The function f(x) = 10x + 45, represents the cost per month of a cell phone
plan when x amount of gigabytes are used OVER the monthly allowance.
Interpret the meaning and value of f(7) *

After considering the given data we conclude that the correct statement that satisfy the given question is \(f(n) = 2 - n\)concerning nonnegative integer.

The given definition is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. The formula for f(n)
Here,
n = nonnegative integer is f(n) = 2 - n.
Now to evaluate that this formula is valid, we can apply mathematical induction.
First, we show that the formula holds for n = 0. Since f(0) = 1 by definition, we have f(0) = 2 - 0 = 1.
Next, we assume that the formula holds for some arbitrary nonnegative integer k.
That is, we assume that f(k) = 2 - k. We then show that the formula also holds for k + 1. By definition of the function f, we have f(k + 1) = f(k) - 1. Substituting our assumption into this equation gives:

f(k + 1) = (2 - k) - 1 = 1 - k

This is precisely the formula we would expect if f(k + 1) were equal to 2 - (k + 1). Therefore, by mathematical induction, we have shown that the formula \(f(n) = 2 - n\)is valid for all nonnegative integers n.
To learn more about mathematical induction
https://brainly.com/question/29503103
#SPJ4

Answer:

4 7/17 yeards or 4.412 yards approximately if the map shows the distance as 3 inches.

Step-by-step explanation:

The actual distance of the Harper from the school = 50 yards. According to the map, the distance from the school = 34 inches. We could say 34 inches represents 50 yards. So, 1 inch could be represented by 50/34 = 25/17 yards. In order to find the actual length of 3 inches in yards, we need to multiply 1 inches value of yards by 3.Therefore, 3 inches = 3* 25/17 = 75/17 = 4 7/17 yeards in decimals 4.412 yards approximately. Therefore,  Harper from home is  4 7/17 yeards or 4.412 yards approximately if the map shows the distance as 3 inches.

x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

a) Solving the system using substitution:

We know that: x+y=2 (i)3x+y=0 (ii)We will solve equation (i) for y:y=2-x

Now, substitute this value of y in equation (ii):3x + (2-x) = 03x+2-x=0 2x = -2 x = -1

Substitute the value of x in equation (i):x + y = 2-1 + y = 2y = 3b)

Solving the system using elimination (linear combination) :

We know that: x+y=2 (i)3x+y=0 (ii)

We will subtract equation (i) from equation (ii):3x + y - (x + y) = 0 2x = 0 x = 0

Substitute the value of x in equation (i):0 + y = 2y = 2c)

Solving the system by graphing:We know that: x+y=2 (i)3x+y=0 (ii)

Let us plot the graph for both the equations on the same plane:

                                graph{x+2=-y [-10, 10, -5, 5]}

                                 graph{y=-3x [-10, 10, -5, 5]}

From the graph, we can see that the intersection point is (-1, 3)d)

We calculated the value of x and y in parts a, b, and c and the solutions are as follows:

Substitution: x = -1, y = 3

Elimination: x = 0, y = 2

Graphing: x = -1, y = 3

We can see that the value of x is different in parts a and b but the value of y is the same.

The value of x is the same in parts a and c but the value of y is different.

However, the value of x and y in part c is the same as in part a.

Therefore, we can say that the solutions of parts a, b, and c are not the same.

However, we can check if these solutions satisfy the original equations or not. We will substitute these values in the original equations and check:

Substituting x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

Therefore, the values we obtained for x and y are the correct solutions.

