A town uses positive numbers to track increases in population and negative numbers to track decreases in population. The population has decreased by 300300300 residents over the past 555 years. The same number of residents left each year. What was the change in the town's population each year?

Final answer:

The dimensions of the price tag are 9 cm by 4 cm, which are found by solving two equations derived from the given area and perimeter.

Explanation:

The student is asking for the dimensions of a rectangular price tag that has an area of 36 square centimeters and a perimeter of 26 centimeters. To solve this, we need to use two formulas: one for area (A = length × width) and one for perimeter (P = 2 × (length + width)).

First, let's denote the length of the rectangle by l and the width by w. The given area, 36 cm2, implies that l × w = 36.

Second, we know the perimeter is 26 cm, which gives us the equation 2 × (l + w) = 26. Dividing both sides by 2, we get l + w = 13.

This system of equations can be solved using substitution or elimination. If we rearrange the perimeter equation to express one variable in terms of the other (for instance, w = 13 - l), we can then substitute this expression into the area equation. Solving for l and w afterwards will give us the required dimensions.

Through solving, we find that the dimensions of the rectangle are 9 cm by 4 cm, since 9 × 4 = 36 and 2(9 + 4) = 26.

2 time legal assistant = 900,000 x 2 = 1,800,000

school teacher = 1,850,000

Difference = 1,850,000 - 1,800,000 = $50,000

Master degree for 26 weeks = 1326 x 26 = 34,476

Associates degree for 42 weeks: 792 x 42 = 33,264

Difference = 34,476 - 33,264 = $1,212

For 20 years she earned: $900,000

Twice that would be $1,800,000

So for 30 years the schoolteacher earns the same amount.

Answer:

The difference between the school teacher and the legal assistant is $50,000. The school teacher earns about twice as much in thirty years. The next answer is $1,212.  

Step-by-step explanation:

The legal assistant makes $1,800,000 in 40 year. The school teacher in 30 years makes 1,850,000. 1,850,000 - 1,800,000= $50,000.

A person with the masters degree mages $34,476 in 26 weeks.The person with the Associates degree make $33,264 in 42 weeks.  

Answer:

[tex]V=36 \pi h\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder (sculpture) is equal to

[tex]V=\pi r^{2}H[/tex]

In this problem we have

[tex]r=12/2=6\ ft[/tex] ----> the radius is half the diameter

[tex]H=h\ ft[/tex]

substitute the values

[tex]V=\pi (6^{2})(h)=36 \pi h\ ft^{3}[/tex]

Answer:

36πh cubic feet

Step-by-step explanation:

To find the volume of a cylinder  with a diameter of 12 feet and a height of h feet, we must know the formula for finding the volume of  a cylinder.

The volume V of a cylinder with a radius r and a height h is given as

V = πR^2h

where π = 22/7

Given that the radius of the given cylinder is 12 feet, the radius r

= 12/2 feet

= 6 feet

The volume v

= π * 6^2 * h

= 36πh cubic feet

Answer:

0.731 < p < 0.775

Step-by-step explanation:

We have a sample proportion of 753/1000 = 0.753

We need to construct a 90% confidence interval for the population proportion.  Since n > 30, we use the corresponding z-value of 1.645.  

See attached photo for the formulas and construction of the confidence interval.

The 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life is 0.749 to 0.757.

To find the 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life, we can use the formula for the confidence interval of a proportion. The formula is: CI = p ± Z * sqrt((p * (1-p))/n), where p is the sample proportion, Z is the z-score corresponding to the desired confidence level, and n is the sample size.

First, we need to calculate the sample proportion: p = 753/1000 = 0.753.

Next, we need to find the z-score for a 90% confidence level. Looking up the z-score in the standard normal distribution table, we find that the z-score for a 90% confidence level is approximately 1.645.

Now we can plug in the values into the formula: CI = 0.753 ± 1.645 * sqrt((0.753 * (1-0.753))/1000).

Calculating the expression inside the square root gives us approximately 0.0027. Plugging this value into the formula gives us the 90% confidence interval for the proportion: CI = 0.753 ± 1.645 * 0.0027.

