10.) A fitness center
charges a $100 initiation
fee plus $40 per month.
f(m) =

Answer:

2.96 cm to the nearest hundredth.

Step-by-step explanation:

V = 3.14 r^2 h

226 = 3.14 * r^2 * 8.2

r^2 = 226 / (3.14*8.2)

r^2 = 8.7774

r =  2.96 cm to the nearest hundredth.

The function f(x) = 1/x is not defined for x = 0, so it cannot be considered as a function from R to R. Similarly, the function f(x) = √x is not defined for x < 0, as the square root of a negative number is not a real number. Therefore, f(x) = √x is also not a function from R to R.

What is a real number?

A real number is a number that can be expressed as a decimal or a fraction, including integers, rational numbers (fractions), and irrational numbers (such as √2 or π). Real numbers can be plotted on the number line and have properties like addition, subtraction, multiplication, and division.

In the case of f(x) = 1/x, the issue arises because division by zero is undefined in mathematics. As x approaches 0 from the positive side, the function approaches positive infinity, and as x approaches 0 from the negative side, the function approaches negative infinity. This discontinuity at x = 0 makes it impossible to define a unique output value for f(0), which is necessary for a function.

For f(x) = √x, the square root function is only defined for non-negative values of x. Taking the square root of a negative number would require introducing complex numbers, but in this case, we are dealing with a real function. Hence, f(x) = √x is not defined for x < 0 and cannot be considered as a function from R to R.

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Answer:

that is x+ 1

Step-by-step explanation:

that's it easy peasy

Solution :

From the figure,

The coordinates of --

A = (-5,-3)

B = (-6,-1)

C = (-3,-1)  

D = (-2,-3)

When it undergoes reflection about x-axis, we have the coordinates of the quadrilateral as

A' = (-5,+3)

B' = (-6,+1)

C' = (-3,+1)

D' = (-2,+3)

Now A'B'C'D' is translated 3 units to right, so the coordinates will be --

A" = (-2,3)

B" = (-3,1)

C" = (0,1)

D" = (1,3)

When the quadrilateral moves third and two units up, we get

A"' = (3,3)

B"' = (2,1)

C"' = (5,1)

D"' = (6,3)

Answer:

Step-by-step explanation:

The triangles' corresponding sides' are proportional and their corresponding angles are congruent therefore, the triangles are sim

The correct option is C). proportional; congruent; similar

When the triangle is dilated from the origin at a scale factor of 2 to create Triangle then, the image of the triangle and the original triangle are similar to each other

However for similar triangles, corresponding angles are equal or congruent, and corresponding sides are in ratio or scaled

For example : A triangle ABC is dilated by a factor of 3 and centered at (-5,-4)

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Answer:

Your answer is 4%

Step-by-step explanation:

7÷175×100 = 4

The area of the circle here is 616cm².

The space a circle takes up in a two-dimensional plane is known as the area of the circle.

Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle.

A = πr², where r is the circle's radius, is the formula for calculating a circle's surface area.

Diameter of circle = 28cm.

So here area of the circle =

π (28/2)²

= 22×14×14/7

= 616 cm²

Therefore, area of the circle here is 616cm².

A circle is a geometric shape that is defined as a closed curve in which all points are equidistant from a single point called the center.

Circles have several properties, including circumference (the distance around the circle), diameter (the distance across the circle passing through the center), and radius (the distance from the center to any point on the circle).

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Difference of (-x² + 9xy) and  (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Given expression,

(-x² + 9xy) - (x² + 6xy - 8y²)

Distributing negative sign

-x² + 9xy - x² - 6xy + 8y²

Adding like terms

- 2x² + 3xy + 8y²

Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).

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Answer:

Angle 1 = 25 degrees

Angle 2 = 65 degrees

Hey there!

3(7n + 6) - 5n

= 3(7n) + 3(6) - 5n

= 21n + 18 - 5n

= 16n + 18

Therefore, your answer should be:

16n + 18

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

the possible outcomes contain the same number of heads and tails are 70.

tell me if i am right

For each coin flip, there are 2 possible outcomes (heads or tails), so for 8 flips, there are \(2^8\) = 256 possible outcomes.

