Find the x is qs bisects pqr and pqr=82

Mr. Barth is creating an arrow across the school parking lot. The area covered by the arrow is calculated to be 70 square units. Step-by-step explanation: I've marked the points on a coordinate grid and connected them with a rough red line, which is shown in the attached image. The arrow's shape consists of a triangle and a rectangle. Therefore, the total area of the arrow equals the triangle's area plus the rectangle's area. The triangle's area is determined using the formula 0.5 * base * height, where the base measures 12 units while the height is 7 units, giving an area of 42. The rectangle's area is calculated as length * height, where length equals 7 and height equals 4, resulting in an area of 28. Hence, the total area of the arrow equals 42 + 28 = 70 square units.

Answer:

40%

Step-by-step explanation:

According to the provided information:

The likelihood of rain on Saturday stands at 25%.

P(Sunday)=25%=0.25

If it rains on Saturday, the probability of rain on Sunday rises to 50%.

P(Sunday|Saturday)=50%=0.5

If it does not rain on Saturday, the chance of Sunday rain is 25%.

P(Sunday|No Rain on Saturday)=25%=0.25

We aim to find the probability of rain on Saturday given that it rained on Sunday, P(Saturday|Sunday).

P(No rain on Saturday)=1-P(Saturday)=1-0.25=0.75

Using Bayes' theorem for conditional probabilities:

P(Saturday|Sunday)=

=

=0.4

Thus, there is a 40% likelihood that it rained on Saturday given the conditions on Sunday.

Answer:

Let the train's speed be denoted as x km/h.

Scenario 1:

Distance = 288 km

Speed = x km/h

Time = Distance divided by Speed

= 288/x hours

Scenario 2:

Distance = 288 km

Speed = (x + 4) km/h

Time = 288/(x + 4) hours

As 288/x is greater than 288/(x + 4)

288/x - 288/(x + 4) = 1

288[1/x - 1/(x + 4)] = 1

[x + 4 - x] / [x(x + 4)] = 1/288

[4 / (x^2 + 4x)] = 1/288

x² + 4x = 1152

x² + 4x - 1152 = 0

x² + 36x - 32x - 1152 = 0

x(x + 36) - 32(x + 36) = 0

(x + 36)(x - 32) = 0

x + 36 = 0, x - 32 = 0

x = -36, x = 32

x = -36 is not valid as speed cannot be negative.

Conclusively, the train's speed = 32 km/h

Answer:

15.7 inches

Step-by-step breakdown:

A slice of a round pie is a sector of a circle.

The perimeter of a slice equals the arc length s plus two times the radius r. P = s + 2r

s = rθ = r(16/360) = r/22.5. Therefore,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826

D = 2r = 2 × 7.826 = 15.7 inches

Thus, the diameter of the cake should be 15.7 inches.

Verification:

It is accurate.

 

Answer:

• The profit can be expressed as 70x + 50
• If 240 phones are sold, the profit amounts to $16,850

Detailed explanation:

The revenue function R(x) is provided as

The cost function C(x) is given as

Profit is calculated by subtracting cost from revenue, expressed as Profit = Revenue − Cost

We substitute the given revenue and cost functions into this formula.

Denote the profit function as P(x).

Therefore, the profit function formula simplifies to 70x + 50

Since x denotes the quantity of phones sold, to find the profit when 240 phones are sold, we substitute x = 240 into the profit expression above.

Hence, selling 240 phones yields a profit of $16,850