MATHEMATICS COLLEGE

2. Customers who purchase a certain model of car can order an engine in any of three sizes. Of all cars of this type sold, 45% have a small engine, 35% have a medium-sized engine, and 20% have a large engine. Of cars with the small engine, 10% fail an emission test within two years of purchase, while 12% of those with the medium size and 15% of those with the large engine fail. If a randomly chosen car of this model fails an emission test within two years, what is the probability it is a car with a small engine

Answers

Answer 1

Answer:

Answer: 0.1397 ; 0.385

Step-by-step explanation:

Given the following :

Small engine population = 45% ; 10% fail

Medium engine population = 35% ; 12% fail

Large engine population = 20% ; 15% fail

Probability that a randomly chosen car fails emission test :

P(failure) = Σ(population % * failure %)

P(failure) = (45%*10%) + (35%*12%) + (20%*15%)

P(failure) = 0.045 + 0.042 + 0.03 = 0.117

B) what is the probability it is a car with a small engine

P = small engine cars with emission failure / total emission failure

= (0.45 × 0.1) / 0.117 = 0.045 / 0.117 = 0.3846

= 0.385

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Answers

Answer:

The area is 225 square inches

Step-by-step explanation:

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A limited edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value,y, after x years? (Round money values to the nearest penny.)

Answers

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Which best describes how to find an equation of the line shown?A. The slope m is rise over run, so y over x =m. Solve for Y to get y=mx.

B. The slope m is run over rise, so x over y=m. Solve for x=ym.

C. The slope m is run over rise, so x over y=m. Solve for y to get y= x over m.

D. The slope m is rise over run, so x over y=m. Solve for x to get x=ym.

Answers

Answer:

A

Step-by-step explanation:

m (slope) = rise = y = y₁ - y₁

run x x₁ - x₁

to get y = mx

therefore, the answer to the question is :

A. The slope m is rise over run, so y over x =m.

Solve for y to get y=mx.

Determine the solution for x2 + 36 > 12x

Answers

$\huge\text{Hey there!}$

$\large\boxed{\mathsf{x^2 + 36 > 12x}}$

$\large\text{SUBTRACT 12x to BOTH SIDES.}$

$\large\boxed{\mathsf{\rightarrow x^2 + 36 - 12x = 12x - 12x}}$

$\large\text{SIMPLIFY IT!}$

$\large\text{NEW EQUATION: }\large\boxed{\mathsf{x^2 - 12x + 36 = 0}}$

$\large\text{FACTOR the LEFT side: \boxed{\mathsf{(x - 6)(x - 6) = 0}}}$

$\large\text{We get: \boxed{\mathsf{x = 6}}}$

$\large\text{CHECK to make sure you have intervals with the equations.}$

$\large\text{Either of these inequalities should work with your given inequality}\downarrow$

$\large\text{YOUR ANSWERS..}$

$\large\boxed{\mathsf{x > 6}}\n\n\large\boxed{\mathsf{x < 6}}$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

Answer:

its d

Step-by-step explanation: i just did it

Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data.System System B
n1=120 n2=100
x1=4.1 minutes x2=3.4 minutes
σ1=2.2minutes σ2= 1.5 minutes

Test at the 0.05 level of significance to determinewhether the population mean checkout times of the two newsystems differ. Which system is preferred?

Answers

Answer:

We conclude that the population means checkout times of the two new systems differ.

Step-by-step explanation:

We are given the result in the following summary of the data;

System System B

n1=120 n2=100

x1=4.1 min x2=3.4 min

σ1=2.2 min σ2= 1.5 min

Let $\mu_1$ = population mean checkout time of the first new system

$\mu_2$ = population mean checkout time of the second new system

So, Null Hypothesis, $H_0$ : $\mu_1=\mu_2$ {means that the population mean checkout times of the two new systems are equal}

Alternate Hypothesis, $H_A$ : $\mu_1\neq \mu_2$ {means that the population mean checkout times of the two new systems differ}

The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{(\sigma_1^(2) )/(n_1) + (\sigma_2^(2) )/(n_2)} }$ ~ N(0,1)

where, $\bar X_1$ = sample mean checkout time of the first new systems = 4.1 min

$\bar X_2$ = sample mean checkout time of the second new systems = 3.4 min

$\sigma_1$ = population standard deviation of the first new systems = 2.2 min

$\sigma_2$ = population standard deviation of the second new systems = 1.5 min

$n_1$ = sample of the first new systems = 120

$n_2$ = sample of the second new systems = 100

So, the test statistics = $\frac{(4.1-3.4)-(0)}{\sqrt{(2.2^(2) )/(120) + (1.5^(2) )/(100)} }$

= 2.792

The value of z-test statistics is 2.792.

Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean checkout times of the two new systems differ.

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