why are whole numbers rational numbers?

The probability that a red card is drawn at least once by the third draw is 0.88.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let, a card is drawn from a standard deck of 52 cards and then placed back into the deck.

In a standard 52 card deck the red cards are 26.

So,

P(red) =  n(red cards) / n(total cards)

          = 26 / 52

P(red) = 0.50

Now, X ≈ Bin (n = 3, P = 0.50)

P(X = x) = (n  x) p^x (1 - p)^n-x

(n  x) = \(\frac{n!}{x!(n-x)!}\)

P(X ≥ 1) = 1 - P(X < 1)

            = 1 - P(X = 0)

            = 1- (3  0)(0.5)^0(0.5)^3

            = 1 - 0.125

             = 0.875

P(X ≥ 1)  = 0.88

Hence, the probability that a red card is drawn at least once by the third draw is 0.88.

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The rental car is getting approximately 37.56 miles per gallon.

To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:

1 km/l ≈ 2.82475 mpg

Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:

13.3 km/l x 2.82475 mpg ≈ 37.56 mpg

So, your rental car is getting approximately 37.56 miles per gallon.

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Answer:

  193.77 < p < 1806.23

Step-by-step explanation:

You want R(p) > 2,100,000, so ...

  -6p^2 +12000p > 2100000

  p^2 -2000p < -350000 . . . . divide by -6

Adding (2000/2)^2 = 1000000 will "complete the square".

  p^2 -2000p +1000000 < 650000 . . . . complete the square

  (p -1000)^2 < 650000

  -√650000 < p -1000 < √650000 . . . . take the square root

  1000 -806.23 < p < 1000 +806.23 . . . .add 1000

  193.77 < p < 1806.23 . . . . range of prices for desired revenue

1 gallon = 4 quarts.

2 gallons = 4 x2 = 8 quarts

She needs 8 quarts total and has 3 quarts.

8-3 = 5

She needs 5 more quarts.

Answer:

$475 + 4% (19 percent) = $494 a year.

Step-by-step explanation:

Step-by-step explanation:

To find 5/6 of the area, multiply the area that was found in part A , as the question states by 5/6.

⅚ × Area found in part A.

a.) Exact result: 10.9375. Approximate: 11 quarts of heavy cream.

b.) Exact result: 65.625. Approximate: 66 eggs.

c.) Exact result: 43.75. Approximate: 44 lemons.

If 400 guest will consume 1.75 pastries, then the total of pastries is:

\(400*1.75=700\)

If one quarter of the pastries will have 2 ounces of lemon filling, then the amount of pastries that will ahve this filling is:

\(700*\frac{1}{4}= 175\)

If 175 will have 2 ounces of lemon filling, then the ounces of lemon filling needed is:

\(175*2=350\)

Then, the mass, in pounds, of lemon filling needed is:

\(350/16=21.875\)

To find the quarts of heavy cream needed, set up a rule of 3 like this:

2 pounds of filling ------------ 1 quart of heavy cream

21.875 pounds of filling ----- x

\(x= \frac{21.875*1}{2} =10.9375\)

The amount of quarts of heavy cream needed is, approximately, 11.

Do the same rule of 3 as in question 1, except that now we substitute the ingredient and que quantity:

2 pounds of filling ------------ 6 eggs

21.875 pounds of filling ----- x

\(x= \frac{21.875*6}{2} =65.625\)

The amount of eggs needed is, approximately, 66.

First, let's find out how many cups of lemon juice are needed through a rule of 3.

2 pounds of filling ------------ 1 cup of lemon juice

21.875 pounds of filling ----- x

\(x= \frac{21.875*1}{2} =10.9375\)

Now, convert the cups to ounces.

10.9375 cups * 8= 87.5 ounces.

Set up another rule of 3 to determine the number of lemons.

2 ounces ------------ 1 lemon

87.5 ounces ----- x

\(x= \frac{87.5*1}{2} =43.75\)

The amount of lemons needed is, approximately, 44.

Answer:

21 square feet

Step-by-step explanation:

In this answer, I have attached an image.

I have split the figure into two parts, A and B.

Area of A: \(6ft \times 2ft= 12\ square\ feet\)

Area of B: \((5ft-2ft)\times 3ft=3ft\times 3ft = 9\ square\ feet\)

Total Area: \(12\ square\ feet+9\ square\ feet=21\ square\ feet\)

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

Answer:

A.

Step-by-step explanation:

I gotchu fam. The first thing that you would want to do is find the slope. The slope is the change in y divided by the change in x. Based on the points on the line, the change in y is 2 because it goes up two, and the change in x is one because it goes over 1. This would make your slope 2/1, or just 2! Now we have our slope, so we want to find our y-intercept. There are two ways that we can do this. The first way is just eyeballing it, but sometimes that's not always accurate. We're just going to do that because its faster (lol). It looks around -2. With this information, we have our entire equation! y=mx+b. we can plug in our information. y=2x-2. And that's how your answer's A! Hope this helps.

