Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.

The time that Nagma takes to complete five rounds is 0.4 hours or 24 minutes.

Travel time is the total time required to pass a certain length of road.

Given,

Length = 180m

Width = 120 m

Speed = 7.5 km/hr

Time of five rounds?

Steps,

The first step that must be done is to find the travel time for one round

Distance of one round = 2(length + width)

Distance of one round = 2(180 + 120)

Distance of one lap = 3 (300)

Distance of one round = 600 m = 0.6 km

Time needed to reach 5 rounds

Time = 5 (distance : speed)

Time = 5 (0.6 : 7.5)

Time = 0.4 hours = 24 minutes

So, the time needed to complete five rounds is 0.4 hours or 24 minutes.

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The cost of Japan and Switzerland tickets are 17.15 dollars and 13.15 dollars respectively.

it would cost $77.75 to buy three tickets in Japan plus 2 tickets in Switzerland. Three tickets in Switzerland plus two tickets in japan would cost $73.75.

Using system of equation,

let

x = cost of each ticket in Japan

y = cost of each ticket in Switzerland

Therefore,

3x + 2y = 77.75

2x + 3y = 73.75

Multiply equation(ii) by 1.5

3x + 2y = 77.75

3x + 4.5y = 110.625

subtract the equations

2.5y = 32.875

y = 32.875 / 2.5

y = 13.15 dollars

Hence,

3x + 2y = 77.75

3x = 77.75 - 2y

3x = 77.75 - 2(13.15)

3x = 77.75 - 26.3

x = 51.45 / 3

x = 17.15 dollars

Therefore,

cost of Japan ticket = 17.15 dollars

cost of Switzerland ticket = 13.15 dollar

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The value of θ is approximately equal to 0.92729522.

The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.

The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.

If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.

θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).

So, the value of θ is approximately equal to 0.92729522.

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The value of θ is approximately equal to 0.92729522.

The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.

The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.

If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.

θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).

Therefore, the value of θ is approximately equal to 0.92729522.

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Answer:

b. stratosphere

Step-by-step explanation:

The ozone layer, located in the stratosphere is responsible for absorbing the most UV radiation. This is because the ozone molecule (O3) is able to absorb UV radiation due to its molecular structure, specifically the presence of three oxygen atoms which allows it to efficiently absorb the UV-C radiation (the most damaging to living organisms). This protects life on Earth from harmful effects of UV radiation, such as DNA damage, skin cancer and other harmful impacts on plants and marine life.

The speed of the passenger train is 80 mph.

Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.

Therefore, we can write the equation:

400/p = 330/f

Expanding the second term and substituting "p" for "f" + 14:

400/p = 330/(p - 14)

Cross multiplying and simplifying:

400 * (p - 14) = 330 * p

Expanding both sides:

400p - 5600 = 330p

Subtracting 330p from both sides:

70p = 5600

Dividing both sides by 70:

p = 80 mph

So the speed of the passenger train is 80 mph.

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The speed of the passenger train is 80 mph.

Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.

Therefore, we can write the equation:

400/p = 330/f

Expanding the second term and substituting "p" for "f" + 14:

400/p = 330/(p - 14)

Cross multiplying and simplifying:

400 * (p - 14) = 330 * p

Expanding both sides:

400p - 5600 = 330p

Subtracting 330p from both sides:

70p = 5600

Dividing both sides by 70:

p = 80 mph

So the speed of the passenger train is 80 mph.

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The minimum sample size required will be 231.

What is Sample Size?

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.

The sample size(n) is 2558.

p = 46%

= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives

1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).

Hence, the confidence interval is given by

= [0.46 ± 0.02]

= [0.44, 0.48]

As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48

2) Margin of error = E

= 0.02

3) Null hypothesis  0.4 percent of US people have dealt with substance misuse in their families.

P = 4/10

= 0.4

Alternative hypothesis  More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.

P > 0.4

95% confidence interval is - [0.44, 0] 48]

We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)

As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.

As a result, the newspaper could make the assertion.

4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.

5) The required minimum sample size is given by:

P is the specified value of population proportion under the null hypothesis = 0.4

= (1.96/0.02)²  (0.4) (1 - 0.4)

= [tex]98^{2}[/tex] (0.4) 0.6

= 230.5

So, the minimum sample size required will be 231.

Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.

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The minimum sample size required will be 231.

What is Sample Size?

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.

The sample size(n) is 2558.

p = 46%

= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives

1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).

Hence, the confidence interval is given by

= [0.46 ± 0.02]

= [0.44, 0.48]

As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48

2) Margin of error = E

= 0.02

3) Null hypothesis 0.4 percent of US people have dealt with substance misuse in their families.

P = 4/10

= 0.4

Alternative hypothesis  More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.

P > 0.4

95% confidence interval is - [0.44, 0] 48]

We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)

As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.

As a result, the newspaper could make the assertion.

4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.

