Question 15
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Carl filled 12 mugs with coffee. Each mug has 250 mL of coffee.
How many liters of coffee did Carl use in all?

After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let x be the cοst οf οne apple pie, and y be the cοst οf οne lemοn meringue pie.

[tex]6x+8y=208[/tex]

[tex]6x+ 2y= 88[/tex]

[tex]-24x - 8y = - 352[/tex]

[tex]6x + 8y = 208[/tex]

[tex]-18x =-144[/tex]

[tex]X = 8[/tex]

[tex]6(8) +8y =208[/tex]

[tex]48+8y=208[/tex]

[tex]8y =160[/tex]

[tex]Y= 20[/tex]

Therefοre, the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

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We first check if all the given values are non-negative. We can see that all the values given are greater than or equal to zero, so this condition is satisfied.

In part a, we are given a set of values and asked to determine if they form a valid probability distribution.

A probability distribution is a function that assigns probabilities to each possible value of a random variable. In order for a set of values to form a valid probability distribution, the following conditions must be met:

All values must be non-negative: This means that the probability of any event cannot be negative. In other words, the probability of any event occurring must be greater than or equal to zero.

The sum of all values must be equal to 1: Since the probability of an event occurring is always between 0 and 1, the sum of all probabilities must add up to 1. This ensures that all possible outcomes of an experiment are accounted for.

In part a, we first check if all the given values are non-negative. We can see that all the values given are greater than or equal to zero, so this condition is satisfied.

Next, we check if the sum of all values is equal to 1. We add up all the given values and get 1.3. Since this value is greater than 1, the sum of probabilities is not equal to 1 and hence, this is not a valid probability distribution.

In parts b, c, d and e, since the given distribution is not valid, we cannot calculate probabilities using it.

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Answer:

x=2

Step-by-step explanation:

(12x-23)(8x-15)

-8x        -8x

(4x-23)(-15)

   +23  +23

(4x)(8)

4/4 8/4

x=2

The time taken for the tub to empty is approximately 9.18 minutes.

Suppose the drain is opened on a tub containing 34 gallons of water.

Water drains out of the bathtub at a rate of 4 gallons per minute.

However, the tap wasn't closed properly, so water is still flowing into the tub at a rate of 0.3 gallons per minute. How many minutes will it take for the tub to empty.

Solution:

We are given:

Initial quantity of water = 34 gallons.

Water flowing out of the tub = 4 gallons/minute.

Water flowing in to the tub = 0.3 gallons/minute

We need to find: Time taken for the tub to empty.

Let us assume that the time taken for the tub to empty is t minutes.

Now, the water that is still present in the tub is (34 - 4t + 0.3t) gallons.

Let us set this expression equal to zero to find the time taken for the tub to empty.

34 - 4t + 0.3t = 0

Simplifying, 34 - 3.7t = 0 or 3.7t = 34 or t = 34/3.7t ≈ 9.18.

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The new mean cost of a box of Cheerios Out Crunch is $4.40. This means that, on average, customers can expect to pay $0.40 more for a box of cereal after the price increase.

The new mean cost of a box of Cheerios Out Crunch after a 10% increase in price would be $4.40.

To see why, we can start with the original mean cost of $4.00 per box. To calculate a 10% increase, we can multiply the original mean cost by 1.10 (or 110% as a decimal), which gives:

$4.00 x 1.10 = $4.40

The mean cost is the proportion of the cost of the multitude of items to the absolute number of items. In Maths, we likewise have the term called "normal". The normal of some random arrangement of information is known as the mean of information.

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Number of different page that numbers contain the digit 1 is 20

We can approach this problem by counting the number of pages that do not contain the digit 1 and subtracting that from the total number of pages, which is 200.

Let's count the number of pages that do not contain the digit 1. We can do this by considering each digit in turn. There are 9 choices for the first digit (it cannot be 1), and 10 choices for each of the remaining digits (since 1 is now allowed). So, there are 9 × 10 × 10 = 900 page numbers that do not contain the digit 1.

Therefore, the number of page numbers that do contain the digit 1 is 200 - 900 = -700.

