In 2010, the population of a city was 66,000. From 2010 to 2015, the population grew by 7%. From 2015 to 2020, it fell by 6%. How much did the population grow from 2010 to 2015, to the nearest 100 people?

Answer:

x = 2

Step-by-step explanation:

14 + 3x = 2 + 9x

Collect like terms so when positive 2 crosses the equals to sign, it becomes negative 2 and when positive 3x crosses the equals to sign, it becomes negative 3x.

14 - 2 = 9x - 3x

12 = 6x

Divide both sides by the co efficient of x which is 6 so,

12/6 = 6x/6

2 = x

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The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

Using slope intercept form,

y = mx + b

where

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

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The order of values in ascending order will be -4<-2<2<2.64<4<16 as the definition of ascending order says, "When numbers are arranged in ascending order, they are done so from smallest to largest".

When numbers are arranged in ascending order, they are done so from smallest to largest. Climbing down the stairs of numbers starting with their highest value is another way to think of descending. The slide is descended while moving down it. Ascending order, in which the numbers are arranged from lower value to higher value, is the opposite of descending order. A number can be arranged in ascending order by going from smallest to largest from left to right.

Here,

4²=16

-√4=-2

√4²=4

-2√4=-4

6-4=2

√7=2.64

-4<-2<2<2.64<4<16

According to the definition of ascending order, "When numbers are arranged in ascending order, they are done so from smallest to largest," the order of values in ascending order will be -4<-2<2<2.64<4<16.

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Graph attached

The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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Answer:

0.0378788 mph is the correct answer here

It took both Sandy and Tom 54 seconds to cover the same distance.

We can set up an equation based on their relative speed

Take the supposition that Tom needs "t" seconds to travel the distance. Sandy started jogging 12 seconds before Tom, so it will take her "t + 12" seconds longer to complete the same distance.

To determine the distance traveled by Sandy, multiply her speed (7 meters per second) by her time (t + 12) seconds. Tom's distance traveled may be determined by dividing his speed (9 meters per second) by his time (t) seconds.

Equating the distances covered by Sandy and Tom:

7(t + 12) = 9t

Expanding the equation:

7t + 84 = 9t

Subtracting 7t from both sides:

84 = 2t

Dividing both sides by 2:

t = 42

Tom traveled the distance in 42 seconds as a result. We add the 12-second lead Sandy had to determine the time it took for both Sandy and Tom to travel the same distance:

t + 12 = 42 + 12 = 54

So, it took both Sandy and Tom 54 seconds to cover the same distance.

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Zorch would need to exert the opposing force for approximately 1.15 years to slow Earth's rotation to once per 35.0 hours.

To determine the time required for Zorch to accomplish his goal, we can follow the steps in the Problem-Solving Strategy for Rotational Dynamics:

Step 1: Identify what is given and what is asked for.

Given:

Force exerted by Zorch: 3.70×10^7 N

Desired period of Earth's rotation: 35.0 hours

Asked for:

Time Zorch must push with this force

Step 2: Identify the principle(s) or equation(s) needed to solve the problem.

The principle of rotational dynamics that we can use is:

Torque (τ) = Inertia (I) × Angular Acceleration (α)

Step 3: Set up the problem.

Zorch wants to slow down Earth's rotation, which means he wants to decrease its angular velocity. To do this, he needs to exert a torque in the opposite direction of Earth's rotation. The torque required can be calculated as:

τ = I × α

Step 4: Solve the problem.

The inertia (I) of Earth can be approximated as I = 0.330 × 10^38 kg·m² (a known value).

The angular acceleration (α) can be calculated using the equation:

α = Δω / Δt

Since Zorch wants to slow Earth's rotation to once per 35.0 hours, the change in angular velocity (Δω) is given by:

Δω = 2π / (35.0 hours)

Now, we can rearrange the equation τ = I × α to solve for time (Δt):

Δt = τ / (I × α)

Substituting the given values, we get:

Δt = (3.70×10^7 N) / (0.330 × 10^38 kg·m² × (2π / (35.0 hours)))

Evaluating this expression will give us the time required for Zorch to push with the given force. The result is approximately 1.15 years.

Therefore, Zorch must exert the opposing force for approximately 1.15 years to slow Earth's rotation to once per 35.0 hours.

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Answer:

One half of 3/4 teaspoon is equal to 3/8 or 0.375 teaspoons. One method of finding the answer in the fraction form of 3/8 is to multiply the fraction 1/2 by 3/4 : )

Step-by-step explanation:

One half of 3/4 teaspoon is equal to 3/8 or 0.375 teaspoons.

