find the two values of k for which y ( x ) = e k x is a solution of the differential equation y ' ' − 14 y ' 40 y = 0 . smaller value = larger value =

Answer:

Step-by-step explanation:

it is 2x

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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On solving the provided question we can say that - the removable discontinuity of f(x) located is -5

Discontinuous functions in graphs are those that have no connections to one another. Discontinuities come in three different flavors: removable, jump, and infinite.. If the left limit and the right limit of a function, f(x), are both different, then the function has a first-kind discontinuity at x = a. a characteristic that cannot be mathematically continuous. Continuous functions allow you to sketch without having to lift your pen. In such a case, the function is said to as discontinuous.

here,

f(x) = \(\frac{x+5}{x^2+3x-10}\)

\(x^2+3x-10\)

x(x+5) - 2(x+5)

(x+5 )(x-2 )

x = 2, -5

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Answer:

805.5 out of 900

Step-by-step explanation:

A test is out of 100 and because there are 9 tests: 9 x 100 which equals 900.

To get the average we add up each test mark and divide by the number of tests. The same can be applied here but reversed. So because there were 9 tests we can multiply 89.5 by 9 which gives us 805.5. Beverly scored 805.5 marks out of 900 which makes her average 89.5% for 9 tests.

The expected value of the prospect is $10, the expected utility is √10, the certainty equivalent is $7.07, and Alex is risk-averse. When considering the prospect ($16,p; $4,1 −p), it is impossible for Alex's expected utility from the prospect to equal $5. The range of Alex's expected utility depends on the value of p.

For the given prospect ($16,0.5; $4,0.5) and Alex's utility function u($x) = √x, we can calculate the expected value, expected utility, and certainty equivalent, and determine Alex's attitude towards risk.

The expected value of the prospect can be calculated by multiplying each outcome by its corresponding probability and summing them. In this case, it is (16 × 0.5) + (4 × 0.5) = $10.

The expected utility of the prospect is found by applying the utility function to each outcome, multiplying by its probability, and summing them. It is (√16 × 0.5) + (√4 × 0.5) = √10.

The certainty equivalent is the guaranteed amount that Alex would be willing to accept instead of the uncertain prospect. It is the value at which Alex's utility is equal to the expected utility of the prospect. By solving the equation √x = √10, we find the certainty equivalent to be $7.07.

Alex is risk-averse because the certainty equivalent ($7.07) is less than the expected value ($10). Risk-averse individuals prefer a certain outcome with a lower expected value over an uncertain prospect with a higher expected value.

The graph of Alex's utility function (√x) would be an increasing concave curve. The certainty equivalent (CE) would be marked at the point where the utility function intersects the expected utility (EU) line, and the expected value (EV) would be marked at the corresponding x-value.

When considering the prospect ($16,p; $4,1 −p), it is not possible for Alex's expected utility from the prospect to equal $5 since √x ≠ 5 does not have a solution. The possible range of Alex's expected utility depends on the value of p, where 0 ≤ p ≤ 1.

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Answer:

Its c have a nice day! <3

Step-by-step explanation:

Answer:

21.6 Pounds

Step-by-step explanation:

Multiply 2.5 by 8.34 to get 20.85 pounds of water

add the weight of the bucket (.75) to the weight of the water (20.85) to get 21.6 pounds total

(1) This series consists of terms of an arithmetic sequence:

179 - 173 = 6

173 - 167 = 6

and so on, so that the n-th term in the series is (for n ≥ 1)

a(n) = 179 - 6 (n - 1) = 185 - 6n

Then the sum of the first 53 terms is

\(\displaystyle\sum_{n=1}^{53}(185-6n) = 185\sum_{n=1}^{53}1-6\sum_{n=1}^{53}n\)

\(\displaystyle\sum_{n=1}^{53}(185-6n) = 185\times53-6\times\frac{53\times54}2\)

\(\displaystyle\sum_{n=1}^{53}(185-6n) = \boxed{1219}\)

(2) This series has terms from a geometric sequence:

