What is equivalent form of the expression 15x + 24ax

yan [13]

It helps demonstrate it since it forms a right triangle in the middle with 2 base lengths and a hypotenuse. The areas of the squares can be plugged into the pythagorean theorem in order to find the answer

3 0

3 years ago

Geometry help needed, thanks!!

Anon25 [30]

Answer:

Part 1) 0.669

Part 2) x=23.78 cm

Step-by-step explanation:

Part 1) we have

cos(48°)

Using a calculator

cos(48°)=0.66913

Round to the nearest thousandth

0.66913=0.669

Part 2) we know that

In the right triangle of the figure

The cosine of angle of 18 degrees is equal to divide the adjacent side to the angle of 18 degrees by the hypotenuse of the right triangle

so

cos(18°)=x/25

x=(25)cos(18°)=23.78 cm

8 0

3 years ago

Write an inequality to represent the graph. a dashed line passing through points 0 comma negative 3 and 2 comma 2 with shading a

scZoUnD [109]

Answer: y > (5/2)*x - 3

Step-by-step explanation:

Ok, the thins we should notice.

The line is shaded, so the values of the line are not solutions of the inequality, then we should use < or >.

The shaded part is above the line, so we have:

y > a*x + b.

A linear relationship can be written as:

f(x) = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now, we know that our line passes through the points (0, -3) and (2, 2)

Then the slope is:

a = (2 -(-3))/(2 - 0) = 5/2.

f(x) = (5/2)*x + b.

To find the value of b, we can replace the values of one of the points in the equation, let's use the point (0, -3)

f(0) = -3 = (5/2)*0 + b

-3 = b

Then the line is:

f(x) = (5/2)*x - 3

Then the inequality is:

y > (5/2)*x - 3

8 0

3 years ago

Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival ti

natima [27]

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

$f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5$

Simplifying:

$f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}$

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

$P(A) = \int_{5}^{15} = \frac{375}{t^4}$

Integral of $\frac{1}{t^4} = t^{-4}$ is $\frac{t^{-3}}{-3} = -\frac{1}{3t^3}$

Then

$\int \frac{375}{t^4} dt = -\frac{125}{t^3}$

Applying the limits, by the Fundamental Theorem of Calculus:

At $t = 15$ , $f(15) = -\frac{125}{15^3} = -\frac{1}{27}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}$

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

$P(B) = \int_{5}^{10} = \frac{375}{t^4}$

We already have the integral, so just apply the limits:

At $t = 10$ , $f(10) = -\frac{125}{10^3} = -\frac{1}{8}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}$

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087$

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

3 0

3 years ago

Fill in the blank to complete the square: 22 + 8x+_

AURORKA [14]

Answer:

7

Step-by-step explanation:

3 0

2 years ago