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2 years ago

Write the inequality represented by the graph below.

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

6 0

Answer:

y > -x + 3

Step-by-step explanation:

find the slope and y-intercept so you can create a linear equation:

y = mx + b ; m = slope and b = y-intercept

slope (m) = (3-0) / (0-3)

m = 3/-3 or -1

we can see the y-intercept by looking at the graph, it is 3

y > -x + 3

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19) Suppose that there are 55 Democrats and 45 Republicans in the US Senate. A committee of seven senators is to be formed by se

andre [41]

Answer:

Probability = 0.12676992

Step-by-step explanation:

The probability of selecting committee of seven composed of all Democrats.

Total number = 45+55= 100

Number of Democrats = 55

Number of committee = 7

Probability= (55C7)/(100/7)

Where C represent combination sign

Probability = (202927725/1.60075608*10^10)

Probability = 0.12676992

7 0

3 years ago

Two cars, one going due east at 25 m / sec and the second going due south at 50/3 m / sec are traveling toward the intersection

valkas [14]

Answer:

30 m/s

Step-by-step explanation:

Let's say the distance from the first car to the intersection is x, and the distance from the second car to the intersection is y.

The distance between the cars can be found with Pythagorean theorem:

d² = x² + y²

Taking derivative with respect to time:

2d dd/dt = 2x dx/dt + 2y dy/dt

d dd/dt = x dx/dt + y dy/dt

We know that x = 200, dx/dt = -25, y = 150, and dy/dt = -50/3.

To find dd/dt, we still need to find d.

d² = x² + y²

d² = (200)² + (150)²

d = 250

Plugging everything in:

250 dd/dt = (200) (-25) + (150) (-50/3)

dd/dt = -30

The cars are approaching each other at a rate of 30 m/s at that instant.

4 0

3 years ago

5. If f(x) = -x2 - 7x +4 and g(x) = -5x - 3, what is the value of f(-2)-g(6)

Alex787 [66]

9514 1404 393

Answer:

Step-by-step explanation:

Evaluate the functions and find the required difference.

f(-2) = -(-2)^2 -7(-2) +4 = -4 +14 +4 = 14

g(6) = -5(6) -3 = -33

Then the difference is ...

f(-2) -g(6) = 14 -(-33) = 14 +33 = 47

5 0

3 years ago

pls solve quickly!: It took a boat 2 hours to reach town A going upstream. The way back was 1h20 min. What is the speed of the b

goldenfox [79]

Answer:

15 mph

Step-by-step explanation:

Given: Boat took 2 hours to reach Town A going upstream.

Speed of stream= 3 mph

Time taken to reach back home= 1 hours 20 minutes

Lets assume distance covered one side be "d" and speed of boat in still water be "s".

∴ Speed of boat in upstream= $(s-3) \ mph$

Speed of boat in downstream= $(s+3)\ mph$

Also converting into fraction of time taken to reach back home.

Remember; 1 hour= 60 minutes

∴ Time taken to reach back home= $60+20= 80\ minutes$

Converting time given into fraction= $\frac{80\ minutes}{60\ minutes} = \frac{4}{3} \ hours$

hence, Time taken to reach back home is $\frac{4}{3} \ hours$

Now forming equation of boat travelling upstream and downstream, considering distance remain constant.

We know, $Distance= speed \times time$

⇒ $(s-3)\times 2= (s+3)\times \frac{4}{3}$

Using distributive property of multiplication

⇒ $2s-6= \frac{4}{3}s +4$

subtracting both side by $\frac{4}{3} s$

⇒ $2s-\frac{4}{3} s-6= 4$

Adding both side by 6

⇒ $2s-\frac{4}{3} s= 10$

taking LCD as 3

⇒ $\frac{2}{3} s= 10$

Multiplying both side by $\frac{3}{2}$

⇒ $s= \frac{3}{2} \times 10$

∴s= 15 mph

Hence, 15 mph is the speed of the boat in still water.

8 0

3 years ago

According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the nu

mixer [17]

Answer:

1.66

Step-by-step explanation:

Calculation to find the standard deviation for the random variable X of the number of students who work full time in samples of size

Using this formula

Standard deviation(X)=√np(1−p)

Where,

n represent the number of students=16

p represent the percentage of all students who work full time=22

Let plug in the formula

Standard deviation(X)=√16(0.22)(1−0.22)

Standard deviation(X)=√(3.52)(0.78)

Standard deviation(X)=√2.7456

Standard deviation(X)=1.656

Standard deviation(X)=1.66 (Approximately)

Therefore the standard deviation for the number of students who work full time in samples of size 16 will be 1.66

8 0

3 years ago