A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t)=(493)4 ^1/2, where t represents the number of years from the time of introduction. What is the quadrupling-time for this population of deer?

Answer:

-85

Step-by-step explanation:

We are given the equation [tex]E^8_{n=1}[/tex][tex](-2)^{n-1}[/tex] and are asked to evaluate it.

This can be solved using the geometric sequence, but first we have to determine our "r", "n", and [tex]a_{1}[/tex].

Of course [tex]a_{1}[/tex] is equal to 1. Therefore,

[tex]a_{1[/tex] = 1

[tex]r=[/tex]

[tex]n=[/tex]

(-2) is the change per number in the sequence, therefore -2 is our "r".

[tex]a_{1[/tex] = 1

[tex]r=-2[/tex]

[tex]n=[/tex]

The number "8" on [tex]E^8_{n-1}[/tex] represents the "n". Therefore 8 is our "n".

[tex]a_{1}=1[/tex]

[tex]r=-2[/tex]

[tex]n=8[/tex]

Use the geometric sequence sum formula and substitute :

[tex]a_{1} \frac{1-r^n}{1-r}[/tex]

[tex]1* \frac{1-(-2)^8}{1-(-2)}[/tex]

[tex]1* \frac{1-(-2)^8}{1+2}[/tex]

[tex]1* \frac{1-256}{1+2}[/tex]

[tex]1* \frac{-255}{3}[/tex]

[tex]1 * -85[/tex]

[tex]-85[/tex]

Complete question

Asif wants to open a lemonade stand during a town fair. He buys a pitcher and lemonade concentrate from a store for this purpose. At the lemonade stand, the cost for each cup of lemonade will be the same. If Asif sells 32 cups of lemonade, he will have a profit of $0. If he sells 45 cups of lemonade, he will have a profit of $16.25. Determine the rate of change for a function that represents Asif's profit, y, in dollars, from selling x cups of lemonade.

Answer:

Step-by-step explanation:

The rate of Change for the function that determines profit :

Slope value, m ;

Slope, m = Rise / Run = (y2-y1) / (x2 - x1)

y2 = 16.25 ; y1= 0 ; x2 = 45 ; x1 = 32

m = (16.25 - 0) / (45 - 32)

m = 16.25 / 13

m = 1.25

Hence, the rate of change in in profit for selling x k cuos of lemonade = $1.25

Answer:

50%

Step-by-step explanation:

Answer:

You're lucky I have the dot plot, other wise this could not be answered.

Median: 7.5

Mean: 7.5

Yes, they are both 7.5.

Answer:

Subtraction

Step-by-step explanation:

In general, there are two things you can do with savings:

withdraw or deposit.

Withdraw essentially means to take out money and deposit is converse.

These two processes can be associated with the mathematical operations subtraction and addition respectively.

Answer:

2 x + (-2)

Step-by-step explanation:

You have two known points (1,0) and (0,-2)

the slope which is the coefficient of x = 2

and the y-intercept = -2

Answer:

177 ft below sea level

Step-by-step explanation:

282

10 x 12 = 120. This represents how man ft the hot air balloon rose.

282 - 120 = 162. Keep in mind your still below sea level.

162 + 15 = 177

You add 15 because the hot air balloon is going down 15 feet which adds to being below sea level. ( Your going deeper/lower)

Answer: P= 5 Hope I helped you

Step-by-step explanation:

[tex] {9}^{2} - 14 = \\ = 81 - 14 = \\ = 67[/tex]

Answer:

Step-by-step explanation:

You must find the value of m in order to evaluate the expression.

[tex]\sf{m^2-14}[/tex]

For m=9

[tex]\sf{9^2-14}[/tex]

Solve.

Use the order of operations.

PEMDAS

First, do exponents.

[tex]\sf{9^2-14}[/tex]

[tex]\sf{9^2=9*9=81}[/tex]

[tex]\sf{81-14}[/tex]

Subtract.

[tex]\sf{81-14=\boxed{\sf{67}}[/tex]

[tex]\Longrightarrow: \boxed{\sf{67}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

RT = 24

Step-by-step explanation:

Diagonals of rectangles bisects each other and equal in length (congruent) to each other.