5) The required minimum sample size is given by:

P is the specified value of population proportion under the null hypothesis = 0.4

= (1.96/0.02)²  (0.4) (1 - 0.4)

=  (0.4) 0.6

= 230.5

So, the minimum sample size required will be 231.

Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.

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The given equation does not represent y as a function of x.

A relation is a function if for every unique x value, there exists only one unique y value. The equation 5x³y = 15 does not define a unique value for y for a given value of x, and therefore does not represent y as a function of x.

The equation 5x³y = 15 does not represent y as a function of x. A function must have exactly one output value for each input value, but this equation doesn't have the unique output restriction.

The equation 5x³y = 15 represents a 3-dimensional surface in the x-y-z plane, where z = 5x³y. It does not define y as a function of x, because for a given x there can be multiple values of y that satisfy the equation. To define y as a function of x, additional information, such as an equation that relates y and x in a one-to-one manner, is needed.

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The number of DVDs sold in any day is one-third the number of DVDs sold the previous day three times the number of DVDs sold the following day.

The exponential function D(t) = 729(1/3)^t models the number of DVDs sold where t is the number of days since the release date and D(t) is the number of DVDs sold.

The definition of an exponential function is given as follows:

y = ab^x.

In which:

For this problem, the parameter values are given as follows:

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No the confidence interval does not provide convincing evidence that the two population proportions are equal.

No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.

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No the confidence interval does not provide convincing evidence that the two population proportions are equal.

No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.

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The correct option is C. Length = 24 feet, width = 18 feet

To measure a rectangular room, use a tape measure, pencil and paper to record the length and width of the room. Then multiply these numbers to get the total area of the room.

The calculation is as follows:

Since 2cm = 6 feet

So,

The length is = 4(6) = 24 feet

And, the width be = 3(6) = 18 feet

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A scale drawing of Julie's living room is shown below:

A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.

If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?

A)Length = 16 feet, width = 12 feet

B)Length = 10 feet, width = 8 feet

C)Length = 32 feet, width = 24 feet

D)Length = 14 feet, width = 12 feet

The solution of the initial value problem is [tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

A differential equation is a mathematical equation that relates a function and its derivatives to some independent variables.

In this case, the differential equation is given by:

dy/dt = t² + 1, t ≥ 0

with the initial value y = 6 when t = 0.

To solve this initial value problem, we can use the method of integrating factor.

We can find the integrating factor for this differential equation by using the formula:

[tex]= > e^{\intP(t)dt,[/tex]

where P(t) = t² + 1

So,

[tex]= > e^{\int P(t)dt} = e^{t^3/3 + t}[/tex]

By the product rule, we have:

[tex]= > d/dt(e^{t^3/3 + t)y} = d/dt(e^{t^3/3 + t)(t^2 + 1)})[/tex]

We can evaluate the integral on the right side using standard integration techniques, and we get:

[tex]= > e^{t^3/3 + t}y = e^{(t^3/3 + t)(t^3/3 + t^2 + t + C)[/tex]

Finally, we can isolate y by dividing both sides of the equation by e^(t^3/3 + t):

[tex]= > y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

To find the value of C, we can use the initial value y = 6 when t = 0:

6 = Ce⁰

So, C = 6.

Therefore, the solution to the initial value problem is:

[tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

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No, it is not required to be accurate. The growth rates of the two functions can vary.

It's not necessary for log f(n) to equal log g(n). Depending on the equation's constants and the inputs to the two functions, the growth rates of the two functions may differ. For instance, log f(n) = 2 log n and log

g(n) = 3 log n,

which are not equal, if

f(n) = n2 and g(n) = n3.

In this instance, log f(n) is equal to (log n) and log g(n) to (log n3), indicating that the two functions grow at various rates. Likely not equal are log f(n) and log g(n) if

f(n) = n and g(n) = n2,

respectively. Log f(n) is defined as (log n) and log Therefore, the statement "log f(n) = (log g(n)" is not necessarily true.

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The closest point on the line 3x - y = 4 to the point A(-2, 3) is (4, 3).

The point on the line closest to point A can be found by finding the line that is perpendicular to the line 3x - y = 4 and passes through A, then finding the point of intersection between the two lines.

To find the perpendicular line, we can use the slope-point form of a line, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. The slope of a line perpendicular to the line 3x - y = 4 is the negative reciprocal of the slope of the line, which is undefined since the line 3x - y = 4 is a vertical line. Hence, the perpendicular line is a horizontal line with slope 0, and it passes through the point A(-2, 3). So, the equation of the line is y = 3.

The point of intersection of the two lines is the point closest to A. Solving the equations 3x - y = 4 and y = 3, we get the intersection point (x, y) = (4, 3).

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Utilize the following formula to convert metres to miles: m/1,609.344=mi (meters divided by 1,609.344 equals miles).

