Part of the population of 6,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 6 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.

Answer:

22, 24, 26, 28, 30

Step-by-step explanation:

If the sum of 5 numbers is 130, that means the average of these numbers is 26.

If it is the average then it is the middle, or the third number. The two numbers before it would then be 22 and 24 by subtracting twos, and the two numbers after it would be 28 and 30 by adding twos.

22, 24, 26, 28, 30

Answer:

22,24,26,28,30

Step-by-step explanation:

I call the unknown number x

I write consecutive numbers in terms of x.

x+ (x+2) + (x+4) + (x+6) + (x+8) = 130

5x + 20 = 130

5x = (130 - 20)

5x = 110

x = 22 = smallest even number

x + 2 = 24 = second even number

x +4 = 26

x + 6 = 28

x + 8 = 30

Here Mass is constant

Using Newtons s law

[tex]\\ \sf \longmapsto F=ma[/tex]

[tex]\\ \sf \longmapsto \dfrac{F}{a}=m[/tex]

[tex]\\ \sf \longmapsto \dfrac{F_1}{a_1}=\dfrac{F_2}{a_2}[/tex]

[tex]\\ \sf \longmapsto \dfrac{8}{4}=\dfrac{F_2}{3}[/tex]

[tex]\\ \sf \longmapsto F_2=\dfrac{24}{4}[/tex]

[tex]\\ \sf \longmapsto F_2=6N[/tex]

Answer:

F = 6N

Step-by-step explanation:

Equation

F = ka

F - force

k - constant of proportionality

a - acceleration

Step 1 - find k  

8N=k*4m/s^2

k=2

Step 2 - find F

F=2*3m/s^s

F=6

Answer:

Clarissa will take 10 hours by herself

Step-by-step explanation:

Let s = time for shawna

s-5 = time for clarissa

The formula for determining the time is

1/a + 1/b = 1/c  where a and b are the times alone and c is the time together

1/s + 1/(s-5) = 1/6

Multiply each side by 6s(s-5) to clear the fractions

6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)

Distribute

6(s-5) + 6s = s(s-5)

Distribute

6s -30 +6s = s^2 -5s

Combine like terms

12s -30 = s^2 -5s

Move everything to the right

0 = s^2 -5s -12s +30

0 = s^2 -17s +30

Factor

0 = ( s-15) (s-2)

Using the zero product property

s-15 =0   s-2 =0

s =15     s=2 ( This is not a reasonable answer since it is less than the time together)

s=15

s-5 = 10

Clarissa will take 10 hours by herself

Step-by-step explanation:

If r and h are the radius and height of the cylinder, then its surface area A is given by :

[tex]A=2\pi r^2+2\pi rh[/tex] ....(1)

We need to find the cylinder's height in terms of its radius and surface area. Subtracting [tex]2\pi rh[/tex] on both sides, we get :

[tex]A-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\A-2\pi r^2=2\pi rh[/tex]

Dividing both sides by [tex]2\pi r[/tex]. So,

[tex]\dfrac{A-2\pi r^2}{2\pi r}=\dfrac{2\pi rh}{2\pi r}\\\\h=\dfrac{A-2\pi r^2}{2\pi r}[/tex]

Hence, this is the required solution.

Answer:

x=144°

Step-by-step explanation:

To work out x, you have to find the other angle in the triangle.

Angles in triangles always add up to 180°, so you would have to add up the 2 angles you have and take it away from 180°.

48+96=144°

180-144=36°

Then, to find x, you have to do 180-36 because angles on a straight line always add up to 180°.

180-36=144°

x=144°

Hope this helps :)

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm \: x \: = \: 96 \degree \: + \: 48 \degree }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm \: x \: = \: 144 \degree }}} \\ [/tex]

Answer:

67 degrees (Answer 2)

Step-by-step explanation:

These two angles must sum up to 180 degreess because they are supplementary.  Then:

7x + 11 + 14x + 1 = 180, or

21x + 12 = 180, or

21x = 168

Solving for x, we divide both sides by 21.  This results in x = 8.

