In 1970, the population of a small town was 4,200. The population is decreasing at a rate of 2.4% per year. Which of the following shows an exponential decay function to find the quarterly decay rate?The population is decreasing by how much percent per quarter?

Answer:

25

Step-by-step explanation:

Answer: 25

find the length of segment QU.  

First, we must find out what the coordinates are.

Q=(4,5) U=(4,10)

Then, Setup your equation by making the first coordinate pair equal. So,

Q= (4,5) would now equal Q=(5,5). That means we added 1. (when you add x ((x=the number you add to make equal)) you add x to the other side as well)

So, now we would add 1 (or how many you got) to U. Thus,

U=(4,10) would now equal Q=(5,10).

Next, set up the equation.

[tex]\sqrt{(Q)^{2} +(U)^{2}[/tex] (Q=(5,5) and U=(5,10).)

* You will now be subtracting the coordinates so, Q=(5-5) and U=(5-10)*

Next, Substitute the equation.

[tex]\sqrt{(5-5^{2} +(5-10)^{2}[/tex]

After, we solve.

[tex]\sqrt{0^{2} +(5-10)^{2}[/tex]

*the sum of two opposites equals 0. 5-5=0*

Next, Subtract (5-10).

[tex]\sqrt{0^{2} +(-5)^{2}[/tex]

Next, 0 raised to any positive power equals 0

[tex]\sqrt{0+(-5)^{2}[/tex]

Next, When adding or subtracting 0, the quantity does not change.

[tex]\sqrt{(-5)^{2}[/tex]

Next, Reduce the index of the radical and exponent 2.

[tex]|-5| = 5[/tex]

So, The length of segment is 5.

Now, find the length of segment Upper Q'U'​, multiply the length of segment QU by the scale factor.

scale factor in this equation is 5.

Now, multiply.

5·5 = 25

So, the length of segment Q'U' is 25.

The length of segment Q'U' after the dilation with a scale factor of 5 is 25 units.

To find the length of segment Q'U'  after the dilation with a scale factor of 5, we can calculate it step by step:

1. Calculate the new coordinates of Q'  and U'  after the dilation with a scale factor of 5 and center (0,0):

Q' coordinates: (4 5, 5 5) = (20, 25)

U' coordinates: (4 5, 10 5) = (20, 50)

2. Determine the distance between Q'  and U' using the distance formula:
- Horizontal distance: 20 - 20 = 0
- Vertical distance: 50 - 25 = 25

3. Calculate the length of segment

 using the Pythagorean theorem:
- Length = sqrt(0^2 + 25^2)
- Length = sqrt(0 + 625)
- Length = sqrt(625)
- Length = 25 units

Therefore, the length of segment Q'U' after the dilation with a scale factor of 5 is 25 units.

The ladder is 9.2 feet up the building

The length (L) of the ladder is given as:

[tex]L = 10ft[/tex]

The distance (d) from the edge of the building is

[tex]d = 4ft[/tex]

The distance up the ladder is the height (h) of the ladder on the wall.

This is calculated using the following Pythagoras theorem

[tex]L^2 = d^2 + h^2[/tex]

So, we have:

[tex]10^2 = 4^2 + h^2[/tex]

Evaluate the exponents

[tex]100 = 16 + h^2[/tex]

Subtract 16 from both sides

[tex]84 = h^2[/tex]

Take square roots of both sides

[tex]9.2 = h[/tex]

Rewrite as

[tex]h =9.2[/tex]

Hence, the ladder is 9.2 feet up the building

Read more about Pythagoras theorems at:

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Answer:a

Step-by-step explanation:

Answer:

arc length "s" = radius * central angle in radians

radius = arc length "s" / central angle

radius = "s" / 1.2

arc length "s" = r * 1.2

Step-by-step explanation:

We have been given that a normal distribution has a mean of 186.4 and a standard deviation of 48.9. We are asked to find the range of value that represents the upper 2.5% of the data.

We know that upper 2.5% of data would be 97.5% of data.

We will use z-score formula to solve our given problem.  

