The population of Leavetown is 123,000 and is decreasing at a rate of 2.375% each year.

What will the population of Leavetown be 100 years from now?

Answer:

12.1244 or [tex]\sqrt{147}[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem and solve for b^2:

7^2+b^2= 14^2

Simplify:

49+b^2= 196

Subtract 49 from both sides:

49-49+b^2= 196-49

Simplifly:

b^2= 147

Unsquare both sides:

[tex]\sqrt{b} = \sqrt{147}[/tex]

Answer: 42

Step-by-step explanation:

30x21=630

630 divided by 15= 42

42x15= 630

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A plane with equation (x/a) + (y/b) + (z/c) = 1, where a,b,c > 0 together with the positive coordinate planes form a tetrahedron of volume V = (1/6)abc. Find the plane that minimizes V if the plane is constrained to pass through the point P(2,1,1).

Answer:

The plane is x/6 + y/3 + z/3 = 1

Step-by-step explanation:

Given

Equation: (x/a) + (y/b) + (z/c) = 1 where a,b,c > 0

Minimise, V = (1/6) abc subject to

the constraint g = 2/a + 1/b + 1/c = 1

First, we need to expand V

V = (abc)/6

Possible combinations of V taking 2 constraints at a time; we have

(ab)/6, (ac)/6 and (bc)/6

Applying Lagrange Multipliers on the possible combinations of V, we have:

∇V = λ∇g

This gives

<bc/6, ac/6, ab/6> = λ<-2/a², -1/b², -1/c²>

If we equate components on both sides, we get:

(a²)bc/12 = -λ = a(b²)c/6 = ab(c²)/6

Solving for a, b and c;

First, let's equate:

(a²)bc/12 = a(b²)c/6 -- divide through by abc, we have

a/12 = b/6 --- multiply through by 12

12 * a/12 = 12 * b/6

a = 2 * b

a = 2b

Then, let's equate:

(a²)bc/12 = ab(c²)/6 -- divide through by abc, we have

a/12 = c/6 --- multiply through by 12

12 * a/12 = 12 * c/6

a = 2 * c

a = 2c

Lastly, we equate:

a(b²)c/6 = ab(c²)/6 -- divide through by abc, we have

b/6 = c/6 --- multiply through by 6

6 * b/6 = 6 * c/6

b = 2

Writing these three results, we have

a = 2b; a = 2c and b = c

Recalling the constraints;

g = 2/a + 1/b + 1/c = 1

By substituton, as have

2/(2c) + 1/c + 1/c = 1

1/c + 1/c + 1/c = 1

3/c = 1

c * 1 = 3

c = 3

Since a = 2c;

So, a = 2 * 3

a = 6

Similarly, b = c

So, b = 3

So, the plane: (x/a)+(y/b)+(z/c)=1;

By substituton, we have

x/6 + y/3 + z/3 = 1

Hence, the plane

So the plane is x/6 + y/3 + z/3 = 1

The equation of the plane that minimizes the volume of the tetrahedron and passes through the point (2,1,1) is x + z = 1.

To find the plane that minimizes the volume of the tetrahedron, we need to find the equation of the plane that passes through the point P=(2,1,1) and has coefficients a, b, and c. We can substitute the coordinates of the point into the equation of the plane and solve for the a, b, and c.

Substituting the coordinates of P into the equation of the plane gives 2a + b + c = 1. Since a, b, and c are all greater than 0, we can set a = 1, b = 0, and c = 1.

Therefore, the equation of the plane that minimizes the volume of the tetrahedron is x + z = 1.

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The trigonometry identity is  [tex]\tan x=\frac{\sin x}{\cos x}[/tex].

What is trigonometry ratios?

Trigonometric ratios are the ratios of the sides of a right triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The tan x is given by (sin x)/ (cos x) as the formula is  [tex]\tan x=\frac{\sin x}{\cos x}[/tex].

This is same as option B.

Therefore, the correct answer is  [tex]\frac{\sin x}{\cos x}[/tex] which is option B.

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Answer:

Y < -1/4x + 2

Step-by-step explanation:

We will see that the line that best fits the data is the one in the first graph (top left one).

To know which line is the best one, what we need to do is:

I know that it is hard to do it with these graphs, as these are kinda small and the measure may be hard to take, so you can just estimate.

By doing that estimation you can see that (only for the two better graphs, I ignored the bottom two).

The first one has a total distance of near 10 units.

The second one has a total distance of near 11 units.

So the graph that fits best the data is the first one (top left).

