an oil tank can take up to 1200 litres of oil

there are already 450 litres of oil in the tank

the price of oil is 81.5p per litre

mr Leonard gets 7.5% discount on the price of oil.

How much discount does he get?

give your answer in £.

If we put the blocks in a line, the possible arrangements are 12600 ways. The factorial of the total blocks is divided by the multiplication of the factorial of each color of the block.

We have

If we put the blocks in a line, determine the possible arrangements!

In that situation, the number of possible arrangements can be calculated by

\(Number \: of \: possible \: arrangements = \frac{Total \: blocks!}{Green! \: Red! \: White! \: Black!}\)

So, the possible arrangements would be

\(= \frac{10!}{4! \: 3! \: 2! \: 1!}\)

\(= \frac{5 \times 6 \times 7 \times 8 \times 9 \times 10}{3! 2!}\)

\(= 5 \times 7 \times 8 \times 9 \times 5\)

= 12600 arrangements

Hence, there 12600 possible arrangements to put the blocks in a line.

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Answer:

1/8

Step-by-step explanation:

Basically, AB and A'B' are proportional. And in order to figure out the scale factor or k, we have to divide A'B' by AB (order of division matters) 1.2/9.6 to figure out the proportion. We get 1/8, and that is our scale factor.

Hope this was helpful

Answer:

The length and width of rectangle are 90 feet and 22.5 feet.

Step-by-step explanation:

Let the,

Now, according to the question substituting all the given values in the formula to find the value of x :

\( \longrightarrow{\pmb{\sf{P = 2(L + W)}}}\)

\( \longrightarrow{\sf{P = 2(L + W)}}\)

\( \longrightarrow{\sf{225= 2 \bigg(x + \dfrac{x}{4} \bigg)}}\)

\( \longrightarrow{\sf{225= 2 \bigg(\dfrac{4x + x}{4} \bigg)}}\)

\( \longrightarrow{\sf{225= 2 \bigg(\dfrac{5x}{4} \bigg)}}\)

\( \longrightarrow{\sf{225= 2 \times \dfrac{5x}{4}}}\)

\( \longrightarrow{\sf{225= \dfrac{2 \times 5x}{4}}}\)

\( \longrightarrow{\sf{225= \dfrac{10x}{4}}}\)

\( \longrightarrow{\sf{10x = 225 \times 4}}\)

\( \longrightarrow{\sf{10x = 900}}\)

\( \longrightarrow{\sf{x = \dfrac{900}{10}}}\)

\(\longrightarrow{\sf{\underline{\underline{x = 90}}}}\)

Hence, the value of x is 90.

Now, we know the value of x. So, calculating the length and width of rectangle :

\(\rule{300}{2.5}\)

Step-by-step explanation:

Probability is the ratio of number of success/ total outcomes

So let calculate each probability

We have six total outcomes here in each scenario.

P(5)=1/6

P(1 or 2)=2/6=1/3

P(odd number )=3/6=1/2

P(not 6)= 5/6

Also

P(not 6)=1-P(6)=5/6

P(even number)=3/6=1/2

P(1,2,3,4)=4/6=2/3

The mean of the team’s distances is 3.75 miles. The median of the team’s distances is 3.5 miles.

To find the mean of the distances run by the Kennedy High School cross-country running team, we will first add up all the distances and then divide by the number of distances. The distances ran by the Kennedy High School cross-country running team are:

3.5 miles, 2.5 miles, 4 miles, 3.25 miles, 3 miles, 4 miles, and 6 miles adding up these distances, we get:

3.5 + 2.5 + 4 + 3.25 + 3 + 4 + 6 = 26.25

So the sum of the distances is 26.25 miles. Now, to find the mean, we will divide by the number of distances, which is 7. Therefore, the mean of the distances is: Mean = Sum of distances / Number of distances

Mean = 26.25 / 7

Mean = 3.75 miles

To find the median of the distances run by the team, we will first arrange the distances in order from smallest to largest:2.5 miles, 3 miles, 3.25 miles, 3.5 miles, 4 miles, 4 miles, 6 miles

Now, we will find the middle value. Since there are 7 distances, the middle value will be the 4th value. Counting from the left, the 4th value is 3.5 miles. Therefore, the median of the distances ran by the team is 3.5 miles.

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The lowest common denominator Skyla could use to rewrite the fractions is 280.

We have,

Value is the relative what merit or important of something it can referred to an intangible concept such as a person principle or a tangible object such as rare coin. Will you very widely across culture society individual it can even very within the same individual overtime. Value is often used to describe the worth of something in terms of its usefulness beauty. Will you can also refer to the moral or ethical standard of a person or group.