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

z = z-score,

x = Random sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

Now we will use normal distribution table to find z-score corresponding to 97.5% area or 0.975.

We can see from the normal distribution table that z-score corresponding to  area 0.975 is [tex]1.96[/tex].

[tex]1.96=\frac{x-186.4}{48.9}[/tex]

Let us solve for x.

[tex]1.96\cdot 48.9=\frac{x-186.4}{48.9}\cdot 48.9[/tex]

[tex]95.844=x-186.4[/tex]

[tex]95.844+186.4=x-186.4+186.4[/tex]

[tex]282.244=x[/tex]

Therefore, the range [tex]x>282.244[/tex] represents the upper 2.5% of the data.

There is no picture how do I help

Answer:

89.4 yd

Step-by-step explanation:

Surface area of a triangular pyramid = B × H ÷ 2

6 × 5.2 ÷ 2 = 15.6

6 × 8.2 ÷ 2 = 24.6

6 × 8.2 ÷ 2 = 24.6

6 × 8.2 ÷ 2 = 24.6

15.6 + 24.6 + 24.6 + 24.6 = 89.4

The final balance is $897.51

Step-by-step explanation:

Answer:

Density of the Cylinder = 2.7 g/mm³

Step-by-step explanation:

Density of a cylinder is calculated using the formula =

Mass of the Cylinder ÷ Volume of the Cylinder

Step 1

The First step is to find the Volume of the Cylinder.

Volume of a Cylinder = πr²h

In the attached image , we are given:

Diameter of the Cylinder = 28mm

Radius of the Cylinder = Diameter ÷ 2 = 28mm ÷ 2

Radius of the Cylinder (r) = 14mm

Height of the Cylinder (h) = 30mm

The Volume of the Cylinder = πr²h

= π × (14mm)² × 30mm

= 18472.564803 mm³

Step 2

The second step would be to find the Density of the Cylinder.

Density of the Cylinder = Mass of the Cylinder ÷ Volume of the Cylinder

Mass of the Cylinder = 50,000g

Volume of the Cylinder = 18472.564803 mm³

Density of the Cylinder = 50,000g ÷ 18472.564803 mm³

= 2.7067167193 g /mm³

Approximately the Density of the Cylinder = 2.7 g/mm³

The surface area of the figure in square yards is 1275 square yards

The surface area of a figure is the tota sum of all the area of the faces.

For the given diagram, it consist of 2 triangles and 3 rectangles

Area of the figure = 3(24 * 15) + (13* 15)

Surfacea area = 3(360) + 195
Surface area = 1080 + 195

Surface area = 1275 square yards

Hence the surface area of the figure in square yards is 1275 square yards

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let t be the number of tacos sold

let b be the number of burritos sold

Step-by-step explanation:

b=2t

4.75t+7.50b=790

To solve the problem, set up two variables T and B for the number of tacos and burritos sold. Two equations are formed: B = 2T (since twice as many burritos as tacos were sold) and 4.75T + 7.50B = 790 (from the total revenue). Solve these to find T and B.

To determine the number of tacos and burritos sold by Jason's food truck, we need to establish two variables: let T represent the number of tacos sold, and let B represent the number of burritos sold. Given that burritos are sold at a ratio of two to every one taco, we can express this relationship with the equation B = 2T. Next, using the given prices of tacos ($4.75) and burritos ($7.50), along with the total revenue of $790, we can write the budget constraint equation as 4.75T + 7.50B = 790. These two equations together form the system of equations that can be solved to find the number of tacos (T) and burritos (B) sold.

Answer:

Plot at 9.3

Step-by-step explanation:

Take the square root of 87.35

sqrt(87.35)

9.346122191

Rounding to the nearest tenth

9.3

Plot at 9.3

Answer:

Step-by-step explanation:

Setting f(x) = -(x + 3)(x + 1) = 0 leads to identifying two roots/solutions of this equation:  x = -3 and x = -1.  The axis of symmetry is a vertical line halfway between these two roots:  x = -2.  This x = -2 is also the x-coordinate of the vertex.  Evaluating f(x) = -(x + 3)(x + 1) at x = -2 gives us the y-coordinate of the vertex:  y = -(-2 + 3)(-2 + 1) = -(1)(-1) = 1.

