Which situation can be represented by the equation 2x + 150 = 5x

Mary has 5 stamps and buys 150 stamps each week. Nick has no stamps and buys 2 stamps each week. When will Marty have

more stamps than Mary?

Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have

the same number of stamps?

Mary has 150 stamps and buys 5 stamps each week. Nick has no stamps and buys 2 stamps each week. When will Marty have

more stamps than Mary?

Mary has 150 stamps and buys 2 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have

the same number of stamps?

Answer: x^2+2x-7/x-1

I gotchu <3

Since the vertex is (0, -3), the quadratic function can be written in vertex form as:

f(x) = a(x - 0)^2 - 3

Where 'a' is a constant that determines the shape of the parabola. Since the end behavior of the function is y --> - Infinite as x --> - infinite and y --> - Infinite as x --> + infinite, the leading coefficient 'a' must be negative.

So, f(x) = -a(x^2 - 0x) - 3

Now, using the given point (1, -7) on the parabola, we can substitute the coordinates into the function and solve for 'a'.

-7 = -a(1^2 - 0(1)) - 3

-7 = -a - 3

a = 10

Therefore, the quadratic function that satisfies the given characteristics is:

f(x) = -10x^2 - 3

Hope this helps :)

The triangle is given as equilateral and the length of the perpendicular of the given equilateral triangle is 13.85.

It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, the longest side of the triangle. This theorem can be used to determine the length of the sides of a right triangle if two sides are known.

The triangle is given as equilateral. As we know he perpendicular in a equilateral triangle divides a line into to equal parts, so

Base= 8+8

= 16

As it is a equilateral triangle, all the sides will be equal.

Now, we can use the Pythagorean theorem to find the length of the perpendicular, which can be found by using the formula:

16²= 8² + x²

x² = 16²- 8²

x = √192

x = 13.85

Thus, the length of the perpendicular of the given equilateral triangle is 13.85.

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The graduated measuring cups are made from something glass or something transparent to markings on the side with different measurements are visible. Option (d) is the correct answer.

The kind of cups for measuring that are sometimes made from glass or something transparent so the markings on the side with different measurements are visible are called graduated measuring cups. These cups are designed to make measuring precise amounts of liquid or dry ingredients easy, and the transparent material allows you to see the measurement markings clearly. Graduated measuring cups are commonly used in baking and cooking, as well as in scientific research and other applications where accurate measurements are essential.

Therefore, Graduated measuring cups is the answer.

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We need approximately 12 servings of Designer Whey and 2 servings of Muscle Milk to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.

Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk needed to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.

From the information given, we know that each serving of Designer Whey provides 20 grams of protein and 3 grams of carbohydrates, and each serving of Muscle Milk provides 16 grams of protein and 9 grams of carbohydrates.

Therefore, we can set up the following system of equations:

20x + 16y = 262

3x + 9y = 54

To solve for x and y, we can use any method of solving a system of equations. For example, we can use substitution:

From the second equation, we can solve for x in terms of y:

x = (54 - 9y)/3 = 18 - 3y

Substituting this into the first equation, we get:

20(18 - 3y) + 16y = 262

Simplifying, we get:

80y = 182

Solving for y, we get:

y = 2.275

Substituting this into the equation x = 18 - 3y, we get:

x = 12.175

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The missing angles of the diagram are:

∠1 = 118°

∠2 = 62°

∠3 = 118°

∠4 = 30°

∠5 = 32°

∠6 = 118°

∠7 = 30°

∠8 = 118°

Supplementary angles are defined as two angles that sum up to 180 degrees. Thus:

∠1 + 62° = 180°

∠1 = 180 - 62

∠1 = 118°

Now, opposite angles are congruent and ∠2 is an opposite angle to 62°. Thus: ∠2 = 62°.

Similarly: ∠3 = 118° because it is congruent to ∠1

Alternate angles are congruent and ∠5 is an alternate angle to 32°. Thus:

∠5 = 32°

Sum of angle 4 and 5 is a corresponding angle to ∠2 . Thus:

∠4 + ∠5 = 62

∠4 + 32 = 62

∠4 = 30°

This is an alternate angle to ∠7 and as such ∠7 = 30°

Sum of angles on a straight line is 180 degrees and as such:

∠8 = 180 - (30 + 32)

∠8 = 118° = ∠6 because they are alternate angles

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[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank A} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1810)(0.025)(5) \implies I = 226.25 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank B} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]A = 1810\left(1+\frac{0.025}{12}\right)^{12\cdot 5} \implies A \approx 2050.73~\hfill \underset{ interest }{\stackrel{2050.73~~ - ~~1810 }{\approx 240.73}} \\\\[-0.35em] ~\dotfill\\\\ 240.73~~ - ~~226.25 ~~ \approx ~~ \text{\LARGE 14.48}[/tex]

Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.

