1.Does the relationship between number of people and the bill appear to be weak, moderate or strong?

2.Does the relationship between number of people and the bill appear to be linear?

3.The equation of the line of best fit is Bill = 5.80 + 11.15 · People. (y=5.80+11.15x) Sketch this line on the scatterplot.

4.Interpret the slope of the line of best fit in the context of this problem.

5.Note that the points in the scatterplot do not all lie on the line. What could explain this variability?

6.Use the equation of the line of best fit to estimate how much would you predict the bill to be for a party of 8?

7.There was one party of 8 whose bill was $82.50. Did they pay more than or less than the predicted amount? How much more or how much less did they pay?

Answer:

  y = 5

Step-by-step explanation:

The triangles will be congruent when corresponding sides are congruent. __

We already have ...

  KL ≅ NP . . . = 15 mm

  JL ≅ MP . . . = 22 mm

So, we need ...

  JK ≅ MN

  4y +12 = 32 . . . . substitute given values

This will be the case when ...

  4y = 20 . . . . . subtract 12

  y = 5 . . . . . . . divide by 4

The value of y that makes the triangles congruent is 5.

The value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

For Geometric sequence, the value of  geometric mean can be found out using the following formula,

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

Here, (a and b) are the two terms of geometric sequence.

The geometric mean of a and 12 is 8√6. Thus,

[tex]x=8\sqrt{6}[/tex]

[tex]b=12[/tex]

Put this value in formula to find the value of a,

[tex]8\sqrt{6}=\sqrt{a\times12}\\[/tex]

Square both side of equation,

[tex](8\sqrt{6})^2=(\sqrt{a\times12})^2\\64\times6=12a\\a=\dfrac{64\times6}{12}\\a=32[/tex]

Thus, the value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

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Step-by-step explanation:

the error:

it is stated that

[tex]\frac{5x}{x+7} +\frac{7}{x} = \frac{5x}{x+7} +\frac{7(7)}{x+7}[/tex]

subtract (5x)/(x+7) from both sides

[tex]\frac{7}{x} = \frac{7(7)}{x+7}[/tex]

multiply both sides by x + 7

7(x+7) = 49x

7x + 49 = 49x

subtract 7x from both sides to isolate x and its coefficient

49 = 42x

thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must always be true, so this is wrong

the solution:

we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x  by 1.

anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.

(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get

[tex]\frac{7}{x} = \frac{7(x+7)/x}{x+7}[/tex]

substitute this for 7/x in our original problem

[tex]\frac{5x}{x+7} +\frac{7(x+7)/x}{x+7} = \frac{5x}{x+7} +\frac{(7x+49)/x}{x+7} = \frac{5x}{x+7} +\frac{7+49/x}{x+7} = \frac{5x+7+49/x}{x+7}[/tex]

1 kilometer = 1000 meters

5000 meters / 1000 = 5 kilometers

5 kilometers x 2 times per day = 10 kilometers per day.

answer: D) 10 kilometers

Answer:

[tex]-\dfrac{b^2}{16a^4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{(2a)^{-2}b^5}{-4a^2b^3}[/tex]

[tex]\textsf{Apply the exponent rule}\quad (ab)^c=a^c \cdot b^c:[/tex]

[tex]\implies \dfrac{2^{-2}a^{-2}b^5}{-4a^2b^3}[/tex]

Separate the variables:

[tex]\implies \dfrac{2^{-2}}{-4}\cdot \dfrac{a^{-2}}{a^2}\cdot \dfrac{b^5}{b^3}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{2^{-2}}{-4}\cdot a^{-2-2}\cdot b^{5-3}[/tex]

[tex]\implies \dfrac{2^{-2}}{-4}\cdot a^{-4}\cdot b^{2}[/tex]

[tex]\textsf{Apply the exponent rule}\quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{-4(2^2)}\cdot \dfrac{1}{a^4}\cdot b^{2}[/tex]

