A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. the patient currently has a bone density of 1, 500 kg / m * g ^ 3 the doctor writes an exponential function to represent the situation. which should the doctor use for a and b in a function written in the form f(x) = a * b ^ x where f(x) represents the bone density after x years ?

Answer:

The mass of Jupiter is about 11.8 times the mass of Venus.

Step-by-step explanation:

Bianca will earn interest of $382.5 for a period of 3years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same.

Simple interest is calculated with the following formula:

S.I. = P × R × T,

where P = Principal, R = Rate of Interest in % per annum, and T = Time

Given,

Principal P = $3000

Rate of interest R = 4.25% = 4.25/100 = 0.0425

Time T = 3 years

Simple interest S.I. = P × R × T

                               = 3000 × 0.0425 × 3

                               = 127.5 × 3

                       S.I.   = $382.5

Hence, Interest Bianca will earn in 3 years = $382.5

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Answer:

Irrational, Rational, and Complex Roots

Step-by-step explanation:

Irrational roots cannot be written as a fraction, for example, √2 is an irrational root because 2 is not a square number

Rational roots can be written as a fraction. For example, √4 is a rational root because it can be either -2 or 2 which are both rational.

Complex/imaginary roots take the form of [tex]a+bi[/tex] where "a" is the real part and "b" is the imaginary part. For example, √(-1) = i which is complex/imaginary.

Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It's worth noting that if we multiply our answer by itself, we get the original polynomial.

A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

Here,

Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial.

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Answer:

the answer to your question is 3.

Answer: graph a and d

Step-by-step explanation:

The perimeter of the rectangle, given that the rectangle has an area of 40 ft² and a length of 8 ft is 26 ft

We'll begin by obtaining the width of the rectangle. The width of the rectangle can be obtained as follow:

Area = Length × Width

40 = 8 × Width

Divide both sides by 8

Width = 40 / 8

Width = 5 ft

Finally, we shall determine the perimeter of the rectangle. Details below:

Perimeter = 2(Lenght + Width)

Perimeter = 2(8 + 5)

Perimeter = 2(13)

Perimeter = 26 ft

Thus, we can conclude that the perimeter is 26 ft

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Answer:

x = 3.25

Step-by-step explanation:

Answer:

Just subtract the answer to what your adding:

7.50 - 4.25 = 3.25

Step-by-step explanation:

Hope it helps! =D

Two triangles will be better than one half times five times thirteen. We'll also have a single rectangular piece. It measures 12 by 10. 20 times 2 equals 40. 13 divided by 2 divided by 2 is equal to 4. I am capable of 44 times two times two. 13 is 52 One is equal to 10 x 2 x 1/2. 12 times 10 is 120, and 5 times 13 is 65. Consequently, the area is 297 square feet (40 plus 52 plus 20 plus 65 plus 120).

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Answer: 297 ft.2

Step-by-step explanation:

To solve the problem, we must first find the slope of the line containing (4, -2) and (x, -6). The slope of a line is calculated as the change in y-coordinates divided by the change in x-coordinates, or (y2 - y1) / (x2 - x1). In this case, the slope of the line containing (4, -2) and (x, -6) is (-6 - (-2)) / (x - 4) = -4 / (x - 4)

Since the line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2,-9) and (3,-4), we know that the product of the slopes of these two lines is -1. We can use that information to find the slope of the second line: -1 = (-4 / (x - 4)) * m, where m is the slope of the second line. Solving for m, we get m = -1 / (-4 / (x - 4)) = (x - 4) / 4.

We can now use the point-slope form of a linear equation to find the equation of the line containing (-2,-9) and (3,-4). The point-slope form is y - y1 = m(x - x1). In this case, we can use (-2,-9) as (x1, y1) and (x - 4) / 4 as m:

y - (-9) = (x - 4) / 4 * (x + 2)

Simplifying we get y = (x-4)/4 + (-9) = (x-4)/4 - 9

Now we can substitute x = -2 and y = -9 to check if it belongs to this line:

-9 = (-2 - 4)/4 - 9

-9 = -2/4 - 9

-9 = -0.5 - 9

-9 = -9.5

It match so this line is the correct one.

The value of x that satisfies the given conditions is x = -2

You can graph this line on a separate sheet of paper by plotting the point (-2, -9) and using the slope (x-4)/4 to find additional points on the line.

The solution of the given system of equation x + y = 5 , 3x + 5y = 15 represents it has one solution given by intersecting lines at point

(x, y ) = ( 5, 0).