The measure of the smaller angle is 7x + 11, which here is 7(8) + 11 = 67 degrees (Answer 2).

Answer:

a ≥ -1/3

Step-by-step explanation:

The square root must be greater than or equal to zero

sqrt(1+3a /25) ≥ 0

Square each side

(1+3a)/25≥ 0

Multiply each side by 25

1+3a≥0

Subtract 1

3a ≥ -1

Divide by 3

a ≥ -1/3

Answer/Step-by-step explanation:

a. The sides of ∆ABC can be labelled as follows, taking θ as the reference point.

Adjacent = side AB

Opposite = side BC

Hypotenuse = side AC

b. I. "<B is an acute angle" => FALSE. It is a right angle (90°)

II. "The side opposite to <C is BC" => FALSE. The side opposite to <C is AB.

III. The side adjacent to <A is AB => TRUE

IV. The side opposite to <B is not the longest. => FALSE. It is the hypotenuse and the longest side.

c. Cos θ = [tex] \frac{adjacent}{hypotenuse} = \frac{AB}{AC} [/tex]

Tan θ = [tex] \frac{opposite}{adjacent} = \frac{BC}{AB} [/tex]

d. Sin C = [tex] \frac{opp}{hypo} = \frac{AB}{AC} [/tex]

Cos C = [tex] \frac{adjacent}{hypotenuse} = \frac{BC}{AC} [/tex]

Tan C = [tex] \frac{opp}{adjacent} = \frac{AB}{BC} [/tex]

Answer:

AA Postulate

Step-by-step explanation:

The bottom lines are parallel. In this case they are also congruent. Combined with the top angle this makes in AA postulate

==================================================

Explanation:

19 = h/3 - 8

19+8 = h/3 - 8+8  .... see note 1

27 = h/3

h/3 = 27

3*(h/3) = 3*27 .... see note 2

h = 81

----------

Answer:

3,6

Step-by-step explanation:

Step-by-step explanation:

Total Surface Area of original cylinder

= (2×(22/7)×9)(9+24)

=18×22/7×33

=1,866.8

Total Surface Area of new cylinder

=(2×(22/7)×9/3)(9/3+24/3)

=(2×(22/7)×3)(3+8)

=6×22/7×11

=207.4

Change or Ratio of org. cylinder to new cylinder

=1,866.8/207.4

=9.0009

6 cm from what im seeing

Answer: 7 cm

Step-by-step explanation:

Answer:

=k=0.25h-7/12

Step-by-step explanation:

4(h-3k)=h+7

=4h-12k=h+7

collecting like terms and leaving characters with k on 1 side, we get;

12k=3h-7

=k=0.25h-7/12

Answer:

(0,-3)

Step-by-step explanation:

2x-y = 3

x+2y = -6

Multiply the first equation by 2 so we can eliminate y

2(2x-y =3)

4x -2y = 6

Add this to the second equation

4x -2y = 6

x+2y = -6

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

5x +0y = 0

x = 0

Now find t

x+2y = -6

0+2y = -6

2y =-6

Divide by 2

y = -3

Answer:

Step-by-step explanation:

Let's try to eliminate y.

First we multiply the first equation by 2,

4x - 2y = 6

x + 2y = -6

Then we add them together

5x = 0

x = 0

Now we plug x into the first equation,

4(0) - 2y = 6

-2y = 6

y= -3

Now we plug x into the second equation,

0 + 2y = -6

2y = -6

y = -3

So our answer is,

(0,-3)

Answer:

(7,-4) ; 12

Step-by-step explanation:

Basically, three corners of a rectangle are already on the graph. If you put a dot at (7,-4), that is the last corner(vertex) that finishes the rectangle

Then to find base of the rectangle, you find the length of the longer side, (the distance between the x coordinates). So you would subtract -5 from 7 and get 12, and 12 is the length of your base.