Calculating this expression gives us the lower and upper bounds of the confidence interval: CI = 0.753 ± 0.0044.

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Answer:

The length of the arc is [tex]27\pi \ cm[/tex]

Step-by-step explanation:

step 1

Find the circumference

we know that

The length of a complete circle is equal to the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=18\ cm[/tex]

substitute

[tex]C=2\pi (18)[/tex]

[tex]C=36\pi\ cm[/tex]

step 2

we know that

A central angle of  [tex]2\pi[/tex] radians subtends the circumference of [tex]36\pi\ cm[/tex]

so

by proportion

Find the length of the arc by a central angle of [tex]\frac{3\pi }{2}[/tex] radians

[tex]\frac{36\pi }{2\pi}\frac{cm}{radians}=\frac{x}{(3\pi/2)}\frac{cm}{radians} \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm[/tex]

Answer: [tex]x=-\frac{3}{5}[/tex]

Step-by-step explanation:

By the negative exponent rule, you have that:

[tex](\frac{1}{a})^n=a^{-n}[/tex]

By the exponents properties, you know that:

[tex](m^n)^l=m^{(nl)}[/tex]

You can rewrite 16 and 9 as following:

16=4²

9=3²

Therefore, you can rewrite the left side of the equation has following:

[tex](\frac{4^2}{3^2})^{(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3^2}{4^2})^{-(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3}{4})^{-2(2x+5)}=(\frac{3}{4})^{(x-7)}[/tex]

 As the base are equal, then:

[tex]-2(2x+5)=x-7[/tex]

Solve for x:

[tex]-2(2x+5)=x-7\\-4x-10=x-7\\-4x-x=-7+10\\-5x=3\\x=-\frac{3}{5}[/tex]

Answer:

4.6 Or 4.60

Step-by-step explanation:

Like the other person said, 4.56. The question says "round to the nearest tenth" so 4.56 rounds to 4.60

Hope it helps~

To determine how many kilometers east Santos walked, we can use the Pythagorean theorem to find the distance traveled for each leg of the journey.

To determine how many kilometers east Santos walked, we need to use the Pythagorean theorem to find the distance traveled for each leg of the journey. Since he ends up 5 kilometers away from his starting position, we can form a right triangle with the hypotenuse representing the total distance walked.

Let's assume Santos walked x kilometers east. The other leg of the triangle represents the 2 kilometers south he walked. Using the Pythagorean theorem, we have x2 + 22 = 52.

This simplifies to x2 + 4 = 25. Subtracting 4 from both sides gives us x2 = 21. Taking the square root of both sides, we find that x ≈ 4.58. Therefore, Santos walked approximately 4.58 kilometers east.

Answer:

D) 8

Step-by-step explanation:

Given function for height =  f(x) = 80(0.5)^x

It shows that the height of ball after any bounce can be calculated by putting bounce number in place of x in this equation.

so, height after first bounce f(1) is calculated by placing 1 in place of x

f(1) = 80(0.5)^1

f(1) = 80(0.5)

f(1) = 40

Similarly, the height after 4th bounce f(4)

f(4) = 80(0.5)^4

f(4) = 80(0.0625)

f(4) = 5  

Therefore, the height of 1st bounce is 40/5 = 8 times higher than the fourth bounce. So, option D is correct.

The first bounce is 8 times higher than the fourth bounce. Option D (8) is correct.

The height of the bouncing ball is given by the function f(x) = 80(0.5)^x, where x represents the number of bounces. To find how many times higher the first bounce is than the fourth bounce, we'll calculate the heights for f(1) and f(4) and then compare them.

Therefore, the first bounce is 8 times higher than the fourth bounce, corresponding to option D (8).

Answer:

B.

Step-by-step explanation:

Because the graph shown is not constant, if you look at when it hits a whole unit. It is increasing because it is moving right.

The true statement is:

B.  

The function indicates that the number of members is increasing at a rate that is not constant.

We could write the data points as is given on the graph as follows:

  x       y

  0      40

  1       50

  2      60

  3      80

  4      100

  5      120

  6      150

  7      190

  8      240

  9      300

  10     370

Hence, the rate of change from x=0 to x=1 is:

[tex]Rate=\dfrac{50-40}{1-0}\\\\\\Rate=\dfrac{10}{1}\\\\\\Rate=10[/tex]

Rate of change from x=3 to x=5 is:

[tex]Rate=\dfrac{120-80}{5-3}\\\\\\Rate=\dfrac{40}{2}\\\\\\Rate=20[/tex]

Hence, the rate is not constant.

Also we could see that with the increasing value of x the y-value also increases.

                  Hence, option: B is the correct answer.

The sides could be 10.2 inches or 15.7 inches.

See the attached picture for the equations:

The number [tex] \pi [/tex] is defined as the ratio between the circumference and the diameter of a circle. In other words, for every circle, we have

[tex]\pi=\dfrac{C}{d}=\dfrac{C}{2r}[/tex]

Since the diameter is twice the radius.

Solving for the circumference, we have

[tex]C=2\pi r[/tex]

So, in your case, the answer is

[tex]C=16\pi[/tex]

Answer:

50.24

Step-by-step explanation:

Answer:4.375 Maybe?

Step-by-step explanation:

Answer:

(u)^{2}+7(u)-8=0

Step-by-step explanation:

Answer:

The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0  

Step-by-step explanation:

Here given (3x + 2)² + 7(3x + 2) – 8 = 0

Substitute 3x + 2 as y

Solving

          y² + 7y – 8 = 0  

The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0  

The possible coordinates for point B that are 10 units away from point A at (2,-3) could be (12, -3), (2, 7), (-8, -3), or (2, -13), moving directly horizontal or vertical.

If point A is located at (2,-3), and there are 10 points between A and B, we're likely looking at points equidistant from A, forming a sort of 'circle' with A at the centre. However, in a Cartesian plane, if the distance between two points is equal to 10 units, there are various possibilities depending on the orientation of the line connecting the two points.

For a point B to be 10 units away from point A at (2, -3), it can move horizontally to the right or left, or vertically up or down. Thus, the possible coordinates for point B would change by 10 units either in the x-coordinate (horizontally) or the y-coordinate (vertically).

Possible Coordinates for Point B

Horizontally to the right: (2+10, -3) = (12, -3)

Vertically up: (2, -3+10) = (2, 7)

Horizontally to the left: (2-10, -3) = (-8, -3)

Vertically down: (2, -3-10) = (2, -13)

Other options like (12, -6), (2, -7), (12, 3), or (-8, 3) do not adhere to being 10 units away from point A directly horizontally or vertically.

The complete question is:

If point A is located at (2,-3) , and there are 10 points between A and B, what * 1 could be the possible coordinates for point B? Choose all that apply. (12,-3) (2,7) (12,-6) (-8,-3) (2,-7) (-8,3) (2,-13) (12,3)

Answer:

[tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]

Step-by-step explanation:

Given in the question an expression

[tex]log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z[/tex]

To Condense this log into a single log we will use logarithm rules

logb(x^y) = y ∙ logb(x)

[tex]\frac{1}3}log_{3} y = log_{3}y^\frac{1}{3}[/tex]

[tex]5log_{3} z = log_{3} z^5[/tex]

logb(x ∙ y) = logb(x) + logb(y)

[tex]log_{3} x + log_{3}y^\frac{1}{3} = log_{3}(x . y^\frac{1}{3} )[/tex]

[tex]logb(x / y) = logb(x) - logb(y)\\log_{3}(x . y^\frac{1}{3} )- log_{3} z^5[/tex]

= [tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]

Answer:

B) 1.

Step-by-step explanation:

x^2 - 8x + 7 = 0

(x - 1)(x - 7) = 0

x= 1, 7.

Answer:

x = 1

Step-by-step explanation:

Please express exponentiation using the symbol  " ^ "  :  x^2 - 8x + 7 = 0

Let's solve this equations using "completing the square:"

x^2 - 8x + 7 = 0

1) Identify the coefficient of the x term.  Here it's -8.

2) take half of that and square it:  we get (-4)² = 16

3) insert " +16 - 16 " between the 8x and the 7:

        x^2 - 8x +  16 - 16  +7 = 0

4)  Rewrite this perfect square:

          (x - 4)² - 16 + 7 = 0  ->   (x - 4)^2 = 9

5)  Solve for (x -4) by taking the square root of both sides:

           x - 4 ± sqrt(9)    ->  x - 4 ± 3

6)  Solve for x:  x = 4  ± 3, or x = 7 and x = 1.  

7)  Take the lesser root of 7 and 1.  That would be x = 1.  Answer B is correct.

Answer:

The answer is

D.16

Step-by-step explanation:

Check the picture below.

notice, we use the 30-60-90 rule to get the length of RT, and then the 45-45-90 rule to get "x".

Answer:

Step-by-step explanation:

Remark

x is going to be the same thing as the hypotenuse of ΔRST.  Find that and you have x.

Givens

<STR = 60°

RT = 2√3

Solution

Sin(60°) = opposite / hypotenuse

Sin(60°) = √3 / 2

Sin (60°)= 2 √3 / hypotenuse

hypotenuse = 2√3 // sin(60°)

hypoteneuse = 2√3 /√3/2

[tex]\text{hypotenuse = }\dfrac{2\sqrt{3}}{\dfrac{\sqrt{3} }{2}} = 2*2[/tex]

The √3's cancel. The answer is 4

========================

ΔRTQ is a right angle isosceles triangle

∴RT = RQ

X = 4

Answer:

  45° or π/4 radians

Step-by-step explanation:

You want the angle whose tangent is 1.

Your calculator can evaluate the inverse tangent function for you.

  arctan(1) = 45° = π/4 radians

Answer:

4 + 12 + 36 + ...

Step-by-step explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]

When we add the terms of a geometric sequence we get a geometric series.

4+12+36+ ... is a geometric series, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]

4 + 12 + 20 + ... is not a geometric series because it has no common ratio

[tex]\frac{20}{12}\ne \frac{12}{4}[/tex]

The second choice is correct

Answer: 100%

Step-by-step explanation:

We are given a Box- plot, in which the minimum value is described by the left whisker is 3 and the maximum value is described by the right whisker is 24.

Since the range of all data values in a data is given from minimum value to the maximum value.

⇒ The percentage of the data values falls between the values of 3 and 24 in the data set shown = 100%

Answer:

A) μ = 590.45 mm; B) σ² = 0.053 mm

Step-by-step explanation:

To find the mean, we add together all of the values and divide by the number of data values:

590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6

There are 8 data values; this gives us

4723.6/8 = 590.45

To find the variance, we subtract each of the data values from the mean.  We then square this difference, and find the mean of the squares:

590.1-590.45 = -0.35; (-0.35)² = 0.1225

590.2-590.45 = -0.25; (-0.25)² = 0.0625

590.3-590.45 = -0.15; (-0.15)² = 0.0225

590.4-590.45 = -0.05; (-0.05)² = 0.0025

590.5-590.45 = 0.05; (0.05)² = 0.0025

590.6-590.45 = 0.15; (0.15)² = 0.0225

590.7-590.45 = 0.25; (0.25)² = 0.0625

590.8-590.45 = 0.35; (0.35)² = 0.1225

(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8

= 0.42/8 = 0.0525 ≈ 0.053

(a) The mean of the glass parts rounded to nearest tenths of millimeters

= 590.45 and (b) Variance in tenths of millimeters is = 0.053 mm.

In a given set of data one which repeats most frequently is called the mode of the given data set.

To obtain the mean we add together all of the values and divide by the number of data values.

590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6

There are 8 data values; this gives us

4723.6/8 = 590.45

To find the variance, we subtract each of the data values from the mean and we square this difference to find the mean of the squares.

