If p is a positive integer, then p(p + 1)(p − 1) is always divisible by

F. 7
G. 5
H. 4
J. 3
K. None of these

Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)

Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:

g(1) = 18

g(6) = 11

If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.

So the correct optionis the last one.

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Answer:

g(x)

=6x−4

=3x

2

−2x−10

Escribe (g∘f)(x) como una expresión en términos de x.

Step-by-step explanation:

Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).

Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:

f(x) = x^2 - 2x + 1

Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:

g(f(x)) = 6f(x) - 4

= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))

= 6x^2 - 12x + 2

Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.

Answer:

Step-by-step explanation:

[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]

But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.

The correct options are:

The data contain a sample of multiple individuals.

The data are collected  are approximately at  the same point in time.

Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.

One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.

Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.

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The function for the value of the account after t years can be written as:

V(t) = 93000(1.08900365)t

The coefficient of 1.08900365 is the annual growth rate (APR) compounded daily. After rounding to four decimal places, it becomes 1.0890.

The percentage of growth per year (APY) is 8.90%. This is the same as APR, but expressed as a percentage.

So the solution equation is 6x + 3 and the total miles is equal to 6x + 3.

Where x represents the length of Lincoln Park School.

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

Mile is a unit of measurement that equals 1760 yards or approximately 1.6 kilometer's. It the mostly used in the continent of North America.

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Answer:

The maximum number of students to whom 48 apples, 60 bananas, and 96 guavas can be distributed equally is 20. Each student will receive 2 apples, 3 bananas, and 4 guavas.

Answer:

................................

Answer:

159 proper subsets.

Step-by-step explanation:

Given a set {2, 4, 6, 8...100}, how many proper subsets are there?

First, find how many subsets there are in 2 - 10:

That's 16.

Then because there are 10 10s in 100, multiply by 10:

16 x 10 = 160

Finally, because it says proper subsets, subtract by 1:

160 - 1 = 159 proper subsets.

Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}

The probability of selecting an officer who is in the Navy given that the officer is African American is 0.192.

Probability calculates the likelihood that an event would happen. The likelihood that an event would occur has a value that lies between 0 and 1 or 0 and 100. The more likely an event would happen, the closer the probability value would be to 1 or 100.

The probability of selecting an officer who is in the Navy given that the officer is African American = number of African Americans that are in the Navy / total number of African Americans

Total number of African Americans = 9162 + 3524 + 1341 + 4282 = 18,309

The probability = 3524 / 18,309 = 0.192

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Answer:

To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we find the antiderivative of f(x):

F(x) = x^2 + (5/3)x + C

where C is the constant of integration.

Next, we evaluate F(5) and F(0):

F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C

F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C

Subtracting F(0) from F(5), we get:

∫[0,5] f(x) dx = F(5) - F(0)

= 25 + (25/3) + C - C

= 25 + (25/3)

= 100/3

Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.

The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.

The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.

Given that, K = 5/9 (F - 459.67).

To obtain F in term of K we isolate the value of F as follows:

K = 5/9 (F - 459.67)

Multiplying both sides by 9/5, we get:

(9/5) K = F - 459.67

Adding 459.67 to both sides, we get:

F = (9/5) K + 459.67

Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

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Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.

The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.

Here,

=> F(x) = sec(x) has a 2 phase.

Because the secant function is periodic, its values recur after a predetermined amount of time.

This interval's length is equal to the secant function's duration.

The formula for the secant function is

=> sec(x) = 1/cos.(x).

The cosine function repeats its values every 2 units of x, which is known as its period.

Consequently, the secant function has a period of 2 as well.

Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.

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Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.

The above statement is True.

In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.

A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.

Sometimes the term linear function has the same meaning as linear map, but not in analysis.

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(a) There are 100,000 different ways for Fiona to select her lunches for the week.

(b) There are 200,000 different ways for Fiona to select her lunches and drinks for the week.

(a) Since Fiona selects one lunch special each day, there are 10 options for Monday, 10 options for Tuesday, and so on, for a total of 10 options for each of the 5 weekdays. Therefore, the total number of ways for Fiona to select her lunches for the week is:

10 × 10 × 10 × 10 × 10 = 10^5 = 100,000

(b) In addition to the 10 lunch specials, Fiona now has 2 options for her drink, either water or tea. So for each of the 100,000 possible lunch selections from part (a), there are 2 possible drink options. Therefore, the total number of ways for Fiona to select her lunches and drinks for the week is:

100,000 × 2 = 200,000

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Here's a graph of the cost function C = 25000p / (100 - p), using graphing utility. The graph shows that the cost function is continuous and defined for all values in its domain.