[tex]\implies -\dfrac{1}{16}\cdot \dfrac{1}{a^4}\cdot b^{2}[/tex]

Simplify:

[tex]\implies -\dfrac{b^2}{16a^4}[/tex]

Answer:

Step-by-step explanation:

Mean: Add all the values and divide by the # of values

Median: The center of the values

Mode: The value that appears the most in the data set

Mean for data set 1: 86

Mean for data set 2: (85+89+71+85+86+91+92+96+87)/2= approximately 86.89

Median for data set 1: 72,75,78,80,88,90,95,98,98

We've sorted it from least to greatest, and the center is 88 because there is 4 values to the left of it, and 4 values to the right. It's at the very center.

Median for data set 2: 71,85,85,86,87,89,91,92,96

The center for this is 87 because it is again, at the absolute center/middle between the data.

Mode for data set 1: 98 because it appears 2 times, which is more often than other values

Mode for data set 2: 85 because it appears most often (2 times) in the data set

Hope this helps! :)

Step-by-step explanation:

[tex] = 2(x - 5) ^{2} + 4(x - 5) + 1[/tex]

Now for the first term use the formula :

[tex] {a}^{2} - 2ab + {b}^{2} [/tex]

[tex] = 2( {x}^{2} - 10x + 25) + 4(x - 5) + 1[/tex]

[tex] = 2 {x}^{2} - 20x + 50 + 4x - 20 + 1[/tex]

[tex] = 2 {x}^{2} - 20x + 4x + 50 - 20 + 1[/tex]

[tex] = 2 {x}^{2} - 16x + 31[/tex]

Answer:

Simplified answer = C = $0.65m + $24.65

Step-by-step explanation:

Add the two initial charges together (from the insurance and the standard charge) and you get $24.65.  Then add the two charges together for each mile which is $0.65 per mile.  Therefore, the total charge on the car is $24.65 + 65 cents every mile driven.

Answer:

612 centimeters = 612 : 10 = 61,2 decimeters

Answer:  " 5.1 " .
____________

Step-by-step explanation:
____________

To find 1 percent (i.e. " 1% " )  of:  510 ;

Note:  1 %  = (1 /100) = (1 ÷ 100) ;

Note the following about "dividing by "100" ;

  We take the number:  "510" in our case;
  and move the decimal point "2 (two) places backward" .
We move it "backward" (instead of "forward") because we are "dividing" ;

and we are moving the decimal point "2 (two)" spaces backward; since we are dividing by "100" ; which has "2 (two) zeros" .
  So:   " (510.) ÷ 100 " ;
               

      Take:  " 510." ; and move the decimal point two (2) spaces backward:
                         5.10.
                             ↩

    To get: " 5.10 " ;  which we can simplify as:
             →  " 5.1 " ; which is our answer.

Hope this is helpful to you!  Wishing you well!
____________

Answer:

84

Step-by-step explanation:

Plug in 9 for k.

5(9)(2) - 6

first: (9)(2) = 9 x 2 = 18

5(18) - 6

second: 5(18) = 5 x 18 = 90

last: 90 - 6 = ?

84

hope this helps

Answer:

Step-by-step explanation:

f(x) = x/(x-7)

The domain is C

7/(7-7) = 7/0 = undefined

Answer: 475 Add 5 more.

Step-by-step explanation:

3 1/2 = 7/2

7/2 ÷ 1/4

7/2 × 4/1

14/2

7 pieces

hope it helps...!!!

Answer:

180

Step-by-step explanation:

First, we have to find out how many boys are in the school:

900 * 0.30 = 270

Now, we know that there are 270 boys. Out of these boys we need to find out how many boys have glasses:

270 * 0.40 = 108

180 is our answer.

