In 2010, the population of a city was 175,000. From 2010 to 2015, the population grew by 7.4%. From 2015 to 2020, it fell by 4.5%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?

The exact value of sec(θ) is 8√(39)/39.

Given information:

In a right triangle,

Perpendicular side = 5, Hypotenuse side = 8.

Then to find exact secθ:

We can use the definition of secant, which is the reciprocal of cosine:

sec(θ) = 1/cos(θ)

In a right triangle, the cosine of an angle is equal to the adjacent side length divided by the hypotenuse length. Therefore, we first need to find the length of the adjacent side of the angle θ.

Let's label the sides of the right triangle as follows:

the hypotenuse side is H, with a length of 8

the perpendicular side is P, with a length of 5

the base side (adjacent to the angle theta) is B

Using the Pythagorean theorem, we can find the length of the base side B:

B² + P² = H²

B² + 5² = 8²

B² + 25 = 64

B² = 64 - 25

B² = 39

B = √(39)

Now we can use the cosine function to find cos(theta):

cos(θ) = B/H

cos(θ) = √(39)/8

Finally, we can find sec(θ) by taking the reciprocal of cos(θ):

sec(θ) = 1/cos(θ)

sec(θ) = 8/√(39) x √(39)/√(39)

sec(θ) = 8√(39)/39

Therefore, the exact value of sec(θ) is 8√(39)/39. This is the simplified form of the expression and cannot be further reduced because the square root of 39 is not a perfect square.

To learn more about the Pythagoras theorem;

https://brainly.com/question/343682

#SPJ1

Answer:

No

Step-by-step explanation:

2.20 and 2.2 are the same

but 2.02 is not the same as the others

To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.

Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:

- Approximately 68% of the data lies within one standard deviation of the mean.

- Approximately 95% of the data lies within two standard deviations of the mean.

- Approximately 99.7% of the data lies within three standard deviations of the mean.

Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.

Therefore, the interval within which about 95% of the data lies is:

1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles

So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).

d = 5t + 20

your answer is there so i'll be on my way, Have a nice day!!

The profit earned if 53 mowers are sold is $1104.50.

To find the profit polynomial, we need to subtract the cost polynomial from the revenue polynomial:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = (-0.5x^2 + 91x) - (38x + 300)

P(x) = -0.5x^2 + 53x - 300

So the profit polynomial is P(x) = -0.5x^2 + 53x - 300.

To find the profit earned if 53 mowers are sold, we substitute x = 53 into the profit polynomial:

P(53) = -0.5(53)^2 + 53(53) - 300

P(53) = -0.5(2809) + 2809 - 300

P(53) = -1404.5 + 2509

P(53) = 1104.5

Therefore, the profit earned if 53 mowers are sold is $1104.50.

To know more about profit follow

https://brainly.com/question/28877938\

#SPJ1

The solution for t is t = log(28/3) / 2,  the Logarithm in base-10.

The equation -3 * 10^(2t) = -28 for t,  the exponential term and then take the logarithm of both sides. Let's go through the steps:

Step 1: Divide both sides of the equation by -3:

(10^(2t)) = -28 / -3

Step 2: Simplify the right-hand side:

(10^(2t)) = 28/3

Step 3: Take the logarithm of both sides using base-10 logarithm (log):

log(10^(2t)) = log(28/3)

Step 4: Apply the power rule of logarithms to bring down the exponent:

2t * log(10) = log(28/3)

Step 5: Since log(10) = 1, we have:

2t = log(28/3)

Step 6: Divide both sides of the equation by 2:

t = log(28/3) / 2

Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.

To know more about Logarithm .

https://brainly.com/question/31117877

#SPJ11

The length of the two tied strings on the number line would be between 96 and 97.

We first need to convert both the lengths of the strings to inches, since the knot's length is given in inches.

The first string is 3 3/4 feet long, which is equivalent to 45 inches (since 1 foot = 12 inches, and 3 3/4 feet = 45 inches).

The second string is 1 1/2 yards long, which is equivalent to 54 inches (since 1 yard = 36 inches, and 1 1/2 yards = 54 inches).

The total length of the two strings before the knot is tied is 45 inches + 54 inches = 99 inches.

Subtracting the length of the knot (2 1/2 inches) from the total length of the two strings gives us:

99 inches - 2 1/2 inches = 96 1/2 inches

Therefore, the length of the two tied strings on the number line would be between 96 and 97.

Since we know that the length is closer to 97 inches than 96 inches, we can mark the length at point 97 on the number line

To learn more about the number lines;

brainly.com/question/24644930

#SPJ1

Answer:

A. 4.29

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers divided by the total numbers present.

