Compare and contrast interpolations and extrapolations based on a scatterplot

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y=-\cfrac{3}{4}x+6[/tex]

Answer:

0.16

Step-by-step explanation:

81 is 1 standard deviation below the mean.  According to the empirical rule, 68% of data lies within 1 standard deviation of the mean; here the equivalent statement would be that half of that, or 34%, lies within 1 standard deviation below the mean.  Half of the area under the standard normal curve, less this 0.34, is the probability that the random variable is below 1 standard deviation beneath the mean.  That comes to 0.16.

On a calculator, you might enter the command normalcdf(-100,81,85,4); on my old TI-83 Plus I get 0.1587, which rounds off to 0.16.

Final answer:

The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.

Explanation:

To find the probability that a normally distributed random variable x is less than 81, P(x < 81), when the mean μ is 85 and the standard deviation σ is 4, we need to use the properties of the normal distribution.

First, we convert the raw score of 81 into a z-score. The formula for calculating a z-score is:

[tex]z = (x - μ) / σ[/tex]

For x = 81, the z-score would be:

z = (81 - 85) / 4

z = -1

Next, we use a standard normal distribution table, a calculator, or software to find the probability that correlates with this z-score. The table lists probabilities to the left of z-scores.

The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.

Answer:

14.4 in

Step-by-step explanation:

2160/ 150= 14.4

Answer:

D

Step-by-step explanation:

7(1–k)

= 1(7) -k(7)  -------------> distributive property

= 7–7k

                              108

                              /     \

                            12     9

                           /  \      /  \

                         4   3    3   3

                        / \

                      2   2

             2y                     5

             / \                     /  \

           2   y                 1    5

<Hope this helps!>

Step-by-step explanation:

all work is pictured and shown

Answer:

x = [tex]\frac{C-By}{A}[/tex]

Step-by-step explanation:

Given

Ax + By = C ( isolate the term in x by subtracting By from both sides )

Ax = C - By ( divide both sides by A )

x = [tex]\frac{C-By}{A}[/tex]

Answer:

Step-by-step explanation:

Solve Ax+By=C for x.:

Ax= - By+C

case 1 : A≠0       x = (- B/A)y+C/A

case 2 : A=0

you have : 0x = - By+C

B=0 :  ox = C     C = 0  infinity of x      C≠0  no solutions

Answer:

It is an identity, the proof is in the explanation

Step-by-step explanation:

csc(A)-cot(A)=tan(A/2)

I'm going to start with right hand side

tan(A/2)=(1-cos(a))/(sin(a))                half angle identity

tan(A/2)=1/sin(a)-cos(a)/sin(a)         separate fraction

tan(A/2)=csc(a)-cot(a)                     reciprocal and quotient identities

Answer:

Undefined

Step-by-step explanation:

You can deduce the solution in two ways: if the slope of m is zero, it is horizontal. So, n is vertical because it must be perpendicular to n. Vertical lines have undefined slope.

Alternatively, if the slope of line m is k, the slope of a perpendicular line n is -1/k. So, if k=0, you can't compute -1/0.

Answer:

it is :119.5714

Step-by-step explanation:

15 3/14+24 1/14+12 2/7+12 2/7+10 1/7+10 1/7+35 3/7=

step by step now:

15 3/14+24 1/14+12 4/14+12 4/14+10 2/14+10 2/14+35 6/14=118 22/14=118+1.5714=119.5714

Final answer:

The sum of the given mixed numbers is 119 and 2/7 after adding the whole numbers separately and then the fractions.

Explanation:

To calculate the sum of the given numbers, we start by adding the whole numbers and the fractions separately. All the fractions have a common denominator, which simplifies the process. Let's proceed with the calculation:

Adding the whole numbers: 15 + 24 + 12 + 12 + 10 + 10 + 35 = 118.

Adding the fractions: 3/14 + 1/14 = 4/14, simplifies to 2/7 because 4/14 is dividable by 2. Then, we add 2/7 + 2/7 + 1/7 + 1/7 + 3/7 = 9/7. But 9/7 is more than 1, so we rewrite 9/7 as 1 whole and 2/7.

