TIMEDDDDD PLEASE ANSWER 15 POINTS

Jolianne worked half as many hours as Andrew. Jolianne makes $10 per hour and has saved $27. Andrew makes $8 per hour and has no money saved. After getting paid, they have the same amount of money.


Andrew claims that only his table and equation are correct, but Jolianne claims that both tables and equations are valid. Which statement regarding their claims is true?

Andrew is correct because t cannot be used to represent the number of hours Jolianne worked.

Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did.

Jolianne is correct because if one lets t = hours Andrew worked, then his equation is valid. If one lets t = hours Jolianne worked, then Andrew worked twice as many so her equation is valid, too.

Jolianne is correct because when solving t in her equation, t = hours Jolianne worked, and when solving for t in Andrew’s equation, t = hours Jolianne worked so they are equal.

Answer:

Step-by-step explanation:

x = number of cars

12x = 3.50x + 34

12x - 3.50x = 34

8.5x = 34

x = 34/8.5

x = 4 <=====he would have to sell 4 cars

In this case, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.

To determine how many cars Luke must sell for his revenue to equal his expenses, let's define the variables and set up the equation.

Let x be the number of cars Luke sells.

Revenue:

Luke sells each car for $12, so his revenue for selling x cars is:

[tex]\[ \text{Revenue} = 12x \][/tex]

Expenses:

Luke's expenses include $3.50 per car and a fixed cost of $34 for tools. So his total expenses for x cars are:

[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]

We need to find the number of cars x such that his revenue equals his expenses:

12x = 3.50x + 34

To solve for x  subtract 3.50x  from both sides:

12x - 3.50x = 34

8.50x = 34

Now, divide both sides by 8.50:

[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]

x = 4

Therefore, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.

Answer:

The answer can be calculated by doing the following steps;

Step-by-step explanation:

Answer:

The approximate length of the radius is 3 feet

Step-by-step explanation:

Given:

circumference of a circle = 18.41 feet

To Find:

approximate length of the radius = ?

Solution:

Let the radius of the circle be r

We know that the circumference of the circle C is given by the formula

C =[tex]2 \pi R[/tex]

Substituting the values, we get

18.41 =[tex]2\times \pi \times R[/tex]

Rearraning the above equation we get

R=[tex]\frac{14.41}{ 2\times \pi}[/tex]

R=[tex]\frac{18.41}{6.28}[/tex]

R= 2.93

R= 3 (approx)

Answer:

Yes, y varies directly with x.

[tex]y=\frac{11}{8} x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{11}{8} =\frac{22}{16} =\frac{33}{24}[/tex]

Hence [tex]y[/tex] varies directly with [tex]x[/tex].

[tex]\frac{y}{x}=\frac{11}{8} \\\\ y=\frac{11}{8} x[/tex]

Answer:

3/5

Step-by-step explanation:

Answer:

slope = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y + 4 = [tex]\frac{3}{5}[/tex](x - 7) ← is in point- slope form

with slope m = [tex]\frac{3}{5}[/tex]

Answer:

y = 0.7865x + 0.2413  

Step-by-step explanation:

[tex]\begin{array}{rrc}\mathbf{x} & \mathbf{y} & \mathbf{\log(y)}\\1 & 13 & 1.114\\2 & 55 & 1.740\\3 & 349 & 2.543\\4 &2407 & 3.381\\5 &16813 & 4.226\\\end{array}[/tex]

I plotted both your original and transformed data in Excel and asked it to display the regression equation for the transformed data.

Your original data are the blue line plotted against the left-hand axis.

Your transformed data are the red line, plotted against the right-hand axis.

The linear regression equation is

y = 0.7865x + 0.2413

The answer is y = 0.7865x + 0.2413  

The Linear regression equation for the transformed data:

We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.

Find the linear regression equation for the transformed data?

(1, 13) 1.114

(2, 55) 1.740

(3, 349) 2.543

(4, 2407) 3.381

(5, 16, 813) 4.226

X            Y           Log(y)

1              13           1.114

2             55         1.740

3             349       2.543

4             2407     3.381

5             16813    4.226

The linear regression equation is y = 0.7865x + 0.2413  

The graph is plotted below:

Original data are the blue line plotted against the left-hand axis and transformed data are the red line, plotted against the right-hand axis.