Sum of numbers:  Instead of having to write out 2.5 twenty-two times and 5.7 twenty-eight times, we can remember that adding 2.5 twenty-two times is the same as multiplying 2.5 and 22 while adding 5.7 twenty-eight times is the same as multiplying 5.7 and 28.  Thus, our numerator for the average is (2.5 * 22) + (5.7 * 28)

Total number of people: We know that there are 50 people in all since 22 + 28 = 50.  Thus, our denominator for the average is 50

Average:  We divide our numerator by our denominator and simplify to find our average:

Average = ((2.5 * 22 + (5.7 * 28)) / 50

Average = (55 + 159.6) / 50

Average = 214.6 / 50

Average = 4.292

Average = 4.29

Thus, the average and our answer is A. 4.29

The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

We have,

We can use the inverse square law to find the distance to the star:

Luminosity / (4π(distance)²) = Apparent brightness

Rearranging this formula to solve for the distance, we get:

distance = √(Luminosity / (4π (Apparent brightness)))

Plugging in the given values, we get:

distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))

Simplifying this expression, we get:

distance = 3.04 × 10^{20} meters

Converting this distance to kilometers, we get:

distance = 3.04 × 10^{17} kilometers

To convert this distance to light-years, we divide by the speed of light in kilometers per year:

distance = (3.04 × 10^{17}) / (9.46 × 10^{12})

Simplifying this expression, we get:

distance = 32.2 light-years

Therefore,

The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

We can actually deduce here that the major league ballpark that I identified is T-Mobile Park in Seattle, Washington.

The distance from home plate to the center field fence is 409 feet and the height of the center field fence is 8 feet.

Thus, to solve for the angle of elevation, we can use the following equation:

tan θ = (y - h) / d

Where:

θ is the angle of elevation

y is the height of the fence

h is the height of the ball

d is the distance to the fence.

tan θ = (8 - 2) / 409

tan θ = 0.602

θ =  [tex]tan^{-1}[/tex] (0.602)

θ = 0.85°

The angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground is 0.85°.

Learn more about angle of elevation on https://brainly.com/question/30738434

#SPJ1

Answer:

3x+10+5x+18=180

8x+28=180

8x= 152

x=19

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]

Answer:

1.75

Step-by-step explanation:

convert to fraction

the maximum area that can be enclosed with a budget of $6000 is 1,500,000 square meters.

Let's assume we purchase x meters of metal bars and y meters of wooden bars. The cost equation can be expressed as:

3x + 2y = 6000   (total cost equation)

We want to maximize the area, which is given by the equation:

Area = x * y

To solve this problem, we can use the method of substitution or elimination. Let's use substitution.

From the total cost equation, we can express x in terms of y:

x = (6000 - 2y) / 3

Now we can substitute this value of x into the area equation:

Area = [(6000 - 2y) / 3] * y

Simplifying further:

Area = (6000y - 2y^2) / 3

The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -2 and b = 6000, so:

y = -6000 / (2 * -2) = 1500

Substituting this value of y back into the cost equation, we can find the corresponding value of x:

x = (6000 - 2 * 1500) / 3 = 1000

Therefore, with a budget of $6000, we can purchase 1000 meters of metal bars and 1500 meters of wooden bars, resulting in the maximum area.

Area = x * y = 1000 * 1500 = 1,500,000 square meters

So, the maximum area that can be enclosed with a budget of $6000 is 1,500,000 square meters.

Learn more about area at https://brainly.com/question/25292087

#SPJ1

Answer:

Marcela used the Associative Property of Addition.

Step-by-step explanation:

The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:

For any three numbers a, b, and c, (a + b) + c = a + (b + c)

For example: (2 + 3) + 4 = 2 + (3 + 4) = 9

So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.

The solution is: the value of s is:

s = 8

Explanation:

The initial equation is:

4s - 28 = 4

So, to solve for s, we can add 28 to both sides:

4s - 28 + 28 = 4 + 28

4s = 32

Finally, we can divide both sides by 4:

4s/4 = 32/4

s = 8

So, the value of s is 8

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

complete question:

What is the value of s for the equation 4s-28=4

This question involves statistical analysis and hypothesis testing, and the provided information does not contain all the necessary information to answer the questions fully and accurately. However, I can provide some general guidance on hypothesis testing and the factors to consider when designing a study.

It is not appropriate to refer to the vaccinated group as the placebo group. A placebo group is a group that receives a treatment that is inactive or does not contain the active ingredient being tested, while the treatment group receives the active treatment. In the case of the COVID vaccine, the treatment group is the group that received the vaccine, while the control group would be the group that did not receive the vaccine. In this scenario, it is important to have a control group to compare the effectiveness of the vaccine to the effectiveness of no intervention.

