Given :. f(X)=2/x²+1

Determine f(x-¹)-x²f(-1)

Answer: BC/FG and AE/AC

Step-by-step explanation:

A student has 8 different choices when choosing a pair of pants and a shirt.

Without using intricate calculations, the likelihood of an event occurring is shown using a probability tree diagram. It shows every consequence that an event might have. A probability tree serves the aim of listing all potential outcomes of an event and calculating the likelihood of each one. A probability tree diagram can be used to indicate conditional probabilities or to show a sequence of independent occurrences.

The student can choose from four shirts and two pairs of pants (black or tan) (yellow, red, green, or white). We multiply the number of options for pants by the number of options for a shirt to get the total number of options:

2 choices for pants × 4 choices for a shirt = 8 total outfit choices

Therefore, a student has 8 different choices when choosing a pair of pants and a shirt.

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So the probability of the cost being between $260 and $412 is 0.5953.

a. The probability that the cost will be $260 or less can be found by calculating the z-score and using a standard normal distribution table. The z-score is calculated as follows:

z = (x - μ)/σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 260, μ = 360, and σ = 88. So the z-score is:

z = (260 - 360)/88 = -1.14

Using a standard normal distribution table, we can find that the probability of the cost being $260 or less is 0.1271.

b. The probability that the cost will be more than $412 can be found by calculating the z-score and using a standard normal distribution table. The z-score is calculated as follows:

z = (x - μ)/σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 412, μ = 360, and σ = 88. So the z-score is:

z = (412 - 360)/88 = 0.59

Using a standard normal distribution table, we can find that the probability of the cost being more than $412 is 0.2776.

c. The probability that the cost will be between $260 and $412 can be found by subtracting the probability of the cost being $260 or less from the probability of the cost being $412 or less. Using the z-scores we calculated in parts a and b, we can find the probabilities from a standard normal distribution table:

P(x ≤ 260) = 0.1271
P(x ≤ 412) = 0.7224

P(260 < x < 412) = P(x ≤ 412) - P(x ≤ 260) = 0.7224 - 0.1271 = 0.5953

So the probability of the cost being between $260 and $412 is 0.5953.

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1,800,000

We have to do 6 x 300,000, which gives us 1,800,000

Answer: D: 3 to 4

Step-by-step explanation:

Answer:

In Sharla's computer club, 4 out of every 7 members and girls. What is the ratio of boys to girls in the club?

Maria filled her bathtub with 15 gallons of water. How many pints of water did she put in the tub?

Step-by-step explanation:

You're welcome.

Answer:

Yes, the perimeter and side length of a square are proportional. This is because a square has four equal sides, so if you increase the length of one side by a certain factor, the perimeter (which is the sum of all four sides) will also increase by the same factor. In other words, if you double the length of a side of a square, you will also double its perimeter. Similarly, if you reduce the length of a side by a certain factor, the perimeter will also be reduced by the same factor. This relationship holds true for all squares, regardless of their size or orientation.

Option A is correct, the experimental probability of not selecting a diamond is 82.5%.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of cards drawn is 40, and the frequency of diamonds drawn is 7.

This means that the frequency of not selecting a diamond is:

40 - 7 = 33

So the experimental probability of not selecting a diamond is:

P(not diamond) = frequency of not selecting a diamond / total number of cards drawn

P(not diamond) = 33/40

P(not diamond) = 0.825

P(not diamond) = 82.5%

Therefore, the experimental probability of not selecting a diamond is 82.5%.

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Answer:

To find the values of a and b that make the power function y = ax^b pass through the points (2,5) and (6,9), we can use the following system of equations:

5 = a2^b

9 = a6^b

We need to solve for a and b in this system.

