An internet cafe charges a fixed amount per minute to use the internet. The cost of using the
internet in dollars is, y = 3/4x. If x is the number of minutes spent on the internet, how many
minutes will $6 buy?
er

Answer:

The sum is 2275

Step-by-step explanation:

Given

[tex]75,76,77....99,100[/tex]

Required

The sum

Using arithmetic progression, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where:

[tex]T_1 = 75[/tex] --- first term

[tex]T_n = 100[/tex] --- last term

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 100 - 75 + 1 = 26[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]

[tex]S_n = 13*175[/tex]

[tex]S_n = 2275[/tex]

Answer:

.33x = 105.60

$371

Step-by-step explanation:

Answer:

63.44

Step-by-step explanation:

its 63.44697 but you round so its 63.44

Answer:

8. 36

Step-by-step explanation:

8.

The diameter of the square is x=[tex]\sqrt{6^{2} +6^{2} }\\[/tex] = [tex]\sqrt{72}[/tex] = 6 [tex]\sqrt{2}[/tex]

The diameter of the square is the diameter of the circle, therefore the radius of the circle is r = 6 [tex]\sqrt{2}[/tex]/2 = 3[tex]\sqrt{2}[/tex]

The area of the shaded region, which is a circle is A= π[tex]r^{2}[/tex] =  π[tex](3\sqrt{2} )^{2}[/tex] = 36π

The factors of 45 are 9 and 5.

A number divisible by 45 needs to be divisible by both 9 and 5.

For a number to be divisible by 9 the sum of the digits must also be divisible by 9 and the number needs to end with either a 0 or a 5 to be divisible by 5.

This means the number needs to end with the 0 so cross out the last number (4)

Now find a sum of 5 remaining numbers divisible by 9.

5 + 1 + 4 + 8 + 0 = 18 which is divisible by 9

Cross out 9,7 and the last number 4 to get the number: 51480

Answer:

Lucy must walk up 80 steps to reach the 6th floor.

Step-by-step explanation:

Since Michael was 1.0 meters tall, and could only reach up to the 1st floor lift button, and from the 1st floor, he had to walk up 100 steps to reach the 6th floor; while Vinh was 1.4 meters tall, and could reach the 5th floor button, and he had to walk up 20 steps to reach the 6th floor; If Lucy was 1.1 meters tall, to determine how many steps did she have to walk up to reach the 6th floor, the following calculation must be performed:

1 = 100

1.4 = 20

1.4 - 1 = 100 - 20

0.4 = 80

0.1 = X

0.1 x 80 / 0.4 = X

20 = X

100 - 20 = 80

Therefore, Lucy must walk up 80 steps to reach the 6th floor.

Answer:

11/6

Step-by-step explanation:

Answer:

4x2+3=

Step-by-step explanation:

1km = 0.621371miles

195 km= ?

cross multiplication

= 121.167 miles

25 miles= 1hour

121.167miles = ?hours

121.167=25x

divide by 25x both sides

=4.84 hours

approx 5hours

She must ride for 5 hours if she wants to bike 195 km.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Given that cyclist rides at an average speed of 25 miles per hour.

Since 1 km = 0.621371 miles

So 195 km = 121.167 miles

The speed of the cyclist (s)  = 24 miles per hour.

Distance covered by the rider = 195 km

Distance covered by the rider (d) = 121.167 miles

By using the formula,  time taken by a body, we calculate the time,

⇒ t = d/s

Substitute the value of d and s in above the equation

⇒ t = 121.167/ 24

Apply the division operation,

⇒ t = 5

Hence, she must ride for 5 hours if she wants to bike 195 km.

Learn more about the average speed here :

brainly.com/question/12322912

#SPJ2

Answer:

69.6

Step-by-step explanation:

sin 55 = x / 85

0.8191520443 = x / 85

x = 69.6

Answer:

5

Step-by-step explanation:

x² - 4x = 5

x² - 4x - 5 = 0

the solution of a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = -4

c = -5

x = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2

x1 = (4 + 6)/2 = 5

x2 = (4 - 6)/2 = -1

since we are looking only for a positive number, x=5 is the answer.

