A small town has two local high schools. High School A currently has 500
students and is projected to grow by 80 students each year. High School B
currently has 700 students and is projected to grow by 30 students each year.
Let A represent the number of students in High School A in t years, and let
B represent the number of students in High School B after t years. Write an
equation for each situation, in terms of t, and determine how many students
would be in each high school in the year they are projected to have the same
number of students.
A
B =
Answer:

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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2 • xy (midsegment) = sum of the bases

Plug in the numbers

2 • 12.5 = 3x + 1 + 15

Add 1 and 15 together

25 = 3x + 16

Subtract 16 on both sides and you should get:

9 = 3x

Divide both sides by 3

9/3 = 3x/3

Answer:

3 = x

The inequality that can be used to find all possible values of T, the time it would take to reach their destination if they travel at an average speed of at least "r" miles per hour, can be expressed as:

T ≤ 475 / r

This inequality states that the time taken (T) should be less than or equal to the distance traveled (475 miles) divided by the average speed (r miles per hour). By dividing the total distance by the average speed, we obtain the maximum time it would take to reach the destination. Any time less than or equal to this value would satisfy the condition of traveling at an average speed of at least "r" miles per hour.

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Answer:

The second one is wrong, so select the rest

A measurable loss of height is an assessment finding in a 65-year-old patient that alerts the nurse to the presence of osteoporosis.

Osteoporosis is a condition characterized by the loss of bone density and strength, leading to increased fragility and risk of fractures. Among the given options, option C, "a measurable loss of height," is a key assessment finding that indicates the presence of osteoporosis. Osteoporosis can cause compression fractures in the spine, leading to a decrease in height. As the bones in the spine weaken and collapse, it can result in a noticeable loss of height over time. This can be measured and documented during a physical assessment.

Frequent falls (option A) may not necessarily be a specific indication of osteoporosis, as falls can occur due to various factors. Aversion to dairy products (option B) may suggest a potential deficiency in calcium intake, which can contribute to osteoporosis, but it alone is not a conclusive sign. Bowed legs (option D) may be related to other conditions but are not a direct indicator of osteoporosis.

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Answer:

13

Step-by-step explanation:

A trapezoid is a quadrilateral (has four sides and four angles) with two parallel opposite sides. These parallel sides are known as the bases.

According to the mid segment theorem of a trapezoid, The mid segment of a trapezoid is half the lengths of the two parallel sides.

Given that TW is the mid segment, UV and RS are the parallel bases, hence:

\(TW=\frac{UV+RS}{2} \\\\-4z+55=\frac{(-z+15)+(-3z+43)}{2} \\\\-4z+55=\frac{-4z+58}{2} \\\\-8z+110=-4z+58\\\\-4z+8z=110-58\\\\4z=52\\\\z=13\)

a different method for unit conversion in a previous class, answer the following questions in a short paragraph. What is the other method you learned? Which part, or parts, of the unit factor method do you feel are easier or harder than the other method? Why? Which method do you prefer for unit conversion: the method you learned before or the unit factor method

9) pi/3 = 180 /3 = 60⁰

the other angle = 90-60=30⁰

10) 2pi/9 = 360/9 = 40⁰

the other angle = 90+40=130⁰

11) arc length = 2pi * r * (θ/360)

= 2pi * 16 * (270/360)

= 75.4 km

12)arc length = 2pi * r * (θ/360)

3 * 180/4 = 135⁰

135/360 =0.375

2pi * 6 * 0.375 =14.13 in

13) arc length = 2pi * r * (θ/360)

= 9 *2pi *(255/360) =40.05 mi

14)arc length = 2pi * r * (θ/360)

=23.56 mi

The computer output provided.

It seems that the experimenter used one factor in the experiment.

It is unclear how many levels of the factor were used, as this information is missing from the output.

The total number of observations in the experiment, which is not given. Estimate the number of replicates based on the degrees of freedom for error, which is 16.

Assuming that each replicate had equal sample size, we can calculate the total number of observations as follows:
\(Total observations = (df for error + df for factor) + 1\)
\(Total observations = (16 + df for factor) + 1\)
\(Total observations = 17 + df for factor\)
Since we do not know the value of df for factor, we cannot determine the exact number of replicates.