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Answer:

78949

Step-by-step explanation:

v = Bh = πr²h = 3.14 x (3x - 4)² x (11x + 10)             x = 7

  = 3.14 x (21 - 4)² x (77 + 10)

  = 3.14 x 289 x 87

  = 78949

Answer:

B) 120

Step-by-step explanation:

(n-2)*180 =

n = 6 (In a hexagon)

(6-2)  * 180 = 4*180

720

720/6 = 120

Answer:

B) 120

Step-by-step explanation:

Total angle in a hexagon:

(6 - 2) × 180

720

Regular polygon has all sides/angles equal

720/6 = 120° each

Answer:

Step-by-step explanation:

The tens place because 3746 rounded to nearest hundred is 3700 and 3746 rounded to the nearest ten is 3750

Final answer:

3,746 rounded to the nearest ten is 3,750, which is greater than 3,746 rounded to the nearest hundred, which is 3,700.

Explanation:

When comparing which is greater, 3,746 rounded to the nearest hundred or to the nearest ten, it's important to understand the concept of rounding. Rounding to the nearest hundred, we consider the tens digit, which is 4, and since it's less than 5, we round down to 3,700. When rounding to the nearest ten, we look at the ones digit, which is 6, and since it's 5 or greater, we round up to 3,750.

Therefore, 3,750 (rounded to the nearest ten) is greater than 3,700 (rounded to the nearest hundred).

Answer:

  16 minutes

Step-by-step explanation:

The number of minutes is expected to be proportional to the number of walls and inversely proportional to the number of minutes. Relative to the effort given, the number of walls is a factor of 4/9, and the number of people is a factor of 7/4. Hence the number of minutes will be ...

  (63 min)×(4/9)×1/(7/4) = (63 min)×(16/63) = 16 min

It will take 16 minutes for 7 people to paint 4 walls.

Final answer:

The probability that Alex applies for his first sick leave on the fifth day is approximately 0.049, assuming that the likelihood of taking a sick day is consistent and independent across all days.

Explanation:

The probability that Alex applies for his first sick leave on the fifth day can be determined using the information given about the second day and the independent nature of the sick leave events. Since the probability of Alex taking his first sick leave on the second day is 0.21, and it is given that the probability of taking a sick day is the same for each day and is independent, we can infer that the probability of not taking a sick leave on any given day is 1 - 0.21 = 0.79. Therefore, for Alex to take his first sick leave on the fifth day, he must not take sick leave on the first four days and then take leave on the fifth, so the probability is calculated as:

(0.79 x 0.79 x 0.79 x 0.79) x 0.21 ≈ 0.049

Here, (0.79)^4 represents the probability that Alex does not take sick leave for the first four days, and 0.21 represents the probability that he takes his first sick leave on the fifth day.

The probability that Alex applies for his first sick leave on the fifth day is 0.0729.

To find this, we need to follow these steps:

1. The probability that he applies for sick leave for the first time on the second day is 0.21. This means he must have been at work on the first day and then applied for sick leave on the second day. Since the events are independent, the probability that he does not apply for sick leave on any day is [tex]\(1 - P(\text{sick leave})\)[/tex]. Therefore, we have [tex]\( P(\text{work on first day}) \times P(\text{sick leave on second day}) = 0.21 \)[/tex].

2. Let ( p ) be the probability that Alex applies for sick leave on a given day. We then have [tex]\( (1-p) \times p = 0.21 \)[/tex].

3. To solve for ( p ), we can find the square root of 0.21, since [tex]\( p^2 = 0.21 \) if \( p = 1-p \)[/tex], which is true when [tex]\( p < 0.5 \)[/tex].

4. The probability that Alex applies for his first sick leave on the fifth day is [tex]\( (1-p)^4 \times p \)[/tex]. We calculate [tex]\( (1-p)^4 \)[/tex] using the ( p ) we found from the square root of 0.21 and then multiply by ( p ).

Let's calculate \( p \) and then use it to find the probability for the fifth day.

There seems to be a mistake in the calculation. I incorrectly assumed that the probability of not taking a sick leave (\(1 - p\)) squared would be equal to the probability of taking the first sick leave on the second day, which isn't necessarily true given that \( p \) is less than 0.5 but not necessarily \( p = 1 - p \).

Let's go through the calculations again step by step:

1. Let ( p ) be the probability that Alex applies for sick leave on a given day. The probability that he does not apply for sick leave on any day is therefore(1 - p).

2. Since the events are independent, the probability that Alex applies for his first sick leave on the second day (having worked on the first day) is the product of the probability that he did not take a sick leave on the first day and the probability that he did take a sick leave on the second day, which can be represented as ( (1 - p) times p ).

3. Given that the probability for the second day is 0.21, we can set up the equation ( (1 - p) times p = 0.21 \) and solve for( p ).

4. Using the value of ( p ) found from the equation, we can then calculate the probability that Alex applies for his first sick leave on the fifth day, which would be [tex]\( (1 - p)^4 \times p \).[/tex]

( p ) from the equation and then determine the probability for the fifth day.

