Amy is 9 years older than her younger sister. if her younger sister is now 1 year old, how many years later will Amy be 4 times as old as her younger sister?​

Answer:

First Part;

As the temperature in the city increases, the number of cups of hot chocolate sold decreases

Second Part;

The approximate value of the slope in number of cups sold per change in temperature is -0.12222

The approximate value of the y-intercept is 20.944 degrees temperature

Step-by-step explanation:

Question;

First Part

What is the relationship between temperature in the city and the number of cups of hot chocolate sold, using your own words

Second Part

How can the line of best fit be made. Give the approximate values of the slope and the y-intercept of the line of best fit

Explanation

The data points are presented in the following table;

[tex]\begin{array}{lcl}x&&y\\20&&20\\30&&18\\40&&20\\35&&15\\50&&20\\45&&20\\60&&14\\65&&18\\80&&10\\70&&8\\40&&2\end{array}[/tex]

A scatter plot is formed from the given data using MS Excel

First part;

From the values of the number of cups sold, y, and the temperature at which they are sold, x, there is correlation between the x and y values, such that as the temperature increases, the number of cups sold decreases, the becomes more rapid as the temperature increases past 50, such that the reason for taking the hot chocolate decreases with increasing temperature

Second Part;

The line of best fit can be found using the least squares regression formula to draw a straight line from the regression equation as follows;

y = a + b·x

[tex]b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }[/tex]

a = [tex]\bar y[/tex] - b·[tex]\bar x[/tex]

Where;

b = The slope

a = The y-intercept

From MS Excel, we have;

[tex]\bar y[/tex] = 15, [tex]\bar x[/tex] = 48.63636

[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) = -410[/tex]

[tex]\sum \left(x_i - \bar x\right )^2 = 3354.545[/tex]

Therefore;

[tex]b = \dfrac{-410}{3354.545} = -0.12222[/tex]

The approximate value of the slope, b = -0.12222 (number of cups sold per unit change in temperature)

a = 15 - (-0.12222)×48.63636 ≈ 20.944

The approximate value of the y-intercept, a = 20.944 (in degrees of temperature).

Answer:

10xsquared - 3x -18

Step-by-step explanation:

just multiply out and combine like terms

10xsqaured +12x -15x -18

= 10xsquared -3x -18

Answer:

find the coordinates and then do subtract the first one, for example for line segment AB, do (1,6) and  (5,1)

(1,6) (5,1)

1-6 = -5

5-1 = 4

answer is -5/4 and that is the slope of the line.

Continue with the rest please like how i did the example

Answer:

140 km

Step-by-step explanation:

according to scale on a map

1 m = 20 km

7 m = ?

7m = 20*7 km

=140 km

Answer:

Here are the step require to divide complex numbers:

Step 1:To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.Step 2:Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.Step 3:Simplify the powers of i, specifically remember that i2 = –1.Step 4:Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.Step 5:Write you answer in the form a + bi.Step 6:Reduce your answer if you can.

Example 1 – Divide: 

Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.



Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.



Step 3: Simplify the powers of i, specifically remember that i2 = –1.



Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.



Step 5: Write you answer in the form a + bi.



Step 6: Reduce your answer if you can. In this case you can’t reduce, so the final answer is:



  Example 2 – Divide: 

Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.



Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.



Step 3: Simplify the powers of i, specifically remember that i2 = –1.



Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.



Step 5: Write you answer in the form a + bi.



Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:



Click Here for Practice Problems

Example 3 - Divide: 

Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.



Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.



Step 3: Simplify the powers of i, specifically remember that i2 = –1.



Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.



Step 5: Write you answer in the form a + bi.



Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:



Click Here for Practice Problems

Example 4 - Divide: 

Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.



Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.



Step 3: Simplify the powers of i, specifically remember that i2 = –1.



Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.



Step 5: Write you answer in the form a + bi.



Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:



Answer:

y = 1/4x

Step-by-step explanation:

y = amount of cubic feet = 15 cubic feet

x = time taken = 60 seconds

y = kx

Where,

k = constant of proportionality

y = kx

15 = k * 60

k = 15/60

k = 1/4

The equation

y = kx

Where

k = 1/4

Becomes,

y = 1/4x

Answer:

The picture is the answer

Step-by-step explanation:

Answer:

The unit I would place in the denominator of my ratio is minutes

Step-by-step explanation:

1 hour = 60 minutes

Converting 14 hours to minutes

= 14 hours/ x minutes = 1 hour /60 minutes

x minutes = 14 × 60 minutes

= 840 minutes

14 hours = 840 minutes

Therefore,

The unit I would place in the denominator of my ratio is minutes

Answer:

$88

Step-by-step explanation:

Randip's balance = initial deposit + sum of deposits - sum of withdrawals

sum of deposits = $34 + $15 = $49

sum of withdrawals =  $17 + $30 = $47

$86 + $49 - $47 = $88

Answer:

88

Step-by-step explanation:

Answer:

To find the value of x we need to simplify this.

The steps to simplifying are simple.

We need to take away, add and do a lot to a bunch of stuff, until we receive our answer.

___________________________

Let's continue.

___________________________

Alright, let's go ahead and show our steps.

