a saving account earns interest at a rate of 7% each month. the initial balance is $100. write an exponential function b(m) to model the growth after m months.

If you choose the lottery, you would be considered a risk taker.

By opting for the lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing, you are demonstrating a willingness to take a chance and accept the uncertainty associated with the potential outcomes. A risk taker is someone who is willing to engage in risky or uncertain situations for the possibility of gaining a favorable outcome. In this case, you are accepting the risk of potentially winning nothing in exchange for the chance to win a larger amount.

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The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

  CD = 3/√2 in

Step-by-step explanation:

You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.

All of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.

In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...

  CD = BD = CB/√2

  CD = 3/√2 in

__

Additional comment

Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...

  CD = 3/√2 = (3/2)√2 = 1.5√2

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Answer:

9 years old.

Step-by-step explanation:

Since the ages of all of these students are being represented in relation to the middle student's age then we can create formulas for each student and then apply them to the formula for the sum of their ages and solve for the middle child's age (M) like so... (oldest child's age is represented by variable O and youngest child's age is represented by variable Y)

O = M + 6

Y = M - 3

30 = (M+6) + M + (M-3)  ... combine like terms

30 = 3M + 3  ... subtract 3 from both sides

27 = 3M  ... divide both sides by 3

9 = M

Now we know that the middle child is 9 years old.

Using combination, 5184 nine-digit numbers can be made using each of the digits 1 through 9 exactly once with the digits alternating between odd and even.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.

If the first letter is even, there are 4 first digit possibilities (not 5 because it can't start with 0), 4 third digit possibilities, 3 fifth digit possibilities, etc., making the total 4!

If an odd number is the first letter, there will be 5!*4! different ones.

Add the two together now.

4*4!*4! + 5!*4!=5184

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The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.

To solve for the mileages at which company A will charge less than company B, we can set up the following inequality:
A < B
where A is the cost of renting from company A and B is the cost of renting from company B. We can plug in the given information to get:
x ≤ A
x > B = y + 40z
where x is the number of miles driven, y is the initial fee for company B, and z is the additional cost per mile for company B.
Now we can substitute the given values to get:
x ≤ A
x > y + 40z
For company A, the cost is a flat rate with unlimited mileage, so A is just the cost listed for one day of rental. Let's say that cost is $100.
For company B, the initial fee is $50 and the additional cost per mile is $0.25. So:
y = 50
z = 0.25
Now we can plug in these values and solve for x:
x ≤ 100
x > 50 + 40(0.25)
x > 65
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.

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The complementary function for the differential equation is ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\). The particular solution for the differential equation is \(Yp(x) = -7e^(^6^x^)\). The general solution for the differential equation is y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) -\(7e^(^6^x^)\).

To find the complementary function for the given differential equation, we assume a solution of the form \(ye(x) = e^(^r^x^)\), where r is a constant to be determined. Plugging this into the differential equation, we get:

\(r^2e^(^r^x^) + 6e^(^r^x^) = 0\)

Factoring out \(e^(^r^x^)\), we obtain:

\(e^(^r^x^)(r^2 + 6) = 0\)

For a nontrivial solution, the term in the parentheses must equal zero:

\(r^2 + 6 = 0\)

Solving this quadratic equation gives us r = ±√(-6) = ±i√6. Hence, the complementary function is of the form:

ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\)

Next, we need to find the particular solution Yp(x) for the differential equation. The particular solution is assumed to have a similar form to the forcing term \(-294x^2^e^(^6^x^).\)

Since this term is a polynomial multiplied by an exponential function, we assume a particular solution of the form:

\(Yp(x) = (A + Bx + Cx^2)e^(^6^x^)\)

Differentiating this expression twice and substituting it into the differential equation, we find:

12C + 12C + 6(A + Bx + Cx^2) = \(-294x^2^e^(^6^x^)\)

Simplifying and equating coefficients of like terms, we get:

12C = 0 (from the constant term)

12C + 6A = 0 (from the linear term)

6A + 6B = 0 (from the quadratic term)

Solving this system of equations, we find A = -7, B = 0, and C = 0. Therefore, the particular solution is:

\(Yp(x) = -7e^(^6^x^)\)

Finally, the general solution for the differential equation is given by the sum of the complementary function and the particular solution:

y(x) = ye(x) + Yp(x)

y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) - \(7e^(^6^x^)\)

This is the general solution to the given differential equation.

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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The characteristic of "Mailing Address" would be considered a qualitative variable.

A qualitative variable is a type of variable that is used to assign information that can't be measured by numbers. Qualitative data is used to label the attributes of the individuals, objects, or other items in the study.Types of Qualitative DataThere are many types of qualitative data, for instance:Nominal Data is data that can't be ranked and the measurements have no specific order or sequence.Ordinal Data is data that can be ranked and that has a definite order or sequence.Below are the options given and among them which is qualitative.Size in Square FeetMailing AddressNumber of BathroomsEstimated Market ValueAmong the given options, Mailing Address is considered a qualitative variable. Therefore, the answer is "Mailing Address".

Quantitative data are generally numerical and can be counted or measured, while qualitative data are descriptive and non-numerical. Qualitative data provide a descriptive view of the information that can be used to form ideas or summarize patterns. Qualitative data are frequently used in qualitative studies, but they can also be used in quantitative studies. However, the characteristics of a house that are qualitative variables can be any type of descriptive data that cannot be measured with a numerical value.Mailing Address is a qualitative variable. Because it is a type of data that cannot be counted or measured, it is a qualitative data type. Qualitative data are often used to describe something or to provide more information than can be given by numbers alone. Therefore, the characteristic of "Mailing Address" would be considered a qualitative variable.

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In the given study, the sample is identified as "c. The 250 students that were monitored. In statistics, a sample is a subset of the population that has been chosen to represent the entire population for study and analysis. Hence, option c) is the correct answer.

Sampling is a crucial component of statistical research since it enables us to draw conclusions regarding the population's characteristics and behavior. A sample is a representative of the population as a whole, chosen to represent the characteristics of the population. It is drawn from a population to examine, evaluate and infer outcomes or generalizations of the entire population.

The given study aims to estimate the textbook costs of first-year students at Drummand University by monitoring the textbook cost of 250 first-year students. Therefore, "c. The 250 students that were monitored" is the sample in the study.

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a quantity of interest that can take on different values is known as a(n)

variable.

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Answer: 23.945 (945 repeated)

Step-by-step explanation:

886/37 is exactly 23.945945995

23 and 35/37 in decimal form

Answer:

1. The growth rate is 2

2. The sample is losing half its mass, so the decay factor is 1/2 or 0.5

Step-by-step explanation:

The growth and decay factor in an exponential function is the number that is being multiplied to the power of x

The height of a triangle is 4.8cm. The length of a perpendicular line segment starting on a side and intersecting the opposing angle defines a triangle's height. Every triangle has three sides, which results in three heights, or altitudes.

The line segment perpendicular to the base of the triangle from its point of highest point is its height. We may apply the Pythagorean Theorem to the triangle the height forms because it forms a right angle with the base. The base of the original triangle will be divided in half by the height since it is isosceles (has two equal sides). Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height. Since this is the smallest side of the triangle, the base would be equal to half of five (2.5). A triangle is said to be equilateral if its three heights are all equal.

If area and base are given: height = 2A/ b = (2 × Area) / base.

Area=8*6/2=48/2=24cm

Height=2*24/10=4.8cm

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Answer: 20+.25(20)=20+5=25

Step-by-step explanation:

Answer:

\( {(x - 2)}^{2} + {(y + 1)}^{2} = 25\)

Step-by-step explanation:

In this case, h=2, k=-1, and r=5, so the equation is

\( {(x - 2)}^{2} + {(y + 1)}^{2} = 25\)

The range of the function c = 50t + 200 is given by [200, ∞).

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the y intercept.

Let c represent the distance travelled in t hours, hence:

c = 50t + 200

The range of the function c = 50t + 200 is given by [200, ∞).

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Divide money earned by hours worked to get the hourly rate of $11.00 per gour.

Answer: C. $11.00 per hour

Answer:

250

Step-by-step explanation:

One quarter of 100 would be 25, so adding a zero to 100 (1000) would also mean adding a 0 to 25. Therefore, 250

In order to find or answer we need to combine terms that have "c" in them.

Now, the terms with c are 0.3c and c; therefore, we can say

Therefore,

Hence, the top left choice is the correct one.

Answer:

C

Step-by-step explanation:

\(12x\sqrt{900x^2y^4z^6}= \\\\12x\sqrt{30^2x^2(y^2)^2(z^3)^2}= \\\\12x(30xy^2z^3)= \\\\360x^2y^2z^3\)

Therefore, the correct answer is choice C. Hope this helps!!

Answer:

43˚

Step-by-step explanation:

If angle 5 is 134˚, then that means angle 2 must be 46.

Inside the triangle, we have three angles. A right angle of 90˚, angle 2 of 46˚ and the unknown angle 1. Since the total sum of the angles in a triangle must be 180, we can solve for angle 1:

180 = 90 + 46 + x

Therefore:

x = 43˚

Angle 1 is 43 degrees.

Hope this helps!

Answer:

17 is the answer

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

\(2^3+3^2\\8+9\\17\)

Answer:

14 inches

Step-by-step explanation:

In the above question, the perimeter formula is given as:

P = 2L + 2W

We are asked to rewrite the formula to solve for L.

This means to make L the subject of the formula

P = 2L + 2W

2L = P - 2W

Divide both sides by 2

L = P - 2W/2

We are to use the above formula to find the length of a rectangle whose width is 7 inches and perimeter is 42 inches.

P = Perimeter

L = Length

W = Width

L = P - 2W/2

L = 42 - 2(7)/2

L = 42 - 14/2

L = 28/2

L = 14 inches

Therefore, the length of the rectangle = 14 inches

Answer:

area = ½bh

= 1/2×11× 15

= 82.5 Square inches

82.5 Square InchesStep-by-step explanation:15x11/2 = 82.5

Answer: q = 8

Step-by-step explanation: Isolate your variable by dividing each side of the equation by factors that do not contain any variable.

I hope this helps you out. :)