If a person with a height of 58 inches takes 2,601 steps per mile, a person with a height of 64 inches takes 2,357 steps per mile, and a person with a height of 76 inches takes 1,985 steps per mile, what is the average number of steps of three 58-inch people, five 64-inch people, and two 76-inch people. Afterwards, find the weighted average number of steps. How does the average compare with the weighted average? Which value is a more accurate representation of the data?

Answer:

30% constituents=20 mL

10% constituents=180 mL

Step-by-step explanation:

x= 30% volume

y=10% volume

For our first equation, we know the total volume is 200 mL and is the sum

x+y=200

y=200-x (1)

For our second equation, we do a mass balance for 200 mL of final solution.

12% w/v = 0.12 g/mL

This means that in 1 mL of solution, we have 0.12 g of NaCl.

For any solution, concentration multiplied by volume will give the mass of NaCl:

Mass in x mL= C*V (g/mL) (mL)

So in 200 mL, we have

0.12*200 (g/mL) (mL)

=24g of NaCl

Cx*Vx + Cy*Vy=24

0.3x+0.1y=24 (2)

Substitute y=200-x into (2)

0.3x+0.1(200-x)=24

0.3x+20-0.1x=24

0.2x=24-20

0.2x=4

Divide both sides by 0.2

0.2x/0.2=4/0.2

x=20

Substitute x=20 into (1)

y=200-x

y=200-20

y=180

30% constituents=20 mL

10% constituents=180 mL

Answer:

8 hours

1 hour

8 hours

0.288675

Step-by-step explanation:

We complete the answer as follows;

mu = mean = 8 hours

sigma = standard deviation= 1 hour

Mu_x bar = mu = 8 hours

sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675

Answer:

D. A discrete data set because there are a finite number of possible values.

Step-by-step explanation:

Assuming in a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. The value given is from a discrete data set because there are a finite number of possible values.

In Mathematics, a discrete data is a data set in which the number of possible values are either finite or countable.

On the other hand, a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable.

Hence, if 725 couples used the XSORT method and 368 of them had baby girls; this is a discrete data because the values (725 and 368) are finite and can be counted.

4x+21+3x-5=121

7x+16=121

x=15

angle ABD =4(15)+21=81

Answer:

12/13

Step-by-step explanation:

First we must calculate the hypotenus using the pythagoran theorem

Now let's calculate sin0

So the exact value is 12/13

Answer:

C.) 12/13

Step-by-step explanation:

In a right angle triangle MN = 12, ON = 5 and; angle N = 90°

Now,

For hypotenuse we will use Pythagorean Theorem

(MO)² = (MN)² + (ON)²

(MO)² = (12)² + (5)²

(MO)² = 144 + 25

(MO)² = 169

MO = √169

MO = 13

now,

Sin O = opp÷hyp = 12÷13

Answer:

D

Step-by-step explanation:

Any number multiplied by an even number will always be even. 10 is an even number.

Answer:

d. 10 times a number is always even

Step-by-step explanation:

multiples of 9 contain 81 and 36 which one is even and the other is odd

multiples of 10 ONLY contain even numbers because   the unit digit for a multiple of 10 is 0.

So whenever you multiply a number by 10 it will be even

Answer:

3

Step-by-step explanation:

let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room

A living room is two times as long as the bedroom, so:

A = 2X

A living room is one and one-half times as wide as a bedroom, so:

B = 1.5Y

The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y

So, AB in terms of XY is:

A*B = (2X)*(1.5Y) = 3(X*Y)

It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the  bedroom.

Answer:

Step-by-step explanation:

Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:

f(1) = 1² - 1 = 1 - 1 = 0

f(2) = 2² - 1 = 4 - 1 = 3

f(3) = 3² - 1 = 9 - 1 = 8

f(4) = 4² - 1 = 16 - 1 = 15

Answer:

Step-by-step explanation:

Part A

(m + n)x = 4x + 5 + 8x - 5

(m + n)x = 12x   The fives cancel

Part B

(m - n)x = 4x + 5 - 8x + 5

(m - n)x = -4x + 10

Part C

The trick here is to put n(x) into m(x) wherever m(x) has an x.

m[n(x)] = 5(n(x)) + 5

m[n(x)] = 5(8x - 5) + 5

m[n(x)] = 40x - 20 + 5

m[n(x)] = 40x - 15

Answer:

  (–8, –6)

Step-by-step explanation:

The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...

  x/(x-intercept) +y/(y-intercept) = 1

  x/(-2) +y/2 = 1 . . . use the given intercepts

  x - y = -2 . . . . . multiply by -2

Then the system is ...

Using the first to substitute into the second, we get ...

  x - (2x +10) = -2

  -8 = x . . . . . . . . . . . add x+2, simplify

  y = 2(-8) +10 = -6

The solution is (x, y) = (-8, -6).

