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7 days ago

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A man starts at the point O on the map below. He chooses a path at random and follows it to point B1, B2, or B3. From that point

, he chooses a new path at random and follows it to one of the points A1 – A7. Suppose the man arrives at point A4, but it is not known which route he took, what is the probability that he passed through each of the three points: B1, B2, B3? Calculate each one.

1 answer:

Zina [3.9K]7 days ago

6 0

Answer: 1 / 27

Detailed breakdown: p (B1) = 1 / 3

p (B2) = 1 / 3

p (B3) = 1 / 3

Probability of (B1 and B2 and B3) = 1 / 3 multiplied by 1 / 3 multiplied by 1 / 3 = 1 / 27

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A college football coach has decided to recruit only the heaviest 15% of high school football players. He knows that high school

Inessa [3926]

Response:

The coach should begin seeking players who weigh at least 269.55 pounds.

Step-by-step explanation:

We have these details from the question:

Average, μ = 225 pounds

Standard Deviation, σ = 43 pounds

The weights follow a bell curve, indicating a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We need to establish the value of x that corresponds to a probability of 0.15

$P( X > x) = P( z > \displaystyle\frac{x - 225}{43})=0.15$

$= 1 -P( z \leq \displaystyle\frac{x - 225}{43})=0.15$

$=P( z \leq \displaystyle\frac{x - 225}{43})=0.85$

Review from the standard normal z table gives us:

$P(z < 1.036) = 0.85$

$\displaystyle\frac{x - 225}{43} = 1.036\\\\x = 269.548 \approx 269.55$

Consequently, the coach should start recruiting players weighing at least 269.55 pounds.

3 0

14 days ago

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom

PIT_PIT [3949]

Answer:

C. 5 degrees of freedom for the numerator and 114 for the denominator

Step-by-step explanation:

Analysis of variance (ANOVA) is utilized to examine the variations among group means within a sample.

The sum of squares represents the cumulative square of variation, which refers to the deviation of each individual value from the grand mean.

Assuming there are $6$ groups and each group contains $j=1,\dots,20$ individuals, the variation can be calculated using the following formulas:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

This also has the property

$SST=SS_{between}+SS_{within}$

The numerator's degrees of freedom in this case is given by $df_{num}=df_{within}=k-1=6-1=5$ where k = 6 represents the number of groups.

The denominator's degrees of freedom in this scenario is indicated by $df_{den}=df_{between}=N-K=6*20-6=114$ .

The total degrees of freedom would be $df=N-1=6*20 -1 =119$ .

Thus, the appropriate answer would be 5 degrees of freedom for the numerator and 119 degrees of freedom for the denominator.

C. 5 numerator and 114 denominator degrees of freedom

8 0

2 days ago

Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has writt

Svet_ta [4341]

Answer:

The inequality used to calculate the number of articles written by Mustafa for his school paper is $x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$ .

Mustafa has authored over 8 articles.

Step-by-step explanation:

Details given:

Total combined number of articles = 22

Let 'x' represent the articles written by Mustafa.

Now stated:

Heloise has authored $\frac{1}{4}$ as many articles as Mustafa.

Heloise's articles number = $\frac{1}{4}x$

Gia has penned $\frac{3}{2}$ as many articles as Mustafa.

Gia's article count = $\frac{3}{2}x$

It follows that;

The total of articles from Mustafa, Heloise, and Gia must be more than or equal to the total combined articles.

Expressing it in an equation gives us;

$x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$

Thus the inequality for finding the number of articles penned by Mustafa for his school project is $x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$ .

Now simplifying the inequality:

By taking the LCM to standardize the denominator, we get:

$\frac{x\times 4}{4}+\frac{1\times1}{4\times1}x+ \frac{3\times2}{2\times2}x\geq 22\\\\\frac{4x}{4}+ \frac{x}{4}+\frac{6x}{4}\geq 22\\\\\frac{4x+x+6x}{4} \geq 22\\\\11x\geq 22\times4\\\\11x\geq 88\\\\x\geq \frac{88}{11} \\\\x\geq 8$

Thus, Mustafa has written in excess of 8 articles.

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11 days ago

Solve for x in this equation: a - bx = cx+d

Inessa [3926]

Answer:

Step1: Take away (cx+d) from both sides of the initial equation

Thus, the value of x from the equation is $x=\frac{a-d}{b+c}$

Detailed explanation:

Considering the equation a-bx=cx+d

To find x:

a-bx=cx+d

Step1: Remove (cx+d) on both sides of the initial equation

a-bx-(cx+d)=cx+d-(cx+d)

a-bx-cx-d=cx+d-cx-d

a-bx-cx-d=0

Rearranging this yields

a-b-bx-cx=0

(a-b)-x(b+c)=0 (combining similar terms)

-x(b+c)=-(a-d)

Thus, the value of x in the initial equation is $x=\frac{a-d}{b+c}$

8 0

6 days ago

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The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns

zzz [4035]

Answer:

The water level rises 2 inches for each minute.

Step-by-step explanation:

The slope indicates the rate of height change

m = (16 - 12)/(4 - 2) = 4/2 = 2

2 inches per minute

A positive slope signifies an increase

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6 days ago