Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modeled by the function y=3.5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary.

The inequality that represent each situations are:

a. 6(n + 3) ≥ 42.

b. 6(n + 3) ≤ 42

c. 6(n + 3) < 42

d. 6(n+3) > 42.

To write the inequality for each of the situations, translate each statement into algebraic expressions and use the appropriate inequality sign where necessary.

Thus, let the unknown number be represented as n.

a. The statement, "at least 42" means not less 42, which is the same as "greater than or equal to 42".

Therefore, the first statement is represented by the inequality, 6(n + 3) ≥ 42.

b. "6 times n and 3 is at most 42" is written as, 6(n + 3) ≤ 42

c. "6 times n and 3 is less than 42" would be translated as: 6(n + 3) < 42

d. "6 times n and 3 is more than 42" would be, 6(n+3) > 42.

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Step-by-step explanation:

6(n+3)>42

this is your answer

arlynn

How would you express the area of he rectangle using the Distributive Property?

area = length * width

area using Distributive Property: 3 (x + 5)

The relation between a and r is 2r

According to the given information

a varies directly with r

a = 8

r = 4

a is directly proportional to r

a ∝ r

a = k r

where k is constant of proportionality

k =  [tex]\frac{a}{r}[/tex]

k = [tex]\frac{8}{4}[/tex]

k = 2

so,

a = k r

putting the value of k in the above equation

we get

a = 2r

The relation between a and r is 2r

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The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.

What is Regression analysis ?

Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

Given, tail length = (3 × weight) + 20

(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.

(b) If weight is 38 gm, then

    tail length = 38 × 3 + 20

                     = 114 + 20 = 134mm.

So, the statement is correct.

(c) We've  tail length = (3 × weight) + 20

we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.

So, the given statement is correct.

(d) The slope is 3 when the tail length is being measured in millimeters.

Now, If we measure it in centimeter = 3/10 = 0.3 cm

∵ 1 mm = 1/10 cm.

So, the given statement is correct.

(e) when a mouse has weight of 29 grams and tail length of 100 mm.

    When the weight is 29 grams, it should have tail length as :

             tail length = 29 × 3 + 20

                              = 107 mm.

  but, tail length is given as 100 mm.

So, the residual for the mouse is -7 i.e. (100 - 107)

Hence, The given statement is correct.

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Answer:

goes from(6,0),(10,1),(14,2) in +ve

To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:

Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.

For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.

Hence t-distribution is suitable when the variance which is standard deviation squared is unknown

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Answer:

------------------------------

The difference of the functions is:

The difference between functions is positive, therefore it is a vertical shift up by 2 units.

Answer:

-------------------

It is assumed you need to add 5 and square root of 4:

Answer:

x = 12/5

Step-by-step explanation:

3 (3x − 1) − 3 (5x − 3) = − (x + 6)

9x − 3 − 15x + 9 = − x − 6

9x − 15x + x = 3 − 9 − 6

− 5x = − 12

5x = 12

x = 12/5

Answer:

[tex]x=\dfrac{12}{5}[/tex]

Step-by-step explanation:

Given equation:

[tex]3(3x-1)-3(5x-3)=-(x+6)[/tex]

Distribute:

[tex]\implies 3 \cdot 3x + 3 \cdot (-1) - 3 \cdot 5x - 3 \cdot (-3)=-x-6[/tex]

[tex]\implies 9x-3-15x+9=-x-6[/tex]

Collect and combine like terms on the left side of the equation:

[tex]\implies 9x-15x+9-3=-x-6[/tex]

[tex]\implies -6x+6=-x-6[/tex]

Add 6x to both sides:

[tex]\implies -6x+6+6x=-x-6+6x[/tex]

[tex]\implies 6=5x-6[/tex]

Add 6 to both sides:

[tex]\implies 6+6=5x-6+6[/tex]

[tex]\implies 12=5x[/tex]

[tex]\implies 5x=12[/tex]

Divide both sides by 5:

[tex]\implies \dfrac{5x}{5}=\dfrac{12}{5}[/tex]

[tex]\implies x=\dfrac{12}{5}[/tex]

Answer: 1.49 x [tex]10^{-5}[/tex]

Step-by-step explanation:

Answer: 1

Let's solve your equation step-by-step.

3x+2=5

Step 1: Subtract 2 from both sides.

3x+2−2=5−2

3x=3

Step 2: Divide both sides by 3.

3x/3 = 3/3

(3x divided by 3 cancels the 3 in 3x making it just x)

x=1

By setting up the equation, we get the system of linear equations are

9x + 7y = 77

3x + 5y = 49

solving these equation Cost to rent a chair = $1.75

cost to rent a table = $8.75

A system of linear equations is a collection of one or more linear equations involving the same variables.

There are several methods for solving systems of linear equations, including:

Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.

Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.

Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.

etc.

To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.

First, solve the first equation for y:

9x + 7y = 77

7y = -9x + 77

y = (-9/7)x + 11

Now substitute this expression for y into the second equation:

3x + 5((-9/7)x + 5(11) = 49

3x - (45/7)x + 55 = 49

solving for x :

x = 1.75

Now substitute this value for x back into the first equation to find y:

y = 8.75

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4 is the constant of proportionality of given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The graph of the relationships ( dogs,cost) is a line that contains the points(0,0) (3,12) and (6,24).

We need to find the constant of proportionality

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

To find the constant of proportionality, we have to divide the value of y by x.

12/3=4

24/6=4

Hence, 4 is the constant of proportionality of given graph.

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The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]

Explain Pythagoras theorem.

The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.

The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.

Using Pythagoras theorem in both the triangles,

Find the hypotenuse in above triangle

[tex]h^2=P^2+B^2[/tex]

[tex]h^2=4+4=8[/tex]

h = [tex]2\sqrt{2}[/tex]

Now, using Pythagoras theorem in below triangle,

[tex]h^2=P^2+B^2[/tex]

[tex]5^2 = x^{2} + 8[/tex]

25 = [tex]x^{2}[/tex] + 8

[tex]x^{2}[/tex] = 25 - 8 = 17

x = [tex]\sqrt{17}[/tex]

Therefore, x = [tex]\sqrt{17}[/tex]

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Answer:

m= -3

Step-by-step explanation:

5(2m+1)-3m=-16

5(2m)+5(1)-3m= -16

10m+5-3m= -16

7m+5= -16

     -5.   -5

7m= -21

/7.    /7

m= -3

Hopes this helps please mark brainliest

And :-3

process:

5(2m + 1) - 3m = - 16

10m+5-3m=-16

7m=-16-5

m=-21/7

m=-3

The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:

y = A · [tex]e^{B\cdot x}[/tex]

Where:

If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:

4 / 5 = A · [tex]e^{-B}[/tex]

20 = A · [tex]e^{B}[/tex]

If we divide the latter expression by the former, then:

25 = [tex]e^{2\cdot B}[/tex]

㏑ 25 = 2 · B

B = (1 / 2) · ㏑ 25

B ≈ 1.609

And the value of A is:

A = 20 / [tex]e^{1.609}[/tex]

A ≈ 4.002

The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

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The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.

The correct long division is shown below.

This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.

The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Now,

Since, The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Hence, We get;

⇒ 7 × 5/8 = 35 / 8

Thus, The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

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Answer:

The vendor sold 212 sodas and 34 hot dogs.

Step-by-step explanation:

Subtract 34 from 246 for the number of sodas sold.

The explicit formula for the geometric sequence 6, -24, 96, ... is

Every term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio

The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.

For the given sequence the first term is a = 6

The common ratio is solved as follows

a * r  = second term

6 * r = -24

r = -24/6

r = -4

check

-24 * -4 = 96 correct

The nth term of a geometric sequence

= ar^(n - 1)

= a * -4^(n - 1)

checking for the third term

= a * -4^(n - 1)

= 6 * -4^(3 - 1)

= 6 * -4^(2)

= 6 * 16

= 96

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$1,556.72 is required to deposit in the account each month.

72% of interest is earned.

a)

It is a classic Ordinary Annuity saving plan. The general formula is

FV = P((1+r)^n-1)/r)--------(1)

where  

FV is the future value of the account.  