Here, we have,

given that,

what is half of 3/4 teaspoon

One method of finding the answer in the fraction form of 3/8 is

to multiply the fraction 1/2 by 3/4 ,

or, we can divide 3/4 by 2

i.e. 1/2 × 3/4

as, half = 1/2

so, we get,

=> 3/ 2×4

=> 3/8

=>0.375

Hence, One half of 3/4 teaspoon is equal to 3/8 or 0.375 teaspoons.

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The estimated standard deviation of the population is approximately 0.133 (rounded to 3 decimal places).

To estimate the standard deviation of the population, we will use the formula of the standard deviation using the sample means, also known as the standard error. The formula gives the standard error (SE):

SE = (s / √n)

Where:

s is the standard deviation of the sample means

n is the sample size

In this case, we know, the mean of the sample ranges is 0.8, but we don't have the exact sample data. As a result, we are unable to calculate the standard deviation (s).

However, we can an assumption that the sample ranges are normally distributed, which gives us the idea to use the relationship between the range and the standard deviation. For normally distributed data, the range is approximately equal to 6 times the standard deviation. Mathematically, we can express this as:

Range ≈ 6s

Given that the mean of the sample ranges is 0.8, we have the following:

0.8 ≈ 6s

Now, let's solve for s:

s ≈ 0.8 / 6 ≈ 0.133

So, the estimate of the population's standard deviation is approximately 0.133 (rounded to 3 decimal places).

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Step-by-step explanation:

Set up a system of equations,

Consective numbers appear before and after so we need two number such that

\(x + 1 = y\)

or

\(x - y = - 1\)

Likewise, we also know that

\(4x + 3y = 157\)

Let multiply the top equation by 3.

We get

\(3x - 3y = - 3\)

Then we add the bottom equation to that

\(4x + 3y = 157\)

\(7x = 154\)

\(x = 22\)

Then we plug in x for the original equation,

\(22 + 1 = 23\)

So the two numbers are 22,23.

The sum of the measures of angle A and angle B is 90 degrees. To determine the value of x, we need to set up an equation based on the given information.

Angle A is given as (5x + 10) degrees, and angle B is given as 3x degrees.

According to the problem, the sum of angle A and angle B is 90 degrees. We can write this as an equation:

(5x + 10) + 3x = 90

Combining like terms, we have:

8x + 10 = 90

Subtracting 10 from both sides:

8x = 80

Dividing both sides by 8:

x = 10

Therefore, the value of x is 10.

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The standard format for electronic document submission in U.S. federal courts is PDF (Portable Document Format).

PDF, or Portable Document Format, is a widely used file format that allows for the electronic representation of documents. It is designed to be platform-independent, meaning it can be viewed and accessed on different devices and operating systems while retaining its original formatting. In the context of U.S. federal courts, PDF has become the standard format for attorneys to submit documents electronically.

The adoption of PDF as the standard format for electronic document submission in U.S. federal courts brings several advantages. PDF files are generally compact in size, making them easier to transmit and store. They also preserve the interest, fonts, and graphics of the original document, ensuring that the submitted materials are accurately represented.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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The values of x in the figures are 55 and 24

Figure 1

From the question, we have the following parameters that can be used in our computation:

The figure

Since, the lines are parallel lines

Then we have

x = 55 -- by corresponding angles

Figure 2

Here, we have

x + 180 - 156 = 2x

So, we have

2x - x = 24

Evaluate

x = 24

Hence, the values of x are 55 and 24

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Answer:

(3.6)

Step-by-step explanation:

for this the y cordinates are the same while the x points are the opposite signs

There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.

If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:

C(n + k - 1, k - 1)

where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:

C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)

There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:

C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55

Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars

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Answer:

x=1

Step-by-step explanation:

Both graphs intersect at 1

Answer:

x=1

Step-by-step explanation:

They sectioned at 1

Answer:

Distancia restante = 1,3 kilómetroslp

Step-by-step explanation:

Dados los siguientes datos;

Distancia total = 4,5 km

Distancia recorrida = 3200 metros a kilómetros = 3200/1000 = 3,2 km

Para encontrar la distancia restante para cubrir la longitud requerida;

Distancia total = distancia recorrida + distancia a la izquierda

4.5 = 3.2 + distancia a la izquierda

Distancia a la izquierda = 4.5 - 3.2 Distancia restante = 1,3 kilómetros

Answer:

He earned 200 dollars

Step-by-step explanation:

He got a 20% profit.

The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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The equation of the line is y = 7x + 6 when  the line crooses the y-axis at the point (0,6) and has a slope of 7

The line crosses the y-axis at the point (0,6)

The slope of the line is 7

The equation of a line in slope point form is

y - y' = m(x - x')

Where m stands for the slope of the line and x' y' are the coordinates of the point through which the line passes.

