The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month.

The table shows that as more minutes are used each month, the total monthly cost will increase at the same rate. Assuming that this is true, what is the total monthly cost for the cell phone if it is used for 2,500 minutes?

Given:

[tex]\sin x=-\dfrac{15}{17}[/tex]

x lies in the III quadrant.

To find:

The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others  are negative.

We know that,

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

[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]

[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]

[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]

x lies in the III quadrant. So,

[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]

[tex]\cos x=-\dfrac{8}{17}[/tex]

Now,

[tex]\sin 2x=2\sin x\cos x[/tex]

[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]

[tex]\sin 2x=-\dfrac{240}{289}[/tex]

And,

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

[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]

[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]

[tex]\cos 2x=\dfrac{289-450}{289}[/tex]

[tex]\cos 2x=-\dfrac{161}{289}[/tex]

We know that,

[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]

[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]

[tex]\tan 2x=\dfrac{240}{161}[/tex]

Therefore, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].

Answer:

option 3, double the height and with of original bottle

The methods which will create the larger water bottle with the intended volume is 1 and IV.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

A water bottle company is designing a new larger cylindrical water bottle that is intended to hold 4 times as much water as the original cylindrical water bottle.

Volume of a cylindrical shape = π r² h

Let V be the original volume.

If radius is doubled, then the new volume is,

V' = π (2r)² h = 4(π r² h) = 4V

So 1 is an option.

When the height is Quadrupled,

V' = π r² 4h = 4(π r² h) = 4V

Hence the correct options are 1 and IV.

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Answer:

226 inches cube

Step-by-step explanation:

The volume of the cylinder is the area of the base X height therefore it would be 3^2 * 3.14 * 8 = 72 * 3.14 = 226.08.

Answer:

151 in^3

Step-by-step explanation:

pi x 3^2 x 5.5 (the approximate water level)

= 155

151 is the closest answer

Answer: 3.6

Step-by-step explanation:

Using pythagorean we can determine that a^2+b^2=c^2

In this case the leg and adjacent make a distance of 2 and 3 we can substitute for a and b so

[tex]2^{2}+3^{2}=c^{2}[/tex]

13=[tex]c^{2}[/tex]

c= 3.605 rounded is 3.6

Answer:

subtraction property for sure its that

Answer:

Bird swoops down by 107 feet to grab a mouse on top of a [tex]3[/tex] foot tall rock

Step-by-step explanation:

Given

The level of mouse from the ground is [tex]3[/tex] foot as it is on the top of a  [tex]3[/tex] foot  tall rock.

The level of bird at which it is flying from the ground is [tex]110[/tex] feet

Change in elevation when the bird swoops down to grab the  mouse

[tex]= 110 -3\\= 107[/tex]feet

Bird swoops down by 107 feet to grab a mouse on top of a [tex]3[/tex] foot tall rock

Answer:

9+4x=25

Step-by-step explanation:

Answer:

L = 6, w = 2

Step-by-step explanation:

Let w = width of rectangle

Let L = length of rectangle

w = L - 4

Area of rectangle = Lw

L (L - 4) = 12

L^2 - 4L = 12

L^2 - 4L - 12 = 0

(L - 6)(L + 2) = 0

L - 6 = 0

L = 6 (the other option doesn't work because dimensions can't be negative)

w = L - 4

w = 6 - 4

w = 2

Double check

A = Lw

A = 6 x 2

A = 12

It matches so we are right.

Answer:

210xyz

Step-by-step explanation:

Given

5x × 6y × 7z

= 5 × x × 6 × y × 7 × z

= 5 × 6 × 7 × x × y × z

= 210xyz

Answer:

400 J

Step-by-step explanation:

Kinetic energy = ½ mv²

mass = 50 kg

velocity = 4 m/s

Kinetic energy = ½×50×(4)²

= ½×50×16

= 50×8

= 400 J

Option Four

[tex]mass(m) = 50kg \\ velocity(v) = 4ms {}^{ - 1} \\ kinetic \: energy = \frac{1}{2} mv {}^{2} \\ = \frac{1}{2} \times 50 \times (4) {}^{2} \\ = 400[/tex]

Answer: 30 meters.

Step-by-step explanation:

Since the scale used by Bruce in the drawing that she made is:

1 milimeter = 10 meters

If the restaurant kitchen is 3 milimeters long in the drawing, the length of the actual kitchen will then be:

1/3 = 10/x

Cross multiply

1 × x = 3 × 10

x = 30

Therefore, the actual length is 30 meters.

Answer:

ANSWER IS C: 71.80

Step-by-step explanation:

hope this helps :D you got this!!

The amount that corresponds to the new monthly payment of Jose is approximately $75.34. Hence, option D is correct.

Credit cards are a widely used financial tool that allow individuals to make purchases on credit. The main use of a credit card is to allow the cardholder to borrow money from the card issuer

If Jose decides to pay off Credit Card B using his savings of $1,750, he will have a remaining balance of $1,154 on Credit Card A.