For instance, "4 added to 2" will have the mathematical formula 2+4.

So, we have the expression:

= x² + 10x + 24

Now, solve when x = 3 as follows:

= x² + 10x + 24

= 3² + 10(3) + 24

= 9 + 30 + 24

= 63

Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

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Correct question:

Evaluate the expression when x = 3.

x² + 10x + 24

a. 81

b. 86

c. 63

d. 60

Answer:

y=4x+5

Step-by-step explanation:

y=mx+b

m=4

b=5

The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00

Calculate the MAD:

First, find the mean of the data set:

mean = (sum of all values) / (number of values)

mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10

mean = 88.00 / 10 = 8.80

Then, find the mean of these absolute deviations:

MAD = (sum of absolute deviations) / (number of values)

MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10

MAD = 4.10 / 10 = 0.41

Calculate the range:

range = maximum value - minimum value

range = 10.00 - 8.00 = 2.00

Find Q1 and Q3:

{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}

Q1 is the median of the lower half, and Q3 is the median of the upper half.

Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}

Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}

Q1 = median of lower half = 8.25

Q3 = median of upper half = 9.25

Calculate the IQR:

IQR = Q3 - Q1

IQR = 9.25 - 8.25 = 1.00

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Answer:  p(θ|x) dθ = 1 − α.

Step-by-step explanation: the critical value is computed based on the given significance level α and the type of probability distribution of the idealized model

Answer: See Bellow

Step-by-step explanation:

Juliet's sample may not be valid for several reasons. Firstly, her sample size of 20 students may not represent the entire student population at her school. If her class is not a random sample of the whole student population, her results may not generalize to the entire school. Additionally, the model may suffer from selection bias if she only surveyed students she knew liked short stories or if she conducted the survey in a way that only sure students responded. Therefore, it is essential to have a large and representative sample to ensure the validity of the conclusions drawn from the survey results.

The Area of square is 64 square unit.

We have the coordinates (-3, -3) and (5, -3).

Using distance formula

d = √ (5 + 3)² + (-3 + 3)²

d= √8² + 0

d= 8 units

So, the Area of square

= d x d

= 8 x 8

= 64 square unit

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In the ANOVA test, degrees of freedom within (dfw) is equal to the total number of observations minus the total number of groups if we have N total observations and k groups, then dfw = N - k.

The ANOVA (Analysis of Variance) test is a statistical method used to compare the means of three or more groups.

Degrees of freedom within (dfw) are determined by the total number of observations minus the total number of groups, and degrees of freedom between (dfb) is simply the number of groups minus one.

On the other hand, degrees of freedom between (dfb) is equal to the number of groups minus 1, which is simply k - 1.

So, the final answer is:

dfw = N - k

dfb = k - 1

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When solving an oblique triangle given three sides, use the inverse cosine form of the Law of cosines to solve for an angle.

When solving an "oblique-triangle" given three sides, we would use the inverse cosine, form of the Law of Cosines to solve for an angle.

The "Inverse-Cosine" function allows us to find the measure of an angle when given the ratio of the lengths of the triangle's sides.

The "Law-of-Cosines" relates the lengths of the sides of a triangle to the cosine of one of its angles.

The "Law-of-Cosines" states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively:

⇒ c² = a² + b² - 2ab × cos(C),

To solve for an angle, we would rearrange the equation to find the cosine of the angle,

⇒ Cos(C) = (a² + b² - c²)/(2ab),

Then, we will take the inverse cosine of both sides of the equation to find the value of the angle,

⇒ C = cos⁻¹((a² + b² - c²)/(2ab)),

This helps us to find the measure of angle C, depending on the units used in the original triangle sides.

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The given question is incomplete, the complete question is

When solving an oblique triangle given three sides, use the _____ form of the Law of cosines to solve for an angle.

The vertex form of the quadratic expression -16x² +160x+120 is -16(x - 5)² + 520.

What is vertex form?

Vertex form is a way to write a quadratic function in the form:

f(x) = a(x - h)²+ k

where "a" is the vertical stretch or compression factor, "h" and "k" are the x-coordinate and y-coordinate of the vertex of the parabola respectively. The vertex form allows you to easily identify the vertex and the direction of the parabola's opening.

To write -16x²+160x+120 in vertex form, we need to complete the square.