Answer:

[tex]1-(5/6)^2[/tex]

31% chance

1 in 3.272727273 rolls

Step-by-step explanation:

Answer:

[tex]\sigma = 1.8[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]

Required

The standard deviation

First, calculate the expected value E(x)

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]

[tex]E(x) = 2.7[/tex]

Next, calculate E(x^2)

[tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]

[tex]E(x^2) = 10.5[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]

[tex]\sigma = \sqrt{3.21}[/tex]

[tex]\sigma = 1.8[/tex] --- approximated

Answer:

Step-by-step explanation:

Total number of balls = 3 + 2 = 5

1)

a)

[tex]Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\[/tex]

b)

[tex]Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]

c)

Probability of at least one black( means BB or BW or WB)

 [tex]=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}[/tex]

d)

Probability of at most one black ( means WW or WB or BW)

[tex]=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}[/tex]

2)

a) Probability both black without replacement

  [tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]

b) Probability  of one black and one white

 [tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]

c) Probability of at least one black ( BB or BW or WB)

 [tex]=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}[/tex]

d) Probability of at most one black ( BW or WW or WB)

 [tex]=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}[/tex]

Answer:

The LCM of 20 and 30 is 60.

Step-by-step explanation:

LCM means the least common multiple.

The LCM of two numbers means the least multiple both numbers share.

Use the listing method:

Multiples of 20:

20, 40, 60, 80, 100, ......

Multiples of 30:

30, 60, 90, 120, 150, ...

The LCM is 60 because that is the least common multiple 20 and 30 have.

Hope this helps

Answer:

[tex]x = - 2[/tex]

[tex]x = - 5[/tex]

Step-by-step explanation:

Give

[tex](x - 5)(x + 12)[/tex]

Apply FOIL Method

[tex]x {}^{2} + 7x - 60 = - 70[/tex]

Add 70 on both sides

[tex] {x}^{2} + 7x + 10[/tex]

Factor

[tex](x + 2)(x + 5)[/tex]

So our roots are

x=-2

x=-5

Answer:

dtet

Step-by-step explanation:

dgbyn

Answer:

total pencil = 5 orange pencils + 8 yellow pencils + 4 green pencils

= 17 pencils

P (g n y) = 4/17 + 8/17

= 0.706

Step-by-step explanation:

1. first find the total number of pencils

2. since there is a replacement the demoinator remains the same

3. find the probability of each green and yellow

4. add the two probability

Answer:

the answer of r is 8 i hope it will help

Given:

The sum of the first three terms = 12

The sum of the first six terms = (−84).

To find:

The third term of a geometric progression.

Solution:

The sum of first n term of a geometric progression is:

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Where, a is the first term and r is the common ratio.

The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).

[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex]               ...(i)

[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex]               ...(ii)

Divide (ii) by (i), we get

[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]

[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]

[tex]r^3+1=-7[/tex]

[tex]r^3=-7-1[/tex]

[tex]r^3=-8[/tex]

Taking cube root on both sides, we get

[tex]r=-2[/tex]

Putting [tex]r=-2[/tex] in (i), we get

[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]

[tex]\dfrac{a(-8-1)}{-3}=12[/tex]

[tex]\dfrac{-9a}{-3}=12[/tex]

[tex]3a=12[/tex]

Divide both sides by 3.

[tex]a=4[/tex]

The nth term of a geometric progression is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get

[tex]a_3=4(-2)^{3-1}[/tex]

[tex]a_3=4(-2)^{2}[/tex]

[tex]a_3=4(4)[/tex]

[tex]a_3=16[/tex]

Therefore, the third term of the geometric progression is 16.

Answer:

the probability that I chose red or blue is 75%

75%

9514 1404 393

Answer:

  (c)  2^r = a

Step-by-step explanation:

The relationship between log forms and exponential forms is ...