When flipping a coin, there are two possible outcomes: heads or tails. So, for one flip, there are two possibilities. For two flips, there are two possibilities for the first flip and two possibilities for the second flip, making a total of 2x2=4 possible outcomes.

For three flips, there are two possibilities for the first flip, two for the second flip, and two for the third flip, making a total of 2x2x2=8 possible outcomes.

Similarly, for four flips, there are 2x2x2x2=16 possible outcomes, and for five flips, there are 2x2x2x2x2=32 possible outcomes.

Continuing this pattern, for eight flips, there are 2x2x2x2x2x2x2x2 = 256 possible outcomes.

This can also be calculated using the formula for combinations, which is \(n! / (r!(n-r)!)\) where n is the number of total flips (in this case, 8) and r is the number of heads that we want to get.

For example, to find the number of outcomes where we get exactly 3 heads and 5 tails, we would use the formula:

\(8! / (3!5!) = 56\)

So, there are 56 possible outcomes where we get exactly 3 heads and 5 tails.

In summary, for each coin flip, there are 2 possible outcomes (heads or tails), so for 8 flips, there are \(2^8 = 256\) possible outcomes.

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The 35% of the animals in the zoo are aquatic based on the stated fraction of animals.

Let us assume the number of aquatic animals to be x. We will solve the fraction. So, the expression representing each number will be -

⅖ + ¼ + x = 1

Taking LCM on Left Hand Side of the equation, we get 20

\( \frac{(2 \times 4) + (1 \times 5)}{20} + x = 1\)

Performing multiplication in numerator on Left Hand Side and solving this fraction

\( \frac{8 + 5}{20} + x = 1\)

\( \frac{13}{20} + x = 1\)

Rearranging the equation in terms of x

x = \(1 - \frac{13}{20} \)

\(x = \frac{20 - 13}{20} \)

\(x = \frac{7}{20} \)

The percentage of aquatic animals at the zoo will be given by the formula -

Percentage = number of aquatic animals/total animals × 100

Percentage =

\( \frac{ \frac{7}{20} }{1} \times 100\)

Cancelling the possible numbers

Percentage = 7×5

Percentage = 35%

Hence, the aquatic animals in the zoo are 35%.

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It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.

Let's use the formula \(A = P(1 + i)^n\),

where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.

For the $2,900 investment at 15% compounded quarterly:

P = $2,900

i = 15% = 0.15/4

= 0.0375 (interest rate per quarter)

For the $3,100 investment at 9% compounded quarterly:

P = $3,100

i = 9% = 0.09/4

= 0.0225 (interest rate per quarter)

Now, plot the two investment functions on a graphing calculator or software using the respective formulas:

Function 1:\(A = 2900(1 + 0.0375)^n\)

Function 2:\(A = 3100(1 + 0.0225)^n\)

Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.

By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.

Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.

Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

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The length of the rectangular countertop is 6x - 4.

To find the length of the rectangular countertop, we have to substitute the given values in the formula for the area of the rectangle, which is A = l × w
12x² + 10x - 12 = (2x + 3) × l
6x² + 5x - 6 = 3x × l + 3 × l
6x² + 5x - 6 = 3lx + 3l
6x² + 5x - 6 = 3l(x + 1)
3l = (6x² + 5x - 6) / (x + 1)
3l = (6x² + 9x - 4x - 6) / (x + 1)
3l = 3(2x² + 3x - 2) / (x + 1)
l = (2x² + 3x - 2) / (x + 1)
l = [(2x - 1) (x + 2)] / (x + 1)
Therefore, the length of the rectangular countertop is 6x - 4.

Summary:
The formula for the area of the rectangle is A = l × w. We substitute the given values in the formula to find the length of the rectangular countertop. After simplifying the expression, the length of the rectangular countertop is found to be 6x - 4.

