On one island there lived two friends, Ana and Banana. One of them always tells the truth, while the other always lies. When asked which one is the liar among them, they said: Ana: "Banana ate ten apples yesterday, and he is telling the truth." Banana: "No, I ate five apples yesterday, and Ana is lying." How many apples did Banana eat yesterday?

The partial sum of the given sequence, 1 + 10 + 19 + ... + 199, can be found by identifying the pattern and using the formula for the sum of an arithmetic series.  Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

To find the partial sum of the given sequence, we can observe the pattern in the terms. Each term is obtained by adding 9 to the previous term. This indicates that the common difference between consecutive terms is 9.

The formula for the sum of an arithmetic series is Sₙ = (n/2)(a + l), where Sₙ is the sum of the first n terms, a is the first term, and l is the last term.

In this case, the first term a is 1, and we need to find the value of l. Since each term is obtained by adding 9 to the previous term, we can determine l by solving the equation 1 + (n-1) * 9 = 199.

By solving this equation, we find that n = 23, and the last term l = 199.

Substituting the values into the formula for the partial sum, we have:

S₂₃ = (23/2)(1 + 199),

= 23 * 200,

= 4600.

However, this sum includes the terms beyond 199. Since we are interested in the partial sum up to 199, we need to subtract the excess terms.

The excess terms can be calculated by finding the sum of the terms beyond 199, which is (23/2)(9) = 103.5.

Therefore, the partial sum of the given sequence is 4600 - 103.5 = 4496.5, or approximately 4497 when rounded.

Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

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Answer:

B.61kg

Step-by-step explanation:

use the formula

force÷acceleration=mass

183÷3=61kg

The price of a box of cereal under the price leadership model is 16 dollars.

The price of a box of cereal under the price leadership model can be calculated by finding the intersection of the marginal cost curve (MC) of the dominant firm and the marginal revenue curve (MR) of the dominant firm. The MR curve has twice the slope of the demand curve, so the equation for the MR curve is MR = 24 – 2Q, where Q is the quantity of boxes of cereal. The MC curve is horizontal, so the equation for the MC curve is MC = 12. The intersection of the two curves occurs at the quantity Q = 8 million boxes of cereal per year, and the corresponding price is P = 16 dollars per box of cereal. Therefore, the price of a box of cereal under the price leadership model is 16 dollars.

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Answer:

2 3/4 kilometers is equal to 2,750 meters

Step-by-step explanation:

Answer:

2 3/4 kilometers is equal to 2,750 meters

Step-by-step explanation:

Answer:

8.1

Step-by-step explanation:

Answer:

0.354882mL

I don't know how much they let you/want you to round it up.

Step-by-step explanation:

1 cup = 236.588mL

236.588 x 1.5 = 354.882mL

354.882/1000 to convert mL to L

0.354882mL

The equation of the lines is,

1. (4, -1); m = 3 : - y = 3x - 13

2. (-8, 0); m = -4 :- y = -4x - 24

3. (-6, -10); m = 1/6 :- y = -1/6x - 9

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of the lines will be,

y = mx + c

y = 3x + c

-1 = 4 x 3 + c

c = -13

y = 3x - 13

y = mx + c

y = -4x + c

0 = -4 x -8 + c

c = -24

y = -x -24

y = mx + c

y = 1/6x + c

-10 = -1 + c

c = -9

y = -1/6x - 9

Therefore, the equation of the lines is,y = 3x - 13 y = -4x - 24 and y = -1/6x - 9.

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Answer:

40,960

Step-by-step explanation:

To find the multiplier, set up an equation like this:

\(5x=-10\)

The above equation will allow us to find what number, when multiplied with 5 will result in -10. If we divide both sides of the equation by 5, we'll find that the number, x, is -2:

\(x=-2\)

We need to find the 14th term. To do this, simply multiply the lattermost number in the sequence by our multiplier, -2.

\(20*(-2)=40\)

Since 5 is the first term in the sequence, -10 is the second term in the sequence, and 20 is the third term in the sequence, 40 is the fourth term. Now we just need to find the next ten so that we can find the 14th term. To do that, repeat the process of multiplying the lattermost number by -2 ten more times:

\(40*-2=-80\\-80*-2=160\\160*-2=-320\\-320*-2=640\\640*-2=-1280\\-1280*-2=2560\\2560*-2=-5120\\-5120*-2=10240\\10240*-2=-20480\\-20480*-2=40960\)

Therefore, the 14th term is 40,960.

Answer:

-40,960

Step-by-step explanation:

you have to add the negative because there partners in crime

We know that SR is parallel to MN and MP is parallel to NP. This means that quadrilateral SRNP has one pair of parallel sides (SR and MN), which is the definition of a trapezoid. Hence, quadrilateral SRNP must be a trapezoid.