The probability that Alex applies for his first sick leave on the fifth day is exactly [tex]\( 0.07203 \)[/tex]. This was calculated by first determining the daily probability of taking sick leave, which is [tex]\( 0.3 \)[/tex], and then using it to calculate the probability of not taking a sick leave for the first four days and then taking one on the fifth day.

Given a cone and a cylinder with the same radius and height, it would take three scoops (cone volumes) to fully fill the cylinder (bucket). So, to fill it 15 times, it would require 45 scoops.

To answer this question, it's critical to understand the concept of volume. The formula for the volume of a cone is 1/3πr²h, and the volume of a cylinder is πr²h. Both the cone and the cylinder have the same radius ('r') and height ('h'), thus the cone's volume is a third of the cylinder's. Hence, it would take three scoops to fill the bucket once.

Since we want to fill the bucket 15 times, we multiply 15 by 3, so it would take 45 scoops of water to fill the bucket 15 times.

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Answer:

v ≈ - 5.29, v ≈ 5.29

Step-by-step explanation:

Given

3v² - 84 = 0 ( add 84 to both sides )

3v² = 84 ( divide both sides by 3 )

v² = 28 ( take the square root of both sides )

v = ± [tex]\sqrt{28}[/tex]

Thus

v = - [tex]\sqrt{28}[/tex] ≈ - 5.29

v = [tex]\sqrt{28}[/tex] ≈ 5.29

Answer:

80°

Step-by-step explanation:

Hello all triangles equal 180 degrees. So, with that being said to solve this you need to do 180-22-78 Which equals 80

Answer:

The third angle is 80 degrees

Step-by-step explanation:

In math, the rule is such that for all triangles, regardless of what kind they are, whether or not the sides are equal or all not equal to each other, the sum of the interior angles must add up to 180 degrees.

Missouri's area is approximately 63,990 square miles, making it the correct option B.

To calculate the area of Missouri, we'll use the formula for the area of a trapezoid:

[tex]\( A = \frac{1}{2} \times (b_1 + b_2) \times h \)[/tex], where

[tex]\( b_1 \)[/tex] and [tex]b_2[/tex] are the lengths of the bases and h is the height.

Given:

b₁ = 198 miles

b₂ = 276 miles

h = 270 miles

Substituting these values into the formula:

[tex]\( A = \frac{1}{2} \times (198 + 276) \times 270 \)[/tex]

[tex]\( A = \frac{1}{2} \times 474 \times 270 \)[/tex]

[tex]\( A = \frac{1}{2} \times 127,980 \)[/tex]

A = 63,990 square miles

So, the correct answer is B. 63,990 mi².

Complete Question:

Missouri has a shape that is similar to a trapezoid with bases of 198 miles and 276 miles and a height of 270 miles. What is the area of the state?

A. 126,360 mi²

B. 63,990 mi²

C. 54,918 mi²

D. None of the Above

Under S would be 1 and 9 under E would be 2 6 8 10 and 12 and 4 goes in the middle

Answer and Step-by-step explanation:

First, from this set of numbers determine which ones are square numbers. Remember that square numbers are those that can be written in the form of k^2, where k is a number.

Square numbers: 1 (because 1^2 = 1), 4 (because 2^2 = 4), and 9 (because 3^2 = 9)  ⇒  There are 3 square numbers

Next, find the number of even numbers.

Even numbers: 2, 4, 6, 8, 10, and 12  ⇒  There are 6 even numbers

Place all the 3 square numbers inside the S circle and all the 6 even numbers in the E circle. However, notice that one number, 4, is both a square number and an even number, so put 4 in the shared portion.

Hope this helps!

Answer:

Width 10y^6 units

Length 7y^2+3 units

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

It is C

Step-by-step explanation:

I took the quiz.

Answer:

4[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Answer:

7 is greater than 5 so round up

4.75 is rounded to 5

Step-by-step explanation:

to round to a place look to the place right after it, to round to the nearest whole number look at the tenth place, right after the decimal place

you see 7

Answer:

69%

Step-by-step explanation:

Since we only have two options, rain or not rain, they have to add to 100%

100 -31 = 69

So not raining is 69%

Answer:

69%

Step-by-step explanation:

Answer:

y=25x-500

Step-by-step explanation:

25 is positive with the x because its the slope and 500 is the cost so you subtract is. 500 is the y intercept

Answer:

Measure of [tex]\angle A = \angle D =60[/tex] and [tex]\angle B=\angle C=120[/tex] in degrees.

Step-by-step explanation:

Given:

A parallelogram where angles A and D measures same also, C and B measures same.

According to the question:

Measure of angle C is twice the measure of angle A.

Let the measure of angle A be "x" degree.

