A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A pair of parallel lines
B. A point
OC. A pair of intersecting lines
OD. A single line

The values of the points on the graph of the concentration of the drug in the bloodstream, indicates;

1 a. 24 mg/L

b. Increases; [0, 2]

Decreasing; [2, 20

c. The drug is at the maximum concentration at t = 2 hours

The maximum concentration is 64 mg/L

d. 8 hours

e. The concentration after 1 week is minute

The concentration after 1 month is more reduced than the concentration after 1 week.

f. The concentration of the drug for the first 20 hours increases in the first 2 hours, then decreases and approaches the x-axis as the x-value increases.

A graph is a visual display of the ordered pair of a function on the coordinate plane.

1. The graph in the question specifies the concentration of the drug in the bloodstream after t hours in mg/L

a. The graph indicates that the concentration after 8 hours is 24 mg/L

b. The interval over which the concentration increases is; [0, 2)

The interval over which the concentration decreases is; (2, 20]

c. The graph indicates that the drug is at its maximum concentration when the time t = 2 hours

The maximum concentration, based on the peak of the graph is 64 mg/L

d. The concentration of the drug is 16 mg/L at t = 10 hours, therefore, the time it takes the concentration to decrease to 16 mg/L from the peak therefore is; 10 hours - 2 hours = 8 hours

e. The shape of the graph indicates that the concentration of the drug in the bloodstream continuously decreases after the first two hours, therefore, the concentration after a week will be approximately 0

The concentration after 1 month will trace amounts

f. The concentration of the drug in the bloodstream over the first 20 hours indicates that concentration increases within the first 2 hours, and decreases rapidly in the next 8 hours, such that after 20 hours, the concentration in the blood is less than 4 mg/L

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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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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 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:

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 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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Fourth month in business, George's new store will have a profit of $4500. The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.

To determine the meaning of (r - c)(4) for George's new store, we need to evaluate the expression (r - c) at x = 4.

Given that r(x) represents the store's revenue and c(x) represents the store's expenses, (r - c)(4) represents the difference between the revenue and expenses of the store after four months.

Substituting x = 4 into the expressions for revenue and expenses, we get:

r(4) = (4)^2 + 6(4) + 10 = 16 + 24 + 10 = 50

c(4) = (4)^2 - 4(4) + 5 = 16 - 16 + 5 = 5

Thus, (r - c)(4) = r(4) - c(4) = 50 - 5 = 45.

Therefore, (r - c)(4) means that after its fourth month in business, George's new store will have a profit of $4500 (since r(x) and c(x) are measured in hundreds of dollars).

The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.

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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.

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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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

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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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:

5 and 6

Step-by-step explanation:

cause

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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Answer:

The correct answer is C.

Step-by-step explanation:

you use y = mx +b

The area of the given parallelogram is 12 yd².

Given that a parallelogram of base 2 yds and height 6 yds,

We need to find the area of the parallelogram,

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal. Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

So, the area of a parallelogram = base × height

so the area of the given parallelogram = 6 × 2 = 12 yd²

Hence the area of the given parallelogram is 12 yd².

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Answer: Range: 14 Interquartile:  5.5

Step-by-step explanation:

The value of f (2) for the function is,

⇒ f (2) = undefined

We have to given that;

The function is defined as;

⇒ f (x) = { x³ + 18x² + 99x + 162  ; x ≤ - 3

          = { (3x - 6) / (x³ - 7x + 6)  ; - 3 < x ≤ 2

          = { √(x² - 4)  ; x > 2

Hence, We can see that;

At x = 2;

Function is defined as;

⇒ f (x) =  (3x - 6) / (x³ - 7x + 6)

Plug x = 2;

⇒ f (2) = (3 × 2 - 6) / (2³ - 7×2 + 6)

⇒ f (2) = (6 - 6) / (8 - 14 + 6)

⇒ f (2) = 0 / 0

⇒ f (2) = undefined

Thus, The value of f (2) for the function is,

⇒ f (2) = undefined

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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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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.

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.

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

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

Answer:

Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.

Step-by-step explanation:

Let's assign variables to the masses involved to solve the problem systematically.

Let's say:

Mass of the trolley = T kg

Mass of the mangoes = M kg

Mass of the watermelons = W kg

According to the given information:

The total mass of the trolley and mangoes is 11 kg:

T + M = 11 -- Equation (1)

The mass of the watermelons is three times the mass of the mangoes:

W = 3M -- Equation (2)

Now, we can use these equations to find the values of T, M, and W.

From Equation (2), we can express M in terms of W:

M = W / 3

Substitute this value of M into Equation (1):

T + W / 3 = 11

Multiply through by 3 to eliminate the fraction:

3T + W = 33 -- Equation (3)

Now, we have a system of two equations (Equation 2 and Equation 3) with two unknowns (T and W). We can solve this system to find the values.

Since we don't have a specific value for any variable, we can express the solution in terms of the variables.

Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.

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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