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Answer:

The given expression at p = 5 can be written as:

[tex]4(p^4)  > 2p -3[/tex]

Step-by-step explanation:

Here, the given expressions are:

[tex](4p^4 ), (2p-3)[/tex]

Now, substitute the value of p = 5 in both the given expressions, we get:

[tex]4(p^4)  = 4(5^4)  = 4 (625)   =  2,500\\\implies 4(p^4) = 2,500[/tex]

Similarly,

[tex](2p-3)  = 2(5) - 3 = 10 -3 = 7\\\implies 2p - 3  = 7[/tex]

So,now comparing  both the values at p = 5, we get:

2,500 > 7

[tex]\implies 4(p^4)  > 2p -3[/tex]

Hence, the given expression at p = 5 can be written as:

[tex]4(p^4)  > 2p -3[/tex]

Answer:

- 133

Step-by-step explanation:

To find the 30 th term substitute n = 30 into the formula, that is

[tex]a_{30}[/tex] = 12 - 5(30 - 1) = 12 - (5 × 29) = 12 - 145 = - 133

Final answer:

The 30th term of the sequence defined by an = 12 – 5(n – 1) is – 133.

Explanation:

To calculate the 30th term of the sequence given by an = 12 – 5(n – 1), we start by substituting the value of n with 30.

[tex]a_{30}[/tex] = 12 – 5(30 – 1)

[tex]a_{30}[/tex] = 12 – 5(29)

[tex]a_{30}[/tex]   = 12 – 145

[tex]a_{30}[/tex] = – 133

The 30th term of the sequence is – 133.

Answer:

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10

5.5-8.1=-2.6

-5-5/3=-15/3-5/3=-20/3

-8 3/8-10 1/6=-67/8-61/6=-445/24

-4.62-3.51=-8.13

Answer:

0.1513...

Step-by-step explanation:

The equation which represents the amount of minutes.m that it will take to fill the pool is 200 = 60 + 10m

Which equation represents the amount of minutes ( m) that it will take to fill the pool?

Let

m = amount of minutes that it will take to fill the pool

Gallons of water in the pool = 60 gallons

Capacity of the pool = 200 gallons

Additional gallons added per minutes = 50 gallons / 5

= 10 gallons per minutes

The equation:

200 = 60 + 10m

200 - 60 = 10m

140 = 10m

Divide both sides by 10

m = 140/10

m = 14 minutes

Therefore, it takes Anita 14 minutes to fill the pool.

Answer:

I think its 19,000/1

Step-by-step explanation:

I don't think there is any explanation :)

Answer:

Hector has spent $37.5.

Step-by-step explanation:

Given:

Total money he cashed = $50

Also Given:

Hector spent [tex]\frac{3}{4}[/tex] of his money the day after he cashed his paycheck of $50.

Let 'm' be the amount of money hector spent.

Now according to question;

amount of money hector spent is equal to [tex]\frac{3}{4}[/tex] times the amount of money he cashed his paycheck.

framing in equation form we get;

[tex]m =\frac{3}{4}\times 50 = \$37.5[/tex]

Hence hector has spent $37.5.

Answer:

The sum of the first 35 terms of the arithmetic sequence when a = 5 and d = 4 is 2555.

Step-by-step explanation:

Given:

a = 5

d =  4

To Find :

The sum of first 35 terms of the arithmetic sequence  = ?

Solution:

Step 1 : finding the 35th term

[tex]a_n = a_1 +(n-1)d[/tex]

[tex]a_35 = 5 +(35-1)4[/tex]

[tex]a_35 = 5 +(34)4[/tex]

[tex]a_35 = 5 +136[/tex]

[tex]a_35 = 141[/tex]

Step 2: Finding the sum of first 35 terms

[tex]S_n = \frac{n(a_1 +a_n)}{2}[/tex]

Substituting the values

[tex]S_n = \frac{35(5+141)}{2}[/tex]

[tex]S_n = \frac{35(146)}{2}[/tex]

[tex]S_n = \frac{35(146)}{2}[/tex]

[tex]S_n = \frac{5110)}{2}[/tex]

[tex]S_n = 2555[/tex]

Answer:

Step-by-step explanation:

