A 1,127-foot tree has grown at a constant rate each year. In the equation below, t is the age of the tree in years.

23t = 1,127

What is the unit rate in the equation above?

Using normal distribution concepts, we can conclude that the correct statement is:

B. Use t when the population is normal and the population standard deviation is not known

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

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Answer:

[tex]d) \ 55\textdegree[/tex]

Step-by-step explanation:

-we apply the relationship of chords intersecting within a circle:

-when two chords intersect to form a vertex of an angle within a circle, the measure of the angle is equal to one-half the sum of the measures of the two arcs intercepted by the angle and its vertical angle:

[tex]\angle AFE=0.5(arc\ EA +arc \ BD)\\\\=0.5(40+70)\\\\=55\textdegree[/tex]

Hence, the measure of ∠AFE is 55°

Answer:

-3,8

Step-by-step explanation:

1) we can factor this since this quadratic function is in the form of

ax^2+bx+c

where we need to find out what*what=c

and what+what=b

since c is -24 and b is -5 we need to figure out the factors of -24 which equal -5:

-8+3=-5

and

-8*3=-24

hence -8 and 3 is our factors, next we will substitute them in place of "b"

so

n^2-8n+3n-24

split this equation in two groups:

group 1) n^2-8n

group 2) 3n-24

gcf of group 1= n

so

n(n-8)

gcf of group 2: 3

so

3(n-8)

next take numbers outside of parentheses and group them together:

so (n+3) (n-8)=0

since  anything times 0 is equal to 0, either (n+3) is 0 or (n-8) is 0

so

n+3=0

n=-3

n-8=0

n=8

hence n=-3,8

Hope this helps!

Answer:

(-35, 0)

step-by-step explanation:

The x-intercept of the line does not exist.

The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept, we need to look for a point on the graph where y is equal to zero. Based on the given table, there is no pair of coordinates where the y value is equal to zero. Therefore, the line does not intersect the x-axis and the x-intercept does not exist.

Answer:

0.65 kilograms

Step-by-step explanation:

Answer:

0.65 kg

Step-by-step explanation:

[tex] \because \: 1 \: gram = \frac{1}{1000} kg \\ \\ \therefore \: 650 \: grams = \frac{650}{1000} \\ \\ \red{ \boxed{\bold {\therefore \: 650 \: grams =0.65 \: kg} }}[/tex]

Answer:

C. 100 cm

Step-by-step explanation:

2x-15=185

+15      +15

2x=200

/2    /2

x=100

Answer:

1. 2a

2. Vertex

3. Center

4. (c-a)

Step-by-step explanation:

The missing black in the paragraph will be 2a, vertex, center, and (c – a).

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of 2a.

2a is used in the equation because the Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.

This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).

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Answer:

t = 3 seconds

Step-by-step explanation:

This is a quadratic equation. First set it up and set it equal to 0 (the ground).

-16t² + 46t + 6 = 0

The quadratic formula is (-b ± √(b² - 4ac))/2a

a= -16

b = 46

c = 6

Plug those numbers into the equation and solve which will result in -.125 or 3.

The time of course can not be negative in this case. Therefore, t=3 seconds.

The ball will hit the ground after 3 seconds.

The problem deals with the quadratic equation representing the motion of the ball. When the ball hits the ground, the height (h) is 0. So, we need to solve the equation -16t^2 + 46t + 6 = 0 for (t). The roots of this quadratic equation can be found using the quadratic formula, t = [-b ± sqrt(b^2 - 4ac)]/2a. Substituting a=-16, b=46, and c=6 into the formula, you will find the solutions are t = 3 seconds and t = -0.375 seconds. Therefore, the ball will hit the ground after 3 seconds. The correct choice is A. 3.

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Step-by-step explanation:

Given

f(x) = 3x - 5

f(-2) = 3 * (-2) - 5

= -6 -5

= - 11

Answer:

f(×)=

Step-by-step explanation:

[tex] f(- 2 )= 3( - 2) - 5 [/tex]

[tex] - 2 = - 6 - 5[/tex]

[tex] - 2 = - 11[/tex]

Answer: r=0.8

Step-by-step explanation:

4r + 8 = 7.2 + 5r

-4r             -4r

8=7.2+r

8-7.2=r

0.8=r

Answer: [tex]r=0.8[/tex]

Step-by-step explanation:

-Solve:

[tex]4r+8=7.2+5r[/tex]

-Subtract [tex]5r[/tex] from both sides:

[tex]4r+8-5r=7.2[/tex]

Combine [tex]4r[/tex] and [tex]5r[/tex] to get [tex]-r[/tex]:

[tex]-r+8=7.2[/tex]

-Subtract [tex]8[/tex] from [tex]7.2[/tex] to get [tex]-0.8[/tex]:

[tex]-r=7.2-8[/tex]

[tex]-r=-0.8[/tex]

-Multiply both sides by [tex]-1[/tex]:

[tex]r=0.8[/tex]

-Result:

[tex]r=0.8[/tex]

Answer:

b

Step-by-step explanation:

The square root of b times the square root of b is simply b.

b^(1/2)*b^(1/2) = b^1 = b

Answer:

About 29

Step-by-step explanation:

575 cans of food / 20 days = About 28.75 cans a day, rounded to 29.

Answer:

28.7 cans

Step-by-step explanation:

We want to find the unit rate for cans per day

To find this, divide the number of cans by the number of days

cans/days

574/20

28.7

About 28.7 cans per day

Answer:

$0.41

Step-by-step explanation:

Take the total cost and divide by the number of cans

2.46/ 6

.41

The price is 41 cents per can or$.41

Answer:

(a) The required recurrence relation for  the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].

(b)The salary of the employee will be $83421.88 in 2017.

(c) [tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]

Step-by-step explanation:

Summation of a G.P series

[tex]\sum_{i=0}^n r^i= \frac{r^{n+1}-1}{r-1}[/tex]

(a)

Every year the salary is increasing 5% of the salary of the previous year plus $1000.

Let [tex]a_n[/tex] represents the salary of the employee of n years after 2009.

Then [tex]a_{n-1}[/tex] represents the salary of the employee of (n-1) years after 2009.

Then [tex]a_n= a_{n-1}+5\%.a_{n-1}+1000[/tex]

             [tex]=a_{n-1}+0.05a_{n-1}+1000[/tex]

             [tex]=(1+0.05)a_{n-1}+1000[/tex]

            [tex]=1.05a_{n-1}+1000[/tex]

The required recurrence relation for  the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].

(b)

Given, [tex]a_0=\$50,000[/tex]

[tex]a_n=1.05a_{n-1}+1000[/tex]

Since 2017 is 8 years after 2009.

So, n=8.

∴ [tex]a_8[/tex]

[tex]=1.05 a_7+1000[/tex]

[tex]=1.05(1.05a_6+1000)+1000[/tex]

[tex]=1.05^2a_6+1.05\times 1000+1000[/tex]

[tex]=1.05^2(1.05a_5+1000)+1.05\times 1000+1000[/tex]

[tex]=1.05^3a_5+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^3(1.05a_4+1000)+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^4a_4+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^4(1.05a_3+1000)+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^5a_3+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^5(1.05a_2+1000)+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^6a_2+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^6(1.05a_1+1000)+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^7a_1+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^7(1.05a_0+1000)+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^8a_0+1.05^7\times1000+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]

[tex]=1.05^8a_0+(1.05^7+1.05^6+1.05^5+1.05^4+1.05^3+1.05^2+1.05+1)1000[/tex]

[tex]=1.05^8 \times 50,000+\frac{1.05^8-1}{1.05-1}\times 1000[/tex]

[tex]=1.05^8\times 50,000+20,000(1.58^8-1)[/tex]

[tex]=70,000\times 1.05^8-20,000[/tex]

≈$83421.88

The salary of the employee will be $83421.88 in 2017.