First, let's factor out the coefficient of x²:

-16(x² - 10x) + 120

Next, we need to add and subtract (10/2)² = 25 to the expression inside the parentheses:

-16(x² - 10x + 25 - 25) + 120

Now we can group the first three terms and factor the perfect square trinomial:

-16((x - 5)² - 25) + 120

Simplifying:

-16(x - 5)² + 520

Therefore, the vertex form of the quadratic expression -16x² +160x+120 is -16(x - 5)² + 520.

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Answer:

Step-by-step explanation:

You will first need to remember when solving equations or inequalities that have a variable you will need to make sure that the variable is on one side alone.

So, b-2>-1 you will add 2 to both sides . Whatever you do to one side of the equal sign or inequality you do to the other side.

b-2>-1

  +2  +2

b > 1  

Also, because it has a line under the greater than or equal to sign you will graph it on a number line as a closed circle with the closed circle on the 1 and the arrow pointing to the right. The symbol in the inequality is the way the arrow should be pointing . ≤ ≥ closed circle < > open circle.

closed circle and arrow pointing to the right →

The second selection is the right one.

Therefore, the volume of the rectangular prism is 87.5 cubic yards.

A prism is a transparent object, usually made of glass or plastic, that refracts or bends light as it passes through it. It has at least two flat surfaces, called faces, that are usually parallel and rectangular in shape, and two non-parallel faces, called bases, which are usually triangular in shape. When light enters a prism, it is refracted, or bent, as it passes through the prism and is separated into its component colors, creating a rainbow effect. Prisms are often used in optics and science experiments to study the properties of light, such as its wavelength and polarization. They are also commonly used in optical instruments such as binoculars, telescopes, and cameras to help focus and direct light.

The volume V of a rectangular prism is given by the formula:

V = length x width x height

In this case, the length is 5 yards, the width is also 5 yards, and the height is 3- and one-half yard.

To calculate the volume, we can plug this value into the formula:

V = 5 yards x 5 yards x 3.5 yards

Simplifying this expression, we get:

V = 87.5 cubic yards

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Answer:

The volume of a rectangular prism is the product of its length, width, and height. In this case, the length is 5 yards, the width is 5 yards, and the height is 3.5 yards. Therefore, the volume of the prism is 5 * 5 * 3.5 = 87.5 cubic yards.

Here is the calculation:

Volume = length * width * height

= 5 yards * 5 yards * 3.5 yards

= 87.5 cubic yards

Step-by-step explanation:

For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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Answer:

data given

Universal set 40people

people who can sew 14

people who can knit 12

people who can do both 5

Step-by-step explanation:

•people who can sew only

=14-5

=9

•people who can knit only

=12-9

=7

Union of people who can sew and the one who can knit

=9+7+5

=21

who do neither

=40-21

=19

: .people neither sew or knit are 19

The size of the square to cut is 5/3 inches and the maximum volume of the box is 266.67 cubic inches.

To find the size of the square to cut and the maximum volume, we can follow these steps:

Let's call the length of each side of the square to be cut x inches. So the dimensions of the base of the box would be (16-2x) inches by (10-2x) inches.

The height of the box would be x inches since we are folding up the sides.

The volume of the box can be found by multiplying the length, width, and height: V = (16-2x)(10-2x)x.

To find the maximum volume, we can take the derivative of V with respect to x and set it equal to zero, since the maximum volume occurs at a critical point.

After taking the derivative and simplifying it, we get the equation 24x^2 - 520x + 1600 = 0.

Solving this quadratic equation, we get x = 5/3 or x = 20/3. Since x must be less than 5 (the length of the shorter side), the only feasible solution is x = 5/3 inches.

Plugging this value of x back into the equation for the volume, we get V = (16-2(5/3))(10-2(5/3))(5/3) = 266.67 cubic inches.

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The distribution in which variable x has binomial distribution are as follow,

Option A) When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

Option D) When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution .

Because there are two independent trials two patients.

With a constant probability of success 30%.

And the outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

This variable X does not follow a binomial distribution.

Because the probability of success is not constant it's the complement of 30%, which is 70%.

Also, the outcome of one trial affects the outcome of the other trials.

As there are only six patients .

Number of patients for whom medicine does not work depends on number of patients for whom it worked.

When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution.

Because there are six independent trials six patients with a constant probability of success (30%) .

The outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with two patients, X is the number of doses each patient needs to take.

This variable X does not follow a binomial distribution.

Because it's not a count of successes out of a fixed number of independent trials.

But rather a continuous variable that can take any non-negative value.

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The above question is incomplete, the complete question is:

For a certain type of hay fever, Medicine H has a 30% probability of working.

In which distributions does the variable X have a binomial distribution?

Select EACH correct answer.

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.