The domain of the function is restricted to 0 ≤ p ≤ 100, since it doesn't make sense to supply recycling bins to more than 100% of the population, or to a negative percentage of the population.

As p approaches 100%, the cost of supplying recycling bins becomes very large, since it becomes increasingly expensive to provide bins to a large portion of the population. As p approaches 0%, the cost also approaches 0, since there are fewer bins needed for a smaller population.

The function has a vertical asymptote at p = 100, since the denominator of the fraction approaches 0 as p approaches 100 from the left. This means that the cost becomes infinitely large as the percentage of the population approaches 100%.

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The smallest integer n such that a_n < 1 is n = -2.

Let the common ratio of the geometric progression be denoted by r. Then we have

a_2 = a_1 × r

a_3 = a_2 × r = a_1 × r^2

a_4 = a_3 × r = a_1 × r^3

a_5 = a_4 × r = a_1 × r^4

So in general, we have

a_n = a_1 × r^(n-1)

Now, we can use the given equation

(a_1357)^3 = a_34

Substituting the expressions above for a_34 and a_1357, we get

(a_1 × r^33)^3 = a_1 × r^3

Simplifying this equation by dividing both sides by a_1×r^3 and taking the cube root, we get

r^10 = 1/ (a_1^2)

Now, we need to find the smallest integer n such that a_n < 1. Using the expression for a_n above, we get

a_n < 1

a_1 × r^(n-1) < 1

r^(n-1) < 1/a_1

Taking the logarithm of both sides (with base r), we get

n-1 < log_r (1/a_1)

n < log_r (1/a_1) + 1

We know that r^10 = 1/ (a_1^2), so

1/a_1 = r^(10/2) = r^5

Substituting this into the expression above for n, we get

n < log_r (1/r^5) + 1

n < -5 + 1

n < -4

Since n is an integer, the smallest possible value for n is -3. However, this does not make sense since we cannot have a negative index for a term in the geometric progression. Therefore, the smallest integer n such that a_n < 1 is n = -2.

To verify this, we can substitute n = -2 into the expression for a_n and see if it is less than 1

a_n = a_1 × r^(n-1)

a_{-2} = a_1 × r^(-3)

Since a_1 > 1, we just need to show that r^3 > 1 to prove that a_{-2} < 1. From the equation r^10 = 1/ (a_1^2), we have

r^3 = (r^10)^(3/10) = (1/a_1^2)^(3/10) > 1

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The given question is incomplete, the complete question is:

Let a_1, a_2, a_3, a_4, a_5, . . . be a geometric progression with positive ratio such that a_1 > 1 and

(a_1357)^3 = a_34. Find the smallest integer n such that a_n < 1.

The midline equation of the function is y = 1.5.

The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.

Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.

Using the definition of the amplitude the midline is the given amplitude.

Hence, the midline equation of the function is y = 1.5.

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Answer:

3

Step-by-step explanation:

Khan Academy

Answer:

38%

Step-by-step explanation:

I learned in class on Friday.

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

[tex]0.38\times \dfrac{100}{100}[/tex]

[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]

Write in percentage notation: 38%

Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

we have 2 possible cases for the coin and 6 possible cases for the die.

so, we have 2×6 = 12 combined possible cases :

heads, 1

heads, 2

heads, 3

heads, 4

heads, 5

heads, 6

tails, 1

tails, 2

tails, 3

tails, 4

tails, 5

tails, 6

out of these 12 cases, which ones (how many) are desired ?

all first 6 plus (tails, 3) = 7 cases

so, the correct probability is

7/12

formally that is calculated :

1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12

the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.

When three dices are rolled.

Total number of outcomes =  = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways =  = 6

From the digits 6,2,5

So, there are 3! ways =  = 6

From the digits 5,4,4

So, there are  ways = 3

From the digits 6,6,1

So, there are  ways = 3

From the digits 3,5,5

So, there are  ways = 3

So, total numbers whose sum is 13=

So, Probability = .

Therefore, the probability of getting sum as 21 on rolling three dice =   .

Answer:

The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.