However, this answer does not make sense since we cannot have negative page numbers. Therefore, there must be a mistake in our calculation. The mistake occurs when we consider the case where the first digit is 1. In this case, there are only 2 digits left to choose from (0 and 2-9), not 10. So, the correct number of page numbers that do not contain the digit 1 is 9 × 2 × 10 = 180.

Therefore, the number of page numbers that do contain the digit 1 is 200 - 180 = 20.

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Answer: 9x4=36

Step-by-step explanation:

Answer:

20 days

Step-by-step explanation:

To find the total time, we will just add up the days.

4 + 3 + 6 + 7 = 20 days.

Answer:

  (d)  not possible to tell from information given

Step-by-step explanation:

You want to know the total completion time for a project with four activities that take 4, 3, 6, and 7 days.

The project completion time will be determined by the dependencies between activities.

If each activity must be completed before the next, then the total time will be 4+3+6+7 = 20 days.

If there are no dependencies and all activities can be done in parallel, then the total completion time is 7 days, the time required for the longest activity.

In short, it is not possible to determine the total time from the information given.

Answer: (-4,5)

Step-by-step explanation:

The new variance is  0.35.

The variance of a random variable measures how spread out the values are from the mean.

The formula for the variance is Var(X) = E[(X - E[X])²], where E[X] is the expected value (or mean) of X.

If the price of a box of Cheerios Oat Crunch increases by 25 cents, the new mean cost would be $4.25. To find the new variance, we can use the formula Var(aX + b) = a²Var(X), where a is a constant and b is a constant. In this case, a = 1 (because we are not changing the units of measurement) and b = 0.25 (because we are adding 25 cents to the price).

Therefore, the new variance is Var(X + 0.25) = Var(X) = Var(X) x 1² = Var(X) = 0.35.

This means that the variance remains the same even though the price has increased. This is because the variance is a measure of how spread out the values are from the mean, and the mean has shifted by the same amount as the price increase. Therefore, the distance between the values and the new mean is the same as the distance between the values and the old mean, so the spread is unchanged.

The variance is a measure of how spread out a set of data is from its mean. It is calculated as the average of the squared differences between each value and the mean. The formula for variance is Var(X) = E[(X - E(X))²], where E is the expected value or mean of X.

In this case, we are given that the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35. This means that the average squared difference between each box's cost and the mean cost is 0.35.

Now, if the price of each box increases by 25 cents, this means that the new mean cost will be $4.25. However, this does not affect the variance directly. This is because the variance only measures how spread out the data is from the mean, and the mean has shifted by the same amount as the price increase.

To see this more clearly, imagine a set of data that has a mean of 4 and a variance of 0.35. If we add 0.25 to each value, we get a new set of data that has a mean of 4.25. However, the spread of the data is still the same; that is, the distance between each value and the new mean is the same as the distance between each value and the old mean. Therefore, the variance remains the same even though the price has increased.

In summary, the variance measures how spread out a set of data is from its mean, and a shift in the mean does not affect the variance directly.

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With the help of probability we can solve our question-

The idea of probability describes the possibility of an event happening.

We frequently have to make forecasts about the future in real life.

We may or may not be aware of the outcome of an event.

When this happens, we declare that there is a chance the event will take place.

In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.

The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of possible outcomes.

s=d/t

75 minutes

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Out of the given options, the correct statement concerning the median is option B: In a right-skewed distribution, we expect that the median will exceed the mean.

What is the median?

Median is defined as the middle value in a given set of data. It can also be referred to as the central point of the distribution when the data is arranged in ascending or descending order. In other words, the median divides the data into two equal parts

.Median can be determined as follows:

Arrange the data in ascending or descending order .The median is the middle value of the data set.If there are two middle values, find the average of these two values .The mean is the average of the set of data. It is calculated by adding up all the values and dividing by the total number of values in the set of data. Hence, it gives an idea about the central tendency of the data set. According to the statement concerning the median, we expect that the median will exceed the mean in a right-skewed distribution. This means that the right tail is longer or more spread out than the left tail. The skewness of a distribution is a measure of its symmetry. A distribution can be classified as left-skewed, right-skewed or symmetrical depending on the shape of its histogram. Thus, option B is the correct statement concerning the median.

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Answer:

Step-by-step explanation:

Given the ratio of CD:DE:EF as 1:6:3 and CF as 20, we can use the sum of segment lengths equation to find the length of EF to be 12 units.