Learn more about equations

brainly.com/question/29538993

#SPJ11

Answer:

1

Step by step explanation:

\(\text{Given that,} ~ f(x) = x^2~ \text{and}~ g(x) = x-1\\\\g(2) = 2-1 = 1\\\\g(f(-1)) = g(1) = 1-1 = 0\\\\f(g(2) + g(f(-1)))= f(1+0) = f(1) = 1^2 =1\)

Answer:

g(2) = 2 - 1 = 1 \\ f( -1 ) = { - 1}^{2} = 1 \\ f(1) + g(1) = \\ f(1) = {1}^{2} = 1 \\ g(1) = 1 - 1 = 0 \\

\(g(2) = 2 - 1 = 1 \\ f( -1 ) = { - 1}^{2} = 1 \\ f(1) + g(1) = \\ f(1) = {1}^{2} = 1 \\ g(1) = 1 - 1 = 0 \\ 1 + 0 = 1 \\ \)

The group of 50 people is the sample size of the probability distribution

The mean of the probability distribution for the selected people who are vegetarian is 0.8

The given parameters are:

Sample Size, n = 50

Selected people, x = 20

Start by calculating the proportion (p)

\(p = \frac xn\)

So, we have:

\(p = \frac {20}{50}\)

\(p = 0.4\)

When 2 people are selected;

We have:

n = 2

So, the mean is:

\(\bar x = np\)

This gives

\(\bar x = 2 * 0.4\)

\(\bar x = 0.8\)

Hence, the mean of the probability distribution for the selected people who are vegetarian is 0.8

Read more about probability distribution at:

https://brainly.com/question/25638875

Answer:

68.46

Step-by-step explanation:

In order to find the angle, we can use the cosine rule:

c²=a²+b²-2abCos(c)

And rearrange for Cos(c)

(please note that c in this case is x)

So,

x=Cos^(-1) (a²+b²-c²)/2ab

By substituting the values, we get x=Cos^(-1)(4²+4²-4.5^2)/2(4)(4)

=68.46

Answer:

7 or 8 hours

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation for an arithmetic sequence is

\(a_n=a_1+d(n-1)\)  where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.

Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:

\(a_n=2+3(n-1)\) which simplifies to

\(a_n=2+3n-3\) and a bit more to

\(a_n=3n-1\) (which should tell you that arithmetic sequences are lines!)

Finding the 13th number simply requires that we replace n with 13 and solve:

\(a_{13}=3(13)-1\) so

\(a_{13}=38\)

Answer:

38

Step-by-step explanation:

This isn't the most efficient way but it's the best I can do.

2, 5, 8, 11....

The pattern is that we add 3 every time.

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38,

1 , 2, 3, 4, 5,  6,   7,    8,    9,   10,  11,   12,  13

We can see that 38 is the 13th term of the sequence.

Using De Moivre's Theorem, the three cube roots of 2 + 2i in trigonometric form are:

√3(cos(θ/3) + i sin(θ/3)), where θ = arctan(1/2)

√3(cos((θ + 2π)/3) + i sin((θ + 2π)/3))

√3(cos((θ + 4π)/3) + i sin((θ + 4π)/3))

These cube roots can be graphed as vectors in the complex plane.

To find the three cube roots of 2 + 2i, we can utilize De Moivre's Theorem. The complex number 2 + 2i can be written in polar form as 2√2(cos(θ) + i sin(θ)), where θ is the angle made by the vector in the complex plane.

Using De Moivre's Theorem, we take the cube root of the modulus (2√2) and divide the angle θ by 3. This gives us the trigonometric form of the cube roots. The three cube roots can be expressed as:

∛(2√2)(cos(θ/3) + i sin(θ/3))

∛(2√2)(cos((θ + 2π)/3) + i sin((θ + 2π)/3))

∛(2√2)(cos((θ + 4π)/3) + i sin((θ + 4π)/3))

To graph these cube roots as vectors in the complex plane, we plot the corresponding magnitudes and angles. The magnitude is ∛(2√2), and the angles are θ/3, (θ + 2π)/3, and (θ + 4π)/3, respectively.

The polar equation T = 2 + 4 cos(θ) represents a cardioid when graphed on the axes. A cardioid is a type of polar graph that resembles a heart shape.

Learn more about De Moivre's Theorem here:

https://brainly.com/question/29750103

#SPJ11

Check the picture below.

The price elasticity of demand (PED) for the logo T-shirts is 1.67, indicating that the demand for T-shirts is elastic. Lowering the price from $15 to $10 increased the total revenue, suggesting that the T-shirt made a good decision in lowering the price. This is because the price change led to a significant increase in quantity demanded and overall revenue.

