A herd of elephants on the savannah is moving in a straight line at 4 kilometers per hour, headed
directly toward a biologist who has been tracking them. Meanwhile, the biologist is also driving toward
them at 69 kilometers per hour. If they started out 14 kilometers apart, how long will it be before they
encounter one another?

Answer:

3 -3

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

-(-x)

This simplifies to positive x

x

Let x = -17

-17

Answer:

-17

Step-by-step explanation:

-(-x)= +x therefore

-{-(-17)}= -17

Answer:

Y=3

Step-by-step explanation:

Bc im right

Answer:

if you track it's growth, you can see the progress.

Step-by-step explanation:

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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The intervals for which the rate of change of the quadratic function, f(x) = -(x + 1)² + 8 is faster than the rate of change of g(x) = -x - 6 are; x ≤ -1.5 and x ≥ -0.5

A quadratic function is a polynomial function with one or more variables in which the highest exponent is two.

The slope of f(x) is; f'(x) = -2·(x + 1)

The slope of g(x) = -1

When the rate of change of f(x) is faster than the rate of change of g(x), we get;

The slope of f(x) > The slope of g(x), therefore;

-2·(x + 1) > -1

From which we get;

|-2·(x + 1)| ≥ |-1|

2·(x + 1) ≥ 1

x + 1 ≥ 1/2

x ≥ 1/2 - 1 = -1/2

x ≥ -1/2 = -0.5

The absolute sign indicates that we get;

x + 1 ≤ -1/2

x ≤ -1/2 - 1 = -1 -1/2 = -3/2 = -1.5

x ≤ -1.5

The interval for which the average rate of change of f(x) is faster than the average rate of change of g(x) are; x ≥ -0.5 and x ≤ -1.5

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Answer:

(0,5) will be linear equation

The number of people that nare expected to vote in the election is 260,000. people.

Simply put, a fraction is a portion of a whole. Mathematically, the number is represented as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers. On the other hand, a complex fraction has a fraction in either the numerator or the denominator.

In this situation, the pre-election survey showed that two out of every three eligible voters would cast ballots in the county election and there are 390,000 eligible voters in the county.

The number of people expected to vote will be:

= Fraction of expected voters × Total number of people

= 2/3 × 390000

= 2 × 130000

= 260000

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Answer:

Game:  1/2 lb; Textbook:  2 lb

Step-by-step explanation:

Let the weights of game and textbook be g and t respectively.

Then 6g + 9t = 21 (pounds), and

8g + 9t = 22 (pounds)

Eliminate the variable t by subtracting the first equation from the second.  We get:

2g = 1 (pounds)

Thus, 1 game weights 1/2 lb.

Since 6g + 9t = 21, and g = 1/2 lb,

3 + 9t = 21, or 9t = 18

Then t = 18/9.  1 textbook weighs 2 lb

Answer:

\(m = (2,6)\)

Step-by-step explanation:

Given

A(5, 8) and B(-1,-4)

Required

Determine the midpoint

Represent the midpoint with m

m is calculated as thus:

\(m = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\)

Where:

\((x_1,y_1) = (5,8)\) ---- A

\((x_2,y_2) = (-1,4)\) ------ B

So, the expression:

\(m = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\)

becomes

\(m = (\frac{5 -1}{2},\frac{8 + 4}{2})\)

\(m = (\frac{4}{2},\frac{12}{2})\)

\(m = (2,6)\)

Hence, the coordinates of the midpoint is: (2,6)

Answer:

b=17

Step-by-step explanation:

b=(45+6)/3

b=51/3

b=17

she bought 17 books since the original price of evereything was 51 dollars before the discount of 6 dollars.

Answer:

A. 84

Step-by-step explanation:

Corporates usually issue bonds dollar-denominated as well as sell them to investors based outside of the U.S throughout the Eurobond market.

Thus the above solution is correct.

