20 POINTS PLZ HELP
Jack is doing an experiment to find the rate of water flow from a tap. He collects the water in a tub and records the height of the water level every five minutes. He then plots the data on a scatter plot. Which equation represents the line of best fit for Jack’s scatter plot?

A. y=14/45x
B. y=45x+15
C. y=45/14x
D. y=14x+45

Answer:

The numbers are 49 and 55

Step-by-step explanation:

The sum of two numbers 104

x+y = 104

their difference 6

x-y = 6

Add the two equations together to eliminate y

x+y = 104

x-y = 6

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

2x = 110

Divide by 2

2x/2 =110/2

x = 55

x+y = 104

55+y =104

Subtract 55 from each side

55-55+y = 104-55

y =49

Final answer:

To find the two numbers that add up to 104 and have a difference of 6, we solve a system of equations and discover that the numbers are 55 and 49.

Explanation:

The question asks us to find two numbers whose sum is 104 and whose difference is 6. To find the numbers, we can set up a system of equations. Let the two numbers be x and y.

x + y = 104 (sum of the numbers)

x - y = 6 (difference of the numbers)

We solve these equations simultaneously. Adding both equations, we get:

2x = 110

x = 55

Substitute x = 55 in the first equation to find y:

55 + y = 104

y = 104 - 55

y = 49

So, the two numbers are 55 and 49.

Answer:

823.7 m²

Step-by-step explanation:

Given the ratio of sides = 5 : 6, then

the ratio of area = 5² : 6² = 25 : 36

let x be the area of the larger prism then by proportion

[tex]\frac{25}{572}[/tex] = [tex]\frac{36}{x}[/tex] ( cross- multiply )

25x = 36 × 572 ( divide both sides by 25 )

x = [tex]\frac{36(572)}{25}[/tex] ≈ 823.7

The surface area of the larger prism is 823.7 ( nearest tenth )

Answer: 823.7

Step-by-step explanation: (5/6)^2, cross multiply with 572/SA, 572*36/25 = 823.68, rounded to the nearest tenth is 823.7

As we can see on the picture we have a rectangle and half of circle.

The areas for half circle and rectangle are:

[tex]

A_{rectangle}=a\cdot b \\

A_{halfcircle}=\frac{A_{circle}}{2}=\frac{\pi r^2}{2}

[/tex]

The area of the figure is the sum of the area of half circle and rectangle. Also the height of a rectangle (6ft) is a diameter of a half circle therefore the radius of half circle is 6ft ÷ 2 = 3ft.

Now we calculate the areas.

[tex]

A_{rectangle}=10\cdot 6=\underline{60} \\

A_{halfcircle}=\frac{3.14\cdot3^2}{2}=\underline{14.13} \\

A_{total}=A_{rectangle}+A_{halfcircle} =60+14.13=\boxed{74.13\approx74}

[/tex]

The area of the figure is approximately 74ft squared.

Hope this helps.

r3t40

Answer:

B

Step-by-step explanation:

2. First you need to know about the pythagorean theorem which is

a^2 + b^2 = c^2. Look at the first picture below for more reference.

Next you use the pythagorean theorem to find out the right triangle sides to then know the length and width of the rectangle.

a = 8

b = unknown

c = 10

Now use algebraic steps. 8^2 + b^2 = 10^2 --) 64 + b^2 = 100 --) b^2 = 36 --)

b = 6 .

Finally you know the length which is 8 + 8 = 16 and the width which is 6, so the area of the rectangle is 16 x 6 = 96. And to look apporpriate 96in.^2 .

Answer:

y = -1/2x +2

Step-by-step explanation:

The linear and quadratic function rules we usually study in algebra come in several forms.

For linear function rules (equations of a line), there are more than half a dozen different forms, each with its own use. A few that often come in handy are the 2-point form, the slope-intercept form, the point-slope form, and the intercept form. Here, the 2-point form can be useful, since you have several points on the line to choose from.