The area of the sandbox of parallelogram shape is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are equal in length and parallel to each other. Additionally, opposite angles of a parallelogram are congruent (i.e., have the same measure).

We can choose any side of the parallelogram as the base, and the distance from that side to the opposite side as the height. Let's choose the side between (-4,0) and (-2,6) as the base. The length of this side is the distance between these two points:

√[(-2-(-4))² + (6-0)²] = √40 = 2√10

The height of the parallelogram is the distance between the line containing (-2,6) and (4,0) and the point (2,-6). We can find the equation of the line containing (-2,6) and (4,0) by finding the slope and y-intercept:

Slope: (0-6)/(4-(-2)) = -6/6 = -1

Y-intercept: y = mx + b -> 0 = (-1)(4) + b -> b = 4

Therefore, the equation of the line is y = -x + 4. We can find the distance between this line and the point (2,-6) by substituting x = 2 into the equation and finding the corresponding y-value:

y = -x + 4 = -2

The distance between the line and the point (2,-6) is the absolute value of the difference between the y-coordinate of the point and the y-coordinate of the line:

|(-6) - (-2)| = 4

Therefore, the height of the parallelogram is 4 feet.

The area of the parallelogram is then:

A = base x height = (2√10) x 4 = 8√10

Rationalizing the denominator, we get:

A = 8√10 x √10/√10 = 80/√10 = 80√10/10 = 8√10

Therefore, the area of the sandbox is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².

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According to the investment, after 15 years, the balance in the account would be $1185.

To calculate the final balance after 15 years, we can use the formula for simple interest:

Simple Interest = Principal x Interest Rate x Time

In this case, the principal is $600, the interest rate is 6.5%, and the time is 15 years.

Simple Interest = $600 x 0.065 x 15

Simple Interest = $585

So the investment of $600 earns $585 in simple interest over 15 years. To find the final balance, we add the interest earned to the initial investment:

Final Balance = Principal + Simple Interest

Final Balance = $600 + $585

Final Balance = $1185

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The directionality of the alternative hypothesis and the support offered by the sample data determine whether the null hypothesis is likewise rejected at the 5% level of significance for a related one-tailed test.

When the two-tailed test rejects the null hypothesis, it means that the sample data, regardless of how we look at it, support the null hypothesis.. A one-tailed test, however, simply considers the evidence in one way. As a result, the null hypothesis should be used if the sample data only show evidence that the alternative hypothesis is true in one direction (for example, greater than).

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Therefore, the correct answer is A. We cannot determine whether g(-13) = 20 or not as -13 is outside the domain of g, but it is a possibility within the Domain range of g.

Determine the values of the independent variable x for which the function is specified in order to find the domain and range of the equation y = f(x). Simply write the equation as x = g(y), and then determine the domain of g(y) to determine the function's range.

Since g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, we can eliminate options B and D as they fall outside the range of g.

Since -13 is outside of the range of g, we are unable to verify whether g(-13) = 20 for option A.

For option C, we are given that g(0) = -2, so option C cannot be true.

Therefore, the correct answer is A. We cannot determine whether g(-13) = 20 or not as -13 is outside the domain of g, but it is a possibility within the range of g.

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the proportion of California college students who currently drink alcohol different from the proportion nationwide p0 = 0.60 (nationwide proportion from CDC)

Information provided; we can determine if the proportion of California college students who currently drink alcohol is different from the proportion nationwide by conducting a hypothesis test. Here are the steps:
The null hypothesis (H0) and alternative hypothesis (H1):
H0: The proportion of California college students who drink alcohol is the same as the nationwide proportion.

(p = 0.60).
H1: The proportion of California college students who drink alcohol is different from the nationwide proportion.

(p ≠ 0.60).
The sample proportion (p-hat), sample size (n), and the population proportion (p0):
p-hat = 0.66 (66% of the 450 California college students surveyed)
n = 450 (sample size)
p0 = 0.60 (nationwide proportion from CDC)
The test statistic (z) using the following formula:
[tex]z = (p-hat - p0) / \sqrt((p0 \times (1 - p0)) / n)[/tex]
A standard normal distribution table or calculator to find the p-value associated with the test statistic.
Compare the p-value to a predetermined significance level (α), usually set at 0.05.
- If the p-value is less than α, reject the null hypothesis (H0), suggesting that the proportion of California college students who drink alcohol is different from the nationwide proportion.
- If the p-value is greater than α, fail to reject the null hypothesis (H0), indicating that there is not enough evidence to suggest a difference between the two proportions.
Determine if the proportion of California college students who drink alcohol is significantly different from the nationwide proportion.

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The process time of the system is 32 min/unit.