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Answer:

28%

Step-by-step explanation:

Answer:

25% of the questions were correct

Step-by-step explanation:

14+42=56

14/56=0.25

Answer: 1:2

24 is half of 48

The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

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The length of v to the nearest 10th of an inch is 2.0 inches.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use the Law of Sines,

Which states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle opposite the angles A, B, and C.

Now,

a = UV = u = 3.4 inches

A = ∠TUV

  = 180° - m∠U - m∠V

  = 180° - 144° - 35°

  = 1°

B = ∠UTV

   = m∠U

   = 144°

C = ∠TVU

  = m∠V

  = 35°

Using the Law of Sines,

v/sin(C) = u/sin(B)

Substituting in the values.

v/sin(35°) = 3.4/sin(144°)

Solving for v.

v = (3.4 × sin(35°)) / sin(144°)

v = 1.97 inches

Therefore,

The length of v to the nearest 10th of an inch is 2.0 inches.

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Answer:

hello your question is incomplete attached below is the complete question

answer : The Integrand converges

Step-by-step explanation:

attached below is the detailed solution to the problem

i) the integrand is not continuous on [ 0, 64 ] hence the integrand is improper

ii) determine if the integrand diverges or converges ( attached below )

The integrand is finite and it converges at 16

Answer:

We conclude that there is not a linear correlation.

Step-by-step explanation:

We are given that a sample of 6 head widths of seals (in cm) and the corresponding weights of the seals (in kg) was recorded.

Given a linear correlation coefficient of 0.948.

Let ρ = population correlation coefficient.

So, Null Hypothesis, \(H_0\) : ρ = 0     {means that there is a linear correlation}

Alternate Hypothesis, \(H_A\) : ρ \(\neq\) 0      {means that there is not a linear correlation}

The test statistics that would be used here One-sample t-test statistics for testing population correlation coefficient;

                            T.S. =  \(\frac{r \times \sqrt{n-2} }{\sqrt{1 -r^{2} } }\)  ~  \(t_n_-_2\)

where, r = sample correlation coefficient = 0.948

           n = sample of head widths of seals = 6

So, the test statistics  =  \(\frac{0.948 \times \sqrt{6-2} }{\sqrt{1 -0.948^{2} } }\)  ~ \(t_4\) 

                                     =  5.957

The value of t-test statistics is 5.957.

Now at 0.01 level of significance, the t table gives a critical value of 4.604 at 4 degrees of freedom for a two-tailed test.

Since our test statistics is more than the critical value of t as 5.957 > 4.604, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that there is not a linear correlation.

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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The formula for y in terms of x and c is given as follows:

\(y = \frac{c^5}{\sqrt{x}}\)

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

An inverse proportional relationship is modeled as follows:

y = k/x.

In this problem, we have that y is inverse proportional to the square root of x, hence the equation is given as follows:

\(y = \frac{k}{\sqrt{x}}\)

When x = c², y = c^4, hence the constant k is obtained as follows:

\(c^4 = \frac{k}{\sqrt{c^2}}\)

k/c = c^4

k = c^5.

Hence the equation is:

\(y = \frac{c^5}{\sqrt{x}}\)

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Answer:

D. \(10^{\circ}\)

Step-by-step explanation:

Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).

Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).

By the inscribed angle theorem, \(\alpha=84^{\circ}\).

Thus, \(\beta=20^{\circ}\).

By the inscribed angle theorem, \(x=10^{\circ}\).

Answer:

488

Step-by-step explanation:

You divide 28453 by 58.3053278689 and get 488.

Answer:

153.86

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

Probability of getting either heads or tails of a coin : 1/2

Probability of getting 1,2,3,4, or 6 on a dice: 5/6

Multiply those two probabilities : 1/2 * 5/6 = 5/12

You have a 5 out of 12 chances of getting heads on a coin AND any number but a 5 on a dice.

Hope this helps!

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

Answer:

The question is incomplete

Answer:

It was 1/3 before

Step-by-step explanation: