One cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used. Write and slice an equation to find the number of minutes you must talk to have the same cost for both calling plans.

Answer:

Final answer is [tex]\frac{80}{3}[/tex].

Step-by-step explanation:

We have been given an infinite geometric series.

Now we need to find it's sum.

common ratio [tex]r=-\frac{1}{5}[/tex].

plug n=1 to get the first term

[tex]a_n=32\left(-\frac{1}{5}\right)^{\left(n-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(1-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(0\right)}[/tex]

[tex]a_1=32\left(1\right)[/tex]

[tex]a_1=32[/tex]

Now plug these values into infinite sum formula

[tex]S_{\infty}=\frac{a_1}{1-r}=\frac{32}{1-\left(-\frac{1}{5}\right)}=\frac{32}{1.2}=\frac{320}{12}=\frac{80}{3}[/tex]

Hence final answer is [tex]\frac{80}{3}[/tex].

The sum of the infinite geometric series given in the problem is 26.6

7.

A geometric series is a sequence of terms in which each term is obtained by multiplying the previous term by a constant ratio. It is a specific type of series where the terms follow a geometric progression.

Formally, a geometric series is expressed as:

a, ar, a[tex]r^2[/tex], a[tex]r^3[/tex], ...

To solve the geometric series sum of the form:

S = a + ar + a[tex]r^2[/tex] + a[tex]r^3[/tex] + ...,

where a is the first term and r is the common ratio, we can use the formula for the sum of an infinite geometric series:

S = [tex]\frac{a}{1 - r}[/tex].

In this case, the given series is:

S = 32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

Comparing this to the standard geometric series form, we can identify that the first term a is 32, and the common ratio r is [tex]\frac{-1}{5}[/tex].

Substituting these values into the formula, we get:

S =  32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

S = [tex]\frac{32}{(1 +\frac{1}{5})}[/tex],

S = [tex]\frac{32}{\frac{6}{5} }[/tex],

S = 32 [tex]\times \frac{5}{6}[/tex],

S = [tex]\frac{160}{6}[/tex]

S = [tex]\frac{80}{3}[/tex] = 26.67.

Therefore, the sum of the given geometric series is 80/3 or approximately 26.67.

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Answer:

oof

Step-by-step explanation:

Answer:

[A.] and [D.]

Step-by-step explanation:

Before we even solve to see which options are true and false, write the polynomial in descending order.

To do this, break the polynomial into terms.

1. -2xy^5

2. 3x^7

3. -10x^3y^6

4. 8x^6

5. 4

To write this in descending order, look at the exponents or degrees.

We have 5 terms [So A. is already a correct option choice] so look at the exponents or degrees for each term

1. -2xy^5  [degree: 6 (x has an exponent, 1)]

2. 3x^7 [degree: 7]

3. -10x^3y^6 [since there are 2 exponents, add them together (degree: 9)]

4. 8x^6 [degree: 6]

5. 4 [degree: 1 (even though it doesn't look like it, 4 actually has an exponent, 1, along with other numbers like 1, 2, 3, 4, 5 etc.)]

-10x^3y^6 has the largest degree, then 3x^7, then 8x^6 and -2xy^5, and lastly 4.

Now, rewrite the polynomial

-2xy^5 + 3x^7 -10x^3y^6 + 8x^6 + 4 = -10x^3y^6 + 3x^7 + 8x^6 -2xy^5 + 4

We already established A.) is a correct answer.

B.) is not correct since our leading term is -10x^3y^6 and -10 would be the leading coefficent.

C.) Is not correct since the degree of the polynomial is 9, since the highest degree is 9

D.) Is correct since 4 has no variables attached to it

E.) Is not correct since the polynomial was not in descending form, we had to do it for them.

Thus, A.) and C.) are the correct answers.