590.1-590.45 = -0.35; (-0.35)² = 0.1225

590.2-590.45 = -0.25; (-0.25)² = 0.0625

590.3-590.45 = -0.15; (-0.15)² = 0.0225

590.4-590.45 = -0.05; (-0.05)² = 0.0025

590.5-590.45 = 0.05; (0.05)² = 0.0025

590.6-590.45 = 0.15; (0.15)² = 0.0225

590.7-590.45 = 0.25; (0.25)² = 0.0625

590.8-590.45 = 0.35; (0.35)² = 0.1225

(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8

= 0.42/8 = 0.0525 and rounded to tenths of millimeters is 0.053

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Answer:

13

Step-by-step explanation:

18-5 = 13

X-5=18

Add 5 to both sides

X=23

Answer: $33.80

Step-by-step explanation: If Hector’s account was overdrawn by $22.80 and then he deposited $56.60 his balance would be $33.80

The formula to solve this is -22.80 + 56.60 = 33.80

Answer:

$33.80

Step-by-step explanation:

i did it on my test got it right

[tex] \frac{55}{11} - \frac{13}{11} = \frac{42}{11} \: or \:3 \frac{9}{11} [/tex]

Answer:

38°

Step-by-step explanation:

The triangle solver app on your calculator, phone, or tablet can solve this for you readily. There are on-line triangle solvers, too.

___

For solution "by hand", the Law of Cosines is useful. It tells you ...

a^2 = b^2 + c^2 -2ab·cos(A)

Then the angle A can be found as ...

cos(A) = (b^2 +c^2 -a^2)/(2ab) = (3^2 +7^2 -5^2)/(2·3·7) = 33/42 = 11/14

A = arccos(11/14) ≈ 38°

_____

In formulas like the Law of Cosines or the Law of Sines, the uppercase letters stand for the measures of angles, and the lowercase letters stand for their opposite side lengths.

So the ratio are 1:2:3:4 and all these add up to 10

Now we divide 360 by 10 resulting to 36

A=(36)

B=(72)

C=(108)

D=(144)

All these add up to 360 and has been divided equally according to the ration provided

Final answer:

To find the measures of the angles in quadrilateral ABCD with ratios 1:2:3:4, we set the angles as x, 2x, 3x, and 4x, and use the fact that their sum equals 360 degrees. Solving for x, we find x to be 36 degrees, which gives us the individual angles as 36 degrees, 72 degrees, 108 degrees, and 144 degrees respectively.

Explanation:

Calculating the Measures of the Angles in a Quadrilateral

Given that the measures of the angles A, B, C, and D in quadrilateral ABCD are in the ratio of 1:2:3:4 respectively, we first need to understand that the sum of the interior angles in a quadrilateral is always 360 degrees. To find the measure of each angle, we should express the ratio in terms of x, which would give us the angles as x, 2x, 3x, and 4x. Summing these and setting them equal to 360 degrees, we get the equation x + 2x + 3x + 4x = 360. Simplifying, we have 10x = 360, which when solved for x yields x = 36 degrees. Therefore, the measures of the angles are:

Angle A = 1x = 36 degrees

Angle B = 2x = 72 degrees

Angle C = 3x = 108 degrees

Angle D = 4x = 144 degrees

Hence, each angle's measure has been found using the given ratio and the property of the sum of interior angles in a quadrilateral.

Answer:

Step-by-step explanation:

You would do this question like this.

4 meats * 2 cheeses * x breads = 24 different kinds of  sandwiches.

8x = 24

8x/8 = 24/8

x = 3

There are 3 different kinds of breads.

Answer:

The baby would be 160 ounces.

Step-by-step explanation:

The baby who weighted 10 pounds, weighs 160 ounces.

Given that at a doctor's appointment, a baby weighed 10 pounds.

From the conversion table, we know that 1 pound is equal to 16 ounces.

Thus 10 pounds is equal to 160 ounces.

Therefore, the baby weighted 160 ounces.  

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Answer:

See below

Step-by-step explanation:

The score increase was 35 points. They claimed an increase of at least 50 points.  For a significance level of 5%, the z-score for the situation needs to be at smaller than -1.645.  For a significance level of 1%, the z-score needs to be smaller than -2.325

The z score for our situation:  z = (385 - 350)/50 = 0.7

The average score of 385 of Tutor O-Rama scores is not significantly different from the average of the other students SAT scores.  The evidence doesn't support their claim of being effective tutoring.