P is the monthly payment (deposit).

r is the monthly percentage yield presented as a decimal.

n is the number of deposits (= the number of years multiplied by 12, in this case).

From this formula, you get the monthly payment:

P=FV(r/(1+r)^-1)----------(2)

Under the given conditions,

FV = $800,000

r = 0.04/12

n = 25*12.  

So, according to formula (2), the monthly payment is

P=800000(0.04/12(1+0.04/12)^25*12-1)

P=800000(0.003/1.713)

P=$1.556.72

Note that of the projected $800,000 the total you deposit will be only  25*12 times $1.556.72 i.e. about 25*12*1.556.72 = 467016 dollars.                    

The rest is what the account will earn/accumulate over the 25 years.

b)

You will earn:  

(8000000-467016/467016)*100

72% of interest is earned.

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The cost for the sheet is $22.60 and a discount of 30% is given.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, the brand of sheets is on sale 30% off with a regular price of $18.00 per sheet.

Therefore, the cost for the sheet will be:

= $18 - (30% × $18)

= $18 - $5.40

= $12.60

The cost for the brand of sheet is $22.60.

Note that the information was incomplete and the calculation was based on the information given.

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The number of liters in the tank after 109 seconds is 60.5 liters.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

2.5 liters = 1 minute

2.5 liters = 60 seconds

Multiply 109/60 on both sides.

109/60 x 2.5 liters = 109 seconds

4.5 liters = 109 seconds

This means,

4.5 liters is drained after 109 seconds

Now,

The liters of water in the tank.

= 65 - 4.5

= 60.5 liters

Thus,

There are 60.5 liters in the tank.

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Answer: 12 symmetries

Step-by-step explanation:

just draw the lines on the star.

The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Data provided in the question:

Total amount to be invested = $140000

Stock                          X       Y

Expected return       14%     10%

Beta                          1.42     1.18

Expected return of portfolio = 17.6%

Now,

let the weight invested n stock X be W

therefore,

Weight of Stock Y = 1 - W

thus,

( W × 14% ) + (1 - w) × 10% = 17.6 %

14W + 10% - 10W = 17.6%

4W = 7.6

W = 1.9

Therefore,

weight of Y = 1 - 1.9 = -0.9

Amount investment in Sock Y = Total amount to be invested × Weight

= 140,000 × ( - 0.9 )

= - $126,000 i.e short Y

Beta of portfolio = ∑ (Beta × Weight)

Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]

Beta of portfolio= 2.698 - 1.062

Beta of portfolio= 1.636

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The coordinate of the vertices of △A'B'C' are A'(3,6), B'(9,-3), and C'(-12, 6). Since the scale factor is 3.

What is coordinate of a point?

The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph.

The coordinate of △ABC are A(1,2), B(3,-1) and C(-4,2).

The scale factor is k = 3.

The x-coordinate of A is 1.

The y-coordinate of A is 2.

The x-coordinate of B is 3.

The y-coordinate of B is -1.

The x-coordinate of C is -4.

The y-coordinate of C is 2.

To find the vertices of △A'B'C', multiplying x-coordinate and y-coordinate by 3.

The x-coordinate of A' is 1 × 3 = 3.

The y-coordinate of A' is 2 × 3 = 6.

The x-coordinate of B' is 3 × 3= 9.

The y-coordinate of B' is -1 × 3 = -3.

The x-coordinate of C' is -4 × 3 = -12.

The y-coordinate of C' is 2 × 3 = 6.

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The value of the function (f⋅g)(3) = 1

The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. It is denoted by the letter f or f(x).  

Here we have

f(x) = − 3x − 2  

g(x) = − x + 2

=> (f · g) = f(g(x))

Now Take x = − x + 2 in f(x)

=> f(g(x)) =  − 3(− x + 2)x − 2  

=  3x − 6 − 2      

=  3x − 8  

From the above calculations,

(f⋅g)(x) =  3x − 8    

Now we need to calculate the value of (f⋅g)(3) as given below

=> (f⋅g)(3) =  3(3) − 8 = 9 − 8 = 1

Therefore,

The value of the function  (f⋅g)(3) = 1

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