[tex]-2-2(-7+b)=-8b+24\qquad\text{use the distributive property}\\\\-2+(-2)(-7)+(-2)(b)=-8b+24\\\\-2+14-2b=-8b+24\qquad\text{combine like terms}\\\\(-2+14)-2b=-8b+24\\\\12-2b=-8b+24\qquad\text{subtract 12 from both sides}\\\\12-12-2b=-8b+24-12\\\\-2b=-8b+12\qquad\text{add}\ 8b\ \text{to both sides}\\\\-2b+8b=-8b+8b+12\\\\6b=12\qquad\text{divide both sides by 6}\\\\\dfrac{6b}{6}=\dfrac{12}{6}\\\\b=2[/tex]

Answer:

45% of 31 days is 13.95 days, theres your answer.

Answer:

$16,991

Step-by-step explanation:

Rate = r = 2.5%

Times = b = 4

A = P [1 + (r / b)]ⁿᵇ

A = $15,000 [1 + (0.025 / 4]⁵ ˣ ⁴

A = $15,000 [1 + 0.00625]²⁰

A = $15,000 [1.00625]²⁰

A = $15,000 x 1.132708

A = $16,991

The midline equation for the sinusoidal function is y = 4 sin(ωx + ∅) - 3, derived by calculating the amplitude and vertical shift within the general function equation.

A function is a mathematical expression, rule, or law that defines the relationship between one variable and another. In mathematics, functions play a crucial role in representing physical relationships and various mathematical concepts. One specific type of function is the sinusoidal function, characterized by its repetitive pattern within a specific time interval.

The general form of a sinusoidal function is given by the equation:

y = A sin(ωx + ∅) + c

Here, A represents the amplitude, ω is the argument, ∅ is the phase difference, and c is the vertical shift known as the midline.

To find the equation of the midline, we use the formula:

A = (Maximum value - Minimum value) / 2

Given that the maximum value is 1 and the minimum value is -7, the amplitude (A) is calculated as:

A = (1 - (-7)) / 2 = 4

The vertical shift (c) is determined to be -3. Substituting these values into the general equation, we obtain the equation of the midline for the sinusoidal function:

y = 4 sin(ωx + ∅) - 3

In summary, the equation of the midline for the sinusoidal function is y = 4 sin(ωx + ∅) - 3.

The amplitude and vertical shift inside the general function equation are used to obtain the midline equation for the sinusoidal function, which is y = 4 sin(ωx + ∅) - 3.

A mathematical phrase, rule, or law that establishes the connection between two variables is called a function.

Functions are essential to the representation of both mathematical concepts and physical relationships in mathematics.

The sinusoidal function is one particular kind of function that is distinguished by its repeating pattern inside a predetermined time frame.

The following formula provides the generic form of a sinusoidal function:

sin(ωx + ∅) + c = A

In this case, amplitude is denoted by A, argument by ω, phase difference by ∅, and vertical shift, or midline, by c.

We utilise the to determine the midline's equation.

A is equal to (Maximum - Minimum) / 2.

A = (1 - (-7)) / 2 = 4 is the formula for calculating the amplitude (A), given that the maximum value is 1 and the minimum value is -7.

It is found that the vertical shift (c) is -3. The equation of the midline for the sinusoidal function is obtained by substituting these values into the general equation: y = 4 sin(ωx + ∅) - 3

In conclusion, y = 4 sin(ωx + ∅) - 3 is the equation of the midline for the sinusoidal function.

The initial fee of a train ticket, given a constant fee per stop, can be calculated by finding the constant fee per stop and subtracting the total of this fee for a given number of stops from the total price for those stops. By this calculation, the initial fee is $2.50.

To determine the initial fee that is related to the price of a train ticket, which consists of an initial fee plus a constant fee per stop, we should first calculate the cost per stop. We can do this by subtracting the price of a ticket for 3 stops from the price of a ticket for 7 stops. So, we get $12.50 - $6.50 = $6.00. We find the difference in the number of stops, which is 7 - 3 = 4 stops. Divide the total price difference by the difference in the number of stops to get the constant fee per each stop: $6.00 / 4 stops = $1.50 per stop. Now we know the constant fee for each stop, so we subtract that from the total price for 3 stops to find the initial fee: $6.50 - ($1.50 * 3) = $2.50. So, the initial fee is $2.50.

