Evaluate f(x)=x/3 -15 when x =27

The probability of drawing 2 red marbles is 0.081 or 8.1%.

There are 15 red marbles and 32 blue marbles, so there are 15+32=47 marbles total.

The probability of pulling a red marble on the first draw is 15/47.

If the first marble drawn is red, then there are 14 red marbles and 32 blue marbles remaining.

So, the probability of pulling a second red marble is 14/46.

To find the probability of both events happening, we multiply the probabilities:

P(both red) = P(first red) × P(second red | first red)

P(both red) = (15/47) × (14/46)

P(both red) = 0.081 (rounded to 3 decimal places)

Therefore, the probability of drawing 2 red marbles is approximately 0.081 or 8.1%.

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Note that he probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long  is 0.6%

The percent of eggs total 100.

Based on the frequency, we now that the eggs that are at least 19.75 mm include:

18.75 - 19.75 = 0.8

those that are less than 22.75mm long are:

19.75-20.75 = 4.0

20.75 - 21.75 = 17.3
21.75 - 22.75 = 37.9

Thus, the total of their frequencies are:

0.8 + 4.0 + 17.3 + 37.9  = those that are less than 22.75mm long but at least 19.75 long.

= 60

Thus, the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long  is 0.6%

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Full Question:

A biologist measured the lengths of hundreds of cuckoo bird eggs. Use the relative frequency distribution below to answer the questions that follow.

what is the probability that one of the eggs selected at random was at least 19.75 mm long but less than 22.75 mm long ? See attached image.

The surface area of the composite figure is 2,283 m².

option A.

The surface area of the composite figure is calculated as follows;

The composite figure is composed of a cube and a cuboid and their total surface area is calculated as follows;

Surface area of the cuboid = 2 (35 m x 9 m  +  35 m x 16 m   +  16 m x 9 m)

Surface area of the cuboid = 2038 m²

Surface area of a cube = 6L²

There is a surface of the cube on the cuboid, which is include in the surface area of the cuboid, so we will subtract that one surface.

Surface area of the cube = 6L² - L² = 5L²

= 5 x (7 m)²

= 245 m²

Total surface area =  2038 m² + 245 m²

Total surface area = 2,283 m²

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Answer:

8.01 ft/sec

Step-by-step explanation:

Distance = 26.2 miles

Time is taken to run the distance = 4.8hrs

Average speed = ??

Average speed = distance/time

= 26.2miles /4.8hr

= 5.46 miles/hr

Convert 5.46 miles/hr to ft/sec

1 mile = 5280 ft

We have 5.46*5280 = 28828.8 ft/hr

28828.8/3600 = 8.01 ft/sec

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The standard equation of the circle with center (-5,12) that passes through the point (-9,15) is (x + 5 )² + (y - 12)² = 25.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given that; the center is (-5, 12) and a point on the circle is (-9, 15).

First, we determine the radius, we can use the distance formula between the center and the point on the circle:

[tex]r = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \\\\r = \sqrt{(-9 - (-5))^2+(15 - 12)^2} \\\\r = \sqrt{(-9 + 5)^2+(15 - 12)^2} \\\\r = \sqrt{(-4)^2+(3)^2} \\\\r = \sqrt{16+9} \\\\r = \sqrt{25} \\\\r = 5[/tex]

Now, center: (-5, 12)

h = -5

k = 12

and r = 5

Plug these into the equation above:

(x - h)² + (y - k)² = r²

(x - (-5) )² + (y - 12)² = 5²

Simplify

(x + 5 )² + (y - 12)² = 25

Therefore, the equation of the circle is (x + 5 )² + (y - 12)² = 25.

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The best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.

The best prediction possible for the number of times you will roll a six in a six-sided die depends on the probability of getting a six in each roll. The probability of getting a six in a single roll of a six-sided die is 1/6 or 16.67%.
Since the rolls are independent events, the probability of rolling a six in any one of the six rolls is still 1/6 or 16.67%. Therefore, the best prediction possible for the number of times you will roll a six is one.
However, it is important to note that probability is not a guarantee, and it is possible to roll a six more than once or not at all. But based on the laws of probability, one is the most likely outcome for the number of times you will roll a six in six rolls of a six-sided die.
In summary, the best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.

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The surface area of the composite solid would be about 576. 05 square feet .

The composite shape is made up of two shapes which are a a cylinder and a pentagonal prism. To find the surface area, you need to find the surface area of these two shapes and then sum these areas.

