A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random sample of 100 online customers and the number of packs ordered by a random sample of 100 walk-in customers.

Two dot plots are shown one below the other. The title for the top dot plot is Online Customers and the title for the bottom plot is Walk In Customers. Below the line for each dot plot is written Number of Packs. There are markings from 1 to 5 on each line at intervals of one. For the top line there are 0, 0, 1, 4, 5 dots respectively for marks from 1 to 5. For the bottom line there are 3, 6, 1, 0, 0 dots respectively for marks from 1 to 5. On the right side, towards the middle of the two plots is shown a dot symbol equal to 10 customers.

Which inference can be drawn about the buying pattern of the online customers versus that of the walk-in customers?

Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 1 pack.
Online customers buy an average of 5 packs compared with walk-in customers, who buy an average of 2 packs.
Online customers buy an average of 4 packs compared with walk-in customers, who buy an average of 2 packs.
Online customers buy an average of 5 packs compared with walk-in customers, who buy an average of 1 pack.

Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.

Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,

30° + ∠y + 30° = 180°

60° + ∠y = 180°

∠y = 180° - 60° = 120°

Hence, the measure of the ∠y is 120°.

Learn more about Supplementary Angles:

https://brainly.com/question/2882938

#SPJ1

Answer:

700π m ~ 2199 m

Step-by-step explanation:

diameter = d = 200 m

2 min 20s = 140 s

1 round / 40 s

140 = 40 * 3 + 20

so the athlete will cover 3 round and half

1 round = d * π

covered = c = 3 * 200 * π + 200/2 * π = 700 * π

[tex]base \: area = 44.3 \: {units}^{2} [/tex]

[tex]volume = 221.5 \: {units}^{3} [/tex]

the height of the given rectangular prism.

[tex]volume= base \: area \times height[/tex]

[tex]height = \frac{volume}{base \: area} [/tex]

[tex]height = \frac{221.5}{44.3} [/tex]

[tex]height = 5 \: units[/tex]

Therefore, the height of the given rectangular prism is 5 units.

The value of height of rectangular prism is,

⇒ h = 5 units

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The rectangular prism below has a base area of 44.3 units² and a volume of 221.5 units³.

Since, The volume of rectangular prism is,

⇒ V = Base area x height

⇒ 221.5 = 44.3 × h

⇒ h = 221.5 / 44.3

⇒ h = 5 units

Thus, The value of height of rectangular prism is,

⇒ h = 5 units

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ2

Earth rotates one full rotation a day

So

It rotates 1° in

It rotates 150° in

To Factorize Something:

 ⇒ means to put it into the simplest terms that when multiplied

     together transforms into the original form

Let's Solve:

  [tex]x^2-25=(x+5)(x-5)[/tex]

Let's Check:

  [tex](x+5)(x-5)=x*x+(-5)x+5x-25=x^2-5x+5x-25=x^2-25[/tex]

Answer: (x+5)(x-5)

Hope that helps!

Answer:

(x + 5)(x - 5)

Step-by-step explanation:

[tex]x^2-25[/tex]

[tex]=x^2-5^2[/tex]

[tex]x^2-5^2=\left(x+5\right)\left(x-5\right)[/tex]

[tex]=\left(x+5\right)\left(x-5\right)[/tex]

Answer:

the first one is 3

second. is -5/2

third is 5/-2

fourth is -1/3

fifth is 3

sixth is 0/-5

Answer:

Square Root of 10: (3, 4) and (2,1)

(-4,-2) and (-3, 1)

(-2, 3) and (1,2)

Square Root of 29:

(3,7) and (5,2)

(5, -2) and (3,3)

(4,-1) and (-1,1)

Step-by-step explanation: Just took the test

Answer:

2 real solutions

Step-by-step explanation:

[tex]f(x)=(x+3)^2-8\\\\0=(x+3)^2-8\\\\8=(x+3)^2\\\\\pm\sqrt{8}=x+3\\\\x=-3\pm\sqrt{8}[/tex]

Therefore, the function set at [tex]f(x)=0[/tex] has two real solutions (x-intercepts).

You can also check the discriminant of the function by expanding it:

[tex](x+3)^2-8=x^2+6x+9-8=x^2+6x+1\\\\b^2-4ac=6^2-4(1)(1)=36-4=32 > 0[/tex]

Since it's greater than 0, there's two real solutions

Answer: -21 + -18t

Step-by-step explanation:

-3(7+6t)

-3 x 7= -21

-3 x 6t= 18t

Answer:

4,771

Step-by-step explanation:

In the number 4771, the hundreds digit (7) is 10 times the tens digit (7).

The variable(s) in each triangle below 9, 12 and 16.

The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle.

Let the base of the triangle be 15.