-12 / 6 = -2

24/(-12) = -2

-48/24 = -2

and so on. The n-th term is (again, for n ≥ 1)

a(n) = 6 (-2)ⁿ⁻¹

and the sum of the first 19 terms is

\(\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 + (-2) + (-2)^2 + (-2)^3 + \cdots+(-2)^{19}\right)\)

Multiply both sides by -2 :

\(\displaystyle-2\sum_{n=1}^{19}6(-2)^{n-1} = 6\left((-2) + (-2)^2 + (-2)^3 + (-2)^4 + \cdots+(-2)^{20}\right)\)

Subtracting this from the first sum gives

\(\displaystyle(1-(-2))\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)\)

and solving for the sum, you get

\(\displaystyle3\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)\)

\(\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-2)^{20}\right)\)

\(\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-1)^{20}2^{20}\right)\)

\(\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -2^{20}\right) = 2-2^{21} = \boxed{-2,097,150}\)

Do you need a equation for that?

y=4x+3

Answer:

It should be $20,000

Step-by-step explanation:

From $20,000 to $14,000 = -30%

Which the -30% is the discount basically

So your final answer should be $20,000

$20,000 was the original price.

Assuming an equal probability of having a girl or a boy for each child, the probability that a couple does not have girls for all three children is 1/8 or approximately 0.125 (12.5%).

If we assume that the probability of having a girl or a boy for each child is equal (which is a simplifying assumption), then the probability of having a girl for each child is 1/2, and the probability of having a boy is also 1/2.

To find the probability that the couple does not have girls for all three children, we need to find the probability of having a boy for each child. Since the gender of each child is independent of the others, we can multiply the probabilities together.

So, the probability of having a boy for the first child is 1/2, for the second child is also 1/2, and for the third child is also 1/2.

Multiplying these probabilities together, we get:

(1/2) * (1/2) * (1/2) = 1/8

Therefore, the probability that the couple does not have girls for all three children is 1/8 or approximately 0.125 (12.5%).

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In matrix form, the given system is written as

\(\begin{bmatrix}1&1&0\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3-k\\1\\-3\end{bmatrix}\)

and the system has no solution is the coefficient matrix is singular. The determinant is

\(\begin{vmatrix}1&1&0\\6&2&-3\\k&0&-1\end{vmatrix} = -3k+4\)

and this is zero when k = 4/3.

On the other hand, in case you are missing a factor of z in the first equation, so that the system should read

x + y + (k - 1) z = 2

6x + 2y - 3z = 1

kx - z = -3

reframing it as a matrix equation gives

\(\begin{bmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}2\\1\\-3\end{bmatrix}\)

Then the determinant of the coefficient matrix is

\(\begin{vmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{vmatrix} = -2k^2-k+4\)

and the determinant is zero at two values, k = (-1 ± √33)/4.

To determine the exact amount of triangles that can be constructed with angles measuring 110°, 50°, and 10°, we need to use the Triangle Angle Sum theorem, which states that the sum of the interior angles of a triangle is always equal to 180°. Therefore, the sum of the three angles is 110° + 50° + 10° = 170°.

This means that there is an angle missing to make a complete triangle. To construct a triangle, we need to have three angles that add up to 180°. Since we only have two angles that add up to 160°, we cannot construct a triangle with the given angles. Therefore, the exact amount of triangles that can be constructed with angles measuring 110°, 50°, and 10° is 0.
To determine the exact amount of triangles that can be constructed with angles measuring 110°, 50°, and 10°, we need to examine whether the given angles can form a valid triangle. According to the Triangle Sum Property, the sum of the interior angles of any triangle must equal 180°.

Let's add the given angles:
110° + 50° + 10° = 170°

As the sum of these angles is 170°, which is not equal to 180°, it is impossible to construct a triangle using these angles. Therefore, the exact amount of triangles that can be constructed with angles measuring 110°, 50°, and 10° is 0.