I hope this helps! Let me know if I did something wrong or you have any questions! Thanks! :)

Answer:

log 64

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ nlogx

• logx + logy ⇔ log xy

Given

2 log 4 + log 2 + log 2

= log 4² + log (2 × 2)

= log 16 + log 4

= log (16 × 4) = log 64

Answer:

A, log 64

Step-by-step explanation:

your answer A, log 64 is correct. i will explain why below:

2 log 4, log 2 and log 2 have the same bases (10), meaning they are able to be added easier. but before we add, we use the Power Rule of Logarithms on 2 log 4

the Power Rule says that we can move an exponent in a logarithm to the front then solve. this also applies to the reverse, as we can move 2 back as an exponent of 4 and solve

2 log 4 ---> log 4² < simplify the exponent and we get log 16

we can now use the Product Rule of Logarithms where log x + log y = log(xy)

we can use that on the first two terms of the addition

log 16 + log 2 ----> log (16 × 2) = log 32

now we can apply the other log 2 to the rule but instead with log 32

log 32 + log 2 ---> log (32 × 2) = log 64

our answer is log 64

Answer:

Assuming you mean baseball in stead of basketball, if must be the 5th floor.

Step-by-step explanation:

"The girl on the fifth floor thinks soccer is boring" implies that on the 5th floor lives the football or baseball fan. However, it cannot be the football fan since it is already known that she lives on 6th.

So the baseball fan, which is Jean, lives on 5th.

Answer:

System of equations:

5r +7.50t = 127.50

r +t = 19

Answer:

t = 13 . . . number of people who ordered taco salads

Step-by-step explanation:

One equation expresses the total bill: the number of each item ordered multiplied by its price, all item subtotals added to make the order total.

The other equation expresses the total number of orders: the sum of the orders of roast beef sandwich and the orders of taco salads.

__

The solution can be found easily by substitution.

r = 19 -t

5(19 -t) +7.50t = 127.50

95 +2.50t = 127.50 . . . . . . simplify

2.50t = 32.50 . . . . . . . . . . subtract 95

t = 13 . . . . . . . . . . . . . . . . . . divide by 2.50

The number who ordered taco salads is 13.

Answer:

- 10 and 60

Step-by-step explanation:

1

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = (3 × - 2) - 4 = - 6 - 4 = - 10

2

To evaluate f(8) substitute x = 8 into f(x)

f(8) = 8² - 4 = 64 - 4 = 60

Answer:

Step-by-step explanation:

[tex]1)\\f(x)=3x-4\\\\f(-2)\to\text{put x = -2 to the equation of the function}\ f(x):\\\\f(-2)=3(-2)-4=-6-4=-10\\2)\\f(x)=x^2-4\\\\f(8)\to\text{put x = 8 to the equation of the function}\ f(x):\\\\f(8)=8^2-4=64-4=60[/tex]

Answer:

each box has 52 in it

Step-by-step explanation:

first you subtract 288 from 548  =260

this is the total number of nails minus the total 1 inch nails

then you divide 260 by 5 because he has five boxes of 2 inch names which means that you have to account for the even number of nails in each box

Answer:

There were 52 2-inch nails in each box.

Step-by-step explanation:

Let the number of nails in each 2 inch box be = x

As Tony bought 288 other nails and 5 boxes of 2 inch nails with a total purchase of 548 nails, we get the following equation;

[tex]288+5x=548[/tex]

[tex]=> 5x=548-288[/tex]

[tex]=> 5x=260[/tex]

x = 52

Hence, there were 52 2-inch nails in each box.

Answer:

9

Step-by-step explanation:

Because every number next to 64 is over

Add 6 to both sides

-102 + 6 = -2(6 - 7x)

Simplify -102 + 6 to -96

-96 = -2(6 - 7x)

Divide both sides by -2

-96/-2 = 6 - 7x

Two negatives make a positive

96/2 = 6 - 7x

Simplify 96/2 to 48

48 = 6 - 7x

Simplify 48 - 6 to 42

42 = -7x

Divide both sides by -7

-42/7 = x

Simplify 42/7 to 6

-6 = x

Switch sides

Answer: x = -6

Answer:

32

Step-by-step explanation:

To find the lcm of 8 and 32 by listing

multiples of 8 are : 8, 16, 24, 32, 40, ....

multiples of 32 : 32, 64, 96, ....

