Sandra is selling root beer in 300 mL bottles. She makes 2 batches of root beer. Each batch makes 3.2 L of root beer. How much root beer will she have left over, after filling her bottles?

a) The necessary sample size for a 95% confidence interval with an interval width of no more than 6% is 147.

b) The necessary sample size for a 99% confidence interval with an interval width of no more than 6% is 263.

(a) To find the necessary sample size for future surveys such that a 95% confidence interval for p has an interval width of no more than 6%, we use the formula:

n = (Zα/2/ME)² × p(1-p)

where Zα/2 is the Z-score for the desired confidence level (1.96 for 95% confidence), ME is the margin of error (0.06), and p is the estimated proportion of patients with pain relief from the pilot survey (14/20 = 0.7). Substituting these values into the formula, we get:

n = (1.96/0.06)² × 0.7(1-0.7) = 146.95

Therefore, This sample size is larger than the sample size in problem 4.6-21(a), which was 100.

(b) To find the necessary sample size for future surveys such that a 99% confidence interval for p has an interval width of no more than 6%, we use the same formula as above but with a Z-score of 2.576 for 99% confidence:

n = (2.576/0.06)² × 0.7(1-0.7) = 262.43

Therefore, This sample size is larger than the sample size in problem 4.6-21(b), which was 176.

Learn more about confidence intervals at

https://brainly.com/question/24131141

#SPJ4

Factor f(x)=3x³ + 7x²2-18x+8 into linear factors is f(x) = (x+4)(3x+7)(x-7/3)

In mathematics, factorization (also known as factoring) is the process of finding the factors of a given mathematical expression or number. A factor is a number or expression that divides another number or expression exactly, leaving no remainder.

For example, the factors of 6 are 1, 2, 3, and 6 because these are the numbers that divide 6 exactly with no remainder. Similarly, the factors of x² - 4 are (x+2)(x-2) because when we multiply these two expressions together, we get x² - 4.

If -4 is a zero of f(x), then x+4 is a factor of f(x) by the factor theorem

f(x) = (x+4)(3x² - 5x - 78)

To factor the quadratic further, we can use the quadratic formula or factoring by grouping:

3x² - 5x - 78 = 0

x = (5 ± √(5² + 4(3)(78))) / (2(3))

x = (5 ± 19) / 6

x = -7/3 or x = 13/3

Therefore, we have:

f(x) = (x+4)(3x+7)(x-7/3)

To know more about remainder, visit:

https://brainly.com/question/29019179

#SPJ1

Answer:

To divide fractions, we can use the reciprocal (or multiplicative inverse) of the second fraction and then multiply the two fractions.

So to solve ⅚ ÷ ⅔, we can write it as:

⅚ ÷ ⅔ = ⅚ × (⅔)⁻¹

where (⅔)⁻¹ is the reciprocal of ⅔, which is 3/2.

So we have:

⅚ ÷ ⅔ = ⅚ × (⅔)⁻¹ = ⅚ × 3/2

We can simplify this expression by canceling out a common factor of 2 in the numerator and denominator:

⅚ ÷ ⅔ = ⅚ × (⅔)⁻¹ = ⅚ × 3/2 = (⅚ × 3) / 2 = 9/12

Therefore, another way to solve ⅚ ÷ ⅔ is the equation:

⅚ ÷ ⅔ = 9/12

Answer:

  y = (x +2)² -3

Step-by-step explanation:

You want the math operators that are needed to properly write the equation of the given parabola in vertex form.

The vertex is the low point on the curve. Its coordinates are (-2, -3).

The vertex form of the equation for a parabola is ...

  y = a(x -h)² +k

You want the equation for (h, k) = (-2, -3). It is ...

  y = a(x +2)² -3

The operators are plus (+) and minus (-).

Answer:

[tex]y = a(x+2)^2-3[/tex]

Explanation:

You are adding the 2 to move the whole function two times to the left and you are subtracting the 3 so that the minimum of the quadratic function is -3.

Answer:

Step-by-step explanation:

[tex]C=2\pi r[/tex]

[tex]1=2\pi\time r[/tex]

[tex]r=\frac{1}{2\pi}[/tex]           ( divided both sides of equation by [tex]2\pi[/tex])

 [tex]r\approx 16cm[/tex]

The wheel's radius is approximately 16cm.

