Which is the graph of f(c)=100(.7)x

Answer:

The number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.

Step-by-step explanation:

We will use the sin function for the height of the Ferris wheel.

[tex]y=A\ sin(B(x+C))+D[/tex]

A = amplitude

C = phase shift

D = Vertical shift

2π/B = period

From the provided information:

A = 15/2 = 7.5 m

[tex]Period=2\\\\\frac{2\pi}{B}=2\\\\B=\pi[/tex]

Compute the Vertical shift as follows:

D = A + Distance of wheel from ground

   = 7.5 + 1

   = 8.5

The equation of height is:

[tex]h(t)=7.5\cdot sin(\pi (t+C))+8.5[/tex]

Now at t = 0 the height is, h (t) = 1 m.

Compute the value of C as follows:

[tex]h(t)=7.5\cdot sin(\pi (t+C))+8.5[/tex]

[tex]1=7.5\cdot sin(\pi (0+C))+8.5\\\\-7.5=7.5\cdot sin\ \pi C\\\\sin\ \pi C=-1\\\\\pi C=sin^{-1}(-1)\\\\\pi C=\frac{3\pi}{2}\\\\C=\frac{3}{2}[/tex]

So, the complete equation of height is:

[tex]h(t)=7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5[/tex]

Compute the number of minutes of the ride that are spent higher than 15 meters above the ground as follows:

h (t) ≥ 15

[tex]h(t)=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))=6.5\\\\sin(\pi (t+\frac{3}{2}))=\frac{6.5}{7.5}\\\\(\pi (t+\frac{3}{2}))=sin^{-1}[\frac{13}{15}]\\\\\pi (t+\frac{3}{2})=60.074\\\\t+\frac{3}{2}=19.122\\\\t=17.622\\\\t\approx 18[/tex]

Thus, the number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.

Answer:

[tex]10x^2-x+3[/tex] miles.

Step-by-step explanation:

It is given that,

Total length of park trail = [tex]10x^2+4x+2[/tex] miles

Total length traveled by hiker = [tex]5x-1[/tex] miles

We need to find the length of trail hiker need to travel to get to the end of the trail.

Required length [tex]=10x^2+4x+2-(5x-1)[/tex]

               [tex]=10x^2+4x+2-5x+1[/tex]

               [tex]=10x^2+(4x-5x)+(2+1)[/tex]

               [tex]=10x^2-x+3[/tex]

Therefore, hiker need to travel [tex]10x^2-x+3[/tex] miles to get to the end of the trail.

Answer:

1) To calculate length of fringe, we need to find the perimeter

The question does not clearly say how much is length and width

Assuming length = 245 and width = 234 inches

P = 2(length + width)

P = 2 ( 245 + 234)

P = 2 (479)

P = 958 inches

2) To calculate length of fringe, when length is increased by 33 inches

P = 2 ( l + w)

P = 2 (278 + 234)

P = 2 x 512

P = 1024 inches

Answer:

The dimensions of the rectangular room is 48 ft by 20 ft

Step-by-step explanation:

Drawing a Diagonal line in a rectangle forms two right angle triangles

The diagonal line will represent the hypotenuse

In a right angle triangle:

Hypotenuse^2= adjacent^2+opposite^3

One wall measures 28 ft longer than the adjacent wall.

Let the adjacent=x ft

Opposite=28+x ft

Hypotenuse=52 ft

Hypotenuse^2= adjacent^2+opposite^3

52^2 = x^2 + (28+x)^2

2704 =x^2 + 784 + 56x + x^2

2704=2x^2+784+56x

2x^2+56x+784-2704=0

2x^2+56x-1920=0

Solve the quadratic equation using the quadratic formula

x= -b +or- √b^2-4ac / 2a

a=2

b=56

c=-1920

x= -b +or- √b^2-4ac / 2a

= -56 +or- √56^2 - (4)(2)(-1920) / (2)(2)