Accordingly :

Measure of each angle C and B = "2x"

Measure of each angle A and D ="x"

Note:

The sum of the measures of the angles of a parallelogram is​ 360°.

⇒ [tex]x+x+2x+2x=360[/tex]

⇒ [tex]6x=360[/tex]

⇒ [tex]x=\frac{360}{6}[/tex]

⇒ [tex]x=60[/tex]

So,

Measure of angle A and D be 60 degrees each.

Measure of angle B and C is 120 degrees each.

The measure of angles A and D in the parallelogram is 60° each, while the measure of angles C and B is 120° each.

The question is about finding the measure of each angle in a parallelogram. Given that the sum of the angles in a parallelogram is 360° and that the measure of angle C is twice the measure of angle A, we can set up equations to solve the problem.

Let's denote the measure of angle A as 'a'. Since angles A and D are of the same measure, the measure of angle D will also be 'a'. The measure of angle C and B are each twice the measure of angle A, so they will be '2a'.

The sum of the measures of all angles in a parallelogram is 360°, we can write the equation: a + 2a + a + 2a = 360°. Simplifying it you get: 6a = 360°. Solve this equation by dividing both sides by 6, you will get a = 60°.

Therefore, in the parallelogram, the measure of angles A and D is 60°, while the measure of angles C and B is twice as much, namely 120°.

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Answer:

We conclude that the new hybrid car has a mean gas mileage of less than 50 miles per gallon which means that the advertiser’s statement is too high.

Step-by-step explanation:

We are given that an automobile manufacturer advertises that its new hybrid car has a mean gas mileage of 50 miles per gallon.

A simple random sample of 30 hybrid vehicles is taken and tested their gas mileage. It was found that in this sample, the average is x = 47 miles per gallon with a standard deviation of s = 5.5 miles per gallon.

Let [tex]\mu[/tex] = mean gas mileage of new hybrid car.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex]  50 miles per gallon   {means that the new hybrid car has a mean gas mileage of more than or equal to 50 miles per gallon}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 50 miles per gallon   {means that the new hybrid car has a mean gas mileage of less than 50 miles per gallon}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

                       T.S.  = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average gas mileage = 47 miles per gallon

             s = sample standard deviation = 5.5 miles per gallon

             n = sample of hybrid vehicles = 30

So, test statistics  =  [tex]\frac{47-50}{\frac{5.5}{\sqrt{30} } }[/tex]  ~ [tex]t_2_9[/tex]   

                               =  -2.988

Now at 0.1 significance level, the t table gives critical value of -1.311 at 29 degree of freedom for left-tailed test. Since our test statistics is less than the critical value of t as -1.311 > -2.988, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the new hybrid car has a mean gas mileage of less than 50 miles per gallon which means that the advertiser’s statement is too high.

In this line equation y=3x+9, you find the values of x and y by plugging in different x-values and calculate corresponding y-values. These (x,y) pairs are points on the line which can be represented on the graph.

The subject of this question is Mathematics, specifically equations of a line. Looking at the initial line equation, the form appears to be y = mx + b, where m is the slope and b is the y-intercept. Based on the given information, m is set to 3 and b to 9.

To find values of x and y, you plug different x-values into the equation and solve for y. For example, if x=1, y would be 3×1+9=12. Thus, for x=1, y=12. This applies on this line for all different x-values.

Remember: different values of x will correspond to different values of y. This relation can be represented graphically by plotting these (x,y) pairs on a graph, and drawing a line through them.

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Answer:b

Step-by-step explanation:

I took the text

Answer:

b

Step-by-step explanation:

Answer:

C. the use of a series of numbers in which each number is an equal distance from the next.

Step-by-step explanation:

The four characteristics of mapping rules are:

1. Classification: This is the grouping of data or information based on given criteria.

2. Order: this is the chronological arrangements of numbers.

3. DISTANCE: This is the range or difference between one unit to the other.

4. Origin

Answer:

x=136

Step-by-step explanation:

The sum of the angles inside a quadrilateral add to 360, so

79+55+110+x=360

Combine like terms

224+x=360

Subtract 224 from both sides

x=136

Answer:

[tex]\pi r^2 h[/tex]

Step-by-step explanation:

[tex]\text{Area of the circle: Area of the Square =}\dfrac{\pi r^2}{4r^2}:1=\dfrac{\pi}{4}:1[/tex]

Height of the cylinder =h

Radius of the Cylinder=r

Base Length of the Prism=2r

Therefore:

Volume of the Prism =[tex](2r)^2h=4r^2h[/tex]

[tex]\text{Volume of the Cylinder =} \frac{\pi}{4}(\text{the volume of the prism)}\\=\frac{\pi}{4}(4 r^2 h) \\=\pi r^2 h[/tex]

Answer:

D

Step-by-step explanation:

i took the test