The 2-point form of the equation of a line is ...

y = (y2 -y1)/(x2 -x1)·(x -x1) + y1

point (x1, y1) and point (x2, y2) can be any pair of the given points, in any order. Let's use the first two for points 1 and 2.

y = (0 -1)/(4 -2)·(x -2) +1

y = -1/2(x -2) +1 . . . . . . . . this is a suitable function rule. In this simplified form, it is in point-slope form, where -1/2 is the slope and (2, 1) is the point.

If you want to simplify this a bit, you can put it into slope-intercept form by eliminating the parentheses and combining the constant terms:

y = -1/2x +2

Answer:

notice that every time x increases by 2, y decreases by 1. So, a first guess would be

y = -1/2 x

But, -1/2 (2) = -1, and y(2) = 1, so we need to add 2 at the start. So,

y = 2 - 1/2 x

Answer:

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

Answer:  b

Step-by-step explanation:

15% of the $96.6 clothes only is $14.49

in order to get over 100 dollars kelly would have to purchase 5 packages of gum

5 times .79 = $3.95

With the gum the total would be $100.55 divided by 20% = $20.11

$20.11 - $14.49 = $5.62  however you need to subtract the price of the gum also

$5.62 - $3.95 = $1.67

B....

Its right trust!

Answer:

8 ft and 14 ft

Step-by-step explanation:

Let one diagonal be x then the other diagonal is 2x - 2

The area (A) of the rhombus is calculated using

A = [tex]\frac{1}{2}[/tex] product of the diagonals, that is

A = [tex]\frac{1}{2}[/tex] x(2x - 2) = 56

Multiply both sides by 2

x(2x - 2) = 112 ← distribute left side

2x² - 2x = 112 ( subtract 112 from both sides )

2x² - 2x - 112 = 0 ← in standard form ( divide through by 2 )

x² - x - 56 = 0

To factor the quadratic

Consider the factors of the constant term (- 56) which sum to give the coefficient of the x- term (- 1)

The factors are - 8 and + 7, since

- 8 × 7 = - 56 and - 8 + 7 = - 1, thus

(x - 8)(x + 7) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 7 = 0 ⇒ x = - 7

However, x > 0 ⇒ x = 8

One diagonal = 8 ft and the other = 2x - 2 = (2 × 8) - 2 = 16 - 2 = 14 ft

Answer:

(5,6)

Step-by-step explanation:

First, count how many units are between b and c, that is 10, half of that is 5 units because they want the mid point so we divided by 2 but now you are going to count 5 units from point b so the y value isn't isn't 5. So from b, count 5 units upwards which lands at 6 so that is the y value. Now you move from their to the right to touch the line (if you understand what i mean) and that would fall at the value of 5. so x is equal 5. Coordinate: (x,y)=(5,6). Hopefully that helped.

The midpoint of the line BC is (5,6).

The midpoint of a line segment is the point equidistant from its endpoints. It is calculated as the average of the x-coordinates and y-coordinates of the endpoints.

Midpoints are crucial in geometry for construction, line segment division, and coordinate geometry. They play roles in physics, engineering, and bisection problems, contributing to spatial reasoning and problem-solving.

The midpoint M of a line segment with endpoints B(x₁, y₁) and C(x₂, y₂) is calculated as:

M = (x₁ + x₂)/2, (y₁ + y₂)/2.

So, for points B(2, 1) and C(8, 11) the midpoint is:

M(2 + 8)2, (1 + 11)/2

= 10/2, 12/2

= (5, 6).

The midpoint of the line BC is (5,6).

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Answer is B. -4,-2,1,3

A quadratic function is graphically represented by a parabola with a vertex located at the origin, below the x-axis, or above the x-axis. .

The points at which the graph crosses or touches the x-axis, give the real roots of the function(or zeros of the function) represented by the graph.

If the graph touches the x-axis and turns back, then it would be a double root at that point. Roots are also called x-intercepts or zeros.

The roots of the graph are Option B -4, -2, 1, and 3.

The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1. y = x^2.

