ELEPHANTS In the wild, an African elephant typically consumes 2.5 × 10² pounds of food a day. If there are approximately 4.15 × 10⁵ African elephants in the wild, how many pounds of food are consumed by African elephants in one day?

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[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]

The value of x is 4.5 rounded to the nearest tenth.

Tangent of a circle is defined as the line which passes through exactly one point on the circle.

Secant of a circle is the line which passes through two points on the circle.

Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.

Using the theorem, we can say here that,

(8 + 2) 2 = x²

x² = 10 × 2

x² = 20

x = √20

x = 4.472 ≈ 4.5

Hence the value of x is 4.5.

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A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.

A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.

The pi is located at station 103+00.

To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:

L = 2πR (D/360)Where:

L = length of the arc in feet.

R = the radius of the curve in feet.

D = the degree of curvature in degrees.

PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature

:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:

L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.

The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.

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Answer:

They're not promise

Step-by-step explanation:

I did it on the calculator

I hope this helps youuu

Have a good day <3

If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.

If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.

Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:

3x : x = 3 : 1

To solve for x, we can cross-multiply:

3x * 1 = x * 3

3x = 3x

We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:

3x = 243

x = 81

Therefore, there are 81 students at Rolling Hills Middle School who have pets.

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The probability of randomly chosen, a 50-year-old or older voter from the winning party is 45.84%

Given the table of values

From the table of values, we have the winning party to be

New Democratic

From the column of New Democratic, we have

Total = 9422

50-year-old or older voter = 4319

So, the required probability is

Probbaility = 4319/9422

Evaluate

Probbaility = 0.45839524517

This gives

Probbaility = 45.839524517%

Approximate

Probbaility = 45.84%

Hence, the probability is 45.84%

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Answer:

Data Visualization Tools

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we need to calculate the annual interest rate from the given APR.

APR = 2.25%

Daily interest rate = 2.25% / 365 = 0.00616438

Now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time in years

In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.

A = 2000(1 + 0.00616438/365)^(365*4)

A = 2000(1.00616438)^1460

A = $2,388.34 (rounded to the nearest cent)

Therefore, the answer is option D) $2,388.34.

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

A mathematical concept known as proportionality describes the relationship between two quantities that have different sizes but keep the same ratio or proportion. In other words, to preserve the same ratio, if one item changes, the other quantity must also change in proportion. For instance, if an automobile's speed and distance are proportionate, doubling the distance it travels will cause the car to go twice as quickly while retaining the same speed-to-distance ratio. Equations or ratios in mathematics are frequently used to express proportionality.

given

We can use the following formula to determine the lower and upper bounds of the 95% confidence interval for the population proportion:

Lower limit: sqrt((p * q) / n) * p - z

Upper limit: sqrt((p * q) / n) = p + z

With q = 1 - p, z is the z-score corresponding to the level of confidence, and p is the sample proportion.

Here, p = 130/520 = 0.25, q = 1 - p = 0.75, n = 520, and the z-score is 1.96 at a 95% confidence level (from the standard normal distribution).

Lower limit: 0.210 (0.25" * 0.75") - 1.96 * sqrt(0.25" * 0.75")

The maximum is equal to 0.25 + 1.96 * sqrt((0.25 * 0.75) / 520) = 0.290.

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

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Answer:

Step-by-step explanation:

A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.

A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.

However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.

A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.

Therefore, the correct answers are C, D, and E.

Figure E is a rotated and reflected version of Figure D that has been shifted to the right and up as a result of this transformation sequence.

The sequence transformation (which may be dependent on n). This is known as a linear sequence transformation. Nonlinear sequence transformations are nonlinear sequence transformations.

We can use the following transformations to map Figure D onto Figure E:

Figure D should be translated 4 units to the right and 1 unit up.

Figure D should be rotated 90 degrees clockwise around the origin.

Cross the y-axis with the resulting figure.

This transformation sequence results in Figure E, which is a rotated and reflected version of Figure D that has been shifted to the right and up.

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If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

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The value of [tex]e^{In 5}[/tex] is equal to 5 which of option B. According to the property of logs and logarithm rules the given equation is done.

The natural log, or log to the base e, is denoted by ln. ln can also be written as [tex]log_{e}[/tex].

So, we can write the given expression as:

[tex]e^{log_{e}^(5) }[/tex]

The property of logs is:

[tex]a^{log_{a}^(x) } = x[/tex]

This means that if the number an is raised to a log whose base is the same as the number a, the answer will be equal to the log's argument, which is x.