Other important factors to consider when designing a study include sample size, randomization, blinding, and the choice of outcome measures. These factors help to reduce bias and ensure that the results are generalizable to the target population.

To perform a hypothesis test comparing the vaccinated group to the control group, the following conditions must typically be met: the samples are independent, the samples are randomly selected from their respective populations, and the samples are normally distributed (or the sample size is large enough, typically n > 30). Additionally, the variances of the two populations should be assumed to be equal unless there is strong evidence to the contrary.

Assuming the conditions for performing a hypothesis test are met, the null hypothesis (H0) is that there is no difference in the number of deaths from COVID between the vaccinated group and the unvaccinated group, while the alternative hypothesis (Ha) is that the vaccine is effective in reducing the number of deaths from COVID. A two-sample t-test can be used to test whether the means of the two groups are significantly different. If the p-value is less than the significance level (alpha) of 0.01, the null hypothesis can be rejected in favor of the alternative hypothesis, and it can be concluded that the vaccine is effective in reducing the number of deaths from COVID.

Once again, please note that the information provided may not be sufficient to provide an accurate analysis of this question, and further information may be necessary to perform an appropriate hypothesis test and draw meaningful conclusions.

The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,

⇒ (x + 3)² + (y - 5)² = 16

We have to given that;

In a circle,

Center = (- 3, 5)

Radius = 4

Since, The standard form of equation of circle is,

⇒ (x - h)² + (y - k)² = r²

Where, (h, k) = center

And, r is radius

Here, Center = (- 3, 5)

Radius = 4

Hence, The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,

⇒ (x - (- 3))² + (y - 5)² = 4²

⇒ (x + 3)² + (y - 5)² = 16

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

Answer:

31

Step-by-step explanation:

Answer:

The median is the middle value in a set of numbers. To find the median for the given set of numbers 31, 35, 28, 31, and 37, we first need to arrange them in numerical order: 28, 31, 31, 35, 37.

Since there are an odd number of values in this set, the median is simply the middle value which is **31**.

MARK AS BRAINLIEST, I DID EXPLANATION AND TOOK A LOT OF TIME!

The value of solution of the expression is,

⇒ - 5 (- 6w + 2u - 5)

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Expression is,

⇒ - 5 (- 6w + 2u - 5)

Now, By using distributive property we get;

⇒ - 5 (- 6w + 2u - 5)

⇒ - 5 × - 6w - 5 × 2u - 5 × - 5

⇒ 30w - 10u + 25

Thus, The value of solution of the expression is,

⇒ - 5 (- 6w + 2u - 5)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.

A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.

Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.

Learn more about complex function on https://brainly.com/question/30980540

#SPJ1

well, here is your pie...

The options provided for the domain and range of the given graph are incorrect. The correct descriptions for the domain and range are as follows:

Domain: The domain represents the set of all possible input values, or the x-values, of the graph. Since no specific information is given about the graph or its equation, the domain is not specified. In this case, the correct answer is:

Domain: Not specified

Range: The range represents the set of all possible output values, or the y-values, of the graph. Similarly, without any specific information about the graph or its equation, the range is not specified. Therefore, the correct answer is:

Range: Not specified

for such more question on domain

https://brainly.com/question/16444481

#SPJ11

The different features for the graphs of f(x) and g(x) is given as follows:

C. y-value when x = 5.

To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The numeric value for the function f(x) at x = 5 is given as follows:

f(5) = 5² = 25.

The numeric value for the function g(x) at x = 5 is given as follows:

g(5) = 3 x 5² = 75.

The options are given as follows:

A. location of the vertex

B. axis of symmetry

C. y-value when x = 5

D. direction parabola opens

A similar problem, also featuring numeric values of a function, is given at brainly.com/question/28367050

#SPJ1

Answer:

20%

Step-by-step explanation:

percent error = (estimated value - real value)/(real value) × 100%

percent error = (54 - 45)/(45) × 100%

percent error = 0.2 × 100%

percent error = 20%

The value of the expression 10 ÷ 40 using the long division method will be 0.25.

The expression is given below.

10 ÷ 40

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The division is given below by the long division method. Then

40 ) 100       ( 0.25

      - 80

         200

      - 200

            0

More about the division link is given below.

https://brainly.com/question/369266

#SPJ1

The most specific correct name for this figure is a trapezoid.

A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.

An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.

A parallelogram has opposite sides parallel. >>>  This figure is not a parallelogram.

A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.