The total number of students in the survey is:

50 + 75 + 125 + 50 = 300

The number of students who voted for the Republican party is:

75 + 50 = 125

Therefore, the probability of selecting a student who voted for the Republican party is:

125/300 = 0.4167 (rounded to four decimal places)

So, the answer is option D: 125/300

(please mark my answer as brainliest)

Answer: 66

Step-by-step explanation:

all 3 of them should equal to 180

so 79+35 is 114

180-114 will give us the answer which is 66

Answer:

A≈1.83m²

Step-by-step explanation:

Using the formulas

A=πr2C=2πr

Solving forAA=C24π=4.824·π≈1.83346m²

Answer:

1.83 (approximate)

Step-by-step explanation:

First, we need to find the radius of the circle.

Using the formula:

[tex]C=2 \pi r[/tex]

We have to reorganize terms:

[tex]r=\frac{C}{2\pi}[/tex]

[tex]\frac{4.8}{2 \times \pi}[/tex]

r ≈ 0.76

Now we have the radius and the circumference in order to find the area.

Use the formulas:

[tex]A= \pi r^2[/tex]

[tex]C=2 \pi r[/tex]

A = C^2/4[tex]\pi[/tex]  = 4.8^2 / 4 * pi = 1.83

The standard form of the equation of the ellipse is (x - 2)^2 / 4 + (y - 3)^2 / 7 = 1

To find the standard form of the equation of the ellipse, we first need to determine some of its properties.

The foci of the ellipse are given as (2, 0) and (2, 6). This tells us that the center of the ellipse is at the point (2, 3), which is the midpoint of the line segment connecting the foci.

The major axis of the ellipse is given as a length of 8. Since the major axis is the longest dimension of the ellipse, we can assume that the length of the major axis is 2a = 8, so a = 4.

Next, we need to determine the length of the minor axis. We know that the distance between the foci is 2c = 6, so c = 3. Since c is the distance from the center of the ellipse to each focus, we can use the Pythagorean theorem to find the length of the minor axis

b^2 = a^2 - c^2

b^2 = 4^2 - 3^2

b^2 = 7

b = sqrt(7)

Now we have all the information we need to write the standard form of the equation of the ellipse. The standard form is

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

where (h, k) is the center of the ellipse. Plugging in the values we found, we get

(x - 2)^2 / 4 + (y - 3)^2 / 7 = 1

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Simplifying remex's works the same way we simplify fractions. In fractions, a rational number is considered to be a simplified form when its numerator and denominator have no other common factors than 1.

Regular expressions are fractions with variables. In rational expressions, the numerator and denominator are polynomials. That is, it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. Because regular expressions are nothing but fractions, we treat them as if they were fractions.

It is not possible to divide a number by 0. Check what 1/0 is with your calculator, it will return an error. Therefore, no regular expression is defined for variable values ​​with a denominator of 0 (because it is a fraction). For example, in the expression x / (x + 2), the denominator becomes zero when x = -2, so it is called the limit of the rational expression x / (x + 2). In other words, we say x / (x + 2) for all values ​​of x but x ≠ -2.

Simplifying a regular expression means reducing the value of a regular expression to its lowest term or simplified form. Simplifying regexps works the same way we simplify fractions. In fractions, a rational number is considered a simplified form when its numerator and denominator have no other common factors than 1. The same works for simplified rational expressions, but the only difference is that there are polynomials in the fraction. Let's see the steps to follow to simplify a regular expression.

Step 1: Factor each numerator and each denominator by taking the common factor.

Step 2: Cancel the common factor.

Step 3: Write the remaining terms in the numerator and denominator.

Step 4: Indicate limits, if any. Note that a constraint is any value that makes the denominator equal 0, including terms canceled during simplification.

Complete Question:

Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.

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The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.

An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.

Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.

For the given question.

geometric mean of a and b :

From the drawn diagram.

a = 4

b = 9

x = √ab

x = √9*4

x = 6

geometric mean: 6

Applying the altitude rule:

h² = x.y

6² = 9*4

36 = 36

Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.

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The distance between the points P and Q is 10 units using the Pythagorean theorem.

The right-angled triangle's three sides are related in accordance with the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of the other two sides. According to the Pythagoras theorem, if a triangle has a right angle, the hypotenuse's square is equal to the sum of the squares of the other two sides.

The coordinates of the point P and Q are (3, 2) and (9, 10).

Using the Pythagoras theorem:

c² = (x2 - x1)² + (y2 - y1)²

Substitute the values:

c² = (9 - 3)² + (10 - 2)²

c² = 36 + 64

c² = 100

c = 10 units.

Hence, the distance between the points P and Q is 10 units using the Pythagorean theorem.

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