Answer:

Please see the attached images

Step-by-step explanation:

Answer:

y = (-2)(3)x

Step-by-step explanation:

Answer:

x is 6

Step-by-step explanation:

6x -28 = 4x - 16

6x = 4X + 12

2X = 12

X = 6

Answer:

The equation of the perpendicular line (PR) to line PQ is; y = -0.5x - 1.5

Step-by-step explanation:

The line is perpendicular to line adjoined by points P(-3,0) and Q(0,6)

The slope of line PQ is;

Slope = change in y ÷ change in x = [tex]\frac{6 - 0}{0 -- 3}[/tex] = 2

The product of slopes of two perpendicular lines = -1

Hence the slope of line PR = -1 ÷ slope of line PQ = -1/2

Taking another point (x,y) and point P(-3,0) the equation of line PR is;

Slope = [tex]\frac{y - 0}{x - -3} = -\frac{1}{2}[/tex]

Cross-multiplying gives;

2y = -x - 3 , y = -x/2 - 3/2 , y = -0.5x - 1.5

Answer:

turn the 10 to 5 and divide 250 by 2 which will give you your l and w subract 2 from your l and add 2 to your  your w

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the area is to be 250 ft^2, one possible set of dimensions would be

25 ft by 10 ft.

If 1 unit on the coordinate plane represents 10 feet, then the dimensions of the drawing would be 2.5 units by 1 unit.

Answer:

a. -2

b. s = 2 and y = -5

c. (2.5, -9)

d. -7x - 2

Step-by-step explanation:

a. In the image, I have used rise over run, which is -8/4 or -2.

b. slope formula is mx + b = y, where m is slope and b is the y-intercept. In the equation 2x - 5y = -10, 2 is the slope and -5 is the y-intercept.

c. Plug in all given numbers into an equation and the ones you do not have will be in the points you need it to be. Once you graph the equation you will receive (2.5, -9).

d. y = mx + b

   5 = (-7)(-1) + b

   5 = 7 + b

   -2 = b

y = -7x - 2  

Answer: (-1, -2)

Step-by-step explanation:

so at first you have (1, 2)

then you were asked to reflect about y=x which is (x, y) = (y, -x)

(1, 2) = (2, -1)

then followed by y=-x which is (x, y) = (-y, -x)

(2, -1) = (-1, -2)

I hope this helps!

Answer:

[tex]\large \boxed{\sf \bf \ \ x^2-6x+45 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

You need to develop the expression.

[tex]y=(x-3)^2+36\\\\=x^2-2 * 3 * x +3^2+36\\\\=x^2-6x+9+36\\\\=x^2-6x+45[/tex]

Thank you.

Answer:

D

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

2.5 * 5 = 12.5

Answer:

-26!!!! :))))

Step-by-step explanation:

Answer:

7 to the 11th power

Step-by-step explanation:

7⁶×7⁵=7¹¹

because a¹×a¹=a¹+¹

Answer:

-(1/(x+h-3)(x-3))

Step-by-step explanation:

y=1/(x-3)

(f(x+h)-f(x))/h=(1/(x+h-3)-1/(x-3))/h=-(1/(x+h-3)(x-3))

Answer:

The expression (-root3·a - a)², can be simplified into the form a² × (4 + 2·√3)

Step-by-step explanation:

The given expression can be written as follows;

(-root3·a - a)² = (-√3·a - a)²

Which can be expanded to give;

(-√3·a - a) × (-√3·a - a) = 3·a² + 2·√3·a² +a²

We collect like terms to get;

3·a² + 2·√3·a² +a² =  3·a² +a²+ 2·√3·a² = 4·a² + 2·√3·a²

We factorize out the common coefficients of the terms  to have;

4·a² + 2·√3·a² = a² × (4 + 2·√3)

Which gives the initial expression (-root3·a - a)², to presented in the form a² × (4 + 2·√3).