3 6/12 rounded to the nearest whole number

Answer:

a) 640 ml

b) 40 ml

Step-by-step explanation:

The ratio of lime to lemonade for the fizzy drink is 5 : 3 or as a fraction that would be

\(\dfrac{\text{Lime juice}}{\text{Lemonade}}= \dfrac{5}{3}\)

\(\text{Therefore the ratio of lemonade to lime }\\\\ = \text{reciprocal of $ \dfrac{5}{3} $} }\\\\= \dfrac{3}{5}\)

Part a)

For  all 400 ml of  lime juice we would need
\(\dfrac{3}{5} \times 400 \;ml = 3 \times 80 = 240 \;ml\)  

Total amount of fizzy drink that can be maade
= amount of lime juice + amount of lemonade

= 400 + 240

= 640 ml

This is the answer to Part a)

Part b)

If Gianni has only 280 ml and is using all 400 ml of lime juice then the amount of lemonade used as calculated in part 1) is 240ml

That means the amount of lemonade left over = 280 - 240 = 40 ml

Complete question is;

Identify the type of sampling​ used: random,​ systematic, convenience,​ stratified, or cluster.

To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans

Answer:

Systematic Sample

Step-by-step explanation:

We are told that the quality control manager selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans.

Thus, the selection is from a large sample of produce.

This is synonymous with systematic sample because systematic sample can be defined as a type of probability sampling in which sample members from a larger population are selected according to a random starting point but with a set periodic interval.

This resonates with the statement in the question about selecting every 18th soup from the production assembly line.

The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.

To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.

With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.

Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.

Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.

Therefore, the correct answer is A. Plus/minus 0.497.

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The complete statement is folk tales and fairy tales

Both folk tales and fairy tales are types of fiction because they are imaginative stories that are not based on factual events or characters.

Folk tales

Folk tales are stories with no known creator. They were originally passed down from one generation to another by word of mouth. Folk tales are a type of traditional literature that is deeply rooted in the culture of a particular region or community.

They often feature supernatural elements, and their origins can be traced back many centuries.

Because they were passed down orally, different versions of the same tale may have developed in different regions, with variations in characters, plot, and theme.

Fairy tales

Fairy tales were often created to teach children behavior in an entertaining way. Fairy tales are a type of story that typically features magical creatures or events and often have a moral or lesson to teach. They were originally intended for both adults and children and were used as a way to teach moral values, societal norms, and important life lessons in an entertaining way.

The fairy tale genre has evolved over time, and modern fairy tales may have different themes and messages than traditional ones.

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Option C, "There are infinitely many solutions," accurately describes the possible solution or solutions of the system when the graphs of the linear equations coincide.

If the graphs of the linear equations in a system are the same line, it means that there are infinitely many solutions to the system.

The equations are equivalent and represent the same line in the coordinate plane. Every point on the line satisfies both equations simultaneously, making it a solution to the system.

This occurs when the equations are dependent, indicating that they are proportional or represent the same relationship between variables.

Therefore, option C, "There are infinitely many solutions," accurately describes the possible solution or solutions of the system when the graphs of the linear equations coincide.

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Answer:

2

Step-by-step explanation:

The initial value is the y value of the first term shown ( when x=1)

y = 2 when x=1

The initial value is 2

Answer:

What is the initial value of the sequence?

Step-by-step explanation:

Edge 2021

The interquartile range is a useful tool for measuring variability in a set of data because it overcomes the difficulty of the range being influenced too much by extreme values

The interquartile range is a measure of variability that is commonly used in statistics to describe the spread of a set of data. It is particularly useful because it overcomes the difficulty of the range being influenced too much by extreme values.

In mathematical terms, the interquartile range is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1).

The upper quartile represents the 75th percentile of the data and the lower quartile represents the 25th percentile of the data.

This means that 25% of the data falls below the lower quartile and 75% of the data falls above the upper quartile.

The interquartile range provides a better representation of the spread of the data because it eliminates the influence of extreme values.

These values, also known as outliers, can have a significant impact on the range and can make it appear as though the data is more spread out than it actually is.

By using the interquartile range, the outliers are excluded and a more accurate representation of the spread of the data is obtained.

Therefore, option (a) is correct.

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The area of the region is (27π/4) square units.

We have,

To find the area of the region inside the circle (x + 3)² + y² = 9 and outside the circle x² + y² = 9, we can use a double integral in polar coordinates.

The region is an annulus (a region between two concentric circles) with the smaller circle centered at (-3,0) and radius 3, and the larger circle centered at the origin and radius 3.