Now let's combine the sums of whole numbers and fractions: 118 + 1 = 119.

Thus, the total sum is 119 and 2/7.

Answer:

13 = m

Step-by-step explanation:

I do not know what that nine is doing there, but you just simply evaluate to arrive at your answer.

Answer: 1 day, 21 hours, and 40 minutes

Step-by-step explanation: To make it less confusing, you can convert all of the days into hours (24 hours in a day)...

126 hours and 20 minutes-80 hours and 40 minutes

7580 minutes-4840 minutes=2740 minutes

We can convert 2740 minutes back into hours and days now...

1 day, 21 hours, and 40 minutes

Or....

Step-by-step explanation: Or you can just subtract, start with minutes and go up from there...

20-40 would be in the negatives and time can’t be negative, so you need to borrow from the hours. So hours is now at 5 and minutes is at 20+40 which is 80. And 80-40=40

We now have...

5 days, 5 hours, and 40 minutes-3 days and 8 hours.

Now we can do the hours...

5-8 also is negative, so we need to borrow from the days. Days is now at 4. There are 24 hours in a day so 24+5=29. Now we can subtract 29-8=21

Now we have 4 days, 21 hours, and 40 minutes

And 4-3 is 1, which means we have 1 day,

21 hours, and 40 minutes as our answer!

The difference between the given time frames 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes after performing the subtraction operation is 1 day, 13 hours, and 40 minutes.

The question is about an arithmetic operation involved in time. This arithmetic operation is subtraction. Given the time frames are 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes. Let's subtract the smaller time frame from the larger one.

So, the difference between 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes is 1 day, 13 hours, and 40 minutes.

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Hi! Let's go over the meanings of each term to find our answer.

Domain of an exponential parent function - the set of all real values of x that will give real values for y in the given function

Range of an exponential parent function - the set of all real values of y that you can get by plugging real numbers into x in the same function

Now we have our answers! All we had to do was go over the meanings, or definitions.

Hope this helps!

- Kylie

Answer:

The domain of exponential parent function is all real values and range is real positive numbers [tex]y>0[/tex].

Step-by-step explanation:

We are asked to find the domain and range of exponential parent function.

We know that an exponential parent function is in form [tex]f(x)=b^x[/tex], where b is the base of function.

We can see from parent exponential function that as x approaches to very large values of x, the value of y increases with no bounds.

As x approaches negative infinity, y approaches to zero.

We know that the domain of a parent exponential function is all real values of x that is [tex](-\infty,\infty)[/tex] in interval notation.

The range of a parent exponential function is positive real numbers that is [tex]y>0[/tex].

Answer:

x + y = 330

9x + 16y = 4650

Step-by-step explanation:

Given that x = children and y = adults, we can say that x + y = 330.

Since the total amount of money collect from both children and adults was $4650, we can say that 9x + 16y = 4650.

So the system that represents the situation is:

x + y = 330

9x + 16y = 4650

Answer:

Answer:

x + y = 330

9x + 16y = 4650

Step-by-step explanation:

Given that x = children and y = adults, we can say that x + y = 330.

Since the total amount of money collect from both children and adults was $4650, we can say that 9x + 16y = 4650.

So the system that represents the situation is:

x + y = 330

9x + 16y = 4650

Answer:

[tex]e^{ln(12)}=12[/tex]

Step-by-step explanation:

I suppose your intended expression is;

[tex]e^{ln(12)}[/tex]

The exponential function, e, and the natural logarithm function, ln, are inverses of each other;

[tex]e^{lnx}=x\\\\lne^{x}=x[/tex]

Therefore, our expression becomes;

[tex]e^{ln(12)}=12[/tex]

Answer:

15 litres

Step-by-step explanation:

129.6 m² needs 8L

1m² needs 8/129.6L

243m² needs (8/129.6)×243 = 15L

To calculate the amount of paint required for a 243m² area, determine the coverage rate from the given data (16.2 m² per litre) and then divide the desired area by the coverage rate. We find that 15 litres of paint are necessary to cover 243m².

