The population of a town increased from 3200 in 2008 to 5700 in 2009. Find the absolute and relative (percent) increase.

Absolute increase:


Relative increase:
%

Give answers accurate to at least 1 decimal place.

Yes the statement of my cousin that rotations, translations, and reflections will result in the congruence of corresponding lines, line segments, and angles is true

Yes, this is true. Congruence refers to the idea that two geometric figures are identical in size and shape. Translations, rotations, and reflections are rigid motions that preserve distances and angles, meaning that corresponding lines, line segments, and angles in the figures will remain congruent after the transformation.

This is because these transformations only involve shifting, rotating, or flipping the figure, but not changing its shape or size.

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Answer: They are equal to one another.

1/5 is equal to 2/10.

First we must find a common denominator that both 2 and 10 can be divided by. 2 is a number that both are divisible by. So we must divide 2/10 by 2,leaving 1/5. This means that the number are equal to one another. So neither are greater than the other.

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Answer:

1

Step-by-step explanation:

There are 15 men in total;

If each committee is to have 8 men (and assuming one man cannot be in multiple committees), we can simply do the following:

15/8 = 1.875

This means only 1 committee can be made containing exactly 8 men.

You can also think of it like this:
If 8 men make up 1 committee, then this leaves 7 (15 - 8) men left;

Since you need 8 men, there is not enough for a second committee (once again, assuming that one man cannot be in more than one committee).

The ratio of malts to shakes is 3:7 if 14 shakes are sold for every 6 malts.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.

Let the number of shakes be S and the number of malts be M.

Given: Number of shakes sold = 14 shakes

Number of malts sold = 6 malts

To find the ratio of malts to shakes:

The ratio of malts to shakes exists given by the expression:

M/S = Number of malts sold/Number of shakes sold

Substituting the given parameters into the formula, we have;

M/S = 6/14

M/S = 3/7

Therefore, the ratio of malts to shakes is 3 : 7.

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The coordinates of the vertices of the image include the following: (-1, 3), (-1, -1), (5, -1), and (7, 3).

In this exercise, we would have to dilate (enlarge) the coordinates of the pre-image by using a scale factor of 2 centered at the point (1, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate 1, we have;

Coordinate 1 = (2, 4)  →  (2(2 - 1) + 1, 2(4 - 5) + 5)

Coordinate 1 = (2, 4)  →  (2(-1) + 1, 2(-1) + 5)

Coordinate 1' = (-1, 3).

For coordinate 2, we have;

Coordinate 2 = (2, 2)  →  (2(2 - 1) + 1, 2(2 - 5) + 5)

Coordinate 2 = (2, 2)  →  (2(-1) + 1, 2(-3) + 5)

Coordinate 2' = (-1, -1).

For coordinate 3, we have;

Coordinate 3 = (3, 2)  →  (2(3 - 1) + 1, 2(2 - 5) + 5)

Coordinate 3 = (3, 2)  →  (2(2) + 1, 2(-3) + 5)

Coordinate 3' = (5, -1).

For coordinate 4, we have;

Coordinate 1 = (4, 4)  →  (2(4 - 1) + 1, 2(4 - 5) + 5)

Coordinate 1 = (4, 4)  →  (2(3) + 1, 2(-1) + 5)

Coordinate 1' = (7, 3).

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Anita can type between 60 and 75 words per minute and it took her 43 minutes to type a 12 page report.

The formula to calculate the total number of words in a report is: (words per minute * minutes) = total words. In this case, anita can type between 60 and 75 words per minute, so to solve for the total words in the 12 page report, we need to average her words per minute. This would be (60 + 75) / 2 = 67.5 words per minute. So, now the equation looks like this: (67.5 words per minute * 43 minutes) = 2,888.5 total words in the report.

To break the equation down further, we can say that for every minute Anita types, she is typing 67.5 words. This means that for every minute she types, she is typing 1.125 pages. In other words, for every 8 minutes she types, she is typing 9 pages. Therefore, to type 12 pages in 43 minutes, Anita is typing approximately 9.2 pages per 8 minutes.