The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠0)

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Answer:

54 minutes

Step-by-step explanation:

We can write a proportion to solve this problem.  Put the number of pages over the minutes

27 pages           324 pages

--------------    = ---------------

4.5 minutes         x minutes

Using cross products

27 * x = 324 * 4.5

27x = 1458

Divide each side by 27

27x/27 = 1458/27

x =54

Answer:

113 beats per minute.

Step-by-step explanation:

904 / 8 = 113

The pulse rate in Salvador is 113 beats per minute.

calculation:

    ⇒number pf heartbeat count = 904

    ⇒time of count= 8 minutes

    ⇒pulse rate= 904/8

                  =113 beats per minute.

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Answer:

y = -x + 4

Step-by-step explanation:

Step 1: Use the subtraction property of equality

6y = -6x + 24

Step 2: Use the division property of equality

y = -x + 4

Answer:

y = -x +4

Step-by-step explanation:

6x+6y= 24

Subtract 6x from each side

6x-6x+6y=-6x+ 24

6y = -6x+24

Divide by 6 on each side

6y/6 = -6x/6 +24/6

y = -x +4

Answer:

2nd statement is true

Step-by-step explanation:

Please use " ^ " to denote exponentation:   f(x) = 4x^2 + 20x + 25.

Take a look at the second statement.  If you'll substitute -2.5 for x, to find f(-2.5), you'll find that the result is 0;  Thus, this second statement is true.

Answer:

The graph touches the x-axis at (–2.5, 0).

Step-by-step explanation:

Given  : f(x) = 4x² + 20x + 25.

To find : Which statement describes the graph .

Solution : We have given

f(x) = 4x² + 20x + 25.

On factoring

4x² + 10x + 10x+ 25 = 0

On taking  common 2x from first two terms and 5 from last two terms.

2x ( 2x + 5 ) +5 (2x + 5 ) = 0

On grouping

(2x +5) (2x +5)  = 0

For 2x +5 = 0

On subtracting 5 both side

2x = -5

On dividing by 2

x = [tex]\frac{-5}{2}[/tex] = - 2.5

x = - 2.5 .

Points (-2.5 , 0)

Therefore, The graph touches the x-axis at (–2.5, 0).

Answer:

The graph is included in the attached pictures

Step-by-step explanation:

The graph for y=4-|x| is shown in the attached picture, the inequality tell us that the region is located below that particular graph including the function, hence you have the second attached picture

Answer:

k=6

Step-by-step explanation:

We are given a graph of the function f(x) and g(x) such that both the graphs are parabola and the graph of g(x) is a shift of graph of f(x) some units to the left.

The vertex of the graph of f(x) is at x=4

whereas the vertex of the graph of the function g(x) is at x= -2.

This means that the graph of g(x) is a shift of the graph of f(x) 6 units to the left.

This means that:

g(x)=f(x+6)

( Since the translation of a function f(x) k units either to the left or to the right is denoted by:

f(x+k)

when k>0 the shift is to the left and if k<0 the shift is to the right.)

This means that the value of k is 6

[tex]

f(x)=x^3-2x^2 \\

f(i)=i^3-2i^2=\boxed{-i+2}

[/tex]

Hope this helps.

r3t40

Answer:

In a part-to-whole ratio, one ratio compares a part to a whole.

In mathematics, a fraction is an example of a ratio that compares a part to a whole. Understanding this is crucial for analyzing parts and how they conform to the whole. Another practical illustration of this concept is through a pie graph, which represents the whole and its parts.

In a fraction, one ratio compares a part to a whole. This goes along with a concept in Mathematics where it's useful to take into consideration the parts that contribute to the totality of a whole. An example of this can be seen in numbers. If we look at the relationship between a part and a whole in a ratio, for example, the mass ratio of copper and chlorine in a certain compound, we can gain significant insights.

Another approach is to use a pie graph, which is a graphical representation showing how a whole is divided into parts. The whole circle showcases the entire group, while each slice or part shows the relative size or percentage it contributes to the whole. This visualization makes it easy to understand the relationship between parts and the whole.