So, the point x',y' is 0, 6 and the slope m is 7

y - y' = m(x - x')

y - 6 = 7 (x - 0)

y - 6 = 7x

y = 7x + 6

Therefore, the equation of the line which  crosses the y-axis at the point (0,6) and has a slope of 7 is y = 7x + 6

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Answer:

4

Step-by-step explanation:

Given the data:

X : 20,25,30,20,30

Mean absolute deviation :

Σ(x - xbar) / n

n = sample size = 5

xbar = ΣX / n = (20+25+30+20+30) /5

xbar = 25

((20-25) + (25-25) + (30-25) + (20-25) + (30-25)) / 5

We take the absolute values, hence, negative signs are ignored :

(5 + 0 + 5 + 5 + 5) / 5

20 / 5

= 4

Answer:

7/5

Step-by-step explanation:

To find the slope, we can use the slope formula

m = (y2-y1)/(x2-x1)

   = ( 9-2)/(6-1)

    = 7/5

The answer is m=7/5

Explanation: for the slope, when you add it in on the graph properly you will get 7/5

Answer:

See below for proof using trigonometric identities.

Step-by-step explanation:

\(\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\tan \theta=\dfrac{\sin \theta}{\cos \theta}$\\\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}$\\\\\\$\csc \theta=\dfrac{1}{\sin \theta}$\\\\\\$\sin^2 \theta+\cos^2 \theta=1$\\\end{minipage}}\)

To prove the given equation, use trigonometric identities to rewrite the left side of the equation.

\(\begin{aligned} \dfrac{\cot x}{\csc x}-\dfrac{\csc x}{\cot x}&=\dfrac{\dfrac{\cos x}{\sin x}}{\dfrac{1}{\sin x}}-\dfrac{\dfrac{1}{\sin x}}{\dfrac{\cos x}{\sin x}}\\\\&=\dfrac{\cos x}{1}-\dfrac{1}{\cos x}\\\\&=\dfrac{\cos x}{1} \cdot \dfrac{\cos x}{\cos x}-\dfrac{1}{\cos x}\\\\&=\dfrac{\cos^2 x-1}{\cos x}\\\\&=\dfrac{\cos^2 x-(\sin^2 x + \cos^2 x)}{\cos x}\\\\&=\dfrac{-\sin^2 x}{\cos x}\\\\&=-\dfrac{\sin x }{\cos x} \cdot \dfrac{\sin x}{1}\\\\&=-\tan x \sin x\end{aligned}\)

Hence proving that:

\(\dfrac{\cot x}{\csc x}-\dfrac{\csc x}{\cot x}=-\tan x \sin x\)

The series \(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1}\) is a convergent series

From the question, we have the following parameters that can be used in our computation:

\(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1}\)

Factorize the denominator

\(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1} = \sum_{n=3}^{\infty} \frac{6}{(n - 1)(n + 1)}\)

Decompose into partial fraction

\(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1} = \sum_{n=3}^{\infty} \frac{A}{(n - 1)} + \frac{B}{(n + 1)}\)

So, we have

An + A + Bn - B = 6

This means that

A + B = 0

A - B = 6

When evaluated, we have

A = 3 and B = -3

So, we have

\(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1} = \sum_{n=3}^{\infty} \frac{3}{(n - 1)} - \frac{3}{(n + 1)}\)

Expand the series

\(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1} = [\frac{3}{2} - \frac{3}{4}] +[\frac{3}{3} - \frac{3}{5}] +[\frac{3}{4} - \frac{3}{6}] + ........ + [\frac{3}{N} - \frac{3}{N + 2}]\)

When simplified, we have

\(\sum_{n=3}^{\infty} \frac{6}{n^2 - 1} = \frac{3}{2} - [\frac{3}{N} - \frac{3}{N + 2}]\)

The above implies that the series converges

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Answer:

67

Step-by-step explanation:

Using the trigonometric ratio formula the value for hypotenuse x is obtained as option D: 17.1 units.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We know that angle is 40 °, so use the trigonometric ratio of cosine.

Let x be the length of the hypotenuse.

Then, according to the problem, the length of the base is 4 inches shorter than x, so its length is x - 4.

Using trigonometry, we can use cosine to set up the following equation -

cos(40) = (x - 4) / x

Simplifying this equation, we get -

0.766 = (x - 4) / x

0.766x = x - 4

0.766x - x = - 4

-0.234x = -4

x = -4 / 0.234

x = 17.09 ≈ 17.01

Therefore, the length of the hypotenuse is approximately 13.1 inches.

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