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Answer:

-786

Explanation:

Move 4^-4 to the numerator using the negative exponent rule 1/x^-n = x^n

-(3×^4)

Raise 4 to the power of 4.

-(3×256)

Multiply 3 by 256.

-1×768

Multiply -1 by 768.

-768

Answer:

1.5

Step-by-step explanation:

Plug in numbers into the distance formula.

y2-y1

____

x2-x1

6 - 3.       3

____.     ___

3 - 5.       -2

3/-2=-1.5

Answer:

3.6 or Sqrt(13)

Step-by-step explanation:

plug into distance formula

(3-5)^2 + (6-3)^2

4 + 9

Sqrt(13)

Sqrt(13) is equal to 3.6055127546

^ is rounded up to 3.6

The sample size for the super rich Category, and Z is the critical value corresponding to the desired confidence level.

a) The independent multinomial populations in this analysis are the income categories "marginally rich," "comfortably rich," and "super rich." We are comparing the proportions of education levels (no college, some college, undergraduate degree, and postgraduate study) within each income category.

b) To determine if the proportions of education levels differ among the three income categories, we can conduct a chi-square test of independence.

We set up the following hypotheses:

H0: The proportions of education levels are the same for the three income categories.

Ha: The proportions of education levels differ among the three income categories.

We can use a chi-square test to analyze the data and calculate the test statistic and p-value.

c) To construct a 95% confidence interval for the difference in proportions with at least an undergraduate degree for individuals who are marginally and super rich, we can use the formula for the difference in proportions:

p1 - p2 ± Z * sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2))

where p1 is the proportion of individuals with at least an undergraduate degree in the marginally rich category, p2 is the proportion in the super rich category, n1 is the sample size for the marginally rich category, n2 is the sample size for the super rich category, and Z is the critical value corresponding to the desired confidence level.

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The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

1x113= 113, nothing else can equal to 113 unless you estimate ig

Step-by-step explanation:

Answer:

I don't know but you might end up with a C

Step-by-step explanation:

OR A D

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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Answer: Option: >

Step-by-step explanation: To compare the fractions 34/40 and 5/8, we can convert them to a common denominator. The least common multiple of 40 and 8 is 40, so we can convert 5/8 to 25/40. Now we can compare the fractions:

34/40 is equivalent to 17/20

17/20 is greater than 25/40

Therefore, the correct answer is >.

Answer:

-0.544m

Step-by-step explanation:

The height of the barnacle is approximately is, 0.657 meters.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Graph y = sin(x)

Boat travel= 7m

Now,

Let y be the height of the barnacle and x be the distance the boat has traveled

i.e, x = 7 meters

to find the height y :

Substitute the value of x =7 meters in [1] we have;

y = sin(7)

≈0.657.

Therefore, by algebra the answer will be 0.657 meters.

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The substance has a half-life of 3 years, which means it decays with rate k such that

\(\dfrac12 = e^{3k} \implies \ln\left(\dfrac12\right) = 3k \implies k = \dfrac13 \ln\left(\dfrac12\right) = -\dfrac{\ln(2)}3\)

a) Starting at 200 mg, the amount of substance y remaining after t years have passed is then

\(y = 200 e^{kt} = \boxed{200 e^{(-\ln(2)/3) \, t}}\)

b) After t = 10 years, you'd be left with

\(y = 200 e^{-10\ln(2)/3} = 200 e^{\ln(2)^{-10/3}} = 200 \cdot 2^{-10/3} \approx \boxed{19.843}\)

mg of the substance.

c) The substance takes T years to decay to 10% of its initial amount such that

\(0.10 = e^{(-\ln(2)/3) \, T}\)

Solve for T :

\(\ln(0.10) = -\dfrac{\ln(2)}3 T\)

\(T = -\dfrac{3\ln(0.10)}{\ln(2)} = -3 \log_2(0.10) \approx \boxed{9.966}\)

years.