To find the initial fee, we need to determine the additional cost per stop. We can do this by using the formula y = mx + b, where y represents the price of the ticket, x represents the number of stops, m represents the constant fee per stop, and b represents the initial fee.

Using the given data, we can set up two equations using the points (3, 6.50) and (7, 12.50).

By subtracting these two equations, we can determine the value of b, which represents the initial fee. Thus, the initial fee is $3.

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The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Assume you drink eight sodas per week & they cost $1.59 each.

We know that there are 52 weeks in a year.

The money can you accumulate over the course of a year if you opt to save the money instead will be

⇒ $1.59 × 52

⇒ $82.68

The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.

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One roll of plain costs $20 and one roll of shiny costs $20 also.

Step-by-step explanation:

Let,

Cost of one roll of plain = x

Cost of one roll of shiny = y

According to given statement;

2x+2y=80     Eqn 1

8x+10y=360    Eqn 2

Multiplying Eqn 1 by 4

[tex]4(2x+2y=80)\\8x+8y=320\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](8x+10y)-(8x+8y)=360-320\\8x+10y-8x-8y=40\\2y=40[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{40}{2}\\y=20[/tex]

Putting y=20 in Eqn 1

[tex]2x+2(20)=80\\2x+40=80\\2x=80-40\\2x=40[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{40}{2}\\x=20[/tex]

One roll of plain costs $20 and one roll of shiny costs $20 also.

Keywords: linear equation, elimination method

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Answer:

10 go into 450 45 times

Step-by-step explanation:

Answer:

k=3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem we have

[tex]y=3x[/tex]

therefore

The constant of proportionality  is k=3

Answer:

k=3

Step-by-step explanation:

i went on knan and it worked

Answer:

The graph of y = f(x) will shift left 6 units, as shown in figure a.

Step-by-step explanation:

A translation means we are able to move the graph of a function up or down - normally called Vertical Translation -  and right or left - commonly called Horizontal Translation.

If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the  x, so it is f(x + 6).

For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.

So, the graph of y = f(x) will shift left 6 units.

Keywords: graph shift, translation

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The graph of y = f(x) will shift left 6 units. The correct option is the third one.

For any function y = f(x), we define an horizontal translation of N units as:

y = f(x + N)

Where if:

N > 0, the translation is to the left.

N < 0, the translation is to the right.

Here we have:

y = f(x + 6)

So this is a translation of 6 units to the left.

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Answer: -50

Step-by-step explanation: A withdrawal means that you're decreasing the amount of money you have.

So a withdrawal of $50 can be written as -50.

Answer:

see explanation

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

(A)

To find k use the given condition y = 2 when x = 10

k = yx = 2 × 10 = 20, thus

y = [tex]\frac{20}{x}[/tex] ← equation of variation

(B)

When x = 4, then

y = [tex]\frac{20}{4}[/tex] = 5

Answer:

D.3

Step-by-step explanation: The full line is equivelent to 3 if you look

To compare the two plans and find the amount of driving for which they cost the same, we can set up an equation and solve for x. The two plans cost the same for 450 miles of driving.

To compare the two plans and find the amount of driving for which they cost the same, we need to set up an equation. Let's assume the amount of driving is represented by the variable x. The total cost for Plan 1 can be calculated as:

Total cost = $46 + $0.13x

The total cost for Plan 2 can be calculated as:

Total cost = $55 + $0.11x

We can set the two equations equal to each other and solve for x:

$46 + $0.13x = $55 + $0.11x

$0.02x = $9

x = $9 / $0.02 = 450

Therefore, the two plans cost the same for 450 miles of driving.

Answer:

Step-by-step explanation:

8) a) No: of sides of a regular polygon = 360° / exterior angle

                                                                = 360°/18° = 20 sides

b) Sum of interior angles of regular polygon = (n-2) * 180°   {n-no:of sides}

                   = (20-2)*180° = 18*180° = 32400°

9) Let the exterior angle be x.

So, interior angle = 140° + x

Interior angle + exterior angle  = 180°

140° +x + x = 180°

140° +2x = 180°

2x = 180° - 140°

2x =40°

x = 40°/2 = 20°

Exterior angle = 20°

Interior angle  = 160°

No: of sides of a regular polygon = 360° / exterior angle

                                                                = 360°/20° = 18 sides

Hint: Always sum of exterior angles of regular polygon is 360°

Should be 5812.95 Students