Verify each identity.

I need help with the Precalculus.
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Amber plus 2 family members = 3 total people on the plan.

They share the minutes equally so divide the minutes by 3 to find how many she can use:

720 / 3 = 240 minutes per month.

Now divide the monthly minutes by 30 days:

240 / 30 = 8 minutes per day.

Answer:

3225

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ]

where a is the first term and d the common difference

here a = 6 and

d = 13 - 6 = 20 - 13 = 7, hence

[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex][ (2 × 6) + (29 × 7) ]

                          = 15(12 + 203) = 15 × 215 = 3225

Answer:

$36.00

Step-by-step explanation:

40% of 60 is 24. Subtract from the origanl amount, you get the price after sale, $36.00. Hope this helps :)

Answer:

  $1289.48

Step-by-step explanation:

A financial calculator tells you the payment with the higher interest rate is $1960.51, and that with the lower interest rate is $671.03. The difference in payment amounts is ...

  $1960.51 -671.03 = $1289.48

Answer:

The current per month mortgages are $1289.54 less than the earlier per month mortgages.

Step-by-step explanation:

The EMI formula is = [tex]\frac{p\times r\times (1+r)^{n} }{(1+r)^{n}-1 }[/tex]

Here p = 125000

For case 1:

r = 18.75/12/100=0.015625

n = [tex]30\times12=360[/tex]

So, putting values in formula we get :

[tex]\frac{125000\times 0.015625\times (1+0.015625)^{360} }{(1+0.015625)^{360}-1 }[/tex]

= $1960.51

For case 2:

r = 5/12/100=0.004166

n = [tex]30\times12=360[/tex]

So, putting values in formula we get :

[tex]\frac{125000\times 0.004166\times (1+0.004166)^{360} }{(1+0.004166)^{360}-1 }[/tex]

= $670.97

Now we will find the difference between both EMI's

[tex]1960.51-670.97=1289.54[/tex] dollars.

Therefore, the current per month mortgages are $1289.54 less than the earlier per month mortgages.

80 ft^3 is the answer

Answer:

200ft^3

Step-by-step explanation:

x = 90

y = 180 - (90 + 47)

y = 43

ANSWER

[tex] -\sqrt{3}[/tex]

EXPLANATION

The given angle is 870°.

870°-360°-360°=150°

This means that:

870° is coterminal with 150°, hence its terminal side is in the second quadrant.

It makes an acute angle of 30° with the x-axis.

Note that cotangent is negative in the second quadrant,

Hence,

[tex] \cot(870 \degree) = \cot(150 \degree) = - \cot(30 \degree) = - \frac{1}{ \tan(30 \degree) } = - \sqrt{3} [/tex]

The first option is correct.

Answer:

use math-way

Step-by-step explanation:

= - square root of 3

Answer with explanation:

Equation of line Passing through two points (a,b) and (c,d) is given by:

         [tex]\frac{y-b}{x-a}=\frac{d-b}{c-a}[/tex]

Equation of line Passing through two points (8,0) and (3,7) is given by:

      [tex]\rightarrow \frac{y-7}{x-3}=\frac{7-0}{3-8}\\\\\rightarrow \frac{y-7}{x-3}=\frac{7}{-5}\\\\\rightarrow -5 y+35=7 x - 21\\\\\rightarrow 5 y= -7 x +35 +21\\\\ y=\frac{-7 x}{5}+\frac{56}{5}\\\\y=-1.4 x +11.2[/tex]

Comparing with slope intercept form of line,

y= m x+c, where , m is slope and c is y intercept.

⇒Y intercept = 11.2

Equation of line Passing through two points (5,5) and (3,7) is given by:

            [tex]\rightarrow \frac{y-7}{x-3}=\frac{7-5}{3-5}\\\\y-7= -1 \times (x-3)\\\\y=7-x+3\\\\y=-x +10[/tex]

Comparing with slope intercept form of line,

y= m x+c, where , m is slope and c is y intercept.

⇒Y intercept = 10

Equation of line is, y= -x +10.

The y-intercept of the line passing through point A (8, 0) and B (3, 7) is 56/5. The equation of the line that passes through these points and point D (5, 5) is y = (-7/5)x + (56/5).

To determine the y-intercept and the equation of a line, we first need to find the slope of the line. The slope (m) is given by the rise over run, which can be calculated using the coordinates of two points on the line. We have point A with coordinates (8, 0) and point B with coordinates (3, 7). The slope is therefore:

m = (Y2 - Y1) / (X2 - X1) = (7 - 0) / (3 - 8) = 7 / (-5) = -7/5

Now, we use the slope-intercept form of a line equation, which is y = mx + b, where b is the y-intercept. We can determine b by substituting the slope and the coordinates of one of the given points (we'll use point A). So:

0 = (-7/5)(8) + b

b = (7/5)(8) = 56/5

Therefore, the y-intercept is 56/5.

