How many liters of water should be added to 18 liters of a 14% bleach solution so that the resulting solution contains only 10% bleach? original (l) added (l) new (l) amount of bleach 2.52 0 amount of solution 18 x 1.8 liters 7.2 liters 15.5 liters 25.2 liters

At 22nd percentile in the distribution of ages of homeless Floridians, an 18 year old would be considered.

Given that 78% of the ages are greater than or equal to 18 years. Hence.

18 years will be (100 - 78)th percentile

i.e. 22nd percentile.

Historically, policymakers and practitioners at every level of government have focused special attention on specific subpopulations.

Decision-makers are often concerned about children and young people due to their vulnerability. People in families with children make up 30 percent of the homeless population. Unaccompanied youth (under age 25) account for six percent of the larger group.

Finally, due to their service to our country, veterans are often analyzed separately from the larger group. They represent only six percent of people experiencing homelessness.

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Answer:

17 / 4

Step-by-step explanation:

To find the right sum, you need to....

Step #1: Find Δx

Step #2: Find [tex]x_k[/tex]

Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx

Step #4: Solve the right-hand sum equation

Answer:

84

Step-by-step explanation:

substitute n = 5 into the expression

16n + 4

= 16(5) + 4

= 80 + 4

= 84

Answer:

The expression will have the value of 84

Step-by-step explanation:

[tex]16n + 4[/tex]

given expression

Thus, plug n=5

[tex]16(5) + 4 \\ 80 + 4 = 84[/tex]

Finally, we get the value 84

Answer:

[tex]\frac{15x^{4}y^{3}}{5x^{3}} \ \ \text{and }\ -10x^{5}\div 2x^{3}y[/tex]

Step-by-step explanation:

the Quotient of Powers Property :

let a be a number where  a ≠ 0

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

……………………

[tex]\frac{15x^{4}y^{3}}{5x^{3}}[/tex]

[tex]= \frac{3 \times 5x^{3}\times x \times y^{3}}{5x^{3}}[/tex]

[tex]= \frac{3 \times x \times y^{3}}{1}[/tex]

[tex]= 3 x y^{3}[/tex]

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

[tex]-10x^{5}\div 2x^{3}y[/tex]

[tex]= [-5 \times (2x^{3}) \times x^2] \div [(2x^{3}) \times y][/tex]

[tex]= -5 \times x^2 \div y[/tex]

[tex]= -5 x^2 \div y[/tex]

Answer:

  A)  (-3, -2)

  B)  (-7, 3) and (-3, -2)

  C)  (4.074, 1.032)

Step-by-step explanation:

An ordered pair is a solution to an equation if it satisfies the equation — makes it true. The given points are solutions to the functions whose graphs pass through those points.

The function p(x) is defined to pass through points (4, 1) and (-3, -2).

The function f(x) is defined to pass through points (-7, 3) and (-3, -2).

These function definitions have point (-3, -2) in common.

(-3, -2) is the solution to the equation p(x) = f(x).

The function f(x) is defined to pass through points (-7, 3) and (-3, -2).

Two solutions to f(x) are (-7, 3) and (-3, -2).

We could identify other solutions, (1, -7) for example, but there is no need since the problem statement already gives us two solutions.

The solution to the equation p(x) = g(x) can be read from the graph as approximately (4.074, 1.032). This is close to the point (4, 1) that is used to define p(x). With some refinement (iteration), we can show the irrational solution is closer to ...

  (4.07369423957, 1.03158324553)

Answer:

A)  (-3, -2)

B)  (1, -7) and (5, -12)

C)  (4, 1) to the nearest whole number

Step-by-step explanation:

Function g(x):

[tex]g(x)=2(0.85)^x[/tex]

Function f(x) (straight line):

Given ordered pairs:

Calculate the slope of the straight line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-3-(-7)}=-\dfrac{5}{4}[/tex]

Using the Point-slope form of linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=-\dfrac{5}{4}(x-(-7))[/tex]

[tex]\implies y=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]

[tex]\implies f(x)=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]

Function p(x) (straight line):

Given ordered pairs:

Calculate the slope of the straight line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-1}{-3-4}=\dfrac{3}{7}[/tex]

Using the Point-slope form of linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=\dfrac{3}{7}(x-4)[/tex]

[tex]\implies y=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]

[tex]\implies p(x)=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]

We have been given two ordered pairs for function f(x) and function p(x).

One of those ordered pairs is the same for both functions.  