Answer: 9.9% (rounded to the nearest tenth

Step-by-step explanation:

At the initial investment of $1600 compounded quarterly for 7 years with an interest of 4.12%, the amount Alyssa will get is $2,131.72.

The powerful investing principle of compounding entails generating returns on both your initial investment and returns you have already received.

You must reinvest your returns back into your account for compounding to take effect.

Consider an investment of $1,000 that yields a 6% return.

The words under and ground, for instance, are combined to get the word subterranean.

So, we know that:

Initial deposit: $1600

Interest: 4.12%

Compounded quarterly for 7 years.

Then, the amount after 7 years would be:

Using the compounding calculator we know that after 7 years Alyssa will have: $2,131.72

Therefore, at the initial investment of $1600 compounded quarterly for 7 years with an interest of 4.12%, the amount Alyssa will get is $2,131.72.

Know more about compounding here:

https://brainly.com/question/28020457

#SPJ1

Complete question:

Alyssa started a savings account with an initial deposit of $1600. The account earns 4.12% interest compounded quarterly for 7 years. Calculate how much money will be in the account after 7 years, assuming Alyssa

makes no additional deposits or withdrawals.

The value of the side a is 12. 8 . Option C

From the diagram shown, we have that;

m<A = 45 degrees

c = 17

m<B = 25

Note that the sum of the angles in a triangle is 180, then, we have;

<A + <B + < C = 180

substitute the values

45 + 25 + < C = 180

collect the like terms

<C = 110

Using the sine rule, we have;

sin A/a = sin B/b = sin C/c

Substitute the values, we get;

sin 45/a = sin 110/17

cross multiply the values, we have;

a = 12. 02/0. 9396

a = 12. 79

Learn about triangles at: https://brainly.com/question/25215131

#SPJ1

The inequality that represents the possible values for the number of hours babysitting and the number of hours landscaping is 12b + 8l ≥ 140.

A mathematical inequality is a statement that two quantities or expressions are not equal. Inequalities are used to compare the relative sizes of numbers or variables and represent constraints or conditions in various contexts, such as optimization problems, systems of linear equations, or financial planning.

Here we have

Harper is working two summer jobs, making $12 per hour babysitting and $8 per hour landscaping. Harper must earn no less than $140 this week.  

Let Harper work for 'b' hours in the baby setting and l hours in landscaping

The amount earned by Haper by babysitting = $ 12 × b = 12b

The amount earned by Haper by landscaping = $ 8 × l = 8l

Here the amount should not be less than $ 140

=> 12b + 8l ≥ 140

Hence,

The inequality that represents the possible values for the number of hours babysitting and the number of hours landscaping is 12b + 8l ≥ 140.

Learn more about Inequality at

https://brainly.com/question/29413699

#SPJ1

Answer:

Let’s start by defining the variables:

Let x be the number of rings manufactured per day.

Let y be the number of chains manufactured per day.

The total number of rings and chains manufactured per day is at most 24. Therefore, we have:

x + y ≤ 24

It takes 1 hour to make a ring and 30 minutes to make a chain. Therefore, we have:

1x + 0.5y ≤ 16

The profit on each ring is Rs. 300 and that on each chain is Rs. 190. Therefore, the total profit can be calculated as:

Total Profit = 300x + 190y

We want to maximize the total profit. This can be done by solving the above equations using linear programming.

The solution to this problem is x = 12 and y = 12. Therefore, the firm should manufacture 12 rings and 12 chains per day to earn the maximum profit

Number of students having one pet=27

A fraction is a number that represents a part of a whole or a ratio of two quantities. It is written in the form of one integer, called the numerator, written above a line, and another integer, called the denominator, written below the line. The denominator represents the total number of equal parts into which the whole has been divided, while the numerator represents the number of those parts that are being considered.

For example, the fraction 3/4 represents three out of four equal parts of a whole. The number 3 is the numerator, and 4 is the denominator.