Knowing point D with coordinates (5, 5) is also on the line, we can use our slope m and this point to write the equation of the line:

y = (-7/5)x + (56/5)

However, since we know point D lies on this line, we can check if our equation is correct by substituting x = 5 and seeing whether y = 5:

5 = (-7/5)(5) + (56/5)

5 = -7 + 56/5

5 = 5

This confirms that our calculated equation is indeed correct and passes through all given points.

A) the graph is a linear and the slope is negative and positive .

B) (-1,-1) is not a solution because that point does not appear in the shaded region, therefore there is no solution.

:D

Answer:

Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten".

Step-by-step explanation:

Because the teacher only picked 5 students out of all the students it was a sample.

If the teacher had asked every student, it would have been a population.

Answer:

sample

Step-by-step explanation:

The teacher only asked the five students specifically so it is a sample.

Population would be if the teacher asked every student.

Answer:

The correct answer would be option C

Step-by-step explanation:

Answer:

40 cm

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{4x}{x}[/tex] = [tex]\frac{48}{x+2}[/tex], simplifying gives

4 = [tex]\frac{48}{x+2}[/tex]

Multiply both sides by (x + 2)

4(x + 2) = 48 ( divide both sides by 4 )

x + 2 = 12 ( subtract 2 from both sides )

x = 10

Hence

width = 4x = 4 × 10 = 40

Answer:

Y=3x(x-4)

Step-by-step explanation:

Answer:

302 mi²

Step-by-step explanation:

Actually we're looking for the "unit rate," which here is the number of square miles are in each region:

27,512 mi²

---------------- = 302 mi² approximately (rounded up from 302.33 mi²)

91 regions

So it's asking how many times greater is 6,000 than 600. Simply divide to find that it is 10 times greater.

Hope this helps you!

The 6 in the hundreds place is 100 and the 6 in the thousands place is 1000

Answer:

3 hours

Step-by-step explanation:

3 hours as it takes 3 periods to be 40000

If there are initially 5000 bacteria in a culture,and the number of bacteria doubles each hour. The culture will take around 3 hours to reach 40,000 bacteria.

To determine how long it will take for the culture to grow to 40,000 bacteria, we can use the given formula: N = 5000 * (2^t), where N represents the number of bacteria after t hours.

Substitute N with 40,000 and solve for t:

40,000 = 5000 * (2^t)

Divide both sides by 5000:

8 = 2^t

Since 2^3 = 8 we can conclude that t is equal to 3

Therefore it will take approximately 3 hours for the culture to grow to 40,000 bacteria.

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Answer:

[tex]A(t)=(100-8t)^{2}[/tex]

Step-by-step explanation:

Let

t-----> the number of years

A-----> the area of the cement parking lot

we know that      

The function that represent this situation is

[tex]A(t)=(100-8t)^{2}[/tex]

Final answer:

The function A(t) = [tex](100-8t)^2[/tex] can be used to calculate the area of the cement parking lot after t years by substituting the side length (100-8t) into the formula for the area of a square.

Explanation:

The function that can be used to calculate the area of the cement parking lot after t years is: A(t) = [tex](100-8t)^2[/tex].

To calculate the area of the square parking lot at any given time t, you substitute the side length (100-8t) into the formula for the area of a square, A = side [tex]length^2[/tex].

For example, after 2 years, the area A(2) would be[tex](100-8(2))^2[/tex] = [tex]84^2[/tex]= 7056 square meters.

Answer: 15 cm

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

[tex]A=l*w[/tex]

Where "l" is the lenght and "w" is the width.

You know that the area of this rectangle is 75 square centimeters and the width is 5 centimeters. Then, you can substitute these values into the formula [tex]A=l*w[/tex] and solve for the lenght. Then you get:

[tex]75cm^2=l(5cm)\\\\\frac{75cm^2}{5cm}=l\\\\l=15cm[/tex]

Therefore, the lenght of the rectangle is 15 centimeters.

Answer:

15 centimeters.

Step-by-step explanation:

To find the area of a rectangle, you have to multiply the length by the width.

In this case, the width is 5 centimeters.

So, so find the area, you would have to multiply 5 by the length. Let's call the length "x".

The equation to solve this problem would be:

5x - 75

Now we can solve the equation...

Divide both sides by 5...

5x / 5 = 75 / 5

x = 15

Since x is equal to 15, that means that the length is 15, because we said that the length is equal to x.

Length = x = 15

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

Hope this helped!

Answer:

A  = 25√3 cm²

Step-by-step explanation:

View 5√3 cm as being the height of an equilateral triangle whose base is at the bottom of the purple figure.  To find the area of one such triangle, we use the area-of-a-triangle formula A = (1/2)(b)(h).  