One way to do this is to divide the second equation by the first equation, which eliminates a and gives:

9/5 = (6/2)^b

Simplifying this gives:

9/5 = 3^b

Taking the logarithm of both sides (with any base) gives:

log(9/5) = log(3^b)

Using the logarithmic property that log(a^b) = b*log(a), we get:

log(9/5) = b*log(3)

Solving for b, we get:

b = log(9/5) / log(3)

Plugging this value of b into one of the original equations (e.g., the first one) gives:

5 = a*2^(log(9/5)/log(3))

Solving for a, we get:

a = 5 / 2^(log(9/5)/log(3))

The probability that the sample proportion will exceed 0.2983 is approximately 0.0708.

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is half.

a) 0.28 percent of Canadians have green eyes. This ratio can be used to calculate the anticipated proportion of sample members who have green eyes:

Estimated number of green eyed individuals = Percentage of green eyed individuals * Sample size

Estimated population of those with green eyes: 600 divided by 0.28

168 persons with green eyes are anticipated.

As a result, we would anticipate that 168 members of the sample have green eyes.

b) The formula for calculating the sample proportion's standard deviation is:

Sample proportion's standard deviation is equal to sqrt[(p * (1-p)) / n].

where n is the sample size, and p is the percentage of people with green eyes (0.28). (600).

Sample proportion's standard deviation is equal to sqrt[(0.28 * (1-0.28)) / 600].

Sample proportion's standard deviation is 0.0258.

As a result, 0.0258 is the sample proportion's standard deviation.

c) We're looking for the likelihood that the sample proportion will be more than 0.2983. As the sample size is large enough to allow for the use of the normal approximation, we may use the conventional normal distribution to determine this probability.

Then, we must use the following formula to standardise the sample proportion:

z = [(P * (1 - P)] / sqrt[(p - P)]

where P is the population proportion (0.28), n is the sample size, and p is the sample proportion (0.2983) that we are interested in (600).

z = (0.2983 - 0.28) / sqrt[(0.28 * (1 - 0.28)) / 600]

z = 1.47

The chance of a standard normal variable reaching 1.47 can be calculated using a standard normal distribution table or calculator and is roughly 0.0708.

Thus, 0.0708 is about how likely it is that the sample proportion will be more than 0.2983.

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The predicted population of the school in 2012 is P = 1060 + 78.14(12) = 2002.68 students. We can round this up to 2003 students.

1. The population grew by _____students.

The population in 2001 was 1138 students, and in 2008, it had risen to 1691 students. Therefore, the population increased by 1691-1138 = 553 students.

2. The population took _____ years to grow from 1138 students to 1691 students.

From the year 2001 to the year 2008, the population increased from 1138 to 1691 students. The number of years it took for this growth is 2008-2001 = 7 years.

3. The average population growth per year is _____ students per year.

To obtain the average growth rate per year, divide the total growth in the population by the number of years between the starting year and the ending year. Therefore, the average population growth per year = (1691 - 1138) / 7 = 78.14 students per year.

4. The population in the year 2000 was _____ students.

Since the population was given for the year 2001, we'll have to work our way backward to find the population in the year 2000. It took 7 years for the population to increase from 1138 to 1691, so if we go back another year, we'll have to subtract the average yearly growth rate, which is 78.14 students. Therefore, the population in 2000 = 1138 - 78.14 = 1059.86 students, which we can round up to 1060 students.

5. An equation for the population P of the school t years after 2000 is P = _____.

We can use the formula for linear growth to determine the population of the school t years after 2000. The formula is P = P0 + rt, where P0 is the initial population (in the year 2000), r is the average annual growth rate, and t is the number of years. Therefore, the equation for the population P of the school t years after 2000 is P = 1060 + 78.14t.

6. The predicted population of the school in 2012 is _____ students.

To predict the population of the school in 2012 using the equation, we need to substitute t = 12 - 2000 = 12 into the equation we derived in part 5. Therefore, the predicted population of the school in 2012 is P = 1060 + 78.14(12) = 2002.68 students. We can round this up to 2003 students.

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The equatiοn fοr the number οf eggs in the refrigeratοr e decreased by 3 equals 15 is, e - 3 = 15.