In summary, the vertex is at (-2, 1) and the two x-intercepts are (-3, 0) and (-1, 0).  The y-intercept is found by  setting x = 0 and finding y:  

f(0) = -(0 + 3)(0 + 1) = -3, or (0, -3)

Next time, please share the answer choices.  Thank you.

Answer:

B

Step-by-step explanation:

Edge 2021

Answer:

B, D

Step-by-step explanation:

These are the correct answers.

Answer:

B. f(x) = x2 – 5x + 4

D. f(x) = –2x2 + 10x – 8

Step-by-step explanation:

guy above me is right

Answer:

The answer would be $184,274.23.

Step-by-step explanation:

After a 4% annual decrease in value over five years, a house that was bought for $226,000 would be worth around $183,896.7.

The student's question pertains to a situation where a house's value depreciates, in this case, at a rate of 4% per year for five years. To find out how much the house would be worth now, we need to employ the formula for depreciations, that is P = P0 (1 - r)^n, where P is the final value, P0 the initial value, r the rate of decrease and n the number of periods the decrease has occurred over.

In this case, P0 would be the initial value of the house $226,000, r would be 4% (or 0.04 as a decimal), and n would be the number of years, which is 5. Substituting these values into the formula gives us and calculated we get P = $226,000 * (1 - 0.04)^5 = $183,896.7.

So after a 4% annual decrease in value over five years, the house that was bought for $226,000 would now be worth around $183,896.7.

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Answer:

Two angles of a quadrilateral : 220 and 90 deg.

The other two angles (x and y) are in ratio 2:3.

We have:

x + y = 360 - 220 - 90 = 50 (property of sum of 4 angles in quadrilateral)

x/y = 2/3 => x = 2y/3

=>2y/3 + y = 50

=> 5y/3 =50

=> 5y = 150

=> y = 30

=> x = 2 x 30/3 = 20

=> Two other angles are 20 and 30 deg

Hope this helps!

:)

Answer:

-0.2, 2.02, 22.2

Explanation:

-0.2 is below zero, 2.02 is 20.18 less than 2.02

Answer:

15 batteries

Step-by-step explanation:

If he puts the batteries in piles of 4, and there is 3 left over, the number of batteries he can have is:

2 piles: 4*2 + 3 = 11

3 piles: 4*3 + 3 = 15

4 piles: 4*4 + 3 = 19

Then, when he puts in piles of 3, there is no batteries left over, so the number of batteries is a multiple of 3.

From the 3 possibilities above (11, 15 and 19), only the number 15 is a multiple of 3, so the number of batteries is 15.

Answer:

1. -5

2. -10

3.  12

4. -6

5. 20

6. -7

7. -10

8. -19

9. 4

10. -5

11. -10

12. 8

13. 2

14. -8

15. -1

16. 9

17. -7

18. 2

19. 4

20. -17

21. 0

22. -10

23. 2

24. 1

25. 9

26. -6

27. -12

28. 4

29. -3

30. -68

Answer:

it was nt quite old enough to be a buck

Step-by-step explanation:

Answer:

(x-6)^2

Step-by-step explanation:

x^2-12x+36

=(x-6)(x-6)

=(x-6)^2

According to the theory of the Triangle Inequality, so, the total of the 2 sides of the triangle must be larger than the length of the third side. Therefore, the possible length of a triangle is given by the difference of two sides x the sum of two sides.

Therefore,

[tex]\to 4.3-2.1< x <4.3+2.1 \\\\\to 2.2< x <6.4 \\\\[/tex]

So, the final answer is "[tex]2.2<x<6.4[/tex]" which is the possible length of x.

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The range of possible sizes for side 'x' is from 1.5 to 4.5, inclusive of both endpoints.