The solution to a pair of equations is their point(s) of intersection.  

Therefore, as both functions pass through (-3, -2), this is their point of intersection and therefore the solution.

The solutions for f(x) are any points on the line of the function f(x).  

To find any two points, substitute values of x into the found equation for f(x):

[tex]\implies f(1)=-\dfrac{5}{4}(1)-\dfrac{23}{4}=-7[/tex]

[tex]\implies f(5)=-\dfrac{5}{4}(5)-\dfrac{23}{4}=-12[/tex]

Therefore, two solutions are (1, -7) and (5, -12).

Part C

The solution to p(x) = g(x) is where the two graphs intersect.  From inspection of the graphs, p(x) intersects g(x) at approximately (4, 1).  

Therefore, the approximate solution to p(x) = g(x) is (4, 1).

To prove this, substitute x = 4 into the equations for p(x) and g(x):

[tex]\implies p(4)=\dfrac{3}{7}(4)-\dfrac{5}{7}=1[/tex]

[tex]\implies g(4)=2(0.85)^4=1.0440125=1.0\:(\sf nearest\:tenth)[/tex]

The actual solution to p(x) = g(x) is (4.074, 1.032) to three decimal places, which can be found by equating the functions and solving for x using a numerical method such as iteration.

Answer:

Step-by-step explanation:

9. the set containing all objects or elements and of which all other sets are subsets.

10. complement --> the amount in only one of teh sets

intersection --> the amount in both sets

11. 14 or -14

13. 46 1/2

14. 2 31/120

15. 1100% profit

16. 1200 gm

17. cube root of 7?

18. 6000 per year

Answer: Real, equal, rational.

Step-by-step explanation:

[tex]-x^2-8x-16=0\\-(x^2+8x+16)=0\\Multiply \ the\ left \ and\ right \ sides\ of\ the\ equation\ by \ -1:\\x^2+8x+16=0\\x^2+2*x*4+4^2=0\\(x+4)^2=0\\x+4=0\\x=-4.[/tex]

The arrow hits the top of a 3 meters tall wigwam at 0.054 seconds

The complete question is added as an attachment

The function is given as:

[tex]h(t) = -9.8t^2 + 28t + 1.5[/tex]

Set the height to 3

[tex]-9.8t^2 + 28t + 1.5 = 3[/tex]

Subtract 3 from both sides

[tex]-9.8t^2 + 28t - 1.5 = 0[/tex]

Apply the following quadratic formula

[tex]t = \frac{-b \pm \sqrt{b^2- 4ac}}{2a}[/tex]

So, we have:

[tex]t = \frac{-28 \pm \sqrt{28^2- 4*-9.8*-1.5}}{2*-9.8}[/tex]

This gives

[tex]t = \frac{-28 \pm \sqrt{725.2}}{-19.6}[/tex]

This gives

[tex]t = \frac{-28 \pm 26.93}{-19.6}[/tex]

Expand

[tex]t = \frac{-28 + 26.93}{-19.6}[/tex] and [tex]t = \frac{-28 - 26.93}{-19.6}[/tex]

This gives

t = 0.054 and t = 2.80

0.054 is less than 2.80

This means that the arrow hits the top of a 3 meter tall wigwam at 0.054 seconds

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Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

Based on the calculations, the coordinates of the mid-point of BC are (1, 4).

First of all, we would determine the initial y-coordinate by substituting the value of x into the equation of line that is given:

At the origin x₁ = 0, we have:

y = 2x + 1

y₁ = 2(0) + 1

y₁ = 2 + 1

y₁ = 3.

When x₂ = 2, we have:

y = 2x + 1

y₂ = 2(2) + 1

y₂ = 4 + 1

y₂ = 5.

In order to determine the midpoint of a line segment with two (2) coordinates or endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate is given by:

Midpoint = (x₁ + x₂)/2

Midpoint = (0 + 2)/2

Midpoint = 2/2

Midpoint = 1.

Midpoint on y-coordinate is given by:

Midpoint = (y₁ + y₂)/2

Midpoint = (3 + 5)/2

Midpoint = 8/2

Midpoint = 4.

Therefore, the coordinates of the mid-point of BC are (1, 4).

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Answer:

227.02

Step-by-step explanation:

[tex]400.00-172.98 \\ \\ =300 - 72.98 \\ \\ =230-2.98 \\ \\ =228-0.98 \\ \\ =227.02[/tex]

Answer:

227.02

Step-by-step explanation:

[tex]400.00\\-172.98[/tex]

To solve: First subtract 172 from 400, resulting in 228, then you may subtract the 0.98, leaving 227.02.