To find out how much paint is required to paint an area of 243m² when 8 litres of paint can cover 129.6 m², we need to calculate the paint coverage ratio and then apply it to the desired area.

First, we calculate the coverage rate of the paint:

Next, we use this rate to determine the amount of paint needed for 243m²:

Therefore, 15 litres of paint are required to paint an area of 243m².

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Answer:

The correct option is C.

Step-by-step explanation:

In a right triangle, the hypotenuse has endpoints XY as shown in the given graph.

Since XY is hypotenuse and Z is third vertex in the triangle, therefore XZ and YZ must be perpendicular at point Z.

The coordinates of X are (-4,2), so draw a vertical line x=-4 and a horizontal line y=2.

The coordinates of Y are (-1,-3), so draw a vertical line x=-1 and a horizontal line y=-3.

From the below figure it is clear that the vertcal and horizontal lines intersect each other at [tex]Z_1[/tex] and [tex]Z_2[/tex].

It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is

[tex]Z=Z_2(-1,2)[/tex]

Since the length of YZ₂ is 5 units and Z=Z₂, therefore the length of YZ is 5 units.

Hence the correct option is C.

Answer:

-15

Step-by-step explanation:

Note that it says x = -9. Plug in -9 for all x inside the expression and solve.

(x² + 9)/(x + 3) = (-9² + 9)/(-9 + 3)

Solve. First, solve the parenthesis, then divide:

(-9² + 9) = (81 + 9) = 90

(-9 + 3) = (3 - 9) = -6

Divide:

(90)/(-6) = -15

-15 is your answer.

~

False.

This is not a function because for something to be a function each x value can only have one y value. In this case two of the points have a value of 1 and their y are different, making them NOT a function

(1, 3)

(1, 2)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 317.93

Step-by-step explanation:

317.93371 when rounded off to nearest hundred, we get 317.93.

Rounding off is the method by which a decimal integer is reduced to its nearest closer value of the next number . After the decimal point, if the value is greater than 5 we increment the numerical value by 1 and if the value is less than 5 we keep the numerical value intact.

The given value is 317.93371 .

Rounding off to nearest hundred means that we will get the rounded off value up to two decimal places.

We can see that the third decimal place is 3 which means that the second decimal place of the number will be kept intact.

Rounded off value is -  317.93 .

Thus, 317.93371 when rounded off to nearest hundred, we get 317.93.

To learn more about rounding off, refer -

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Answer:

Both the lines would have the same slope since they are parallel. The lines would not however have the same y-intercept.

Step-by-step explanation:

This is because in order for lines to be parallel the lines must have the same slope, otherwise they would meet at some point. They would not have the same y-intercept because if both the y-intercept and the slope were the same it would be the same line.

Answer:

Both lines are parallel, so they have the same slope. However, the y-intercepts of the lines are not the same. For the lines to be parallel, the slopes of the lines must be the same. If both the y-intercept and slope are the same, they are the same line, so they do not have the same y-intercept.

Answer:

Kate’s photo get 14 likes

Step-by-step explanation:

Let

x ----> Kate's likes

y ---> Ali's likes

we know that

y=42 likes ----> equation A

y=3x ----> equation B

Solve by substitution

Substitute equation A in equation B and solve for x

42=3x

Divide by 3 both sides

x=42/3

x=14 likes

Kate's photo got 14 likes.

The student is dealing with a basic algebra problem that involves setting up and solving an equation. To find out how many likes Kate's photo got, we can let x represent the number of likes on Kate's photo. Given that Ali's photo got 42 likes, which is three times as many as Kate's photo, we can write the equation as:

3x = 42

To find x, we divide both sides of the equation by 3:

x = 42 / 3

x = 14

Therefore, Kate's photo got 14 likes.

Answer:

You MUST use parentheses around denominator 8+x, or ANY denominator that consist of more than a single number of variable. 

Also, don't use lower case and upper case interchangeably. 

