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bogdanovich [222]

3 years ago

15

An airline has six flights from New York to California and seven flights from California to Hawaii per day. If the flights are t

o be made on separate days, how many different flight arrangements can the airline offer from New York to Hawaii?
a) 6*7=42
b) 6+7=13
c) 67 = 279936
d) 76 = 117649

1 answer:

Ilya [14]3 years ago

3 0

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

Number of flights from New York to California = 6

Number of flights from California to New York = 7

Since if the flights are to be made on separate days,

So, they are independent events.

So, the number of different flight arrangements that can be made offer from New York to Hawaii would be

$6\times 7\\\\=42$

Hence, Option 'a' is correct.

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The volume of clay used to build a cylindrical pillar with a height of 9 centimeters is 324π cubic centimeters. What is the area

elena-s [515]

Given:
V = 324 cu cm
h = 9 cm

Since the formula for the volume of a cylinder is V = AreaBase*height

AreaBase = V/height = 324cu cm/ 9 cm
AreaBase = 113.04 square centimetres

Therefore, the area of the pillar in square centimeters is 113.04.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

5 0

3 years ago

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A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago, the age of the father was five tim

arlik [135]

Answer:

20

Step-by-step explanation:

To solve this you have to make a system of equations.

Since the father and son's age sum up to 60, the first equation will be:

f + s = 60

Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:

6 - (5s) = f

Now, you have to solve the first equation to let it equal to s

f + s = 60

f = 60 - s

Plug in

6 - 5s = 60 - s

+s +s

6 - 4s = 60

-6 -6

---------------------

-4s = 54

----- -----

-4 -4

s ≅ 14

14 + 6 = 20

5 0

1 year ago

Read 2 more answers

Find the sum of the first 25 terms in this geometric series:<br> 8 + 6 + 4.5...

Ksivusya [100]

Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{3}{4}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=8$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=8\left(\frac{3}{4}\right)^{n-1}$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}$

$=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}$

$=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32$

$=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}$

$=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}$ ∵ $\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}$

$=32\cdot \frac{4^{25}-3^{25}}{4^{25}}$

$=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}$

$=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}$ ∵ $\mathrm{Factor}\:32:\ 2^5$ , $\mathrm{Factor}\:4^{25}:\ 2^{50}$

so

$=\frac{4^{25}-3^{25}}{2^{45}}$ ∵ $\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}$

$=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}$

$=32-\frac{3^{25}}{2^{45}}$ ∵ $\frac{4^{25}}{2^{45}}=32$

$=32-0.024$ ∵ $\frac{3^{25}}{2^{45}}=0.024$

$=31.98$

Therefore, the sum of the first 25 terms in this geometric series: 31.98

3 0

3 years ago

Please please please please please answer A through D

muminat

Answer:

A: Yes, As more gallons are used the longer the shower is

B: 5 minutes, 20 minutes

C: (30,10), someone who uses 30 gallons of water will be in the shower for 10 minutes

D: I'm going to assume that your teacher wants you to find the slope in which I will use the slope formula and the points (0,0) and (30,10)

(10-0)/(30-0)=1/3=.33333 which means that for every gallon of water used you will be in the shower for .33333 minutes longer

Step-by-step explanation:

A: Yes, As more gallons are used the longer the shower is

B: 5 minutes, 20 minutes

C: (30,10), someone who uses 30 gallons of water will be in the shower for 10 minutes

D: I'm going to assume that your teacher wants you to find the slope in which I will use the slope formula and the points (0,0) and (30,10)

(10-0)/(30-0)=1/3=.33333 which means that for every gallon of water used you will be in the shower for .33333 minutes longer

7 0

2 years ago

Here’s another one that I’m having trouble with

Alla [95]

The total is 94 units.

A square has four equal sides so...

(5x-1)+(4x+3)+(5x-1)+(4x+3)=94

Combine like terms

19x+4=94

Subtract 4 from both sides

94-4=90

18x=90

Divide by 18 on both sides

90/18=5

X=5

Plug 5 in for x on the length of PQ

4(5)+3

20+3=23

Length of PQ=23 units

6 0

3 years ago

Read 2 more answers