The least common multiple of 8 and 32 is 32

Answer:

Step-by-step explanation:

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.  That +2 shifts this result UP by 2 units.

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.

We have given that function

y=1/(x+5)+2

We have to determine,

The graph of this function compares with the graph of the parent function, y=1/x.

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.

That +2 shifts this result UP by 2 units.

Therefore the graph of the y=1/x is given below.

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Answer:

A and B

Step-by-step explanation:

A. -9<-4  ....TRUE

B. |-10| >| 2 |  => 10 > 2 ...TRUE

C. | -3 | < | 2 |   => 3 > 2  ....FALSE

D. 6< - 12 ....FALSE

Answer A and B

Answer:

0.41 per cup

Step-by-step explanation:

in 3 gallons of liquid is 48 cups so 19.68 and divide by 48 so 19.68/48=0.41

Answer:

$0.41 per cup

Step-by-step explanation:

there are 16 cups in a gallon

after that multiply 16 times 3 which would be 48

Now divide $19.68 divided by 48

check---

0.41 times 48 = 19.68

Answer:

p > 5 and p <-8

Step-by-step explanation:

To solve this, you first need to isolate p.

First add 6 on both sides of the equation:

[tex]-6 + |2p+3| >7\\\\(+6) -6 + |2p+3| >7 +6\\\\2p + 3 > 13[/tex]

Then subtract 3 from both sides of the equation.

[tex]2p+3-3>13-3\\\\2p > 10\\[/tex]

The divide both sides by 2.

[tex]\dfrac{2p}{2}>\dfrac{10}{2}\\\\p>5[/tex]

Another solution is possible because of the absolute value.

If [tex]|2p+3|>13[/tex]

Then [tex]|2p+3|<-13[/tex]

Thus we can solve the second solution:

[tex]|2p+3|<-13[/tex]

[tex]2p+3<-13[/tex]

Isolate P again by subtracting both sides by 3

[tex]2p+3-3<-13-3[/tex]

[tex]2p<-16[/tex]

Then divide both sides by 2:

[tex]\dfrac{2p}{2}<-\dfrac{16}{2}[/tex]

[tex]p<-8[/tex]

Answer:

p > 5, p < -8

Step-by-step explanation:

We are given the following inequality and we are to find its solution:

[tex]-6+|2p+3|>7[/tex]

Adding 6 to both sides to get:

[tex]-6+6+|2p+3|>7+6[/tex]

[tex]|2p+3|>13[/tex]

We know the absolute rule that [tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex].

So [tex]2p+3>13[/tex] or [tex]2p+3<-13[/tex]

[tex] 2 p > 1 3 - 3 [/tex], [tex] 2 p < - 1 3 - 3 [/tex]

[tex] 2 p > 1 0 [/tex], [tex] 2 p < - 1 6 [/tex]

[tex]p>\frac{10}{2}[/tex], [tex]p<\frac{-16}{2}[/tex]

p > 5, p < -8

Answer:

2x + 2(3) + 5

Step-by-step explanation:

Given expression

2(x + 3) + 5

In order to solve the expressions or to simplify the expressions, basic mathematical rules are considered.

Basic mathematical rules include the BODMAS. The order is Brackets, of powers, division, multiplication, addition and then subtraction is solved at last.

For the given expression, the 2 outside the bracket (x+3) will be multiplied inside first.

=> 2(x+3) + 5

Step 1:

=> 2x + 2(3) + 5

Step 2:

=> 2x + 6 + 5

Step 3

=> 2x+11

So the first step is 2x + 2(3) + 5 ..

Answer:

2x + 2(3) + 5

Step-by-step explanation:

let's firstly convert the mixed fractions to improper fractions and then subtract, bearing in mind that the LCD of 4 and 2 is 4.