= -56 +or- √3136 - (-15,360) / 4

= -56 +or- √3136+15,360) / 4

= -56 +or - √ 18496/ 4

= -56 +or- 136 / 4

x= -56 + 136 / 4

=- 56/4 + 136/4

= -14+34

=20

OR

x= -56 - 136/4

= -56/4 - 136/4

= -14 - 34

= -48

The value of x can't be negative, so will use the positive value of x which is 20

Recall,

Adjacent=x

=20 ft

Opposite=28+x ft

=28+20

=48 ft

The dimensions of the rectangular room is 48 ft by 20 ft

[tex]\text{In this question, we're trying to find the quotient}\\\\\text{The quotient is basically the result or answer when you divide a number}\\\\\text{To find the quotient, divide 36 by 6}\\\\36\div6=6\\\\\boxed{\text{Answer: 6}}[/tex]

Answer:

6

Step-by-step explanation:

6x6=36 so, 36÷6=6

Answer:

403

Step-by-step explanation:

Simply multiply 0.65 and 620 together to get 403 as your answer.

Answer: 403

Step-by-step explanation:

65% of any number is the same as multiplying it by 0.65.  0.65 * 620 = 403

Answer:

a. No, because she will need money a year from now. Generally, stocks are long term investments. It is very unlikely that she will get a return on her investment in a year.

Step-by-step explanation:

Stocks are a riskier investment in comparison to bonds, and may pay higher interest rates, but still require the investment to "sit" for a long period of time. Like a 3 month (APY of about .50%), 6 month (APY of about .30%), 8 month (APY of about .10%), etc. bond, stocks will not grow considerably in a short amount of time.

Answer:

Figure 1.

Step-by-step explanation:

The triangle pairs are missing, I researched and was able to find the triangle pairs attached to the question. I will attach the triangles, and in addition to that we will say the reasons that each one meets or does not meet with respect to the conditions of the question.

Only the first figure shows that the pairs of triangles can be mapped to each other using two reflections.

Here reflection can be done through the XY side followed by reflection through the YT side. So when we reflect the triangle XYZ through the XY side, we get the triangle XYT and then we reflect the triangle XYT through the YT side and we get the triangle PYT.

Answer:

Just here saying its not figure one it b the one above me is wrong sorry for the people who um listen to him like me

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of a sphere is

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

Where r is the radius

diameter = radius × 2

To find the diameter we must first find the radius

Volume = 34cm³

That's

[tex]34 = \frac{4}{3} \pi {r}^{3} \\ \\ 34 \times 3 = 4\pi {r}^{3} \\ \\ 102 = 4\pi {r}^{3} \\ {r}^{3} = \frac{102}{4} \pi \\ \\ r = \sqrt[3]{ \frac{51}{2\pi}} \\ \\ r = 2.01 \\ \\ r = 2.0 cm[/tex]

Diameter = 2 × 2cm

Hope this helps you

Answer:

The answer is 4

Step-by-step explanation:

Answer:

$342

Step-by-step explanation:

Let the total cost of the dinner = C

If it was shared equally by k employees who attended the dinner and each of the k employees who shared the cost of the dinner paid $19.

We have:

[tex]\dfrac{C}{k}=19 \\\\C=19k[/tex]

If the total cost(C) had been shared equally by k + 1 employees who attended the dinner, each of the k + 1 employees would have paid $18.

This written mathematically is:

[tex]\dfrac{C}{k+1}=18 \\\\C=18(k+1)[/tex]

Equating the cost, C from both equations

19k=18(k+1)

19k=18k+18

19k-18k=18

k=18

Therefore, the total cost of the dinner,

C=19k

=19 X 18

=$342

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) , thus

f(x) + g(x)

= 2x + 1 + x² - 7 ← collect like terms

= x² + 2x - 6 → C

Answer:

r=3

Step-by-step explanation:

First we add 2 to both sides.

That leaves us with 10r=30

Then we can divide both sides by 10

r=3

Answer:

R=C

Step-by-step explanation:

got 100 on edge

Answer:

20

Step-by-step explanation:

Answer:20

Step-by-step explanation:

Answer:

The growth rate is 7.2%

Step-by-step explanation:

First thing we need to do here is to set up an exponential equation;

This can be written as follows;

F = I(1 + r)^t

where F is the future value = 20,000

I is the initial value = 10,000

r is the rate in percent which we want to calculate

t is time in years = 10 years

Substituting the values in the question into the exponential equation, we have;

20,000 = 10,000(1 + r)^10

divide both side by 10,000

2 = (1+r)^10

Find the 10th root of both sides

1+ r = 2^(1/10)

1 + r = 1.07177346254

r = 1.07177346254-1 = 0.07177346253

Let’s approximate r as 0.072

Now this to percentage?

That would be 72/1000 * 100% = 7.2%

Answer:

a) P(X=x) = p× (1-p)^(x-1)

b) P(X=3) = 0.081

c) P(X≤5) = 0.40951

d) Mean of X= 10

e) Var(X)= 90

Step-by-step explanation:

This is a question on geometric distribution.

In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.

This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)

For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}

We stop the trials when we get a success.

From the question, there are 10 numbers

The probability of success = p = 1/10

For the solutions of the question from (a-e), See attachment below.

f(x) = P(X= x)

Where P(X= x) is the probability of X taking on a value x

Answer:

A) 348 square m

Step-by-step explanation:

Surface area of the figure

[tex] = 2(15 \times 6 + 6 \times 4 + 15 \times 4) \\ = 2(90 + 24 + 60) \\ = 2 \times 174 \\ = 348 \: {m}^{2} \\ [/tex]

Answer:

90:55

Step-by-step explanation:

18 + 11 = 29

145/29 = 5

5 x 18 = 90

5 x 11 = 55

Step-by-step explanation:

The expression:

[tex]\frac{1}{1+a} + b^{-1} + \frac{1}{1+b} + c^{-1} + \frac{1}{1+c} + a^{-1}[/tex]

It is possible that there are values for a, b, and c, but are omitted. If this is not the case, then the expression can be rewritten in another form. These are about all that can be done.

The second case is more plausible, given there are no values given for a, b, and c.

The expression can be rewritten as:

[tex]a^{-1}+b^{-1}+c^{-1} + \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}[/tex]

When a number has an index of -1, it is the same as taking the reciprocal of the number.

That is;

[tex]a^{-1} = \frac{1}{a}[/tex]

Therefore, the whole expression gives:

[tex]\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}[/tex]

Taking the common denominator in the first three expressions, we have

[tex]\frac{a+b+c}{abc} + \frac{1}{1+a} +\frac{1}{1+b} + \frac{1}{1+c} \\[/tex]

It is also possible to take the common denominator of the whole whole expression, this will however, make the expression look more tedious, rather than simple.

The expression:

It is possible that there are values for a, b, and c, but are omitted. If this is not the case, then the expression can be rewritten in another form. These are about all that can be done.

The second case is more plausible, given there are no values given for a, b, and c.

The expression can be rewritten as:

When a number has an index of -1, it is the same as taking the reciprocal of the number.

That is;

Therefore, the whole expression gives:

Taking the common denominator in the first three expressions, we have

It is also possible to take the common denominator of the whole whole expression, this will however, make the expression look more tedious, rather than simple.

Answer:

121.43%

Step-by-step explanation:

Data provided in the question

Median salary in US men for year 2010 = $42,500

Median salary in US women for the year 2010 = $35,000

Based on the above information, the percentage of the median salary for US women is

= Salary of men ÷ Salary of women × 100

= $42,500 ÷ $35,000 × 100

= 121.43%

basically we applied the above formula so that the percentage could come

Answer:

C

Step-by-step explanation:

Given

- 5, - 1, 3, 7, 11

There is a common difference d between consecutive terms, that is

11 - 7 = 7 - 3 = 3 - (- 1) = - 1 - (- 5) = 4

This indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 5 and d = 4 , thus

[tex]a_{n}[/tex] = - 5 + 4(n - 1) = - 5 + 4n - 4 = 4n - 9

Answer:

plz give brainliest

Step-by-step explanation:

Points A, B, and C lie on a line.

Point A is between points B and C.

Starting at point A and going past point B, you have ray AB.

Starting at point A and going past point C, you have ray AC.

If you think of angle BAC, it is a straight angle of 180 degrees.

You have the two rays AB and AC forming a line and an angle.

Answer:

Periodic phenomena means that the phenomena has a (almost) constant time period or space period.

As you know, the trigonometric functions cos(x) and sin(x) also have a constant period of 2*pi, so these functions are really useful to model periodic phenomena.

Now, the problem may be that the trigonometric functions may be useful to describe the "periodic" part, but not to describe the actual phenomena.

An example of this can be a square alternating current.

While it has a constant period like a trigonometric function, the trigonometric functions can not really model the "square" part of this current (you know that the sinusoidal functions actually are curves and continuous)

Here comes something called the Fourier Series, that are series of the form:

F(x) = a₀ + ∑(aₙ*cos(nx) + bₙ*sin(nx))

That can be used to model almost any periodic phenomena, but the actual Fourier Series may be hard to construct.

Answer:

m = -2/3

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in our coordinates into the formula:

m = (3 - 7)/(3 + 3)

m = -4/6

m = -2/3

Answer:

-2/3

Step-by-step explanation:

In order to find the slope, we need to find the change in y over change in x

For y: 7-3=4

For x: -3-3=-6

4/-6

We can simplify it into 2/-3

Answer:

option b

Step-by-step explanation:

replace x and y with the x and y of the ordered pair

option a: 2(4)+4(5)=6(4)-5

solve

8+20=24-5

28=19  not true

option b:2(5)+4(4)=6(5)-4

solve

10+16=30-4

26=26  true

Answer:

Erica has 51 action figures and Ricardo has 17 action figures.

Step-by-step explanation:

First, label your variables.

x=the number of action figures Erica has

y=the number of action figures Ricardo has

You know that they have 68 total action figures so x+y=68.

Erica has 3 times as many as Ricardo so 3y=x. Then solve for x and y.

x+y=68    3y=x   (Substitue 3y for x)

3y+y=68   (Then combine like terms)

4y=68  (Divide each side by 4)

y= 17

Now that you know that Ricardo has 17 action figures, you can plug 17 in for y in either equation to find x.

3(17)=x

x=51

To check your answers, you can plug them back into the original equations.

Answer:

Erica:51 action figures; Ricardo: 17 action figures

Reason:

68/4=17

17*3=51<- this is the amount of action figures that Erica has.

17 <-this is the amount of action figures that Ricardo has.

17 (Ricardo) + 51 (Erica) = 68 (total amount)

Options

Answer:

(D)g(3) = 18

Step-by-step explanation:

Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of                       0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Then the following properties must hold

We consider the options and state why they are true or otherwise.

Option A: g(5)=12

The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

Option B: g(1) = -2

The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

Option C: g(2) = 4

The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

Option D: g(3) = 18

This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.

Therefore, Option D could be true.

Answer: g(3) =18

Step-by-step explanation: thats probably all you need

Answer:

10 to the left I believe

Step-by-step explanation:

Answer:

-5(t - 70) = -60

t - 70 = 12 -- Divide by -5

t = 82 -- Add 70

Answer:

The answer is below

Step-by-step explanation:

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $19 monthly fee and charges an additional $0.13 for each minute of calls. The second plan has a $24 monthly fee and charges an additional $0.08 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal

Answer: Let the number of minutes of calls that will cost the two plans to be equal be x. The first plan has a $19 monthly fee and charges an additional $0.13 for each minute of calls, therefore the total cost in x minutes = $19 + $0.13x

The second plan has a $24 monthly fee and charges an additional $0.08 for each minute of calls, therefore the total cost in x minutes = $24 + $0.08x

For the two plans to be equal, the cost of the first plan should be equal to the cost of the second plan. i.e.:

$19 + $0.13x =  $24 + $0.08x

Solving for x:

[tex]$19 + $0.13x = $24 + $0.08x\\0.13-0.08=24-19\\0.05x=5\\x=5/0.05=100\\x=100\ minutes[/tex]

It would take 100 minutes of calls for the costs of the two plans to be equal