MATHEMATICS COLLEGE

A study is being conducted to compare the average training time for two groups of airport security personnel: those who work for the federal government and those employed by private security companies. From a random sample of 12 government-employed security personnel, average training time was 72 hours, with a sample standard deviation of 8 hours. In a random sample of 16 privately employed security personnel, training time was 65.4 hours, with a sample standard deviation of 12.3 hours. Assume that training time for each group is normally distributed. Use the following notations:μ1: The mean training time for the population of airport security personnel
employed by the federal government.
μ2: The mean training time for the population of airport security personnel
employed by private security companies.
The goal of the statistical analysis is to determine whether the sample data support the hypothesis that average training time for government-employed security personnel is higher than those employed by private security companies.
1. What is the null hypothesis H0?
Select one:
a. μ1- μ2 <= 0
b. μ1- μ2 < 0
c. μ1- μ2 =/ 0
d. μ1- μ2 > 0
2. What is the alternative hypothesis Ha?
Select one:
a. μ1- μ2 > 0
b. μ1- μ2 <= 0
c. μ1- μ2 = 0
d. μ1- μ2 >= 0

Answers

Answer 1

Answer:

Answer:

1.a. H₀: μ₁ - μ₂ ≤ 0

2.b. H₁: μ₁ - μ₂ > 0

Step-by-step explanation:

Hello!

The objective is to compare the average training time for two groups of airport security personnel.

Group 1: Security personnel that works for the federal government

n= 12

X[bar]= 72 hs

S= 8hs

Group 2: Security personnel from private companies

n= 16

X[bar]= 65.4 hs

S= 12.3 hs

The goal of the analysis is to test if the average training time for government-employed security personnel is higher than those employed by private security companies, symbolically: μ₁ > μ₂

The null and alternative hypotheses are complementary and exhaustive.

The null hypothesis always represents the "no change situation" and therefore always carries the = symbol. Generally, the researcher's claim is stated in the alternative hypothesis.

With all this in consideration, the hypotheses for this experiment are:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

I hope this helps!

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50 pts Alessandro wrote the quadratic equation -6=x^2+4x-1 in standard form. What is the value of c in his new equation? c= -6 c= -1 c= 5 c= 7

Answers

Answer:

Step-by-step explanation: c on edg

Answer: c=5

Step-by-step explanation:

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Simplify the expression
$\sqrt[3]{686x {}^(4) } y {}^(7)$

Answers

The expression can be simplified as $7x\sqrt[3]{ 2x} y^7$ .

What is an expression?

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

Given:

The expression = $\sqrt[3]{686x^4} y^7$

Factorize 686 we get 7³ × 2

= $\sqrt[3]{7^3* 2x^4} y^7$

= $7x\sqrt[3]{ 2x} y^7$

Therefore, the expression can be simplified as $7x\sqrt[3]{ 2x} y^7$ .

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Final answer:

The simplified form of the expression \sqrt[3]{686x {}^{4}} * y {}^{7} is 2y^7x * \sqrt[3]{x}. This is achieved by breaking down 686 into its prime factors and simplifying under the cube root.

Explanation:

To simplify the given expression \sqrt[3]{686x {}^{4} } y {}^{7}, we first break down 686 into its prime factors. 686 = 2 * 7 * 7 * 7 or 2 * 7^3. Now we can simplify the given expression by solving it inside the cube root first: \sqrt[3]{2 * 7^3 * x^4}, which simplifies to 2y^7x * \sqrt[3]{x}

\sqrt[3]{686x {}^{4}} * y {}^{7} = 2y^7x * \sqrt[3]{x}

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During a game of cards, Megan divided the deck of cards into 4 equal groups. She then placed (3 ofher cards in the center of the table. If Megan now has
5 cards in her hand, how many cards were in the
entire deck?

Answers

There were originally 3 cards in the entire deck.

Let's denote the number of cards in the entire deck as $D$.

Megan divided the deck into 4 equal groups, so each group has $(D)/(4)$ cards.

She placed 3 cards in the center, and now she has 5 cards in her hand.

So, the equation representing this situation is:

$(D)/(4) - 3 + 5 = D$

Now, let's solve for $D$:

$(D)/(4) + 2 = D$

Multiply both sides by 4 to get rid of the fraction:

$D + 8 = 4D$

Subtract $D$ from both sides:

$8 = 3D$

Divide both sides by 3:

$D = (8)/(3)$

However, the number of cards in a deck must be a whole number, so we round up:

$D = 3$

Therefore, there were originally 3 cards in the entire deck.

Answer: 32

Step-by-step explanation: If she had 8 in her had and placed 3 cards down she would have 5 and if there were 8 cards in each group then, 8x4=32

What is the area of this triangle?

Answers

Answer:

Option (D)

Step-by-step explanation:

Formula for the area of a triangle is,

Area of a triangle = $(1)/(2)(\text{Base})(\text{Height})$

For the given triangle ABC,

Area of ΔABC = $(1)/(2)(\text{AB})(\text{CD})$

Length of AB = $(y_2-y_1)$

Length of CD = $(x_3-x_1)$

Now area of the triangle ABC = $(1)/(2)(y_2-y_1)(x_3-x_1)$

Therefore, Option (D) will be the answer.

PLEASE PLEASE PLEASE HELP. This is a geometry worksheet.

Answers

Answer:

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