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3 years ago

9

The total cost of apples is directly proportional to the number of pounds purchased. Deven bought 10 pounds of apples for $25. H

ow many pounds of the same kind of apples could he buy for $60? (A) 45 (B) 150 (0) 4 O) 24

1 answer:

Nina [5.8K]3 years ago

5 0

I think it’s a cause if just divide and multiply

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The line l is tangent to the circle with equation x² + y2 = 169 at the point P.

timofeeve [1]

Given:

The equation of a circle is

$x^2+y^2=169$

A tangent line l to the circle touches the circle at point P(12,5).

To find:

The gradient of the line l.

Solution:

Slope formula: If a line passes through two points, then the slope of the line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is

$m_1=\dfrac{5-0}{12-0}$

$m_1=\dfrac{5}{12}$

We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.

Product of slopes of two perpendicular lines is always -1.

Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.

$m\times m_1=-1$

$m\times \dfrac{5}{12}=-1$

$m=-\dfrac{12}{5}$

Therefore, the gradient or slope of the tangent line l is $-\dfrac{12}{5}$ .

6 0

2 years ago

Suppose that an airline quotes a flight time of 128 minutes between two cities. Furthermore, suppose that historical flight reco

ANTONII [103]

Answer:

(a) The probability density function of <em>X</em> is:

$f_{X}(x)=\frac{1}{b-a};\ a$

(b) The value of P (129 ≤ X ≤ 146) is 0.3462.

(c) The probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.

Step-by-step explanation:

The random variable <em>X</em> is defined as the flight time between the two cities.

Since the random variable <em>X</em> denotes time interval, the random variable <em>X</em> is continuous.

(a)

The random variable <em>X</em> is Uniformly distributed with parameters <em>a</em> = 10 minutes and <em>b</em> = 154 minutes.

The probability density function of <em>X</em> is:

$f_{X}(x)=\frac{1}{b-a};\ a$

(b)

Compute the value of P (129 ≤ X ≤ 146) as follows:

Apply continuity correction:

P (129 ≤ X ≤ 146) = P (129 - 0.50 < X < 146 + 0.50)

= P (128.50 < X < 146.50)

$=\int\limits^{146.50}_{128.50} {\frac{1}{154-102}} \, dx$

$=\frac{1}{52}\times \int\limits^{146.50}_{128.50} {1} \, dx$

$=\frac{1}{52}\times (146.50-128.50)$

$=0.3462$

Thus, the value of P (129 ≤ X ≤ 146) is 0.3462.

(c)

It is provided that a randomly selected flight between the two cities will be at least 3 minutes late, i.e. <em>X</em> ≥ 128 + 3 = 131.

Compute the value of P (X ≥ 131) as follows:

Apply continuity correction:

P (X ≥ 131) = P (X > 131 + 0.50)

= P (X > 131.50)

$=\int\limits^{154}_{131.50} {\frac{1}{154-102}} \, dx$

$=\frac{1}{52}\times \int\limits^{154}_{131.50} {1} \, dx$

$=\frac{1}{52}\times (154-131.50)$

$=0.4327$

Thus, the probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.

6 0

3 years ago

A=6 cm,b=9cm,and c =3 cm

Crazy boy [7]

The lengths of sides a and c add to 9 cm, the length of side b.
In a triangle, the the sum of the lengths of any two sides must be greater than the the length of the third side. These dimensions do not make a triangle.

Is this really what you meant? Why did you use capital A for a side? Or is A an angle, and it measures 6 deg, not 6 cm?

4 0

3 years ago

PLEASE PLEASE HELP!!! Match each pair of matrices with its product matrix.

Butoxors [25]

Answer:

Step-by-step explanation:

Did the calculations myself, probably too late for these to be of any use but I'll leaave them here anyways for anyone else that needs it in the future. Love yall!

4 0

3 years ago

12.09 to the nearest tenth

Gwar [14]

12.1 because 9 is greater than 5.

6 0

3 years ago

Read 2 more answers