Thus

US = RT

US = 2(RO)

4x - 16 = 2(x + 2)

4x - 16 = 2x + 4

2x = 20

x = 10

RT = 2(RO)

= 2(x+2)

= 2(10 + 2)

= 2(12)

= 24

Answer:

Answer is in picture and explanation below.

Step-by-step explanation:

Continuing from the picture,

Area of Metal base = Area of Bigger Circle - Area of Hollow Circle

=

[tex]1156\pi {mm}^{2} - 225\pi {mm}^{2} \\ = 931\pi {mm}^{2} [/tex]

Volume of Cylinder = Area of Metal base x Height (Length in this case)

=

[tex]931\pi {mm}^{2} \times 40 \\ = 37240\pi {mm}^{3} [/tex]

Answer:

Hence Brand B is the better buy, since the unit cost is smaller than A

Step-by-step explanation:

Given data

Brand A

Has a pack of 28 pencils for $5.29

unit cost

=5.29/28

=$0.19

Brand B

Has a pack of 48 pencils for $8.47

unit cost

=8.47/48

=$0.18

Answer:

3x - 5

Step-by-step explanation:

Given that f(x) = 5x - 2 and g(x) = 2x+3

f(x) - g(x) = 5x-2 - (2x+3)

Expand

f(x) - g(x)  = 5x - 2 - 2x - 3

Collect like terms

f(x) - g(x) = 5x - 2x -2-3

f(x) - g(x)  = 3x - 5

Hence the required answer is 3x - 5

Answer:

The line with a slope of 1/2 is steeper

Step-by-step explanation:

Here, we want to get which slope is steeper

mathematically, when we want to know the line that has a steeper slope, we compare the value of the slopes

The line with a slope that is of greater value will be steeper

Mathematically, 1/2 is a greater number than 1/3

That simply means 1/3 is less steep and thus, the line with the slope of 1/2 is the steeper line

The Triangle RST is missing, so i have attached it.

Answer:

A) TZ = 34

B) ZW = 17

C) SY = 69

D) XZ = 21

Step-by-step explanation:

To form the centroid, we see median drawn from the centre of all three sides.

Thus means the 3 sides are divided into 2 and as such;

XS = XT

YR = YT

WR = WT

Now, for median that forms centroid, the two parts are usually not the same length but instead in the ratio 2:1. That means one portion of the line segment is twice the length of the other.

Thus, by inspection of the given triangle, we can say that;

SZ = 2(ZY)

TZ = 2(ZW)

RZ = 2(XZ)

A) Now, we are given TW = 51

TW is made up of TZ and ZW

But since TZ : ZW = 2:1, it means that;

TZ = ⅔ × TW

TZ = ⅔ × 51

TZ = 34

B) From earlier, we saw that TZ = 2(ZW).

Thus; 34 = 2(ZW)

ZW = 34/2

ZW = 17

C) We are given ZY = 23.

From earlier, we saw that;SZ = 2(ZY)

Thus; SZ = 2(23)

SZ = 46

From the attached image we can see that;

SY = SZ + ZY

Thus;

SY = 46 + 23

SY = 69

D) We are given RZ = 42.

From earlier, we saw that;

RZ = 2(XZ)

Thus;

42 = 2(XZ)

XZ = 42/2

XZ = 21

Answer:

Increase in surface area =  126 cm²

Step-by-step explanation:

Surface area of the rectangular prism has the dimensions as

Length = 42 cm

Width = 35 cm

Height = 64 cm

Total surface area of the rectangular prism = 2(lb + bh + hl)

Here, l = Length of the box

b = Width of rectangular box

h = height

Total surface area = 2(42×35 + 35×64 + 64×42)

= 2(1470 + 2240 + 2688)

= 12796 cm²

If height is increased by by 1.5 cm, new height of the box = 64 + 1.5 = 65.5 cm

Surface area of the box = 2(42×35 + 35×65.5 + 65.5×42)

= 2(1470 + 2240 + 2751)

= 12922 cm²

Increase in surface area = 12922 - 12796

                                          = 126 cm²

Answer:

7m^2+13

Step-by-step explanation:

7m^2 + 10m + 3

Add the numbers ;10+3=13

=7m^2+13

Hope this helped!!!

