Jasmine pays £52.40 for 40 litres of petrol. What is the cost per litre?

The point which is the center of the ellipse whose equation is; (y+5)²/121+(x-9)²/49=1 s in the task content is; (-5, 9).

It follows from convention that the equation of an ellipse usually takes the form;

(y-h)²/a²+(x-k)²/b²=1 in which case, the center of the ellipse is given by the point; (h, k).

On this note, By comparison of the actual equation and the standard equation, it follows that;

+5 = -h and consequently, h = -5,

-9 = -k and consequently, k = 9.

Ultimately, the point which is the center of the

ellipse is; (-5, 9).

Remark: The equation of the ellipse which is missing in the task content is; (y+5)²/121+(x-9)²/49=1

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Answer: D. (9, −5)

Not (-5, 9)

Step-by-step explanation:

Answer:

x< 1/2 x>3/4

Step-by-step explanation:

Sorry i don't know how to put the equal sign but i hope this helps!

Answer:

To find the probability that on two consecutive mornings the person will miss the bus at least one morning, we can use the complement rule. The complement of missing the bus is catching the bus. Therefore, the probability of missing the bus on both mornings is (0.4) x (0.4) = 0.16. The probability of not missing the bus on both mornings is (1 - 0.4) x (1 - 0.4) = 0.36. To find the probability of missing the bus at least one morning, we can subtract the probability of not missing the bus on both mornings from 1: P(missing bus at least once) = 1 - P(not missing bus on both mornings) P(missing bus at least once) = 1 - 0.36 P(missing bus at least once) =

I. sugar content is approximately (11.72, 12.08) grams.

II. we would need a sample size of at least 465 servings to achieve a 95% confidence interval that specifies the mean within ±0.1.

III. confidence level of the interval (11.81, 11.99) is approximately 95%.

Confidence Interval = Sample Mean ± (Critical Value)× (Standard Deviation / √(n))

Where:

Sample Mean = 11.9 g (average sugar content)

Standard Deviation = 1.1 g

n = Sample Size (number of servings)

Critical Value = The value corresponding to the desired confidence level. For a 95% confidence level, the critical value is approximately 1.96.

Substituting the given values into the formula:

Confidence Interval = 11.9 ± (1.96) ×(1.1 / sqrt(140))

Calculating the confidence interval:

Confidence Interval = 11.9 ± (1.96) × (1.1 / 11.8322)

Confidence Interval = 11.9 ± (1.96) × (0.0929)

Confidence Interval = 11.9 ± 0.1817

Confidence Interval ≈ (11.72, 12.08)

Therefore, the 95% confidence interval for the sugar content in a one-cup serving of the breakfast cereal is approximately (11.72, 12.08) grams.

II. To determine the sample size needed for a 95% confidence interval that specifies the mean within ±0.1, we can use the following formula:

Sample Size (n) = [(Critical Value ×Standard Deviation) / Margin of Error]²

Where:

Critical Value = 1.96 (corresponding to the 95% confidence level)

Standard Deviation = 1.1 g

Margin of Error = 0.1 g

Substituting the given values into the formula:

Sample Size (n) = [(1.96 ×1.1) / 0.1]²

Sample Size (n) = (2.156 / 0.1)²

Sample Size (n) = 21.56²

Sample Size (n) ≈ 464.8036

Rounding up to the nearest whole number, we would need a sample size of at least 465 servings to achieve a 95% confidence interval that specifies the mean within ±0.1.

III. The confidence level of the interval (11.81, 11.99) can be determined by calculating the margin of error and finding the corresponding critical value.

Margin of Error = (Upper Limit - Lower Limit) / 2

Margin of Error = (11.99 - 11.81) / 2

Margin of Error = 0.18 / 2

Margin of Error = 0.09

To find the critical value, we need to determine the z-value (standard normal distribution value) corresponding to a two-tailed confidence level of 95%. The z-value is found using the cumulative distribution function (CDF) or a standard normal distribution table. For a 95% confidence level, the z-value is approximately 1.96.

Since the margin of error is equal to half the width of the confidence interval, we can set up the equation:

Critical Value×(Standard Deviation / √(n)) = Margin of Error

Substituting the given values:

1.96× (1.1 / √(n)) = 0.09

Solving for n:

√(n) = (1.96 ×1.1) / 0.09

√(n) = 21.56

n ≈ 464.8036

Rounding up to the nearest whole number, we obtain n ≈ 465.

Therefore, the confidence level of the interval (11.81, 11.99) is approximately 95%.

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B

this is the answer

The supply of styluses is falling at a rate of 0.0144p² styluses per week.

