In 2010 an item cost $9.00. The price increase by 1.5% each

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

Answer:

M=2,179.29

The average exceeds the estimate

Her expenses would need to be $1,625.00

Step-by-step explanation:

1.) What is the mean of her friends' personal expenses?

The mean is defined as the average expense value, calculated as follows:

2.) Is the average higher or lower than the estimate?

Given the estimate of $2,110, the average is indeed higher than this estimate.

3.)What amount of personal expenses would Ashley need to maintain a combined average of $2,110 with her friends' amounts for that school year?

Her needed amount of expenses would be $1,625.00.

Answer:

The earnings gap, over a career spanning 30 years, between men and women totals $1,200,150

Step-by-step explanation:

Calculated annually.

The typical male earns $90,761 each year.

The typical female earns $50,756 per annum.

Therefore, the annual difference is:

90,761 - 50,756 = 40,005

Across 30 years:

30*40,005 = 1,200,150

The earnings gap over a 30-year career, when comparing men and women, is $1,200,150

Answer:

First, we must calculate the slope

m=Y2-Y1/X2-X1

= 9 - (-6) / 12 - (-8)

= 15/20

= 3/4

Therefore, the equation with the slope of 3/4 is Y=3/4x

The triangle is positioned within the circle, with its vertices lying on the circle's edge - since the center of the circle is located on the hypotenuse, that hypotenuse serves as the diameter (D) of the circle.

:

D = 120 feet

:

Calculating the circumference of the circle gives: 22/7 * 120 = 377.14 feet.

The perimeter of the triangle is calculated as 120 + 60 + 103.92 = 283.92

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1) The combined distance around both circle and triangle totals 661.06 feet.

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2) The vertices for the triangle's central area must touch the circular pool - to find the center of the pool, draw perpendicular bisectors from two of the triangle's sides; where they meet is the center.

The distance from the center to any vertex of the triangular area represents the radius of the

circular pool.

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3) The intersection of the triangle's angle bisectors indicates the center of the shark tank.

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4) The pool's volume is calculated as ((π * 60^2) - area of triangle) * 4 =

(11314.285) - (1/2 * 103.92 * 60) * 4 = 32786.74 cubic feet.

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5) 8196.685 * x < 30000

x < 3.66 feet

The average depth needs to be below 3.66 feet

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