Area of pentagonal prism :

= 5 a h + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) a ²

a = 4 ft

h = 7 ft

Area of the pentagonal prism is:

= 5 x 4 x 7 + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) 4 ²

= 195.05528 square feet

Area of cylinder:

= 2 π r h + 2 π r ²

= 2 π x 6 x 4 + 2 π x 6  ²

= 376.99112 square feet

The surface area is therefore :

= 195.05528 + 376.99112

= 576. 05 square feet

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Answer:

5 and 6

Step-by-step explanation:

cause

Answer:

18 gallons

Step-by-step explanation:

18 gallons because 1/3 equals 2/6 and 3/6 equals 1/2 so 3 gallons is 1/6. then just 6×3

Hope this helped

According to the information, we can infer that the sign should read: "Area of land: 178.35 square meters."

To find the area of the trapezoid, we need to use the formula:

where,

From the figure, we can see that:

Substituting these values into the formula, we get:

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sec(theta) = 1/cos(theta)

I believe that is your option D

Answer:

C(x) = 2x^3 + 2x^2 - 18x - 11

Step-by-step explanation:

Step 1: To model the water used by the car wash on a shorter day, we can subtract the amount of water saved from the original water usage function.

Step 2: Therefore, we can define the new function C(x) as: C(x) = W(x) - D(x)

Step 3: Substituting the given functions for W(x) and D(x), we get: C(x) = (3x^3 + 4x^2 - 18x + 4) - (x^3 + 2x^2 + 15)

3x^3 + 4x^2 - 18x + 4 -x^3 - 2x^3 - 15

Step 4: Simplifying by combining like terms, we get:

C(x) = 2x^3 + 2x^2 - 18x - 11

Step 5: Therefore, the function C(x) that models the water used by the car wash on a shorter day is: C(x) = 2x^3 + 2x^2 - 18x - 11

If there are 220 pieces of 20 cents, then there are 380 pieces of 50 cents in the container.

Thabang conserves money by depositing coins in a money box. There are 600 coins in the money box, including 20- and 50-cent pieces.

We proceed as follows to determine how many 50 cent pieces are in the container if there are 220 pieces of 20 cent.

Assume that,

x = number of 20 cents

y = number of 50 cents

So, the total number of cents in the container is 600,so

x + y = 600

Making y the formula's subject, we therefore get that

y = 600 - x

Since x = 220

y = 600 - 220

y= 380

So, there are 380 fifty cents.

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The correct Question is

Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents

It is found that x = -1/3 is the point of inflection again for function f(x) = 3x⁴ + 2x³ - 5x - 12.

Since the second variation of the function f(x) = 3x⁴ + 2x³ - 5x - 12 and then solving for the values of x where the second derivative equals zero

f'(x) = 12x³ + 6x² - 5

f''(x) = 36x² + 12x

We should discover the solutions to the equation f"(x) = 0 for x to determine the locations of inflection:

36x² + 12x = 0

12x(3x + 1) = 0

If x = 0 or x = -1/3, the equation is true.

Here F"(x) > 0 demonstrates that the graph of f(x) is concave if x 1/3.

Concavity in the curve of f(x) at -1/3 x 0 shows that f"(x) 0.

When x is greater than zero, then f"(x) is greater than zero, showing that f(x graph) is concave up.

When x = 0, the graph's concavity does not change, making x = 0 not an inflection point =only x = -1/3

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Answer:

The correct answer is C.

Step-by-step explanation:

you use y = mx +b

6E6 is a number written in scientific notation, which means that it represents 6 times 10 raised to the power of 6. To write this number in standard form, we need to evaluate the exponent and write the number in expanded form.

6E6 = 6 x 10^6

Evaluating the exponent 6 means multiplying 6 by 10 six times:

6 x 10^6 = 6 x 10 x 10 x 10 x 10 x 10 x 10

Simplifying the expression, we get:

6 x 10^6 = 6,000,000

Therefore, 6E6 in standard form is 6,000,000.

The correct answers are:

The explanation for each response can be given as:

a. The population of this study would be all AIDS patients who have revealed symptoms and are receiving the new AIDS antibody drug.

b. Two reasons why the data may differ are:

  1. Variability in the patient's overall health and response to the treatment.

  2. Differences in the time of diagnosis and initiation of treatment among the patients.

c. It is not possible to determine if one researcher is correct and the other is incorrect solely based on the collected data. Multiple factors, such as the patient's individual characteristics and treatment protocols, could influence the outcomes.

d. The data may not be identical because each researcher is following a different set of patients, and individual patient experiences and outcomes can vary. Additionally, differences in data collection methods or other external factors could contribute to variations.

e. The sampling method used by the first researcher, randomly selecting [tex]40[/tex] states and then selecting one person from each state, is a combination of stratified sampling (based on states) and simple random sampling (within each state).

f. The second researcher used a non-random sampling method by choosing [tex]40[/tex] patients they knew. This method is known as convenience sampling. Concerns regarding this data set include potential bias in patient selection, as the researcher's personal knowledge could introduce subjectivity and may not represent a diverse range of patients receiving the treatment.