We can say that the experimenter used at least 17 observations in total.
To fill in the missing information in the ANOVA table, we need to know the number of levels of the factor and the number of replicates. Assuming that there were k levels of the factor and n replicates, we can calculate the following:
\(SS factor = MS factor \times (n - 1) \times k\)

\(MS factor = SS factor / (k - 1)\)
\(F = MS factor / MS error\)

P-value = probability of obtaining an F-statistic as extreme as the observed value, assuming the null hypothesis is true
Without knowing the values for k and n, we cannot fill in the missing information in the ANOVA table.
Finally, based on the information given, we cannot draw any conclusions about differences in the factor-level means. We need more information about the experiment, such as the hypothesis being tested, the nature of the factor, and the specific levels being compared, in order to make any meaningful conclusions.

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Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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The inverse of the function f(x) = √(x+1) is \(f^-1\)(x) = x² - 1.

Given a function f(x), its inverse function, denoted as \(f^-1\)(x), is a function that takes the output of f(x) and returns the original input. In other words, if y = f(x), then x = \(f^-1\)(y).

To find the inverse of the function f(x), we follow these steps:

Step 1: Replace f(x) with y:

   y = √(x+1)

Step 2: Interchange x and y:

   x = √(y+1)

Step 3: Solve for y:

   x² = y+1

   y = x² - 1

Step 4: Replace y with f^-1(x):

   f^-1(x) = x² - 1

Therefore, the inverse of the function f(x) = √(x+1) is \(f^-1\)(x) = x² - 1.

To verify this, we can check that (\(f^-1\) o f)(x) = x and (f o \(f^-1\))(x) = x for all x in the domain of the functions:

(\(f^-1\) o f)(x) = \(f^-1\)(f(x)) = (√(x+1))² - 1 = x

(f o \(f^-1\))(x) = f(\(f^-1\)(x)) = √((x² - 1) + 1) = √(x²) = |x| + 1

Since the range of f(x) is [0, infinity), we restrict the domain of \(f^-1\)(x) to [1, infinity) to ensure that the inverse is a function.

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Answer:

The answer is 70°, mark me as brainliest

Answer:

I am thinking c, but I do not know

Step-by-step explanation:

I am sure but if not c then b

The graph of y = f(x) will have a downward concave shape for x < 0, and an upward concave shape for x > 0. The curve will have a local maximum at x = 0.

To determine this :

A curve with these properties is called a "saddle shape" or "saddle point." To sketch such a curve, imagine the graph of y = f(x) as a surface in 3D space, where the height at any point (x, y) is given by f(x). The curve y = f(x) is the intersection of this surface with the xy-plane.

The condition f"(x) < 0 for x < 0 means that the surface is "curving downward" in the negative x direction, while f"(x) > 0 for x > 0 means that the surface is "curving upward" in the positive x direction.

Therefore, the graph of y = f(x) will have a downward concave shape for x < 0, and an upward concave shape for x > 0. The curve will have a local maximum at x = 0.

The resulting graph will resemble a horse saddle, with the "saddle point" at the origin.

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48397*15%*5= 36297.75

answer = 36397.75

The correct answer is as follows: a) The data set that has the greatest sample standard deviation is Data set (ii).

b) Data set (ii) has the largest mean and mode, but the smallest median and the largest standard deviation.

(a) The data set that has the greatest sample standard deviation is Data set (ii).

The sample standard deviation is a measure of the amount of variation or dispersion of a set of data values.

In this case, Data set (ii) has more entries that are farther away from the mean, which results in a larger standard deviation.

(b) The data sets are the same in terms of containing the same numbers (11, 12, 13, 14, 15, 16, and 17).

However, they differ in terms of the order in which these numbers are arranged.

In addition, they differ in terms of the mean, median, mode, and standard deviation.

For example, Data set (ii) has the largest mean and mode, but the smallest median and the largest standard deviation.

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Answer:

x = 1/2 or x = 2/3

Step-by-step explanation:

6x^2 = 7x - 2

=> 6x^2 - 7x + 2 = 0

=> 6x^2 - 3x - 4x + 2 = 0

=> 3x (2x - 1) -2 (2x - 1) = 0

=> (2x - 1) (3x - 2) = 0

2x - 1 = 0

=> 2x = 1

=> x = 1/2

or

3x - 2 = 0

=> 3x = 2

=> x = 2/3

Hopefully this helps!!