[tex]\mathrm{Multiply\:both\:sides\:by\:}3x-32[/tex]

[tex]\frac{2}{3x-32}\left(3x-32\right)=35\left(3x-32\right)[/tex]

_____________________

[tex]Simplify = \\2=35\left(3x-32\right)[/tex]

_____________________

[tex]\mathrm{Switch\:sides}\\35\left(3x-32\right)=2[/tex]

_____________________

[tex]\mathrm{Divide\:both\:sides\:by\:}35\\\frac{35\left(3x-32\right)}{35}=\frac{2}{35}[/tex]

_____________________

[tex]\mathrm{Simplify}\\3x-32=\frac{2}{35}[/tex]

_____________________

[tex]\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{\frac{1122}{35}}{3}[/tex]

_____________________

[tex]Simplify = \\x=\frac{374}{35}[/tex]

_____________________

Therefore, the answer is x = 374/35

Answer:

sinB = [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{12}{13}[/tex]

The Trigonometric ratios is 12/13

The branch of mathematics concerned with specific functions of angles and their application to calculations.

We have,

H= 13, B= 5 and P=12

So,

sin B= Perpendicular/ Hypotenuse

        = 12/13

hence, sin B=  12/13

Learn more about trigonometry here:

https://brainly.com/question/14746686

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Answer:

square root of 5 - 4

Step-by-step explanation:

Answer:

square root of 5 +4

Answer:

x ≈ 27.2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 54°

Opposite Leg = 22

Hypotenuse = x

Step 2: Solve for x

Answer:

less than is the correct answer

Answer:

the actual area of the room is 35 inches

Step-by-step explanation:

you have to multiply 7 by 5.

Answer:

713 puercos

Step-by-step explanation:

Sea T el número total de puercos

Número de cerdos = 57

Porcentaje = 8%

Para encontrar el número total de puercos;

Porcentaje = 8/100 * T = 57

8T/100 = 57

8T = 5700

T = 5700/8

T = 712,5 ≈ 713 puercos

Por lo tanto, el granjero tiene 713 puercos en total.

Answer:

85%

Step-by-step explanation:

First, let's add up the ratios and use it to divide 120. That way we can find out how many people each ratio is.

17 +3 = 20

120/20 = 6

Each individual ratio is equal to 6.

17 * 6 = 102

3 * 6 = 18

102/120 = percentage of who passed

= 0.85

85 percent of learners passed.

3p²q - 6 pq²

3pq (p - 2q )

I think this is the solution

Answer:

62.8 mm

Step-by-step explanation:

pie = 3.14

radius = 10 mm

circumference of a circle = 2πr

=2*3.14*10

=62.8 mm

Answer: I cant see the problem

Step-by-step explanation:

Answer:

Where is the question?

Step-by-step explanation:

Answer:

The family of lines that are parallel to [tex]2\cdot x + y = 6[/tex] is of the form [tex]2\cdot x + y = k, \,k\neq 6[/tex]. A possible solution is [tex]2\cdot x + y = -2[/tex].

Step-by-step explanation:

Let be [tex]2\cdot x + y = 6[/tex] the equation of a line, another line is parallel to it if and only if it is of the form:

[tex]2\cdot x + y = k, \,k\neq 6[/tex]  (1)

Then, a possible solution is [tex]2\cdot x + y = -2[/tex].

Answer:

1/2

Step-by-step explanation:

There are two possible outcomes when flipping a coin

heads or tails

P( tails) = number of favorable outcomes / total outcomes

            = 1/2

Answer:

p is tails and its saying you flip a fair coin, meaning you have a 50 50 chance which means you have a 50% chance of getting heads and same with tails.

Step-by-step explanation:

therefore, p is 0.5

have a great day!!

Answer:

The numbers are 3 and 5

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

3^2=9

5^2=25

25+9=34

3*5=15

Answer:

64

Step-by-step explanation:

(a+b)²= a²+b²+2ab = 34+(2×15)= 64

Answer:

2nd one : y = -4/x

3rd one : y + x/2 = 9

4th one

5th one : y = x^2

6th : 5.8x - y = 2.3

Step-by-step explanation:

Not sure about these. You might want to wait for another person to answer

Have a nice day!

Answer:

[tex]{ \tt{circumference \approx\pi \: d}} \\ \approx{ \tt{3.14 \times 15}} \\ \\ \approx47.124 \: inches[/tex]

Answer:

The answer is DE

Step-by-step explanation:

I learned about it in school.

The radius of a circle with center O is DO. Therefore, option B is the correct answer.

Given that, a circle, with center O, represents a radius of the circle.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

Here, DO and OC is the radius of a circle with center O.

The radius of a circle with center O is DO. Therefore, option B is the correct answer.

To learn more about the circle visit:

https://brainly.com/question/11833983.

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Explanation:

We replace x with 3 and use PEMDAS to evaluate

8*x+23

8*3+23

24+23

47

Answer:

[tex]47[/tex]

Step-by-step explanation:

[tex]8x + 23[/tex]

[tex]8(3) + 23[/tex]

[tex]24 + 23[/tex]

[tex]47[/tex]