[tex]\bf \stackrel{mixed}{8\frac{3}{4}}\implies \cfrac{8\cdot 4+3}{8}\implies \stackrel{improper}{\cfrac{35}{4}}~\hfill \stackrel{mixed}{7\frac{1}{2}}\implies \cfrac{7\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{15}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{35}{4}-\cfrac{15}{2}\implies \stackrel{\textit{using the LCD of 4}}{\cfrac{(1)35~~-~~(2)15}{4}}\implies \cfrac{35-30}{4}\implies \cfrac{5}{4}[/tex]

Answer:

ε₀= 0.035

Step-by-step explanation:

The question is on residual/ error which is the vertical distance between the actual value of y and the estimated value of y.

General formulae is;

ε₀= y₀ - y₁

From the graph attached, the point on the line y=5x+2  is (5.407,29.035)

ε₀= 29.035- 29.000

ε₀= 0.035

The Answer is in the picture below...

the area of the pool and deck can be calculated by using the expression [tex]500 + 90x + 4x^2[/tex]

The dimension of the pool are:

25 ft long and 20 ft wide

We know that the deck extends x ft away from every side of the pool.

Thus, the total length of the pool and deck together is 25 + 2x ft, and the total width is 20 + 2x ft

Area of rectangle can be found using the formula:

[tex]Area = length \times breadth[/tex]

Putting in values we get:

[tex](25 + 2x) \times (20 + 2x)[/tex]

On simplifying we get:

[tex](25 + 2x) (20 + 2x) = 500 + 50x + 40x + 4x^2 \\\\(25 + 2x) (20 + 2x) = 500 + 90x + 4x^2[/tex]

Thus the area of the pool and deck can be calculated by using the expression [tex]500 + 90x + 4x^2[/tex] ft²

Answer:

Option C is Correct

Step-by-step explanation:

Given:

[tex]\sqrt{648}= \sqrt{2^a.3^b}[/tex]

We need to check the values of a and b such that the given equation remains true

1. a= 3 and b=2

[tex]\sqrt{648}= \sqrt{2^3.3^2}\\25.4 = \sqrt{72}\\25.4 \neq 8.4[/tex]

So, Option A is incorrect

2. a=2 and b= 3

[tex]\sqrt{648}= \sqrt{2^2.3^3}\\25.4 = \sqrt{108}\\25.4 \neq 10.3[/tex]

So, Option B is incorrect

3. a=3, b=4

[tex]\sqrt{648}= \sqrt{2^3.3^4}\\25.4 = \sqrt{648}\\25.4= 25.4[/tex]

So, Option C is correct.

4. a= 4, b=3

[tex]\sqrt{648}= \sqrt{2^4.3^3}\\25.4 = \sqrt{432}\\25.4 \neq 20.7[/tex]

So, Option D is incorrect.

Answer:

The estimated cost for the labor is less than or equal to [tex]\$150.77[/tex]

Step-by-step explanation:

Let

n -----> the estimated cost for the labor

we know that

The inequality that represent this situation is equal to

[tex]49.23+n\leq 200[/tex]

Solve for n

[tex]n\leq 200-49.23[/tex]

[tex]n\leq \$150.77[/tex]

For this case we have a quadratic equation, [tex]x ^ 2 + 28x-60 = 0[/tex], of the form [tex]ax ^ 2 + bx + c = 0[/tex]

Where:

[tex]a = 1\\b = 28\\c = -60[/tex]

We can solve the equation by factoring, that is, we bias two numbers that multiplied give as a result -60 and added as a result 28.

These numbers are:

[tex]+30\ and\ -2\\+ 30-2 = + 28\\+ 30 * -2 + -60[/tex]

Then, the factorization is given by:

[tex](x-2) (x + 30) = 0[/tex]

The roots are:

[tex]x_ {1} = 2\\x_ {2} = - 30[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 30[/tex]

Answer:

63,8%

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses,  that makes a proportion of 638 out of  1,000 people, or 63,8 / 100 people... so 63.8%

I would say the sample is not representative of the reality.... because I don't think so many people wear glassed.

Answer:

KL does not name the same line.