So, the area is:

Area= 1/2*b*h

       = 1/2*15*20

       = 150.

Let the base of the triangle be 25.

So, the area is:

Area= 1/2*b*h

  150= 1/2*25*h

       = 300/25

    h =12

Now, using Pythagoras Theorem

15²= h²+x²

15²=12²+x²

225-144= x²

x²= 81

x=±9

Now, x+y=25

            y=16

Thus , values are 9,12 and 16.

Learn more about Area of Triangle here:

https://brainly.com/question/27683633

#SPJ1

Hi Student!

The first step that we need to take before solving this problem is understand what we need to do and what information we are given to do that.  So first they are asking for us to determine the solution (or find theta) in both degrees and radians.  The information that is given to us is the equation [tex]8* cos (\theta) = 4[/tex].

After completing the initial step, the next step is to actually start solving the equation for the unknown which in this case is theta or the angle.

Divide both sides by 8

Multiply by the inverse of cos

After solving for the unknown or theta, we were able to determine that the solution for our equation is 60 degrees.  Now we can move onto the final step which is to convert our answer to radians to complete the final part of the problem statement.

We can convert from degrees to radians by multiplying by π/180 which would get rid of degrees and give us radians.

Plug in the values

Simplify the expression

Therefore, our final answer is that our solution in degrees is 60 degrees and our solution in radians is π/3.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &25\\ r=rate\to 300\%\to \frac{300}{100}\dotfill &3\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=25(1 + 3)^{x}\implies A=25(4)^x~\hfill f(x)=25(4)^x[/tex]

4 is really 1 + 3, namely the growth rate is 300/100 or 300%.

so the quantity today, is 300% more than yesterday, so whatever it was yesterday plus three times that much, so the quantity is 4 times as large as yesterday's.

Based on the calculations, the two (2) statements which are true are:

Mathematically, range can be calculated by using this formula;

Range = Highest number - Lowest number

Range 1 = 71 - 32

Range 1 = 39.

Range 2 = 71 - 3

Range 2 = 68.

Therefore, the range of Data Set 2 is not smaller than the range of Data Set 1.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

For the total number of Data Set 1, we have:

F(x) = 32 + 41 + 51 + 63 + 66 + 71

F(x) = 324.

Substituting the parameters into the formula, we have:

Mean = [F(x)]/n

Mean 1 = [324]/6

Mean 1 = 54.

For the total number of Data Set 2, we have:

F(x) = 32 + 41 + 51 + 3 + 66 + 71

F(x) = 324.

Substituting the parameters into the formula, we have:

Mean 2 = [264]/6

Mean 2 = 44.

Difference = Mean 1 - Mean 2

Difference = 54 - 44

Difference = 10.

Therefore, the mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.

For the standard deviation of Data Set 1, we have:

SD₁ = √(1/n × ∑(xi - u₁)²)

SD₁ = √(1/5 × ∑(32 - 54)² + 1/5 × ∑(41 - 54)² + 1/5 × ∑(51 - 54)² + 1/5 × ∑(63 - 54)² + 1/5 × ∑(66 - 54)² + 1/5 × ∑(71 - 54)²)

SD₁ = 15.34.

For the standard deviation of Data Set 2, we have:

SD₂ = √(1/n × ∑(xi - u₂)²)

SD₂ = √(1/5 × ∑(32 - 44)² + 1/5 × ∑(41 - 44)² + 1/5 × ∑(51 - 44)² + 1/5 × ∑(3 - 44)² + 1/5 × ∑(66 - 44)² + 1/5 × ∑(71 - 44)²)

SD₂ = 24.88.

Therefore, the standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.

Read more on mean here: https://brainly.com/question/9550536

#SPJ1

Answer:

Step-by-step explanation:

Slope of f(x) :

Y-intercept of g(x) :

The 1st option is correct.

Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.117.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate are given as follows:

[tex]n = 45, \pi = \frac{9}{45} = 0.2[/tex]

Hence the margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.2(0.8)}{45}}[/tex]

M = 0.117.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

82cm

Step-by-step explanation:

The volume of the larger box is 240% that of the volume of the smaller box.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables

Volume of smaller box = area of base * height = 125 cm² * 12 cm = 1500 cm³

Volume of larger box = area of base * height = (1.6 * 125 cm²) * (12 + 6) cm = 3600 cm³

Ratio of volume = 3600/1500 = 2.4 = 240%

The volume of the larger box is 240% that of the volume of the smaller box.

Volume of the smaller box

Area of base of larger box

Volume

Percentage

15.3%

1) Lotte buys 50 cans for £17.

2) Sells 32 cans for 50 penny each.

3) Sells remaining for 20 penny each.

