The definition of parallel lines requires the undefined terms line and plane, while the definition of perpendicular lines requir

Answer:

P(0) = 0.6825

P(1) = 0.2607

Step-by-step explanation:

Based on the provided data, there were 107 homicide incidents and a total of 280 city-years recorded.

Let us denote the variable representing homicides per city-year as X.

The mean value of X can be calculated with the following formula:

\begin{array}{c}\\{\rm{Mean}} = \frac{{107}}{{280}}\\\\ = 0.382\\\end{array}

Mean=   107/280 = 0.382

The average number of homicides per city-year \left( {\lambda = \mu } \right)(λ=μ) is 0.382.

a. To find the probability of no homicides occurring:

\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}

P(X=0) =  e  −0.382  (0.382)⁰​/1

= (0.6825)(1) /1

P(X=0) = 0.6825

Thus, the chance of experiencing zero homicides P(0) is 0.6825.

b. To determine the probability of one homicide occurring:

\begin{array}{c}\\P\left( {X = 1} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^1}}}{{1!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {0.382} \right)}}{1}\\\\ = 0.2607\\\end{array}

P(X=1) =  e  −0.382  (0.382)¹​/1

= (0.6825)(0.382)/1

P(X=1) = 0.2607

Thus, the probability of having one homicide P(1) is 0.2607.

​

Hi! The goal of the Chi-Square Goodness of Fit test is to determine if observed frequencies of a categorical variable align with the expected historical or theoretical values in the population. Having the sales proportions of the top-five compact cars, we compare them against 400 compact car sales data from Chicago to see if there are discrepancies. Specifically, we have: - Chevy Cruze 24% ⟹ P(CC) = 0.24 - Ford Focus 21% ⟹ P(FF) = 0.21 - Hyundai Elantra 20% ⟹ P(HE) = 0.20 - Honda Civic 18% ⟹ P(HC) = 0.18 - Toyota Corolla 17% ⟹ P(TC) = 0.17 The hypotheses established are: H₀: P(CC) = 0.24; P(FF) = 0.21; P(HE) = 0.20; P(HC) = 0.18; P(TC) = 0.17 H₁: There is a discrepancy between expected and observed outcomes. With α set at 0.05, the statistic calculated is based on Oi (observed frequency) and Ei (expected frequency). The initial step involves calculating expected frequencies using: Ei = n * Pi, where Pi is the theoretical proportion for each category stated in the null hypothesis. The test conducted is right-tailed, and so is the p-value, calculated as: P(X²₄ ≥ 11.23) = 1 - P(X²₄ < 11.23) = 1 - 0.98 = 0.02. Since the p-value is lower than α, we reject the null hypothesis, indicating that Chicago's market shares for the five compact cars differ from those reported by Motor Trend.

To solve this problem, simply sum all of the grocery expenses and then divide that total by 4...

Answer:

No

Step-by-step explanation:

According to the Pythagorean Inequality Theorem, the sum of the two shorter sides must exceed the length of the third side.

4+6=10  

11 is still greater than 10.

Hence, constructing such a triangle is not feasible.

Answer:

Nina's speed in MPH:  12.706 miles per hour

Nina is quicker than Sophia.

Step-by-step explanation:

To solve this problem, we will convert feet per second to miles per hour and subsequently compare Nina's speed to that of Sophia's.

Nina rides at 63360 feet in 3400 seconds. To perform this conversion, we know that there are 5280 feet in a mile and 3600 seconds in an hour. Applying these conversions, we can calculate the speed in miles per hour.

(63360 feet / 3400 seconds) * (1 mile / 5280 feet) * (3600 seconds / 1 hour) = 12.706 miles per hour.

Thus, it follows that Nina rides her bike at a rate of 12.706 miles per hour, whereas Sophia rides her bicycle at a rate of 10 miles per hour.

This indicates that Nina rides faster than Sophia by 2.706 miles per hour (12.706 - 10).

Cheers.