To determine the exact rate of change in supply, we need to look at the equation provided: 500p²x² = 1996. We can rearrange this equation to solve for x, which represents the supply of styluses:

x² = (1996/500p²)

x = √(1996/500p²)

Now, we can differentiate this equation with respect to time to find the rate of change in supply:

dx/dt = (-1/2)(1996/500p²)(-1000p²/1996)*dp/dt

Simplifying this equation, we get:

dx/dt = (6/25)p²dp/dt

Using the information provided in each situation, we can plug in the appropriate values to find the rate of change in supply:

In the first situation, where the price is rising at 12 cents per week, dp/dt = 0.12. Plugging this into the equation above, we get:

dx/dt = (6/25)(p²)(0.12) = 0.0288p²

This means that the supply of styluses is rising at a rate of 0.0288p² styluses per week.

In the second situation, where the price is falling at 6 cents per week, dp/dt = -0.06. Plugging this into the equation above, we get:

dx/dt = (6/25)(p²)(-0.06) = -0.0144p²

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where E is the electric field, σ is the charge per unit area, and ε₀ is the permittivity of free space.Electric field = σ/2ε₀ = 6.50 x 10⁻⁹ C/m² / 2(8.85 x 10⁻¹² F/m)Electric field = 3.68 x 10⁴ N/C Therefore, the electric field due to the charged sheet is 3.68 x 10⁴ N/C.

A square insulating sheet 70.0 cm on a side is held horizontally. The sheet has 6.50 nc of charge spread uniformly over its area. The question is asking for the electric field due to this charged sheet.Using the equation below, we can solve for the electric field due to the sheet.E

= σ/2ε₀.where E is the electric field, σ is the charge per unit area, and ε₀ is the permittivity of free space.Electric field = σ/2ε₀

= 6.50 x 10⁻⁹ C/m² / 2(8.85 x 10⁻¹² F/m)Electric field

= 3.68 x 10⁴ N/C Therefore, the electric field due to the charged sheet is 3.68 x 10⁴ N/C.

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Answer:

i don't think you're in high school

#1. 15.84 (6.6 * 2.4)

#2 193.2 (27.6 * 7)

#3 B and E

Step-by-step explanation:

6.6 * 2.4

27.6 * 7

Answer:

No. of miles Jake rode today = 6.6×2.4 times

= 15.84 miles

1 gallon of gas = 27.6 miles

7 gallons of gas = 193.2 miles

Myla's car can go 193.2 miles with 7 gallons of gas.

All expressions except 7.33×6.

well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}\)

\(417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}\)

SAS................

.........................

Answer:

D)

Step-by-step explanation:

5x5+5=30

8x9+7=79

24x3+28=100

Answer:

There is 160.81 % of increase.

Step-by-step explanation:

Given that,

The average size of a privately owned farm in a particular country was 171 acres.

Now, the average size of a privately owned farm in the country had increased to 446 acres.

We need to find the percent increase.

\(\%=\dfrac{\text{increase}}{\text{original}}\times 100\\\\\%=\dfrac{446-171}{171}\times 100\\\\\%=160.81\%\)

So, there is 160.81 % of increase.

Answer:

A fraction, colon, words

The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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Answer:

$2,000 and $3,000

Step-by-step explanation:

The computation is shown below:

Given that

The Number of shares is 100

The Increase from $20 to $30

If the per share is $20, so the earning of the shareholder is

= 100 shares × $20

= $2,000

And ,if the per share is $30, so the earnings of the shareholder is

= 100 shares × $30

= $3,000

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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The upper and lower control limits for the X-bar chart are approximately 53.87 and 50.78,

The upper and lower control limits for the X-bar chart, we need to calculate the sample mean (X-bar) and the sample standard deviation (S) of the data. Once we have these values, we can use the formulas for control limits.

From the given table, let's calculate the X-bar and S:

Sample Size (n) = 5

Sample Values: 51, 52, 53, 55, 50

The X-bar (sample mean)

X-bar = (Sum of sample values) / n

X-bar = (51 + 52 + 53 + 55 + 50) / 5

X-bar = 261 / 5

X-bar = 52.2

The range (R)

R = Maximum value - Minimum value

R = 55 - 50

R = 5

The average range (R-bar)

R-bar = (Sum of ranges) / n

R-bar = (5 + 5 + 5 + 5 + 5) / 5

R-bar = 25 / 5

R-bar = 5

The standard deviation (S)

S = R-bar / d2

(d2 is a constant depending on the sample size, in this case, n = 5)

Using the d2 value for n = 5 from the control chart constants table, we find d2 = 2.326.

