Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 320 minutes and the cost was $143.00. In July she used 710 minutes and the cost was $279.50.

Answers

Answer 1

The cost function expressed as the number of times spent calling is cost function = c(x) = 31 + 0.35x

How to solve for the cost function

The cost function that can be written as per the number of units that she used is given as

c(x) = a + bx

x = 320

a + 320b = 143

When x = 710

we would have

a + 710b = 279

subtract the equations

710 b - 320 b = 279 - 143

390b = 136

b = 136/390

= 0.35

Put the value of b in equation 1

a + 320 x 0.35 = 143

a + 112 = 143

a = 31

cost function =

c(x) = 31 + 0.35x

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complete question

A) Express the monthly cost C as a function of a, the number of minutes of calling time she used.


Related Questions

Someone is 18 1/2 inches long when they are born and their twin is 20 3/4 inches long. What is the difference between how big they are.

Answers

2 1/4 inch difference between the the two

6. The question is in the screenshot

Answers

Answer:

None of these

Step-by-step explanation:

We can estimate f'(9) by finding the slope of the secant through the two points closest to (9, f(9)).

[tex]\frac{f(10)-f(8)}{10-8}=\frac{16-10}{2}=3[/tex]

Stephanie brings a 10% off coupon if the sweater cost 22.00 how much does she pay after she uses the coupon

Answers

Answer:

22/10

=2.2

22-2.2=19.8

Stephanie pays £19.8

is 4 33/100 a repeating decimal

Answers

Answer:

no

Step-by-step explanation:

4 33/100 is equal to 4.33, it is 4.33, not 4.33 with the dot on it, it means recurring decimal. It is jot a recurring decimal. :)

Ten grams is what percent of 1 ounce? Round your answer to the nearest tenth percent.

Answers

Answer:

0.4oz

Step-by-step explanation:

conversion factor 1oz = 28.35g

(10g/1)(1oz/28.35g) cross out grams

    10/28.35oz = 0.3|527 = 0.4oz

               

Solve for x in the equation 3x2-18x+5=47-
Ox-3+√23
Ox-3± √51
Ox-3+√41
O x-3+√5

Answers

Answer:

x = 3 ± √23

Step-by-step explanation:

Simplify the quadratic equation.

[tex]3x^2-18x+5 = 473x^2-18x+5-47 = 0\\3x^2-18x-42 = 0\\\\a = 3\\b = -18\\c = -42\\\\x = (-(-18)\pm\sqrt{ (-18)^2-4(3)(-42) )} \div 2(3)\\x = (18\pm\sqrt{ 324+504)} \div 6\\x = (18\pm\sqrt{ 828}) \div 6[/tex]

Simplify further.

[tex]x = (18\pm\sqrt{ 23\times 36}) \div 6\\x = (18\pm6\sqrt{ 23}) \div 6\\x = 6(3\pm\sqrt{23}) \div 6[/tex]

Thus, the solution is

x = 3 ± √23

Hope this helps.

x = 3 + √23 and x = 3 - √23 are the two solutions of the given quadratic equation.

What is a Quadratic equation?

ax²+bx+c=0, with a not equals to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

To solve for x in the equation 3x^2 - 18x + 5 = 47, we can begin by simplifying the equation:

[tex]3x^2 - 18x - 42 = 0[/tex]

Next, we can divide both sides of the equation by 3 to get:

[tex]x^2 - 6x - 14 = 0[/tex]

To solve for x, we can use the quadratic formula:

[tex]x =\frac{ (-b \pm \sqrt{(b^2 - 4ac))} }{ 2a}[/tex]

In this case, a = 1, b = -6, and c = -14, so we have:

[tex]x = \frac{(-(-6) \pm \sqrt{((-6)^2 - 4(1)(-14)))}}{2(1)} \\x = \frac{(6 \pm \sqrt{(36 + 56))}}{ 2} \\x = (6 \pm \sqrt{92}) / 2[/tex]

Simplifying the radical, we get:

x = (6 ± 2√23) / 2

Dividing both the numerator and denominator by 2, we get:

x = 3 ± √23

Therefore, the two solutions to the equation [tex]3x^2 - 18x + 5 = 47[/tex] are x = 3 + √23 and x = 3 - √23.

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a) Write 1.76 x 10³ as an ordinary number.
b) Write 3.21 x 10 as an ordinary number.
c) Write 850 000 000 in standard form.
d) Write 0.0000509 in standard form.

Answers

Answer:

a 1760.

b 32.1

c 8.5 × 10^8

d 5.09×10^-5

ANSWR ASAP ILL GIVE BRAINLYEST AND 5 STAR

Answers

The missing steps of the expression are as follows;

[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷452 - 10.4 ÷ 4

How to solve an expression?

The expression can be solved as follows:

step 1

[tex](\frac{3^{2} + 4 }{|-0.25|} ) - 10.4[/tex] ÷ 4

Step 2

The absolute value will remove the minus sign of the denominator.

[tex](\frac{3^{2} + 4 }{0.25} ) - 10.4[/tex] ÷ 4

Step 3

We have to find the square of the 3 in the numerator. Therefore, the step 3 will be as follows:

[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷ 4

Step 4

We have simplify the numerator.

[tex](\frac{13 }{0.25} ) - 10.4[/tex] ÷ 4

Step 5

52 - 10.4 ÷ 4

Step 6

Using PEMDAS rule, we have to solve the division sign. Therefore, the step 6 is as follows;

52 - 2.6

Step 7

49.4

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Given the function f(x) = −2x2 + 4x − 7, find f(−4).

Answers

Answer:

A is the answer of the question

The basketball team has developed a carnival game at
homecoming to raise money for new uniforms. They are
charging $3 per ticket to play. The expected pay out for each
play is $1.75. What can you conclude from this situation?
C

Answers

Answer:

Step-by-step explanation:kfn

The sum of the square of a positive number and the square of 2 more than the number is 20. What is the number?

Answers

Answer:

2

Step-by-step explanation:

2^2 is 4 and two more than 2, which is 4, is 16 when squared. 16+4=20

How do i solve 5+2(6+3 ÷ 3)

Answers

Answer:

19

Step-by-step explanation:

Arrange into parentheses and start at the innermost parentheses

[tex]5 + (2 \times (6 + (3 \div 3)))[/tex]

Start with 3 ÷ 3

[tex]3 \div 3 = 1[/tex]

Continue with the other parts of the equation in order

[tex]1 + 6 = 7\\7 \times 2 = 14\\14 + 5 = 19\\= 19[/tex]

Hope this helped you understand better, have a great day!

17. TRAFFIC SIGNS The diagram shows a sign used to warndrivers of a school
zone or crossing. Measure and classifyeach numbered angle.

Answers

each numbered angle is

1. right angle

2. obtuse angle

Road signs, often known as traffic signs, are posted along the side of roadways or above them to inform and direct drivers. Simple wooden or stone milestones were the oldest types of signs. Later, directional signs with arms were developed, such as the fingerposts used in the United Kingdom and their wooden equivalents in Saxony. Since the 1930s, as traffic volumes have increased, many nations have adopted pictorial signs or have similarly standardized and simplified their signs in an effort to overcome linguistic barriers and improve traffic safety. Such pictorial signals are typically based on international norms and use symbols (often silhouettes) in place of words. These signs were initially created in Europe and have since been adopted in varied degrees by the majority of nations.

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The complete question is attached below

Every rhombus is a parallelogram

Answers

Answer: A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.

Step-by-step explanation:

After a 25%increase, the price is 300€.how many euros was the increase?

Answers

Step-by-step explanation:

the €300 as current price is 125% relative to the original price. in other words : 1.25 times the original price.

to get the amount of the increase we need to get the original price first and then subtract the original price from the current price.

to get the original price we need now to divide the actual price by 1.25 to undo the increase.

the original price

OP = 300/1.25 = €240

the price increase (of 25%) was then

300 - 240 = €60

8.
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.

Answers

The measure of the central angle m∠VWU is 69 degrees

How to find central angles?

Central angle is the angle formed by two arms and having the vertex at the centre of a circle.

The diameter of a circle runs from the centre of a circle.

The diameter SU and RT intersect each other at point Q.

Therefore,

m∠VWS = m∠TWU (Vertically opposite angles)

m∠VWU = m∠SWT (Vertically opposite angles)

Hence,

m∠TWU = 111 degrees.

Therefore,

m∠VWU = 360 - 111 - 111  /2

m∠VWU = 360 - 222 / 2

m∠VWU = 138 / 2

m∠VWU = 69 degrees

Therefore, the measure of the central angle m∠VWU is 69 degrees

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Use sigma notation to represent the sum of a geometric series with a first term of 3 and a common ratio of 10/9

Answers

The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;

∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, K = 1 to n.

What is Geometric series?

A geometric series is a list of numbers having a common ratio. Each term after the first is gotten by multiplying the previous one by the common ratio.

Given that;

The first term is 3 and the common ratio is 10/9.

Now, A geometric sequence has the form:

a, ar , ar², ar³, . . .

Hence, The nth term of a geometric sequence is;

⇒ ∑ [tex](ar^k^-^1)[/tex]     where, k = 1 to n.

Therefore, the sum of geometric series with a first term of 3 and a common ratio of 10/9 is:

⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, k = 1 to n.

So, The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;

⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, k = 1 to n.

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The half life of the isotope dubnium-263 is 29 seconds. A sample of dubnium-263 was first measured to have 1024 atoms. After t seconds, there were only 32 atoms of the isotope remaining.

Write an equation in terms of t that models the situations
Question based on Khan Academy

Answers

The radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}

What is radioactive decay?

Radioactive decay is the spontaneous disintegration of atoms with the emission of radiation.

What is half life of a radioactive isotope?

The half life of a radioactive isotope is the time it takes for half the number of atoms in a given sample to disintegrate.

How to Write an equation in terms of t that models the situations?

To model the situation, we use the equation for radioactive decay which is given below

[tex]N = N_{0}e^{-{\lambda}t}[/tex] where

N = Number of atoms remaining after t seconds, N₀ = initial number of atoms, λ = decay constant = 0.693/T where T = half life of isotope and t = time of decay

Given that the half life of the isotope dubnium-263 is 29 seconds and  sample of dubnium-263 was first measured to have 1024 atoms. Then, after t seconds, there were only 32 atoms of the isotope remaining. we have that

N = 1024 atoms, N₀ = 32 atoms, T = 29 s

So, λ = 0.693/29 s = 0.0239 /s

So, susbtituting the values of the variables into the equation, we have

[tex]N = N_{0}e^{-{\lambda}t}[/tex]

[tex]32 = 1024e^{-(0.0239/s)t}[/tex]

So, the radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}

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Simplify 5¹⁰ ^ 5²




...........................................

Answers

It should be noted that simplifying 5¹⁰ × 5² will be 5^12.

How to calculate the value?

It should be noted that these values have to do with powers. In this case, since that have same base and we want to multiply, we will add their powers.

Therefore, 5¹⁰ × 5² will be:

= 5¹⁰ × 5²

= 5^12

In conclusion, the value will be 5 raise to power 12

Therefore, based on the information, it should be noted that the value of 5¹⁰ × 5² will be 5^12.

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Simplify 5¹⁰ × 5²

Aliyah has $94 in 13 bills in her wallet, including ones, fives, and twenties. If she has one less twenty dollar bill than she has one dollar bills, how many of each denomination does Aliyah have in her wallet?

Answers

Answer:

$1 x 4

$20 x 3

$5 x 6

Step-by-step explanation:

$94

at least 4 $1 bills

$90

at least 3 $20  ($60)

$30

the remaining $30 can be made up of 6 $5 bills

4 + 3 + 6 = 13 bills total

the function f(x) is an unshifted exponential function which goes through the points (2,5) and (3,4).

A. what is the equation for f(x)
B. Find f(10) and f(100)

Answers

[tex]f(x) = ae {}^{bx} \\ f(2) = 5 \: \: \: \: \: f(3) = 4[/tex]

[tex]5 = ae {}^{2b} \: \: \: \: \: \: \: 4 = ae {}^{3b} \\ divide \: both \: systems \\ e {}^{b} = \frac{4}{5} \: \: \: \: so \: \: \: b = ln(0.8) \\ solving \: for \: a \: we \: get \: that \: a = \frac{125}{16} [/tex]

[tex]f(x) = \frac{125}{16} e {}^{ln(0.8)x} [/tex]

[tex]f(10) = \frac{125}{16} e {}^{10ln(0.8)} = \frac{65536}{78125} \approx0.838861 \\ f(100) = \frac{125}{16} e {}^{100ln(0.8)} = \frac{4 {}^{98} }{5 {}^{97} } \approx1.59 \times 10 {}^{ - 9} [/tex]


How many ways can Nick choose 5 pizza toppings from a menu of 8 toppings if each topping can only be chosen once?

Answers

In combination, 56 ways can Nick choose topping can only be chosen .

What is permutation and combination?

Subsets of a set can be created in two separate ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colors. Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.

given that Nick choose pizza = 5

menu of toppings if each topping =8

chosen once  = 8c5

                        =>   8! / (5!(8−5)!)

                         =>  56

       

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Which graph represents a function? A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 2, negative 2), ( 1, 1), and (2, negative 2). A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 3, negative 3), (negative 1, 1), and (1, 4). A coordinate plane shows 4 points with the following coordinates: (negative 4, 4), (negative 4, 1), (negative 2, 1), and (2, 1). A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 3, negative 3), (1, negative 4), and (1, 1).

Answers

The ordered pair that represents a function is:

⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

The given points are;

(-3, -3), (-2, 2), (1, 1), (2, -2)

(-3, 3), (-3, -3), (-1, 1), (1, 4)

(-4, 4), (-4, 1), (-2, 1), (2, 1)

(-3, 3), (-3, -3), (1, -4), (1, 1)

Now, For an ordered pair to be a function, either of the following must be true:

Each x-value have exactly one corresponding y-value.

