Statesville's population in 2010 was about 24,500, and was growing by about 1% each year. If this continues, what will Statesville's population be in 2016?

Answer:

63

Step-by-step explanation:

The elements listed above that are required for an inverse trig problem to find a missing angle include the following:

A. A right triangle.

D. The length of at least 2 sides.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Generally speaking, the length of at least two (2) sides is an element that is required for an inverse trig problem in order to find a missing angle in a right angled triangle.

In conclusion, both a right triangle and the length of at least two (2) sides must be provided in order to find a missing angle in a right angled triangle.

Read more on right triangle here: brainly.com/question/27884177

#SPJ1

The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

Learn more about equation of a circle: https://brainly.com/question/1506955

#SPJ1

The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

Learn more about weight here:

https://brainly.com/question/17490356

#SPJ1

To obtain the most accurate four-digit rounding approximation for the roots of a quadratic equation, it is important to consider the nature of the coefficients and choose the appropriate form of the quadratic formula to use.

In the given exercise, the goal is to find the most accurate approximations to the roots of two given quadratic equations using four-digit rounding arithmetic. The first equation is

\(x^2 + 62.10x + 1 = 0\)

and the second equation is

\(1.002x^2 - 11.01x + 0.01265 = 0\)

The roots of the quadratic equation are found using the quadratic formula (1.1) which states that the roots of \(ax^2 + bx +c = 0\) , when a ≠ 0, are given by

\(x1 = (-b + \sqrt {(b^2 - 4ac)}) / 2a\)

\(x2 = (-b - \sqrt {(b^2 - 4ac)}) / 2a\)

However, in some cases, when \(b^2\) is much larger than 4ac, the calculation for x1 involves the subtraction of nearly equal numbers, resulting in a poor approximation and a large relative error. To overcome this issue, an alternate form of the quadratic formula (1.2) can be used by rationalizing the numerator. This gives a more accurate approximation for x1.

The alternate form of the quadratic formula (1.3) should not be used for x2 if b is a negative number as it results in both the subtraction and division of nearly equal numbers. This would lead to a large relative error.

Learn more about quadratic equations :

https://brainly.com/question/30098550

#SPJ4

3/4 + 1/2 = 1 1/4

1 1/4 + 2 = 3 1/4

answer = 3 1/4r

Answer:

13/4r

Step-by-step explanation:

3/4r+2/1r+1/2r

3/4x1/1r+2/1x4/4r+1/2x2/2r

3/4r+8/4r+2/4r

13/4r = 3 1/4r

please mark as brainliest!!!

Answer:

2,016 pi cubic units

Step-by-step explanation:

The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers

The correlation coefficient is 0.53

The correlation coefficient (r) is calculated as:

\(r = \frac{n(\sum xy) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2}}\)

Using the given parameters, we have:

\(r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1257^2][20 * 836 - 116^2}}\)

Evaluate the exponents

\(r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1580049][20 * 836 - 13456}}\)

Evaluate the products

\(r = \frac{164980 - 145812}{\sqrt{[1976460 - 1580049][16720 - 13456}}\)

Evaluate the differences

\(r = \frac{19168}{\sqrt{[396411*3264}}\)

Evaluate the product

\(r = \frac{19168}{\sqrt{1293885504}}\)

Evaluate the root

\(r = \frac{19168}{35970.6}\)

Evaluate the quotient

\(r = 0.53\)

Hence, the correlation coefficient is 0.53

Read more about correlation coefficient at:

https://brainly.com/question/1564293

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

Learn more about concept of similarity click;

https://brainly.com/question/32217666

#SPJ1

a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

Learn more about quotients:

https://brainly.com/question/629998

#SPJ1

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640

#SPJ1

get 2 shaded x tiles, 5 clear x tiles, and 1 clear tile.

Answer:

drag one tile into the product then click check. Then drag five into the product then click check. Then drag one tile into the product and click check..

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

The formula for density is D = m/V

Therefore the units of density is

Density = grams/cm^3

Answer:

A. 7 years old

Step-by-step explanation:

6x-7=35 is the equation.