Answer:

(-8,-6)

Step-by-step explanation:

Got it right on edge soooo <3

Answer:

1/2 or 0.5

Step-by-step explanation:

To find out what 2/3 is out of 3/4, we just have to multiply them together to get our exact answer.

[tex]\frac{2}{3} *\frac{3}{4}=\frac{6}{12}=\frac{1}{2}[/tex]

Our final answer is 1/2 or 0.5.

Answer:

6

Step-by-step explanation:

We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.

We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.

Answer:

3(sqrt42) ft

Step-by-step explanation:

If l is side length of square patio, then area of patio would be l^2.

l^2 = 378

l = sqrt378 = 3(sqrt42)

Answer:

C

Step-by-step explanation:

The critical value we are asked to state in this question is the value of the z statistic

Mathematically;

z-score = (x- mean)/SD/√n

From the question

x = 11.58

mean = 12

SD = 1.93

n = 80

Substituting this value, we have

z= (11.58-12)/1.93/√80 = -1.946

Answer:

.006

:)

Step-by-step explanation:

8 servings can David make with the current amount of spice.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

The rice-to-spice ratio = 15:1

The 75 grams of rice in one serving will require

⇒75/15

⇒5 gram of spice.

David's inventory of 40 gram of spice is enough for

40 g/(5 g/serving) = 8 servings

Hence, 8 servings can David make with the current amount of spice.

Learn more about Ratio

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Answer:

8 colors

Step-by-step explanation:

There should be at least 8 different colors available for coloring the sections. The one color is used to color all the small triangles on the upper most and lower most lines, then there will be required another color so that the edges does not matches with the previous color. For the bigger hexagon shapes in the center we will require different colors for all of them because all of the hexagon shapes touches a line and an edge with each other.

Answer:

its 2 trust me

Step-by-step explanation:

its two cause if you think about it and color in the hexagons and triangles two different colors it works

Answer:

D.$80

Step-by-step explanation:

$5.26 x 15.5= $81.53

The closest amount to $81.53 is D.$80

Answer and Step-by-step explanation: To find the B-coordinate vector of x:

[tex]b_{1} = \left[\begin{array}{ccc}1\\2\\-3\end{array}\right][/tex] , [tex]b_{2} = \left[\begin{array}{ccc}-4\\-7\\11\end{array}\right][/tex], x = [tex]\left[\begin{array}{ccc}-10\\-17\\27\end{array}\right][/tex]

The augmented matrix will be:

[tex]\left[\begin{array}{ccc}1&-4&-10\\2&-7&-17\\-3&11&27\end{array}\right][/tex]

Transforming into reduced row-echelon form:

= [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&-1&-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&0&0\end{array}\right][/tex]

= [tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\0&0&0\end{array}\right][/tex]

The values for the vector will be:

x = 2

y = 3

The B-coordinate vector is of the form:

V = [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]

The B-coordinate vector of x is V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]

Answer:

Standard form: [tex]12x+3y-2=0[/tex]

A = 12, B = 3 and C = -2

Step-by-step explanation:

Given:

The equation:

[tex]y= -4x + \dfrac{2}3[/tex]

To find:

The standard form of given equation and find A, B and C.

Solution:

First of all, let us write the standard form of an equation.

Standard form of an equation is represented as:

[tex]Ax+By+C=0[/tex]

A is the coefficient of x and can be positive or negative.

B is the coefficient of y and can be positive or negative.

C can also be positive or negative.

Now, let us consider the given equation:

[tex]y= -4x + \dfrac{2}3[/tex]

Multiplying the whole equation with 3 first:

[tex]3 \times y= 3 \times -4x + 3 \times \dfrac{2}3\\\Rightarrow 3y=-12x+2[/tex]

Now, let us take all the terms on one side:

[tex]\Rightarrow 3y+12x-2=0\\\Rightarrow 12x+3y-2=0[/tex]

Now, let us compare with [tex]Ax+By+C=0[/tex].

So, A = 12, B = 3 and C = -2

Answer:

8w : 3.8974342 ≈ 3.9 or 4 (hope it help)

Step-by-step explanation:

1w : 2

2w : 2 + 10% = 2.2

3w : 2.2 + 10% = 2.42

4w : 2.42 + 10% = 2.662

5w : 2.662 + 10% = 2.9282

6w : 2.9282 + 10% = 3.22102

7w : 3.22102 + 10% = 3.543122

8w : 3.543122 + 10% = 3.8974342

3.8974342 ≈ 3.9 or 4

Answer:

option B

hope it was useful for you

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Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

Area of a circle = [tex]\pi r^2[/tex]

Finding the area of the circle, we need to know what the radius of the circle is. So, We would get the area of the circle.