To summarize, Anita can type between 60 and 75 words per minute and it took her 43 minutes to type a 12 page report. Using the formula (words per minute * minutes) = total words, we can calculate that the total number of words in the report is 2,888.

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4a - 8 + 4a - 8 + 4a - 8 = 180°

The sum of interior angle of triangle is 180°

12a - 24 = 180°

12a = 204

[tex]a = \frac{204}{12} \\ [/tex]

a = 17°

1) to obtain the value of x, we must equate AC and BD based on the diagonal properties of a rectangle. Note that a rectangle's diagonal divides it into two congruent right triangles.

A rectangle's diagonals are all the same length. A square is a quadrilateral whose diagonals bisect each other, intersect at right angles, and are congruent.

Thus,

Since BD = AC

2x + 19 = 5x - 2

To solve the equation 2x + 19 = 5x - 2, we need to isolate x on one side of the equation.

First, we can simplify both sides by combining like terms. Subtracting 2x from both sides gives:

19 = 3x - 2

Next, we can isolate x by adding 2 to both sides:

21 = 3x

Finally, we can solve for x by dividing both sides by 3:

x = 7

Therefore, the solution to the equation 2x + 19 = 5x - 2 is x = 7

b) The Properties of Parallel Lines Intersected by a Transverse Postulate states that when a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are supplementary. This means that

∠LMN + ∠MNK = 180°

Thus,

115 +  ∠MNK = 180

∠MNK = 180 - 115

∠MNK = 65°

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Answer:

It's 3

Step-by-step explanation:

Answer:

323/7 or about 46.143

Step-by-step explanation:

We can infer that the measure of B + C is 90 degrees, so 6x + 1 + 8x - 11 must be equal to 90.

6x + 1 + 8x - 11 = 90
14x - 10 = 90

14x = 100

x = 100/14

x = 50/7

Solve for the measure of C by substituting x with 50/7.

50/7 * 8 = 400/7

400/7 - 11 = 323/7

the measure of C is 323/7

Answer:

$12,581.53

Step-by-step explanation:

The balance of an account after having interest compounded annually can be represented using the equation:

[tex]A = P(1 + r)^{t}[/tex]

where [tex]A[/tex] is the final balance, [tex]P[/tex] is the principal (starting amount), [tex]r[/tex] is the rate of interest, and [tex]t[/tex] is the number of years that interest is applied.

We can plug the given values into this equation and solve for [tex]A[/tex].

[tex]P = \$10,000[/tex]     [tex]r = 4.7\%[/tex]     [tex]t = 5[/tex]

[tex]A = 10,000(1 + 4.7\%)^{5}[/tex]

[tex]A \approx \$12,581.53[/tex]

So, Sally's balance in an account that had $10,000 before being compounded for 5 years at an interest rate of 4.7% is $12,581.53.

Answer:

see explanation

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

consider the slope of the middle dotted line

with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line

m = [tex]\frac{-2-(-4)}{3-(-3)}[/tex] = [tex]\frac{-2+4}{3+3}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

consider the slope of the line of reflection ( the solid line )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, 3) ← 2 points on the line

m = [tex]\frac{3-0}{-2-(-1)}[/tex] = [tex]\frac{3}{-2+1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3

note the product of the slopes = [tex]\frac{1}{3}[/tex] × - 3 = - 1

indicating the lines are perpendicular to each other

Answer: 1200 dollars

Step-by-step explanation:For this question we use the formula:

principal amount x interest rate/100 x time

4000 x 6/100 x 5

4000 x 0.06 x 5

1200

Answer:

$5,387.42

Step-by-step explanation:

Use the formula:

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\\[/tex]

where A = amount accrued (principal + interest)
P = initial deposit

r = annual interest rate as a decimal

n = number of times compounded annually

t = number of years

Given
P = 4000
r = 6/100 = 0.06
n = 4 times a year
t = 5 years

[tex]A = 4000\left( 1 + \dfrac{0.06}{4}\right)^{4\cdot 5}\\\\A = 4000 ( 1+ 0.015)^{20}\\\\A = 4000 (1.015)^{20}\\\\A = \$5,387.42[/tex]

m and n are the two numbers that form the fraction which is the probability of a randomly chosen positive divisor of [tex]10^99[/tex] being an integral multiple of [tex]10^88[/tex].

