Cory is a bird-watcher. He estimates that 30% of the birds he sees are American robins, 20% are dark-eyed juncos, and 20% are song sparrows. He designs a simulation. Let 0, 1, and 2 represent American robins Let 3 and 4 represent dark-eyed juncos. Let 5 and 6 represent song sparrows. Let 7, 8, and 9 represent other birds The table shows the simulation results. According to the simulation, what is the probability that at least one of the next five birds he sees is a song sparrow?

A.)0.35
B.)0.2
C0.65
D.)0.5​

there is no drawing how should I do

Answer:

the answer should be 1,600,000

Step-by-step explanation:

hope this helps ya!!

Answer:

Step-by-step explanation:

1,5x0,000   x holds the place that you'll want to note if it's 5 or larger, to determine if you round up or down.   Because in the problem you've been given, it's an 8,   so round up

1,600,000  is the answer then.  

[tex]I=\displaystyle \int ^{\pi}_{\tfrac{\pi}3} \dfrac{ \sin x}{1 + \cos^2 x} dx\\ \\\\\text{let,}\\\\~~~~~u=\cos x\\\\\implies \dfrac{du}{dx} =-\sin x\\ \\\implies \sin x~~ dx = -du\\\\\text{When}~~ x = \pi , ~~ u = \cos \pi = -1\\\\\text{When}~~ x = \dfrac{\pi}3 , ~~u = \cos \dfrac{\pi}3 =\dfrac 12\\ \\\\I =- \displaystyle \int ^{-1}_{\tfrac 12} \dfrac{du}{1+u^2}\\\\\\[/tex]

  [tex]=\displaystyle \int ^{\tfrac 12}_{-1} \dfrac{du}{1+u^2}~~~~~~~~~~;\left[\displaystyle \int^{a}_b f(x) dx = - \displaystyle \int^{b}_a f(x) dx ,~ b < a\right]\\\\\\=\left[\tan^{-1} u \right]^{\tfrac 12}_{-1}~~~~~~~~;\left[ \ddisplaystyle \int \dfrac{dx}{ 1+ x^2} = \tan^{-1} x + C \right]\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \tan^{-1} 1\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \dfrac{\pi}4 \\\\\\=1.249[/tex]

Answer:

A = 5 [tex]\frac{5}{6}[/tex] ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ) , then

A = [tex]\frac{1}{2}[/tex] × 5 × 2 [tex]\frac{1}{3}[/tex] ← convert to improper fraction

   = [tex]\frac{5}{2}[/tex] × [tex]\frac{7}{3}[/tex]

   = [tex]\frac{5(7)}{2(3)}[/tex]

   = [tex]\frac{35}{6}[/tex]

   = 5 [tex]\frac{5}{6}[/tex] ft²

Answer:

24

Step-by-step explanation:

Use the triangle area formula: A=1/2 (base)(height)

Plug in what we know: 216=1/2(18)(h)

Solve for h: (1/2)(18)=9.

216/9=24.

So, h=24

To check, plug it into the formula: 1/2(18)(24)= 216

Answer:

3x-5?

Step-by-step explanation:

I hope im right.

radius= 7 ft

the circumference of the circle.

[tex]c = 2\pi \: r[/tex]

[tex]c = 2 \times \pi \times 7[/tex]

[tex]c = 43.9823[/tex]

[tex]c = 43.98 \: ft[/tex]

therefore, the circumference of the circle is 43.98 ft

Answer:

117/108

Step-by-step explanation:

First, let's find the area of the shaded parts. Since the shaded squares and triangles are the same size, then all shaded squares have sides 3 in. by 3 in. because the shaded square in the middle has sides 3 in. by 3 in.

We can also see that the shaded triangles have legs 6 in. and 6 in. because one of the shaded triangles in the figure are labeled 6 in by 6 in.

Now we can find the area of the shaded square and triangle (area of a square is side^2 while the area of a triangle is base*height/2).

Shaded Square Area: 3^2 = 9 in^2

Shaded Triangle Area: 6*6/2 = 18 in^2

There are 5 shaded squares and 4 shaded triangles, so we can determine the shaded area now:

Shaded Area: 9*5 + 18*4 = 45 + 72 = 117 in^2

Now we need to find the area of the white rectangles and the area of the white triangles. We can see that the sides of the white rectangles are 6 in. and 3 in. We can also see that the sides of the white triangles are 3 in and 3 in.

Now we can find the area of the white rectangle and the white triangle.

White Triangle Area: 3*3/2 = 9/2 = 4.5 in^2

White Rectangle Area: 3*6 = 18 in^2

There are 4 white rectangles and 8 white triangles, so we can determine the white area now:

White Area: 4*18 + 8*4.5 = 72 + 36 = 108 in^2

The ratio of the area of the shaded pieces to the area of the white pieces is 117/108.

Answer:

5mm

Step-by-step explanation:

Because, the radius is: It is the line between any point on the circle and the midpoint of the circle..