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The equations that have the same solution set are equations 1, 3, 5, and 6.

To determine which equations have the same solution set without solving them, we can analyze the equations and identify any properties that indicate equivalent solutions. Let's examine each equation:

1. WIN + 1 = 6x

2. 4 - 6x + 1 = 3

3. 6x - x = 6x

4. 4 - x + 1 = 6x

5. x = 6x

6. 5 = 30x

7. 5 = 42x

Equations with the same solution set:

- Equations 1 and 3 both have the term "6x" on one side and a different expression on the other side. They indicate that the solution for x is the same.

- Equations 5 and 6 both have the same equation "x = 6x", which implies the solution for x is the same.

Therefore, the equations that have the same solution set are equations 1, 3, 5, and 6.

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Answer:

The correct answers are

Step-by-step explanation:

1 2 6

Answer:

b=3:25 and b:c=105 3:25/105

Step-by-step explanation:

{3}{25}}{105}={1}{875}=0.00114

{3}{25.105}

{3}{2625}

=1/875

Hope this helps

so parallel is just numbers with the same slope but different x value

and perdicular is the One with different signs and oppisite reciprocals

a) perpendicular because -2 is the oppisite sign and reciprocal of 1/2

b)neither

c) niether

and B)

a) 3x-2

b)y=5/2 +4

i think

Answer:

A. Being above 180 centimeters and having black hair are independent of each other.

Step-by-step explanation:

These are instinctively two characteristics that are not related and the table data proves it.

If they were dependent, you would have only people with black hair above 180 cm, and all people with black hair would be above 180 cm.

You can be above 180 cm and have black, brown or blonde hair. The table shows a proportion of people > 180 cm about equal (around 30% of the sampling) for each hair color.

And people above 180 cm only represent 30% of the people with black hair.

Option: A is the correct answer.

     A. Being above 180 centimeters and having black hair are independent of each other.

Height :         Less than  175 cm  175-180 cm Above 180 cm     Total

Hair  Color

   Black                    38                        32                  30               100

  Brown                    27                        24                  19                70

  Blonde                    21                        33                  26                80

  Total                    86                89                  75                250

Two events A and B are said to be independent if:

     [tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

else they are dependent.

A)

Being above 180 centimeters and having black hair are independent of each other.

Let A denote Black hair

and B denote above 180 cm.

[tex]P(A)=\dfrac{100}{250}=\dfrac{10}{25}[/tex]

and [tex]P(B)=\dfrac{75}{250}=\dfrac{3}{10}[/tex]

This means that:

 [tex]P(A)\times P(B)=\dfrac{10}{25}\times \dfrac{3}{10}=\dfrac{3}{25}[/tex]

Also,

[tex]P(A\bigcap B)=\dfrac{30}{250}=\dfrac{3}{25}[/tex]

Since,

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

Hence, events A and events B are independent.

        Hence, option: A is correct.

90% out of 105% which would be 0.85

Answer: 0.85

Step-by-step explanation:

Let A be the event that the customer orders a pizza and B be the event that the customer orders a salad.

Then , we have [tex]P(A)=80\%=0.80[/tex]

[tex]P(B)=15\%=0.15[/tex]

[tex]P(A\cap B)=10\%=0.10[/tex]

Now, the probability that he or she  orders either a pizza or a salad is given by :-

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow\ P(A\cup B)=0.80+0.15-0.10=0.85[/tex]

Hence, the required probability = 0.85

Answer:

q

Step-by-step explanation:

The equation of a line in the form

y = mx ( m is the slope ) passes through the origin

y = 2x is in this form

The only graph to pass through the origin is q

Answer:

1/6 (1 gallon of orange juice for every 6 gallons of apple juice)

Step-by-step explanation:

4/24=24/4x1/36

This is because you reverse the division (or fraction) into a easier to solve equation, and the 1/36 is there to balance out that change.

