Which equation represents a line that passes through (–9, –3) and has a slope of –6?

Answer:

1. Conduct four flips of a fair coin; heads will stand for teenagers who like to watch films in theaters, while tails represent those who prefer otherwise.

2. Draw four cards from a standard deck, where red suits indicate those who enjoy going to theaters for movies, and black suits indicate the opposite.

4. Roll a six-sided die four times; even numbers will denote teenagers who favor theater viewings, while odd numbers will denote those who do not.

Step-by-step explanation:

The procedure involves repeating an action four times, each time presenting a 50/50 probability.

To elaborate on point 1, the flipping of the coin occurs four times, with a fair coin presenting each outcome with equal chances.

For point 2, drawing four cards allows for a balanced chance of pulling either a red or black card from the deck.

Point 3 inaccurately states performing the action three times, so it is incorrect.

In point 4, rolling the die four times also adheres to a 50/50 ratio for even versus odd outcomes.

Point 5 is incorrect because the range of 0-5 consists of six figures, while 6-9 includes only four, failing to create a balanced 50/50 scenario.

M∠ rst + m∠ vst = 180°
3 x + 7° + 9 x + 17° = 180°
12 x + 24° = 180°
12 x = 180° - 24°
12 x = 156°
x = 156°: 12
x = 13°
m ∠ rst = 3 · 13° + 7° = 39° + 7° = 46°
m ∠ vst = 180° - 46° = 134°
Answer:
A ) 46° and 134°

Response:

Detailed explanation:

Probability for an event is calculated as the ratio of the size of the event space compared to that of the sample space.

The sample space encompasses all possible outcomes.

Event space represents the number of favorable outcomes for the event in question.

Thus

Let

x ------> size of event space

y ----- → size of sample space

so

Calculate the probability of the first student being left-handed

we have

substituting values

Simplify

Calculate the probability of the second student being left-handed

we have

substituting values

Calculate the probability that both selected students will be left-handed

Multiply the probabilities together.

Convert to percentage

Multiply by 100

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.

The result is 10/117. We have three distinct letters and four unique non-zero digits. For letters, we have 26 options from A to Z. For digits, there are 9 choices from 1 to 9. As all selections must be distinct, we find the total number of codes as 26 × 25 × 24 × 9 × 8 × 7 × 6. For the specified code, we focus on the combinations with 5 vowels and 4 even digits, leading to a calculation of 5 × 25 × 24 × 8 × 7 × 6 × 4. Probability can thus be expressed as the ratio of these outcomes, yielding: 5 × 25 × 24 × 8 × 7 × 6 × 4 divided by 26 × 25 × 24 × 9 × 8 × 7 × 6.