To get this value, she would need to find the least common multiple of the denominators, which are 17, 20, 56, 8, and 15. To do this, she would list out the prime factors of each denominator and then multiply the highest number of each prime factor together.

17: 1 x 17

20: 2 x 10

56: 2 x 2 x 7

8: 2 x 2 x 2

15: 3 x 5

The highest number of each prime factor is 17, 10, 7, 2, and 5, so the least common multiple of the denominators is 17 x 10 x 7 x 2 x 5, which equals 280. This would be the lowest common denominator she could use to rewrite the fractions.

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complete question:

Skyla is trying to order the fractions below. Her first step is to rewrite each fraction with a common denominator. What is the lowest common denominator she could use? 17 20 56 8 15​

If you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image.

What is extrapolation and interpolation?

Extrapolation is an estimation based on extending a known sequence of data beyond what is absolutely known.

Interpolation is the estimation of a value in a sequence of values between two known values.

Bit plane slicing is a lossy compression technique, which means that some information from the original image is lost during the compression process. The purpose of bit plane slicing is to reduce the size of an image by removing less significant bits from each pixel. As a result, the quality of the image is reduced.

1st-order extrapolation and 2D bilinear interpolation are techniques used to estimate or predict missing or unknown values from a given set of data. These techniques can be used to enhance the quality of an image, but they cannot recover the original image in cases where information has been lost through compression or degradation. In other words, they can only improve the quality of the image to a certain extent, but they cannot restore it to its original state.

So, if you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image, although they may help to improve its quality to some extent.

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The probability that none of the packs are defective is 0.478. The probability that five packs are defective is 0.000455.The probability that all the packs are defective is 2.8243e-14.The probability that 7 or more packs are defective is 0.00416 (approx).

A shipment of 10,000 Karak tea packs is produced by the company Chai Karak. If 7% of the packs are defective, what is the probability that: none of the packs are defective, five packs are defective, all the packs are defective, and seven or more packs are defective?  The number of trials, n, is 10 and the probability of a defective tea pack is 0.07. Therefore, the number of successful trials, X, follows a binomial distribution. Formula for binomial distribution: P(X = k) = nCk × pk × (1 − p)n−kWhere nCk = number of combinations of n things taken k at a time = n! / (k! (n-k)!)a. The probability that none of the packs are defective P(X = 0):P(X = 0) = nC0 * p0 * (1-p)n-0= 10C0 * 0.07^0 * (1-0.07)^10= 1 * 1 * 0.478= 0.478Therefore, the probability that none of the packs are defective is 0.478.

The probability that 5 packs are defective:P(X = 5) = nC5 * p^5 * (1-p)n-5= 10C5 * 0.07^5 * (1-0.07)^5= 252 * 0.0000028 * 0.649= 0.000455Therefore, the probability that five packs are defective is 0.000455.

The probability that all the packs are defective:P(X = 10) = nC10 * p^10 * (1-p)n-10= 10C10 * 0.07^10 * (1-0.07)^0= 1 * 2.8243e-14 * 1= 2.8243e-14Therefore, the probability that all the packs are defective is 2.8243e-14.

The probability that 7 or more packs are defective: P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = 7) = nC7 * p^7 * (1-p)n-7= 10C7 * 0.07^7 * (1-0.07)^3= 120 * 0.0000953677 * 0.657= 0.00416P(X = 8) = nC8 * p^8 * (1-p)n-8= 10C8 * 0.07^8 * (1-0.07)^2= 45 * 0.0000024969 * 0.859= 0.000011P(X = 9) = nC9 * p^9 * (1-p)n-9= 10C9 * 0.07^9 * (1-0.07)^1= 10 * 0.00000005 * 0.93= 4.65e-7P(X = 10) = nC10 * p^10 * (1-p)n-10= 10C10 * 0.07^10 * (1-0.07)^0= 1 * 2.8243e-14 * 1= 2.8243e-14P(X ≥ 7) = 0.00416 + 0.000011 + 4.65e-7 + 2.8243e-14= 0.00416Therefore, the probability that 7 or more packs are defective is 0.00416 (approx).

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The factor of x in x / 3 = 7 / 9 is 21 / 9

The equation is

x / 3 = 7 / 9

The equation is the mathematical statement that shows the relationship between one expression and another expression with an equal sign. The inequality signs will not be a part of equation. The equation that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication.

