A sports trainer has monthly costs of $80 for phone service and $40 for his website and advertising. In addition he pays a $15 fee to the gym for each session in which he works with a client.

Required:
a. Write a function representing the average cost
b. Find the number of sessions the trainer needs if he wants the average cost to drop below $16 per session.

Answer:

B: A systematic random sample

Step-by-step explanation:

Systematic sampling is a type of probability sampling in which members of a larger population are chosen at random from a larger population but at a fixed, periodic interval. This interval, also known as the sampling interval, is calculated by dividing the population size by the sample size desired. Despite the fact that the sample population is chosen in advance, systematic sampling is still considered random if the periodic interval is set in advance and the starting point is chosen at random.

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

area is 1/2bh

in an euqilateral triangle, all sides are equal so base and height are 12

1/2 x 12 x 12

1/2 x 144= 72 (B)

Answer: Choice C. [tex]36\sqrt{3}[/tex]

This is the same as writing 36*sqrt(3)

===================================================

Work Shown:

x = 12 = side length of equilateral triangle

A = area of equilateral triangle

A = 0.25*sqrt(3)*x^2

A = 0.25*sqrt(3)*12^2

A = 0.25*sqrt(3)*144

A = 0.25*144*sqrt(3)

A = 36*sqrt(3) .... answer is choice C

Side note: the area approximates to 62.354 square units.

Answer: C) complementary angle and D) right angle

Step-by-step explanation:

A is wrong because supplementary angles add up to 180 and this shows a right angle not a straight line

B is wrong because this a right angle not a straight angle

C is correct because complementary angles are two angles that add up to 90 degrees. angle EFH is split into EFG and GFH which adds up to 90 degrees.

D is correct because you can see the right angle symbol for angle EFH

The given angles shown in the figure are right angles and complementary angles.

Supplementary angles are two angles that add up to 180 degrees.

A straight angle is an angle that measures exactly 180 degrees.

It is a straight line, so it forms a straight angle.

A complementary angle is a pair of angles that add up to 90 degrees.

∠EFG and ∠GFH together are complementary angles as their sum is 90 degrees.

A right angle is an angle that measures exactly 90 degrees.

∠EFH is a right angle.

To learn more on Angles click:

https://brainly.com/question/28451077

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Answer:

The equation of the new function is [tex]g(x) = 7x + 9[/tex]

Step-by-step explanation:

Vertically compress by a factor of 7.

Vertically compressing a function by a units is the same as:

[tex]g(x) = f(ax)[/tex]

In this question:

[tex]f(x) = x, a = 7[/tex]. So

[tex]g(x) = f(7x) = 7x[/tex]

Shift up 9 units.

Shifting a function up a units is the same thing as adding a to the function. In this case, [tex]a = 9[/tex], and then:

[tex]g(x) = 7x + 9[/tex]

The equation of the new function is [tex]g(x) = 7x + 9[/tex]

Volume of the sphere = 4/3πr³

905 1/7 = 4/3*22/7*r³

6336/7 = 4/3*22/7*r³

r³ = (6336*7*3)/(4*22*7)

r³ = 133056/616

r³ = 216 

r = ∛216

r = 6 cm 

So, diameter = 6*2 = 12 cm

Surface area of the sphere = 4πr²

= 4*22/7*6*6

= 3168/7

Surface area of the sphere = 452.57 sq cm

Hope it helps.

What you know about rollin' down in the deep?

When your brain goes numb, you can call that mental freeze

When these people talk too much, put that sh*t in slow motion, yeah

I feel like an astronaut in the ocean, ayy

What you know about rollin' down in the deep?

When your brain goes numb, you can call that mental freeze

When these people talk too much, put that sh*t in slow motion, yeah

I feel like an astronaut in the ocean

Answer:

True.

Step-by-step explana

-4/5 + 4/5 is 0

Answer:

40

Step-by-step explanation:

If you take 15, and divide it by the 3 out of the 3/8 left, you get 5. You then multiply 5 by 8 to get the full amount of candies she had before sharing, 40.

I hope this helped!

Thanks!

Your friend in answering,

~Steve

Answer:

40.

Step-by-step explanation:

If 15 candies are the rest of 3/8, then the total candies were 40.

Answer:

You have 500 marbles.

The longest side of the biggest equalateral triangle that you can make with your marbles is 31

Step-by-step explanation:

28 + 4 = 32

So our equation is:

TR(32) - 28

Now find Triangular Number 32: (32 *33)/2=528

528 - 28 = 500

So, we have 500 marbles

Now we need to find the longest side of the biggest equalateral triangle that you can make make with your marbles

Let's go back to 28 + 4 = 32

One row above 32 is 31

So the longest side of the biggest equalateral triangle that you can make with your marbles is 31

Hope this helps!

Answer:

D. cannot be determined

Step-by-step explanation:

that is kind of a trick question.

right based on the given information none of the 3 methods can be applied.

we don't have all 3 sides for SSS

we don't have 2 angles for AA

and we don't have 2 sides with their included angle for SAS.

but it can still be determined (they ARE similar), as this is a special case of SSA, where it is clear that the corresponding congruent angles are located at the same position relatively to the corresponding similar lines.

you can discuss this with your teacher, if you are interested.

AND - we can easily determine any of the other missing pieces (side and angles). these missing pieces then will correspond exactly to their counterparts in the other triangle (the 2 angles in ABC are equal to the 2 angles in DEF, the missing sides file the same scaling factor as the other known sides). and then any of the 3 methods can be applied.

so, this is actually tricky ...

Answer:

-3

Step-by-step explanation:

in these equations the slope is multiplied by x which is -3 in this one.

Answer:

[tex]-3[/tex]

Step-by-step explanation:

The equation of a line is [tex]y=mx+b[/tex], and m is the gradient which is the slope. Hence, the number with x is the slope, which is [tex]-3[/tex].

Hope that helped.

Answer:

0.75 or 3/4

Step-by-step explanation:

f(-2) = 3•2^-2

f(-2) = 3•0.25

f(-2) = 0.75 or 3/4

Hope this helps! :)

Answer: n+4

Step-by-step explanation:

Answer:

Check explanation

Step-by-step explanation:

I'll give you my way of solving it and you can figure it out from there.

<CEA = <DEB due to vertical angles

AE = ED due to midpoint theorem

<CAD = <ADB due to alternating angles theorem

thus two triangles congruent due to ASA

Answer:

b) What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal? (Round your answer to four decimal places.)

Step-by-step explanation:

Answer:

[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]

Step-by-step explanation:

Given

[tex]\cos(x - y)[/tex]

Required

State the formula

From trigonometry identity, the formula of [tex]\cos(x - y)[/tex] is:

[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]

9514 1404 393

Answer:

  21

Step-by-step explanation:

Rearranging the given ratio, we can find the ratio of boys to the total.

  boys : (boys +girls) = 7 : (7+8) = 7 : 15

Then the number of boys is ...

  (7/15)(45) = 21

There are 21 boys in the classroom.

Answer:

5.01

Step-by-step explanation:

Reference angle (θ) = 24.3°

Length of side Opposite to reference angle = 2.06

Let the side length (Hypotenuse) we're looking for be represented as x

Apply SOH:

Sin θ = Opp/Hyp

Substitute the values into the equation

Sin 24.3° = 2.06/x

Multiply both sides by x

x × Sin 24.3° = 2.06/x × x

x × Sin 24.3° = 2.06

Divide both sides by Sin 24.3°

(x × Sin 24.3°)/Sin 24.3° = 2.06/Sin 24.3°

x = 5.01 (nearest hundredth)

Answer:

A = -1

B = -3

Step-by-step explanation:

you need to do all the multiplication on both sides and then simply compare the factors of the various powers of x.

