A group of 80 frogs was observed. The mean distance of their hops is 69 inches with a standard deviation of 3.5 inches. How many frogs would you expect to jump more than 72.5 inches?

Using the intersecting chord theorem:

a x b = c x d

x+21 * 4 = x+3 * 10

Simplify:

4x+84 = 10x+30

Subtract 30 from both sides:

4x + 54 = 10x

Subtract 4x from both sides:

54 = 6x

Divide both sides by 6:

x = 9

Answer:

x=9

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

ab = cd

(x+21) *4 = (x+3)*10

Distribute

4x+84=10x+30

Subtract 4x from each side

84 = 10x-4x+30

84 = 6x+30

Subtract 30 from each side

54 = 6x

Divide by 6

54/6 = 6x/6

9=x

[tex]\\ \sf\longmapsto tan\Theta=\dfrac{P}{B}[/tex]

[tex]\\ \sf\longmapsto tan40=\dfrac{48}{x}[/tex]

[tex]\\ \sf\longmapsto 0.8=\dfrac{48}{x}[/tex]

[tex]\\ \sf\longmapsto 0.8x=48[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{48}{0.8}[/tex]

[tex]\\ \sf\longmapsto x=60[/tex]

Answer:

x = 57.2

Step-by-step explanation:

first : the third angle is (the sum of all angles in a triangle is always 180 degrees) : 180 - 90 - 40 = 50 degrees.

law of sines :

x/sin(50) = 48/sin(40)

x = 48 × (sin(50)/sin(40)) = 57.2

Answer: 1/6

Step-by-step explanation:

Probability of getting heads = 50/100

= 1/2

Probability of tossing a 3 or 5 = 2/6

= 1/3

Now probability of getting both = 1/2×1/3

= 1/6

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Answer:

1/6

Step-by-step explanation:

There are two possible outcomes for tossing a coin

heads and tails

P(heads)= heads/ total = 1/2

Rolling a die has 6 possible outcomes 1,2,3,4,5,6

P*3 or 5) = 3 or 5 /total = 2/6 = 1/3

Multiply the probability of independent events together

1/2 * 1/3 = 1/6

Answer:4 ans x is -32/10

7 ans b  is 6

10 ans x is 25/7

13 ans x is 9/2

Step-by-step explanation:

please mark this answer as brainlist

Answer:

v is 198 m/s

Step-by-step explanation:

[tex]v = \sqrt{gh} \\ v = \sqrt{9.8 \times 4000} \\ v = 198 \: m {s}^{ - 1} [/tex]

Answer:

hope that helps i don't know it either tho

Answer:

4

Step-by-step explanation:

Im assuming you mean the first and second equation equal each other:

3x+2=2x+6

x=4

Step-by-step explanation:

Solution:Total length of the board=95 cm

:One piece must longer 13 cm than other piece

Equation:95cm=X+X+13cm

:95cm-13cm=2x

:82cm=2x

:X=41 cm-Length of the smaller piece

:X=41cm +13cm=54cm-Length of the larger piece

Therefore the length of the smaller piece is 41cm and the length of the larger piece is 54cm.

Answer:

15 feets 2 inches

Step-by-step explanation:

Given the widths :

1st dresser = 5 feets 5 inches

2nd dresser = 5 feets 10 inches

3rd dresser = 3 feets 11 inches

Their combined width is :

5ft + 5ft + 3 ft + 5in + 10in + 11in

13 feets 26 inches

Recall :

1 foot = 12 inches

26 inches = 26/12 feets = 2 feets 2 inches

Hence,

13 feets + 2feets 2 inches

Combined width = 15 feets 2 inches

Answer:

213.3

Step-by-step explanation:

The volume of a pyramid is 1/3 base times height.

Using this formula, our square base is 8*8, or 64 square units.

Multiplying that by the height, 10. We get 64*10, 640.

Finally dividing by 3, we have 213.3333333333...

Rounding that to the nearest tenth, 213.3.

The volume of the given square pyramid is 480 cubic centimeter.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, Slant height of pyramid is 10 cm and base is 8 cm.

The volume of square based pyramid =a²h/3.

Now, volume = (8²×10)/3

= 213.33 cubic centimeter

Therefore, the volume of a square pyramid is 213.33 cubic centimeter.

To learn more about the volume visit:

https://brainly.com/question/13338592.

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Let the no be x

ATQ

[tex]\\ \sf\longmapsto 2x+5=13[/tex]

[tex]\\ \sf\longmapsto 2x=13-5[/tex]

[tex]\\ \sf\longmapsto 2x=8[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{8}{2}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

Answer:

b=x+1

Step-by-step explanation:

The equation is:

[tex]2x^2}+x-1=\frac{1}{2} b(4x-2)[/tex]

Isolate b by subtracting and dividing.