In algebra, x and X are different, as are y and Y. 

f(x) = y = 3x/(8+x) 

Switch x and y, solve for y: 

x = 3y/(8+y) 

x(8+y) = 3y 

8x+xy = 3y 

8x = 3y−xy 

8x = y(3−x) 

y = f⁻¹(x) = 8x/(3−x)

I hope this helps, love 

Step-by-step explanation:

Step-by-step answer with explanations:

Recall that a coordinate pair such as (5,-1) has two components.

The first (5, -1) means that the point is situated at x=5.

The second (5, -1) means that the point is situated at y=-1.

Now, a horizontal line through (5,-1) means that ALL points on the line have y-coordinate equal to -1, so that any point with y=-1 will lie on this horizontal line.  An example would be (-2,-1).

A vertical line through (5, -1) means that ALL points on the line have x-coordinate equal to 5, so that any point with x=5 will lie on this vertical line.  An example would be (5,4).

Answer:

its D

Step-by-step explanation:

ur welcome =)

Answer:

8,640 ft^2

Step-by-step explanation:

There are 144 square inches per square foot, therefore 144x60=8,640 ft^2

Hello There!

There are 32.5 kilograms in 32,500 grams.

STEPS

Write the number of grams

Divide by 1,000 because a kilogram is 1,000 grams

Answer:

D y= -2 (x-8)2 -3

Step-by-step explanation:

The equation of the new parabola will be y = -2(x + 2)² + 1. Then the correct option is A.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation of the parabola is given below.

y = -2(x - 3)² + 4

If this parabola is shifted 5 units to the left and 3 units down. Then replace x with x + 5 and subtract 3 from the equation.

Then the equation of the new parabola will be given as,

y = -2(x + 5 - 3)² + 4 - 3

y = -2(x + 2)² + 1

The condition of the new parabola will be y = - 2(x + 2)² + 1. Then, at that point, the right choice is A.

More about the equation of the parabola link is given below.

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Answer:364.6

Step-by-step explanation:

Answer:

Table 3 and 4

Step-by-step explanation:

Let us understand the coordinates symmetry of the graphs of quadratic equations.

In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as polynomial contains [tex]x^2[/tex] in it.

Thus by analysing the tables we see that in table 3 , y= -10 gets repeated and in table 4 , y =4 and y=-4 repeated. Hence they are the graph of a quadratic polynomial

ANSWER

[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]

EXPLANATION

The given equation is

[tex] {x}^{2} - 5x - 5 = 0[/tex]

The solution is given by the formula

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

where a=1, b=-5, c=-5

We substitute into the formula to get;

[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 5)} }{2(1)} [/tex]

We simplify to get,

[tex]x = \frac{ 5 \pm \sqrt{ 45} }{2} [/tex]

The solutions are:

[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]

The equation has no complex roots.

Answer:

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

To find the solutions of given equation

It is given  x² - 5x - 5 = 0

here a = 1, b = -5 and c = -5

x = [-b ± √(b² - 4ac)]/2a

 =  [--5 ± √((-5)² - 4*1*-5)]/2*1

 = [5 ± √(25 + 20)]/2

 =  [5 ± √(45)]/2

 =  [5 ± 3√5]/2

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Answer:

In the explanation

Step-by-step explanation:

Going to start with the sum identities

sin(x+y)=sin(x)cos(y)+sin(y)cos(x)

cos(x+y)=cos(x)cos(y)-sin(x)sin(y)

sin(x)cos(x+y)=sin(x)cos(x)cos(y)-sin(x)sin(x)sin(y)

cos(x)sin(x+y)=cos(x)sin(x)cos(y)+cos(x)sin(y)cos(x)

Now we are going to take the line there and subtract the line before it from it.

I do also notice that column 1 have cos(y)cos(x)sin(x) in common while column 2 has sin(y) in common.

cos(x)sin(x+y)-sin(x)cos(x+y)

=0+sin(y)[cos^2(x)+sin^2(x)]

=sin(y)(1)

=sin(y)