A quadrilateral has four enclosed sides. Quadrilaterals include the following shapes: It was produced by Raphael. It has four sides. The shape has only one set of parallel sides and no straight angles.

In order to prove that quadrilateral SRNP is a trapezoid, we need to show that it has one pair of parallel sides.

We know that SR and MP are both medians of triangle MNP, which means they each pass through the midpoint of the opposite side. Let's call the midpoint of MN point Q.

Since SR passes through the midpoint of MN at point Q, we know that SR is parallel to side MN (by the converse of the midpoint theorem). Similarly, we can show that MP is parallel to side NP (by using the midpoint of MP and the midpoint of NP).

Therefore, we have shown that SR is parallel to MN and MP is parallel to NP. This means that quadrilateral SRNP has one pair of parallel sides (SR and MN), which is the definition of a trapezoid. Hence, quadrilateral SRNP must be a trapezoid.

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The difference in housing prices in the fifth year is $7,125.

Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.

$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.

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The researchers are currently applying steps 1 and 2 of the statistical process, which involve formulating a research question and designing a study to answer that question.

The researchers are in the initial stages of the statistical process, specifically focusing on steps 1 and 2. Step 1 involves formulating a research question, which in this case is whether reviewing material consistently within an hour after class improves exam performance compared to waiting until the day before the exam. The researchers have identified this question as the basis for their study.

Step 2 of the statistical process involves designing a study to answer the research question. In this case, the researchers are deliberating between an observational study and an experiment to determine which approach would be more appropriate. This decision-making process is crucial in the study design phase.

The researchers are considering factors such as the need for control, manipulation of variables, and potential biases to determine the most suitable approach for investigating the relationship between reviewing material timing and exam performance.

Overall, the researchers are in the initial stages of the statistical process, actively formulating their research question and designing the study to address that question.

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The rate of pour in feet per hour is approximately 2.51 feet per hour.

First, we need to convert the dimensions to feet:

Length = 151 feet 4 inches = 151.33 feet

Height = 14 feet

Thickness = 16 inches = 1.33 feet

Next, we need to calculate the volume of the wall:

Volume = Length x Height x Thickness

Volume = 151.33 x 14 x 1.33

Volume = 2813.89 cubic feet

To convert cubic feet to cubic yards, we divide by 27:

Volume = 2813.89 / 27

Volume = 104.22 cubic yards

Given the daily placement rate of 375 cubic yards per 8-hour day, we can calculate the rate of pour in cubic yards per hour:

Rate of pour = 375 / 8

Rate of pour = 46.88 cubic yards per hour

Finally, we can convert the rate of pour to feet per hour by dividing by the cross-sectional area of the wall:

Cross-sectional area = Height x Thickness

Cross-sectional area = 14 x 1.33

Cross-sectional area = 18.62 square feet

Rate of pour in feet per hour = Rate of pour in cubic yards per hour / Cross-sectional area

Rate of pour in feet per hour = 46.88 / 18.62

Rate of pour in feet per hour ≈ 2.51 feet per hour

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Answer:

the answer is D .I think I may not be wrong

Using PEDMAS, the result of the expression is 3

Simplification of an expression is the process of reducing a mathematical expression to its simplest form while retaining the same value. This is done by using various rules and techniques, such as combining like terms, using the distributive property, and applying the order of operations.

The goal of simplification is to make the expression easier to work with and understand. It also helps to avoid errors when solving problems or simplifying more complex expressions.

In the given problem, we can apply PEDMAS to solve the expression;

3 - 5 + 3(2 - 1) + 4 / 2 = 3

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Translation: What is the correct result of this arithmetic expression 3-5+3(2-1)+4/2

Answer:

Okay first you need to use the formula: V=\(\pi r^{2} *h\)

All you need to do is plug in those numbers.

Like this: V= \(\pi *1^{2}*8\)

which is = 25.13 \(cm^{3}\)

Ta-da!! lol. Have a great day!

Three statements are correct: B, C, and D.

Statement A is incorrect. The technique of blocking is not indicated when only a random component is present.

Blocking is a statistical method used to remove or reduce the effects of nuisance factors or sources of variation in a dataset. Random components alone do not require blocking.

Statement B is correct. Blocking is indicated when both random and trend components are present. Trend refers to a systematic change in the data over time, and blocking can help separate the trend from other factors.

Statement C is correct. Blocking is also indicated when both random and seasonal components are present. Seasonality refers to regular patterns or cycles in the data, such as monthly or yearly variations. Blocking can help account for these seasonal effects.

Statement D is correct. Blocking is generally indicated when a dataset contains a combination of random, trend, and seasonal components.

In such cases, blocking can be used to extract each component separately and analyze their individual effects on the data.