Fraction of students having 1 pet=1/2

Number of students having one pet=53×1/2=26.5≈27

To know more about numerator, visit:

https://brainly.com/question/7067665

#SPJ1

Answer:6

Step-by-step explanation:

there is a law for that:

5*12=x*(x+4)

60=x*x+4x

x*x+4x-60=0

(x+2)*(x+2)-64=0

(x+2)(x+2)=8*8

x+2=8

x=6

Answer:6

Step-by-step explanation:there is a law for that:5*12=x*(x+4)60=x*x+4xx*x+4x-60=0(x+2)*(x+2)-64=0(x+2)(x+2)=8*8x+2=8x=6

Answer:

14

Step-by-step explanation:

70/5 is 14

ez cheesey toes

Answer:

y = 3x -7

Step-by-step explanation:

Since we already know that the slope is 3 and it goes through the point (3,2).

We can use - Slope intercept form: y = mx + b to find the y-intercept first.

Using the given info:

m = 3

x = 3

y = 2

Thus,

2 = 3(3) + b

2 = 9 + b

2- 9 = 9- 9  + b

-7 = b

Hence, the y-intercept is -7.

As a result,

y = mx + b        >> plug it in

y = 3x -7

RevyBreeze

Answer:

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

Inverse variation equation:

We have:

Substitute initial values and find the value of k:

The equation now becomes:

Find the value of V when P = 5:

Hence the answer is 166.4 in³.

The correct number line that shows the solution to the inequality y - 2 < -5 is the first option: "A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded."

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The inequality can be rewritten as y < -3, which means that y is less than -3. The open circle at -3 indicates that -3 is not included in the solution set, and everything to the left of it, which represents numbers less than -3, should be shaded.

Therefore, the correct number line that shows the solution to the inequality y - 2 < -5 is the first option: "A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded."

To learn more about inequalities from the given link:

https://brainly.com/question/30231190

#SPJ1

Answer:

888 offices

Step-by-step explanation:

Since there are a total of 24 floors in the building and each floor has a total of 37 offices on it, we have to multiply the number of floors by the number of offices in total:

[tex]24 \times 37 = 888[/tex]

The number of offices in the building amounts to a total of 888, indicating a significant amount of workspace available within the premises.

To calculate the total number of offices in the building, we need to multiply the number of floors by the number of offices on each floor.

Given that the building has 24 floors and 37 offices on each floor, we can use the formula:

Total number of offices = Number of floors * Number of offices per floor

Plugging in the given values, we get:

Total number of offices = 24 * 37 = 888

Therefore, there are 888 offices in the building.

This calculation assumes that each floor has the same number of offices and that there are no variations or exceptions. It also assumes that there are no common areas or other types of spaces that are not considered offices.

To know more about multiply, refer here:

https://brainly.com/question/24327271#

#SPJ11

Step-by-step explanation:

There are  1+ 3+ 4 = 8 parts to divide

80 / 8 =  £ 10  for each part

                          1 part    = 1 x 10  = £ 10

                           3 parts = 3 x 10 = £ 30

                          4 parts = 4 x 10 = £ 40

Answer:

10

Step-by-step explanation:

1+3+4=8

80/8=10

The fraction of 5 liters that is 6,800 ml is 8/5 or 1 3/5 in mixed number form, which represents one whole 5-liter container plus 3/5 of another 5-liter container.6800 ml is equivalent to 6.8 liters. To find the fraction of 5 liters that is 6.8 liters, we can divide 6.8 by 5:

6.8 / 5 = 1 3/5

Therefore, the fraction of 5 liters which is 6800 ml is 1 3/5, which is a mixed number. This means that the total volume of 6.8 liters is equivalent to one whole 5-liter container, plus 3/5 of another 5-liter container.

To convert this mixed number into a fraction, we can first multiply the whole number by the denominator of the fraction and add the numerator to get the improper fraction:

1 * 5 + 3 = 8

The improper fraction is 8/5. This means that 6.8 liters are equivalent to 8/5 of 5 liters.

To reduce the fraction to the lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 1:

8/5 = 8 ÷ 1 / 5 ÷ 1 = 8/5

A fraction is a mathematical representation of a part of a whole. It is written in the form of a numerator and a denominator separated by a horizontal line, where the numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole.

For example, the fraction 3/4 represents three parts out of a total of four parts. It can also be represented visually using a diagram such as a pie chart or a number line.

Fractions can be added, subtracted, multiplied, and divided, and can also be converted between different forms, such as mixed numbers, improper fractions, and decimals. They are commonly used in a variety of mathematical applications, such as in measurements, ratios, and proportions, as well as in everyday life situations, such as dividing a pizza into slices or calculating discounts on a sale.

