30 POINTS!!<br><br> Which construction correctly shows how to bisect ∠X?

The Atlantic bluefin tuna is the largest and most endangered of the tuna species. They are found throughout the North Atlantic O

Maksim231197 [3]

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

3 0

2 years ago

A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to th

solmaris [256]

Answer:

Total number of riders that ride on carpool daily = 2000

Total Cost of one way ticket = $ 5.00

Total Amount earned if 2000 passengers rides daily on carpool = 2000 × 5

= $10,000

If fare increases by $ 1.00

New fare = $5 + $1

= $6

Number of passengers riding on carpool = 2,000 - 100 = 1,900

If 1,900 passengers rides on carpool daily , total amount earned ,if cost of each ticket is $ 6 = 1900 × $6 = $11400

As we have to find the inequality which represents the values of x that would allow the carpool service to have revenue of at least $12,000.

For $ 1 increase in fare = (2,000 - 1 × 100) passengers

For $ x increase in fare, number of passengers = 2,000 - 100·x

= (2,000 - 100·x) passengers

New fare = 5 + x

New Fare × Final Number of passengers ≥ 12,000

(5+x)·(2,000 - 100 x) ≥ 12,000

5 (2,000 - 100 x) + x(2,000 - 100 x) ≥ 12,000

10,000 - 500 x + 2,000 x - 100 x² ≥ 12,000

100 - 5 x + 20 x - x² ≥ 120

- x² + 15 x +100 - 120 ≥ 0

-x² + 15 x -20 ≥ 0

x² - 15 x + 20 ≤ 0

⇒ x = 1.495

x ≥ $ 1.495, that is if we increase the fare by this amount or more than this the revenue will be at least 12,000 or more .

Also, f'(x) = 0 gives x = 7.5

⇒ The price of a one-way ticket that will maximize revenue is $7.50

7 0

2 years ago

A discount store normally sells DVDs for $14.44. If the DVDs go on sale for $13.72, which of the following is closest to the per

Xelga [282]

Answer:

4.9%

Step-by-step explanation:

To find the percentage you first find the decrease in price, divide it by the original price then multiply it by 100.

(14. 44-13. 72)

= -------------------- ×100

14. 44

0. 72

= -------- × 100

14. 44

= 0. 72× 6. 925207759

= 4. 986149584

~ 4. 9

5 0

2 years ago

A 12-centimeter rod is held between a flashlight and a wall as shown. Find the length of the shadow on

choli [55]

Answer:

48 cm

Step-by-step explanation:

Given:

Distance of rod from the wall = 45 cm

Distance of rod from the light = 15 cm

Length of rod = 12 cm

We can see that <DAM and <BAF are equal

Also, <DMA and <BFM are equal because they are corresponding angles

To find the length of the shadow, let's take the equation

$\frac{DM}{BF} = \frac{AM}{A.F}$

Where.:

DM = ½ of length of the rod = ½*12 = 6

A.F = 15 + 45 = 60 cm

AM = 15 cm

Therefore,

$\frac{DM}{BF} = \frac{AM}{A.F}$

$= \frac{6}{BF} = \frac{15}{60}$

Cross multiplying, we have:

15 * B.F = 60 * 6

15 * B.F = 360

$BF = \frac{360}{15}$

BF = 24 cm

The shadow on the wall =

2 * BF

= 2 * 24

= 48 cm

The shadow on the wall is 48 cm

7 0

1 year ago

In regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample point the sample space S for

Minchanka [31]

Answer:

i) There are 40320 possible orders

ii) There are 336 possible orders for the first 3 positions.

Step-by-step explanation:

Given: The number of finalists = 8

The number of boys = 3

The number of girls = 5

To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!

The number of possible orders = 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.

nPr = $\frac{n!}{(n - r)!}$

Here n = 8 and r = 3

Plug in n =8 and r = 3 in the above formula, we get

8P3 = $\frac{8!}{(8 - 3)!}$

= $\frac{8!}{5!} \\= \frac{1.2.3.4.5.6.7.8}{1.2.3.4.5}$

= 6.7.8

= 336

So there are 336 possible orders for the first 3 positions.

3 0

2 years ago

30 POINTS!! Which construction correctly shows how to bisect ∠X?