Many gas stations give a discount for using cash instead of a credit card. A gas station gives a discount of 10 cents per gallon

Each 16-ounce serving contains 330 mg of caffeine. For 8-ounce servings:
330 mg divided by 2 equals 165 mg.
The limit for caffeine intake is capped at 600 mg.
Calculating for three servings: 165 mg * 3 = 495 mg, which is under the limit.
Calculating for four servings: 165 mg * 4 = 660 mg, exceeding the maximum amount.
Thus, a person can consume 3 full 8-ounce servings daily while remaining within the safety limit.

Result:

6.1°; 425.86 m.

Step-by-step breakdown:

The information provided states that the airplane is at an altitude of 5.7 miles above ground level, while the "radius of Earth is about 4000 miles." Thus,

θ = 2 × cos^-1 (a/ (a + b)), where a = 4000 miles, and b = 5.7 miles.

θ = 2 × cos^-1 (4000/ (4000 + 5.7)) = 6.1°.

To calculate the distance in meters:

Change in distance = 6.1° /360° × 2π × 4000 miles = 425.86 meters.

Consequently, BD⌢ measures at 6.1° and the distance corresponding to this section of Earth is 425.86 meters.

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice's formula is applicable for any t > 0 minutes, while Briana’s is only applicable when

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They complete the race when their total distance equals 5 kilometers. For Alice:

t/4 = 5

t = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 25

2t = 26

t = 13 minutes

c. They reach the same point when they have traveled the same distance, expressed as:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using the quadratic formula:

Only the second solution fits this scenario because the race concluded before they took 31.49 minutes.

The y-coordinate of P' is -10.

Step-by-step explanation:

It is given that triangle PQR has vertices at P(–2, 6), Q(–8, 4), and R(1, –2).

The translation rule is

To determine the image of point P, referred to as P', we must substitute the coordinates of P(-2,6) to arrive at;

Thus, the y-coordinate of P' is -10.

Answer
The resultant number is 412630