As given in the question,

Given system of equation is :

x + y = 5 __(1)

3x + 5y = 15 ___(2)

The standard rule to get the solution of the system of equation is given by :

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂= 0

One solution  :

a₁ / a₂ ≠ b₁ / b₂

No solution :

a₁ / a₂ = b₁ / b₂ ≠ c₁/c₂

Infinitely many solution :

a₁ / a₂ = b₁ / b₂ = c₁/c₂

Here in the given system of equation:

1/3 ≠ 1/5

One solution exist.

Solve by elimination method.

Multiply (1) by 3 and subtract from (2) we get,

3x + 5y = 15

3x + 3y = 15

      2y = 0

⇒y =0

Substitute y =0 in (1) we get,

x = 5

It represents both the lines intersect at point ( x, y) = ( 5,0)

Therefore , the given system of equation has one solution equal to

intersecting point ( x, y) = ( 5,0).

The above question is incomplete , the complete question is :

Determine whether the system of equation has no solution, one solution, or infinitely many solution. If the system of equation has one solution, name it.

x + y = 5

3x + 5y = 15

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The probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.

1. There are a total of 15 SweetTarts in the bag (4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts).

2. The probability of drawing a yellow SweetTart first is 2/15.

3. The probability of drawing a yellow SweetTart second is 1/14 (since one yellow SweetTart has already been drawn).

4. The probability of drawing a yellow SweetTart third is 2/13 (since two yellow SweetTarts have already been drawn).

5. The overall probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.

The probability of drawing a yellow SweetTart three times in a row is (2/15) x (1/14) x (2/13) = 0.0002692.

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Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = [tex]2^{4}[/tex], where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

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The required dimensions of the dilated kitchen is 8.5 inch by 13.09.

The scale factor is defined as the ratio of modified change in length to original length.

Here,
Current dimension of the graph = 8.5 inch by 11 inch
Final dimension of the graph = 24 inch by 36 inch

Now,
Dilated dimension of the kitchen
Length = 24 / 8.5 × 3 = 8.5 inch

Width = 36/11 × 4 = 13.09

Thus, the required dimensions of the dilated kitchen is 8.5 inch by 13.09.

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f(x)=mx+b. The function's value is f(x). The line's slope is m. When x is equal to 0, the function's value is equal to b.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function.  Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

iven

f(x)=mx+b. The function's value is f(x). The line's slope is m.

When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.

The x-value coordinate's is given by x.

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The Remainder Theorem states that if a polynomial P(x) is divided by (x - c), the remainder is P(c). To find the factor of a polynomial using the Remainder Theorem, you can use the following steps:

Example:

P(x) = x^3 + 3x^2 + 2x -6

Factor = (x-2)

P(2) = 8 + 12 + 4 - 6 = 0

So, the factor of P(x) is (x-2)

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Option b is correct monthly payment = $163.07

A loan of $7,500 with an 11% interest rate compounded monthly over a time period of 5 years.

Monthly Payment = Amount / Discount factor

Discount factor [tex]D = \frac{1-(1+i)^{n} }{i}[/tex]

where,

Amount = $7500

Rate= 11%=0.11

[tex]i = \frac{0.11}{12} = 0.0091[/tex] ( by using division)

Time = 5 years

Time (n) = 5 × 12 = 60

Now, put i and n in the Discount factor,

[tex]D = \frac{1-(1+i)^{n} }{i}[/tex]

[tex]D = \frac{1-(1+0.009)^{-60} }{0.009}[/tex]

[tex]D = \frac{1-(1.009)^{-60} }{0.009}[/tex]

[tex]D = \frac{0.421 }{0.009}[/tex]

D = 46.77

Monthly payment (M),

[tex]M = \frac{Amount}{Discout factor} = \frac{A}{D}[/tex]

[tex]M = \frac{7500}{46.77}[/tex] ( by using division)

Monthly payment = 163.07

Therefore, Option b is the correct monthly payment = $163.07.

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The required amount of sweets Steve will get is 42.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
Ali and Steve share some sweets in a ratio of 2:7 Steve gets 30 more sweets than Ali.

Let the amount of sweet Ali and steve be x and y,
According to the question,
x / y = 2/7

x = 2y/7 - - - - (1)

And

y = 30 + x

From equation 1
y = 30 + 2y / 7
5y = 30 × 7
y = 42

Now,
x = 2 × 42 /7
x = 12

Thus, the required amount of sweets Steve will get is 42.