Answer:

the answer to 2/5x+7=-11 is X=-45

Step-by-step explanation:

Multiply both sides by 5 to get rid of the division giving you 2x+35=-55

isolate the x Value by moving all non x numbers to one side giving you 2x=-90

divide by 2 to get X alone giving you x=-45

Answer:

x = 2

y = 15

Step-by-step explanation:

As the triangle is split with a line that is parallel to the base:

[tex]\implies x:6=6:18[/tex]

[tex]\implies \dfrac{x}{6}=\dfrac{6}{18}[/tex]

[tex]\implies x=\dfrac{6\cdot 6}{18}[/tex]

[tex]\implies x=\dfrac{36}{18}[/tex]

[tex]\implies x=2[/tex]

Similarly:

[tex]\implies y:20=6 : (6+x)[/tex]

[tex]\implies y:20=6:8[/tex]

[tex]\implies \dfrac{y}{20}=\dfrac68[/tex]

[tex]\implies y=\dfrac{6 \cdot 20}{8}[/tex]

[tex]\implies y=\dfrac{120}{8}[/tex]

[tex]\implies y=15[/tex]

Answer:

x= 5.18

y= 16.97

Step-by-step explanation:

Solve Y first-

trigonometric theorems-

[tex]c^2 =a^2 + b^2\\\\b^2 =c^2 - a^2[/tex]

[tex]y^2 =18^2-6^2 \\y^2 =324 - 36\\y^2= 288\\\sqrt{2} = \sqrt{288} \\ y=16.97[/tex]

solve x-

20-16.97=3.03

x=5.18

(I'm not sure if the answers are correct. I tried my best. I was confused to solve x though. )

Answer:

$2.25 per lb

Step-by-step explanation:

x = 4.50/2

x = $2.25 per lb

Answer:

Step-by-step explanation:

what does each block mean

Answer:

The answer is C and D.

Step-by-step explanation:

(-4)^1/2 = undefined

(-16)^1/4 = undefined

(-32)^1/5 = -2

(-8)^1/3 = -2

Answer:

9÷10

Step-by-step explanation:

9÷10=0.9

Answer:

8

Step-by-step explanation:

8+12+4+3+14+1+9+13=64, 64/8=8

Answer:

44.6

Step-by-step explanation:

First, to answer this question, we need to find the mean of this data set. When finding the mean, you use the same process you use when averaging.

So we would do: 8 + 12 + 4 + 3 + 14 + 1 + 9 + 13/8

Our new fraction turns into 64/8, which we can then divide to give us 52.625. We can round up our new number to give us 52.6

We now need to find the absolute value of the difference between each data value and mean. In simple terms, we use the answer we got from our fraction and subtract it from each number in our cluster of numbers/data set. Keep in mind when subtracting you will get some negative numbers, but in this scenario we take away any negative sings, so we don't end up with any negative numbers.

8 - 52.6 = -44.6 = 44.6

12 - 52.6 = -40.6 = 40.6

4 - 52.6 = -48.6 = 48.6

3 - 52.6 = -49.6 = 49.6

14 - 52.6 = -38.6 = 38.6

1 - 52.6 = -51.6 = 51.6

9 - 52.6 = -43.6 = 43.6

13 - 52.6 = -39.6 = 39.6

Finally, we need to to the same process we used in our first step, just use the new numbers we have instead of our old numbers.

This gives us 356.8/8, which when divided, will leave us with 44.6.

Therefore, our answer is 44.6

Answer:

The answer is c

Step-by-step explanation:

Answer:

Given equation:  [tex]y=x^2+1[/tex]

Therefore, we can say that any point on the curve has the coordinates [tex](a, a^2+1)[/tex]  (where a is any constant)

To find the gradient of the tangent to the curve at any given point, differentiate the equation.

Given equation:

[tex]y=x^2+1[/tex]

[tex]\implies \dfrac{dy}{dx}=2x[/tex]

Therefore, the gradient at point [tex](a, a^2+1)[/tex] is [tex]2a[/tex]

Using the point-slope form of linear equation, we can create a general equation of the tangent at point [tex](a, a^2+1)[/tex]:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\ \implies y-(a^2+1)& =2a(x-a)\end{aligned}[/tex]

[tex]\implies y=2ax-2a^2+a^2+1[/tex]

[tex]\implies y=2ax-a^2+1[/tex]

Given that the tangents pass through point (-1, -3), input this into the general equation of the tangent:

[tex]\begin{aligned}y &=2ax-a^2+1\\ \implies -3 & =2a(-1)-a^2+1\end{aligned}[/tex]

[tex]\implies 0=-2a-a^2+1+3[/tex]

[tex]\implies a^2+2a-4=0[/tex]

Use the quadratic formula to solve for a:

[tex]\implies a=\dfrac{-2\pm\sqrt{2^2-4(1)(-4)}}{2(1)}[/tex]

[tex]\implies a=\dfrac{-2\pm2\sqrt{5}}{2}[/tex]

[tex]\implies a=-1 \pm \sqrt{5}[/tex]

Input the found values of a into the general equation of the tangent to create the equations of the two lines:

