Your neighborhood gym tracked how many days
number of days per week a member worked out.
each of its members worked out over the past week. Let G = the
Number of Days

Probability

Interpret the standard deviation of G.
O The mean number of days a member worked out would typically be
about 1.6764 from the expected number of
days
The mean number of days a member worked out
days.
typically be about 2.2913 from the expected number of
The number of days a member worked out would typically be about 1.6764 from the expected number of days.
The number of days a member worked out would typically be about 1.6764 from the mean about 68% of the
tme.

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.

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Answer:

a = -1/6

b = 7/6

c = 1

Step-by-step explanation:

[tex]f(x)=ax^3+2x^2+bx+c\\\\f(0)=a(0)^3+2(0)^2+b(0)+c\\\\1=c[/tex]

[tex]f(1)=a(1)^3+2(1)^2+b(1)+1\\\\4=a+2+b+1\\\\4=a+b+3\\\\1=a+b\\\\1-b=a[/tex]

[tex]f(-2)=(1-b)(-2)^3+2(-2)^2+b(-2)+1\\\\8=-8+8b+8-2b+1\\\\8=6b+1\\\\7=6b\\\\\frac{7}{6}=b[/tex]

[tex]1-b=a\\\\1-\frac{7}{6}=a\\ \\-\frac{1}{6}=a[/tex]

So, the true equation would be [tex]f(x)=-\frac{1}{6}x^3+2x^2+\frac{7}{6}x+1[/tex] if you substitute the coefficients and the constant.

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:

Slope of f(x) :

Y-intercept of g(x) :

The 1st option is correct.

Answer:

option d -1 is the answer

Answer:

I think C (19) might be wrong though

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

Answer:

3 1 4 7 9 3 8

Step-by-step explanation:

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

Answer:

  7 millicuries

Step-by-step explanation:

A period of 10 days is 2 times the half-life of 5 days.

In the first 5 days, the amount of the chemical decayed by half from 28 millicuries to 14 millicuries. In the next 5 days, it decayed by half again, from 14 millicuries to 7 millicuries.

10 days later, 7 millicuries of the chemical remains.

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.

Answer:

the solution of the equation.

Step-by-step explanation:

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]

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Answer:

0.940

Step-by-step explanation:

100 = 36 x pi x r^2

now divide both sides by 36pi

r^2 = 0.88419412...

then square root both sides

r = 0.94031597...

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.

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Answer:

Step-by-step explanation:

The value of the given trigonometric function is 1.1547.

The main trigonometric ratios are: sinβ, cosβ and tg β. From these ratios, you can calculate other trigonometric ratios such as sec β, cossec β and cotg β.

These ratios help you find the angles and the sides of a rectangle triangle.

The question asks [tex]\frac{2 *sin(30)}{cos (30}[/tex], for the angle 30° you have sin=1/2 and cos= [tex]\frac{\sqrt{3} }{2}[/tex].

Thus,

[tex]\frac{2 *sin(30)}{cos (30}=\frac{2 *\frac{1}{2} }{\frac{\sqrt{3} }{2} }=\frac{1}{\frac{\sqrt{3} }{2} }= \frac{2}{\sqrt{3} } =\frac{2\sqrt{3} }{3}=1.1547[/tex]

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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

[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.

[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

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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:

233km

Step-by-step explanation:

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%

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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.

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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.

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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:

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:

Step-by-step explanation:

(9-5+X)+ (39+211)

whats the Solution?

(9 - 5 + x) +  (39 + 211) =

4 + x + 39 + 211 =

254 + x

Answer:

254 + x

Step-by-step explanation:

(9 - 5 + x) +  (39 + 211) =

4 + x + 39 + 211 =

254 + x

Hope this helps

:)

Earth rotates one full rotation a day

So

It rotates 1° in

It rotates 150° in

The new coordinates of A is (-12,8)

To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is called mapping.

For any dilation the mapping will be (x,y) → (kx,ky).

Convert the point (x, y) to (-y, x) in order to rotate 90 degrees counter clockwise.

The given point is A(-4 ,6) ,after it has been rotated the new coordinates are A(-6,-4)

After reflecting it over x axis the new coordinated will be (-6,4)

Then dilating it with a scale factor of 2

The new coordinates of A is (-12,8)

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The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

To determine the surface area from the net of the box, we simply calculate the area of each shape.

From the given figure, we have the following shapes and dimensions:

The area is then calculated using:

Area = Areas of the rectangle + Area of the triangle

So, we have:

Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7

Evaluate the sum of products

Area = 430.35

Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

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Answer:577.35 square feet

Step-by-step explanation:

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