If he transfers the balance of Credit Card A to the new card with a low introductory rate of 8%, he will incur a balance transfer fee of $60.

The total balance transferred =  $1,154 + $60 = $1,214.

To determine his new monthly payment, we need to calculate the monthly interest rate on the new card.

At an annual interest rate of 8%, the monthly interest rate is :

8% / 12 = 0.67%.

Using an online loan calculator or spreadsheet, we can calculate that the monthly payment required to pay off a balance of $1,214 in 18 months at a monthly interest rate of 0.67% is $75.34 (rounded to the nearest cent).

Therefore, the answer is D. $75.34, which represents Jose's new monthly payment.

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Answer:

1,-1

Step-by-step explanation:

because section be is for +,-

Answer:

1,-1

Step-by-step explanation:

Answer:

161

Step-by-step explanation:

the sum of the two interior angles equals that exterior angle

121+40=161

Answer:

It decreased by 61.5%

Step-by-step explanation:

Answer: 17.156

Step-by-step explanation:

A rational number is any number that has a pattern (in decimals) and can be written as a fraction. 17.156 is a terminating decimal. So its a predicting pattern  therefore is a rational number.

[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]

[tex] - 4(2w + 1)[/tex]

[tex]\huge\red{\boxed{\tt{\colorbox{pink}{Solution:}}}}[/tex]

[tex] - 8w - 4[/tex]

Bind the expression with the common factor -4

[tex] - 8w - 4[/tex]

Answer: −4(2w+1)

Step-by-step explanation: Hope this help :D

Answer:

3 feet

Step-by-step explanation:

3 feet is more because 35 inches = 2 feet and 11 inches.

Answer:

D) FJ is a perpendicular bisector

If Taylor is producing graphic T-shirts that will come in three different colors then about 275 graphic T-shirts should be white.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Since Taylor randomly surveyed 100 people and 55 of them said they prefer the white T-shirt

we can estimate the proportion of people who prefer the white T-shirt as:

p = 55/100 = 0.55

We can assume that this proportion is a good estimate of the true proportion of people who will prefer the white T-shirt among all potential customers.

To estimate the number of people who will prefer the white T-shirt among 500 potential customers

The formula for the expected value of a binomial random variable is

E(x) = np

Substituting the values, we get:

E(x) = 500 × 0.55 = 275

Therefore, about 275 graphic T-shirts should be white.

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Answer:

Yes

Step-by-step explanation:

I'm assuming this is right

Answer:

[tex]y = \frac{1}{2}x + 4\\\\[/tex]

Cayla started with 44 stamps

Step-by-step explanation:

Let x = the number of stamps in Cayla's stamp collection;

[tex]y=\frac{1}{2}x + 4[/tex]

[tex]26 = \frac{1}{2}x + 4\\\\22 = \frac{1}{2}x\\\\44 = x[/tex]

Answer:

2 1/5+6 4/5 =  9

6 5/12 -2 1/12 = 4 1/3

11 8/9+4 1/3 =16  2/9

7 1/6-5 3/4 = 1  5/12

11/18+ 6 1/10 = 6 64/90

15 1/3- 2 5/8 = 12  17/24

Step-by-step explanation:

Using the technique of mixed numbers to add the fractions

2 1/5+6 4/5

=2+6 + 1/5+4/5     add the whole numbers separately and then the fractions

=8 5/5= 9

6 5/12 -2 1/12

=6-2 + 5-1/12

=4 4/12

= 4 1/3

11 8/9+4 1/3

=11+4 +8/9+1/3     adding the whole numbers separately

=15 + 8+3/9

= 15+11/9             adding the fractions separately

= 15+1+2/9

= 16+2/9

=16  2/9

7 1/6-5 3/4

= 7-5 +1/6 -3/4   subtracting the whole numbers separately

= 2+ 2-9/12   subtracting the fractions separately

= 2-7/12  

= 24-7/12

= 17/12

=1  5/12

11/18+ 6 1/10

= 11/18 + 61/10

= 110 +1098/180

= 1208/180

= 6 128/180

= 6 64/90

15 1/3- 2 5/8

=15- 2 + 1/3- 5/8

=13 + 8- 15/24

= 13 + -7/24

= 312-7/24

= 12 17/24

Answer:

it is parrell

Step-by-step explanation:

Answer:

Anderess?

Step-by-step explanation:

Answer:

22/75

Step-by-step explanation:

To find the average add up the values and divide the sum by the number of values.

Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem

=1/2+1/5+1/5+1/10+7/15

The least common denominator (LCD) is: 30.

Rewriting as equivalent fractions with the LCD:

=15/30+6/30+6/30+3/30+14/30

Rewriting numerators over the common denominator,

=15+6+6+3+1430

Totaling the numerator:

=44/30

Reducing the fraction:

=22/15

Dividing by the number of values: 5

22/15÷5=22/15×15=22/75

Average of the fractions is:

Average=22/75