so,

-9x² - 9×A×x + 2 = 3×B×x² + 6x -Bx - 2 + 4

-9x² - 9×A×x + 2 = 3×B×x² + (6-B)x + 2

the x-less constants 2 = 2 are correct. now we need to compare the factors for the other parts of x.

we have left and right only one expression of x²

-9x² on the left

3×B×x² on the right

therefore,

-9 = 3×B

=> B = -3

otherwise the equation would not be correct for all values of x.

the only other parts remaining are

-9×A×x = (6-B)x = (6 - -3)x = (6+3)x = 9x

=>

-9×A = 9

-A = 1

A = -1

remember, all parts of the left and of the right side must be equal for the equation to be true in all cases.

Answer:

Step-by-step explanation:

Wage = rate / hr * the number of hours worked.

Wage = ?

rate = 15.45

time = 29.25 hours

Wage = 15.45 * 29.25

Wage = 451.91

Answer:

C.4/9

Step-by-step explanation:

You add the black marbles, blue marbles, and the white marbles together, which equal 18. Out of the 18 marbles, 8 of them are white so it would be 8/18.

but you have to simplify it. 8 and 18 have 2 as the greatest common factor. 8 divided by 2 is 4 and 18 divided by 2 is 9. Finally its 4/9 since you cant simplify it even more.

Answer:

63,5

Step-by-step explanation:

pi r bình pnhân  hươnh g

no fancy math here, just some reasoning with words. I just feel like it

for one step in x-direction the value of the function doubles, so the common factor is 2.

so let's trace it back

(1,-6)

(0, -3)

For an exponential function the y-intercept is the "initial value".

do let's write is as a function

[tex]y = - 3 \times {2}^{x} [/tex]

you could also use the points and plug their numbers into the general formula, but I felt this explanation could give you more understanding, since it's meant to be more intuitive.

hope it helps

Answer:

Answer: 3) R(n) = 1200(1.002)n - 100n

Step-by-step explanation:

After n months, which function represents Chet’s net worth, R(n)?

(1) R(n) = 1200(1.002)n + 100n

(2) R(n) = 1200(1.002)12n + 100n

(3) R(n) = 1200(1.002)n - 100n

(4) R(n) = 1200(1.002)12n - 100n

Answer: 3) R(n) = 1200(1.002)n - 100n

Net worth is the amount of his savings minus his debt,

Everything in the problem is in terms of months, so there is no need to multiply the exponent by 12, which would convert n years into months.

Answer:

a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.

b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.

c) Expected number of acceptable specimens among the ten is 7.938.

d) Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

Step-by-step explanation:

a )

[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]

b )

[tex]c = 1.96 * 3 = 5.88[/tex]                    { Since Z = 1.96 for 95% CI refer table.}

c )

Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]

d )

Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

Answer: The length of DC is 3 units

Step-by-step explanation:

The Basic proportionality theorem states that if a line is parallel to one side of a triangle and intersects the other two at different points, then the other two sides are divided in the same ratio.

The given image is attached below.

From the BPT theorem, we can say that:

[tex]\Rightarrow \frac{AE}{EB}=\frac{AD}{DC}[/tex]

We are given:

AE = 12 units

EB = 4 units

AD = 9 units

Putting values in above equation, we get:

[tex]\Rightarrow \frac{12}{4}=\frac{9}{DC}\\\\\Rightarrow DC=\frac{9\times 4}{12}\\\\\Rightarrow DC=3 units[/tex]

Hence, the length of DC is 3 units

Answer:

The answer is 3 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bisection implies dividing a given segment into equal haves by construction. So that in the given question, angle ABC would be divided into equal parts.

After drawing segment AB to given length, use a compass to construct the required angle ABC. Then use the ends of the arc for the angle to bisect the angle.

The construction to this question is herewith attached to this answer for more clarifications.