100 adults were asked how they keep fit.
Each adult goes to the gym, runs or cycles.
45 of these adults are female.
30 of the 52 adults who go to the gym are female.
35 adults run.
9 males cycle.
One of the females is chosen at random.
Write down the probability that she runs.

97.5% of American women have shoe sizes that are no more than 11.47.

Lets try to solve the question,

Given values ,

Dev (u) = 8.47

Standard deviation (x) = 1.47

So we e have to find the percentage of American women whose shoe size's are not more than 11.47 P(x<11.47).

Lets find z score by using empirical formula.

=> [tex]z= (x-u) / a[/tex]

=> [tex]11.47-8.47/1.5[/tex]

=> [tex]z= 2[/tex]

Now we have to find [tex]P(z < 2)[/tex] . Using the empirical rule, we know that 97.5% data lies below 2 standard deviations above mean.

Therefore the 97.5% of American women have shoe sizes that are no more than 11.47.

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The value of the composite function f(g(x)) is 5x + 2

Composite functions are functions inside another function. Given the following functions:

f(x) = 5√x+1 - 2

g(x) = x² - 1

Determine the composite function f(g(x))

f(g(x)) = f(x² - 1)

f(x² - 1) = 5√x² - 1+1 - 2

f(x² - 1) = 5√x² + 2

f(x² - 1) = 5x + 2

Hence the value of the composite function f(g(x)) is 5x + 2

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Answer:

the answer is D

Step-by-step explanation:

Answer:

x = | 1 |

Step-by-step explanation:

how are u in college doing this???

Answer:

1

Step-by-step explanation:

(x+8)=9

x+8=9

x=9-8

x=1

Answer:

Morgan

Step-by-step explanation:

because the pythagoras theorem is

H

[tex] {h1}^{2} = {b}^{2} + {h2}^{2} [/tex]

where h1=hypotenuse

h2=height

b=base

Answer:

P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

Step-by-step explanation:

As we know that, if A and B are two events then

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

Answer:

GH=12

Step-by-step explanation:

Definition of a perpendicular Bisector: a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts.

Therefore it divides the line GI into two equal parts. That means that GH=HI and it was given that HI=12.

Answer:

no solution

Step-by-step explanation:

| | is a notation for absolute value, which is the distance that a number is from 0.

you can think of this as the "positive version" of a number

so, |-x| will become: x

We can plug this into the equation, and solve like we would for any variable

3 + 7 = 6 - |-x|  {simplify}

3 + 7 = 6 - x   {simplify}

10 = 6 - x

Now, we can isolate x (isolate = get it alone)

10 = 6 - x

-6     - 6    {subtract 6 from both sides}

 4 = -x         {multiply both sides by -1 to get positive x}

·-1   ·-1

- 4 = x

{check solution:}

3 + 7 = 6 - | -4 |

10 = 6 - 4

10 = 2

FALSE

because this solution has been found to be false, there is no possible value for x

we write this as: no solution

[tex]3+7=6-|-x|\\10=6-|x|\\|x|=-4\\x\in\emptyset[/tex]

The dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

We can think of this as a right triangle, where the hypotenuse measures 30 inches, and the angles of the triangle are 30°, 60° and 90°.

If we step on the 30° angle, the length will be the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opposite cathetus)/(hypotenuse).

Replacing what we know:

sin(30°) = length/30 in

length = sin(30°)*30in = (1/2)*30 in = 15in

And the adjacent cathetus will be the width, then we can use:

cos(θ) = (adjacent cathetus)/(hypotenuse).

Replacing what we know:

cos(30°) = width/(30 in)

width = cos(30°)*30in = (√3/2)*30in = (√3)*15in

Then the dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

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Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

the slope is always the ratio of

y coordinate change / x coordinate change

in our case, x is the time (minutes), and y is the water height (inches).

we see, the longer the pool get filled, the higher the water gets. logical, right ?

by checking the data points we see :

with every 2 minutes passing the water height increases by 4 inches.

so, the slope is +4/+2 = 2/1 = 2

and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.

every 2 minutes 4 inches more.

so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.

and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.

Answer: x=0

Step-by-step explanation:

[tex]x=4+(4x-4)\\\\x=4+4x-4\\\\x=4x\\\\3x=0\\\\\boxed{x=0}[/tex]

The solution to the equation x = 4 + (x + 4) is 0.

The correct option is "one real solution".

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Expanding the expression on the right-hand side, we have:

x = 4 + (4x - 4)

x = 4x

Subtracting 4x from both sides, we get:

x - 4x = 0

-3x = 0

Dividing both sides by -3, we get:

x = 0

Therefore, there is one solution to the equation x = 4 + (4x - 4) as the equation simplifies to 0.

So the correct answer is 0, "one real solution".

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The corollary of the statement tends that its not the Poisson experiment.

It is a statistical approach to follow properties that The experiment outcomes that can be opted as successes or failures. That gives a outcome in a specified region is known in average number of successes i.e. (μ).

The probability of a given task is not a Poisson experiment because the mean number of successful  outcomes in its domain neither constant nor given.

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Answer:

put 1/2as a value of x in the equation and then solve .then the answer will be -1

Answer:

[tex]C.\ f\left( \frac{1}{2} \right) =-1[/tex]

Step-by-step explanation:

[tex]f\left( x\right) =\frac{\sqrt{2x+3} }{6x-5}[/tex]

In order to calculate f(1/2) ,all we have to do

is replacing x by 1/2 in the expression of f.

Then

[tex]f\left( \frac{1}{2} \right) =\frac{\sqrt{2\left( \frac{1}{2} \right) +3} }{6\left( \frac{1}{2} \right) -5 }[/tex]

        [tex]=\frac{\sqrt{1+3} }{3-5}[/tex]

        [tex]=\frac{\sqrt{4} }{-2}[/tex]

        [tex]=\frac{2}{-2}[/tex]

        [tex]=-1[/tex]

The graph is shown in the attached image.

The height of the tree to the nearest tenth of a meter is 73.7m

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

base = 13 m

angle of elevation = 53

Using trigonometry

tan 53 = P/B

5.671 = P/ 13

P= 5.671 * 13

P= 73.723

Hence, the height of the tree is 73.7 m.

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Answer:

Perimeter of rectangle2 =  k × perimeter of rectangle 1

area of rectangle 2  =  k² × area of rectangle 1

Step-by-step explanation:

• rectangle 1 :

Length x

Width y

perimeter1  =  2×(x + y)

area1  = x × y

……………………

•• rectangle 2 :

Length kx

Width ky

Perimeter2  =  2×(Kx + ky)

area2  = kx × ky

……………………………………………

therefore,

Perimeter of rectangle 2

= 2×(Kx + ky)

= 2×k×(x + y)

= k×2×(x + y)

= k × perimeter of rectangle 1

On the other hand,

area of rectangle 2

= Kx × ky

= k×k×(x × y)

= k²×(x × y)

= k² × area of rectangle 1

Part 1: Finding radius

The radius of a circle is defined as the distance from the center to a point on the circle's circumference.

Using the distance formula,

[tex]r=\sqrt{(-7-8)^{2}+(-1-7)^{2}}=\boxed{17}[/tex]

Part 2: Finding the point with x-coordinate -15

Let the y coordinate of the point be y. Then, we have the point (-15, y). Substituting into the distance formula,

[tex]\sqrt{(-15-(-7))^{2}+(-1-y)^{2}}=17\\\\64+(-1-y)^{2}=289\\\\(-1-y)^{2}=225\\\\-1-y =\om 15\\\\y=\boxed{-16, 14}[/tex]

Answer:

Domain: [1, infinity)

Range: All real numbers or (- infinity, + infinity)

Step-by-step explanation:

Hope this helps

Answer: 180 degrees

Step-by-step explanation:

A rotation of 180 degrees about the origin maps [tex](x,y) \longrightarrow (-x, -y)[/tex].

Answer:

180

Step-by-step explanation:

took the test

Answer:

Step-by-step explanation:

Answer:

According to the graph, g(x) is stretched by what seems to be 5, so g(x) is (x^2) / 25. (Square the stretching/compressing factor so 5^2 became 25). We also divide x^2 by this because it is being stretched. You multiply if it's being compressed.

You can check this by plugging 5 for x and trying to get 1.

g(x) = x^2 / 25

g(5) = 5^2 / 25 --> 25/25

g(5) = 1

g(x) = (x^2)/25

Answer:

the answer is 64

Step-by-step explanation:

now atleast mark me brainliest answer

Answer:

7/6=2/7/6

7/6=2

7/6=27/6

7/6=2

7/6

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

Length of the arc of a circle:

s = 7.34 units

The measure of central angle:

θ = 81 degrees =  1.413 radians

s = rθ

r is the radius of the circle

7.34 = r(1.413)

r = 5.19 ≈ 5.2 units

Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

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Answer:

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

Step-by-step explanation:

Answer: The second table.

Step-by-step explanation: The y coordinates are getting smaller over time, so I believe the second one would be the correct answer. I hope this helps!  :)

Answer: [tex]x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(-3)(6)}}{2(-3)}[/tex]

Step-by-step explanation:

a = -3 , b = -2, and c = 6.

The correct substitution of the values a, b, and c from the equation 0=-3x² - 2x + 6 into the quadratic formula is

x = (-(-2) ± √((-2)² - 4(-3)(6))) / (2(-3)).

The correct option is A.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

To use the quadratic formula with the equation 0=-3x² - 2x + 6, we need to substitute the values of a, b, and c into the formula.

In this case, we have:

a = -3

b = -2

c = 6

Substituting these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)² - 4(-3)(6))) / (2(-3))

Simplifying this expression, we get:

x = (2 ± √(4 + 72)) / (-6)

x = (2 ± √76) / (-6)

We can simplify further by factoring out the square root of 4 from the radical:

x = (2 ± 2√19) / (-6)

Therefore, the required value of x is x = (-(-2) ± √((-2)² - 4(-3)(6))) / (2(-3)).

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Answer:

The correct answer is B, the second option

Step-by-step explanation:

(-2, 5/3)

Solve for the first variable in one of the equations, then substitute the result into the other equation.

The solution of the given equation (x + 5) - ( 2x - 3) = 6 is 2.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

(x + 5) - ( 2x - 3) = 6

To solve;

(x + 5) - ( 2x - 3) = 6

Distribute the negative;

(x + 5) - 2x + 3 = 6

we need to get the like terms together;

x - 2x + 5+ 3 = 6

-x + 8 = 6

Subtract 8 from both sides, we get;

-x = -2

x = 2

Hence, the solution of the given equation is 2.

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Answer:

3.33, or 3 1/3

Step-by-step explanation:

Expected value:

[tex](9 \times \frac{2}{9} ) + (12 \times \frac{1}{9} ) = 2 + \frac{4}{3} = 2 + 1 \frac{1}{3} = 3 \frac{1}{3} [/tex]