The number e and the base of log are the same in the given case. As a result, the answer to the expression will be the log argument, which is 5.

Therefore, the value of [tex]e^{log_{e}^(5) }[/tex] = [tex]e^{In 5}[/tex] = 5. Correct option is option B.

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Answer: x= 71

Step-by-step explanation:

Since each triangle has a sun of all the angles to equal 180, we can figure what is X.

The GCF (Greatest Common Factor) of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that is common to all the terms in the polynomial.

To understand this better, consider a polynomial like 6x²y³ + 9x³y². The GCF of this polynomial would be 3x²y², which is the largest factor that can divide both terms evenly.

Notice that the exponent of each variable in the GCF is the smallest exponent among the corresponding variable terms in the polynomial.

This is because any factor that is common to all terms in the polynomial must be able to divide each term without leaving a remainder. Therefore, the exponent of each variable in the GCF must be less than or equal to the exponent of that variable in every term of the polynomial.

In summary, the GCF of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that can divide all terms in the polynomial evenly, and therefore, it must have the smallest exponent of each variable among all terms in the polynomial.

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Answer:

If you add two positive numbers together you will get a positive.

Step-by-step explanation:

Answer:4x + 3x + 2x - 4 - 3

Step-by-step explanation:Hope this helps

The number of distinct sequences of letters is 8 × 26⁷.

How many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die?

We have to find the number of distinct sequences of letters that can be made. Here, the word 'die' can occur in any position of the ten-letter sequence. Therefore, we have to find the number of distinct sequences of seven letters that can be formed, which are not related to the word 'die'. The number of distinct sequences of seven letters that can be formed with no restrictions is:

26 × 26 × 26 × 26 × 26 × 26 × 26 = 26⁷

The word 'die' has three letters, and it can be placed in any of the eight positions of the seven-letter sequence (that is not related to the word 'die'). We have a total of 8 possibilities to choose where to put the word 'die'.Thus, the number of distinct sequences of letters is:

8 × 26⁷ (or) 703, 483, 260, 800.

The number of distinct sequences of letters is 8 × 26⁷.

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Answer:

There were 62 people on the train to begin with.

Step-by-step explanation:

Firstly,i I subtracted 21 with 18 so i got 3.

It means that the train got 3 more people from the start.

Then i subtracted 65 with 3.

And so i got 62.

The closest option is (A) (3,3), which is the correct solution to the system of equations.

To find the solution to the system of equations, we need to substitute the value of y in the first equation with the value given in the second equation:

-6x + y = -21 ...(1)

2x - 1/3 y = 7 ...(2)

Substituting y=7 in the first equation, we get:

-6x + 7 = -21

Simplifying the above equation:

-6x = -28

Dividing both sides by -6, we get:

x = 28/6 = 14/3

Substituting x=14/3 and y=7 in the second equation, we get:

2(14/3) - 1/3(7) = 7

Simplifying the above equation, we get:

28/3 - 7/3 = 7

21/3 = 7

Therefore, the solution to the system of equations is (14/3, 7).

Hence, the answer is not in the given options, but the closest option is (A) (3,3), which is not the correct solution to the system of equations.

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Answer:

Step-by-step explanation:

All you have to do is subtract 6 from 14. The answer is 8. If the question is something like this one, always take the remainder and subtract it from how many you had in the beginning to get the answer.

Good luck

Peyton

Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.

To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.

In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:

P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)

Using a calculator or statistical software, we can evaluate this expression to find:

P(X = 7) ≈ 0.170

This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.

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Using graphs,

The ordered pair, (6,15) represents here the cost of 6 pounds of noodles that is $15.

A structured representation of the data is all that the graph is. It assists us in comprehending the info. Data are the numerical details gathered by observation. Data is a derivative of the Latin term datum, which means "something provided."

Data is continuously gathered through observation once a research question has been formulated. After that, it is arranged, condensed, and categorised before being graphically portrayed.

Here in the question,

As we can see that the graph is a relation between the number of noodles in pounds and the cost of noodles in dollars has been given and compared.

So, as per the question,

The ordered pair that represents here the cost of 6 pounds of noodles is (6,15).

As, from the graph:

When noodles in pounds is 6, cost in dollars is 15.

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The complete question is:

the points on the graph show how much chee pays for different amounts of noodles, complete the statement about the graph

2x + y = -7

y= -7-2x

put this value in 2nd equation

3x=6+4(-7-2x)

3x=6-28-8x

11x= -22

x= -2

y= -7-2(-2)

y= -7+4

y= -3

Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.

The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.

This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.

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