A cell phone provider offers a plan that costs $40 per month plus $0.10 per text message sent or received. A comparable plan costs $70 per month but offers unlimited text messaging. How many text messages would have to be sent or received in order for the plans to cost the same each month?

The correct answer is:

4.

Explanation:

The number 40 is written in this stem-and-leaf plot as 4|0.  60 is written as 6|0.  There are 4 leaves between these numbers; 5, 5, 5 and 5, with the stem of 4.  This means the numbers are 45, 45, 45 and 45.  There are only 4 between these two numbers.

Answer:

Step-by-step explanation:

The completed problem is

[tex]5 \times 70=5\times 7 \ tens.\\5 \times 70=35 \ tens=350[/tex]

Basically, the process is only about separating tens from units, so basically "tens" represents the zero, that's why we only multiply 5 and 7 digits, and add the zero at the end. It's an easier way to multiply tens.

present dimensions = 5*7

dimensions after scaling with factor 3 = 15*21

dimensions after reducing by scale factor 0.5 = 7.5*10.5

area of rectangle = length * breadth

so area of yearbook = 7.5*10.5 = 78.75

because, 78.75<80

so, the yearbook will fit in area of 80 inches^2

Final answer:

The numbers 4.5, 6, and 7.5 can form the sides of a right triangle as their squared lengths satisfy the Pythagorean theorem where 4.5² + 6² equals 7.5².

Explanation:

To determine whether the numbers 4.5, 6, 7.5 can form the sides of a right triangle, we can apply the Pythagorean theorem.

This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

According to the given numbers, if we assume that 7.5 is the length of the hypotenuse, then:

4.5² + 6² should equal 7.5²

Calculating each term gives us:

Adding the squares of the possible legs:

20.25 + 36 = 56.25, which is indeed the square of the hypotenuse. This confirms that 4.5, 6, and 7.5 can indeed form a right triangle.

Answer: 3 dimes

Step-by-step explanation:

Let n represent the number of nickels and d represent the number of dimes Reese has in his pocket.

Given system : [tex]n+d=11........(1)\\5n+10d=70............................(2)[/tex]

Divide equation (2) by 3 on both sides, we get

[tex]n+2d=14................................(3)[/tex]

Subtract equation (1) from (3), we get

[tex]d=3[/tex]

Hence, there are 3 dimes in Reese's pocket.

Answer:

3 dimes are in Reese's pocket.

Step-by-step explanation:

Here, n represent the number of nickels and  d represent the number of dimes.

Given the system of equations:

[tex]n+d = 11[/tex]           .....[1]

[tex]5n+10d = 70[/tex]             .....[2]

Multiply both sides by 5 in [1] we have;

[tex]5n+5d=55[/tex]             .....[3]

Subtract equation [3] from [2] we have;

[tex]5d = 15[/tex]

Divide both sides by 5 we have;

d = 3

Therefore, 3 dimes are in Reese's pocket.

Answer:

The required expression is [tex]25-2g[/tex]

She left with 23 tokens after playing 1 game.

She left with 17 tokens after playing 4 game.

She left with 13 tokens after playing 6 game.

She left with 5 tokens after playing 10 game.

She left with 1 tokens after playing 12 game.

Step-by-step explanation:

Consider the provide information.

Part (A)

At a video arcade, Jenny buys 25 tokens. She uses two tokens for each game She plays.

Let the number of games she plays represented by g.

For each game she need to use 2 tokens.

Thus for g games she will use 2g tokens.

Thus, the required expression is: [tex]25-2g[/tex]

Part (B) Find the number of tokens Jenny has left after playing 1,4,6,10 and 12 games.

The number of tokens Jenny has left after playing 1, is:

[tex]25-2(1)[/tex]

[tex]25-2[/tex]

[tex]23[/tex]

Hence, she left with 23 tokens after playing 1 game.

The number of tokens Jenny has left after playing 4, is:

[tex]25-2(4)[/tex]

[tex]25-8[/tex]

[tex]17[/tex]

Hence, she left with 17 tokens after playing 4 game.

The number of tokens Jenny has left after playing 6, is:

[tex]25-2(6)[/tex]

[tex]25-12[/tex]

[tex]13[/tex]

Hence, she left with 13 tokens after playing 6 game.