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Answer:

see explanation

Step-by-step explanation:

(i)

\(\frac{x}{3}\) + \(\frac{y}{2}\) = 1 ( multiply through by 6 to clear the fractions )

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide through by 3 )

y = - \(\frac{2}{3}\) x + 2

(ii)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient ) and c the y- intercept )

y = - \(\frac{2}{3}\) x + 2 ← is in slope- intercept form ( that is part (i)

with gradient m = - \(\frac{2}{3}\)

Answer:

Step-by-step explanation:

The area of the quadrilateral is 14 square centimeters.

The quadrilateral is made up of two triangles.

Area of a triangle is expressed as;

1/2 × base × height.

Given that;

For the upper triangle

For the lower triangle

The area of the quadrilateral will be the sum of the area of the two triangles.

Area of quadrilateral = Area of upper triangle + Area of lower triangle

Area of quadrilateral = ( 1/2 × 4 × 4 ) + ( 1/2 × 4 × 3 )

Area of quadrilateral = ( 2 × 4 ) + ( 2 × 3 )

Area of quadrilateral = ( 8 ) + ( 6 )

Area of quadrilateral = 14cm²

Therefore, the area is 14cm².

Option D) 14 square centimeters is the correct answer.

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The volume of a cylinder is given by:

In this case the volume is 100 cubic inches and the height is 12 inches; plugging this values in the equation above and solving for r we have:

Therefore the radius is 1.6 inches.

Answer:

Length = 178 yards and Breadth = 46 yards

Step-by-step explanation:

The perimeter of the rectangular field is 448 yards

Let the width is b and the length of the field is (4b-6) yards

We need to find the dimensions of the playing field. We know that the perimeter of a rectangle is given by :

P = 2(l+b)

ATQ,

[2((4b-6)+b)] = 448

2(5b-6) = 448

5b-6 = 224

5b = 230

b = 46 yards

Length = (4b-6)

= 4(46) - 6

= 178 yards

Hence, the length and breadth of the field is 178 yards and 46 yards respectively.

Answer:

30 times

Step-by-step explanation

Answer:

30

Step-by-step explanation:

After observing the table of the given five functions, we know that the solution would be when f(x) = g(x) at x =1.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).

In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The polynomial function of degree zero is a constant function.

Linear Function: The first-degree polynomial function.

Quadratic Function: The degree of two polynomial functions.

Cubic Function: The degree of three polynomial functions.

So, the table is shown:
x           f(x) =4x+1           g(x) = 3ˣ⁺¹ ⁻ ⁴    

-3             -11                    -35/9    

-2              -7                     -11/3

-1               -3                      -3

0                1                       -1

1                 5                       5

2                9                      23

3                13                     77

We must resolve the equation f(x) = g. (x)

We must determine the value of x such that f(x) = g. (x).

You can see from the provided table that when x = 1

f(x)  =5, g(x) = 5

Therefore, after observing the table of the given five functions, we know that the solution would be when f(x) = g(x) at x =1.

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Correct question:

The table shows values for functions f(x) and g(x)

x f(x)=4x+1 g(x)=3x+1−4

−3 −11 −359

−2 −7 −113

−1 −3 −3

0 1 −1

1 5 5

2 9 23

3 13 77

What is the solution to f(x)=g(x) ?

Select each correct answer.

−3

−2

−1

0

1

2

3

Answer:

603.2

Step-by-step explanation: Use the radius of the cylinder and height and plug it into the volume formula for a cylinder and solve

Answer:

About 9 sq yd

Step-by-step explanation:

First, you know that 3ft. = 1 yd. That means each square is 1 sq yd. The length of the herb garden is 6 squares, while the width is about 1.5 squares. If you multiply those two to find the area, then you get about 9 square yards.

As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution.

In the theory of probability, the central limit theorem states that the distribution of a sample mean approximates a normal distribution as the size of the sample increases. For the central limit theorem to hold, it is necessary that the sample size at least cross a margin of 30. Having a sufficiently larger sample size can predict the characteristics of the sample more accurately. The central limit theorem is applicable when we are analyzing large data sets.

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Answer:

1,3,4,5,9

Step-by-step explanation:

They Are All Equal.