The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?


F.2084
G.2044
H.2043
J.2085

Answer:

42

Step-by-step explanation:

(adjacent straight angles sum up to 180)

3x+54=180

x=42

Answer:

50

Step-by-step explanation:

The given angles in the triangle are vertically opposite angles. Hence;

9x - 4 = 8 + 7x

Collect the like terms

9x - 7x = 8 + 4

2x = 12

x = 12/2

x = 6

Get the bolded angle

Bolded angle= 8 + 7x

Blded angle = 8 + 7(6)

Bolded angle = 8 + 42

Bolded angle = 50

Answer:

7 boxes

Step-by-step explanation:

We can use ratios to solve

12 bars            42 bars

----------    = ---------------

2 boxes      x boxes

Using cross products

12x = 2 *42

12x = 84

Divide by 12

12x/12 = 84/12

x = 7

Answer:

Step-by-step explanation:

No. 1 “The printing of more

currency notes will increase inflation.”

9514 1404 393

Answer:

Step-by-step explanation:

a) Let p and d represent the prices of a bag of popcorn and a drink, respectively.

Mohamed's purchase is ...

  2p +3d = 18.25

Miguel's purchase is ...

  4p +2d = 27.50

__

b) We can subtract half the second equation from the first to get an equation for the cost of a drink.

  (2p +3d) -1/2(4p +2d) = (18.25) -1/2(27.50)

  2d = 4.50 . . . . . . simplify

  d = 2.25 . . . . . . divide by 2

  4p +2(2.25) = 27.50 . . . . substitute for d in the second equation

  4p = 23.00 . . . . . . . . . subtract 4.50

  p = 5.75 . . . . . . . . . divide by 4

The cost of a bag of popcorn is $5.75; the cost of a drink is $2.25.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator does a nice job of graphing these equations.

__

The very steep slope suggests the graph will need somewhat different vertical and horizontal scales in order to show anything useful.

Answer:

<5 and <7 are corresponding angles.

Step-by-step explanation:

<5 and <7 are corresponding angles.  They are on the same side of the transversal and on the same position on each of the parallel lines

Answer:

[tex]\$32[/tex]

Step-by-step explanation:

Let the cost of the game be [tex]x[/tex]. Since one-fourth of the cost of the game is equal to 8 dollars, we have the following equation:

[tex]\frac{1}{4}x=8[/tex]

Multiply both sides by 4 to isolate and solve for [tex]x[/tex]:

[tex]x=8\cdot 4=\boxed{\$32}[/tex]

Answer:

1.333333333333

Step-by-step explanation:

Answer:

y = (-1/5)x + 23/5

Step-by-step explanation:

Given:

Two points;

(-2,5) and (3,4)

Find:

Equation of slope

Computation:

y = mx + b

5 = m(-2) + b

5 = -2m + b .......... Eq1

4 = m(3) + b

4 = 3m + b .......... Eq2

Eq2 - Eq1

-1 = 5m

m = -1/5

5 = -2m + b

5 = -2(-1/5) + b

5 = 2/5 + b

b = 23/5

y = mx + b

y = (-1/5)x + 23/5

Answer:

Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times

Step-by-step explanation:

The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.

The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.

hence, option B is correct

Answer:

hey um I cant see the picture

Answer:

a. 0.302 dB/s

b. 2.34 dB/s

c. 1.24 dB/s

Step-by-step explanation:

a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.

Since P = 10log(W/W₀), its rate of change with respect to time is

dP/dt = dP/dW × dW/dt

dP/dW = d[10logW - 10logW₀]/dt

dP/dW = d[10lnW/2.303 - 10logW₀]/dt

= 10/2.303W - 0

= 10/(2.303W)

dP/dt = dP/dW × dW/dt

dP/dt = 10/(2.303W) × dW/dt

Since dW/dt = 0.5 when W = 7.2, then

dP/dt = 10/(2.303 × 7.2) × 0.5

dP/dt = 10/16.5816 × 0.5

dP/dt = 0.603 × 0.5

dP/dt = 0.302 dB/s

b) If the variable sound power W is given by W = t² + t + 1, find the rate of change of the sound pressure P, at time t = 3s.

Since P = 10log(W/W₀), its rate of change with respect to time is

dP/dt = dP/dW × dW/dt

dP/dW = d[10logW - 10logW₀]/dt

dP/dW = d[10lnW/2.303 - 10logW₀]/dt

= 10/2.303W - 0

= 10/(2.303W)

and dW/dt = d(t² + t + 1)/dt = 2t + 1

So, dP/dt = dP/dW × dW/dt

dP/dt = 10/(2.303W) × (2t + 1)

dP/dt = 10(2t + 1)/(2.303W)

dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]

we then substitute t = 3 into the equation

dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]

dP/dt = 10(2(3) + 1)/[2.303((3)² + 3 + 1)]

dP/dt = 10(6 + 1)/[2.303(9 + 3 + 1)]

dP/dt = 10(7)/[2.303(13)]

dP/dt = 70/29.939

dP/dt = 2.34 dB/s

c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)

