Tim's phone service charges $24.93 plus an additional $0.21 for each text message sent per month. If
Tim's phone bill was $30.18, which equation could be used to find how many text messages, x, Tim
sent last month?

Answer:

\(5^{-2}\)

Step-by-step explanation:

Primd factorize 25

25 = 5*5 = 5²

\(\sf \dfrac{1}{25}=\dfrac{1}{5^{2}} \\\\= 5^{-2}\)

HINT:

\(\dfrac{1}{a^{m}}=a^{-m}\)

Answer:

300$

Step-by-step explanation:

If he save 10 for every 50, you  just divide. 60/10 = 6. He saved 6 times, if each time he saves he has 50 extra dollars, 6 * 50 = 300 because 6*5 = 30 and there is a extra 0 so 30 and 0 is 300

Answer: \(12\pi\)

Step-by-step explanation:

The formula for area of a circle is \(\pi r^2=A\)

The formula for circumference of a circle is \(2r\pi=C\)

Where r is the radius

A is area

C is circumference

Knowing this we can sub our values in and solve for r in the formula for area

Divide both sides by \(\pi\) to isolate r

\(\pi r^2=A\\\pi r^2=36\pi \\\frac{\pi r^2}{\pi } =\frac{36\pi }{\pi } \\r^2=36\)

Take the square root of both sides

\(r^2=36\\\sqrt{r^2} =\sqrt{36} \\r=6\)

Now sub the value of r into the formula for circumference

\(2r\pi =C\\2(6)\pi =C\\12\pi\)

Answer:

\(12\pi \: c \: m\)

step by step explanation:

\(area \: of \: a \: cirle = \pi \: r {}^{2} \\ circmferene \: of \: a \: circle = 2 \:\pi \: r \\ 36\pi = \pi \: r {}^{2} \\ 36 = r {}^{2} \\ r = 6 \\ for \: circmference \\ 2 \times \pi \: \times 6 = 12\ \: \pi \: cm \)

Answer:

Sorry please accept i need points for an answer

Step-by-step explanation:

172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.

Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.

Here,
Original network address with a prefix  = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets =  172.16.0.0/20.

172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.

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Answer:

62 + 6d + 4 = 180

6d + 66 = 180

6d = 114

d = 19

In the given research study, the independent variable is the daily dosage of aspirin, and the dependent variable is the heart attack rate in men.

The independent variable, in this case, is the factor that the researcher manipulates or controls. It is the dosage of aspirin administered to the participants on a daily basis. The researcher can vary the dosage levels to examine the potential impact on the heart attack rate.

On the other hand, the dependent variable is the outcome or result that the researcher measures or observes. It is the heart attack rate in men, which is expected to be influenced by the different dosages of aspirin. The researcher will collect data on the occurrence of heart attacks in men based on the dosage levels of aspirin to analyze any potential relationship or effect.

By examining the relationship between the independent variable (daily dosage of aspirin) and the dependent variable (heart attack rate in men), the researcher aims to determine if there is a correlation or causal relationship between the two factors.

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Answer:

Hey there!

Step 1:

\(6p = - 42\)

Write the equation

Step 2:

\(p = \frac{ - 42}{6} \)

take 6 to other side to divide it with-42

\(p = - 7\)

after dividing 6 with -42 we will get -7

\(\small{\purple {\sf \underline{hope\: it\: helped\: you✿}}}\)

6p = -42

The value of p.

6p = -42

or, p = -42/6

or, p = -7

The value of p is -7.

Answer:

Below

Step-by-step explanation:

The solution set is just the point where the two graphed lines cross....this point is common to BOTH lines and thus is the solution (2,2)

Answer:

43

Step-by-step explanation:

Use the mean formula:

mean = (sum of elements) / (number of elements)

Let x represent the fourth number, and solve for x:

mean = (sum of elements) / (number of elements)

40 = (35 + 41 + 41 + x) / 4

40 = (117 + x) / 4

160 = 117 + x

43 = x

So, the fourth number is 43

Answer:

43

Step-by-step explanation:

Step-by-step explanation:

x = number of years after 2007.

x = 0 for 2007.

PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).

PC(x) = 0.8x + 52

0 <= x <= 5

in 2007 (x = 0) the average adult ate 52 pounds.

in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.

so, in 2012 (x = 5) the average adult will eat

PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.

The function grows without bound or approaches negative infinity as x becomes very large or very small, then the equation for the horizontal asymptote is either y = infinity or y = negative infinity, respectively.

Without knowing the specific function and transformation, it is difficult to provide a specific equation for the transformed function and horizontal asymptote. However, in general, the equation for a transformed function can be written as:

y = a*f(b(x - h)) + k

Where a, b, h, and k are constants that represent the amplitude, period, horizontal shift, and vertical shift of the function, respectively. f(x) is the original function, and the transformation involves scaling, shifting, or reflecting the function. Depending on the transformation, one or more of the constants a, b, h, and k may change.

The equation for the horizontal asymptote depends on the behavior of the function as x approaches positive or negative infinity. If the function approaches a constant value as x becomes very large or very small, then the equation for the horizontal asymptote is simply that constant value. If the function grows without bound or approaches negative infinity as x becomes very large or very small, then the equation for the horizontal asymptote is either y = infinity or y = negative infinity, respectively.

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Solution:

Given:

A coefficient is a number multiplied by a variable.

Hence,

Therefore, the coefficient is 2.

Answer:

a) 5x

b) 6xy

c) 6xy

hope this answer helps you....

The correct answer is option C. The y-intercept of f(x) is (0, -2), and the y-intercept of g(x) is (0, 5).

What is statistics ?

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides a framework for understanding and making decisions based on data. Statistics is used in a wide range of fields, including business, economics, social sciences, engineering, and medicine.

To find the y-intercept of a linear function, we need to determine the value of y when x is equal to 0. For function f(x), we can see from the table that f(0) = -2, which means that the y-intercept of f(x) is (0, -2).

For function g(x), we are given that g(x) = -2x + 5. When x is equal to 0, we have:

g(0) = -2(0) + 5 = 5

This means that the y-intercept of g(x) is (0, 5).

Therefore, the correct answer is option C. The y-intercept of f(x) is (0, -2), and the y-intercept of g(x) is (0, 5).

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Answer:

y=-2x+6

Step-by-step explanation:

When it comes to parallel lines the slopes are the same they just have different y-intercepts.

Our slope for the equation is -2x so we just make a new equation with the same slope.

Since we are asked to put it with a y-intercept of 6 we just add +6 at the end.

Giving us y=-2x+6.

To find the probability that it takes Anand 444 or more days to forget a new vocabulary word, we can use the geometric probability formula, which is given by:

Where x is the number of independent trials (in this case, the number of days that Anand goes without reviewing the word), p is the probability of success (in this case, the probability that Anand does not forget the word on a given day), and P(x) is the probability of success on the xth trial.

In this case, we are looking for the probability that it takes Anand 444 or more days to forget the word, so we want to find P(444). We know that the probability of success (not forgetting the word) on a given day is 70%, or 0.7. Plugging these values into the formula gives us:

P(444) = (1 - 0.7)^(444-1) * 0.7

= 0.3^443 * 0.7

= 0.000107 * 0.7

= 0.000075

Rounding to the nearest hundredth, we find that the probability that it takes Anand 444 or more days to forget the word is 0.00.

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Their annual state income tax could be $4050  if there is $2,000 deduction for married couples and $900 for each dependent or child.

What is percentage?

percentage can be defined as the product of ratio of given value , total value and hundred.

Given,

The Cabrera family makes $92,800 annually and has 2 children. The state in which they live allows a $2,000 deduction for married couples and $900 for each dependent or child. The tax rate is 4.8%.  

As it is a family so $2,000 deduction for married couples

and they are having two childs so we will deduct another $1800 .

so now the actual amount  = $92800 - $2000 - $1800

Amount = $90000

The tax rate = 4.5%

that is amount to be paid = 4.5 % of 90000

= 4.5 / 100  *  90000

= 45/1000  *  90000

= 45 * 90

= 4050

Hence, Their annual state income tax could be $4050 .