Step-by-step explanation:

You'll recognize that if you go from KM, it stays on the same. You go from MN it stays on the same line. KN also stays on the same line. By K and L are two completely different lines. L can only be with N or J

Answer:

NL

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

m - slope

b - y-intercept

We have y-intercept b = -2. Substitute:

We have the point (4, 12) → x = 4, y = 12. Put them in the equation:

12 = 4m - 2         add 2 to both sides

14 = 4m       divide both sides by 4

14/4 = m → m = 3.5

Answer:

y = 3.5x - 2

Step-by-step explanation:

We know that the y-intercept of our equation is -2, so our current equation is: y = mx - 2. Now we have to find m, which is the slope. Now, we plug in the points into the equation y = mx - 2, and we get 12 = 4m - 2. Thus, m is 3.5. Our final equation is y = 3.5x - 2.

Answer:

40%

Step-by-step explanation:

4÷10x100=40

As you have 10 players total and 4 players scored between 31 and 40 points

Answer:

w = 4 m

Step-by-step explanation:

The volume (V) of a cuboid is

V = lwh ( l is length, w is width and h is height )

Given V = 144 m³, then

lwh = 144 ( substitute l = 3 and h = 12 )

3 × w × 12 = 144

36w = 144 ( divide both sides by 36 )

w = 4

The volume of a rectangular prism is given by the product of its dimension: let w, h, l be the width, height and length of the prism, we have

[tex]V = whl[/tex]

In your case, everything is given except the width:

[tex]144 = w\cdot 3 \cdot 12 \iff 144 = 36w \iff w = \dfrac{144}{36} = 4[/tex]

Answer:

12.6 units²

Step-by-step explanation:

Since PX is a tangent to the circle then OP  and PX are at right angles.

A ΔOPX = 12, thus

OP × PX = 12, that is

6OP = 12 ( divide both sides by 6)

OP = 2 ← radius of circle

Area of circle = πr² = π × 2² = 4π ≈ 12.6 units²

Final answer:

When evaluating the expression -3x³ - 4x for x = -1, by plugging in the value and simplifying the expression, we obtain the result of 7.

Explanation:

The question at hand requires us to evaluate the expression -3x³ - 4x when x = -1. To do this, we substitute -1 for x into the expression and simplify. Here's the step-by-step calculation:

Therefore, when we evaluate the expression -3x³ - 4x for x = -1, the result is 7.

Answer:

B, C, F, H

Step-by-step explanation:

Just search up how to solve equations

Answer: B. x+2=10

C. x-4=4

F. 3x=24

H. [tex]\dfrac{x}{8}=1[/tex]

Step-by-step explanation:

To check whether 8 is a solution of the given equation or not , we need to substitute the value of 8 in the place of x check whether equation is truw or not.

A. [tex]x+6=2[/tex]

At x= 8, we have

[tex]8+6=2\Rightarrow\ 14=2[/tex] , which is not true , it means 8 is not a solution of this equation.

B. x+2=10

At x= 8, we have

[tex]8+2=10\Rightarrow\ 10=10[/tex] , which is true , it means 8 is a solution of this equation.

C. x-4=4

At x= 8, we have

[tex]8-4=4\Rightarrow\ 4=4[/tex],  which is true , it means 8 is a solution of this equation.

D. x-2=10

At x= 8, we have

[tex]8-2=10\Rightarrow\ 6=10[/tex] , which is not true , it means 8 is not a solution of this equation.

E. 2x=4

At x= 8, we have

[tex]2(8)=4\Rightarrow\ 16=4[/tex] , which is not true , it means 8 is not a solution of this equation.

F. 3x=24

At x= 8, we have

[tex]3(8)=24\Rightarrow\ 24=24[/tex],  which is true , it means 8 is a solution of this equation.

G. [tex]\dfrac{x}{2}=16[/tex]

[tex]\dfrac{8}{2}=16\Rightarrow\ 4=16[/tex], which is not true , it means 8 is not a solution of this equation.

H. [tex]\dfrac{x}{8}=1[/tex]

At x= 8, we have

[tex]\dfrac{8}{8}=1\Rightarrow\ 1=1[/tex],  which is true , it means 8 is a solution of this equation.

Hence, the required equations :

B. x+2=10

C. x-4=4

F. 3x=24

H. [tex]\dfrac{x}{8}=1[/tex]