We're given that points C, D, E, and F lie on the same line segment in that order, with the ratio CD:DE:EF equal to 1:6:3. This means that the length of segment CD is 1x, the length of segment DE is 6x, and the length of segment EF is 3x, for some common factor x.

We're also given that CF (the total length of the segment from C to F) is equal to 20. So that we can set an equation:

CD + DE + EF = CF

Substituting the values we know from the ratio and CF:

1x + 6x + 3x = 20

Combining like terms:

10x = 20

Solving for x:

x = 2

Now we can use this value of x to find the lengths of each segment:

CD = 1x = 1(2) = 2

DE = 6x = 6(2) = 12

EF = 3x = 3(2) = 6

So the length of segment EF is 12 units.

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√49 is less than 7.1212. In other words, 49−−√ is less than 7.1212.

what is a decimal number?

A decimal number is a real number that is expressed in the decimal system, which is a system of numeration using the base 10. In this system, each digit can take on one of ten possible values, 0 through 9, and the value of each digit is determined by its position relative to the decimal point.

To compare the numbers √49 and 7.1212, we need to find their numerical values.

√49 = 7, since 7 multiplied by itself gives 49.

7.1212 is already a decimal number, so no calculation is required.

To approximate 7.1212, we can look at the digits after the decimal point:7.1212

0.1212

--------

7.0000 + 0.1212

--------

7.1212

Now we can see that 7 is less than 7.1212. Therefore, √49 is less than 7.1212. In other words, 49−−√ is less than 7.1212.

So, the comparison between the two numbers is:

√49 < 7.1212 or 49−−√ < 7.1212.

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Answer: Therefore, the area that is only planted in corn can be expressed as the polynomial y^2 + 14y.

Step-by-step explanation:

The area of the square piece of land is given by the product of its length and width:

Area of square piece of land = (y + 7) * (y + 7)

The area of the small square that was planted with radish is 7 ft. by 7 ft. Therefore, its area is:

Area of small square = 7 * 7 = 49

The area that is only planted in corn is the difference between the area of the square piece of land and the area of the small square that was planted with radish:

Area planted in corn = (y + 7) * (y + 7) - 49

Expanding the expression on the right side, we get:

Area planted in corn = y^2 + 14y + 49 - 49

Simplifying further, we get:

Area planted in corn = y^2 + 14y

The volume of a rectangular prism is 140 inches.

What is the rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given: A box, in the shape of a rectangular prism, has a length of 3 1/2 inches, a width of 4 inches, and a height of 10 inches.

Length = 3 1/2

Width = 4

Height = 10

The volume of the box is the product of its dimensions

V = Length × width × Height

V = 3 1/2 × 4 × 10

V = 140

Hence, the volume of a rectangular prism is 140 inches.

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A total of 800 people were in Funland Amusement Park to watch the noontime parade.

To calculate the total number of spectators present for the noontime parade, we need to add the number of visitors from the morning to the number of newcomers.

The park started with 500 guests, and as anticipation for the parade built up, 300 more individuals joined the crowd.

By combining these two amounts (500 + 300), we can determine that a total of 800 people were in Funland Amusement Park to watch the noontime parade.

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At Funland Amusement Park, there were initially 500 visitors present in the morning. As excitement for the noontime parade grew, an additional 300 people arrived just before the event. How many attendees were in the park to witness the parade?

Barbara can make six different compound machines if order matters.

There are three different simple machines that Barbara can use. Let's call them A, B, and C.

If order matters, then for the first machine, Barbara can choose any of the three simple machines. For the second machine, she can choose any of the remaining two simple machines. And for the third machine, she can choose the last remaining simple machine.

Therefore, the total number of different compound machines that Barbara can make is:

3 x 2 x 1 = 6

So Barbara can make six different compound machines.

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The maximum price that consumers are willing to pay for the product is represented by the y-intercept of the parabola, which is 1200. This means that when there is no demand for the product (x=0), the price of the product is 1200 dollars.

The given demand function for a product in dollars is p=1200-0.2x-0.0001x², where 'p' represents the price of the product and 'x' represents the quantity demanded by the consumers.

