MATHEMATICS COLLEGE

3. (03.06) Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2​

Answers

Answer 1
Answer:

Answer:

The answer is

\huge y + 3 = (1)/(2) (x - 6) \n

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

y - y_1 = m(x - x_1)

where

m is the slope

( x1 , y1) is the point

From the question we have the final answer as

y + 3 = (1)/(2) (x - 6) \n

Hope this helps you

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The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9.Required:
a. What is the probability that he must stop at both signals?
b. What is the probability that he must stop at the first signal but not at the second one?
c. What is the probability that he must stop at exactly one signal?

Answers

Answer: a. 0.05

b. 0.40

c. 0.85

Step-by-step explanation:

Let F= Event that a certain motorist must stop at the first signal.

S =  Event that a certain motorist must stop at the second signal.

As per given,

P(F) = 0.45 , P(S) = 0.5 and P(F or S) = 0.9

a. Using general probability formula:

P(F and S) =P(F) + P(S)-  P(F or S)

= 0.45+0.5-0.9

= 0.05

∴ the probability that he must stop at both signals = 0.05

b. Required probability = P(F but (not s)) = P(F) - P(F and S)

= 0.45-0.05= 0.40

∴ the probability that he must stop at the first signal but not at the second one =0.40

c. Required probability = P(exactly one)= P(F or S) - P(F and S)

= 0.9-0.05

= 0.85

∴   the probability that he must stop at exactly one signal = 0.85

Final answer:

The probability of stopping at both signals is 0.225, the probability of stopping at the first one but not the second one is 0.225. The probability of stopping at exactly one signal is 0.675.

Explanation:

The probability theory can be used to answer these questions. The probabilities of stopping at various traffic signals can be calculated using some assumptions about the independence of the events.

  1. The probability of the motorist having to stop at both signals can be found by multiplying the individual probabilities, assuming that these are independent events. So, P(stop at both signals) = P(stop at first signal) * P(stop at second signal) = 0.45 * 0.5 = 0.225.
  2. The probability of him stopping at the first signal but not at the second one is again found by multiplying the probability of stopping at the first by the probability of not having to stop at the second. Therefore, P(stop at first, not at second) = 0.45 * (1 - 0.5) = 0.225.
  3. To find the probability that the driver must stop at exactly one signal, we can subtract the probability of stopping at both signals from the probability of stopping at least one signal. So, P(stop at one signal) = P(stop at at least one signal) - P(stop at both signals) = 0.9 - 0.225 = 0.675.

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Jose can eat 5/8 of a pizza in 1/4 hours. How many hours will it take him to eat the whole pizza?

Answers

Answer: 2/5 of an hour

Step-by-step explanation:

ok so 5/8 = .625 just to begin with...

and as a ratio it would be .625 = .25

                                            8/8 (1)    

So I did .25x1=.25

.25x.625= 0.4 or as a fraction 2/5

If x2 = 40, what is the value of x?

Answers

if you mean 2x=40 x=20 
but if you mean x^2=40 i think its x=80
You have to divided by 2 on both sides and you get x=20. Checking your answer you multiply 20 by 2 which is 40. 

6. A music video website received 5.000comments on a new song they released
The next day, the artist performed the song
on television and an additional 1500
comments were made on the website. What
was the percent of increase? ​

Answers

Answer:

30%

Step-by-step explanation:

To be able to calculate the percent of increase between two numbers, you have to divide the increase by the initial number and multiply by 100:

Increase= 1,500

Initial number=5,000

Percent of increase=(1,500/5,000)*100

Percent of increase=0.3*100

Percent of increase=30%

According to this, the answer is that the percent of increase was 30%.

Which are true regarding the statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid”? Check all that apply. It is a conditional statement that can be written as “If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid.” The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides. The hypothesis is: it is a trapezoid. The conclusion is: a quadrilateral having exactly one pair of parallel opposite sides. The conclusion is: it is a trapezoid.

Answers

The statement is "The conclusion is: it is a trapezoid." the correct option is D.

What is a quadrilateral?

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

We are given that;

The statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid”

Now,

The following statements are true regarding the statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid":

It is a conditional statement that can be written as “If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid.”

The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides.

The conclusion is: it is a trapezoid.

Therefore, by quadrilaterals the answer will be "The conclusion is: it is a trapezoid."

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Answer: A,B,E

Step-by-step explanation:

Find the area of a circle with a radius of 11 inches. Use a 3.14. The area of the circle is approximatelyinches. Enter only the number.

Answers

The area of the circle is 379.94 square inches.

What is area of a circle?

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the area of a circle with a radius of 11 inches.

Here, area of a circle is

A=3.14×11²

= 3.14×121

= 379.94 square inches

Therefore, the area of the circle is 379.94 square inches.

Learn more about the area of a circle here:

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Answer:

A = 379.94 square inches

Step-by-step explanation:

The area of a circle equation is:

A = pi *  r^2

Fill in what you know and solve:

A = 3.14 * 11^2

A = 3.14 * 121

A = 379.94
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