(c)

Given, [tex]a_0=\$50,000[/tex]

[tex]a_n=1.05a_{n-1}+1000[/tex]

We successively apply the recurrence relation

[tex]a_n=1.05a_{n-1}+1000[/tex]

    [tex]=1.05^1a_{n-1}+1.05^0.1000[/tex]

   [tex]=1.05^1(1.05a_{n-2}+1000)+1.05^0.1000[/tex]

   [tex]=1.05^2a_{n-2}+1.05^1.1000+1.05^0.1000[/tex]

   [tex]=1.05^2(1.05a_{n-3}+1000)+(1.05^1.1000+1.05^0.1000)[/tex]

   [tex]=1.05^3a_{n-3}+(1.05^2.1000+1.05^1.1000+1.05^0.1000)[/tex]

                    ...............................

                   .................................

  [tex]=1.05^na_{n-n}+\sum_{i=0}^{n-1}1.05^i.1000[/tex]

 [tex]=1.05^na_0+1000\sum_{i=0}^{n-1}1.05^i[/tex]

 [tex]=1.05^n.50,000+1000.\frac{1.05^n-1}{1.05-1}[/tex]

 [tex]=1.05^n.50,000+20,000.(1.05^n-1)[/tex]

 [tex]=(50,000+20,000)1.05^n-20,000[/tex]

 [tex]=70,000 . \ 1.05^n-20,000[/tex]

[tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]

The employee’s salary is dictated by the recurrence relation where S_n = S_(n-1) + 1000 + 0.05*S_(n-1). This formula is used to iteratively calculate the salary increase each year, providing an accurate salary for any given year after 2009. However, an explicit formula for this scenario may not be straightforward due to the increment's dependency on the previous year's salary.

The subject of this problem is recurrence relation, a mathematical concept that uses a formula to establish the relationship between successive terms in a numerical sequence. The employee's salary problem can be expressed by the following recurrence:

S_n = S_(n-1) + 1000 + 0.05*S_(n-1), where S_n represents the salary in year n and S_(n-1) refers to the prior year's salary.

To calculate the salary in 2017, you start with the initial salary in 2009 and apply the formula for each subsequent year. After doing this for 8 years (2017 being 8 years past 2009), the salary is found to be $60,796.32.

Unfortunately, a simple explicit formula may not exist for this scenario because of percentage increment based on the previous year's salary. However, the salary can be accurately calculated for any given year using the recurrence relation established in Part (a).

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The volume of rotation of region R is [tex]192\pi[/tex] cubic units.

Given information:

Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis.

Region R is rotated about the line y=-2.

So, the region R is a rectangle with length 6 units (x=0 to x=6), and the height of the rectangle is 4 units (y=0 to y=4).

After rotating this rectangle about y=-2, we will get a hollow cylinder.

The outer radius of the cylinder will be,

[tex]R=4-(-2)=6[/tex]

The inner radius of the cylinder will be,

[tex]r=0-(-2)=2[/tex]

And the length of the cylinder is 6 units.

So, the volume of the solid formed after the rotation will be,

[tex]V=\pi R^2L-\pi r^2L\\V=\pi L(R^2-r^2)\\V=\pi \times 6(6^2-2^2)\\V=\pi\times 6 \times 32\\V=192\pi[/tex]

Therefore, the volume of rotation of region R is [tex]192\pi[/tex] cubic units.

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To find the volume of the solid formed by rotating region R about the line y=-2, we use the washer method which results in a volume of 216π cubic units.

The problem involves calculating the volume of a solid of revolution, which is formed when a two-dimensional region is rotated around a line that does not intersect the region.

Region R is defined as the area bounded by y=4, x=6, the y-axis, and the x-axis. The volume of the solid formed by rotating this region around the line y=-2 can be calculated using the washer method, which involves integrating over the area of concentric washers.

The general formula for the volume V of a washer is given by V = π∫[R2(x) - r2(x)]dx , where R(x) and r(x) are the outer and inner radii of the washers, respectively. In this case, the outer radius is R(x) = 4 - (-2) = 6 and the inner radius is r(x) = -2 - (-2) = 0.