To calculate the price elasticity of demand (PED), we can use the following formula:

PED = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

Given that Q1 = 25, Q2 = 50, P1 = $15, and P2 = $10, we can substitute these values into the formula:

PED = ((50 - 25) / ((50 + 25) / 2)) / (($10 - $15) / (($10 + $15) / 2))

Simplifying this expression:

PED = (25 / 37.5) / (-5 / 12.5)

PED = (-2/3) * (-2.5) = 1.67

The price elasticity of demand (PED) for the logo T-shirts is 1.67.

Since PED is greater than 1, it indicates that the demand for T-shirts is elastic. This means that a decrease in price by 1% will result in a greater than 1% increase in quantity demanded. To determine if lowering the price was a good decision, we can analyze the effect on total revenue. The price-total revenue test states that:

If PED is elastic (greater than 1), a decrease in price will lead to an increase in total revenue.

If PED is inelastic (less than 1), a decrease in price will lead to a decrease in total revenue.

If PED is unit elastic (equal to 1), a change in price will have no effect on total revenue.

Let's calculate the total revenue at both prices:

Total Revenue at $15 = $15 * 25 = $375

Total Revenue at $10 = $10 * 50 = $500

Comparing the total revenue at each price, we can see that lowering the price from $15 to $10 increased the total revenue from $375 to $500. Therefore, the T-shirt made a good decision in lowering the price because it led to an increase in total revenue.

To know more about price elasticity,

https://brainly.com/question/26309888

#SPJ11

The probability of getting exactly 2 sets of 3 (of the same kind) in a 7-card hand from a regular deck of cards is: 0.000410

We have to use this formula

No. of ways to get 2 ranks that appears 3 times x ways of getting 1 card from 44 cards / ways to select 7 from 52 cards

Hence we would have

13C2 * 4C3 * 4C3 *44C1 / 52C7

= 78 *4 * 4 * 44 /133784560

= 0.000410

Read more on probability here: https://brainly.com/question/24756209

#SPJ4

There are infinitely many solutions to an equation with two variables.

We know that an equation is a mathematical statement that contains equal symbol between two mathematical expressions.

In this question need to solve  an equation with x and y in one equation.

Consider an equation with two variables: 5x + y = 8

If we solve given equation for x then it would be,

5x + y = 8

5x + y - y = 8 - y

5x/5 = (8 - y)/5

x = (8 - y)/5

for any arbitrary real value value of y we can find the value of x.

This means there are infinitely many solutions.

If we solve given equation for y then it would be,

5x + y = 8

5x + y - 5x = 8 - 5x

y = 8 - 5x

for any arbitrary real value value of x we can find the value of y.

Therefore, an equation with two variables has infinitely many solutions.

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Answer: x=54

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The researcher can use certain formulas for finding confidence intervals and hypothesis testing in this scenario.

For confidence intervals, the formula for the mean difference would be used, which is the average of the weight changes in the sample.

This formula calculates the range within which the true population mean difference is likely to fall.

To conduct hypothesis testing, the researcher can use the formula for the t-test for a single sample.

This test compares the mean difference observed in the sample to a hypothesized value and determines whether there is enough evidence to support or reject the hypothesis.

To check the assumptions necessary for this test, the researcher would need additional information. The assumptions typically include:

1. Random sampling: It is important to ensure that the subjects were randomly selected from the population to generalize the results.

2. Normality: The weight changes should follow a normal distribution within the population.

The researcher would need to assess the normality assumption, such as by examining the distribution of weight changes or using statistical tests like the Shapiro-Wilk test.

3. Independence: The weight changes of one subject should not be influenced by the weight changes of another subject.

This assumption can be violated if the subjects are related or if there are repeated measurements on the same subjects.

By checking these assumptions and using the appropriate formulas, the researcher can make confidence intervals and perform hypothesis testing to draw conclusions about the effects of the drug on weight loss in the population.

To know more about intervals, visit:

https://brainly.com/question/11051767

#SPJ11

The closest value to the volume of the water tower tank with a spherical tank diameter of 6 meters is 113.04 m3.