[tex]\begin{aligned}a=-1+\sqrt{5}\implies y & =2(-1+\sqrt{5})x-(-1+\sqrt{5})^2+1\\ y & =(-2+2\sqrt{5})x-(6-2\sqrt{5})+1\\ y & =(-2+2\sqrt{5})x+2\sqrt{5}-5 \end{aligned}[/tex]

[tex]\begin{aligned}a=-1-\sqrt{5}\implies y & =2(-1-\sqrt{5})x-(-1-\sqrt{5})^2+1\\ y & =(-2-2\sqrt{5})x-(6+2\sqrt{5})+1\\ y & =(-2-2\sqrt{5})x-2\sqrt{5}-5 \end{aligned}[/tex]

Therefore, the equations of the two lines that pass through the point (-1, -3) and are tangent to the graph of [tex]y=x^2+1[/tex] are:

[tex]y=(-2+2\sqrt{5})x+2\sqrt{5}-5[/tex]

[tex]y=(-2-2\sqrt{5})x-2\sqrt{5}-5[/tex]

We are asked to solve the integral:

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}}[/tex]

Re write as

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)\{1-\tan (x)\}}}[/tex]

Using (1/cos x) = sec(x), we have

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\sec^{2}(x)dx}{1-\tan (x)}}[/tex]

Now, substitute 1 - tan (x) = t, so that -dt = sec²(x) dx

[tex]{:\implies \quad \displaystyle \sf -\int \dfrac{1}{t}dt}[/tex]

[tex]{:\implies \quad \sf log|t|+C}[/tex]

[tex]{:\implies \quad \boxed{\displaystyle \bf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}=-log|1-\tan (x)|+C}}[/tex]

Where, C is any Arbitrary Constant

Answer:

Look up the website for those answers, I've gotten those type of worksheets before.

Step-by-step explanation:

There should be a pdf or document of the answers and if you can't find it I'll help you!

Answer:

Step-by-step explanation:

The rate of change is defined as the derivative of the function, or also known as the slope. The derivative here would be 3. Another function which has the same rate of change would be any function with a slope of 3. A few example are:

f(x) = 3x + 1

f(x) = 3x + 2

Answer:

x=8

Step-by-step explanation:

If you combine like terms (5x and 4x) it would become:

x+9 = 17

subtract 9 on both sides

x=8

Answer:

8

Step-by-step explanation:

Answer:

12/5 is the answer of your questions

thank you!!

Answer:

(x - 4)^2 + (y - 6)^2 = 100

Answer:

  D.  y = 1.5x +5

Step-by-step explanation:

The offered answer choices are equations in slope-intercept form. The constant in the equation is the y-intercept, the value of distance when time is zero.

   y = mx +b . . . . m is slope; b is y-intercept

__

The table tells you that the distance value is 5 when the time value is 0. In the equation, that means ...

  b = 5

Only one answer choice matches:

  y = 1.5x +5

Answer:

  radius: 14.96 in

  length: 47 in

Step-by-step explanation:

The dimensions of the package with maximum volume can be found by differentiating the volume function, subject to the constraint on the dimensions.

__

The volume of the cylindrical package is ...

  V = πr²h

The constraint on the dimensions is ...

  circumference + length = 141 inches

  2πr +h = 141 . . . . . at maximum volume

Solving the second equation for h, we can write the volume function in terms of r alone:

  h = 141 -2πr

  V = πr²(141 -2πr) . . . . substitute for h

  V = 141πr² -2π²r³ . . . eliminate parentheses

__

Differentiating with respect to radius, we find the radius at maximum volume must satisfy ...

  V' = 282πr -6π²r² = 0

Dividing by 6πr, we can simplify this to ...

  47 -πr = 0

  r = 47/π ≈ 14.96 . . . . inches (radius)

  h = 141 -2πr = 47 . . . inches (length)

This is about optimization problems in mathematics.

Dimensions; Height = 48 inches; Radius =  48/π inches

We are told the combined length and girth is 144 inches.

Girth is same as perimeter which is circumference of the circular side.

Thus; Girth = 2πr

If length of cylinder is h, then we have;

2πr + h = 144

h = 144 - 2πr

Now, to find the dimensions at which the max volume can be sent;

Volume of cylinder; V = πr²h

Let us put 144 - 2πr for h to get;

V = πr²(144 - 2πr)

V = 144πr² - 2π²r³

Differentiating with respect to r gives;

dV/dr = 288πr - 6π²r²

Radius for max volume will be when dV/dr = 0

Thus; 288πr - 6π²r² = 0

Add 6π²r² to both sides to get;

288πr = 6π²r²

Rearranging gives;

288/6 = (π²r²)/πr

48 = πr

r = 48/π inches

Put 48/π for r in h = 144 - 2πr to get;

h = 144 - 2π(48/π)

h = 144 - 96

h = 48 inches

Step-by-step explanation:

Answer:

It is larger by [tex]4*10^2[/tex]  times

Step-by-step explanation:

You use exponential division for this problem

first, divide 8 by 2

8/2 = 4

Then, look at 10^9 and 10^7

The bases of those numbers are the same, so you can just subtract the exponents since you're dividing.

[tex]10^9 / 10^7 = 10^{9-7} = 10^2[/tex]

Combine those two together to get:

4 * 10^2