Therefore, the volume V is:

V = π∫06[62 - 02 ]dx = π∫0636dx = 36π∫06dx = 36π[6] = 216π cubic units.

Answer:

The length of minor arc AB is 8

Step-by-step explanation:

In this question, we are asked to calculate the length of the minor arc.

Mathematically, the length of an arc can be calculated using the formula below;

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by the arc which is 120° according to the question, r is the radius of the circle which is 4 according to the question.

Plugging these values, we have

Length of minor arc AB = 120/360 × 2 × 22/7 × 4 = 8.34 = 8 to the nearest integer

The length of the minor arc AB in circle O with a radius of 4 and a central angle of 120 degrees, rounded to the nearest integer, is 8 units.

In the context of circle geometry, the length of a minor arc can be calculated by using the formula: arc length = (central angle/360) x (2π x radius). Given in the problem, we have a radius of 4 units and a minor arc with a measure of 120 degrees. Substituting the given values into the formula, the arc length becomes (120/360) x (2π x 4) which simplifies to (1/3) x (8π) = 8π/3 units.

However, the question asks for the minor arc length to the nearest integer. In this case, you would calculate 8π/3 which approximately equals 8.37758, but when rounded to the nearest integer, it would be 8.

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Answer:

The wrong sampling method was used.

Step-by-step explanation:

In convenience sampling, first few responses are considered and not all parameters are considered. This is the easiest method of sampling but least effective

(D) The wrong sample method was used.

The term 'sample' can mean -

Therefore, the correct answer if the problem is (D) the wrong sample method was used.

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Answer:

241 clients

Step-by-step explanation:

His problem can be solved using the principle of proportionality or rule three.

We can take advantage of the proportion between respondents who tell us the number of respondents and how many expect to go on vacation and the total number of workers, therefore:  

                         Respondents /// Whole company

Vacations                  21                          x

Total                          45                        516

then x equals:

x = (516 * 21) / (45)

x = 240.8

x = 241 clients

This means that approximately 241 clients expect to go on vacation throughout the company.

Answer:

241

Step-by-step explanation:

its the answer for khan academy

hope this helps

Answer:

F25 A B S14 BOTH S AND F IS 32IN THE MIDDLE

Step-by-step explanation:

14 study Spanish, 25 study French.

71 total students - 14 - 25 = 32

A 32 would be put in the middle where the circles overlap, which means 32 students are studying both languages.

B) only French would be the 25 shown in the circle marked F

C) 14 + 32 = 46 total students study Spanish

The approximate loudness of a rock concert with a sound intensity of 10⁻¹

is 110 Db.

Since the loudness L measured in decibel (Db) of a sound intensity I is given by

L = 10㏒(I/I₀) where

Since we want to determine  the approximate loudness of a rock concert with a sound intensity of 10⁻¹. So, I = 10⁻¹

So, substituting the values of the variables into L, we have

L = 10㏒(I/I₀)

L = 10㏒(10⁻¹/10⁻¹²)

L = 10㏒10¹¹

L = 11 × 10㏒10

L = 110㏒10

L = 110 (since ㏒10 = 1)

So, approximate loudness of a rock concert with a sound intensity of 10⁻¹

is 110 Db.

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Answer:110

Step-by-step explanation:

took the test

Answer:

10

Step-by-step explanation:

35/7 = 5, so the white marbles appears 5 times often.

If we have 2 green marbles and we want to maintain the same ratio of green to white marbles (so the same assumption that white appears 5 times often) we need to multiply that by 5.

Answer:

Sales Price = $21.00

New Price = $39.00

Step-by-step explanation:

Convert 35% into a decimal and multiply that with the $60.00. After you get the product, which is $21.00, you then need to subtract $21.00 from $60.00 and that gets you $39.00.

Answer:

The angle is 84 degrees

Step-by-step explanation:

Let's call the angle by 'x'.

the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.

If the supplement is sixteen times the complement, we can write the following equation:

(180 - x) = 16 * (90 - x)

180 - x = 1440 - 16x

16x - x = 1440 - 180

15x = 1260

x = 84

The angle is 84 degrees.

