Name
MATH 1342
Lab 12 - Ch.10 - Hypothesis Testing
Critical Thinking, Communication Skills, Empirical/Quantitative Skills
2. A machine is designed to fill jars with 16 ounces of coffee. A quality control inspector
suspects that the machine is not filling the jar with the full 16 ounces. A sample of 20 jars has
a mean of 15.8 ounces and a standard deviation of 0.32 ounce. Is there enough evidence to
support the inspector's claim that the mean number of ounces of coffee in the jars is less than
16? Use a = .05.
1.
Hand H
2.
3.
Critical value(s)
4.
Graph
5.
Test Statistic
6.
P-value
7.
Reject H. or Do Not Reject H.
8.
Conclusion

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.

[tex]A(t) = A(0)e^{-kt}[/tex]

[tex]0.7278A(0) = A(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.7278[/tex]

[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]

[tex]-10k = \ln{0.7278}[/tex]

[tex]k = -\frac{\ln{0.7278}}{10}[/tex]

[tex]k = 0.03177289938 [/tex]

Then

[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]

[tex]A(5) = 0.8531[/tex]

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Answer:

a) true

b) false

c) false

Step-by-step explanation:

remember: if a negative exponent is in the numerator, move the expression to the denominator and make the exponent positive and if a negative exponent is in the denominator, move the expression to the numerator and make the exponent positive

a explanation- 7a x 1/b^3 = 7a/b^3

b explanation- z^-5/12 = 1/12z^5

c explanation- 1/-7x^-1 = -7x

... please give brainliest if you can :)) ...

Answer:

Mean = 52

Standard Deviation = 13.64

Step-by-step explanation:

mean = 260/5

= 52

Standard Deviation = [tex]\sqrt{\frac{930}{5} }[/tex] = 13.64

I wasn't sure about my answer so used the Gauthmath app

because it's value will always be same

Answer:

This value doesn't depend on x or y

It'll be the same things always

Answer:

Perimeter: 3/4

Area: 9/16

Step-by-step explanation:

The ratio of the perimeters is equal to the ratio of the sides so:

18/24 = 3/4

Ratio of Area = (Ratio of Sides)^2

(3/4)^2 = 9/16

I wasn't sure about the answer so I used Gauthmath

Answer: Approximately $1,300

Step-by-step explanation:

There is around 52 weeks in a normal year.

$25 · 52 = $1300

Answer:

1300

Step-by-step explanation:

There are 52 weeks in a year

52 * 25 = 1300

Answer:

show us a screenshot or image

or type it out, copy paste

Step-by-step explanation:

Find the amount of the increase:

27800 - 23400 = 4,400

Find number of years: 2012 - 2008 = 4 years

Divide amount of change by number of years:

4,400 / 4 = 1,100 people per year.

Answer:

$147

Step-by-step explanation:

0.15x = $22.05

Divide both sides by 15

22.05/0.15 = $147

Answer:

Step-by-step explanation:

x^2 - 9x + 3 = 0 is a quadratic whose coefficients are a = 1, b = -9 and c = 3.

Use the quadratic formula to solve it.

The discriminant, b^2 - 4ac, is 81 - 4(1)(3), or 81 - 12, or 69.

The roots are:

      -b ± √(discriminant)

x = -------------------------------

              2a

And these roots in this particular problem are:

      -(-9) ± √69                    9 ± √69

= ------------------------------- = ----------------

              2(1)                                2

Answer:

Dependent variable = Total daily cost

Independent variable = number of items manufactured

2500 ;

9750

Step-by-step explanation:

Given the cost function in. A manufacturing company :

C(x) = 7.25x + 2500 ; Where

C(x) = total daily cost

x = number of items manufactured

The Independent variable is the variable whose value causes a change in the measured variable, this is the number of items manufactured, and the variable which charges as the predictor variable charges is the dependent variable (Total daily cost).

2.)

C(0) ;

C(x) = 7.25x + 2500

Put x = 0

C(0) = 7.25(0) + 2500

Cost = 2500

This is the total daily cost even if no items are produced, this is probably the fixed cost of daily production.

3.)

C(1000)

C(x) = 7.25x + 2500

Put x = 1000

C(0) = 7.25(1000) + 2500

Cost = 7250 + 2500

Cost = 9750

This is the total cost including variable cost of producing 1000 items.

Answer:

B. 35°

Step-by-step explanation:

First, find the two interior angles that are adjacent to angles 90° and 125° respectively.

Thus:

Interior angle 1: 180° - 90° = 90° (linear pair)

Interior angle 2: 180° - 125° = 55° (linear pair)

P + 90° + 55° = 180° (sum of interior angles in a triangle)

P + 145° = 180°

Subtract 145° from each side

P = 180° - 145°

P = 35°

Answer: there are 100 centimeters in 1 meter. Meters to centimeters multiply by 100. Centimeters to meters divide by 100.

Step-by-step explanation:

Meters to centimeters multiply by 100

(10,000 m ) (100) = 1,000,000 cm.

(100 m) (100) = 10,000 cm.

Centimeters to meters divide by 100.

100 cm / 100 = 1 meter

10,000 cm /100 = 100 m

6 minutes / 30 minutes

Divide the top and bottom by 6.

1 minute / 5 minutes

Fraction in lowest terms: 1/5

Hope this helps!

21

12^2 = 144

144 - 123 = 21

11^2 = 121

12^2 = 144

Between these

Answered by Gauthmath must click thanks and mark brainliest

Answer:

506

Step-by-step explanation:

8³-9×2÷3

= 512 - 9 × 2 ÷3

= 512 - 9 × ⅔

= 512 - 3 × 2

= 512 - 6

= 506

PEDMAS rule

P: Parentheses

E: Exponent

D: Division

M: Multiplication

A: Addition

S: Substraction

Answer:

After 10 months, the loan and value of the car will both be equal to $7,500.

Step-by-step explanation:

Value of the loan after x months:

[tex]y_l = 10000 - 250x[/tex]

Value of the car after x months:

[tex]y_c = 8000 - 50x[/tex]

Which statement describes when Melinda’s loan will be equal to the value of the car?

They are equal when:

[tex]y_l = y_c[/tex]

So

[tex]10000 - 250x = 8000 - 50x[/tex]

[tex]200x = 2000[/tex]

[tex]x = \frac{2000}{200}[/tex]

[tex]x = 10[/tex]

Equal after 10 months:

Value of [tex]y(10) = 8000 - 50(10) = 7500[/tex]

Thus, the correct option is:

After 10 months, the loan and value of the car will both be equal to $7,500.

Answer:

The answer is c because6X^3 minus 5X^3 is just X^3 and 3Y^2 plus 2Y^2 is 5Y^2.

Answer:

$16186.20

Step-by-step explanation:

Assuming that P represents the initial amount, A represents the end amount, r represents the annual interest rate, m represents the amount of times compounded per year, and t represents the amount of years, we can write this as

A = P(1+r/m)^(mt)

Since 12,000 is invested, that is the initial amount. To find the interest rate as a decimal from a percent (as we need it in decimal form for this formula), we can divide the percent by 100 to get 6%/100 = 0.06 as our interest rate. Because there are 12 months in a year, the interest is compounded 12 times a year, and since it takes 5 years, t=5. Our formula is now

A = 12000 * (1+0.06/12)^(12 * 5)

A = 12000 * (1+0.06/12) ^(60)

A = 16186.20 rounded to the nearest cent

Answer:

1/144

Step-by-step explanation:

(-1/12)^2

(-1/12)*(-1/12)

1/144

Answer: Hello your question is incomplete attached below is the missing

n ( 1 + n )

Step-by-step explanation:

P( Bob hits target ) = 1/3

P( Eve hits target ) = 2/3

P( Carol hits target ) = 1

Compute the P that Bob wins in a duel against Eve alone

P(Bob hits the target in first shot ) = n = 1/3

P(Bob hits the target in second shot ) = n^2 = ( 1/3 * 1/3 ) = 1/9

hence the probability of Bob winning( i.e. P( Bob wins Event E1  ) = n + n^2 = n ( 1 + n )

Answer:

Please write out in english

Step-by-step explanation:

I cannot help unless you can translate.

Answer:

The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Western residents:

39% out of 640, so:

[tex]p_1 = 0.39[/tex]

[tex]s_1 = \sqrt{\frac{0.39*0.61}{640}} = 0.0193[/tex]

Eastern residents:

51% out of 540, so:

[tex]p_2 = 0.51[/tex]

[tex]s_2 = \sqrt{\frac{0.51*0.49}{540}} = 0.0215[/tex]

Distribution of the difference:

[tex]p = p_2 - p_1 = 0.51 - 0.39 = 0.12[/tex]

[tex]s = \sqrt{s_2^2+s_1^2} = \sqrt{0.0215^2+0.0193^2} = 0.0289[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.12 - 2.575*0.0289 = 0.0456[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.12 + 2.575*0.0289 = 0.1944[/tex]

The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).

Answer:

49.09°

Step-by-step explanation:

c = circumference = 2×π×r

= 2× 22/7 ×7 = 44 ft

θ = 6/c × 360°

= 6/44 × 360° = 49.09°

Answer:

37.5%

Step-by-step explanation:

A=P(1+r)^t

363=192*(1+r)^2

1.375=1+r, r=0.375=37.5%

Answer:

3

Step-by-step explanation:

3 - 3/x

----------------

1 - 1/x

Multiply the top and bottom by x

x(3 - 3/x)

----------------

x(1 - 1/x)

3x -3

------------

x-1

Factor the numerator

3(x-1)

-------

x-1

Cancel like terms

3

-----

1

3

Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

                                                           = [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]

Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.

Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]

                                         = 364 square inches

Therefore, area of the metal sheet required = 364 square inches

Answer:

2y + y = 12

3y = 12

y = 4

now , x = 2y

x = 2 ( 4 )

x = 8

hope that helps ✌

Answer:

44.85

Step-by-step explanation:

There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85