There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities? There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?

Answer:

Step-by-step explanation:

[tex]3\sqrt2=\sqrt{3^2\cdot2}=\sqrt{18}\\\\2\sqrt3=\sqrt{2^2\cdot3}=\sqrt{12}\\\\18>17>15>14>13>12\ \implies\ 3\sqrt2>\sqrt{17}>\sqrt{15}>\sqrt{14}>\sqrt{13}>2\sqrt{3}[/tex]

{√16 = 4 is rational}

Answer:

The expression in standard form is -3 + 6i

Step-by-step explanation:

Writing complex equation in standard form we have;

-3 + yi = x + 6i

We transfer the real and imaginary parts to be on different sides of the equation as follows;

yi - 6i = x + 3

We factorize the imaginary part;

i(y-6) = x + 3

We note that the real portion on the left hand side of the equation is zero, therefore, we have;

i(y-6)  + 0= x + 3

x + 3 = 0

Therefore, x = -3

Substituting the value of x in the first equation, we have;

-3 + yi = -3 + 6i

Comparing gives;

y = 6

The expression in standard form is -3 + 6i.

Answer:

D)

Step-by-step explanation:

a number: n

difference of 17 and a number: 17 - n

4 times the difference of 17 and a number: 4(17 - n)

4 times the difference of 17 and a number is 84: 4(17 - n) = 84

Answer:

4x – 3 + 2x = 33

6x = 36

x = 6

D. x = 6

the correct answer is:

A. 9/-6

Answer: -8/-4

Step-by-step explanation:

When a negative integer gets divided my another negative integer, it results in a positive number. This means that we can eliminate all the negative symbols in this problem

18/9 = 2

Now all is left to determine which other expression is equivalent to 2

In the expression -10 / 5, since there is only one negative symbol, the postulate for negative number division states that two negative integers makes a positive number, and there is one negative integer and one positive whole number.

18/2 = 9 = incorrect

12/3 = 4 = incorrect

-10/5 = -2 = incorrect

8/4 = 2 = correct

So the expression -8/-4 is equivalent to the expression -18/-9

Answer:

Its D

Step-by-step explanation:

took the test its right, yw

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

Answer:

answer D

Step-by-step explanation:

hello,

[tex]f(x)=-5^x-4 \ and \ g(x)=-3x-2\\(f-g)(x)=f(x)-g(x)=-5^x-4+3x+2=-5^x+3x-2[/tex]

hope this helps

The value of function (f - g) (x) is,

⇒ 5ˣ + 3x - 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Functions are,

⇒ f (x) = - 5ˣ - 4

⇒ g (x) = - 3x - 2

Hence, We get;

The value of function (f - g) (x) is,

⇒ (f - g) (x)

⇒ f (x) - g(x)

⇒ (5ˣ - 4) - (- 3x - 2)

⇒ 5ˣ - 4 + 3x + 2

⇒ 5ˣ + 3x - 2

Thus, The value of function (f - g) (x) is,

⇒ 5ˣ + 3x - 2

Learn more about the function visit:

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Answer:

Step-by-step explanation:

the translation of y = |x| 2.5 units to the left is:

y = |x+2.5|

Answer:

23 años

Step-by-step explanation:

Para resolver la situación, consideremos que x es la edad de la persona. Sabemos que dentro de seis años esta tendrá el doble de la edad que tenía hace cuatro años. La edad dentro de 6 años se puede expresar como x+6 y esto será igual al doble de la edad que tenía hace cuatro años, lo que se puede expresar como 2(x-4). De acuerdo a esto:

x+6=2(x-4)

x+6=2x-8

6+8=2x-x

x=14

Ahora que sabemos que la edad de la persona es 14 años, le sumamos 9 y esto da como resultado 23 y esta es la edad que la persona tendrá en 9 años.

The equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3

The equation of a line can be represented as follows;

y = mx + b

where

Therefore,

parallel line have the same slope

(5, 35)(10, 50)

m = 50 - 35 / 10 - 5 = 15 / 5 = 3

Hence,

(4, 15)

y = 3x + b

15 = 3(4) + b

15 - 12 = b

b = 3

Therefore, the equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3

learn more on equation of a line here: https://brainly.com/question/19043210

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Answer:

m∠1 = 145°

m∠3 = 35°

m∠4 = 145°

m∠5 = 145°

m∠6 = 35°

m∠7 = 35°

m∠8 = 145°

Step-by-step explanation:

In the picture attached,

line 'm' and line 'l' are the parallel lines and another line intersects these lines is a transverse.

m∠2 = 35°

Since ∠1 and ∠2 are supplementary angles,

m∠1 + m∠2 = 180°

m∠1 + 35° = 180°

m∠1 = 180° - 35°

m∠1 = 145°

∠1 ≅ ∠4 [Vertical angles]

m∠1 = m∠4 = 145°

∠2 ≅ ∠3 [Vertical angles]

m∠2 = m∠3 = 35°

∠3 ≅ ∠6 [Interior alternate angles]

m∠3 = m∠6 = 35°

Similarly, ∠4 ≅ ∠5 [Interior alternate angles]

m∠4 = m∠5 = 145°

∠6 ≅ ∠7 [Vertical angles]

m∠6 = m∠7 = 35°

Answer:

D.(-4,-8) and(2,4)

Step-by-step explanation:

y=-2x

y=x²-8

this means that the two equations are equal because they both add up to y

thus; x²-8=-2x

formulae=Ax²+bx+c=0

x²+2x-8=0

find two numbers which multiplied will give you x² and when added will give you 2x that is x and x

x²+x+x-8=0

x(x+1)+1(x-8)=0

(x+1)(x-8)=0

1)x+1=0. x= -1

1)y=-2x

y=-2(-1)=2

y=2

2)y=x²-8

y=1²-8= -8

y= -8

note*this means that the answer should have both 2 and -8 thus d is the answer

Answer:

Step-by-step explanation:

A∩B={x| x∈a and x∈B}

a) A∩B={4,6}

b) A∩B={ 4,9}

c) A∩B={yellow,green}

Answer:

-4 points

Step-by-step explanation:

Since each incorrect answer is worth the same amount of negative points, use the equation below.

3x = -12      DIvide both sides by 3

x = -4 points  

Answer:

5 cm

Step-by-step explanation:

We khow that the altitude of this triangle is 1cm shorter than the base

that's a quadratic equation . Let's calculate the dicriminant .

Let Δ be the dicriminant

We have a negative value and a positive one

The altitude is a distance so it can't be negative

H= 5cm

Answer:

2:55. That's Two hours and 55 minutes.

Step-by-step explanation: From 8:20 to 11:20 would be three hours. But the actual time is five minutes less. There are 60 minutes in one hour. So change one hour to 60 minutes and subtract 5 minutes.

2:60 - :05 = 2:55

Answer:

2 hours and 55 minutes

Step-by-step explanation:

Take 11:15 and subtract 8:20

11 : 15

-8:20

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

We need to borrow from the hours

11 becomes 10 and 1 hour = 60 minutes so add 60 to the 15

10 :75

-8:20

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

2: 55

This is 2 hours and 55 minutes

Answer:

2869

Step-by-step explanation:

7,840 - 4,971

Subtract.

= 2869

Answer:

0 2,869

hopefully this helped :3

Answer:

Solution,

[tex] {w}^{3} - w( {w}^{2} + 2w - 1) + 2w \\ = {w}^{3} - {w}^{3} - 2 {w}^{2} + w + 2w \\ = - 2 {w}^{2} + 3w[/tex]

Some rules:

[tex]( + ) \times ( + ) \ = ( + ) \\ ( - ) \times ( + ) = ( - ) \\ ( + ) \times ( - ) = ( - ) \\ ( - ) \times ( - ) = ( + )[/tex]

Hope this helps...

Good luck on your assignment..

THIS IS THE COMPLETE QUESTION BELOW;

The probability of pulling a green marble out of a bag of colored marbles is 2:5. If you were to pull colored marbles out of the bag one at a time, and putting the marble back each time for 600 tries, approximately how many time would you select a green marble?? ( explanation too) 7th grade Math

Answer:

We would approximately pick a green marble 240 times

Step-by-step explanation:

Given from the question the probability of pulling a green marble out of a bag of colored marbles is 2:5

Let us denote the number of trials as X

Now the approximately number of times a green marble can be selected would be

=2/5 times

From the question we are given 600 trials

which implies our x=600

Therefore, the number of times we would pick a green marble is:

2/5 × 600 times

≈ 240 times

Therefore, we would approximately pick a green marble 240 times

Answer:

If the ratio of edge lengths is 3:5, I'm going to assume that the perimeters are going with the same ratio.

Therefore, the ratio would be 345:575.

Hope this is right and helps :)

Step-by-step explanation:

68$53++83(-$(7(3($++$

Answer:

The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)

Step-by-step explanation:

Notice that when we start with the function [tex]f(x)=x^3[/tex], and then transform it into the function: [tex]g(x)=(x-4)^3-7[/tex]

what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).

Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).

then the point (0, 0) after the translation becomes: (4, -7)

Answer:4, -7

Step-by-step explanation:

Hi there! Hopefully this helps!

The answer is: 0.016

Here is how I got that answer:

16/1000=0.016

Answer:

Step-by-step explanation:

£16÷1000=0.016p

Answer:

Step-by-step explanation:

Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.

The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.

The system is

6h + 1d = 40

4h + 3d = 36

The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,

1d = 40 - 6h.

Now that we know what d equals, we can sub it into the second equation where we see a d. In order,

4h + 3d = 36 becomes

4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!

4h + 120 - 18h = 36 and

-14h = -84 so

h = 6.

That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:

1d = 40 - 6(6) and

d = 40 - 36 so

d = 4.

That means that each duck costs $4.

Answer:

you need 2 cups of sugar

Step-by-step explanation:

1/2 cups of sugar = 3/4 cup of flour

x = 3 cups of flour

1/2*3 = 3/4x

3/2 = 3/4x

x =3/2 ÷ 3/4

x =2

Answer:

[tex]\huge\boxed{\sqrt{65}\approx8.062}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have two points (4, 0) and (-3, 4).

Substitute:

[tex]d=\sqrt{(-3-4)^2+(4-0)^2}=\sqrt{(-7)^2+4^2}=\sqrt{49+16}=\sqrt{65}[/tex]

Answer:

Hasty generalization fallacy

Step-by-step explanation:

Fallacy can be said to be a reasoning which leads to the wrong interpretation of a statement or an argument. Although some people intentionally make fallacious statements just to score cheap points or to please the listening audience, but some make fallacious unknowingly, either due to carelessness or by being lackadaisical.

In this case the writer, without enough investigation and proof, comes to a very hasty conclusion that "all doctors are the same". This is termed a hasty conclusion because the writer only had dealings with just two docotors(Dr. Ames and Dr. Collins). So saying all doctors are the same just because of two instance is a rather rash statement.

Therefore, the fallacy commited by the writer here is a fallacy of hasty generalization.

Hasty generalization fallacy occurs when someone has a limited information on a population but makes a conclusion based on a larger population than he/she should.

Answer:

WXYZ can not be a rectangle because consecutive sides are not perpendicular to each other.

Step-by-step explanation:

The given vertices are W(-4,3), X(1,5), Y(3,1) and Z(-2,-1).

Plot these points on coordinate plane and draw the quadrilateral as shown below.

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using this formula, we get

[tex]m_{WX}=\dfrac{5-3}{1-(-4)}=\dfrac{2}{5}[/tex]

[tex]m_{XY}=\dfrac{1-5}{3-1}=\dfrac{-4}{2}=-2[/tex]

Now,

[tex]m_{WX}\times =\dfrac{2}{5}\times (-2)=-\dfrac{4}{5}\neq -1[/tex]

Here, WX and XY are two consecutive sides of quadrilateral but the product of their slopes is not equal to -1. It means they are not perpendicular to each other.

Since, all interior angles of a rectangle are right angles, therefore, WXYZ can not be a rectangle.

Answer:

The correct option is option (3) 4 ÷ 25.

Step-by-step explanation:

The expression in terms of m and n is:

[tex]F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}[/tex]

Exponent rule of division:

[tex]a^{x}\div a^{y}=a^{x-y}[/tex]

Compute the value of the expression for m = -5 and n = 3 as follows:

[tex]F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}[/tex]

[tex]F(-5,3)=[\frac{2\csdot (-5)^{-1}\cdot (3)^{5}}{3\cdot (-5)^{0}\cdot (3)^{4}}]^{2}[/tex]

             [tex]=\{\frac{2}{3}\times [(-5)^{-1-0}\times (3)^{5-4}}]\}^{2}\\\\=\{\frac{2}{3}\times \frac{-1}{5}\times 3\}^{2}\\\\=\{-\frac{2}{5}\}^{2}\\\\=\frac{4}{25}[/tex]

Thus, the correct option is option (3) 4 ÷ 25.

Answer:

4/25

Step-by-step explanation:

I just did the test