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Answer:

this can be solved using trigonometry

"He did not apply the order of operations correctly. He should have performance the subtraction before the division. The correct answer is 23, not 7."

Bob did not apply the order of operations correctly. He should have performed the subtraction (3 - 3) before the division (÷ 3). The correct order of operations is to perform any calculations inside parentheses first, then perform any exponents, then perform any multiplication or division (from left to right), and finally perform any addition or subtraction (from left to right).

Applying the correct order of operations to the expression 3m - 3 ÷ 3, we get:

Therefore, the correct answer is 23, not 7.

It is important to always apply the order of operations correctly in mathematical expressions to ensure that the correct answer is obtained. Failure to follow the correct order of operations can lead to incorrect answers and misunderstandings.

This question should be provided as:

Bob used these steps to evaluate 3m - 3 ÷ 3 for m = 8. Complete the explanation about his error.

He did not apply the order of operations correctly. He should have performance the _______ before the ______. The correct answer is _____, not 7.

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Answer:

60 miles

Step-by-step explanation:

We know

3/5 = 0.6

one-quarter of an hour = 15 minutes

So, we know

0.6 mile in 15 minutes

2 1/2 hours = 150 minutes

0.6 times 10 = 60 miles

So, the bird flies 60 miles in 2 1/2 hours.

Kevin needs the following ingredients for the recipe for 3 people 90g strawberry jelly, 6 sponge fingers, 315 ml custard, and 135g tinned fruit.

To find the amounts of each ingredient to make this recipe for three people we must carry out the following procedure:

1. We must make a rule of three to find the exact amounts of each ingredient as shown below:

According to the above, the following ingredients are needed for this recipe:

Note: This question is incomplete because there is some information missing. Here is the complete information:

120g strawberry jelly

8 sponge fingers

420ml custard

180 g tinned fruit

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The length of each piece to the nearest inch is 16 inches.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Total length of the board = 2 meters

Gillian cuts the board into 5 equal pieces.

Length of each piece of the board in meters = 2 / 5 = 0.4 meter

We know that,

1 meter = 39.37 inches

0.4 meter = 39.37 × 0.4

                = 15.748 inches

                ≈ 16 inches

Hence the length of each piece of the board is approximately 16 inches.

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The 36.5 °C when converted to Fahrenheit it is equal to 97.7 °F.

                                  = 97.7

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The new price of the car after the 4% reduction is $18,240

Percentage is simply number or ratio expressed as a fraction of 100.

Given that,

To determine the new price of the car after reduction;

New price = Initial price × ( 100% - 4% )

New price = Initial price × ( 96% )

Note that 96% is the same as 96/100

New price = $19,000 × 96/100

New price = $19,000 × 0.96

Multiply  $19,000 and 0.96

New price = $18,240

Therefore, the new price is $18,240.

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The statement that describes a key feature of function g if [tex]g(x)=e^x-7[/tex]  is Horizontal asymptote of y= -7.

A horizontal line that is not a part of a function's graph but is essential because it directs the graph's x values is known as a horizontal asymptote.

A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote.

A line that is asymptotically sloped, vertical, or both has the equation x = a, y = a, or y = ax + b

In this instance, the declaration that enumerates the primary property of the function g if g(x) = [tex]e^x[/tex] - 7 is that the horizontal asymptote of y = -7.

This can be seen from the equation given.

Therefore option (d) is correct

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option:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:D

The expression modeled by the number line: -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 is the sum of the first ten negative integers. The expression can be written as $-1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10$

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Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.

Avery can interpret 302 = 3 by understanding that 30 is the total amount of soup to be divided, and 2 represents the number of equal parts she wants to divide the soup into. This means that Avery can divide the 30 cups of soup into 3 equal containers, each containing 10 cups of soup.

Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.

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Answer:

8

Step-by-step explanation:

Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).

So 12 = 4+x, and x = 8.

The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

(x^2 + 4x + 8)(2x - 1)

now, we know,

(a+c)*b = ab+cb

so, we get,

⇒2x^3+8x^2+16x-x^2-4x-8

⇒2x^3+7x^2+12x-8

Hence, The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.

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The true equation is m∠A + m∠B = 180°

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Here, we have

Given:  the dot indicates the center of the circle.

we have to find which equation is true.

"The angle formed by a diameter at the circumference is always a right angle (that is 90 degrees).

We concluded that the true equation is m∠A + m∠B = 180°

Hence, the true equation is m∠A + m∠B = 180°

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The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4)

What is center of dilation?

A dilation's center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure.

The center of dilation is the origin, so to find the new coordinates of each vertex, we need to multiply the original coordinates by the scale factor of 2.

A(2, 2) becomes A'(2 * 2, 2 * 2) = A'(4, 4)

B(4, 4) becomes B'(4 * 2, 4 * 2) = B'(8, 8)

C(-4, 2) becomes C'(-4 * 2, 2 * 2) = C'(-8, 4)

So, The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4).

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