Which are the solutions of he quadratic equation ? x2 = 9x + 6

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

Answer:

At the α = 0.10 level, there is no substantial evidence indicating that the average vertical jump for students at this school differs from 15 inches.

Step-by-step explanation:

A hypothesis test is necessary to verify the assertion that the average vertical jump of students diverges from 15 inches.

The null and alternative hypotheses are:

The significance level is set at 0.10.

The sample mean recorded is 17, and the sample standard deviation is 5.37.

The degrees of freedom are calculated as df=(20-1)=19.

The t-statistic is:

The two-tailed P-value corresponding to t=1.67 is P=0.11132.

<pSince this P-value exceeds the significance level, the result is not significant. Therefore, the null hypothesis remains unchallenged.

At the α = 0.10 level, there is no compelling evidence that the average vertical jump of students at this school deviates from 15 inches.

Let the events be defined as follows:
A=Nathan suffers from an allergy
~A=Nathan does not suffer from an allergy
T=Nathan receives a positive test result
~T=Nathan does not receive a positive test result

According to the provided data,
P(A)=0.75 [ probability indicating that Nathan is allergic ]
P(T|A)=0.98 [ probability of obtaining a positive test result if Nathan is allergic to Penicillin]

We aim to calculate the probability that Nathan is both allergic and tests positive
P(T n A)

Using the definition of conditional probability,
P(T|A)=P(T n A)/P(A)
By substituting the known values,
0.98 = P(T n A) / 0.75
We then solve for P(T n A)
P(T n A) = 0.75*0.98 = 0.735

Hope this assists you!!