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Since y is directly proportional (direct proportion) to x, the value of x when y = -7.93 is equal to 1.3.

Mathematically, a direct proportion is also referred to as direct variation and it can be represented with the following mathematical expression:

y = kx

Where:

Since y varies directly (direct proportion) with x, the variable x and y must remain in a constant ratio.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12.2/-2

Constant of proportionality (k) = -6.1

Now, we can determine the new value of x as follows:

k = y/x

x = y/k

x = -7.93/-6.1

x = 1.3

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Answer:

...

Step-by-step explanation:

...

The answer choice which correctly represents that which can be simplified using the product rule as required is; ( 11² a-⁵ ) ( 11 a⁹ b⁷ ) / 5².

It follows from the task content that the expression which correctly represents that which can be simplified using the product rule be determined.

By observation; it follows that the expression; ( 11² a-⁵ ) ( 11 a⁹ b⁷ ) / 5² is such that; the terms can be combined using the product rule as follows;

( 11² • 11 ) (a-⁵ • a⁹ ) (b⁷ ) / 5².

Hence, from the product rule of indices involving terms with same base but different exponents; we have;

11³ • a⁴ • b⁷ / 5²

Consequently; the resulting expression is; 11³a⁴b⁷ / 5².

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Answer:

The answer is below

Step-by-step explanation:

The electrical resistance R of a wire varies inversely with the square of its diameter d:

R ∝ 1 / d

Let k represent the constant of proportionality, hence we can represent the statement as an equation:

\(R=\frac{k}{d^2}\\ \\when\ R=0.5 \Omega,d=2\ mm\\\\0.5=\frac{k}{2^2} \\\\k=2\\\\The\ equation\ becomes :\\\\R=\frac{2}{d^2}\\ \\When\ d=3, we\ find\ R\\\\R=\frac{2}{3^2} \\\\R=0.22\ \Omega\)

If a customer bought ten 1-liter containers of grape juice, the milliliters of juice she bought is 10,000 milliliters, using multiplication.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation is widely used in unit conversions, just like division operation.

1 liter = 1,000 milliliters

10 1-liter containers = 10,000 milliliters (1,000 x 10)

Thus, the customer bought 10,000 milliliters of grape juice or ten 1-liter containers, based on multiplication operation in unit conversion.

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let's convert the mixed fractions to improper fractions and the subtract.

\(\stackrel{mixed}{5\frac{3}{8}}\implies \cfrac{5\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{43}{8}} ~\hfill \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{15}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{8}~~ - ~~\cfrac{15}{4}\implies \cfrac{(1)43~~ - ~~(2)15}{\underset{\textit{using this as the LCD}}{8}}\implies \cfrac{43-30}{8}\implies \cfrac{13}{8}\implies {\Large \begin{array}{llll} 1\frac{5}{8} \end{array}}\)

Answer:

16 girls on each team and 20 boys on each team.

Hope I helped you.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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The ogive curve for the data has to be obtained by first converting the data into a continuous class one and then plotting the less than cumulative frequency table obtained.

Here we have the data

0-3.9    4.0-7.9    8.0-11.9    12.0-15.9    16.0-19.9    20.0-23.9    24.0-27.9

  63          26          24              37                23               11                  16

Now first we need to convert this to a continuous distribution

We will get

Classes                  Frequency

-0.95-3.95                   63  

3.95-7.95                     26

7.95-11.95                     24

11.95-15.95                    37

15.95-19.95                   23

19.95-23.95                    11

24.0-27.95                     16

Now we need to construct a less than table

Less than                           Cumulative frequency

3.95                                                    63  

7.95                                                    89

11.95                                                   113

15.95                                                 150

19.95                                                 173

23.95                                                 184

27.95                                                200

Now to make an Ogive curve we need to plot the less than column at the x-axis and the frequency on the y-axis. Then draw a free hand line to connect all the points. This will give us our ogive curve

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Complete Question

A sample of 200 high school students was asked how many hours per week they spend watching television. The following frequency distribution presents the results.

0-3.9    4.0-7.9    8.0-11.9    12.0-15.9    16.0-19.9    20.0-23.9    24.0-27.9

  63          26          24              37                23               11                  16

Construct a relative frequency ogive for the frequency distribution.

The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

199999/1000000

Step-by-step explanation:

Answer:

10.

Step-by-step explanation (the required tall of the tree is AQ):

1) ΔBCP ~ ΔBAQ, it means BC/AB=CP/AQ=BP/BQ;

2) BC/AB=CP/AQ, it means 4/20=2/AQ, then AQ=2*20/4=10 [m].