Total cost for 32 cans:

price of each can × total cans

50 penny × 32

1600 penny

Remaining Cans : 50 - 32 = 18 cans

Total cost of this 18 cans:

20 penny × 18

360 penny

[tex]\boxed{\bf 100 \ penny \ (p) = 1 \ pound \ ( \sf \£ )}[/tex]

Total Gained : 1600 + 360 = 1960 pence ≈ £19.6

Profit : selling price - cost price : 19.6 - 17 = £2.6

Profit In percentage:

[tex]\sf \dfrac{(selling \ price - cost \ price)\ x \ 100}{cost \ price}[/tex]

[tex]\rightarrow \sf \dfrac{2.6\ x \ 100}{17}[/tex]

[tex]\rightarrow \sf 15.294 \%[/tex]

[tex]\rightarrow \sf 15.3 \% \ \ (rounded \ to \ nearest \ three \ significant \ figure)[/tex]

Lottie's percentage profit based on the provided information is 15.29%

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per cent refers to one hundred percent.

The cost will be  £17 according to the question

Total  amount generated are;

32 cans * £0.50=£16

18 cans * £0.20=£3.60

Then the total will be £16 + £3.60 = £19.60

Profit =  amount generated- cost

=£19.60 - £17

= £2.60

The percentage profit:

[tex]= \frac{2.60}{17} * 100 \\\\=[/tex]

15.29%

Learn more about percentage at

https://brainly.com/question/24877689

#SPJ3

Answer:

8 quarts

Step-by-step explanation:

There are 4 quarts in 1 gallon

So in 2 gallons there would be 4 × 2 = 8 quarts

Its 2 Lquid gallons = 8 Liquid quart

Answer:

125

Step-by-step explanation:

JIK is congruent to MIL so they both equal 55. 360-55=305-55=250. now MIJ and LIK are gonna be equal so you can divide 250 by 2 which gives you 125. if you add them up it equals 360, a full circle! pls give me brainliest!

Answer:

Step-by-step explanation:

1) a) r =  7 cm

 [tex]\sf \boxed{\text{Volume of sphere=$\dfrac{4}{3}\pi r^3$}}[/tex]

                             [tex]\sf =\dfrac{4}{3}*3.14*7*7*7\\\\= 1436 \ cm^3[/tex]

 [tex]\sf \boxed{\text{\bf Surface area of sphere = $4\pi r^2$}}[/tex]

                                           = 4*3.14 * 7 * 7

                                           = 615.44 cm²

b) r= 8.4 cm

     [tex]Volume = \dfrac{4}{3}\pi r^3[/tex]

                  [tex]\sf =\dfrac{4}{3}*\dfrac{22}{7}*8.4*8.4*8.4\\\\= 2483.7 \ cm^3[/tex]

   Surface area = 4*3.14*8.4*8.4

                         = 887.04 cm²

      a) r = 6 cm

     [tex]\sf \boxed{\text{\bf Volume of hemisphere =$\dfrac{2}{3} \pi r^3$}}[/tex]

                                                [tex]\sf =\dfrac{2}{3}*3.14*6*6*6\\\\= 452.16 \ cm^3[/tex]

        [tex]\sf \boxed{\text{\bf Surface area of hemisphere=3 \pi r^2}}[/tex][tex]\sf \boxed{\text{\bf Surface area of hemisphere = $3 \pi r^2$}}[/tex]

                                                            = 3 * 3.14 * 6 * 6

                                                             = 339.12 cm²

If the two prisms are stacked on top of each other then the height of the prism is 30 inches. Then the volume of the prism will be 1080 in³.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

A toy store is building a display with two rectangular prisms.

The base of each prism is a square with an edge length of 6 inches.

One prism is 10 inches tall and the other is twice as tall.

The two prisms are stacked on top of each other.

Then the total volume of the display will be

The volume of the prism will be

Volume = Base area × Height

Then the height of the second prism will be

h₂ = 2 × 10 = 20 inches

Then the volume of the prism will be

Volume = 6 × 6 × 10 + 6 × 6 × 20

Volume = 360 + 720

Volume = 1080 cubic inches

More about the rectangular prism link is given below.

https://brainly.com/question/12649592

#SPJ1

If a histogram has one-minute increments representing the data, we will see that:

If there are is a histogram which has one-minute increments to represent the data, the shape will be that of a normal curve thanks to most data being  between the 6 and 9 minute mark.

The fact that the histogram will have a normal curve means that the mean will be approximately equal to the median because the mean and median are usually equal for normal distributions.

Find out more on normal distributions at https://brainly.com/question/23418254.

#SPJ4

Answer:

If a histogram has one-minute increments representing the data, we will see that:

A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes

The shape of the histogram can be approximated with a normal curve.