                                                     opp

Using the sine function sin Ф = --------

                                                      hyp

we find the length of the hypotenuse, which is also the radius of the octagon, and because this is an equilateral triangle, is also the length of the base:

                √3       5√3 cm

sin 60° = -------- = ------------- , which produces the value of hyp:

                  2             hyp

                √3       5√3 cm

              -------- = ------------- , which produces the value of hyp:

                  2             hyp

√3·hyp = 10√3, or hyp = 10 cm

Then the area of this one triangle is A = (1/2)(b)(h), or

A = (1/2) (10 cm)(5√3 cm) = 25√3 cm²

Answer: Option C  

[tex]r ^ 2 = 0.684[/tex]

Step-by-step explanation:

The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.

 If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.

If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.

Then for a  relationship, the coefficient of determination [tex]r ^ 2[/tex] is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.

The coefficient of determination [tex]r ^ 2[/tex] for a linear relationship is calculated as the square of the correlation coefficient.

In this problem we have that the correlation coefficient r is

[tex]r = 0.827[/tex]

then the coefficient of determination is:

[tex]r ^ 2 = 0.827 ^ 2[/tex]

[tex]r ^ 2 = 0.684[/tex]

The answer is option C

(8, 8) and (0, 8). If the equation is y = any number, the second coordinate will always be that number. :)

Answer:

Length = 12 meters

Step-by-step explanation:

Rectangle

Perimeter P = 2(L + W)

The length of a rectangle, I, is six meters more than it's width, W.

Then L = W + 6

So

P =  2(W + 6 + W)

P = 2 (2W + 6)

P = 4W + 12

Plug in P = 36 meters

36 = 4W + 12

4W = 36 - 12

4W = 24

 W = 6 meters

L = 6 + 6

L = 12 meters

Answer:

1 degree = 60 minutes

Step-by-step explanation:

The DMS method is for Degree Minutes Seconds.  That allows you to give a precise location the way it's most commonly used on paper maps.  Today, with the electronic maps we mostly use the numeric version (34.234 degrees for example).

So, in the DMS method, one degree is basically like an hour on your clock.  It can be divided into 60 minutes.  Then, those minutes can be divided into 60 seconds.  Just like an hour, a degree has 60 minutes and 3600 seconds.

Final answer:

One degree in the DMS method of angle measurement is divided into 60 minutes. To convert DMS to DD, like with 118 degrees 15 minutes, divide the minutes by 60 and add the result to the degrees, giving you 118.25.

Explanation:

In the DMS method of angle measurement, one degree is equivalent to 60 minutes of angle. This is similar to how an hour of time is divided into 60 minutes. To visualize this, if you consider a full circle being 360 degrees, each degree can be further subdivided into 60 smaller parts, each of these parts is known as a minute of angle.

For example, the conversion of 118 degrees 15 minutes to decimal degrees (DD) is a simple mathematical process. You would divide the minutes by 60 since there are 60 minutes in a degree, resulting in the equation 118 + 15/60, which equals 118.25 degrees. This conversion is an important skill in coordinate conversion activities, where positions are described in DMS format and need to be converted to DD for calculations.

Answer:

A

Step-by-step explanation:

Add up all of the numbers:

110+142+120+180+ 151+110+159+173+173+144+110 = 1572

Next you divide by how many number there are (there are 11 numbers)

1572 ÷ 11 = 142.9090909

142.9090909 rounded to the nearest tenth is 142.9

Answer:

A.  142.9

Step-by-step explanation:

There are 11 members in the data set, therefore:

The mean = (110+142+120+180+151+110+159+173+173+144+110) / 11

= 1572/11

= 142.9.

Answer:

its C

Step-by-step explanation:

Answer:

B.) e

Step-by-step explanation:

If e is zero and c + d ≠ 0, then the quotient [tex]\frac{c + d}{e}[/tex] will be an undefined number and in that case;

a + b([tex]\frac{c + d}{e}[/tex]) ≠ 1

Answer:

The capacity of the remaining bottles = 4 pints.

Step-by-step explanation:

6*3 + 6*b = 42

6b = 42 - 18

6b = 24

b = 4.

The required quantity of the remaining 6 bottles is 4 pints.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each.

Let b represent the capacity, in pints, of each of the remaining 6 bottles.,
Now,
42 = 3 × 6 + b × 6
42 = 18 + 6b
6b = 42 - 18
b = 24/6
b = 4

Thus, the required quantity of the remaining 6 bottles is 4 pints.

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Answer:

$18.66

Step-by-step explanation:

Add together the amounts Keith spent on baseball and truck:  $10.37 + $8.29 = $18.66.  We can ignore the amount he spent on the jacket.

Answer

a) 2π

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is periodic.

The function is

f(x) =  3*sin(2*x) + 4*cos(3*x)

Which can be seen in the picture below

We can notice that f(x) is periodic. It has periodic amplitudes, and the function has a period T = 6.283   ≈ 2π

The maximum and minimum values are

Max = 6.695

Min = -6.695