We can rewrite the equations of the circles in polar coordinates as:

(x + 3)² + y² = 9

And,

r² + 2r cos(theta) + 9 = 9

r² + 2r cos(theta) = 0
r = -2 cos(theta)

And,

x² + y² = 9

r² = 9

The region can be described as 0 ≤ r ≤ 3 and -π/2 ≤ θ ≤ π/2 since we are only interested in the part of the region above the x-axis.

The area of the region can be calculated using the following double integral:

A = ∫∫R r dr dθ

where R is the region in polar coordinates.

We can integrate with respect to r first:

A = ∫(-π/2)^(π/2) ∫0³ r dr dθ

= ∫(-π/2)^(π/2) [(1/2) r²]_0³ dθ

= ∫(-π/2)^(π/2) (9/2) dθ

= (9/2) [θ]_(-π/2)^(π/2)

= (9/2) [π - (-π/2)]

= (9/2) (3π/2)

= (27π/4)

Thus,

The area of the region is (27π/4) square units.

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Answer:

No, Bill needs more than 4 pounds of apples to make apple strudel.

Step-by-step explanation:

If 4 pounds isn't enough then neither would 3.5. So he need more pounds to make the strudel.

The solution to the logarithm equation is log5(2x-7) = 0 is x = 4.

What is logarithm ?

A logarithm is a mathematical function that represents the exponent to which a fixed number, called the base, must be raised to produce a given value. In other words, a logarithm is the inverse operation of exponentiation.

For example, if we have the equation \(10^3 = 1000\), the logarithm of 1000 with base 10 is 3, because \(10^3 = 1000\). Similarly, the logarithm of 8 with base 2 is 3, because \(2^3 = 8.\)

According to the question:

To solve for x in the equation:

log5(2x-7) = 0

We can use the definition of logarithms which states that log_b(x) = y is equivalent to \(b^y = x.\)

Applying this to the given equation, we get:

\(5^0 = 2x - 7\)

\(1 = 2x - 7\)

\(2x = 8\)

\(x = 4\)

Therefore, the solution to the equation is log5(2x-7) = 0 is x = 4.

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The pressure above the water is 15 lb/in^2 and for every 10 ft, the pressure rises 4.54 lb/in^2

The equation would be:

If x = 0, the pressure in the surface is 15 lb/in^2, for each 10 ft of x, the pressure rises 4.54 lb/in^2

Now to solve when the pressure is 80 lb/in^2, we subtitute in the equation:

And solve for x:

Then the answer to question 2 is 1.43ft

This is basically a linear equation. The slope is the 4.54lb/in^2 for each 10ft. Then we need to adjust the 10ft of x, to reprensents each step of 10 ft for x. And we need to add the 15lb/in^2 for the surface pressure. With all this, we can construct the function of the pressure dependant of the deepness x.

There is a probability of approximately 31.43% that three students selected at random from the class will all be girls.

To find the probability that all three selected students are girls, we need to calculate the probability of selecting a girl on the first draw, then a girl on the second draw, and finally a girl on the third draw.

The probability of selecting a girl on the first draw is 12/16 (since there are 12 girls out of a total of 16 students).

After one girl has been selected, there will be 11 girls left out of a total of 15 students, so the probability of selecting a girl on the second draw is 11/15.

After two girls have been selected, there will be 10 girls left out of a total of 14 students, so the probability of selecting a girl on the third draw is 10/14.

So, the overall probability of selecting three girls in a row is:

(12/16) x (11/15) x (10/14) = 0.3143 or approximately 31.43%

Therefore, there is a probability of approximately 31.43% that three students selected at random from the class will all be girls.

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Answer:

True

Step-by-step explanation:

Since babysitting and working at the grocery store are two different things, you would need two different variables.

So x and y would be the correct representation.

Hope this helps ya!!

Answer: 91

Step-by-step explanation: 2+89=91

The differential equation

\(M(x,y) \, dx + N(x,y) \, dy = 0\)

is considered exact if \(M_y = N_x\) (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function \(f(x,y)=C\) such that \(f_x=M\) and \(f_y=N\).

We have

\(M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)\)

\(N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)\)

and \(M_y=N_x\), so the equation is indeed exact.

Now, the solution \(f\) satisfies

\(f_x = \tan(x) - \sin(x) \sin(y)\)

Integrating with respect to \(x\), we get

\(\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx\)

\(\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)\)

and differentiating with respect to \(y\), we get

\(f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}\)

\(\implies \dfrac{dg}{dy} = 0 \implies g(y) = C\)

Then the general solution to the exact equation is

\(f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}\)

Answer: Option (1)

Step-by-step explanation:

\(\angle DMA\) is another name for angle 3, but not \(\angle DME\).