Answer: 14384 ways

Step-by-step explanation:

With 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:

E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.

The marble arrangements are: (7,0,0,0) in 4!/3! = 4 ways, (6,1,0,0) in 4!/2! = 12 ways, (5,2,0,0) in 4!/2! = 12 ways, (5,1,1,0) in 4!/2! = 12 ways, (4,3,0,0) in 4!/2! = 12 ways, (4,2,1,0) in 4! = 24 ways, (4,1,1,1) in 4!/3! = 4 ways, (3,3,1,0) in 4!/2! = 12 ways, (3,2,2,0) in 4!/2! = 12 ways, (3,2,1,1) in 4!/2! = 12 ways, (2,2,2,1) in 4!/3! = 4 ways.

Total of ways = 4+12+12+12+12+24+4+12+12+12+4 = 120 as previously determined above for identical marbles and distinct jars.

Taking into account distinct colored marbles, the number of ways of marble distribution into 4 jars becomes as follows:

For (7,0,0,0) = 4*(7!/7!) =4. For (6,1,0,0) = 12*[7!/(6!)(1!)] = 84. For (5,2,0,0) =

12*[7!/(5!)(2!)] = 252. For (5,1,1,0) = 12*[7!/(5!)(1!)(1!)] = 504. For (4,3,0,0) =

12*[7!/(4!)(3!)] = 420. for (4,2,1,0) = 24*[7!/(4!)(2!)(1!)] = 2,520. For (4,1,1,1) =

4*7!/(4!)(1!)(1!)(1!)] = 840. For (3,3,1,0) = 12*]7!/(3!)(3!)(1!) = 1,680. For (3,2,20) = 12*]7!/(3!)(2!)(2!) = 2,520. For (3,2,1,1) = 12*]7!/(3!)(2!)(1!)(1!) = 5,040. For (2,2,2,1) = 4*]7!/(2!)(2!)(2!)(1!) = 2,520.

Total of ways as requested for distinct colored marbles and distinct jars = 4+84+252+504+420+2,520+840+1,680+2,520+5,040+2,520 = 14,384.

Answer:

Ok, we have two words:

"Signature"

The letters are: "S I G N A T U R E"

9 different letters.

Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.

For the first slot, we have 9 options.

For the second slot, we have 8 options (because on is already taken)

For the second slot, we have 7 options and so on.

Now, the total number of combinations is equal to the product of the number of options in each selection:

C = 9*8*7*6*5*4*3*2*1 = 362,880.

Now, our second word is Restaurant.

The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.

So first we do the same as beffore, 10 slots and we start with 10 options.

The total number of combinations will be:

C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

A lot of combinations, but we are counting only unique words.

For example, as we have two R, we are counting two times the word:

Restaurant (because we could permutate only the two letters R and get the same word)

So we must divide by two for each letter repeated.

we have 3 letters repeated, we divide 3 times by 2.

C = ( 3,628,800)/(2*2*2) = 453,600

Answer:

Volume of water in the pool is 3,182 ft^3

Step-by-step explanation:

In this question, what we want to calculate is the volume of water in the pool.

We proceed as follows;

diameter of pool = 30ft

depth: 2 to 7ft linearly

average depth = (2 + 7)/2 = 9/2 = 4.5 ft

Volume = area * average depth

V = pi * radius^2 * 4.5

where radius = diameter/2 = 30/2 = 15 ft

V = pi * 15^2 * 4.5

V = 22/7 * 225 * 4.5

V = 3,182.14 ft^3

which is 3,182 ft^3 to nearest whole number

The volume of water in the pool is; Volume = 3181 ft³

We are given;

Diameter of swimming Pool; d = 30 ft

Thus; radius; r = d/2 = 30/2 = 15 ft

We are told that the depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end.

Thus, average depth is;

h_avg = (2 + 7)/2

h_avg = 4.5 ft

Formula for area is; A = πr²

Thus;

A = π × 15²

A = 225π

Formula for volume here is;

Volume = Area × depth

Volume = 225π × 4.5

Volume = 3180.86 ft³

Approximating to a whole number gives;

Volume = 3181 ft³

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Answer:

AB = 2 sqrt(35)   (or 11.83 to two decimal places)

Step-by-step explanation:

Refer to diagram.

ABO'P is a rectangle (all angles 90)

=>

PO'  =  AB

AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)

using Pythagoras theorem.

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

Answer:

12

Step-by-step explanation:

The second diagram is most helpful for finding the surface area.

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Answer:

the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

C) 59

Step-by-step explanation:

Recall that;

[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]

Therefore, we can evaluate the series;

[tex]\sum_{k=1}^{6}(25-k^2)[/tex]

by summing the values of the series within that interval.

the values of the series are evaluated by substituting the corresponding values of k into the equation.

[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]

So, the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]