The question "What is the range of possible sizes for side xxx?" refers to finding the possible values that the variable 'x' can take. From the information provided, we understand that 'x' can be any number in the inclusive range from 1.5 to 4.5, which can be denoted mathematically as 1.5 ≤ x ≤ 4.5. This means that the smallest value 'x' can be is 1.5, and the largest value is 4.5. The range of possible sizes for 'x' is therefore between 1.5 and 4.5, including both of these endpoints.

Answer:

The answer is A. (x+6)(x−7)

Step-by-step explanation:

I used a calculator.

Answer:

other person is right...

Step-by-step explanation:

its right on plato/edmentum though.

Answer:

24 m^2

Step-by-step explanation:

The area of a kite is the product of the diagonals divided by 2.

If the diagonals have lengths a and b, then area = ab/2

area = ab/2

a = horizontal diagonal = 2 m + 6 m = 8 m

b = vertical diagonal = 3 m + 3 m = 6 m

area = (8 m)(6 m)/2 = (48 m^2)/2 = 24 m^2

Answer:

(5y−1)(y+1)

Step-by-step explanation:

Answer:

(y + 1 )

Step-by-step explanation:

Given

5y² + 4y - 1

Consider the factors of the product of the y² term and the y- term which sum to give the coefficient of the y- term

product = 5 × - 1 = - 5 and sum = + 4

The factors are + 5 and - 1

Use these factors to split the y- term

5y² + 5y - y - 1 ( factor the first/second and third/fourth terms )

= 5y(y + 1) - 1(y + 1) ← factor out (y + 1) from each term

= (y + 1)(5y - 1)

The missing factor is (y + 1)

Answer:

-49

Step-by-step explanation:

it would be this because first we would have to figure out what 6*10 is that why we know what to distribute . so once we figure it out , which is 70 . We would then subtract 14 from 70 . Since 7 is right next to 2 we would then multiply it to get to 14. Once we get that you should get 56, from there you would subtract 56 to 105 , and get your answer.

Answer:

y = (x - 1)^2 - 8

Step-by-step explanation:

Your answer from part A should be: (x - 1)^2 = 8

You are simply changing the format of the equation from

0 = (x - 1)^2 - 8 to y = (x - 1)^2 - 8

Hope this helps!

Answer:

y = (x-1)² - 8

Step-by-step explanation:

The response from part A is (x – 1)2 = 8, where h = 1 and c = 8.

Set the equation equal to 0:

0 = (x – 1)2 – 8.

Substitute y for 0 and keep the equation rewritten in the form y = (x – h)2 – c:

y = (x – 1)2 – 8.

Answer:

25/324

Step-by-step explanation:

Make a table of possible products:

[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&1&2&3&4&5&6\\2&2&4&6&8&10&12\\3&3&6&9&12&15&18\\4&4&8&12&16&20&24\\5&5&10&15&20&25&30\\6&6&12&18&24&30&36\end{array}\right][/tex]

Of the 36 results, 10 are greater than 15.

The probability the product is greater than 15 on a single roll is 10/36 = 5/18.

The probability the product is greater than 15 on two rolls is (5/18)² = 25/324.

Answer:

True

Step-by-step explanation:

As there are infinite numbers, the list of multiples are also infinite.

Multiples of 6 : 6, 12 , 18 , 24 ..............

Answer:

True; yes.

Step-by-step explanation:

Think about it, what does etc, etc mean? It means repetitive-a pattern, in a sort of way. So here are some multiples of 6:

6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,210,216,222,228,234,240,246,252,258,264,270,276,282,288,294,  etc.

As you can see, all I'm doing is adding 6 to every step I go. So when you say there is an infinite number, then these multiples are going to be infinite.

Answer:

4(8 + 11).

Step-by-step explanation:

32 - 44

The greatest common factor is 4 so we have

4(8 + 11).

Answer:

about 6.6 years

Step-by-step explanation:

41,500=14,000*.45*x

41,500=6,300*x

41,000/6,300=x

6.5873=x

6.6=x

Answer:

24.7

Step-by-step explanation: