determine the 2nd and 3rd terms of a geometric sequence of which T1 =5 and T4=40​

9514 1404 393

Answer:

  a. 1.48 seconds

Step-by-step explanation:

You want to find the larger value of t such that h(t) = 10.

  -16t^2 +25t +8 = 10

  16t^2 -25t +2 = 0 . . . . subtract the left side to get standard form

Using the quadratic formula, we find the values of t to be ...

  t = (-(-25) ± √((-25)^2 -4(16)(2)))/(2(16)) = (25±√497)/32

  t ≈ 0.08 or 1.48

The ball goes in the hoop about 1.48 seconds after it is thrown.

__

Additional comment

The quadratic formula tells us the solution to ...

  ax² +bx +c = 0

is given by ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, we have a=16, b=-25, c=2. Of course, our variable is t, not x, but the relation is the same.

9514 1404 393

Answer:

  A. 5 should have been subtracted in step 4

Step-by-step explanation:

No question is stated, so there is no "answer."

__

If we assume the question is, "What error did Keith make?" then choice A properly describes it.

Step 4 should look like ...

  x -5 = 7y . . . . . . . 5 should be subtracted from both sides

and the final result should be ...

  g(x) = (x -5)/7

This question is incomplete, the complete question is;

United Airline flights from Newark to Seattle are typically booked to capacity. However, due to United’s current lenient rebooking policies, on average 17 customers (with a standard deviation of 10) cancel or are no shows for these flights. The average revenue collected on this flight is is $145/seat. However, if the flight is overbooked and the airline needs to rebook a ticketed passenger, United typically gives the customer a free round-trip ticket for a future flight. The cost of this free round-trip ticket averages $330. By how many seats should United overbook for this route?

Answer:

the number of seats that should be overbooked is approximately 12

Step-by-step explanation:

Given the data in the question;

average = 17 customers

standard deviation = 10

Cost of under booking the flight ( underage ); Cu = $145

Cost of overbooking the flight ( Overage ); Co = $330

we calculate the service level

service level = Cu / ( Cu + Co )

we substitute

Service level = 145 / ( 330 + 145 )

= 145 / 475

Service level = 0.3053

In excel, we use NORMSIV function to determine the z-value

z-value = NORMSIV ( 0.3053 )

z -value = -0.509

Now, the number of seats (Q) that should be overbooked will be;

Q = Average cancellations + Z-value × S.D

we substitute

Q = 17 + ( -0.509 × 10 )

Q = 17 + ( -5.09 )

Q = 17 - 5.09

Q = 11.91 ≈ 12

Therefore, the number of seats that should be overbooked is approximately 12

Answer:

B. 9

Step-by-step explanation:

We are given that y varies inversely with x. Recall that inverse variation has the form:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

We are given that y = 18 when x = 12. Hence:

[tex]\displaystyle (18)=\frac{k}{(12)}[/tex]

Solve for k. Multiply both sides by 12:

[tex]k=12(18)=216[/tex]

Thus, our equation is:

[tex]\displaystyle y=\frac{216}{x}[/tex]

We want to find x when y = 24. Substitute:

[tex]\displaystyle \frac{24}{1}=\frac{216}{x}[/tex]

Cross-multiply:

[tex]24x=216[/tex]

Divide both sides by 24. Hence:

[tex]x=9[/tex]

Our answer is B.

Answer:

B

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 18 when x = 12 , then

18 = [tex]\frac{k}{12}[/tex] ( multiply both sides by 12 )

216 = k

y = [tex]\frac{216}{x}[/tex] ← equation of variation

When y = 24 , then

24 = [tex]\frac{216}{x}[/tex] ( multiply both sides by x )

24x = 216 ( divide both sides by 24 )

x = 9

Answer:

$325.50

Step-by-step explanation:

1) 210÷100 = 2.1

  2.1×55 = 115.5

  210 + 115.5 = 325.5

2) 210×55 = 11550

   11550÷100 = 115.5

   210 + 115.5 = 325.5

Answer:

Area: 360 cm

Perimeter: 44 cm

Step-by-step explanation:

To calculate the area, you must multiply the length x width.

If you need help calculating the perimeter too, just add all your lengths and widths together twice.

Answer:

300%

Step-by-step explanation:

because 9/3×100=900/3=300 so it is 300%

Answer:

300%

Step-by-step explanation:

9/3 * 100%

900%/3 = 300%

Answer:

9

Step-by-step explanation:

Let the number be X

From the problem we have the following equation:

7x - 17 = 3x + 19

-> 4x = 36

-> x = 9

Answer:

9

Step-by-step explanation:

that is the procedure above

Answer:

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Independent events:

If two events, A and B are independent, the probability of both events happening is the multiplication of the probabilities of each event happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Probability of getting a head on the coin:

Head or tails, fair coin, so:

[tex]P(A) = \frac{1}{2}[/tex]

Probability of getting the number 2 on the die:

6 numbers, one of which is 2, so:

[tex]P(B) = \frac{1}{6}[/tex]

What is the probability of getting a head on the coin and the number 2 on the die?

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Answer:

4:30

because 9:30 minus 4:30 = 5:00 and 5:00 minus 30 =4:30

Answer:

[tex]P(\bar A) = 0.5[/tex]

Step-by-step explanation:

Given

[tex]P(A) = 0.5[/tex]

Required

[tex]P(\bar A)[/tex]

To do this, we make use of complement rule:

[tex]P(\bar A) = 1 - P(A)[/tex]

So, we have:

[tex]P(\bar A) = 1 - 0.5[/tex]

[tex]P(\bar A) = 0.5[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{3x + 5}{2x + 7}[/tex] = 5

do cross multiplication

3x + 5 = 5(2x + 7)

3x + 5 = 10x + 35

5 - 35 = 10x - 3x

-30 = 7x

-30/7 = x

20 A

since there are 7 angles given it means that the polygon is heptagon as heptagon has 7 sides.

sum of interior angle of heptagon = (n-2)*180

(7-2)*180

5*180

900

Now ,

110 + 90 + 150 + 102 + 110 + 170 + x = 900

732 + x = 900

x = 900 - 732

x = 168 degree

20 B

since 5 angles are given it means that the polygon is pentagon as pentagon has 5 sides.

sum of interior angles of a pentagon = (n-2)*180

(5-2)*180

3*180

540 degree

Now ,

110 + 95 + 120 + 114 + x = 540

465 + x = 540

x = 540 - 465

x = 75 degree

21

let one rational number be x

according to the question,

1/7 * x = 2

x/7 = 2

do cross multiplication

x = 14

Answer:

Her food cost as a percentage of sales is 33.58%.

Step-by-step explanation:

Since Chef Amy does beginning inventory on Thursday night and finds that she has $ 4697 in food products in the restaurant, and throughout the week she purchases:

$ 668 produces

$ 2206 meat

$ 2488 dry goods

$ 3755 dairy

The following Thursday she does ending inventory and finds that she has $ 3518 in food.

She looks at her sales de ella and finds that she made $ 30658 over the same 7 day period.

To determine what her food cost is as a percentage of sales (her food cost percentage), the following calculation must be performed:

4,697 + 668 + 2,206 + 2,488 + 3,755 = 13,814

13,814 - 3,518 = 10,296

30,658 = 100

10,296 = X

10,296 x 100 / 30,658 = X

1,029,600 / 30,658 = X

33.58 = X

Therefore, her food cost as a percentage of sales is 33.58%.

Answer:

B

Step-by-step explanation:

We want to determine an equivalent trignometric identity with the given expression:

[tex]\cos (x) - \cos^3 (x)[/tex]

We can factor out a cos(x):

[tex]=\cos (x) (1-\cos^2 (x))[/tex]

Recall from the Pythagorean Identity that:

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Therefore:

[tex]\displaystyle \sin^2(x) = 1 - \cos^2(x)[/tex]

Substitute:

[tex]=\cos(x)(\sin^2(x))=\cos(x)\sin^2(x)[/tex]

Our answer is B.

Answer:

D

Step-by-step explanation:

i think it's correct if not I'm sorry

Answer:

[tex]C = 48.6[/tex]

Step-by-step explanation:

Given

[tex]Area= 4.5m^2[/tex]

[tex]a =4[/tex]

[tex]b = 3[/tex]

Required

Find angle C

The area of the triangle will be calculated using:

[tex]Area = \frac{1}{2}ab \sin C[/tex]

So, we have:

[tex]4.5= \frac{1}{2} * 4 * 3 * \sin C[/tex]

[tex]4.5= 6 * \sin C[/tex]

Divide both sides by 6

[tex]0.75= \sin C[/tex]

Take arc sin of both sides

[tex]\sin^{-1}(0.75)= C[/tex]

[tex]48.6 = C[/tex]

[tex]C = 48.6[/tex]

Answer:

0.30

Step-by-step explanation:

Find the probability by adding the probabilities together for having two and four honors classes.

25% offer two honors classes and 5% offer four honors classes. Add these together:

25 + 5

= 30

So, there is a 30% probability that the school offers an even number of honors classes.

The correct answer is 0.30.

Answer:

45.712

Step-by-step explanation:

We need to find the Zscore of the area of 15 percent of the distribution ; using a Z table or calculator ;

Zscore of 15% of the distribution is : - 1.036

Using the Zscore formula :

Zscore = (x - mean) / standard deviation

Where, x = score

-1.036 = (x - 54) / 8

Cross multiply

-1.036 * 8 = x - 54

-1.288 = x - 54

x = - 8.288 + 54

x = 45.712

Answer:

x-intercept=3

y-intercept=4

z-intercept=2

Step-by-step explanation:

Answer:

14 to 132

Step-by-step explanation:

We are given that there are 132 boys and 14 adults. Since the question is only asking for the ratio of adults to boys, we don't have to worry about the number of girls in this question. From here, we see that the question is asking for the ratio of adults to boys, so we put it in that exact order. Our answer is 14 to 132. I hope this helps and please don't hesitate to reach out with more questions!