This demand function is a quadratic function that takes the form of a downward-sloping parabola. It has a negative coefficient for the squared term, which means that the parabola opens downwards. This implies that as the quantity demanded increases, the price of the product will decrease, but only up to a certain point.

The maximum price that consumers are willing to pay for the product is represented by the y-intercept of the parabola, which is 1200. This means that when there is no demand for the product (x=0), the price of the product is 1200 dollars.

As the quantity demanded increases, the price of the product decreases at a decreasing rate. This is because the coefficient of the x-term (-0.2) is smaller than the coefficient of the x²-term (-0.0001x²), which means that the effect of quantity on price decreases as the quantity demanded increases.

However, beyond a certain point, the price starts to increase again, indicating a decrease in demand. This is because the quadratic function is concave downwards, and there is a maximum point (vertex) on the parabola. The quantity demanded at this point is given by the formula

x = -b/2a, where a and b are the coefficients of the x² and x terms, respectively.

Overall, the demand function represents the relationship between the price of the product and the quantity demanded by the consumers. By understanding this relationship, producers can make informed decisions about pricing and production levels to maximize their profits.

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Assuming the triangles in the pair above are similar, the value of x is equal to 11.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

UV/VW = SU/ST

(5x + 11)/88 = 18/24

By cross-multiplying, we have the following:

24(5x + 11) = 18(88)

120x + 264 = 1,584

By rearranging and collecting like-terms, the value of x is given by:

120x = 1,584 - 264

120x = 1,320

x = 1,320/120

x = 11.

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Answer:

sp

Step-by-step explanation:

1) The difference between the MP and VAT is

mp- VAT AMT. And as we know the formula to find

sp in presence of MP and VAT amt is sp

sp=Mp- Vat AMT

2). For MP after discount is also sp.

sp =MP - discount amt

The odd one out from the three given ratios 3:6, 3:9 and 6:12 is 3:9 as 3x2 = 6 and 6x2 = 12 but 3x3 = 9.

A ratio is a means to compare two numbers that are similar or to demonstrate a relationship.

In the previous illustration, B and G are terminology. G is referred to as the consequent term, and B as the antecedent word.

Ratios are used to compare items with the exact same type. To analyze the proportion of boys to girls in your class, for instance, we might use a ratio. Another illustration would be to assess the ratio of peanuts to all other nuts in a container of mixed nuts.

The given ratios are;

3:6,3:9 and 6:12

Here the pattern follows:

3x 2 = 6

3x 3 = 9

6x 2 = 12

Thus, odd one out will be the ratio 3:9.

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Answer:

The top and the bottom statement are correct. This is an independent compound event because the first choice does not affect the second choice.

Answer:

Step-by-step explanation:

If one serving size is 1/3 of a cup, we know that there are 3 servings in 1 cup.

Our ratio is

3 servings : 1 cup

If we now have a 6 cup bag, we simply solve for it using our ratio

3 : 1

x : 6

1*6 = 6

3*6 = 18

so, x = 18.

There are 18 servings in a 6 cup bag of jelly beans

Hope this helps!

The length of time it would take you to pay off the balance at $ 50 per month is 29.5 months.

The monthly payment on the credit card if one was to pay off the debt in 2 years is $132.34.

To find out how long it will take to pay off the credit card balance, we can use the TVM (Time Value of Money) solver.

First, we need to convert the APR to a monthly interest rate:

i = (1 + 0.19)^(1/12) - 1 ≈ 0.0149 or 1.49% (monthly interest rate)

Now, we can use the TVM formula to find the number of periods (n):

PV = PMT x (1 - (1 + i)^(-n)) / i

1,245 = 50 x (1 - (1 + 0.0149)^(-n)) / 0.0149

Solving for n:

n = 29.5 months

To find the monthly payment on the credit card, we are given:

PV (Present Value) = $2,456.80

n (number of periods) = 2 years x 12 months/year = 24 months

APR (Annual Percentage Rate) = 23.99%

We can use the TVM formula to find the monthly payment (PMT):

PV = PMT x (1 - (1 + i)^(-n)) / i

2,456.80 = PMT x (1 - (1 + 0.0182)^(-24)) / 0.0182

Solving for PMT:

PMT = $132.34

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