Step-by-step explanation:

half-life means that after the given period of time there is only half of the original quantity left.

and after another period, then half of that remaining half is gone. and so on. it is a never-ending story ...

m(t) = 200/(2^(t/3))

after 3 years 200 has to be divided by 2¹. after 2×3 years by 2² (as the half of the half is a quarter). and so on.

so, after 10 years we have then

m(10) = 200/(2^(10/3)) = 200/cubic root(2¹⁰) =

= 200/cubic root(1024) = 19.84251315... mg

how long does it take to reduce the 200 mg to 10% = 20 MG?

20 = 200/(2^(t/3))

1 = 10/(2^(t/3))

2^(t/3) = 10

t/3 = ln(10)/ln(2)

based on the rules of logarithms (the log of a number to a certain base a is always any other log of that number divided by the same log type of the original number base a).

t/3 = 3.321928095...

t = 9.965784285... years

Andrew is concerned about the high turnover rate if he is tracking how many positions he has to fill and how many times he fills the same position and is worried that too many people are leaving his organization.

The turnover rate is the proportion of employees who leave a company over a specific period of time.

The turnover rate is expressed as a percentage of the total workforce.

High turnover rates can suggest that employees are unhappy with their jobs or that the company is experiencing financial difficulties.

A high turnover rate might result in a decrease in productivity, decreased morale among the remaining employees, and increased expenditures on recruiting and training new employees.

Thus, it is evident that Andrew is concerned about the high turnover rate.

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Answer:

S = 3

S = 5

S = 7

S = 9

Step-by-step explanation:

t = 3s + 2

when t = 11

11 = 3s + 2

11 – 2 = 3s

9 = 3s

s = 3

t = 3s + 2

when t = 17

17 = 3s + 2

17 – 2 = 3s

15 = 3s

s = 5

t = 3s + 2

when t = 23

23 = 3s + 2

23 – 2 = 3s

21 = 3s

s = 7

t = 3s + 2

when t = 29

29 = 3s + 2

29 – 2 = 3s

27 = 3s

s = 9

I HOPE ALL THIS HELPS

RATE AS BRAINLIEST PLS

The points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

The coordinate plane is a two-dimensional space formed by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin. Each point in the plane is identified by a pair of numbers called its coordinates, where the first number represents its position along the x-axis and the second number represents its position along the y-axis. Coordinates are typically written as (x, y), with the x-coordinate listed first and the y-coordinate listed second. The coordinate plane is commonly used in mathematics to graph and analyze equations, functions, and geometric shapes.

Let x be the number of bags of popcorn and y be the number of bags of cotton candy. Then the cost constraint is:

3x + 7y ≤ 56

We also have the constraint that Chris needs at least 7 bags of popcorn:

x ≥ 7

To graph these constraints, we can rewrite them in slope-intercept form:

y ≤ (-3/7)x + 8

x ≥ 7

The first inequality has a slope of -3/7 and a y-intercept of 8, and the second inequality is a vertical line at x = 7.

To plot the points that are part of the solution set, we can simply plug them into the two inequalities and see if they are true. The points that satisfy both inequalities are part of the solution set.

(3, 7) satisfies both inequalities:

7 ≤ (-3/7)(3) + 8

3 ≥ 7

(2, 2) does not satisfy the first inequality:

2(7) > 3(2) + 7

(8, 1) satisfies both inequalities:

1 ≤ (-3/7)(8) + 8

8 ≥ 7

(10, 2) satisfies both inequalities:

2 ≤ (-3/7)(10) + 8

10 ≥ 7

(5, 5) does not satisfy the first inequality:

5(7) > 3(5) + 7

Therefore, the points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

To graph these on the coordinate plane, we can plot the vertical line x=7 and the line y= (-3/7)x + 8, and then shade in the feasible region below the line and to the right of the vertical line.

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Answer:

14 dollars in one day

35 dollars if he works five days a week

49 dollars if he works 7 days a week

Step-by-step explanation:

Answer:

$14.00

Step-by-step explanation:

$7.00 x 2= $14.00

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