  [tex]\log_2(a)=r\ \Leftrightarrow\ 2^r=a[/tex]

__

Additional comment

I find this easier to remember if I think of a logarithm as being an exponent.

Here, the log is r, so that is the exponent of the base, 2.

This equivalence can also help you remember that the rules of logarithms are very similar to the rules of exponents.

Answer: Choice C)  [tex]2^r = a[/tex]

This is the same as writing 2^r = a

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

Explanation:

Assuming that '2' is the base of the log, then we'd go from [tex]\log_2(a) = r[/tex] to [tex]2^r = a[/tex]

In either equation, the 2 is a base of some kind. It's the base of the log and it's the base of the exponent.

The purpose of logs is to invert exponential operations and help isolate the exponent. A useful phrase to help remember this may be: "if the exponent is in the trees, then we need to log it down".

The general rule is that [tex]\log_b(y) = x[/tex] converts to [tex]y = b^x[/tex] and vice versa.

9514 1404 393

Answer:

Step-by-step explanation:

I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.

You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.

  100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10

The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.

The trinomial can be rewritten using these factors as ...

  2x^2 +5x +20x +50

Then it can be factored by grouping consecutive pairs:

  (2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)

_____

Additional comment

It doesn't matter which of the factors of the pair you write first. If our rewrite were ...

  2x^2 +20x +5x +50

Then the grouping and factoring would be (2x^2 +20x) +(5x +50)

  = 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring

width = x

length = 3 + x

perimeter = x + x + ( 3 + x ) + (3+x)

18 = x + x + ( 3 + x ) + (3+x)

x + x + ( 3 + x ) + (3+x) = 18

6 + 4x = 18

4x = 12

x = 3

Answer:

A number is right 12 centimetres

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

Step by step solution :

STEP

1

:

Equation at the end of step 1

(((x3) - 2x2) + 2x) - 1 = 0

STEP

2

:

Checking for a perfect cube

2.1 x3-2x2+2x-1 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-2x2+2x-1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 2x-1

Group 2: -2x2+x3

Pull out from each group separately :

Group 1: (2x-1) • (1)

Group 2: (x-2) • (x2)

Answer:

(-7, -1) =(x1,y1)

(8, 5)=(x2,y2)

now

[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]

[tex]or = \frac{5 + 1} {8 + 7} [/tex]

[tex]or = \frac{6}{15} [/tex]

[tex]or = \frac{2}{5} [/tex]

Step-by-step explanation:

hope it is helpful to you ☺️

Answer:

B

Step-by-step explanation: Because Donald asks a more broad and open question which people could give different answers too

Answer:

D) y = –5x + 4x^2 + 2

Step-by-step explanation:

You can tell by the first number being positive or negative. To check use Desmo graphing calculator and enter your equation for next time.

Answer:

The 3rd

Step-by-step explanation:

If x goes to infinity, f(x) goes to infinity too:

[tex]lim \: \frac{2 {x}^{2} }{3x - 1} = lim \frac{2x}{3 - \frac{1}{x} } = \frac{ 2 \times \infty }{3 - 0} = \infty [/tex]

Answer: 5%

Step-by-step explanation:

In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:

= 3/4 × 160

= 120

In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:

= 120 + 6

= 126

The percentage increase will be:

= Increase / Old vehicle owners × 100

= 6/120 × 100

= 1/20 × 100

= 5%

The Percentage increase is 5%.

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

[tex]\frac{1}{\lambda} = 13[/tex]

[tex]\lambda = \frac{1}{13}[/tex]

As we know,

The cumulative distributive function will be:

⇒ [tex]1-e^{-\lambda x}[/tex]

hence,

In the first 5 years, the probability of failure will be:

⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]

                    [tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]

                    [tex]=1-e^(-\frac{5}{13})[/tex]

                    [tex]=1-0.6807[/tex]

                    [tex]=0.3193[/tex]