The grid of numbers with a row and column sum of 30 is

3   15  12

17   11   2

10  4   16

The grid in the question has a row sum and column sum of 15

The question implies that we create a similar grid with a row sum and column sum of 30

Represent the grid as follows:

a    b   c

d    e    f

g   h    j

So, we have the following sum of rows

a + b + c = 30

d + e + f = 30

g + h + j = 30

And, we have the following sum of rows

a + d + g = 30

b + e + h = 30

c + f + j = 30

Using trial by error, we have:

3 + 15+ 12  = 30

17 + 11 + 2 = 30

10 + 4 + 16 = 30

When the columns are added, we have

3 + 17 + 10 = 30

15 + 11 + 4 = 30

12 + 2 + 16 = 30

Hence, the grid of numbers is

3   15  12

17   11   2

10  4   16

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Answer:

87

Explanation:

This is an arithmetic sequence with common difference: 7 and first term: 17

Arithmetic sequence:

a + (n - 1)d                    where n is term position, d is difference, a is first term

17 + (n - 1)7

7n + 10

The eleventh term:

7n + 10

7(11) + 10

77 + 10

87

To Find :-

Solution :-

Given A.P.,

First term (a) is 17.

Common difference (d) = 24 - 17 => 7

We know that :

Here n would be 11.

>> t11 = 17 + (11 - 1) 7

>> t11 = 17 + (10) 7

>> t11 = 17 + (10) × 7

>> t11 = 17 + 70

>> t11 = 87

Therefore, eleventh term in the sequence is 87.

Answer:

5%

Step-by-step explanation:

price after discount :

9 600 - 9 600×40%

= 5760

Original price (price without profit) :

let x be the original price of the device.

x + x × 20% = 5760

Then

x = (5 760×100)÷120

  = 4 800

Original price increased by 30% :

4 800 + 4 800×30%

= 6 240

the discount needed to increase the profit by 10% :

[(9 600-6 240)÷9 600]×100

= 35%

Then

to increase the profit by 10% ,we have to reduce

the percent of discount to :

40% - 35%

= 5%

Daniel’s  answer was  wrong because he used  square root instead of the cubed root.

From the expression , which is [tex]t = 5.825 \sqrt[3]{3590/p}[/tex]

Then we can perform some operations to Solve for the value of  p.

Then we can make division on the  both sides of the equation  using 5.825 , then we have

2.304 = [tex]} (3590/p)^{\frac{1}{3}[/tex]

We can cube the both side of the equation to will eliminate the radical and  we will have

12.174 = 3590/p

then ,  p = 294.89  which implies that Natasha’s answer is correct.

Therefore , Daniel’s  answer was  wrong because he used  square root instead of the cubed root.

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The surface area of the given figure is 288 km²

From the question, we are to determine the surface area of the figure

The given figure is a square-base pyramid

Surface area of the pyramid = (10×10) + 4× 1/2(10×9.4)

Surface area of the pyramid = (100) + 2(94)

Surface area of the pyramid = 100 + 188

Surface area of the pyramid = 288 km²

Hence, the surface area of the given figure is 288 km²

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Answer: x = 3.5

Step-by-Step Solution:

Let us first label the figure.

Let the Triangle be ABC with a line DE || BC.

Now, in ∆ABC,

DE || BC (given)

=> AD/DB = AE/EC (by B.P.T)

Substituting the given values,

AD/DB = AE/EC

2/4 = x/7

1/2 = x/7

2x = 7

x = 7/2

=> x = 3.5

Therefore, x = 3.5

By using properties of right triangles and trigonometric functions, we conclude that the length of the side BC is 19 units.

In this problem we can use trigonometric functions to determine the length of the side BC in three steps:

Step 1

BE = AB/tan 60°

BE = 19√2 /4

Step 2

BD = BE/cos 45°

BD = 19/2

Step 3

BC = BD/sin 30°

BC = 19

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Juan's home is about 12 kilometers from Adam's.

In the study of mathematics and science, measurement is the fundamental idea. By quantifying an object's or event's qualities, we can compare them to those of other objects or occurrences. When discussing the division of a quantity, the phrase "measurement" is most frequently employed.

The distance between Adam's and Juan's residences on the map in centimeters is simply multiplied by the number of kilometers that each centimeter on the map represents, which in this case is 6, to determine how far Adam's house is from Juan's.