More than one x-values have the same corresponding y-values.

And, If any of the following conditions is true, then the ordered pair is not a function,

One x-value have multiple corresponding y-values.

More than one x-values have the multiple corresponding y-values.

From the given options, only ordered pair (-3, -3), (-2, 2), (1, 1), (2, -2) satisfies the condition to be a function.

Because none of its x-values have multiple corresponding y-values.

And, Other ordered pairs are either one-to-many or many-to-many.

So, The ordered pair that represents a function is:

⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)

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Find the area of the triangle below.
Be sure to include the correct unit in your answer.
15 cm
7 cm
22 cm
0
Question 2

Answers

The area of the triangle with the given dimensions are 77cm.

According to the statement

We have to find that the area of the triangle.

So, For this purpose, we know that the

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

From the given information:

15 cm

7 cm

22 cm

Then

The base of the triangle is 7 cm and the height of the triangle is a 22cm.

Then

A = 1/2 × b × h.

A = 1/2 × 7 × 22.

Now solve it then

A = 154/2

A = 77cm.

So, The area of the triangle with the given dimensions are 77cm.

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Triangle ABC is dilated with a scale factor of 3. Round all your results to the nearest tenths place (one decimal place), if necessary.

Answers

The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Triangle ABC is dilated with a scale factor of 3. Then the scale factor will be 3.

If the side BC is 5.4 units long, then the length of the side B'C' will be

B'C' = 3 x BC

B'C' = 3 x 5.4

B'C' = 16.2 units

If the side A'B' is 8.2 units long, then the length of the side AB will be

AB = A'B' / 3

AB = 8.2 / 3

AB = 2.7 units

If the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

There is no effect of dilation on the angle. Then the angles will remain the same.

The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

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a1=3 and a8= -6561
find: ratio r

Answers

Answer:

-4920.75 or 18

Step-by-step explanation:

I'm not quite sure if this is correct because I got two diffrent soultions for a.

In a1=3 I got a=3

In a8= -6561 I got a= -820.125

So i plugged my two solutions in to find a6

I got

18

or

-4920.75

That doesn't really seem correct, but I tried!!

set of even numbers less than 15

Answers

Step-by-step explanation:

for positive numbet (2, 4, 6, 8, 10, 12, 14)

 2, 4, 6, 8, 10, 12, and 14.

Step-by-step explanation:

even number is 2,4,6,8.....

odd number is 1,3,5,7.......

wish you have a great day

Determine if the sequence below is arithmetic or geometric and
determine the common difference / ratio in simplest form.
This is
equal to
17, 13, 9, ...
V sequence and the
is

Answers

The sequence is an arithmetic sequence due to the presence of a common difference.

Arithmetic and Geometric sequence

An arithmetic sequence is a sequence that has a common difference while a geometric sequence is a sequence with a common ratio. For instance, given the sequence below:

a, b, c, d...

The sequence is an arithmetic sequence if;

common difference = b - a = c - b = d - c

The sequence is a geometric progression if;

common ratio = b/a = c/b = d/c

Given the sequence 17, 13, 9, ...

d = 13 - 17 = 9 - 13

d = -4

Since the sequence has a common difference, hence the given sequence is an arithmetic progression.

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can someone please help?

Answers

Approximately 7.4 is 1.9 times larger than 3.9.

[tex]10^{-8}[/tex]  is 3 times smaller than [tex]10^{-5}[/tex] .

7.4 x [tex]10^{-8}[/tex] is 1.9 x x [tex]10^{-3}[/tex] smaller than 3.9 x [tex]10^{-5}[/tex].

What is the scientific notation?

Scientific notation is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, when 100 is written in scientific notation it becomes 1 x 10².

For negative numbers, the sign in front of the power would be negative. For example, 0.0012 becomes 1.2 x [tex]10^{-3}[/tex] in scientific notation.

0.000039 becomes 3.9 x [tex]10^{-5}[/tex]

Difference between 7.4 and 3.9 : 7.4 / 3.9 = 1.9

Difference between [tex]10^{-8}[/tex] and x [tex]10^{-5}[/tex]

= [tex]10^{-8 - (-5)}[/tex]

= [tex]10^{-8 + 5}[/tex]

= [tex]10^{-3}[/tex]

[tex]10^{-8}[/tex]  is three times smaller than  [tex]10^{-5}[/tex]

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Which of the following shows 16 more than a number, written as an algebraic expression?

16n
16 − n
n − 16
16 + n

Answers

Answer:

16 + n

Step-by-step explanation:

Whenever something says "more" it typically includes addition.

It says 16 more than a number, meaning that you add 16 to an number (n)

*Please mark brainliest

Answer:

16 + n

Step-by-step explanation:

I got 100% on the test

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