Add 7 to both sides, which gives you 6x=42.

Then both sides by 6, so 6/6=x and 42/6=7

So, x=7.

Since x is his daughter's age, x=7, so his daughter is 7.

6x-7≈35

or,6x=35+7

or,6x≈42

or,x=42÷6

x≈7

The coordinates of the rectangle in the picture include the following: B. (-8, -4), (-8, 2), (6, 2), (6, -4).

In Mathematics and Geometry, a rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles that are formed are right angles.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Therefore, we have the following coordinates;

Coordinates = (-8, -4), (-8, 2), (6, 2), (6, -4).

Read more on rectangle here: https://brainly.com/question/486045

#SPJ1

The statement true for A, C and E is the second statement r → p ∨ q.

Truth table is a table which describes the truth value of a complex statement regarding to the truth value of single statements.

Given is a truth table.

Consider r → p ∨ q, for the statements A, C and E.

For A, p is true and q is true, then p ∨ q is true. So r is true.

For C, p is true and q is false, then p ∨ q is true. So r is true.

For E, p is false and q is true, then p ∨ q is true. So r is true.

Hence the correct statement is r → p ∨ q.

Learn more about Truth Tables here :

https://brainly.com/question/29155453

#SPJ1

Answer:

Step-by-step explanation:

Yes, the ratios 4:6 and 2:3 are equivalent.

To see why, we can compare the proportions of the two ratios by dividing each term by the smaller term in each ratio.

In the ratio 4:6, if we divide both terms by 4, we get:

4/4 : 6/4 = 1 : 3/2

In the ratio 2:3, if we divide both terms by 2, we get:

2/2 : 3/2 = 1 : 3/2

Since both ratios reduce to the same proportion of 1 : 3/2, we can conclude that the ratios 4:6 and 2:3 are equivalent.

Ratios are mathematical expressions that compare two or more quantities. When two ratios are equivalent, it means that they represent the same proportion, even if the numbers in the ratios are different.

To compare the ratios 4:6 and 2:3, we divided each term in each ratio by the smallest term. This is because dividing each term by the same number will keep the proportion of the ratio the same.

For example, in the ratio 4:6, dividing both terms by 4 gave us the proportion of 1 : 3/2, which is the same as the proportion of 2:3 when divided by 2. This means that, even though the numbers in the two ratios are different, they represent the same proportion, and therefore the ratios are equivalent.

It's important to note that when comparing ratios, it's best to reduce the ratios to their simplest form so that the proportions are more easily compared.

Answer:

In the given expression, 10x + 8, the numerical coefficient is 10 and the literal coefficient is x. The number 8 is not considered as a coefficient since the value is a constant.

Answer: 10 + 8

Step-by-step explanation: If you want to find a coefficient you need to only remove the variable from the expression. For example what is the coefficient of 4x its 4. Please mark as the brainliest!

The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

Read more about Joint cost

brainly.com/question/31392604

#SPJ1

Hello!

\(\large\boxed{a = -1}\)

y = 2x³ + ax² - x + 3

Find the derivative using the power rule:

y' = 6x² + 2ax - 1

Substitute in the given slope and x value to solve for a:

3 = 6(1)² + 2(1)a - 1

3 = 6 + 2a - 1

4 = 6 + 2a

-2 = 2a

a = -1

Answer:

a = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Calculus

The definition of a derivative is the slope of the tangent line.

The derivative of a constant is equal to 0.

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

y = 2x³ + ax² - x + 3

y'(1) = 3

Step 2: Differentiate

Step 3: Solve for a

The Product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

To find the product and simplify completely, you need to perform multiplication and simplify the resulting fraction. Here, we are multiplying the following fractions and mixed numbers:1, 5/8, 2, and 3/5.The first step is to convert the mixed numbers into improper fractions.

We do that by multiplying the whole number by the denominator, and then adding the numerator.For 1 5/8, we get:$$1 \frac{5}{8} = \frac{8}{8} \times 1 + \frac{5}{8} = \frac{13}{8}$$For 2, we get:$$2 = \frac{2}{1} = 2 \times \frac{1}{1} = \frac{2}{1}$$For 3/5, we leave it as is since it's already a fraction.