Answer:

24 mph

Step-by-step explanation:

1 hour of 36 mph

3 hours of 20 mph

(36 + 20 + 20 + 20)/4

96/4

24

Answer:

24 mph

Step-by-step explanation:

36 miles = 1 hour

60 miles = 3 hours

36+60= 96

1+3+4

96/4= 24

Answer:

$2550

Step-by-step explanation:

Calculation to determine the amount of retained earnings at the beginning of Year 2

Using this formula

Beginning Retained Earnings + Revenue − Expenses − Dividends = Ending Retained Earnings

Let plug in the formula

Beginning Retained Earnings + $3,200 − $1,700 − $1,100 = $2950

Beginning Retained Earnings= $2,950-$400

Beginning Retained Earnings = $2,550

Therefore the amount of retained earnings at the beginning of Year 2 is $2550

Answer:

The volume of the sphere is 2048 in³.

Step-by-step explanation:

The volume of a sphere is given by:

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

Where:

r: is the radius = 8 in

Having the radius and by using 3 for π, the volume is:

[tex] V = \frac{4}{3}*3 (8 in)^{3} = 2048 in^{3} [/tex]

Therefore, the volume of the sphere is 2048 in³.

I hope it helps you!        

Answer:

[tex]m = \frac{1}{12}[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (36,6)[/tex]

[tex]f(x) = \sqrt x[/tex] ----- the equation of the curve

Required

The slope of f(x)

The slope (m) is calculated using:

[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex](x,y) = (36,6)[/tex] implies that:

[tex]a = 36; f(a) = 6[/tex]

So, we have:

[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex]m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}[/tex]

If [tex]f(x) = \sqrt x[/tex]; then:

[tex]f(36 + h) = \sqrt{36 + h}[/tex]

So, we have:

[tex]m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}[/tex]

Multiply by: [tex]\sqrt{36 + h} + 6[/tex]

[tex]m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}[/tex]

Expand the numerator

[tex]m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}[/tex]

Collect like terms

[tex]m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}[/tex]

[tex]m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}[/tex]

Cancel out h

[tex]m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}[/tex]

[tex]h \to 0[/tex] implies that we substitute 0 for h;

So, we have:

[tex]m = \frac{1}{\sqrt{36 + 0} + 6}[/tex]

[tex]m = \frac{1}{\sqrt{36} + 6}[/tex]

[tex]m = \frac{1}{6 + 6}[/tex]

[tex]m = \frac{1}{12}[/tex]

Hence, the slope is 1/12

Answer:

[tex]z + 4 = 15 \\ z + 4 - 4 = 15 \\ z = 15 - 4 \\ z = 11[/tex]

z>11

Answer:

She should ride the train for 6 trips and the bus for 2 trips in order to minimize her cost.

Step-by-step explanation:

Let x represent the number of times that she travels using the train and let y represent the number of times she travels using the bus. Since she makes at least 8 trips to the place, hence:

x + y ≥ 8

Also, she plans to spend no more than 9 hr in travel time. Hence:

x + 1.5y ≤ 9

x ≥ 0, y ≥ 0.

Plotting the above equations on geogebra online graphing tool, the solution is (6, 2), (8, 0) and (9, 0).

If a train trip costs ​$6 and a bus trip costs ​$5, The cost equation (C) is:

C = 6x + 5y

At point (6, 2): C = 6(6) + 5(2) = $46

At point (8, 0): C = 6(8) + 5(0) = $48

At point (9, 0): C = 6(9) + 5(0) = $54

Therefore the minimum cost is at (6, 2). She should ride the train for 6 trips and the bus for 2 trips in order to minimize her cost.

Answer:

you mean the mean not the meaning right?

The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.

Answer:

The probability that the company will receive 7 property damage claims on a randomly selected day is 0.137

Step-by-step explanation:

Given,

[tex]\lambda=6[/tex],

The probability mass function of Poisson distribution is used for evaluating the probability of the company will receive 7 property damages claims on any selected day is,

[tex]\begin{aligned}P(X=K)&=e^{-6} \times \dfrac{6^7}{7!}\\&=0.002478\times\dfrac{279936}{5040}\\&=\dfrac{693.89136}{5040}\\P(X=7)&=0.1365927874\\P(X=7)&=0.137\; (\rm{rounded \;off})\end{aligned}[/tex]

To learn more about this, please refer to the below link:

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Answer:

let inverse f(x) be m:

[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]

substitute x in place of m:

[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]