The equation is

x / 3 = 7 / 9

Move the 3 to the right hand side of the equation

x = (7/9) × 3

x = 21/9

Hence, the factor of x in x/3 = 7/9 is 21/9

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Answer:

0

Step-by-step explanation:

(f-g)(x) = 12-sqrt(x)

plugging in 144, we get 12 - 12 = 0

one could also do f(x)-g(x) which would yield 24-24=0

Answer:

the correct answer is A

Step-by-step explanation:

i put B because thats what the first user said it was  and i got it wrong on my quiz, the quiz shows the corret answer is A

Answer:

2 (4x+9y)

Step-by-step explanation:

Simplified:

8x+18y

The value of  0e^0d0 is -1 if the integral in this exercise converges after applying limit.

A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.

We are assuming the:

\(=\int\limits^0_{-\infty} {\theta e^{\theta}} \, d\theta\)

Applying limit;

\(=\lim_{n \to \infty} \int\limits^0_{-n} {\theta e^{\theta}} \, d\theta\)

After solving the integral:

\(=\lim_{n \to \infty} (e^{\theta})|^0_-_p\)

= -(1-0)

= -1

Thus, the value of  0e^0d0 is -1 if the integral in this exercise converges after applying limit.

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The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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The number of  combinations of random samples  of 5 students can be selected is 56, here, the correct answer is 60.

To find the number of combinations of selecting a random sample of 5 students from a group of 12 students, you can use the formula for combinations which is:

C(n, k) = n! / (k!(n-k)!)

where C(n, k) represents the number of combinations, n is the total number of students (12 in this case), and k is the number of students to be selected (5 in this case). The exclamation mark (!) represents a factorial, which means the product of all positive integers up to that number.

Using the formula, we can calculate the number of combinations:

C(12, 5) = 12! / (5!(12-5)!)
= 12! / (5!7!)
= (12×11×10×9×8) / (5×4×3×2×1)
= 95,040 / 1,680
= 56.52 (rounded)

Since the number of combinations must be a whole number, the correct answer is 56, which is not among the given answer choices. However, the closest answer choice to 56 is 60.

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Answer:

165 km

Step-by-step explanation:

We know the ratio of map distance to actual distance is 1 cm : 15 km

Multiplying both sides by 11, we have 11 cm : 165 km

The older machine takes 3.8 hours to complete the remaining work.

Given DataA new machine requires 12 hours to complete one-half mile of road.An older machine requires 15 hours to complete one-half mile of road.

The new machine is brought in for 3 hours then it develops a mechanical problem and stops working.Now the older machine is brought in to complete the work.

We have to calculate the time taken by the older machine to complete the remaining work.SolutionLet the remaining work be X.

Then,The work done by the new machine in 3 hours= Time × Work Rate= 3 × Work Rate of New Machine. (as the total work is same and it's one-half mile of road, so Work done is the same)

The remaining work= Total work – Work done by the new machine= 1/2 mile road – 3 × Work Rate of New Machine. (as the total work is to pave one-half mile road and Work done by the new machine is 3 × Work Rate of New Machine)

This remaining work is done by the older machine and we know that the older machine completes one-half mile road in 15 hours, i.e., Work Rate of Older Machine = 1/15 mile/hour.

Time taken by the older machine to complete the remaining work is given by the following formula:

Time taken = Work/Rate= (1/2 – 3 × Work Rate of New Machine)/ Work Rate of Older Machine= (1/2 – 3 × 1/12)/1/15= 3.75 hours.

Therefore, the older machine takes 3.75 hours to complete the remaining work.Hence, the required answer is 3.75 (rounded to one decimal place).Answer: 3.8 hours.

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Answer:

m = 21

Step-by-step explanation:

13m = 273

m = 273/13

m = 21

Hope this helps!

Answer:

easy 4·65

Step-by-step explanation:

Answer:

$9.63

Step-by-step explanation:

100 + 75 = 175

5.50/100 X 175 = 9.625

monetary unit round to 2dp

9.63

Answer:

1 hour after 2 weeks

Step-by-step explanation:

She rides 3 days a week, and 10 minutes a day. Multiplying 3 and 10 gets you 30 minutes a week. Over a 2 week period, that is 60 minutes (1 hour)

Answer:

140 mins

Step-by-step explanation:

add 70+20

Answer:

−54v−27y+36

Step-by-step explanation:

hope this helped

have a good day ^^

the function f(x) = |x+1| + |x-1| is differentiable in the intervals (-∞, -1) U (-1, 1) U (1, ∞). Hence, the correct option is A.

To determine where the function f(x) = |x+1| + |x-1| is differentiable, we need to consider the points where the function may have a corner or a sharp point. These occur where the absolute value terms change direction.

