A football team carried out a report to see the impact of stretching on preventing injury. Of the 45 footballers in the squad 36 stretch regularly. Of those who stretch, 6 got injured last year. There was a total of 10 injured players last year.
The results can be presented in a frequency tree. What fraction of players who don't stretch get injured?

The option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

P(Male or Type B) = (number of male + number of type B - number that are both)/total population

[tex]\rm = \dfrac{103 + 50- 38}{200 }[/tex]

= 0.575

P(Male | Type B) = (number of male people inside the type B)/(number of Type B people)

= 38/(38 + 12)

= 0.76

0.575 < 0.76

P(Male or Type B) < P(Male | Type B)

Thus, the option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76

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If

(2 sin(x) - 1) (2 cos²(x) - 1) = 0

then either

2 sin(x) - 1 = 0   or   2 cos²(x) - 1 = 0

sin(x) = 1/2   or   cos(2x) = 0

The first equation gives two families of solutions,

x = arcsin(1/2) + 2nπ = π/6 + 2nπ

x = π - arcsin(1/2) + 2nπ = 5π/6 + 2nπ

where n is any integer; we get the solutions x = π/6 and x = 5π/6 in the interval 0 ≤ x < 2π when n = 0.

The second equation also gives two families of solutions,

2x = arccos(0) + 2nπ = π/2 + 2nπ

2x = -arccos(0) + 2nπ = -π/2 + 2nπ

Divide both sides by 2 :

x = π/4 + nπ

x = -π/4 + nπ

Then the solutions we want are x = π/4 and x = 5π/4 (when n = 0 and 1 in the first family, respectively) and x = 3π/4 and x = 7π/4 (when n = 1 and 2 in the second family).

We have 6 solutions, so A is the correct choice.

Answer:

Step-by-step explanation:

Comment

If two secants intersect outside a circle (as these two do) then the angle at which they meet is 1/2 the difference between the intersected arcs. Put much simpler <DCF = 1/2 (arc EG - arc DF)

Givens

Arc EG = 127

Arc DF = 49

Solution

<DCF = 1/2(127 - 49)

<DCF = 1/2(78)

<DCF = 39

Answer:

8.04

Step-by-step explanation:

If the last digit in 8.041 is less than 5, then remove the last digit.

I hope this helps!

Answer:

Since the angle of EFC = 33°, DAF = 33° because DAF and EFC have the same angle.

Answer:

where is the digram may i see the digram

Answer:

B

Step-by-step explanation:

the range of y=|x| is not all real numbers its [0,inf)

sign - ...

Zekrom

Answers for different section are given below;

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, given function;

  f(x) = -x² - 4x + 6

1.    If we take -1 common from the given function, we get

                     f(x) = -1 (x² + 4x - 6)

                    f(x) = -1 (x² + 4x) + 6

     Thus, first block contains -1 and second block contains 4.

2.   Then we add half of the coefficient of x², (b/2)², inside the bracket and subtract it outside a times, a(b/2)².

                f(x) = -1 ( x² + 2. 2x + 2²) +2² + 6

                f(x) = -1 ( x² + 4x + 2²) +4 + 6

Thus, first block contains -1, second block contains 4, third block contains 4, and fourth block contains 4.

3. Then we factorize the bracket and simplify outside the bracket;

               f(x) = -1 (x + 2)² + 10

Thus, first block contains -1, second block contains 2 and third block contains 10.

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Answer:

Step-by-step explanation:

(√6 - √2)/4

Answer:

(5,20)

Step-by-step explanation:

divide both sides of (10, 40) by the same number 2 and you will get (5,20). The points should all lie on the same straight line to form a proportional relationship.

Answer: 5,20

Step-by-step explanation:

Answer:

11.3057558

Step-by-step explanation:

Step-by-step explanation:

the problem description is seemingly contradicting itself.