The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

Step-by-step explanation:

Answer:

3 1 4 7 9 3 8

Step-by-step explanation:

The opposite faces are D and F, A and C, and B and E. Then the correct options are A, B, and E.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

This net will be folded to form a prism.

A net of a rectangular prism.

From top to bottom, the rectangles are labeled B, D, E, and F.

The left side is labeled A and the right side is labeled C.

Then the pairs of faces will be opposite one another when the prism is created will be

BD, DE, EF, FB, AD, DC, CF, FA, AB, BC, BE, and EA all are the adjacent side faces.

AC, BE, and DF are the opposite faces.

Then the correct options are A, B, and E.

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ1

Answer:

3units squared

Step-by-step explanation:

1/2 the base times the height

1/2 * 2 * 3 = 3

Answer:

Start at (0,1) and then go up 4 spaces over 1 to the left and repeat going up 4 over 1. To complete the graph by getting it to go behind the y intercept of (0,1) you go from the y intercept down 4 over 1 to the right and repeat going down 4 over 1.

For plotting a line, we need to plot points [tex](0,1)[/tex] and [tex](\frac{-1}{4},0)[/tex] on the cartesian plane and join them to form a line.

For plotting a line, we only need two points to graph a line. With that idea, we take advantage of the two “convenient” points which can easily be solved algebraically from the equation of the line; namely, the x-intercept (x,0) and y-intercept (0,y).

[tex]y = 4x + 1\\\\Put\ x = 0 \\y = 1\\we\ get\ (0,1)\ as\ a\ point\ lying\ on\ the\ line. \\\\Put\ y = 0 \\x = \frac{-1}{4} \\we\ get\ (\frac{-1}{4} ,0)\ as\ a\ point\ lying\ on\ the\ line. \\[/tex]

Learn more about plotting a line here

https://brainly.com/question/16321364

#SPJ2

Answer: A= 68 square centimeters

Step-by-step explanation:

A= [tex]B^{1}[/tex] +[tex]B^{2}[/tex]/2 x h

6+11=17

17/2=8.5

8.5 x 8= 68

Answer:

680

Step-by-step explanation:

Use the binomial coefficient where you choose [tex]k=3[/tex] numbers out of [tex]n=17[/tex] possible numbers and find the total amount of combinations since order does not matter:

[tex]\displaystyle \binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{17}{3}=\frac{17!}{3!(17-3)!}\\\\\binom{17}{3}=\frac{17!}{3!(14)!}\\\\\binom{17}{3}=\frac{17*16*15}{3*2*1}\\\\\binom{17}{3}=680[/tex]

Thus, you can make 680 three-non-repeating-number codes

Answer:

CD ≈ 26.0 cm

Step-by-step explanation:

using the sine ratio in right triangle ABD

sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{BD}[/tex] = [tex]\frac{12}{BD}[/tex] ( multiply both sides by BD )

BD × sin35° = 12 ( divide both sides by sin35° )

BD = [tex]\frac{12}{sin35}[/tex] ≈ 20.92 cm

using the sine rule in Δ BCD

[tex]\frac{BD}{sinC}[/tex] = [tex]\frac{CD}{sinB}[/tex] , that is

[tex]\frac{20.92}{sin52}[/tex] = [tex]\frac{CD}{sin102}[/tex] ( cross- multiply )

CD × sin52° = 20.92 × sin102° ( divide both sides by sin52° )

CD = [tex]\frac{20.92sin102}{sin52}[/tex] ≈ 26.0 cm ( to 3 significant figures )

Answer:

CD = 26.0 cm (3 sf)

Step-by-step explanation:

Sine Rule for side lengths

[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find length BD:

[tex]\implies \sf \dfrac{AB}{\sin ADB}=\dfrac{BD}{\sin BAD}[/tex]

[tex]\implies \sf \dfrac{12}{\sin 35^{\circ}}=\dfrac{BD}{\sin 90^{\circ}}[/tex]

[tex]\implies \sf BD=\dfrac{12\sin 90^{\circ}}{\sin 35^{\circ}}[/tex]

[tex]\implies \sf BD=20.92136155...cm[/tex]

Find length CD:

[tex]\implies \sf \dfrac{BD}{\sin BCD}=\dfrac{CD}{\sin DBC}[/tex]

[tex]\implies \sf \dfrac{20.921...}{\sin 52^{\circ}}=\dfrac{CD}{\sin 102^{\circ}}[/tex]

[tex]\implies \sf CD=\dfrac{20.921...\sin 102^{\circ}}{\sin 52^{\circ}}[/tex]

[tex]\implies \sf CD=25.96941667...cm[/tex]

Therefore, CD = 26.0 cm (3 sf)

Answer:

8

Step-by-step explanation: