Which is the BEST description of the data in the scatterplot?

Answers:

a) The equation is [tex]y = 196(0.77)^x[/tex]

b) See image attachment below

c) See image attachment below

d) Week 10

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Explanation:

a)

One common template for an exponential equation is [tex]y = a*b^x[/tex] where 'a' is the starting amount and b is the growth or decay factor.

a = 196 is the starting amount of people who saw the movie per showtime

b = 1-0.23 = 0.77 is the decay factor. If the view count goes down by 23%, then we keep the remaining 77%

Therefore we go from [tex]y = a*b^x[/tex] to [tex]y = 196(0.77)^x[/tex]

x = number of weeks

y = number of people, per viewing, who saw the movie for the particular week

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

b)

Plug in x = 0 to find that y = 196

Plug in x = 1 to get y = 150.92 which rounds to y = 151 since we're talking about the number of people

Repeat for x = 2 all the way up to x = 9 to account for the first ten weeks. We stop at 9 instead of 10 because we started at x = 0.

The table is shown in the attachment below next to the graph.

I'm not sure why your teacher put a dollar sign over the second column of the table when it should be the number of people. It might be a typo. If they meant to do it, then there's missing information about ticket prices.

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c)

The graph is shown below. You can plot each (x,y) point on the same grid and then draw a curve through them. A much quicker way is to use software like GeoGebra (which is what I used) or Desmos or a pocket calculator. There are tons of many options to pick from. Feel free to choose your favorite.

The blue dashed segments on the graph visually help verify the result of part (d). We have y = 20 lead to an x value somewhere between x = 8 and x = 9. When submitting the graph to your teacher, you'll leave out the blue dashed segments.

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

d)

Refer to the table we made in part (b). We have x = 9 lead to y = 19 approximately which is when y is below 20 people. Recall that x = 0 refers to week 1, so x = 9 refers to week 9+1 = 10. Week ten is where the view count drops below 20 people per showing.

If you wanted to use the graph in part (c), then you'd follow the blue dashed line mentioned earlier. Start at the y axis at y = 20. Trace the blue dashed line until reaching the curve. Then drop straight down to arrive somewhere between x = 8 and x = 9. Round up to x = 9. Then make the adjustment to go from x = 9 to week ten.

If you want an algebraic method, then follow the steps below.

Plug in y = 20 and solve for x. We'll need to involve logarithms to isolate the exponent.

[tex]y = 196(0.77)^x\\\\20 = 196(0.77)^x\\\\20/196 = (0.77)^x\\\\0.1020408 \approx (0.77)^x\\\\(0.77)^x \approx 0.1020408\\\\\text{Log}\left((0.77)^x\right) \approx \text{Log}(0.1020408) \\\\x*\text{Log}\left(0.77\right) \approx \text{Log}(0.1020408) \\\\x \approx \text{Log}(0.1020408)/\text{Log}\left(0.77\right) \\\\x \approx 8.7325564 \\\\[/tex]

This rounds up to x = 9 leading to week ten as the answer.

As confirmation

[tex]y = 196(0.77)^x = 196(0.77)^8 \approx 24.22 \approx 24\\\\y = 196(0.77)^x = 196(0.77)^9 \approx 18.65 \approx 19\\\\[/tex]

Answer:

We can model this as an exponential equation.

General form of an exponential equation: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

As the movie theatre lost 23% of its audience each week, the growth (decay) factor will be 100% - 23% = 77%  →  0.77

Given:

Substitute the given values into the formula to create the exponential equation:

[tex]y=196(0.77)^x[/tex]

[tex]\begin{tabular}{| c | r |}\cline{1-2} \bf weeks & \bf audience \\\cline{1-2} 1 & 150.92\\\cline{1-2} 2 & 116.21\\\cline{1-2} 3 & 89.48\\\cline{1-2} 4 & 68.90\\\cline{1-2} 5 & 53.05\\\cline{1-2} 6 & 40.85\\\cline{1-2} 7 & 31.46\\\cline{1-2} 8 & 24.22\\\cline{1-2} 9 & 18.65\\\cline{1-2} 10 & 14.36\\\cline{1-2}\end{tabular}[/tex]

**all values rounded to 2 dp**

see attached for graph

Set y < 20 and solve for x:

[tex]\begin{aligned}196(0.77)^x & < 20\\\\(0.77)^x & < \dfrac{5}{40}\\\\\ln (0.77)^x & < \ln\left(\dfrac{5}{49}\right)\\\\x\ln (0.77) & < \ln\left(\dfrac{5}{49}\right)\\\\x & > \dfrac{\ln\left(\dfrac{5}{49}\right)}{\ln (0.77)}\\\\x & > 8.732555795\end{aligned}[/tex]

Therefore, the movie audience will fall below 20 people per viewing during the 9th week.

Answer:

14

Step-by-step explanation:

1. Add 7 to both sides

2. This leaves us with x=14

Using the binomial distribution, it is found that the probability that exactly three workers owns a car is given by:

A. 0.267.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that exactly three workers owns a car is given by P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.267[/tex]

Hence option A is correct.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

Answer:X + (2 and 1/2) - 3/4 = 5 and 1/4

X + 2 and 2/4 - 3/4 = 5 and 1/4 <--- common denominator

X + 10/4 - 3/4 = 21/4

X + 7/4 = 21/4

X = 21/4 - 7/4 = 14/4 = 7/2 = 3 and 1/2

Step-by-step explanation:

so first you must calculate the total amount of marbles there are, that being addition : 1+4+2+6+4+5 = 24 in total. now you want to make that into a fraction, 24/24 marbles, once again all together, so the probability of not getting a black marble is 5/24 and probability of not getting a green is 2/24.

[tex]3\times 5 +4 \times 2- 3\\\\=15+8-3\\\\=12+8\\\\=20[/tex]

Answer:

10 grams

Step-by-step explanation:

200 x 5 = 1000

If we move the decimal over two places left we get :

10.00

That means that there are 10 grams of sugar in 200 grams of 5% sugar syrup

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Have a nice day.

Answer:

To convert 30 yards to feet, multiply by 3.

Step-by-step explanation:

We have to find out how many feet is in 1 yard and we have to multiply by 3 to find the answer. So the answer is multiply by 3

Answer:

B)

E)

Step-by-step explanation:

       translation                                   Dilation

M(x,y) ——————>M”(x”,y”)=(x+5,y+8) ——————> M’(x’,y’)=(3x”,3y”)

S(-5,-8) ——————>S”(x”,y”)=(0,0) ——————> S’(x’,y’)=(0,0)

R(-7,-6) ——————>R”(x”,y”)=(-2,2) ——————> R’(x’,y’)=(-6,6)

Q(-8,-10) ——————>Q”(x”,y”)=(-3,-2) ——————> Q’(x’,y’)=(-9,-6)

Maturity Value: 9,159.08

Interest: 1,359.08

Answer:

Angle A=60

Step-by-step explanation:

If ABC is approximately equal to DEF, A=D.

So x+30=2x

x+30=2x -> 30=x

If A=x+30 and x=30 then 30+30=60.

Answer:

The angle is 90°, and the type of angle is a right angle.

Step-by-step explanation:

That is a right angle, the little box and the straight lines indicate that is one. A right angle will always be 90°.

The function f(n)=−48⋅(-¼)^n is a geometric sequence

The recursive definition of f(n) is f(1) = 12;  f(n) = f(n - 1) . -¼

The function is given as:

f(n)=−48⋅(-¼)^n

Calculate f(1)

f(1)=−48⋅(-¼)^1

This gives

f(1) = 12

Calculate f(2)

f(2)=−48⋅(-¼)^2

This gives

f(2) = -3

Calculate the common ratio (r)

r = f(2)/f(1)

So, we have:

f = -3/12

Simplify

r = -1/4

Recall that: r = f(2)/f(1)

This gives

-1/4 = f(2)/f(1)

Make f(2) the subject

f(2) = -1/4* f(1)

Express 1 as 2 - 1

f(2) = -1/4* f(2 - 1)

Substitute 2 for n

f(n) = -1/4* f(n - 1)

Rewrite as:

f(n) = f(n - 1) . -¼

Hence, the recursive definition of f(n) is f(1) = 12;  f(n) = f(n - 1) . -¼

Read more about sequence at:

https://brainly.com/question/7882626

Answer:

x^3 / 6

Step-by-step explanation:

Multiply the three dimensions to get the volume

x * x/2 * x/3 =  

The expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.

It is defined as the combination of constants and variables with mathematical operators.

It is given that, the length is x, width x/2, and height is x/3.

The volume of the rectangular prism is the product of the length, width, and height.

V= length × width × height

V=x × x/2 × x/3

Apply the multiplication operation in the fraction

Simply multiply the numerators to obtain the product's numerator and the denominators to obtain the product's denominator in order to multiply two fractions.

V=x³/6

Thus, the expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.

Learn more about the expression here:

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Answer:

If both objects started with no charge, they would carry opposite charges of the same magnitude after rubbing.

Step-by-step explanation:

When one insulator is rubbed against another, some electrons on one insulator might travel to the surface of the other insulator. Electrons are neither lost nor created in this process- they are just moved from one surface to the other.

Let the two insulators in this question be denoted as [tex]A[/tex] and [tex]B[/tex]. Assume that both insulators were initially not charged.

Let [tex]{\rm e}[/tex] denote the fundamental charge. Each electron carries a negative charge of [tex](-1\; {\rm e})[/tex]. Assume that [tex]n[/tex] electrons are moved from insulator [tex]A\![/tex] to insulator [tex]B\![/tex]:

In other words, the insulator that lost some electrons (which are negatively charged) now carries less negative charge and becomes positively charged. In contrast, the insulator that gained some electrons now carries more negatively charge becomes negatively charged.

The amount of electrons on the two objects combined stays unchanged. Thus, the amount of charge one insulator lost is equal to what the other insulator gained. Therefore, the sign of the charge on the two insulators would be different, but the magnitude (absolute value) of the charge would be equal.

Therefore, the two objects would be oppositely charged, with the magnitude of the charge on them being equal.

Answer:

Step-by-step explanation:

the median is 26.5, but rounding that up the median will be 27. you can find this by determining the middle number of the data set.

So here we are given that a || b and c || d, so the quadrilateral formed by the intersection of the four lines is just a parallelogram, so recall the property of parallelogram that parallelogram's opposite angles are always equal and the interior angles on the same side add up to 180°, and the property of angles that the alternate angles are always equal (that's angles Like in the Shape Z) and vertically opposite angles are equal (like in shape of X) and the property of linear pair i.e the sum of all angles on a plane line is 180°.

Now, as angles 3 and 7 are on a line d, so their sum will just be 180°, by property of linear pair

[tex]{:\implies \quad \sf m\angle 3+m\angle 7=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 7+74^{\circ}=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 7=180^{\circ}-74^{\circ}}[/tex]

[tex]{:\implies \quad \boxed{\bf{m\angle 7=106^{\circ}}}}[/tex]

Also, as angles 8 and 3 are vertically opposite angles, so they will be same, so we have

[tex]{:\implies \quad \boxed{\bf{m\angle 8=74^{\circ}}}}[/tex]

Now also, angle 7 and angle 11 are opposite angles of the parallelogram, so they will be equal, so we have :

[tex]{:\implies \quad \boxed{\bf{m\angle 11=106^{\circ}}}}[/tex]

Also, the interior angles on same side of Parallelogram add upto 180°, so we can have ;

[tex]{:\implies \quad \sf m\angle 11+m\angle 13=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 13+106^{\circ}=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 13=180^{\circ}-106^{\circ}}[/tex]

[tex]{:\implies \quad \boxed{\bf{m\angle 13=74^{\circ}}}}[/tex]

Also, Opposite angles of Parallelogram are equal, so angle 6 will be equal to angle 13, so angle 6 will be 74° and we also know the Vertically Opposite angles are equal. So, for angle 1 we have

[tex]{:\implies \quad \boxed{\bf{m\angle 1=74^{\circ}}}}[/tex]

Now, we are end with the conclusion :

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Measure of Angle 3 is given, that is : Angle 3 = 74°

And the lines a and b are parallel, similarly line c and d are parallel to each other as well.

Now, let's just use property of angles on parallel lines to find measure of each angle we have been asked.

[tex]\qquad \tt \dashrightarrow \: \angle1 = \angle3 = 74 \degree[/tex]

[ By Corresponding Angle pair ]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \tt \dashrightarrow \: \angle7 + \angle3 = 180 \degree[/tex]

[ By Linear Pair ]

[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - \angle3 [/tex]

[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - 74[/tex]

[tex]\qquad \tt \dashrightarrow \: \angle7 = 106 \degree[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \tt \dashrightarrow \: \angle8 = \angle3 = 74 \degree[/tex]

[ By Vertical opposite angle pair ]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \tt \dashrightarrow \: \angle7 = \angle11 = 106 \degree[/tex]

[ opposite angles of a Parallelogram ]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \tt \dashrightarrow \: \angle13= \angle3 = 74 \degree[/tex]

[ by Corresponding Angle pair ]

Answer:

20.52 cm²

Step-by-step explanation:

[tex]\textsf{Area of a semicircle}=\sf \dfrac12\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\textsf{Area of a triangle}=\sf \dfrac12bh \quad \textsf{(where b is the base and h is the height)}[/tex]

Given:

[tex]\begin{aligned}\implies \textsf{Shaded area} & =\sf \dfrac12\pi r^2-\sf \dfrac12bh\\ & = \sf \dfrac12 \cdot 3.14 \cdot 6^2-\dfrac12 \cdot 12 \cdot 6\\ & = \sf 56.52-36\\ ^& = \sf 20.52\:\:cm^2\end{aligned}[/tex]

Answer:

20.52cm^2

Step-by-step explanation:

from the picutre we can see that this is a semicircle with 2 right angle triangles inside it. to find the area we will solve for the semi circle then solve for the triangles and and subtract

circle area is [tex]\pi r^{2}[/tex] leaving the semicircle to be [tex]\frac{\pi r^{2} }{2}[/tex] for the semi circle

next we need the radius. since the diameter is given, we can solve for r by dividing it in two

12 ÷ 2 = 6

so the area of the semi circle is [tex]\frac{\pi 6^{2} }{2}[/tex]

this gives 18[tex]\pi[/tex]cm^2 if we simplify

next the triangles, since they are equal in size we can treat them as a square and stack them. this is because they have equal side lengths so when stacked they form a square:

base x height divided by 2 times 2 would be the normal process to find two equal triangles but you can see the division and multiplication cancel out

6x6= 36cm^2

finally subtracting the areas to find the shaded region and use 3.14 as pi

18[tex]\pi[/tex]cm^2 - 36cm^2 = 20.52cm^2

Answer:

2 + [tex]\sqrt{3}[/tex]

Step-by-step explanation:

In decimal form, it is also 3.73205080...

hope this helps :)

Answer:

in the problem 17 the answer is 30 becase you times 6 and 6 and you git 30.problem 18 you do the same thing

Step-by-step explanation:

hope this helps if not let me now

Answer:

£828

Step-by-step explanation:

The first step to solve this problem is to find the surface area of the solid box. The formula for surface area for a rectangular prism is [tex]2(wl+hl+hw)[/tex]where w is width, l is length, and h is height. Plugging values in gives [tex]2(90*90+70*90+70*90)=41400[/tex] cm^2.

Because each cm^2 of paint costs £0.02, a ratio can be created.

[tex]\frac{1}{0.02} =\frac{41400}{x}[/tex]

Cross multiplying gives: [tex]x=828[/tex], so to paint the whole outside of the box, it would cost £828.

Answer:

option A is the correct answer

Answer:

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The number of blocks in each row, from bottom to top, is: 23, 23, 23, 21, 19, 17, 15, 13, 11.

Step 1: Let's assume the number of blocks in each row of the bottom 3 rows is "x."

Step 2: The next six rows will each have 2 blocks fewer than the row below it. So, the number of blocks in each of these rows can be represented as:

x - 2, x - 4, x - 6, x - 8, x - 10, x - 12.

Step 3: Now, we can calculate the total number of blocks in all the rows.

For the bottom 3 rows, there are a total of 3 * x = 3x blocks.

For the next six rows, there are a total of (x - 2) + (x - 4) + (x - 6) + (x - 8) + (x - 10) + (x - 12) = 6x - 42 blocks.

Step 4: The total number of blocks in the wall is given as 165 blocks. So, we can set up an equation:

3x + 6x - 42 = 165

Step 5: Now, solve for x:

9x - 42 = 165

9x = 165 + 42

9x = 207

x = 207 / 9

x = 23

Step 6: Now that we have the value of x, we can find the number of blocks in each row:

The bottom 3 rows: x = 23 blocks each.

The next six rows:

x - 2 = 23 - 2

       = 21 blocks,

x - 4 = 23 - 4

       = 19 blocks,

x - 6 = 23 - 6

       = 17 blocks,

x - 8 = 23 - 8

        = 15 blocks,

x - 10 = 23 - 10

         = 13 blocks,

x - 12 = 23 - 12

         = 11 blocks.

So, the number of blocks in each row, from bottom to top, is: 23, 23, 23, 21, 19, 17, 15, 13, 11.

To know more about blocks:

https://brainly.com/question/13004935

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x=8

Hope it helps.

Do comment if you have any query.

[tex]12x-5 = 91\\\\\implies 12x = 91+5\\\\\implies 12x = 96 \\\\\implies x= \dfrac{96}{12}\\\\\implies x = 8[/tex]

Answer:

(5,0)

Step-by-step explanation:

The # 5 is on the x axis and there is no value for the y since it is 0. This means that this ordered pair will be located on the x-axis.

Step-by-step explanation:

Angle of a circle = 360

x + 90 + 84 + 16 = 360

x + 190 = 360

x = 170°