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The image of the point after a reflection over the line y = -x is (-6, 8)

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

Point = (-8, 6)

Transformation rule

A reflection over the line y = -x

The rule of a reflection over the line y = -x is

(x, y) = (-y, -x)

Using the above as a guide, we have the following:

Image = (-6, 8)

Hence the image of the point after a reflection over the line y = -x is (-6, 8)

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The solution of measure of angle e is,

⇒ e = 58 degree

We have to given that,

Two lines are intersect each other.

Hence, By definition of linear pair angle, we get;

⇒ e + 122 = 180

Subtract 122 from both sides to isolate e.

This gives us,

⇒ e = 180 - 122

⇒ e = 58

Therefore, The solution of measure of angle e is,

⇒ e = 58 degree

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The ordered pair of the two sequences are (6, 4), (8, 10), (9, 28)

Given data ,

The first sequence is add 10, then divide by 2 starting from 2

The second sequence is multiply by 3, then subtract 2 starting from 2

On simplifying , we get

Let the first number be 2

So , ( 2 + 10 )/2 = 6

Now , ( 2 x 3 ) - 2 = 4

And , the first ordered pair is ( 6 , 4 )

Now , ( 6 + 10 ) / 2 = 8

And , ( 4 x 3 ) - 2 = 10

So , the second ordered pair is ( 8 , 10 )

Now , ( 8 + 10 ) / 2 = 9

And , ( 10 x 3 ) - 2 = 28

So , the third ordered pair is ( 9 , 28 )

Hence , the sequence is solved and (6, 4), (8, 10), (9, 28)

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Answer:

scienific scienific

Step-by-step explanation:

The surface area of four boxes is 4032cm².

To calculate the surface area of one box, we need to find the area of each of its six faces and then add them up.

The top and bottom faces are both squares with sides of 12cm, so each has an area of 12cm x 12cm = 144cm².

The front and back faces are both rectangles with dimensions of 12cm x 15cm,

So each has an area of 12cm x 15cm = 180cm².

The two side faces are also rectangles with dimensions of 12cm x 15cm, so each has an area of 12cm x 15cm = 180cm².
Adding up the areas of all six faces, we get:
144cm² + 144cm² + 180cm² + 180cm² + 180cm² + 180cm² = 1008cm²
Therefore, the surface area of one box is 1008cm².
To find the surface area of four boxes, we just need to multiply the surface area of one box by 4:
The surface areas of all the faces together:

(144 x 2) + (180 x 2) + (180 x 2) = 504 sq.cm

The surface area of one box is 504 square centimeters.

Since you want the surface area of four boxes, simply multiply this number by 4:

504 sq.cm x 4 = 2016 sq.cm
1008cm² x 4 = 4032cm²
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Answer: Range: 14 Interquartile:  5.5

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

The pattern is

2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37

So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers

Answer:

5th term is 26.

Step-by-step explanation:

5-2 =3. 10 - 5 = 5. 17 - 10 = 7.

notice how the differences are 3, 5, 7?

there's a gap of 2 between each difference.

so, let's call our next term in the sequence a.

a - 17 = (7+2).

a - 17 =9.

a = 26.

so, 5th term is 26.

Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his Budget is less than R7200, then it would not be enough.

We are not provided with any information in the question, so we cannot answer it as is. However, we can use the formula provided to calculate the total floor area to be tiled:

Area of a rectangle = length x width

Let's say the length is L and the width is W. Then, the total floor area to be tiled is:

Total floor area = L x W

We are not given the values of L and W, so we cannot calculate the exact total floor area. However, we can assume that Tshego has already calculated the total floor area to be 32 m².

To determine how many boxes of tiles Tshego will need, we need to know the size of each box of tiles and the total area that one box can cover. Let's assume that each box of tiles covers an area of 1 m².

If the total floor area to be tiled is 32 m², and an extra 10% of the number of tiles must be added for cutting and breakages, then the total area to be covered with tiles would be:

Total area to be covered = 32 m² x 1.1 = 35.2 m²

Therefore, Tshego would need 36 boxes of tiles to cover the entire floor area.

To determine if Tshego's budget is enough to finish the tiling project, we need to know the cost of each box of tiles and the total cost of the project. Let's assume that each box of tiles costs R200.

The total cost of the project would be:

Total cost = Number of boxes x Cost per box

Total cost = 36 x R200 = R7200

If Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his budget is less than R7200, then it would not be enough.

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