The volume of a sphere can be calculated using the formula V = (4/3)π\(r^{3}\), where V is the volume and r is the radius of the sphere. In this case, the diameter of the spherical tank is given as 6 meters, so the radius (r) is half of that, which is 3 meters.

Substituting the radius value into the formula, we have V = (4/3)π(\(3^{3}\)) = (4/3)π(27) ≈ 113.04 m3.

Among the given options, 113.04 m3 is the closest value to the volume of the water tower tank. It represents the approximate amount of water that the tank can hold.

Learn more about volume here:

https://brainly.com/question/28058531

#SPJ11

Answer:10.3

Step-by-step explanation:

Answer:

40.3°

Step-by-step explanation:

sin x/ (5.3) = sin 90/ (8.2)

sin x = (5.3 sin 90) / 8.2

= 5.3/8.2

x = arcsin (5.3/8.2)

= 40.3° to 1 dp

The measure of angle x using Trigonometry is 40.263215° or 40.3.

Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.

Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.

From the figure,

Perpendicular = 5.3 m

Hypotenuse = 8.2 m

Using Trigonometry

sin x = P / H

sin x = 5.3/ 8.2

sin x = 0.6463

Using Inverse Trigonometry

x = \(sin^{-1}\)(0.6463)

x= 40.263215°

Thus, the measure of angle x is 40.3.

Learn more about Trigonometry here:

https://brainly.com/question/12068045

#SPJ4

Herman must sell 27 glasses of lemonade to break even.

To create a linear cost function, we need to determine the relationship between the number of glasses of lemonade made (q) and the cost of making that quantity (c).

From the given data, we have two points: (19, $2) and (83, $5). We can use these points to find the slope of the line and then determine the cost function.

Using the formula for the slope of a line:

slope = (change in cost) / (change in quantity)

slope = ($5 - $2) / (83 - 19)

slope = $3 / 64

Now, let's use the point-slope form of a linear equation to find the cost function:

c - $2 = ($3 / 64)(q - 19)

To break even, the cost (c) should equal the revenue earned from selling the lemonade. Revenue is calculated by multiplying the number of glasses sold (q) by the selling price per glass ($0.15).

c = $0.15q

Setting the cost equal to revenue:

$0.15q = ($3 / 64)(q - 19) + $2

Solving this equation will give us the value of q when the cost equals the revenue (break-even point).

Simplifying the equation:

0.15q = (3/64)(q - 19) + 2

Solving for q:

0.15q = (3/64)q - (57/64) + 2

(49/64)q = (57/64) + 2

(49/64)q = (185/64)

q = (185/64) * (64/49)

q = 185/49

q ≈ 3.775

Since we cannot sell a fraction of a glass, Herman must sell at least 4 glasses of lemonade to break even.

Herman needs to sell at least 27 glasses of lemonade to break even. This calculation is based on the given cost data and the selling price per glass.

To know more about sell visit:

https://brainly.com/question/28420607

#SPJ11

Answer:

4

Step-by-step explanation:

Given

\(\frac{2ab}{c}\) , substitute the given values into the expression

= \(\frac{2(-1)(-4)}{2}\)

= \(\frac{2(4)}{2}\)

= \(\frac{8}{2}\)

= 4

Values provided below

\(\\ \tt\longmapsto sin180=0\)

\(\\ \tt\longmapsto cos270=cos90=0\)

\(\\ \tt\longmapsto csc360=1/0=\infty\)

\(\\ \tt\longmapsto tan90=\infty\)

\(\\ \tt\longmapsto cot90=0\)

\(\\ \tt\longmapsto sec270=\infty\)

Note the rule

Answer:

csc 360°

tan 90°

cot 90°

sec 270°

Step-by-step explanation:

Hope this helps

To find the unit price, we need to divide the price by the amount of ounces:

$1.19 for 12 ounces:

$1.59 for 16 ounces:

We can see that in the 4º decimal place, the first option has a 1 and the second option has a 3. Thus, is better to buy the second option

To 3 decimal places:

First option: $0.099 per ounce

Second option: $0.099 per ounce

Answer:

What is pi? Pi the ratio of the circumference of any circle to the diameter of that circle.

