Question 3
1 pts
Use the diagram to answer the question. Find the measure of the
arc in degrees, type in a number only.

Answer:

Step-by-step explanation:

Let the yellow counters be represented by 'y' and black counters by 'b'.

Originally

After removing 21 counters

Taking the first ratio, equate it to b.

Now, substitute for 'b' in the second ratio.

Now, to find b :

Answer:

12

Step-by-step explanation:

Given ratio

yellow : black = 3 : 1

⇒ yellow : black = [tex]3x : x[/tex]

If 21 yellow counters are removed and the ratio becomes 5 : 4

[tex]\implies \textsf{yellow - 21: black = 5 : 4}[/tex]

[tex]\implies (3x - 21):x=5:4[/tex]

[tex]\implies \dfrac{3x - 21}{x}=\dfrac54[/tex]

[tex]\implies 4(3x - 21)=5x[/tex]

[tex]\implies 12x-84=5x[/tex]

[tex]\implies7x=84[/tex]

[tex]\implies x=12[/tex]

Substituting [tex]x=12[/tex] into the original ratio:

[tex]\implies \textsf{yellow : black} =3(12) : (12)=36:12[/tex]

So the total number of black counters = 12

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

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

=======================================================

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.

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

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.

Maturity Value: 9,159.08

Interest: 1,359.08

Answer:

The answer is C

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

it rlly easy

Answer:The answer is D

Step-by-step explanation:

I know this because all the area of each face is equal to 10+10+52+32+40 and that is equal to 144in. squared

Answer:

D :)

Step-by-step explanation:

wait, have you smiled today? its very important:)

Answer:

CTRL C to copy and CTRL V to paste

Step-by-step explanation:

please mark brainliest and btw if you dont want to get plagarized use quillbot

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:

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

Step-by-step explanation:

The radius,r is 1 unit

The sum of angles is = π + π/4

5π/4

The length of the arc = (5π/4)/2π • 2πr

= 5π/4 units

Answer:

4000

Step-by-step explanation:

40 x 100

Answer:

2

Step-by-step explanation:

I think it's 2 if it is wrong pls correct me

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:

£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:

16.50 + 10.50p ≤ 90

Step-by-step explanation:

add the parking amount and the ticket cause per person (p) to make it less than or equal to $90 since that’s the only amount of money that could be used

Answer:i dont think so..

Step-by-step explanation:

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: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

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

#SPJ2

Answer:

Part A) The length of rectangle is [tex]3x[/tex] [tex]cm[/tex]

Part B) The perimeter of the square is [tex]3x[/tex] [tex]cm[/tex]

Part C) [tex]20[/tex] [tex]cm[/tex]

Part D) [tex]39[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Part A) Find the length of the rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]P=8x[/tex] [tex]cm[/tex]

[tex]W=x[/tex] [tex]cm[/tex]

substitute and solve for L

[tex]8x=2(L+x)[/tex]

[tex]4x=(L+x)[/tex]

[tex]L=4x-x=3x[/tex] [tex]cm[/tex]

Part B) Find the perimeter of the square

we know that

The perimeter of a square is

[tex]P=4b[/tex]

we have that

[tex]b=(1/4)L[/tex]

substitute the value of L

[tex]b=(1/4)3x=(3/4)x[/tex] [tex]cm[/tex]

Find the perimeter of the square

Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4

Find the value of rectangle's perimeter

[tex]P=8x[/tex] [tex]cm[/tex] ------> [tex]P=8(4)=32[/tex] [tex]cm[/tex]

Find the value of square's perimeter

[tex]P=3x[/tex] [tex]cm[/tex] ------> [tex]P=3(4)=12[/tex] [tex]cm[/tex]

Find the difference

[tex]32[/tex] [tex]cm[/tex] [tex]-12[/tex] [tex]cm[/tex] [tex]=20[/tex] [tex]cm[/tex]

Part D) Find how many square cm greater the rectangle's area is than the square's area if x=4

Find the value of rectangle's area

[tex]A=(3x)(x)=3x^2[/tex] [tex]cm^2[/tex] ------> [tex]A=3(4^2)=48[/tex] [tex]cm^2[/tex]

Find the value of square's area

[tex]A=((3/4)x)^2[/tex] [tex]cm^2[/tex] ------> [tex]A=((3/4)(4))^2 = 9[/tex] [tex]cm^2[/tex]

Find the difference

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.

Answer:

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

Step-by-step explanation:

In decimal form, it is also 3.73205080...

hope this helps :)

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:

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:

119

Step-by-step explanation:

all angles in a triangle add up to 180

180-61-58=61

so missing inner angle is 61

then to solve 1:

180-61=119