Answer:

x=17

Step-by-step explanation:

There are two congruent angles so we can double the given values and set that equal to 360. After setting that equal to 360 you find that x is equal to 17, then you plug that into the original equations and get your angles

Complete Question:

Juanita makes leather lanyards to sell. She

charges a base fee and a cost per inch of

the finished lanyard. The line shows the

cost y for x inches of lanyard. Write an

equation for the line in slope-intercept

form.

*See attachement for the graph given

Answer:

y = ½x + 5

Step-by-step explanation:

Equation in slope-intercept takes the following form, y = mx + b

m = slope = change in y/change in x

b = y-intercept

Let's find m and b using the graph given

✔️Slope of the line using two points form the graph, say (0, 5) and (2, 6):

Slope (m) = ∆y/∆x = (6 - 5)/(2 - 0) = 1/2

Slope (m) = ½

✔️ y-intercept (b) is the y-coordinate of the point where the line intercepts the y-axis = 5. When y = 5, x = 0. Therefore,

b = 5

✔️To write the equation of the line, substitute m = ½ and b = 5 into y = mx + b:

y = ½x + 5

Step-by-step explanation:

[tex] - 5 - ( - 4) = - 5 + 4 = - 1 \\ - 4 - ( - 5) = - 4 + 5 = 1 \\ - 4 - (5) = - 4 - 5 = - 9 \\ 4 - ( - 5) = 4 + 5 = 9[/tex]

Therefore ranking them from least to most:

[tex] - 4 - (5) \\ - 5 - ( - 4) \\ - 4 - ( - 5) \\ 4 - ( - 5)[/tex]

Answer:

x = 24.75

Step-by-step explanation:

28/8 = 2x+3/15

420 = 16x +24

396 = 16x

x = 24.75

2(24.75) +3 =

49.5 + 3 = 52.5

Answer:

x=9

Step-by-step explanation:

let's find the scale factor of the enlargement ∆ABC of ∆ADE

k=28/20=7/5 or 1.4

Now k×|AD|=|AB|

Therefore

k×|DE|=2x+3

7/5×15=2x+3

21=2x+3

21-3=2x

2x=18

x=9

let me know if I was right

Answer:

m =  [tex]\frac{4}{3}[/tex]

Answer: 32

Step-by-step explanation: 4/2=2 16*2=32

Answer:

Step-by-step explanation:

Root:

n≈0.00833333 m + 0.666667

Root for the variable n:

n≈-0.0833333 (-0.1 m - 8)

Derivative:

d/dm(0.1 m + 8 - 12 n) = 0.1

Indefinite integral:

integral(8 + 0.1 m - 12 n) dm = 0.05 m^2 - 12 m n + 8 m + constant

Definite integral over a disk of radius R:

integral integral_(m^2 + n^2<R^2)(0.1 m - 12 n + 8) dm dn = 8 π R^2 + 0

Definite integral over a square of edge length 2 L:

integral_(-L)^L integral_(-L)^L (8 + 0.1 m - 12 n) dn dm = 32 L^2 + 0

Answer:

3) 81.5 in²

Steps:

D = 32/π = 10.18..

r = 10.18/2 = 5.09

A = π × r²

A = π × 25.93

A = 81.48 ≈ 81.5 in²

in one formula:

A = π(32/π × 1/2)²

A = 81.5 in²

Answer:5.09 sq. inches

Step-by-step explanation:

C = 2π × r

32 = 2π × r

[tex]\frac{32}{2\pi }[/tex] = r

r = 5.09295817894, rounded equals 5.09, so, option 1 is correct

Answer:

-421 feet

Step-by-step explanation:

If she started at 243 feet, subtract 782 feet which is -539 feet. Then add 118 feet which is -421 feet. This is how my sister did it so I hope it helps!