Why is pi day celebrated on March 14th? Be cause March 14 represents the value of Pi. March is the third month of the year, which is also the initial number of the value. The following number is 14, hence the March 14 date.

When is pi Approximation Day

celebrated? July 22

What does the symbol π mean? Pi

What is the diameter of a circle? Diameter is the length of the line through the center that touches 2 points on the edge of the circle.

What is the radius of a circle? The radius is half of the diameter.

How do you find the area of a circle? The area of a circle is pi times the radius squared. A = π r2

How do you find the circumference of a circle?

Two times it radius multiplied by pi or pi times its diameter.

What year was Pi Day first celebrated? 1988

Answer:

6+1.25t

Step-by-step explanation:

W(in the 1st month)=6+1.25

W(in the 2nd month)=6+1.25+1.25

W(in the 3rd month)=6+1.25+1.25+1.25

W(in the t months)=6+t(1.25)

Term 11=a+10d

Here

a=10

d= 7-10= -3

Term 11;

=10+(10×-3)

=10+(-30)

= -20 is the answer

Thank you Hope it helps dear

Answer: -32

Step-by-step explanation:

a=10, d = 7-10 = -3

First find which term is -62

an = -62

a = (n-1) d= -62

Putting values

10 + (n-1)(-3) = -62

10 + (n(-3) -1 (-3) = -62

10 - 3n + 3 = -62

13 - 3n = -62

-3n = -62-13

n = 75/3 = 25

We need to find out 11th term from the last term ie., 25 - 10 = 15th term

So we need to find a14

an = a +(n-1) d

a15 = 10+ (15-1) (-3)

= 10 + 14 (-3)

= 10 -42

= -32

So the 11th term from the 15th term from the first = -32

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

Learn more about correlation coefficient here:

brainly.com/question/29704223

#SPJ11

Answer: Y= x/176397

X= 176397y

Step-by-step explanation: I hope this helps. Have a brilliant day ! - Lily ^_^

The equation of the perpendicular line to the curve y = f(x) at x = 25 is:

y = (-10/33)x + 3220/33.

To find the derivative of the function f(x) = 3x + 3√x, we can use the sum rule and the power rule for derivatives.

(a) To evaluate f'(25), we differentiate each term separately:

f(x) = 3x + 3√x

Differentiating the first term:

f'(x) = d/dx (3x) = 3

For the second term, we need to use the chain rule since it involves the square root:

f'(x) = d/dx (3√x) = 3 * d/dx (√x) = 3 * (1/2) * (1/√x) = (3/2√x)

Now we can evaluate f'(25):

f'(25) = 3 + (3/2√25) = 3 + (3/2 * 5) = 3 + (3/10) = 3 + 0.3 = 3.3

Therefore, f'(25) = 3.3.

(b) To find the equation of the perpendicular line to the curve y = f(x) at x = 25, we need to determine the slope of the perpendicular line. The slope of the perpendicular line will be the negative reciprocal of the slope of the tangent line to the curve at x = 25.

The slope of the tangent line is given by f'(25) = 3.3.

Therefore, the slope of the perpendicular line is -1/3.3 = -10/33.

To find the equation of the perpendicular line, we need a point on the line. The point on the original curve y = f(x) at x = 25 is:

f(25) = 3(25) + 3√(25) = 75 + 3(5) = 75 + 15 = 90.

So, the point on the perpendicular line is (25, 90).

Using the point-slope form of a line, the equation of the perpendicular line is:

y - y₁ = m(x - x₁)

Substituting the values:

y - 90 = (-10/33)(x - 25)

Expanding and rearranging:

y - 90 = (-10/33)x + 250/33

Bringing y to the left side:

y = (-10/33)x + 250/33 + 90

Simplifying:

y = (-10/33)x + 250/33 + 2970/33

y = (-10/33)x + 3220/33

Therefore, the equation of the perpendicular line to the curve y = f(x) at x = 25 is:

y = (-10/33)x + 3220/33.

To know more about equation click-

http://brainly.com/question/2972832

#SPJ11