Answer:

84⁰

Step-by-step explanation:

Complement = 90 - x

Supplement = 180 - x

Given:

180 - x = 16(90 - x)

180 - x = 1440 - 16x

15x = 1260

x = 84

Answer:

0.68 * 62 = 42.16 kilos

Step-by-step explanation:

0.32 * 62 = 19.84

62 - 19.84 = 42.16 kilos

0.68 * 62 = 42.16 kilos

Answer:

42.16kg

Step-by-step explanation:

32% of 62= 19.84

62-19.84=42.16

Answer:

12 inches

Step-by-step explanation:

In this question, we are asked to calculate the width of a rectangle having a length 9 inches less than twice it’s width and given the area of the rectangle.

First, we identify that the length is 9 inches less than twice the width

meaning if length is l and width is w; then l = (2w-9) inches

Mathematically the area of the rectangle is l * w ; meaning w * (2w-9)

This has a value equal to 180

w * (2w-9) = 180

opening the bracket;

2w^2 -9w = 180

2w^2 -9w - 180 = 0

solving this quadratic equation;

w = 12 or -7.5

since width cannot be negative, w = 12 inches

Answer:

The width of the triangle is 18.65 inches

Step-by-step explanation:

From the question, we have;

Length, L = Width, W - 9

Also the area is given by

L × W = 180

Therefore, we have

(W - 9) × W= 180

W² - 9·W = 180

W² - 9·W - 180 = 0

Factorizing or solving with quadratic formula

[tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

a = 1

b = -9 and

c = -180

we get

(W + 9.65)(W-18.65) =0

Therefore W = - 9.65 or  18.65

Therefore, the Width, W = 18.65 and the length = W - 9 = 18.65 - 9 =9.65

The width of the triangle = 18.65 inches.

Write it as an equation:

X - 10 = 6x + 3

Now solve for x:

Subtract 3 from both sides:

x-13 = 6x

Subtract 1 x from both sides:

-13 = 5x

Divide both sides by 5:

x = -13/5

Answer:

x = -2.6.

Step-by-step explanation:

Let the number be x, then:

x - 10 = 6x + 3

x - 6x = 3 + 10

-5x = 13

x = -13/5

= -2.6.

Answer:

Therefore the probability that a pen from the first box and a crayon from the second box are selected is [tex]\frac5{16}[/tex]

Step-by-step explanation:

Probability:

The ratio of the number of favorable outcomes to the number all possible outcomes of the event.

[tex]Probability=\frac{\textrm{The number favorable outcomes}}{\textrm{The number all possible}}[/tex]

Given that,

Three plain pencils and 5 pens are contained by the first box.

Total number of pens and pencils is =(3+5)=8

The probability that a pen is selected from the first box is

=P(A)

[tex]=\frac{\textrm{The number pens}}{\textrm{Total number of pens and pencils}}[/tex]

[tex]=\frac{5}{8}[/tex]

A second box contains three colored pencils and three crayons.

Total number of pencils and crayons is =(3+3)=6

The probability that a crayon is selected from the second box is

=P(B)

[tex]=\frac{\textrm{The number of crayon}}{\textrm{Total number of crayons and pencils}}[/tex]

[tex]=\frac{3}{6}[/tex]

Since both events are mutually independent.

The required probability is multiple of the events

Therefore the required probability is

[tex]=\frac58\times \frac36[/tex]

[tex]=\frac5{16}[/tex]

The one that is an the inverse of y = 3 Superscript x is y = 3x is f-1(x) = 1/3x.

The use of the idea of inverse function to look for the solution is given below:

Note that, y = 3x

Then let f(x) = y = 3x

One will need to Switch x and y and as such, x = 3y

Then one should express y in terms of x and as such, y = 1/3 x

Since f(x) = y ⇒ x = f-1(y)

Then f-1(y) = 1/3x

Therefore, the inverse of y = 3x is f-1(x) = 1/3x.

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