The number of tokens Jenny has left after playing 10, is:

[tex]25-2(10)[/tex]

[tex]25-20[/tex]

[tex]5[/tex]

Hence, she left with 5 tokens after playing 10 game.

The number of tokens Jenny has left after playing 12, is:

[tex]25-2(12)[/tex]

[tex]25-24[/tex]

[tex]1[/tex]

Hence, she left with 1 tokens after playing 12 game.

Raphael used the Property of Equality to justify his manipulation of the second equation.

The property that justifies Raphael's manipulation is the Property of Equality. According to this property, if two expressions are equal, then subtracting or adding the same quantity to both sides of the equation will still give you an equal equation. In this case, Raphael changed the second equation to -8x - 2y = -2 by subtracting 1 from both sides of the equation.

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Final answer:

To find k to make a quadratic expression a perfect square of a binomial, we must compare coefficients and solve equations for a and b. Finally, by substituting the values of a and b, the value of k can be determined as 16.

Explanation:

To find k so that 25x^2 + 40x + k is the square of a binomial, we aim to express 25x^2 + 40x + k as the square of the binomial form (ax + b)^2. Comparing coefficients gives us:

2ab = 40 (from the linear term)

a^2 = 25 (from the quadratic term)

Solving these equations, we find a = 5 and b = 4. Therefore, the value of k is 16.

Answer:

9216 see explanation

Step-by-step explanation:

area of a rectangle =l×b

let the area and the breadth of the rectangle be x an y respectively

Now

x×y=64cm^2

as we have to multiply the length and breadth both by 12 the new area will be x×y=64×12×12 so the new area would be 9216

Answer:

[tex]\displaystyle 9126\:yd.^2[/tex]

Step-by-step explanation:

Explanation:

[tex]\displaystyle wl = A[/tex]

First, let us list the factours of 64:

[tex]\displaystyle 1, 2, 4, 8, 16, 32, 64[/tex]

Any two factours of 64 would do [two eights would wourk of cource, but the park is not square-shaped]:

[tex]\displaystyle 9126 = [2(12)][32(12)] \\ 9126 = [4(12)][16(12)][/tex]

Either way, you still get the same result. By the way, NO court will ever be one yard, so I never included it, but again, you get the overall idea.

I am joyous to assist you at any time.

Scott is incorrect thinking his stick is longer; both received identical 1 foot sticks, so total lengths remain the same despite the number of pieces they are cut into.

The student's question involves Scott believing that because he has more pieces, the total length of his stick is longer than Vivian's. Scott and Vivian both received a 1 foot stick and divided it into equal pieces; Scott into 7 pieces and Vivian into 5.

This problem is related to the concept of division where each person divides their total length equally among the number of pieces, which means the length of each individual piece changes, but the total length of the stick remains the same. Scott is not correct; the total lengths of their sticks are identical, each being 1 foot in length before cutting, regardless of the number of pieces they've been cut into.

Answer:

c) [tex]5^{6}[/tex]

Step-by-step explanation:

We have been given that there are [tex](5^3)^2\cdot 5^0[/tex] hens in a bird enclosure. We are asked to find the total number of hens in the enclosure.

Using exponent property [tex]a^0=1[/tex], we will get:

[tex](5^3)^2\cdot 1[/tex]

[tex](5^3)^2[/tex]

Using exponent property [tex](a^b)^c=a^{b\cdot c}[/tex], we will get:

[tex]5^{3\cdot 2}[/tex]

[tex]5^{6}[/tex]

Therefore, there are total number of hens in the enclosure would be [tex]5^{6}[/tex].

Final answer:

To find the number of units that the worker produces during the first three hours, we need to calculate the integral of the production function from 0 to 3. The production function is given as 100te^-0.5t. Using the power rule and the exponential rule of integration, we can find that the worker produces approximately -300e^-1.5 units during the first three hours on the job.

Explanation:

To find the number of units that the worker produces during the first three hours, we need to calculate the integral of the production function from 0 to 3.
The production function is given as 100te^-0.5t.
To integrate this function, we can use the power rule and the exponential rule of integration.

Now, we can plug in the values from 0 to 3 in the integral and calculate the result.

Therefore, the worker produces approximately -300e^-1.5 units during the first three hours on the job.