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He must work for 10 hours a day to complete the job in 10 days. 10 hours per day is the optimal amount of time to finish the job in 10 days

1. Begin by setting up an equation. Let x be the number of hours worked.

2. 8 hours x 12 days = 96 hours

3. We want to finish the job in 10 days, so 10x = 96

4. Solve for x. 10x = 96, x = 9.6

5. Since we can't work partial hours, round up to 10 hours. Therefore, the man must work 10 hours a day to complete the job in 10 days.

To finish the job in 10 days, the man must work for a total of 100 hours. This means he must work for 10 hours a day to complete the job in the allotted time. Working 8 hours a day would take 12 days, and working 9 hours a day would take 11.11 days. Therefore, 10 hours per day is the optimal amount of time to finish the job in 10 days.

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Assumption 1: [tex]\triangle ABE \sim \triangle ACD/tex]

[tex]\frac{x}{10}=\frac{3}{15} \implies x=2[/tex]

Assumption 2: [tex]\triangle ABE \sim \triangle ADC[/tex]

[tex]\frac{x}{15}=\frac{3}{10} \implies x=4.5[/tex]

A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.

It is referred to as being unfair when two terms are joined by a sign like "not equal to," "more than," or "less than." The inequality illustrates the relationship between variables and numbers in terms of greater than and less than.

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality'. So, a lack of balance results in inequality.

Given that a rental car company charges $50 per day to rent a car and $0.15 for every mile driven.

The equation of inequality will be written as,

C ≥ [tex]0.15m + 50x[/tex]    

Here, C is the total cost, m is the number of miles, and x is the number of days.

C ≥ [tex]0.15m + 50x[/tex]    

C ≥ ( [tex]0.15*100[/tex] ) + [tex]50x[/tex]

130 ≥ 19.5 + [tex]50x[/tex]

130 - 19.5 ≥ [tex]50x[/tex]

[tex]50x[/tex] ≤ 110.5

x ≤ 110.5 / 50

x ≤ 2.21 days

Therefore,

A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.

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The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

The cost of adult ticket be x and child ticket be y respectively.

Now as per sum ,

(i) 5x + 13y = 59 and,

(ii) 5x + 9y = 47

Subtracting equation (ii) from (i) we get,

13y - 9y = 59 - 47

⇒ 4y = 12

⇒ y = 3

putting y = 3 in equation (ii) we get

5x + 9*3 = 47      ⇒ x = 20/5 = 4

The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

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Answer:

x = 11

Step-by-step explanation:

We'll have to get X alone by doing the opposite of what the current equation is showing

67 = 7x-10. I usually turn the numbers around cause it looks better...

7x-10 = 67

We see it's subtracting 10, so we'll add 10 on both sides

7x = 67 + 10

7x = 77

Since 7x is being multiplied, we'll divide on both sides

x = 77/7

x = 11

Answer: -11

Step-by-step explanation:

rearrange it so it's -7x-10=67

add 10 to itself and 67

then you get -7x=77

then divide 77 by -7

and you get -11

i hope this was right :)

Answer:

656

Step-by-step explanation:

The equivalent expression is  -1.9b + 7.8.

There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Combine similar phrases now:

The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.

When we combine the term b's coefficient, we get

1.3b + 7.8–3.2b

= (1.3−3.2)⋅b + 7.8

By condensing the equation, we obtain

= (- 1.9) +b + 7.8

= −1.9b + 7.8

There is a condensed equivalent formula of -1.9b + 7.8.

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Sarah will make 6 baskets in her next 6 shots.

If Sarah made a basket on one of her first shots in a basketball game, and she continues to make baskets at the same rate, we can use that information to predict the number of baskets she will make in her next 6 shots.

Since we know that Sarah made a basket on one of her first shots, we can assume that the probability of her making a basket on any given shot is 1/1 or 100%.

If the probability of Sarah making a basket on any given shot is 100%, then we can expect her to make a basket on all 6 of her next shots. Therefore, Sarah will make 6 baskets in her next 6 shots.

Therefore, Sarah will make 6 baskets in her next 6 shots.

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How many crickets did Greta feed Lizzy?

Answer:

56

Step-by-step explanation:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Since Gretta fed Draco 77 crickets just do:

77 ÷ 11

= 7

Then:

8 x 7

= 56

You're welcome

Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.

A relationship that explains how two variables relate to one another is represented by the word "functions," which is frequently used in mathematics. There are three: a variable, which can be any type of input, and predictor variables, which are the results of the function or equation.

Here,

A quadratic function's "width" can be calculated using the coefficient before the variable.

The graph will be narrower than the parent graph if the coefficient is more than one (f(x)=x2), and

wider if the coefficient is less than one. Thus, from widest to narrowest:

f(x)=0.5x²

f(x)=3x²

f(x)=-5x²

Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.

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