Regular expressions for the given sets of binary strings: 1. All binary strings except empty string: `1+0*` 2. Begins with 1 and ends with 1: `1(0|1)*1` 3. Ends with 00: `(0|1)*(00)` 4. Contains at least three 1s: `(0*10*){3,}`

The regular expressions for the given sets of binary strings are as follows:
1. All binary strings except the empty string:
  - Regular expression: `1+0*`
  - Explanation: The regular expression `1+0*` matches any binary string that starts with one or more 1s, followed by zero or more 0s. This ensures that the empty string is not included.

2. Binary strings that begin with 1 and end with a 1:
  - Regular expression: `1(0|1)*1`
  - Explanation: The regular expression `1(0|1)*1` matches any binary string that starts with 1, followed by zero or more occurrences of either 0 or 1, and ends with 1.

3. Binary strings that end with 00:
  - Regular expression: `(0|1)*(00)`
  - Explanation: The regular expression `(0|1)*(00)` matches any binary string that contains zero or more occurrences of either 0 or 1, followed by 00 at the end.

4. Binary strings that contain at least three 1s:
  - Regular expression: `(0*10*){3,}`
  - Explanation: The regular expression `(0*10*){3,}` matches any binary string that contains three or more occurrences of the pattern 0*10*, where 0* matches zero or more 0s and 1 matches a single 1.

These regular expressions provide a clear and concise way to match the specified sets of binary strings using basic operations such as concatenation, alternation, and repetition. It's important to note that there may be other valid regular expressions that can also match the given sets of strings.

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Answer:

cubic-degree of 3

Step-by-step explanation:

its not the first two, because they have way more waves

CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)

We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:

1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.

To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so

Z' = 1.96)
s = sample standard deviation
n = sample size

Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92

Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41

Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.

Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67

Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72

Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately

(5.80, 7.72)

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Answer:

b = y - mx

Step-by-step explanation:

Given

y = mx + b ( isolate b by subtracting mx from both sides )

y - mx = b

Answer:

b=y-mx

Step-by-step explanation:

You need to get b by itself, so you subtract mx.

The equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 in the form of y = mx + b is y = (6/49)x - 29/49 .

The function whose tangent line is to be found out is f(x)=(x-5)/(x+1) ;

to find the tangent equation , we differentiate the function ;

the function f(x) is of the form g(x)/h(x) ;

On differentiating g(x) and h(x) , we get that g'(x) = h'(x) = 1 ;

We get ; f'(x) = [1(x+1))-(1(x-5)]/(x+1)² ;

⇒ f'(x) = [x+1-x+5]/(x+1)² ;

⇒ f'(x) = 6/(x+1)² ;

Now, we x = 6 in the derivative to find slope of tangent at that point.

So , ⇒ f'(6) = 6/(6+1)²

⇒ f'(6) = 6/49

Now the slope is =  6/49 ,  the value of y in (6,y) by putting in x = 6 into the original function:

⇒ f(6) = (6 - 5)/(6 + 1)

⇒ f(6) = 1/7

We currently know a point (6,1/7) = (x₁,y₁) and slope of tangent, which is 6/49.

now using  point slope form to find equation of tangent.

⇒ y-y₁ = m(x-x₁)

⇒ y - 1/7 = (6/49)(x-6)

⇒ y = (6/49)x - 29/49

Therefore , The equation of the tangent is y = (6/49)x - 29/49 .

The given question is incomplete , the complete question is

What is the equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 . Enter your answer as an equation in the y = mx + b form ?

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By knowing the circumference of the base of the cone, we see that the radius is 4 centimeters.

Notice that in the first figure, the length of the arc AB is L = 8π cm.

Then, that arc will be the bottom part of the cone. Then we can see that the circumference of the base of the cone will be equal to the length of the arc.

And remember that for a circle of radius R (like the base of the cone), the circumference is:

C = 2πR.

Then we will get:

8π cm = C =  2πR

( 8π cm)/ 2π = R

4cm = R

The radius of the cone is 4cm.

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The given expression 5sin(95°)cos(75°) can be rewritten as 5 * (1/2)[sin(10°) + sin(20°)] using the product-to-sum identity.

To rewrite the expression 5sin(95°)cos(75°) using the product-to-sum identities, we can use the formula:

sin(A)cos(B) = (1/2)[sin(A+B) + sin(A-B)]

Let's apply this formula step by step:

Start with the given expression: 5sin(95°)cos(75°)

Use the product-to-sum identity for sin(A)cos(B):

5sin(95°)cos(75°) = 5 * (1/2)[sin(95° + 75°) + sin(95° - 75°)]

Simplify the angles inside the sine function:

5 * (1/2)[sin(170°) + sin(20°)]

Use the fact that sin(170°) = sin(180° - 10°) = sin(10°) (sine function is symmetric around 180°):

5 * (1/2)[sin(10°) + sin(20°)]

So, the given expression 5sin(95°)cos(75°) can be rewritten as 5 * (1/2)[sin(10°) + sin(20°)] using the product-to-sum identity.