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9 +8}{-3 +2}\implies \cfrac{-1}{-1}\implies 1[/tex]

Answer:

Step-by-step explanation:

(-9 + 8)/(-3 + 2)= -1/-1= 1

Answer:

8%

Step-by-step explanation:

assume simple interest rate = r

interest = 1000 * 4 * r = 320

r = 320/4000 = 0.08 = 8%

Step-by-step explanation:

1 and 2 are negative

3 and 5 are none

4 and 6 are positive

Answer:

TV = 8 , SV = 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

given ST = TV , then

TV = 8

using Pythagoras' identity in the right triangle

SV² = ST² + TV² = 8² + 8² = 64 + 64 = 128 ( take square root of both sides )

SV = [tex]\sqrt{128}[/tex] = [tex]\sqrt{64(2)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{2}[/tex] = 8[tex]\sqrt{2}[/tex]

Explanation:

By definition, the floor is assumed to be level and that means the floor is at a 0 degree angle. The shelf must also have this same angle relative to the floor so we have the shelf and floor as parallel planes. For more info, check out the converse of the corresponding angles theorem.

Answer:

864.

Step-by-step explanation:

1) the required volume can be calculated according to the formula (see also the attachment):

V=Area(BKS)*height;

2) if to see the triangle ABC (see the attachment), then m∠C=90°; m∠A=30° and m∠B=60°;

3) the length of AC=BC*cot(m∠A)=2√3*√3=6 [cm];

4) if AC=6 [cm], then BS=36-2*BC=24 [cm];

5) in the equilateral triangle BKS BS=BK=KS=24 [cm], then the Area(BKS)=BS²√3/4=144√3 [cm²];

6) if the height is 2√3 [cm] and Area(BKS)=144√3 [cm²], then

V=144√3*2√3=864 [cm³].

Answer:

T = 12

Step-by-step explanation:

8t+1=97

We move all terms to the left:

8t+1-(97)=0

We add all the numbers together, and all the variables

8t-96=0

We move all terms containing t to the left, all other terms to the right

8t=96

t=96/8

t=12

Answer:

  (a) higher by 0.25%

Step-by-step explanation:

The error in the estimate is found by comparing the estimated rate to the actual rate.

__

The rate of estimated closing costs is ...

  (estimated cost)/(home cost) × 100% = 6375/170000×100% = 3.75%

The actual rate is 4.00%.

  actual - estimate = 4.00% -3.75% = 0.25%

The actual closing costs were higher than the estimate by 0.25%.

Answer:

y = x/3 +5

Step-by-step explanation:

Step1 : finding the slope

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

(3,6) and (−3,4)

m = [tex]\frac{4-6}{-3-3}[/tex]

m = 1/3

Solving for the equation

y-y1 = m(x-x1) , (3,6)

y-6 = 1/3(x-3)

y = x/3 -1 +6

y = x/3 +5

Answer:

nonlinear because the second row isn't going up by the same number

Answer:

1/17 or 0.059

Step-by-step explanation:

7/17 + (-6/17) = 7/17 - 6/17 = 7-6/17 = 1/17

Answer:

S = $76 and P = $236

Step-by-step explanation:

Let the sodas be S and the patties P. So

4S + 6P = 840  and 5S + 5P = 800

By substitution method we will have the solution

5S + 5P = 800

5S = 800 - 5P

S = 800 - 5P

          5

We'll sustitute S with this equation

4S + 6P = 840

[tex]4(\frac{800 - 5P}{5})[/tex] + 6P = 80

4(800 - 5P) + 6P(5) = 840

3200 - 20P + 30P = 840

-20P + 30P = 840 - 3200

10P = -2360

P = -2360

        10

P = -236

Since the cost of the patty can't be negative, P = $236

Now that we know the cost of the patty, we can calculate the cost of the soda

S = 800 - 5P

          5

S = 800 - 5(236)

             5

S = 800 - 1180

             5

S = -380

        5

S = -76

Here S can't be negative, so S = $76

Answer:

A. 90°

Step-by-step explanation:

A perpendicular on a straight line creates 2 right angles.

We know the value of a right angle is 90°.

Hence :

∠2 = 90°