S = 5 / 2.326

S ≈ 2.15

Now that we have X-bar and S, we can calculate the control limits:

Upper Control Limit (UCL) = X-bar + (A2 × S /√(n))

Lower Control Limit (LCL) = X-bar - (A2 × S / √(n))

Using the appropriate constant A2 for n = 5 from the control chart constants table, we find A2 = 0.577.

UCL = 52.2 + (0.577 × 2.15 / √(5))

UCL ≈ 53.87

LCL = 52.2 - (0.577 × 2.15 / √(5))

LCL ≈ 50.78

Therefore, the upper and lower control limits for the X-bar chart are approximately 53.87 and 50.78, respectively.

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Answer:

x = 30

Step-by-step explanation:

2x - 6

-----------  =  9

    6

2x - 6

-----------  =  9(6)

    6(6)

2x - 6 = 54

     +6    +6

2x = 60

÷2    ÷2

x = 30

I hope this helps!

Answer:

7/50 = x/75

x = 10.5

therefore he would run 10.5 miles in 75 minutes

Answer:

In 75 minutes, she runs (7/50) x 75 = 10.5.

She runs 10.5 miles in 75 minutes.

Step-by-step explanation:

Answer:

b)4 11/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

To factor the equation u^2 - 4u + 4, we need to find two numbers that add up to -4 and multiply to 4.

The two numbers are -2 and -2 because:

-2 + (-2) = -4 and (-2)(-2) = 4

Using these numbers, we can factor the equation as:

u^2 - 4u + 4 = (u - 2)(u - 2) = (u - 2)^2

Therefore, the factored form of the equation is (u - 2)^2.

Answer:

9

Step-by-step explanation:

3*2=6

6+3=9

Most important condition for sound conclusions as per statistical inference is given by ,

option a. Data come from a well-designed random sample or randomized experiment.

The most important condition for sound conclusions from statistical inference is ,

The data that comes from a well-designed random sample or randomized experiment.

Random sampling or randomization helps ensure that the sample is representative of the population.

This allows for generalizations and statistical inferences to be made with a high degree of confidence.

This is a fundamental principle of statistics and is essential for the validity of statistical conclusions.

The other conditions listed may also be important in certain contexts.

But they are not as fundamental as the requirement for a representative sample.

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The dot plots is an illustration of charts and graphs

The average score of period 7 is greater than the average score of period 1

From the dot plots in the complete question, we have the following frequency tables

Period 1                                                          Period 7

Score     Students                                          Score     Students

55           1                                                         65           1

70           1                                                         75           3

75           6                                                         80         5

80           6                                                         85         6

85           2                                                         90         3

90           3                                                         95        2

95           1                                                                

The average is calculated using:

\(\bar x = \frac{\sum fx}{\sum f}\)

For period 1, we have:

\(\bar x_1 = \frac{55 * 1 + 70 * 1 + 75 * 6 + 80 * 6 + 85 * 2 + 90 * 3 + 95 * 1}{1 + 1 + 6 + 6 + 2 + 3 + 1}\)

Evaluate the sum

\(\bar x_1 = \frac{1590}{20}\)

Evaluate the quotient

\(\bar x_1 = 79.5\)

For period 7, we have:

\(\bar x_7 = \frac{65 * 1 + 75 * 3 + 80 * 5 + 85 * 6 + 90 * 3 + 95 * 2}{1 + 3 + 5 + 6 + 3 + 2}\)

Evaluate the sum

\(\bar x_7 = \frac{1660}{20}\)

Evaluate the quotient

\(\bar x_7 = 83\)

By comparison, 83 is greater than 79.5

Hence, the average score of period 7 is greater than the average score of period 1

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Answer:

Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

Answer:

I am pretty sure it is:  1,990. let me know if I am wrong. I think is correct though.

Step-by-step explanation:

Answer:

1990$

Step-by-step explanation:

The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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Answer:

w=54

Step-by-step explanation:

Answer:

W = 54

Step-by-step explanation:

Angles on a straight line add up to 180

180 - 126 = 54

When measuring the effects of a new diuretic medication, hourly urine output represents the ratio level of measurement.

What is ratio level of measurement?

Ratio level of measurement is a type of measurement that features a true zero point, meaning that the value 0 represents the absence of the characteristic being measured.

Some examples of ratio level measurements include weight, height, length, distance, speed, and many others. In this case, the hourly urine output of subjects is measured to determine the effects of a new diuretic medication.

The hourly urine output is a ratio measurement because it has a true zero point, which is the absence of urine output. In other words, if there is no urine output, the value would be 0, which represents the absence of the characteristic being measured.

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