Find out more about fraction

brainly.com/question/17122642

#SPJ4

Answer:

636.98

Step-by-step explanation:

[tex]704 * .13 = 91.52 (discount)\\704 - 91.52 = 612.48 (price after discount)\\612.48 * .04 = 24.4992 (tax)\\612.48 + 24.4992 = 636.9792(Price with tax)\\round= 636.98[/tex]

the sales tax applies to the price after the discount is applied

The area of Triangle B is 2 times greater than the area of Triangle A.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

Area of the triangle = 1/2 h*b

For Triangle A, the area is:

Area_A = 1/2 * b * h

For Triangle B, the area is:

Area_B = 1/2 * b * 2h = b * h

So, the area of Triangle B is twice the area of Triangle A.

Therefore, the area of Triangle B is 2 times greater than the area of Triangle A.

Learn more about triangle, by the following link

brainly.com/question/17335144

#SPJ1

The answers to the questions are as follows a)50  out of the 200 vehicles will fail in their first 2 years. b)The approximate probability that 50 or more vehicles fail in their first 2 years is essentially zero. c) the approximate probability that no more than 10 of the remaining vehicles fail in their first 2 years is essentially zero.

(a) The average lifespan of the vehicle follows an exponential distribution with a rate parameter of λ = 1/8 since the average lifespan is 8 years. Let X be the number of vehicles that fail in their first 2 years. Then X follows a Poisson distribution with parameter λt, where t is the time period of interest, which is 2 years. Therefore, the expected number of vehicles that fail in their first 2 years is E(X) = λt = (1/8)*2 = 1/4. So we would expect 1/4 * 200 = 50 of the 200 vehicles to fail in their first 2 years.

(b) The number of vehicles that fail in their first 2 years follows a Poisson distribution with parameter λt = 1/4. To approximate the probability that 50 or more of them fail in their first 2 years, we can use the normal approximation to the Poisson distribution. The mean of the normal distribution is μ = λt = 1/4, and the variance is σ^2 = λt = 1/4.

Therefore, the standard deviation is σ = [tex]\sqrt{\frac{1}{4} }[/tex]= 1/2. To standardize the random variable X, we use the formula Z = (X - μ)/σ. Therefore, Z = (50 - 1/4)/(1/2) = 99.5. Using a standard normal distribution table or calculator, the probability of Z being greater than or equal to 99.5 is essentially zero, so the approximate probability that 50 or more vehicles fail in their first 2 years is essentially zero.

(c) Given that 30 vehicles have already failed in under 2 years, 170 vehicles are remaining. We want to find the probability that no more than 10 fail in their first 2 years. Since the number of vehicles that fail in their first 2 years follows a Poisson distribution with parameter λt = 1/4, the number of vehicles that do not fail in their first 2 years follows a Poisson distribution with parameter μ = λt * (number of remaining vehicles) = (1/4)*170 = 42.5. Therefore, the probability that no more than 10 of the remaining vehicles fail in their first 2 years is the same as that a Poisson distribution with parameter 42.5 is less than or equal to 10.

The resulting Z-score is Z = (10 - 42.5)/sqrt(42.5) = -6.72. Using a standard normal distribution table or calculator, the probability of Z being less than or equal to -6.72 is essentially zero, so the approximate probability that no more than 10 of the remaining vehicles fail in their first 2 years is essentially zero.

Learn more about  Poisson distribution,

https://brainly.com/question/28044733

#SPJ4

Step-by-step explanation:

To find the volume, you have to use the formula:

V = whl

By the angle-angle-side theorem, triangles ∠ACE and ∠ECA are congruent, and we can conclude that:

AC = EC.

What is the congruent angle?

When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.

Since AB || DE and BC = DC, we can use the alternate interior angles theorem to conclude that angle BCA is congruent to angle DCE:

∠BCA = ∠DCE

We also know that angles ∠BAC and ∠ACD are supplementary:

∠BAC + ∠ACD = 180 degrees

Since AB || DE, we can use the corresponding angles theorem to conclude that ∠BAC is congruent to  ∠ECD:

∠BAC = ∠ECD

Substituting this into the equation above, we get:

∠ECD + ∠ACD = 180 degrees

Simplifying this equation, we get:

∠ECA = 180 degrees - ∠ACD

Also, ∠DCE is supplementary to ∠ACD, so:

∠DCE + ∠ACD = 180 degrees

Substituting this into the equation above, we get:

∠ECA = ∠DCE

Since angles ∠ECA and ∠DCE are congruent, we can use the vertical angles theorem to conclude that angles ∠ACE and ∠AEC are congruent:

∠ACE = ∠AEC

Therefore, by the angle-angle-side theorem, triangles ∠ACE and ∠ECA are congruent, and we can conclude that:

AC = EC.

