List all the factors of the number 48.

Which function below is the inverse of f(x) = The quantity of seven x plus one, over two.?A) f−1(x) = two over the quantity of s

Law Incorporation [45]

<span>The given function is f(x) = (7x + 1)/2. Write it as y = (7x)/2 + 1/2. To determine the inverse do these 3 steps. Step 1: Swap x and y to obtain x = (7y)/2 + 1/2. Step2: Solve for y. First, multiply through by 2 to obtain 2x = 7y + 1. Second, subtract 1 from each side to ontain 2x - 1 = 7y. Third, divide through by 7 to obtain (2x - 1)/7 = y. Step 3: Set y to the inverse of f(x) to obtain f^(-1) (x) = (2x - 1)/7.</span>

6 0

3 years ago

Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 o

Irina-Kira [14]

Answer:

a

$P(X < 12) = 0.3660$

b

$P(X < 12) = 0.1521$

Step-by-step explanation:

Considering question a

From the question we are told that

The mean is $\mu = 12.01 \ oz$

The standard deviation is $\sigma = 0.35 \ oz$

The standard error of mean is mathematically represented as

$\sigma_{x} = \frac{\sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{0.35}{\sqrt{144} }$

=> $\sigma_{x} = 0.02917$

Generally the probability that the mean volume of a random sample of 144 bottles is less than 12 oz is mathematically represented as

$P(X < 12) = P(\frac{X - \mu }{\sigma_{x}} < \frac{12 - 12.01 }{0.02917 } )$

$\frac{X -\mu}{\sigma_{x} } = Z (The \ standardized \ value\ of \ X )$

$P(X < 12) = P(Z < -0.3425 )$

From the z table the area under the normal curve to the left corresponding to -0.3425 is

$P(X < 12) = P(Z < -0.3425 ) = 0.3660$

=> $P(X < 12) = 0.3660$

Considering question a

From the question we are told that

The mean is $\mu = 12.03 \ oz$

Generally the probability that the mean volume of a random sample of 144 bottles is less than 12 oz is mathematically represented as

$P(X < 12) = P(\frac{X - \mu }{\sigma_{x}} < \frac{12 - 12.03 }{0.02917 } )$

$P(X < 12) = P(Z < -1.0274 )$

From the z table the area under the normal curve to the left corresponding to -1.0274 is

$P(X < 12) = P(Z < -1.0274 ) =0.1521$

=> $P(X < 12) = 0.1521$

3 0

3 years ago

Write the equation of the circle graphed below

Norma-Jean [14]

Answer:

The equation of the circle is

(x + 2)² + (y + 2)² = 9

Centered at (-2, -2), with radius of 3 units.

Step-by-step explanation:

The general equation of a circle is given as

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle, and r is the radius.

Looking at the graph, the center is the red dot. It corresponds to -2 on the y-axis, and -2 on the x-axis. So, the center (h, k) is (-2, -2).

The radius is the distance from the center of the circle to the edge of the circle. The red dot is the edge of the circle, there are 3 lines that represent 3 units, so we have a radius of 3 units.

Using these in the general equation, we have

[x - (-2)]² + [y - (-2)]² = 3²

(x + 2)² + (y + 2)² = 9

And this is the equation.

6 0

3 years ago

Solve triangle ABC given that A = 56°, B = 57°, and b = 9.00. Round the length of the sides to the nearest hundredth

daser333 [38]

Answer:

Part 1) $C=67^o$