[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}-sin(\theta ) \right)~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&3\\ \theta =&\stackrel{radians}{\frac{2\pi }{3}}\\ &\stackrel{degrees}{120} \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left(\cfrac{\pi (120) }{180}-sin(120^o) \right)\implies A=\cfrac{9}{2}\left(\cfrac{2\pi }{3}-\cfrac{\sqrt{3}}{2} \right) \\\\\\ A \approx \cfrac{9}{2}(1.23)\implies A\approx 5.535[/tex]

The constant p is determined by the half-life of 1600 years, and since after one half-life, the amount of the element is half of its initial value, we find that x=1/2 and y=1/1600, as e^p can be expressed as (1/2)^(1/1600). Therefore, option (a) is the correct answer.

The equation Q(t) = Q(0)e^pt describes an exponential decay process, such as the decay of a chemical element over time. Given that the half-life of the chemical element is 1600 years, after this period the quantity of the element will be half of its original amount. According to the properties of exponential decay, we know that after one half-life, Q(t) = Q(0)/2.

Substituting t = 1600 into the equation and knowing that Q(1600) = Q(0)/2, we get Q(0)/2 = Q(0)e^(1600p). Simplify by dividing both sides by Q(0), resulting in 1/2 = e^(1600p). To find p, take the natural logarithm of both sides, yielding ln(1/2) = 1600p ln(e), and since ln(e) = 1, we have p = ln(1/2)/1600.

Now, to express e^p as x^y, with both x and y being rational numbers, we look for a rational base x that can represent e^ln(1/2), which simplifies to (1/2). So, x would be 1/2, and because the half-life is 1600 years, y will be proportional to the fraction of that time. Hence, y = t/1600, where t is time in years. From this, you can infer that the base x equals 1/2 and y is 1/1600 for each year surpassing the half-life. Therefore, the correct answer is (a) x = sqrt(1/2), y = 1/1600.

Answer:

D

Step-by-step explanation:

Answer:

D.-$21

Step-by-step explanation:

Answer:

Common difference = 5.

Step-by-step explanation:

General term of an arithmetic sequence is a1 + (n - 1)d where a1 = first term and d = common difference.

So here the first term is  8 + (1-1)d = 8 and the 10th term = 8 + (10-1)d = 53

giving 8 + 9d = 53

9d = 45

d = 5.

To calculate the common difference in an arithmetic sequence, subtract the first term from the tenth term and divide by 9 (the number of terms subtracted by one). In this case, (53-8)/9 gives the common difference as 5.

The student's question regards finding the common difference in an arithmetic sequence. In an arithmetic sequence, the difference between any two consecutive terms is constant. This is called the 'common difference'.

To find the common difference, you subtract the first term from the tenth term and divide by the number of terms subtracted by one. In this case, the tenth term is 53 and the first term is 8. So, you subtract 8 from 53, giving you 45. Then you divide 45 by (10-1), which is 9, giving a common difference of 5. Therefore, the common difference for this arithmetic sequence is 5.

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The answer is:

The correct option is the second option:

[tex]\frac{5}{2},\frac{-1}{2}[/tex]

We are given the following expression:

[tex]\frac{2+-\sqrt{9}}{2}[/tex]

Now, solving we have:

First solution:

[tex]\frac{2+\sqrt{9}}{2}=\frac{2+3}{3}=\frac{5}{2}[/tex]

Second solution:

[tex]\frac{2-\sqrt{9}}{2}=\frac{2-3}{3}=\frac{-1}{2}[/tex]

Hence, we have that the correct option is the second option:

[tex]\frac{5}{2},\frac{-1}{2}[/tex]

Have a nice day!

Answer:

The correct answer is second option

5/2, -1/2

Step-by-step explanation:

From the attached figure we can see that,

(2 ± √9 )/2

To find the simplified form of (2 ± √9 )/2

(2 ± √9 )/2 = (2 + √9 )/2 or (2 - √9 )/2

(2 + √9 )/2 = (2 + 3)/2 = 5/2

(2 - √9 )/2 =  (2 - 3)/2 = -1/2

Therefore simplified form of (2 ± √9 )/2 are

5/2 and -1/2

The correct answer is option 2