You end up with b= x+1

Answer:

the answer is 4x2

Step-by-step explanation:

p(X)-q(X) = x4 + 2x2 + 1 - ( x4 - 2x2 + 1 )

p(X)-q(X) = x4 + 2x2 + 1 - x4 + 2x2 - 1 )

p(X)-q(X) = 2x2 + 2x2

p(X)-q(X) = 4x2

Answer:

p(x) - q(x) = 4x²

Step-by-step explanation:

p(x) - q(x)

= [tex]x^{4}[/tex] + 2x² + 1 - ([tex]x^{4}[/tex] - 2x² + 1)  ← distribute parenthesis by - 1

= [tex]x^{4}[/tex] + 2x² + 1 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms

= 4x²

Answer:

40

Step-by-step explanation:

B I D M A S

(90 - 25 + 5) = 70

1/2 x 70 = 35

10 ÷ 5 = 2

5 x 2 =10

6 + 9  = 15

15 - 10 = 2

.... cba

Answer:

Step-by-step explanation:

We need to first find the perimeter of this oddly-shaped rink. We have a rectangle for which we are enclosing 3 of its sides, and the fourth "side" is a half-circle. Let's find the perimeter (or circumference) of the circle, divide it in half because we have half a circle, then add in the remaining 3 sides from the rectangle, shall we?

C = πd. The diameter of the circle is the same as the shorter length in the rectangle, 26. Therefore,

C = (3.14)(26) so

C = 81.64 m for a whole circle, and for half of that circle, the circumference is

C = 40.82 m

Now we can find the perimeter of the rink:

40.82 + 61 + 26 + 61 = p so

p = 188.82 m

If the fencing costs $6.20 per meter and we have 188.82 m, then the total cost is

[tex]cost=\frac{6.20dollars}{meter}*188.82meters[/tex]. The label "meter" cancels out, leaving us with

cost = $1170.82

Answer:

Answer = 0

Step-by-step explanation:

√2+√3 - √2-√3

  = 0

Hope this  answer helps you :)

Have a great day

Mark brainliest

Answer:

3(4p-2) + 3= 2p-5

12p-6 +3 = 2p-5

10p-3=-5

10p=-2

p=-1/5

There is one solution.

hope this helps!

Answer:

one solution

-0.2

Step-by-step explanation:

3(4p - 2) +3 = 2p - 5         Remove the brackets on the left

12p - 6 + 3 = 2p - 5           Combine

12p  - 3 = 2p -5                  Subtract 2p from both sides

12p - 2p - 3 = -5                Combine

10p - 3 = - 5                       Add 3 to both sides

10p = -5 + 3

10p = - 2                            Divide by 10

p = - 0.2

Answer:

a = 53

Step-by-step explanation:

Start with d

The ends of d + 53 are diameter ends. That means that d + 53 is a right angle

d + 53 = 90

d = 90 - 53

d = 37

Next, find b. The end points of b are the same end points as for 53 degrees. B is the central angle of 53 which means b = 2 * 53

b = 106

c is the supplement of b

c + b = 180

b = 106

c + 106 = 180

c = 180 - 106

c = 74

The triangle containing a and c is isosceles because 2 of the 3 angles are opposite radii. The lowest angle is also a because it is opposite one of the radii.

a + a + 74 = 180

2a = 180 - 74

2a = 106

a = 106/2

a = 53

Hard to believe, but there it is.

Answer:

7

Step-by-step explanation:

Let the each leg be x so,

√(x²+x²)=√98

or, √(2x²)=√98

or, x√2=7√2

or, x=7

Answer:

P' = (2, -2)

Step-by-step explanation:

You have the x-value and the y-value of the pre-image, so all you have to do is plug that into the translation statement (x + 9 , y - 3).

Since x = -7 and y = 1 that would be (-7 + 9, 1 - 3), or (2, -2).

[tex]\\ \sf\longmapsto 16-2r=3r+6r+1[/tex]

[tex]\\ \sf\longmapsto 16-2r=9r+1[/tex]

[tex]\\ \sf\longmapsto 16-1=9r+2r[/tex]

[tex]\\ \sf\longmapsto 11r=15[/tex]

[tex]\\ \sf\longmapsto r=\dfrac{15}{11}[/tex]

Answer: r = 15/11

Step-by-step explanation:

Given

16 - 2r = 3r + 6r + 1

Combine like terms

16 - 2r = 9r + 1

Add 2r on both sides

16 - 2r + 2r = 9r + 1 + 2r

16 = 11r + 1

Subtract 1 on both sides

16 - 1 = 11r + 1 - 1

15 = 11r

Divide 11 on both sides

15 / 11 = 11r / 11

[tex]\boxed{r=\frac{15}{11} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

12x^7.

Step-by-step explanation:

3x^3(4x^4)=

3*4 * x^(3+4)

= 12x^7.

Answer:

P1 =(-6,-2)

P1=8

P2(-4,-1)

P2=5

(Answer:

P(Bl or Yl) = 45%

(Pk on 2nd draw) = 18%

Step-by-step explanation:

There are a total of 20 marbles (3 + 4 + 5 + 8) in the bag. Since each marble is replaced once drawn, there is no change in the total count from one draw to another (unconditional probability).

So

P(Bl or Yl) = (5 + 4)/20 = 9/20 = .45 = 45%

Then

P(Pk on 2nd draw) = P(1st draw) * P(2nd draw)

     = 9/20 * 8/20 = 72/400 = 9/50 = .18 = 18%

Answer:

d. 7

Step-by-step explanation:

A parallelogram has equal opposite sides that are parallel to each other. Therefore, opposite interior angles would be congruent to each other.

Thus:

3x - 17 = 25 - 3x

Add 3x from each side

3x - 17 + 3x = 25 - 3x + 3x

6x - 17 = 25

Add 17 to both sides

6x - 17 + 17 = 25 + 17

6x = 42

Divide both sides by 6

6x/6 = 42/6

x = 7