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3 years ago

The graph shows a dilation with respect to the origin of rhombus RHOM. what is the factor of dilation?

Mathematics

2 answers:

Maslowich3 years ago

7 0

Answer:

2/3

Step-by-step explanation:

Sonja [21]3 years ago

3 0

Answer: A

Step-by-step explanation:

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Work out the gradient of the straight line that passes through (2,6) and (6,12)

Furkat [3]

Answer:

The gradient of the straight line that passes through (2, 6) and (6, 12) is $m = \frac{3}{2}$ .

Step-by-step explanation:

Mathematically speaking, lines are represented by following first-order polynomials of the form:

$y = b + m\cdot x$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$m$ - Slope.

$b$ - Intercept.

The gradient of the function is represented by the first derivative of the function:

$y' = m$

Then, we conclude that the gradient of the staight line is the slope. According to Euclidean Geometry, a line can be form after knowing the locations of two distinct points on plane. By definition of secant line, we calculate the slope:

$m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}$ (2)

Where:

$x_{A}$ , $y_{A}$ - Coordinates of point A.

$x_{B}$ , $y_{B}$ - Coordinates of point B.

If we know that $A(x,y) = (2,6)$ and $B(x,y) = (6,12)$ , then the gradient of the straight line is:

$m = \frac{12-6}{6-2}$

$m = \frac{6}{4}$

$m = \frac{3}{2}$

The gradient of the straight line that passes through (2, 6) and (6, 12) is $m = \frac{3}{2}$ .

5 0

2 years ago

In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$