The function |x+1| changes direction at x = -1, and the function |x-1| changes direction at x = 1. Therefore, these points may potentially be non-differentiable.

To determine if the function is differentiable at these points, we can check if the left-hand and right-hand derivatives exist and are equal at these points.

At x = -1:

For x < -1, both |x+1| and |x-1| simplify to -(x+1) - (x-1) = -2x. The derivative is constant and equal to -2.

For x > -1, both |x+1| and |x-1| simplify to (x+1) + (x-1) = 2x. The derivative is constant and equal to 2.

Since the left-hand derivative (-2) and the right-hand derivative (2) are not equal, the function is not differentiable at x = -1.

At x = 1:

For x < 1, |x+1| simplifies to -(x+1) and |x-1| simplifies to (x-1). The derivatives are -1 and 1, respectively.

For x > 1, both |x+1| and |x-1| simplify to (x+1) + (x-1) = 2x. The derivative is constant and equal to 2.

Since the left-hand derivative (-1) and the right-hand derivative (1) are not equal, the function is not differentiable at x = 1.

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The lower bound of the 90% confidence interval for the true average menstrual cycle length is 27.4.

a) Calculation for the lower bound of 90% confidence interval: The formula for calculating the confidence interval is, :

Lower Limit = X - Zα/2 × (σ/√n) Where, X = sample mean Zα/2 = 1.645σ = sample standard deviation= sample size Putting the given values into the formula, Lower Limit = 28.86 - 1.645 × (4.24/√50)≈ 27.4

The upper bound of the 90% confidence interval for the true average menstrual cycle length is 30.3.

b) Calculation for the upper bound of 90% confidence interval: The formula for calculating the confidence interval is,:

Upper Limit = X + Zα/2 × (σ/√n) Where ,X = sample mean Zα/2 = 1.645σ = sample standard deviation = sample size Putting the given values into the formula, Upper Limit = 28.86 + 1.645 × (4.24/√50)≈ 30.3

The confidence interval is (27.4, 30.3) and the hypothesized value is 29.5.

c) Hypothesis testing:According to the hypothesis, women's menstrual cycles are typically the same length as a lunar month - 29.5 days. So, we can check if the interval from (a,b) supports this hypothesis or not by comparing the hypothesized value with the confidence interval.

As we see that the hypothesized value is within the interval, we can say that the interval from (a,b) supports the hypothesis. Therefore, the answer is Yes.

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Answer:

20

Step-by-step explanation:

We already have our first value 3.4 and the second value 17. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

Step 1 ---> 3.4 = 17% × Y

Step 2 ---> 3.4 = 17/100 × Y

Multiplying both sides by 100 and dividing both sides of the equation by 17 we will arrive at:

Step 3 ---> Y = 3.4 × 100/17

Step 4 ---> Y = 3.4 × 100 ÷ 17

Step 5 ---> Y = 20

Finally, we have found the value of Y which is 20 and that is our answer.

This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.

This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.

In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.

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Answer:

156

Step-by-step explanation:

Hey There!

The angle that is equal to 156 and the angle labeled x are corresponding angles meaning that they are congruent angles. Therefore x=156

Answer:

60

Step-by-step explanation:

They're made up of two 30 degree angles so it's 60 because 30 + 30 = 60.

The value of k in the equation g(x) = k * f(x) is given by k = b / f(a), where (a, b) is the known point, and f(a) is the value of the function f(x) evaluated at x = a.

To find the value of k in the equation g(x) = k * f(x), we will follow these steps:
1. Substitute the known point (x, g(x)) into the equation.
2. Solve for k.
Step 1: Substitute the known point (x, g(x)) into the equation.

We are given a known point (x, g(x)), but the specific values are not provided in the question. Let's assume the known point is (a, b), where 'a' is the x-value and 'b' is the g(x)-value. Now, we substitute these values into the equation:
b = k * f(a)
Step 2: Solve for k.
Now, we need to isolate k in the equation:
k = b / f(a)
Thus, the value of k in the equation g(x) = k * f(x) is given by k = b / f(a), where (a, b) is the known point, and f(a) is the value of the function f(x) evaluated at x = a.

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Answer:

$11.20 per hat.

and $5.60 per bag

Keisha has $13.20 left over

Step-by-step explanation:

First, I multiplied .70 by 16 and got 11.20 per hat

Then, I multiplied .35 by 16 and got 5.60 per bag

Lastly, I added 11.20 to 5.60 and got 16.80, and subtracted 16.80 from  30 and got 13.20.....