Since dP/dt = dP/dW × dW/dt and dP/dW = 10/(2.303W) and W = cos(0.2t), dW/dt = -0.2sin(0.2t)

So, dP/dt = dP/dW × dW/dt

dP/dt = 10/(2.303W) × -0.2sin(0.2t)

dP/dt = -20sin(0.2t)/(2.303W)

dP/dt = -20sin(0.2t)/(2.303cos(0.2t))

dP/dt = -20tan(0.2t)/2.303

when t = 15, we have

dP/dt = -20tan(0.2 × 15)/2.303

dP/dt = -20tan3/2.303

dP/dt = -20 × -0.1425/2.303

dP/dt = 2.8509/2.303

dP/dt = 1.238

dP/dt ≅ 1.24 dB/s

Answer:

4080 gm

Step-by-step explanation:

To bake one cake, it will take us 650 gm flour and 30 gm sugar. When we add both of them together, it gives 680 gm (650+30). But this is only for one cake. To find the total amount of flour and sugar needed to bake 6 cakes, we will have to multiply 680 by 6. That will give you 4080 gm which is your final answer.

Answer:

B. L BAT = L CAT

Step-by-step explanation:

__________

Answer:

For example, 6(1001) + 3(110) = 6006 + 330 = 6336 is a palindrome. Since 11 is a factor of both 1001 and 110, we conclude that all four digit palindromes are divisible by 11.

Answer:

The answer is "9 and 7".

Step-by-step explanation:

Given:

[tex]A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right][/tex]

Using formula:

[tex]|A-\lambda \cdot I|= 0\\\\[/tex]

[tex]\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\[/tex]

[tex]\to \lambda=7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda=9\\\\[/tex]

Answer:

m∠A = 32°

Step-by-step explanation:

8^2 = 12^2 + 15^2 - 2*12*15*cosA

Answer:

B

Step-by-step explanation:

did it on edge

Answer:

1/3a

Step-by-step explanation:

[tex] \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} [/tex]

Answer:

16

Step-by-step explanation:

From the question given above, the following data were obtained:

1 = 1

2 = 4

3 = 9

4 =?

Observing the data, we can see that the numbers on the right side are simple the squares of the numbers on the left side. This is illustrated below:

1 = 1² = 1

2 = 2² = 4

3 = 3² = 9

Thus, we shall use the same logic to obtain that of 4. This is illustrated below:

4 = 4² = 16

Thus the answer to the question is 16.

Step-by-step explanation:

everything can be found in the picture

Answer: [tex]6x^3 +30x^2 +4x+20[/tex]

Step-by-step explanation:

[tex](6x^2 +4)(x+5)\\\\ =6x^3 +30x^2 +4x+20[/tex]

Answer:

7 square root 9^4

Step-by-step explanation:

Answer:

quadratic formula is ur answer for letter B

Check the picture below.

so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so

[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]

now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena

[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]

Answer:

3 feet

Step-by-step explanation:

Let x be the width of the grass strip.

So the length of the grass strip=18+2x

Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2

But the available grass seed is enough for 234 ft squared

4x^2+66x=234

4x^2+66x-234=0

x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)

x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8

x={-66+-(90)}/8

Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)

So the width of the strip is 3 feet.

Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet

Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet

Therefore the strip is 3 feet wide

Answer:

1

Step-by-step explanation:

Slope = change in y over change in x

If you look at the graph as y goes up 1 x goes up 1

So slope = 1/1 or just 1

Answer:

m=1

Step-by-step explanation:

Hi there!

We're given the graph of a line and we need to find the slope of the line

There are many ways to do this, but the easiest is to calculate it from two points

The formula for the slope (m) calculated from 2 points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points

So we can take 2 points from the graph of the line to find the slope

For example, let's take (-1,0) and (0,1)

Let's label their values to avoid any confusion before we substitute their values into the formula

[tex]x_{1}[/tex]=-1

[tex]y_{1}[/tex]=0

[tex]x_{2}[/tex]=0

[tex]y_{2}[/tex]=1

now substitute into the formula *remember: we have SUBTRACTION in the slope formula

m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

substitute

m=[tex]\frac{1-0}{0--1}[/tex]

simplify

m[tex]\frac{1}{0+1}[/tex]

simplify again

m=[tex]\frac{1}{1}[/tex]

divide

m=1

Therefore the slope of the line is 1

Hope this helps! :)

Answer:

-3/2

Step-by-step explanation:

Additive inverse of 2 = -2

Multiplicative inverse of 2 = ½

→ Sum = -2 + ½

→ Sum = (-4 + 1)/2

→ Sum = -3/2

Answer:

B-100 If the price of tacos is $1.75, th consumers will buy 100 tacos

Answer:

x+4=72

x=72-4

x=68

Step-by-step explanation:

let x be one number and 4 be anothe number then sum of the two number be x and 4