A statement demοnstrating the equality οf twο expressiοns is knοwn as an equatiοn. Variables, cοnstants, and mathematical οperatiοns are οften included. Equatiοns are tοοls fοr prοblem-sοlving and representing relatiοnships between quantities.

Accοrding tο the questiοn states that the number οf eggs in the refrigeratοr e decreased by 3 equals 15.

It means that the equatiοn can be represented as,

e - 3 = 15

e = 18

Therefοre, the equatiοn is, e - 3 = 15.

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Equation connecting C and d is C = 5/3 d.

Direct Proportion of two quantities can be defined as that when one of the quantity increases, the other one also increases and vice versa.

(a) Given that,

C is directly proportional to d.

Equation can be written as C = kd, for some constant k.

Also, given,

C=100 when d=60

100 = 60k

k = 100/60 = 10/6 = 5/3

Equation is C = 5/3 d

(b) When d = 45 km

C = 5/3 × 45 = 75

Cost of transporting goods for 45 km is $75.

(c) When C = $120,

120 = 5/3 d

d = 120 × 3/5 = 72 km

Hence the distance is 72 km when the cost of transporting goods is $120.

Hence the equation is C = 5/3 d.

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Answer:

459 cases per 100,000 people.

Step-by-step explanation:

To calculate the prevalence of DMD, we need to know the number of people living with the condition at a specific point in time. We can estimate this number by multiplying the annual incidence rate by the average duration of the disease:

Prevalence = Annual incidence rate x Average duration of the disease

Annual incidence rate = 0.017% = 17 cases per 100,000 people per year

Average duration of the disease = 27 years

Therefore, the prevalence of DMD can be estimated as:

Prevalence = 17 cases per 100,000 people per year x 27 years = 459 cases per 100,000 people

So, approximately 459 people out of 100,000 are living with DMD. This can also be expressed as a percentage by multiplying the above value by 100, which gives:

Prevalence = 459 cases per 100,000 people x 100% = 0.459% of the population

Therefore, the prevalence of DMD is approximately 0.459% or 459 cases per 100,000 people.

B3 is in the image of A, and the vector x that demonstrates this is x = [ 5 ][ 2 ] [ 2 ].

To determine whether a vector is in the image of A, we need to solve the equation Ax = b for x. If there is a solution for x, then the vector is in the image of A.

For b1:
A x = [ 2 ]
[ 4 ] [ -7]
We can set up a system of equations:
0x + 1y - 1z = 2
0x + 2y - 2z = 4
1x + 2y + 3z = -7
Solving this system, we find that there is no solution for x, y, and z. Therefore, b1 is not in the image of A.

For b2:
A x = [ 3 ]
[ -10 ] [ 4 ]
We can set up a system of equations:
0x + 1y - 1z = 3
0x + 2y - 2z = -10
1x + 2y + 3z = 4
Solving this system, we find that there is no solution for x, y, and z. Therefore, b2 is not in the image of A.

For b3:
A x = [ 0 ]
[ 0 ] [ 11 ]
We can set up a system of equations:
0x + 1y - 1z = 0
0x + 2y - 2z = 0
1x + 2y + 3z = 11
Solving this system, we find that there is a solution for x, y, and z: x = 5, y = 2, and z = 2. Therefore, b3 is in the image of A, and the vector x that demonstrates this is x = [ 5 ]
[ 2 ] [ 2 ].

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Answer: 88

Step-by-step explanation:

Plug 8 in for q

11 x (8) = 88

Answer:

Step-by-step explanation:

Q has y-coordinate of 4 => the distance from origin to y-coordinate is 4 units, which is one leg of the right triangle

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

with c = 5, a = 4

5^2 = 4^2 + b^2

b^2 = 25 - 16 = 9

b = √9 = 3

so Q has coordinates (-3,4)

Answer:

The fraction that is not equivalent to 25% is 2/5.

To see why, we can start by converting 25% to a fraction. Recall that "percent" means "per hundred," so 25% is equal to 25/100 or 1/4.

