 

Horizontal distance = 

Slope of BC = -12 ÷ 4 = -3

The slope BC = -3 is the value we want so, tile 1 pair with tile 4

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

Let's do A(-10, 5) and B(12, 16)

Vertical distance = 16 - 5 = 11

Horizontal distance = 12 - -10 = 22

Slope AB = ¹¹/₂₂ = ¹/₂

The perpendicular slope would be -1 ÷ ¹/₂ = -2

Try C(18, 4)  with B(12, 16)

Vertical distance = 16 - 4 = 12

Horizontal distance = 12 - 18 = -6

Slope BC = ¹²/₋₆ = -2

Slope BC and slope AB perpendicular, so tile 3 matches with tile 6

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

Let's try A(12, -14) and B(-16, 21)

Vertical distance = 21 - -14 = 35

Horizontal distance = -16 - 12 = -28

The slope AB = ³⁵/-₂₈ = ⁵/₋₄

We need the perpendicular slope to be -1 ÷ -⁵/₄ = ⁴/₅

Try C(-11, 25)

Vertical distance with B = 25 - 21 = 4

Horizontal distance with B = -11 - -16 = 5

The slope = ⁴/₅

Tile 7 matches tile 8

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

Take A(-12, -19) and B(20, 45)

Vertical distance = 45 - -19 = 64

Horizontal distance = 20 - -12 = 32

Slope AB = ⁶⁴/₃₂ = 2

We need the perpendicular slope to be -1 ÷ 2 = -¹/₂

We have C(6, 52) and checking the slope with B(20, 45)

Vertical distance = 45 - 52 = -7

Horizontal distance = 20 - 6 = 14

The slope is ⁻⁷/₁₄ = -¹/₂

Tile 9 pairs with tile 2

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

Conclusion

Tile 1 ⇒ Tile 4

Tile 3 ⇒ Tile 6

Tile 7 ⇒ Tile 8

Tile 9 ⇒ Tile 2

Tile 5 and Tile 10 do not have pairs

5 0
3 years ago
In a class of 40 students, the number of girls is 10 more than the number of boys. We have to find the number of girls and the n
Nadusha1986 [10]

Answer:

b=15 g=25

Step-by-step explanation:

lets translate that story problem to mathematics equations

the problem told that no. of girls are 10 more than no of boys so this will =

g=b+10

then in class there are 40 students that means

g+b=40

now we have to equations with two variables then we should substitute

(b+10)+b=40

lets remove the brackets

2b+10=40 subtract 10 from both sides

2b=30 now divide both by 2

b=15 so g=25 after you write the equation once again with the new proof or number

6 0
2 years ago
Helpppp I need this for rn thank youuuuu❤️
irinina [24]

Answer:

-1,7

0,-3

1,-7

5,47

Step-by-step explanation:

-x-=+

6 0
3 years ago
Read 2 more answers
Almost all companies utilize some type of year-end performance review for their employees. Human Resource (HR) at a university's
balu736 [363]

Answer:

The Answer is 76.

Step-by-step explanation:

Given the normal distribution " 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable'',  we can see that exemplary employees are top 10% rated employees.

We have the formula for normal distribution:

z=(X-M)÷σ

where z is the <em>minimum z-score </em>for top 10% employee, X is the <em>minimum </em>score for top 10% employee, M is the <em>mean</em> of the score distribution, σ is the <em>standard deviation</em> of the score distribution.

The z-score we are looking for is the value "a" that separates the highest 10% from the lowest 90% i.e. P(z≤a)=0.90

If we look at z-table, corresponding value for a is 1.28155

We can now put the values in the formula:

1.28155=\frac{X-50}{20}

So X=(1.28155×20)+50=75.631

Therefore minimum score for exemplary employee is 76.

3 0
3 years ago
A sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. Turning the radius-reduction screw on t
zheka24 [161]

Answer:

Area_lawn = 393.75 π ft^2

Step-by-step explanation:

Maximum radius : 30 feet

Minimum radius:  30 feet - 0.25*(30feet)  =  22.5 feet

(25 percent reduction)

To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.

Since the sprinklers have a circular area:

Area = π*radius^2

Max area  = π*(30 ft)^2 = 900π ft^2

Min area  = π*(22.5 ft)^2 = 506.25π ft^2

Maximum area of lawn that can be watered by the sprinkler:

Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2

Area_lawn = 393.75 π ft^2

5 0
3 years ago
Read 2 more answers
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