Let the probability of a randomly chosen positive divisor of [tex]10^99[/tex]being an integral multiple of 10^88 be represented as m/n.

Since [tex]10^99[/tex]is a multiple of [tex]10^88[/tex], its positive divisors will also be multiples of [tex]10^88[/tex].

Therefore, the probability that a randomly chosen divisor of [tex]10^99[/tex]is an integral multiple of [tex]10^88[/tex] will be 1, i.e., m/n = 1.

Therefore, m+n = 1+1 = 2

Hence, the value of (m+n) is 2.

m and n are two numbers that form a fraction in lowest terms, which is the probability that a randomly chosen positive divisor of [tex]10^99[/tex] is an integral multiple of [tex]10^88[/tex]. To find the value of (m+n), we need to first determine the value of m and n. To do this, we must first calculate the total number of positive divisors of [tex]10^99[/tex]that are integral multiples of [tex]10^88[/tex]. We can then divide this number by the total number of positive divisors of [tex]10^99[/tex] to get the fraction. The numerator of this fraction is m and the denominator is n. The sum of m and n is the answer to the question. This is because the fraction gives us the probability that a randomly chosen positive divisor of [tex]10^99[/tex] is an integral multiple of [tex]10^88[/tex], and the sum of m and n is the total number of positive divisors of[tex]10^99[/tex], which is the denominator of the fraction. Therefore, the value of (m+n) is the sum of the numerator and denominator of the fraction.

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[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+2}=y ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (4)^2-4(2)(2)\implies \text{\LARGE 0}\qquad \stackrel{\textit{two real positive solutions}}{\textit{two x-intercepts}}[/tex]

Answer:

x = 8

Step-by-step explanation:

To solve the equation x(x - 2) = 48 for x, we can first expand the left side:

x^2 - 2x = 48

Next, we'll add 2x to both sides to isolate x^2:

x^2 = 48 + 2x

Then, we'll subtract 2x from both sides:

x^2 - 2x = 48

Now we have a quadratic equation that we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -2, and c = 48. Plugging these values into the formula:

x = (-(-2) ± √((-2)^2 - 4(1)(48))) / 2(1)

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

So the two solutions are x = (2 + 14) / 2 = 8 and x = (2 - 14) / 2 = -6.

Keep in mind that x cannot be negative in this context as it represents a measurement. Therefore, x = 8 is the only solution that has a meaningful value in this context.

Step-by-step explanation:

x(x-2)=48

Remove the parentheses

x²-2x=48

Move the constant to the left

x²- 2x - 48=0

Rewrite the expression

x² + 6x - 8x - 48 = 0

Factor the expressions

x(x+6) - 8(x+6) = 0

Separate into possible cases

(x+6) (x-8)=0

x + 6 = 0

x - 8 = 0

x = - 6 or x = 8

Answer:

Step-by-step explanation:

The entry "EQUIPMENT $12,000" is listed as a debit in the T-account, which means it is an increase in assets. Therefore, the correct answer is (b) increase in assets.

The value of the unknown variable in the equation is -16

Linear equations are equations that has a leading degree of 1.

Given the linear equation below

-2 = 2 + v/4

We need to calculate for the unknown variable 'v'

Subtract 2 from both sides

-2-2 = v/4

-4 = v/4

Swap

v/4 = -4

Multiply both sides by 4

v = -4 8 4

v = -16

Hence the value of the unknown variable from the equation is -16.