2 * 6 = 12

Which is our response.

Juan's home is about 12 kilometers from Adam's.

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Answer:

3 tiels are in the factor 2: 2 are labeled x and 1 is labeled negative

Answer: B

Step-by-step explanation:

A sector is a part of a circle that is formed by two radii, and an arc. So that the length of the safety railing required is 31.4 feet.

A sector is a part of a circle that is formed by two radii, and an arc, thus forming a central angle.

Thus the required length of safety railing can be considered as the arc of the sector.

So that;

length of an arc = (θ / [tex]360^{o}[/tex]) * 2[tex]\pi[/tex]r

where θ is the measure of the central angle of the sector, and r is the radius of the sector.

From the given question, θ = 45°, and r = 40 feet.

So that,

length of the safety railing = (45° / [tex]360^{o}[/tex]) * 2 * 3.14 * 40

                                 = 0.125 * 2* 3.14* 40

length of safety railing = 31.4

Therefore, the length of the safety railing required is 31.4 feet.

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There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

According to the given question.

Total number of items, n = 12

Total numbers of items to be selected, r = 5

Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.

[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]

Where,

[tex]^{n} P_{r}[/tex] is the total number of permutations.

n is the total number of objects.

r is teh total number of objects to be selected.

Therefore,

The number of different groups or permutaions of 5 items that can be selected from 12 distinct group

[tex]^{12} P_{5}[/tex]

[tex]= \frac{12!}{(12-5)!}[/tex]

[tex]= \frac{12!}{7!}[/tex]

[tex]= \frac{12\times11\times10\times9\times8\times7!}{7!}[/tex]

= 12 × 11 × 10 × 9 × 8

= 95040

Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

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Answer:

8%

Step-by-step explanation:

The approximate difference between the theoretical and experimental probabilities for rolling an even number is 8%

Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes. As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

Theoretical probability of rolling a cube and getting a even number is 1/2 or 50% as number of odd numbers and number of even numbers are equal.

Experimental probability = Favorable outcomes/Total outcomes

Experimental probability = 10/24 = 5/12 ≅ 42%

Thus approximate difference between these two equals 50% - 42% = 8%

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The amount of money that you will have to save to buy a car at the $9,500 price is $556.11 ($9,500 - $8,943.89).

The amount of money needed can be determined by calculating the future value of $7,500 invested at 4.5% for 4 years.

Then, the result, which is the future value, $8,943.89, is deducted from the $9,500 price, to determine the additional savings required.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value can also be determined using an online finance calculator, as follows.

N (# of periods) = 4 years

I/Y (Interest per year) = 4.5%

PV (Present Value) = $7,500

PMT (Periodic Payment) = $0

Results:

FV = $8,943.89

Total Interest = $1,443.89

Thus, the amount of money that you will have to save to buy a car at the $9,500 price is $556.11.

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We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

Given the following data:

Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

In order to calculate the airplane’s ground speed, we would apply the law of cosine:

C² = A² + D² - 2(A)(D)cosθ

Substituting the given parameters into the formula, we have;

C² = 700² + 60² - 2(700)(60)cos45

C² = 434,203.03

C = √434,203.03

C = 658.94 kph.

In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

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Answer:

$0.95/lb

Step-by-step explanation:

1 ton = 2000 lb

3 tons = 3 × 1 ton = 3 × 2000 lb = 6000 lb

$5700/(6000 lb) = $0.95/lb

Answer: $0.95/lb

Step-by-step explanation:

3 tons = 6000 pounds

Therefore, using ratio and proportion rules,

6000/5,700 = 1/x

x = 5700/6000 = 0.95

The price is $0.95, or 95 cents per pound.

The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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Answer:

length = 235 yd

width = 58 yd

Step-by-step explanation:

Let the width be W.

L = 4W + 3

perimeter = 2(L + W)

perimeter = 2(4W + 3 + W)

perimeter = 2(5W + 3) = 10W + 6

We are told the perimeter = 586 yd

10W + 6 = 586

10W = 580

W = 58

L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235

length = 235 yd

width = 58 yd

By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)

In this question we have the graph of a exponential function, whose expression have to be found based on the definition of exponential function:

y = a · bˣ      (1)

Where:

Now we find the values for a and b:

Initial value (x = 0, y = 3)

3 = a · b⁰

a = 3

Base of the exponential function (x = 1, a = 3, y = 6)

6 = 3 · a

a = 6 / 3

a = 2

By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)

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