Note: The values of sin(10°) and sin(20°) can be evaluated using a calculator or reference table to obtain their approximate decimal values.

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The given expression 5sin(95°)cos(75°) can be rewritten as 5 * (1/2)[sin(10°) + sin(20°)] using the product-to-sum identity.

To rewrite the expression 5sin(95°)cos(75°) using the product-to-sum identities, we can use the formula:

sin(A)cos(B) = (1/2)[sin(A+B) + sin(A-B)]

Let's apply this formula step by step:

Start with the given expression: 5sin(95°)cos(75°)

Use the product-to-sum identity for sin(A)cos(B):

5sin(95°)cos(75°) = 5 * (1/2)[sin(95° + 75°) + sin(95° - 75°)]

Simplify the angles inside the sine function:

5 * (1/2)[sin(170°) + sin(20°)]

Use the fact that sin(170°) = sin(180° - 10°) = sin(10°) (sine function is symmetric around 180°):

5 * (1/2)[sin(10°) + sin(20°)]

So, the given expression 5sin(95°)cos(75°) can be rewritten as 5 * (1/2)[sin(10°) + sin(20°)] using the product-to-sum identity.

Note: The values of sin(10°) and sin(20°) can be evaluated using a calculator or reference table to obtain their approximate decimal values.

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Answer

B

Step-by-step explanation:

I know it

If rain fell for two hours and totaled four centimeters, the rain rate would be two centimeters per hour.

Rebecca took note of the amount of rain that fell on Wednesday. If the rain poured for two hours and totaled four centimeters.

To determine the rate at which the rain fell, we need to know both the amount of rain that fell and the duration of the rain.

the rate of the rain = amount of rain/duration of the rain

As per the question, if the rain fell for a period of 2 hours and a total of 4 cm of rain fell, then the rate of the rain would be :

the rate of the rain = amount of rain/duration of the rain

the rate of the rain = 4 cm of rain fell/ 2 hours

Apply the division operation, and we get

the rate of the rain = 2 cm per hour

Hence, the correct answer would be option (B).

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The question seems to be incomplete the correct question would be:

Rebecca recorded the amount of rain last Wednesday. If the rain fell for a period of 2 hours and a total of 4 cm of rain fell. what rate did the rain fall? A. 5/2 cm per hour

B. 2 cm per hour

C. 2/5 cm per hour

D. 1/2 cm per hour

Answer:

The new interest rate is about 0.1038.

As a percent, this is about 10.4%.

Step-by-step explanation:

We are given:

\(\displaystyle A=250(1.1)^t\)

From this, we can determine that the interest rate is compounded annually at 10%.

We want a new equation that keeps A and P but the interest rate is compounded quarterly.

Compound interest is given by:

\(\displaystyle A=P(1+\frac{r}{n})^{nt}\)

Since we are compounding quarterly, n = 4. Since the rate is 10%, r = 0.1. P stays at 250. Therefore:

\(\displaystyle A=250(1+\frac{0.1}{4})^{4t}\)

Add:

\(\displaystyle A=250(1.025)^{4t}\)

Rewrite:

\(A=250((1.025)^4)^t\)

So:

\(A\approx 250(1.1038)^t\)

Therefore, the approximate new interest rate is 1.1038 - 1 or about 0.1038.

As a percent, this will be 0.1038 or about 10.4%.

The standard deviation of the sample mean is also known as the standard error of the mean. It can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is $2 and the sample size is 100. So, the standard deviation of the sample mean is $2/sqrt(100) = $2/10 = $0.2. Is there anything else you would like to know?

I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

Answer:

120 calories in 1 cup, 720 in 6 cups

Step-by-step explanation:

I divided 90 by 3 to get 1/4 cup and then multiplied it by 4 to get for one cup. From there I multiplied by 6

Answer:

1 cup=120 calories    6 cups=720 calories

Step-by-step explanation:

We know that there are 90 calories in 3/4 of a cup and we can figure out that 30 calories are in each 1/4 of a cup because 90 divided by 3 equals 30 then just add 30 calories to 90 and get 120.  Finally just do 120 times 6 and get 720 .

Problem

1 1/3 divided by 40 by using the algorithm method

Solution

For this case we can do this first:

And then we can divide this number by 40 like this: