The maximum heart rate is the highest heart rate achieved during maximal exercise. In general, you get the most benefits and reduce the risks when you exercise within your target heart rate zone. Usually this is when your exercise heart rate (pulse) is about 80 percent of your maximum heart rate. The formula M = 0.8 ( 220 − A ) M = 0.8 ( 220 - A ) , gives the recommended maximum heart rate, M M , in beats per minute, for a person who is A A years of age. Determine the age of a person whose target heart rate is 128 beats per minute. The recommended maximum heart rate is 128 beats per minute for a person who is years old.

Complete question is;

In a class of 40 students, 17 have ridden an airplane, 28 have ridden boat, 10 have ridden a train, 12 have ridden an airplane and a boat, 3 have ridden a train only, and 4 have ridden airplane only. Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three. How many students have used all three modes of transportation?

Answer:

4 students

Step-by-step explanation:

Let the number of students who used airplane be A

Let the number of students who used boat be B

Let the number of students who used train be C

Now, we are told that 17 rode plane.

Thus; A = 17

28 rode boat; B = 28

10 rode train; C = 10

12 rode airplane and boat; A ∩ B = 12

4 rode plane only; A' = 4

3 rode boat only; C' = 3

Total number of students; T = 40

Now, total number of students is represented by;

T = A - B - C - (A ∩ B) - (B ∩ C) - (C ∩ A) + (A ∩ B ∩ C)

We don't have (B ∩ C) and (C ∩ A).

Now, the can be derived from the expression of C' which is;

C' = C - (B ∩ C) - (C ∩ A)

C' = C - [(B ∩ C) + (C ∩ A)]

We are given C' = 3 and C = 10

Thus;

3 = 10 - [(B ∩ C) + (C ∩ A)]

10 - 3 = [(B ∩ C) + (C ∩ A)]

7 = [(B ∩ C) + (C ∩ A)]

Rearranging the total number of students equation, we now have;

T = A - B - C - (A ∩ B) - [(B ∩ C) + (C ∩ A)] + (A ∩ B ∩ C)

Where;

(A ∩ B ∩ C) is the number of students that used all three modes of transportation.

Thus, plugging in the relevant values;

40 = 17 + 28 + 10 - 12 - 7 + (A ∩ B ∩ C)

40 = 36 + (A ∩ B ∩ C)

(A ∩ B ∩ C) = 40 - 36

(A ∩ B ∩ C) = 4

Answer:

about 172.82

Step-by-step explanation:

Answer:

83.23

Step-by-step explanation:

to work out surface area of a  right cone u

A=πr(r+h2+r2)

hope this helps

im not sure if its right tho

Answer:

The claim is rejected

Step-by-step explanation:

Claim: UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13).

Null hypothesis: [tex]H_0: \mu = 48500[/tex]

Alternate hypothesis :[tex]H_a : \mu \neq 48500[/tex]

n = 50

Since n is more than 30 .

So we will use Z test

x=43350

Standard deviation = 15000

[tex]Z=\frac{x-\mu}{\frac{s}{\sqrt{n}}}\\Z=\frac{43350-48500}{\frac{15000}{\sqrt{50}}}\\Z=-2.42[/tex]

Refer the z table

p value = 0.00776

[tex]\alpha = 0.01[/tex]

p value < [tex]\alpha[/tex]

So, We are failed to accept null hypothesis

Hence The claim is rejected

Answer:

-11

Step-by-step explanation:

This is the answer because:

1) First, multiply the negative sign with the positive sign.

Negative x Positive = Negative

Equation: -7 - 4

2) Now, multiply the negative sign with the negative sign.

Negative x Negative =  Positive  

Equation: 7 + 4 = 11

3) Finally, add the greater number's sign (-7) in front of the number.

-11

Hope this helps! :D

Answer: B,D,E. Step-by-Step explanation

Transformation that preserve lengths are rigid transformation.

The options that support Maggie's claim are:

All transformations are rigid transformation, except dilation.

Dilation are of two types

Either of the two above, do not preserve length

This means that:

Options (d) and (e) will not preserve the lengths of the rectangle, because they represent dilation

Hence, the correct options that will preserve the length of the rectangle are: (a), (b) and (c)

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Answer:

c. supplementary angles

Step-by-step explanation:

Answer:

C. 36

because can not be expressed as a ratio

Answer:

163

Step-by-step explanation:

Step-by-step explanation:

When metamorphic rock melts it turns into magma.

Answer:

(f - g)(x) = -x - 6

(f + g)(x) = 3x - 4

(f*g)(4) = -9

Step-by-step explanation:

These are your equations:

f(x) = x - 5

g(x) = 2x + 1

To find (f - g)(x), subtract g(x) from f(x).

(f - g)(x) = x - 5 - (2x + 1)

(f - g)(x) = x - 5 - 2x - 1

(f - g)(x) = -x - 5 - 1

(f - g)(x) = -x - 6

To find (f + g)(x), add f(x) with g(x).

(f + g)(x) = x - 5 + 2x + 1

(f + g)(x) = 3x - 5 + 1

(f + g)(x) = 3x - 4

To find (f*g)(4), you need to first find (f*g)(4).  You can do this by multiplying f(x) wih g(x).

(f*g)(x) = (x - 5)(2x + 1)

(f*g)(x) = 2x² - 9x - 5

Now that you have (f*g)(x), solve with x as 4.

(f*g)(4) = 2(4)² - 9(4) - 5

(f*g)(4) = 2(16) - 9(4) - 5

(f*g)(4) = 32 - 36 - 5

(f*g)(4) = -9

The required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
f(x)=x-5
g(x) = 2x+1

According to the question,
[f + g ](x) = x - 5 + 2x + 1 = 3x - 4

[f + g ](x) =  3x - 4

[f - g ](x) =  x - 5 - 2x - 1
[f - g ](x) = -x - 6

(f.g)(x) = (x - 5)(2x + 1)
(f.g)(x) = 2x² -4x -5

(f.g)(4) = 2[4]² - 4[4] - 5
         = 32 - 16 - 5
         = 11
(f.g)(4) = 11

Thus, the required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.

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Answer:

The probability is   [tex]P(X  >300 ) = 0.97219 [/tex]

Step-by-step explanation:

From the question we are told that

 The capacity of  an Airliner  is  k =  300 passengers

 The sample size n =  320 passengers

  The probability the a randomly selected passenger shows up on to the airport

    [tex]p = 0.96[/tex]

Generally the mean is mathematically represented as

    [tex]\mu  =  n*  p[/tex]

  => [tex]\mu  =  320 *  0.96[/tex]

    => [tex]\mu  = 307.2[/tex]

Generally the standard deviation is  

    [tex]\sigma =  \sqrt{n *  p *  (1 -p ) }[/tex]

=>  [tex]\sigma =  \sqrt{320  *  0.96 *  (1 -0.96 ) }[/tex]

=> [tex]\sigma =3.50 [/tex]

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

  [tex]P(X  > k ) =  P( \frac{ X -\mu }{\sigma }  >  \frac{k - \mu}{\sigma } )[/tex]

Here [tex]\frac{ X -\mu }{\sigma }  =Z (The \ standardized \  value \  of  \ X )[/tex]

=>[tex]P(X  >300 ) =  P(Z >  \frac{300 - 307.2}{3.50} )[/tex]

Now applying  continuity correction we have

    [tex]P(X  >300 ) =  P(Z >  \frac{[300+0.5] - 307.2}{3.50} )[/tex]    

=>    [tex]P(X  >300 ) =  P(Z >  \frac{[300.5] - 307.2}{3.50} )[/tex]

=>    [tex]P(X  >300 ) =  P(Z >  -1.914 )[/tex]

From the z-table  

    [tex]P(Z >  -1.914 ) =  0.97219[/tex]

So

    [tex]P(X  >300 ) = 0.97219 [/tex]

Answer:

True

Step-by-step explanation:

There must be a constant of proportionality.

Hope this helps!

Answer:

58

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Absolute value measures the distance between the number and 0. The distance between -4 and 0 is 4, and the distance between 0 and 4 is 4. Therefore, they are equal.

Answer:

yes

Step-by-step explanation:

the l l symbol is the absolute value symbol, it counts how far the number is from zero meaning that the outcome is always positive.

Answer:

(-3,3)

Step-by-step explanation:

Answer:

12.2 12.3 12.4 12.5

Step-by-step explanation:

Answer:

32km

Step-by-step explanation:

Answer:

The answer is

[tex] \huge y + 1 = 15(x - 3) \\ [/tex]

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

From the question we have the final answer as

[tex]y + 1 = 15(x - 3)[/tex]

Hope this helps you

Answer:

There are 0 number of edges on a cylinder

Answer:

ur answer is 11 hopefully that's help

Answer:

4

Step-by-step explanation:

2 × 2 = 4

Answer:

8.64

Step-by-step explanation:

8.64

[tex]12\;percent\;of\;72=8.64[/tex]

Answer:

balance $4

Step-by-step explanation:

12 - 8 = 4

Answer:

$4

Step-by-step explanation:

$ = 12 - 8

12 - 8 = $4

Answer:

(x-14)^2+(y-3)^2=9

Step-by-step explanation:

equation of a circle is (x-h)^2+(y-h)^2=r^2

so center is (14,3) and is tangent externally means

(x-14)^2+(y-3)2=3^2

(x-14)^2+(y-3)^2=9 answer

The equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]

The standard formula for finding the equation of a circle is expressed as:

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

where

(a, b) is the centre

r is the radius

Given the center at (14, 3)

If the equation of a circle is externally tangent to the given circle and has a center at (14, 3), then the radius will be 3

Substitute the radius and the centre into the expression above to have:

[tex](x-14)^2 + (y-3)^2=3^2\\(x-14)^2 + (y-3)^2=9[/tex]

Hence the equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]

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Answer:

the answer is B because it make a 90* angle

Answer:

6 months is: 15675

2 months is: 5172.75

1 month is: 2586.37

15 months is: 38795.62

the missing number is: 12 months

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + x - 2 = 10

2x - 2 = 10

2x = 12

x = 6

y = 6 -2

y = 4

(6,4)

Answer:

Hello! I'm sorry I couldn't get to your question sooner. I just completed this quiz!

The equation of the circle that represents the dartboard is (x-10)^2 + (y-17/3)^2 = 9/16, where the origin is the lower-left corner of the room and the unit of the radius is feet.  

The position of Sasha's dart is represented by the coordinates (10.25,5). Sash's dart does land on the dartboard.

This quiz was completed on k12, lesson 3.03.

The question is an illustration of equation of circles.

From the question, we understand that:

[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex] ---- the height at which the dartboard was hung

[tex]\mathbf{d = 18\i n }[/tex] ---- the diameter of the dartboard

[tex]\mathbf{B = 10ft}[/tex]  --- the bull's eye

[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] --- Sasha's dart

Equation of the circle

First, we convert all units to feet

This is done by dividing inches units by 12

[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex]

[tex]\mathbf{h = 5\ ft\ + \frac{8}{12}\ ft }[/tex]

[tex]\mathbf{h = 5\ ft\ + \frac{2}{3}\ ft }[/tex]

Take LCM

[tex]\mathbf{h = \frac{15 + 2}{3}\ ft }[/tex]

[tex]\mathbf{h = \frac{17}{3}\ ft }[/tex]

[tex]\mathbf{d = 18\i n }[/tex]

[tex]\mathbf{d = \frac{18}{12}ft}[/tex]

[tex]\mathbf{d = \frac{3}{2}ft}[/tex]

Divide by 2 to calculate radius

[tex]\mathbf{r = \frac{3}{2*2}ft}[/tex]

[tex]\mathbf{r = \frac{3}{4}ft}[/tex]

The equation of the circle is represented as:

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

In this case:

[tex]\mathbf{a = B = 10ft}[/tex] -- the distance between the bull's eye and the wall

[tex]\mathbf{b = h = \frac{17}{3}\ ft }[/tex] ---- the height at which the dartboard was hung

So, we have:

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

[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = (\frac 34)^2}[/tex]

Evaluate the exponents

[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]

Hence, the equation of the circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]

Does Sasha’s dart land on the dartboard?

Yes her dart lands on the dartboard because

[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] is within the circumference of the dartboard

Read more about equation of circles at:

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