Now that we have all the numbers as fractions, we can multiply them:$$\frac{13}{8} \times \frac{2}{1} \times \frac{3}{5} = \frac{13 \times 2 \times 3}{8 \times 1 \times 5} = \frac{78}{40}$$

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:$$\frac{78}{40} = \frac{2 \times 39}{2 \times 20} = \frac{39}{20}$$

Therefore, the product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

For more questions on Product .

https://brainly.com/question/30404163

#SPJ8

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

For more questions on algebraic fraction:

https://brainly.com/question/11875858

#SPJ8

Answer:

d. x = 7

Step-by-step explanation:

\(\frac{32}{8} = \frac{28}{x}\)

Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":

8 * 28 = 224

32 * x = 32x

\(32x = 224\)

Divide both sides by 32:

\(\frac{32}{32} = \frac{224}{32}\)

[x = 7]

The solution to the equation 3/2w + 5 = -7 is w = -1/8 .

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the data in the question;

3/2w + 5 = -7

Subtract 5 from both sides of the equation

3/2w + 5 - 5 = -7 - 5

3/2w = -7 - 5

Add -7 and -5

3/2w = -12

Multiply both sides of the equation by 2w

2w(3/2w) = 2w(-12)

3 = 2w(-12)

3 = -24w

-24w = 3

Divide both sides of the equation by -24

(-24w)/(-24) = 3/(-24)

w = -3/24

w = -1/8

Therefore, w = -1/8 is the solution to the equation 3/2w + 5 = -7.

Learn to solve more equations here: https://brainly.com/question/9236233

#SPJ1

Answer:

Step-by-step explanation:

x² + 3x - 70 = 0

x² + 3x = 70

x² + 3x + (3/2)² = 70 + (3/2)²

(x + 3/2)² = 70 + 9/4 = 289/4 = (17/2)²

so

x + 3/2 = ±17/2

x = ±17/2 - 3/2

x₁ = 17/2 - 3/2 = 14/2 = 7

x₂ = -17/2 - 3/2 = -20/2 = -10

x² = -10x - 30

x² + 10x = -30

x² + 10x + (10/2)² = -30 + (10/2)²

x² + 10x + 25 = -30 + 25 = -5

(x + 5)² = -5

\(x+5 = \pm\sqrt{-5}\\x + 5 = \pm i \sqrt{5}\\x = -5\pm i \sqrt{5}\\\\x_1 = -5+ i \sqrt{5}\\\\x _2= -5- i \sqrt{5}\\\)

Given the polynomial:

Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Step-by-step explanation:

Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
\(20x=1450\)
\(x= 72.5\)
If we just used the Alexanders it would of took 72 hours and 30 minutes.

Now lets look at the Jenkins family sprinkler, lets define it as Y.
\(25y=1450\)
\(y = 58\)
With only the Jenkins it would of took 58 hours.

Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
\(20x= 725\)
\(x=36.25\)

Jenkins
\(25y=725\)
\(y=29\)

Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.

Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take \(\frac{5}{4}\) hours. We know that 1 hour contains 60 minutes, which means \(\frac{1}{4}\) of a hour contains 15 minutes.

So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.

So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the

Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Answer:

x = 8

y = 1

Step-by-step explanation:

  x + y = 9

- ( x - y = 7)

-------------------

      2y = 2

        y = 2/2

        y = 1

   x + y = 9

x + ( 1 ) = 9

         x = 9 - 1  

         x = 8

Answer:

y=3x+2

Step-by-step explanation:

First find the slope or m in the line of equation y=mx+b

to find slope you need two points, plug in to y2-y1 / x2-x1

so lets use points (0,2) (1,5)

5-2 / 1-0 = 3

m=3

we have y=3x + b

now we find b by pugging in a point, let's use (0,2)

2 = 3(0) + b

b= 2

y=3x+2

please give thanks by hitting the heart button :)

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~