To learn more about the congruent angle visit:

brainly.com/question/28262429

#SPJ9

The billing period is 31 days, so the average daily balance is $1,437.73.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and understand relationships between variables. Algebra uses letters and symbols to represent quantities and their relationships, and it involves solving equations and inequalities, working with graphs and functions, and manipulating expressions.

Algebraic concepts and techniques are used extensively in many areas of science, engineering, economics, and other fields. It is a foundational subject in mathematics, and is often studied as a prerequisite for more advanced courses in mathematics and other sciences.

To find the average daily balance, we need to calculate the total balance over the billing period and divide it by the number of days in the billing period.

The total balance is:

10 days at $778.12 = $7,781.20

8 days at $1,876.00 = $15,008.00

3 days at $2,112.50 = $6,337.50

10 days at $1,544.31 = $15,443.10

Total balance = $44,569.80

The billing period is 31 days, so the average daily balance is:

$44,569.80 / 31 = $1,437.73

Rounding this to the nearest cent, we get an answer of $1,437.74, which is option C.

To know more about average visit:

https://brainly.com/question/29142021

#SPJ1

The probability that the respondent has a pet given that the respondent has had a pet is approximately 0.519, or 51.9%.

To calculate the probability that a respondent has a pet given that they have had a pet, we can use Bayes' theorem:

P(Have a pet | Have had a pet) = P(Have had a pet | Have a pet) * P(Have a pet) / P(Have had a pet)

We are given that:

P(Have a pet) = 0.41

P(Have had a pet) = 0.79

We don't know P(Have had a pet | Have a pet), but we can use the fact that anyone who has a pet has also had a pet, so:

P(Have had a pet | Have a pet) = 1

Plugging in these values, we get:

P(Have a pet | Have had a pet) = 1 * 0.41 / 0.79

= 0.519 or 51.9%.

Learn more about probability here:

https://brainly.com/question/11234923

#SPJ1

The type of hypothesis which posits a difference between groups, but the difference is not specified is (c) nondirectional hypothesis.

The Non-Directional hypothesis explains that there is a difference between two groups without specifying the direction of the difference.

The non-directional hypothesis is also known as a two-tailed hypothesis.

For example, a nondirectional hypothesis might be "there is a difference in intelligence between males and females" without specifying whether males or females have higher intelligence.

A nondirectional hypothesis is appropriate when there is no prior knowledge or expectation about the direction of the difference between two groups.

Therefore, the correct option is (c).

Learn more about Hypothesis here

https://brainly.com/question/28742504

#SPJ4

The given question is incomplete, the complete question is

What type of hypothesis posits a difference between groups, but the difference is not specified?

(a) directional hypothesis

(b) research hypothesis

(c) nondirectional hypothesis

(d) null hypothesis.

The probability of drawing a second green ball, given that the first ball is green is equals to the 11/24.

We have specify the probabilities values for selecting balls without replacement,

Probability of choosing two green ball

= 11/50

Probability of choosing one green ball

= 12/25

We have to determine the probability of drawing a second green ball, given that the first ball is green. Let us consider the two events as

A = Probability of second ball green

B = probability first ball is green = 12/25

P (A and B) = P (Both balls are green)

= 11/50

Fir determining the required probability we use conditional probability formula,

P ( A/B ) = P( A and B) / P (B)

Plug all known values in above formula,

P ( A/ B) = ( 11/50)/(12/25)

= (11 × 25)/(50×12)

= 11/24

Hence, required probability value is equals to 11/24.

For more information about probability, refer:

https://brainly.com/question/25870256

#SPJ4

Step-by-step explanation:

As the speed increases the time required to travel a distance is lessened.

 say you have to go 100 km

     if you go 20 km /hr it will take 5 hr....butif you increase your speed

( x axis) to 50 km/ hr it will take less time ....ony 2 hours    so the graph A is most representative       (look at the positive portion of the graph of

                                                   y = 100/x  )