"without replacement" means that you don't put the picked item back into the bag or "pool" of items.

and that means that after Rebecka picked a puppy, Aaron CANNOT pick the same one at all.

but then it says that they both may select the same one. which means it is WITH replacement.

so, what is it now ?

I have to give you both answers, and you will have to clarify with your original question or directly with your teacher what is the true condition.

in any case, a probability is always

desired cases / total possible cases.

WITH replacement (they can both pick the same puppy) :

there are 10 puppies, from which 3 are poodles.

so, total possible cases = 10, desired cases = 3

the probability to pick a poodle at the 1st pick = 3/10.

the picked puppy goes back.

the probability to pick a poodle at the 2nd pick = 3/10.

the probability that both picks are poodles is

3/10 × 3/10 = 9/100 = 0.09

WITHOUT replacement :

the first picked puppy is not returned to the group of 10 puppies, so, it can't be picked again, and the number of available puppies gets less as each puppy is removed. this changes the probabilities.

at the beginning we have 10 puppies, from which 3 are poodles.

the probability to pick a poodle at the 1st pick = 3/10.

the picked puppy does NOT go back.

now we have 9 puppies for Aaron to pick from. and for our desired cases for the second pick we have to combine it with the outcome, that the first pick was a poodle.

that means we have only 2 poodles left in the group of 9 puppies.

the probability to pick a poodle at the 2nd pick = 2/9.

the probability that both picks are poodles is therefore

3/10 × 2/9 = 6/90 = 1/15 = 0.066666666...

If the angles of a triangle are all equal, then the sides of a triangle are all equal. The correct answer is option A.

A triangle having all the three sides equal and all the angles equal is called the equilateral triangle.

As we can see that if the triangle is having all the angles equal then all three sides of the triangle must be equal. The triangle is termed the equilateral triangle.

Therefore the angles of a triangle are all equal, then the sides of a triangle are all equal. The correct answer is option A.

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To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:

[tex]y=a(x-r)(x-s)[/tex]

We're given:

[tex]y=a(x-r)(x-s)[/tex]

⇒ Plug in the given information:

[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]

[tex]a=-\dfrac{1}{2}[/tex]

One possible answer is 120°

Using limits, it is found that the end behavior of the function is given as follows:

As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In this problem, the function is:

[tex]f(x) = \frac{8x - 1}{2x - 9}[/tex]

Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:

Hence the correct statement is:

As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

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Answer:

D

Step-by-step explanation:

If BCD was reflected over the x axis then the coordinates will be B(-1,0) C(-1,2) and D(-4,1).

Given BCD is a triangle having coordinates (-1,0),(-1,-2),(-4,-1).

When the triangle is reflected over the x axis then all the values of y will change from negative to positive and the values of x remains same because in the second and third quadrant the values of x remains same and in the second quadrant the values of y used to  be positive  and in the third quadrant the values of y used to be negative.

So coordinates of B will change from (-1,0) to (-1,0)

coordinates of C will change from (-1,-2) to (-1,2)

coordinates of D will change from (-4,-1) to (-4,1)

New coordinates will be (-1,0) (-1,2) (-4,1).

Hence if BCD was reflected over x axis the new coordinates will be (-1,0) (-1,2) (-4,1).

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We have:

For a parabola like:

[tex]y = a*x^2 + b*x + c[/tex]

The vertex is at:

[tex]x = -b/2a[/tex]

In this case, we have:

[tex]y = -2x^2 -4x + 14[/tex]

So the vertex is at:

[tex]x = 4/2*(-2) = -1[/tex]

To get the y-value, we need to evaluate in x = -1.

[tex]y = -2*(-1)^2 - 4*(-1) + 14 = -2 + 4 + 14 = 16[/tex]

So the vertex is (-1, 16)

To do that we just evaluate in x = 0.

[tex]y = -2*0^2 -4*0 + 14 = 14[/tex]

The vertical intercept is (0, 14).

Using Bhaskara's formula we get:

[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*(-2)*14} }{2*-2} \\\\x = \frac{4 \pm 11.31 }{-4}[/tex]

So the two roots are:

x = (4 + 11.31)/(-4) = -3.83

x = (4 - 11.31)/(-4) = 1.83

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Answer:

Midpoint is the average of the two points. Find it as follows:

The complete question is

"Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?

p = 1

p = q

q = 1

pq = 1"

The statement that must be true would be from option D; pq = 1.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that the expression “p dollars for every q item” describes a unit price,

So, the equation will be formed as

p x q = 1

pq = 1

Hence, the statement that must be true would be from option D; pq = 1.

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Answer:

5m-3

Step-by-step explanation:

Answer:

5m-3

Step-by-step explanation:

Question:

A fair die is tossed.

Find the probability of obtaining an even number

Answer:

sample space=(1,2,3,4,5,6)

number of favourable outcomes=3

Event A= (outcome is even)

             = (2,4,6)

Total number of outcomes=6

Thus, P(even number)=3/6

                                      =1/2

Question 2:

A drawer contains 10 identical handkerchiefs of which 2 are white, 5 are blue, and 3 are pink. A handkerchief is drawn at random. what is the probability that it is white or pink?

Answer:

total number of outcomes=10

P(the handkerchief is white or pink)=2+3/10

                                                          =5/10

                                                          =1/2

Answer:

A

Step-by-step explanation:

5/44=0.11kg

Answer:

I think A

Step-by-step explanation:

I think A would be the answer.

Have a nice day !

The range and domain of the graphs have been determined .

Domain is the value that can be an input to the function and the range is all the value a function can obtain.

From the given graphs ,

For Graph 1

It can be seen that the line extends from x = -5 to +4

where -5 is not included

therefore the domain is given by

D = { x| -5 < x ≤4}

and the range is

R = {y | -3 < y≤4}

For Graph 2

The input value x extends from -∞ to +∞

so the domain is

D = { x| - ∞ ≤ x ≤ +∞ }

and the range is given by

R = {y | - ∞ ≤ y ≤ 3}

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Answer:

No, the table does not represent a function.

Step-by-step explanation:

By definition, a function will not have 2 or more results for the same input.

The table shows two values of y for the same x:  (2,1) and (2,4).  The same input, 2, results in two different values, 1 and 4.

See attached image.

Answer:

-31/30, -32/30, -33/30, -45/30, -49/30.

Step-by-step explanation:

-2/3 and -1 make denominators 30

-60/30 and -30/30

put any five

Answer:

1st option

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 2, 1 ) and r = 3 , then

(x - (- 2) )² + (y - 1)² = 3² , that is

(x + 2)² + (y - 1)² = 9 ← expand factors using FOIL

x² + 4x + 4 + y² - 2y + 1 = 9

x² + 4x + y² - 2y + 5 = 9 ( subtract 9 from both sides )

x² + 4x + y² - 2y - 4 = 0 , that is

x² + y² + 4x - 2y - 4 = 0 ← in general form

Answer:

[tex]\textsf{1)} \quad x^2+y^2+4x-2y-4=0[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies (x-(-2)^2+(y-1)^2=3^2[/tex]

[tex]\implies (x+2)^2+(y-1)^2=9[/tex]

Expand and simplify:

[tex]\implies (x+2)^2+(y-1)^2=9[/tex]

[tex]\implies x^2+4x+4+y^2-2y+1=9[/tex]

[tex]\implies x^2+y^2+4x-2y+5=9[/tex]

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

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Answer:

x ≤ - 1

Step-by-step explanation:

2x - 8 ≤ - 10 ( add 8 to both sides )

2x ≤ - 2 ( divide both sides by 2 )

x ≤ - 1

Answer:

x ≤ -1

Step-by-step explanation:

Given,

2x - 8≤ -10

Solution:

Add 8 to both sides:

Divide both sides by 2:

Value of x is ≤ -1.