Now, we can check each of the answer choices to see if they are equivalent to 1/4:

1/4 is already in the form of 1/4, so it is equivalent to 25%.

5/20 can be simplified by dividing both the numerator and denominator by 5, which gives 1/4. So 5/20 is also equivalent to 25%.

25/100 is the same as 1/4 (we converted 25% to 1/4 earlier), so it is equivalent to 25%.

This leaves us with 2/5 as the answer choice that is not equivalent to 25%. We can see this by converting 2/5 to a percent:

2/5 = 0.4

0.4 x 100% = 40%

So 2/5 is equivalent to 40%, which is not the same as 25%.

Answer: [tex]2/5[/tex] second option

Step-by-step explanation: 1/4 is equal to 25% because if you multiply by 100 and divide by 4 that will equal 25. 5/20 simplified to 1/4 which we know is 25%, 25/100 also does too. Therefore, the answer is 2/5 because it simplifies to 40% which isn't 25%.

The graph of the function x^2/9 - y^2/49 = 1 is graph (d)

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

x^2/9 - y^2/49 = 1

The above equation is an hyperbola

An hyperbola that has its center at the origin is represented as

x^2/a^2 - y^2/b^2 = 1

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

a^2 = 9

b^2 = 49

Evaluate

a = ±3

b = ±7

This means that the semi-major axis is a = 3 and the semi-minor axis is b = 7.

The graph with the above feature is graph (d)

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Answer:

10:50 am, if you have to round the hour it would be 11 am on monday

Step-by-step explanation:

What I like to do for these type of problems is to add the 24hrs first so it would still be 9 am just on monday then we still have 1 hour and 50 minutes to add so

so it would be 10:50 am, if you have to round the hour it would be 11 am on monday

Answer:

10:50 am Monday

Step-by-step explanation:

Subtract 24 hours from 25 to skip a day.

25hours -24 hours=1 hour

It is monday 9am

Now we add 1 hour.

10 am monday

Add 50 minutes:

10:50 am Monday

The quotient of (12x^(3)-9x^(2)-21x+22) divided by (3x-3) is 4x^2 + 6x + 7, and the remainder is 0.

To find the quotient, use long division. First, divide the highest degree term of the numerator by the highest degree term of the denominator: 12x3 ÷ 3x = 4x2. Multiply the denominator by the quotient, then subtract this product from the numerator:

12x3 - 3x(4x2) = 9x2 - 4x2 = 5x2.

Divide the highest degree term of the new numerator by the highest degree term of the denominator: 5x2 ÷ 3x = 5x. Multiply the denominator by the quotient, then subtract this product from the numerator:

9x2 - 3x(5x) = -21x - 15x = -36x.

Divide the highest degree term of the new numerator by the highest degree term of the denominator: -36x ÷ 3x = -12. Multiply the denominator by the quotient, then subtract this product from the numerator:

-21x - 3x(-12) = 22 - (-36) = 58.

Divide the highest degree term of the new numerator by the highest degree term of the denominator: 58 ÷ 3 = 19. Since the degree of the numerator is lower than the degree of the denominator, 19 is the remainder.

Therefore, the quotient of (12x3 - 9x2 - 21x + 22) divided by (3x - 3) is 4x2 + 6x + 7, and the remainder is 0.

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For the equation y = 5, the slope of is obtained as option D: 0.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

From the graph it can be seen that the line is for the function -

y = 5

So, the coordinate points are (0,5).

Write the equation in slope-intercept form y = mx + b.

Here m is the slope and b is the y-intercept.

So, this will be -

5 = m(0) + b

We can see that the value for m is 0.

Therefore, the slope value is 0.

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The equation of the line of best fit is a mathematical representation of the relationship between two variables. It is typically written in the form,

y = mx + b.

where m is the slope and b is the y-intercept. To find the equation of the line of best fit for a set of data, you can use a graphing calculator or statistical software to calculate the slope and y-intercept.