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Answer:

Step-by-step explanation:

Part A:

x = # of days

R:  1 hr + 3/4 hr/day(x)

J:  4 hr + 1/2 hr/day(x)

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

3/4x - 2/4x = 3

1/4x = 3

x = 12 days

After 12 days of practicing (not including the first Saturday), they each will have practiced 10 hours

Part B:

Saturday plus 12 more days →

Saturday 1-Sun 2- Mon 3-Tues 4-Wed 5-Thurs 6-Fri 7-Sat 8-Sun 9-Mon 10-Tues 11-Wed 12-Thursday

They both will have practiced 10 hours on the second Thursday after they started on Saturday

The simplified form of the expression (mp)⁶ is equal to m⁶×p⁶.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

The given expression is (mp)⁶.

We know, 2²×2² = 2⁴ but 2²×3² = (2×3)² = 6².

Therefore, (mp)⁶ = m⁶×p⁶.

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For this data, the median is the best indicator of central tendency.

The correct option is B.

A summary measure called a measure of central tendency, also known as a measure of central or a measure of central placement, aims to summaries the entirety of a set of data using a single number that corresponds to the middle or central of its distribution.

The mean, median, mode, and the midpoint are the four indicators of central tendency. The arithmetic mean of the maximum and minimum values in a data set is used here to define the midpoint or mid-extreme of a set of statistical data values.

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I understand that the question you are looking for is:

A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students. However, one of the participants fails to solve the problems so the researcher has an undetermined score. What is the best measure of central tendency for these data?

a) the mean

b) the median*

c) the mode

d) central tendency cannot be determined for these data

Answer: 1,638

Step-by-step explanation:

Answer:

1638

                 koejdoejdojeeddeddd                              

Part C: The ordered pair (0, 150) represents the initial value in the table. The initial value represents the altitude of the airplane when it started descending, i.e., the altitude of the airplane before it began its descent.

Part D: The rate of change in this equation is -5, which is the coefficient of x. The rate of change represents the decrease in altitude, in feet, per minute as the airplane descends for a landing. In other words, the altitude decreases by 5 feet for every minute that the airplane descends.

Answer:

The correct answer is C. $575. The business bought equipment with $150 cash and put $425 on credit, so the total value of the asset is $575 ($150 + $425).

Answer:

see below

Step-by-step explanation:

3540/3820 = 93%

so 7% decline

if linearly = every year decline 7%

so back in 1990, 3 years ago, the population was

p° = 3820/(1-7%)^3 =3820/.8=4749

so from 1990

p = 4749 * (1-7%)^t

2009 is 16 years from 1993

so p = 3820 * (1-7%)^16 =1196

Answer:

  A)  P(t) = 3820 -70t

  B)  2700

Step-by-step explanation:

You want a linear equation for the moose population that changed from 3820 in 1993 to 3540 in 1997, and you want the predicted population in 2009.

The slope of the linear function can be found from ...

  m = (p2 -p1)/(t2 -t1)

If we let t represent years after 1993, then this is ...

  m = (3540 -3820)/(4 -0) = -280/4 = -70

P(t) = 3820 -70t . . . . . . . . population is 3820 when t=0, 70 less each year

2009 is 16 years after 1993, so we want P(16):

  P(16) = 3820 -70·16 = 3820 -1120

  P(16) = 2700

The population is predicted to be 2700 in 2009.

On each roll of a 6-sided die, we have 6 possible outcomes.

Then if we roll it twice, we will have 36 outcomes.

The outcomes where the sum is 4 are:

roll 1     roll 2    sum

1             3           4

3            1            4

2           2           4

Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:

P = 3/36

P = 1/12

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a) The function is increasing on the following interval: (3, ∞).

b) The function is not decreasing on any interval of it's domain.

c) The function is not constant on any interval of it's domain.

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Answer:

2

Step-by-step explanation:

To divide 1 7/11 by 2 1/2, you first have to convert both numbers to have a common denominator. The smallest common denominator between 11 and 2 is 22. So, you convert 1 7/11 to be 2 14/22, and convert 2 1/2 to be 11/22. Then, you can divide 2 14/22 by 11/22 which gives 2.