Answer:

x = \(\frac{2}{3}\) , x = \(\frac{1}{2}\)

Step-by-step explanation:

6x² = 7x - 2 ( subtract 7x - 2 from both sides )

6x² - 7x + 2 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × 2 = 12 and sum = - 7

The factors are - 3 and - 4

Use these factors to split the x- term

6x² - 3x - 4x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(2x - 1) - 2(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(3x - 2) = 0

Equate each factor to zero and solve for x

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = \(\frac{2}{3}\)

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = \(\frac{1}{2}\)

Answer:

Nolan's time is 100 seconds.

Step-by-step explanation:

Kong took 85 seconds.

Nolan took x seconds.

Kong took 15% fewer seconds than Nolan, so Kong's time is 85% of Nolan's time.

Kong's time is

85% of x or 0.85x

Kong's time is 85 seconds

0.85x = 85

x = 85/0.85

x = 100

Nolan's time is 100 seconds.

Simple random sampling is least likely to guarantee that the sample will be representative and unbiased.

Simple random sampling is a technique that is used in research in which each member of the population is given an equal chance of being selected. It's the most straightforward and most basic technique for selecting a random sample. Sampling is a statistical method used to gather and analyze data from a subset of a population to provide estimates, hypotheses, or projections of the whole population. A sample is a subset of a population chosen to represent it since it would be difficult to collect data on the entire population. A sample is thus chosen using sampling techniques, which are statistical approaches for choosing representative samples that guarantee unbiased and precise results.

Biased sampling is a type of sampling method that can lead to misleading or erroneous conclusions. It happens when the sample that has been chosen is not representative of the population it is meant to represent. Biased sampling occurs when the selection method used to obtain the sample is flawed.

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Answer:

Step-by-step explanation:

Answer:

All you have to do is find the diameter and divide it by 2. I'm sorry if I can't give you a direct answer because I cannot see the diagram.

Step-by-step explanation:

Answer:

7=2.75

8=18

9=3.625

10=29

Step-by-step explanation:

The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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Balloon's altitude = 43.7ft as

change in altitude/500 = tan 5°  

change in altitude = .0875*500

                              =43.7ft

The number of  individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5% is at least 246.

To determine the sample size needed for a 90% confidence interval with a margin of error no more than 5%, we can use the formula:

n = (\(z^{2}\) * p * q) / \(E^{2}\)

where:
n = sample size
z = z-score for the desired confidence level (in this case, 1.645 for 90%)
p = proportion of individuals who believe global warming is not a problem (0.8)
q = 1 - p (0.2)
E = margin of error (0.05)

Plugging in these values, we get:

n = (\(1.645^{2}\)* 0.8 * 0.2) / \(0.05^{2}\)
n ≈ 246

Therefore, at least 246 individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5%. The answer is at least 246.

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The given box has the shape of a cuboid, since its height is greater than its width. Thus, the maximum volume for such box is 11200 \(in^{3}\).

The volume of an object is a measure of it containing capacity. Since the given box has a taller height than its width, then it has the shape of a cuboid. The volume of a cuboid is given as:

volume = length x width x height

            = area x height

Given that the sum of the perimeter of its base and its height is not more than 108 inches, we can say; let the sides of the square base be represented by l and its height by h.

Then;

4l + h = 108

Therefore, maximum volume for the box can be attained when l = 20 inches and h = 28 inches.

So that;

4(20) + 28 = 80 + 28

                 = 108 inches

Thus;

maximum volume = area of the square base x height

                        = 400 x 28

maximum volume = 11200 \(in^{3}\)

The maximum volume for such a box would be 11200 \(in^{3}\).

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Solution

we need to convert the following expression:

four less than half a number n

Then the best answer is:

Answer:

Vertical line (straight up and down)

Step-by-step explanation:

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Answer:

Step-by-step explanation:

the slope of any line is rise/run. What this means is that you have the change in y value divided by the change in x. If you have two points whos x value stays the same, or does not change, you have the change in y divided by 0. Dividing any number by 0 gives you the answer “undefined”.