      Alternatively, you can use the formula for the slope of a line (m = (y2 - y1)/(x2 - x1)) and the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line of best fit. Once you have the slope and y-intercept, you can plug these values into the equation y = mx + b to find the equation of the line of best fit.

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The average percentage change in population in California from 2000-2009 is 1.35% and population in 2015 will be 39306963.

What is average?

In mathematics, the average is a value that represents the central or typical value in a set of numbers. There are several types of averages, including the mean, median, and mode.

The mean is the most commonly used type of average, and it is calculated by adding up all the numbers in a set and then dividing the sum by the total number of numbers. For example, the mean of the set {3, 5, 8, 12} can be calculated as:

mean = (3 + 5 + 8 + 12) / 4 = 7

Now,

To calculate average of percentage change from 2000-2009

we have to add percentage change for every year

and that will be = 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93

=12.21%

then average=12.21/9=1.35%

hence,

          The average percentage change in population in California from 2000-2009 is 1.35%.

The population in 2015 will be = 37000000 + (1.35)⁶ × 37000000/100

=37000000+2306963.15

=39306963

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Answer: Without knowing the specifics of the spinner, it's not possible to list all the possible outcomes.

However, we can determine the total number of possible outcomes by multiplying the number of outcomes for each event. For example, if the coin has two possible outcomes (heads or tails) and the spinner has six possible outcomes, then the total number of possible outcomes would be:

2 (outcomes for the coin) x 6 (outcomes for the spinner) = 12 possible outcomes

If you provide me with the specific details of the spinner (such as the number of sections and what each section represents), I could list all the possible outcomes.

Step-by-step explanation:

Answer: What else? Is that the whole sentence to this story i dont get it?

Step-by-step explanation:

The most appropriate formula to use in this situation (patient with a bacterial infection and prescribed with Amoxicillin) is Clark's rule, and the dose to administer every 12 hours would be 108.4 mg.

The best formula to use in this situation is the Clark's rule, which is used to calculate the dose of medication for a child based on their weight and the adult dose. The formula is as follows:

In this case, the weight of the child is 21.1 pounds and the adult dose is 771 mg every 12 hours. Plugging these values into the formula, we get:

Rounding to the nearest tenth of a milligram, the child dose would be 108.4 mg and to administer every 12 hours.

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By answering the above question, we may state that It is challenging to graphs offer a more precise interpretation of the graph without additional context and information about its intended use.

Mathematicians make graphs to visually express or chart facts or values in a logical way. Usually, a graph point will convey the connection between two or more objects. A graph is a non-linear data arrangement comprised of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as charts and graphs, pie charts, and line graphs. a triangle-shaped logarithmic graph.

Giving a precise interpretation is challenging without knowing the line's equation or the context of the graph. However, generally speaking, the fact that the line passes through the point (-10, 2) indicates that it is on the line.

The graph could compare two distinct types of data or separate variables, such time and distance. The point (-10, 2) on the line, for instance, may indicate that if someone worked for 10 hours, they would receive $2. This is an example of a graph demonstrating the link between the number of hours worked and the amount of money made.

It is challenging to offer a more precise interpretation of the graph without additional context and information about its intended use.

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Sum of the first 15 terms of the series given is = 10485.36

What is sequence and series?

A sequence is a collection or sequential arrangement of numbers that adheres to a predetermined order or set of criteria. A series is created by adding the terms of a sequence. In a sequence, a single sentence could appear more than once.

Sequences can be divided into two categories: endless sequences and finite sequences. By merging the terms of the sequence, series are defined. A series may, in exceptional cases, also have a sum of infinite terms.

In the given question,

Antonio is working with a new geometric series generated by the following equation:

A(n) = 12(1.5) ⁿ-1

Now to find the sum of the first 15 terms of the series,

S(n) = a{rⁿ)-1}/r-1

So, we have,

a = 12

r = 1.5

n = 15

Using the values in the equation:

S (15) = 12 (1.5¹⁵ - 1)/1.5-1

= 12 × (437.89-1)/0.5

= 12 × 873.78

= 10485.36

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