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Answer:

Table B has a constant proportionality between x and y of 0.6

In general, the energy levels of a system increase as the system gets closer. This is because when objects get closer, the force between them increases, which increases the potential energy of the system.

The potential energy of a system is related to the energy levels of the system, so increasing the potential energy leads to higher energy levels.

To see this mathematically, let's consider a system of two particles with masses m1 and m2, separated by a distance r, and interacting via a potential energy function U(r). The total energy of the system, E, is given by:

E = 1/2 m1 v1^2 + 1/2 m2 v2^2 + U(r)

where v1 and v2 are the velocities of the particles. We can simplify this expression by using the reduced mass μ, defined as:

1/μ = 1/m1 + 1/m2

and the relative distance vector r = r2 - r1. Then, we have:

E = 1/2 μ v^2 + U(r)

where v is the relative velocity of the particles.

If we assume that the particles are moving in a circular orbit with radius r, we can use the centripetal force to relate v to r:

v^2 = F_c/m = U'(r)/μr

where F_c is the centripetal force and U'(r) is the derivative of U with respect to r. Substituting this into the expression for E, we get:

E = U'(r)/2μ + U(r)

The first term on the right-hand side represents the kinetic energy of the system, while the second term represents the potential energy. The total energy E is conserved, so it must be a constant.

Now, suppose we decrease the distance r between the particles. This means that U'(r) is negative (since the force is attractive), so the first term on the right-hand side decreases, while the second term increases. Thus, the total energy E must increase to stay constant.

Therefore, we can conclude that when objects get closer, their energy levels get higher.

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The Cartesian equation equivalent to the polar equation r = 3cos(θ) is

x = 3cos^2(θ)

y = 3cos(θ) * sin(θ)

To rewrite the polar equation r = 3cos(θ) as a Cartesian equation, we can use the following conversion formulas:

x = r * cos(θ)

y = r * sin(θ)

Substituting r = 3cos(θ) into these formulas, we get:

x = 3cos(θ) * cos(θ)

y = 3cos(θ) * sin(θ)

Simplifying these expressions, we have:

x = 3cos^2(θ)

y = 3cos(θ) * sin(θ)

Therefore, the Cartesian equation equivalent to the polar equation r = 3cos(θ) is:

x = 3cos^2(θ)

y = 3cos(θ) * sin(θ)

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Answer:

(18,−21)

Step-by-step explanation:

Dilation: multiply each coordinate

(x,y)\rightarrow (3x,3y)

(x,y)→(3x,3y)

Dilations multiply by scale factor

(\color{red}{6},\color{blue}{-7}) \rightarrow (3\cdot \color{red}{6},3\cdot \color{blue}{-7})=\mathbf{(18,-21)}

(6,−7)→(3⋅6,3⋅−7)=(18,−21)

Answer:

18,-21

Step-by-step explanation:

I hope this helps

Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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Based on the data, table that shows a proportional relationship is the first table.

Data is said to be proportional if it increases or decreases at a constant rate.

The first table has proportional data because the height increases by 5 centimeters everyweek, which shows a constant rate.

Note: This question is incomplete; below I attach the missing section:

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Answer:

L = \(\sqrt{97} \)ft

Step-by-step explanation:

L = \(\sqrt{r^2 + h^2} \)

r = 8/2 = 4ft

h = 9ft

L = \(\sqrt{4^2 + 9^2} \)

L = \(\sqrt{16 + 81} \)

L = \(\sqrt{97} \)

Answer:

28 miles

Step-by-step explanation:

subtract the pay to the additional pay

The system of equations are solved and the value of x and y are -4 and 12 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

4x + 3y = 20   be equation (1)

3x + 2y = 12   be equation (2)

Multiply equation (1) by 3 and equation (2) by 4 , we get

12x + 9y = 60   be equation (3)

12x + 8y = 48   be equation (4)

Subtracting equation (4) from equation (3) , we get

y = 12

Substituting the value of y in equation (2) , we get

3x + 2 ( 12 ) = 12

Subtracting 24 on both sides , we get

3x = -12

Divide by 3 on both sides , we get

x = -4

Hence , the system of equations are solved

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