In summary, statements B, C, and D correctly describe the situations in which the technique of blocking is indicated, while statement A is incorrect.

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If the null hypothesis is true and there is no treatment effect, the expected value on average for the F-ratio would be 1.00. The correct answer is option (b) 1.00

In hypothesis testing using the F-test, the F-ratio is calculated by dividing the variance between groups (treatment effect) by the variance within groups (random variation). When the null hypothesis is true and there is no treatment effect, the numerator (variance between groups) and the denominator (variance within groups) would be similar, resulting in an F-ratio close to 1.

Therefore, the correct answer is b. 1.00, as the expected value for the F-ratio would be around 1 when the null hypothesis is true and there is no treatment effect.

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Using the Combination formula,

Total number of ways there to paint 10 hotel rooms in a hotel with five colours is 527 ways .

We have given that,

total number of rooms available for paint = 10

number of colour avaliabile for painting = 5

Atmost three rooms can be painted green i.e

the number of ways for atmost three rooms are painted green = ¹⁰C₃ + ¹⁰C₂ + ¹⁰C₁ = 120 + 45 + 10 = 175

similarly, the number of ways for atmost three rooms are painted red = 175

the number of ways for atmost three rooms are painted blue = 175

Now, one room is remained for painting and two colours are available for it

the number of painting the remained room with aany of two available colours i.e black and white

= 2 ways

thus , total ways to paint the 10 hotel rooms with five different paints are (175×3 +2) = 527

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Answer:

41.19

Step-by-step explanation:

Answer:

multiply 8 and 7 and divid that by two then round that two the nearest hundreth.

Step-by-step explanation:

Mr. Adams divides 183 markers equally among the 24 students in his class. To find the least number of extra markers in the box, divide the total markers (183) by the number of students (24). The result is 7 with a remainder of 15. So, the least number of extra markers in the box is 15.

Mr. Adams divides 183 markers equally among the 24 students in his class, which means each student gets 7 markers. However, since 7 does not divide evenly into 183, there will be some markers left over. To determine the least number of extra markers in a box, we need to find the remainder when 183 is divided by 24.
Using long division, we get:

   24 | 183
       -----
         7  6
         -----          
This means that there are 6 markers left over that Mr. Adams puts in a box. Therefore, the least number of extra markers in a box is 6.
Mr. Adams divides 183 markers equally among the 24 students in his class. To find the least number of extra markers in the box, divide the total markers (183) by the number of students (24). The result is 7 with a remainder of 15. So, the least number of extra markers in the box is 15.

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The decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.

To determine the decimal value of the 2 in the hexadecimal number F42AC16, we need to understand the positional value system of hexadecimal numbers. In hexadecimal, each digit represents a power of 16. The rightmost digit has a positional value of 16^0, the next digit to the left has a positional value of 16^1, the next digit has a positional value of 16^2, and so on.

In the given hexadecimal number F42AC16, the 2 is the fifth digit from the right. Its positional value is 16^4. Calculating the decimal value: 2 * 16^4 = 2 * 65536 = 131,072. Therefore, the decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.  None of the provided options (a) 409610, b) 51210, c) 25610, d) 210) matches the correct decimal value of 131,072.

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Answer:

y = 6x + 3

Step-by-step explanation:

Since you can't have a negative y in a y = mx + b equation you have to make it postive. You also have to do everything you do on one side to the other. To do this you have to multiply everything by -1. This will make everything positive b/c it cancels out the other negative. (Two negatives equals a positive) You should be left with y = 6x + 3. The -1 cancelled the -y, -6x, and -3 so you add 3 instead of subtract it.

y = 6x + 3

Answer:

your question is not technically detailed enough

Step-by-step explanation:

provide more information Sir

The sides having the length as 6cm , 10cm and 13cm represents a Scalene Triangle .

A Triangle in which the measure of all sides are different is called a Scalene Triangle ,

A Triangle in which the measure of any two sides is equal is called as Isosceles Triangle ,  and

A Triangle in which the measure of all sides are equal it is called a Equilateral triangle .

the measure of the sides is given as : 6cm 10cm and 13cm ;

we can see that all the three sides are of different length .

Therefore , the given triangle is an Scalene Triangle .

The given question is incomplete , the complete question is

What kind of triangle is represented by the sides having the length as 6cm , 10cm and 13cm ?

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The solutions the system of equations have is (-3, 5)

From the question, we have the following parameters that can be used in our computation:

y = -x + 2

x - 3y = -18

Simplify the equations

So, we have

x + 3x - 6 = -18

Next, we have

4x = -12

So, we have

x = -3

Recall that

y = -x + 2

So, we have

y = 3 + 2

Evaluate

y = 5

Hence, the solution is (-3, 5)

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