A pool company claims that for optimal results customers should use 20 cups of 73% chlorine solution to treat their pools unfortunately the company only has an 80% chlorine solution and a 60% chlorine solution In stock how many cups of Each chlorine solution should be mixed to create the optimal solution?

Answer:

Step-by-step explanation:

To find the values of the angle which makes maximum r you use the derivative of r

[tex]\frac{dr}{d\theta}=\frac{1}{3}sin(3\theta)[/tex]

If you equals this derivative to zero you obtain the value of the angle:

[tex]\frac{dr}{d\theta}=0\\\\cos3\theta=0\\\\3\theta=\frac{\pi}{2}\\\\\theta=\frac{\pi}{6}[/tex]

However, the values of 5π/6 and 9π/6 are also available, because makes the sinusoidal function equal  to 1.

hence, the answer is:

[tex]\theta_1=\frac{\pi}{6} \\\\\theta_2=\frac{5\pi}{6}\\\\\theta_3=\frac{9\pi}{6}=\frac{3\pi}{2}[/tex]

answer b

The maximum values of r for the polar equation r=4+3 sin 3θ occur at the angles where sin 3θ = 1, within the range of 0 to 2π. Solving the equation 3θ = nπ/2 for odd integers n gives the values of θ where r is maximum, which must be checked against the range [0, 2π].

We can find the maximum values of r for the polar equation r=4+3 sin 3θ by looking for the values of θ that give the maximum value for the sinusoidal function sin 3θ.

Since we know that the sine function reaches its maximum value of 1, we can find the values of θ that satisfy the condition sin 3θ = 1 within the given range of θ from 0 to 2π.

Thus, the equation becomes r = 4 + 3(1), which simplifies to r = 7.
Now, we seek to solve 3θ = nπ/2 where n is an odd integer since the sine function is maximum at π/2, 3π/2, 5π/2, and so on. Therefore, we obtain θ values of π/6, π/2, 5π/6, etc., until we reach the limit of 2π.

We must also consider the range of the function which brings us to the fact that θ must lie within [0, 2π].
Thus, we have to evaluate this for values such as θ = π/6, 5π/6, 3π/2, and so on, checking which of these are within the specified range and hence can be considered valid solutions where maximum r values occur.

Answer:

12

Step-by-step explanation:

f(x)=3x+9

f(12) = 3*12 +9

       36+9

        45

f(8) = 3*8+9

     =24+9

     = 33

f(12) - f(8) = 45-33

                    12

Answer:

19 !

Step-by-step explanation: make me brainlist

Answer:

D

Step-by-step explanation:

2  ( x − 3 )

x  ( x + 1 )

Answer:

ANSWER IS D

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

To solve this, we can add 9 to each side of the equation. This will cancel out the 9 to only leave x by itself on one side

Once we add 9 to each side, we will be left with x=17

Answer:

1)option b

2)option a

Step-by-step explanation:

1) circumference = 62.8 in

=> 2πr= 62.8

=> r= 62.8/(2×3.14)= 10 in

diameter = 2×10 in = 20 in

2)diameter = 14m

radius = 7 m

Area of the circle= πr² =3.14(7)²=3.14×49

= 153.86

=153.9 m²

Answer:

Q1) B

Q2) A

Step-by-step explanation:

Q1) The equation for working out the circumference of a circle is 2 × π × r or π × d, but here we are asked to do the reverse so,

π × d = 62.8

d = 62.8 ÷ π

d = 19.9

So the answer to the Q1) is 20 inches

Q2) We have to work out the area of the circle so we utilise the formula

π × r² . We only have the diameter but we can half it to find the radius so

14 ÷ 2 = 7. So 7 is the radius, now we substitute into the formula π × r²

3.14 × 7² = 153.86

Answer:

The answer is a

Step-by-step explanation:

On a coordinate plane, a line goes through points (negative 1, negative 2) and (0, 1).

The linear function that does not have the same y-intercept  as the other functions is: Option A

How to find the y-intercept?

The general form of the equation of a Line in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

1) In this graph, the y-intercept which is where the line crosses the y-axis is: y = 1

2) The y-intercept in the equation y = -8x + 3 is:

y = 3

3) The y-intercept here will be:

y = 3

4) The y-intercept in the equation y = 2x + 3 is:

y = 3

The 90% confidence interval = 48.603 < μ < 55.397

Explanation:

Given:

Mean = 52

Standard deviation = 14.6

Sample size, n = 50

Confidence Interval, c = 90%

                                  c = 0.9

Significance level, α = 1 - c

                                  = 1 - 0.9

                                  = 0.1

Critical value, z(α/2) = z(0.05) = 1.645

Critical value = ± 1.645

Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]

                             [tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]

Limits of 90% confidence interval are given by:

Lower limit = μ - E

                  = 52 - 3.397

                  = 48.603

Upper limit = μ + E

                  = 52 + 3.397

                  = 55.397

Thus, 90% confidence interval = 48.603 < μ < 55.397

Steph's parents need to buy 1654 meters more of fencing.

To find out how many more meters of fencing Steph's parents need to buy, let's first calculate the perimeter of the square fence.

Since all sides of a square are equal, if each side measures 666 meters, then the perimeter of the square is:

[tex]Perimeter = 4 * Side[/tex]

Given that each side measures 666 meters:

[tex]Perimeter = 4 * 666[/tex]

Now, let's calculate the total perimeter:

[tex]Perimeter = 4 * 666[/tex]

[tex]Perimeter = 2664 meters[/tex]

Now, let's see how much fencing they already have and how much more they need to buy:

[tex]Fencing already obtained = 1010 meters[/tex]

[tex]Fencing needed = Perimeter - Fencing already obtained[/tex]

[tex]Fencing needed = 2664 meters - 1010 meters[/tex]

[tex]Fencing needed = 1654 meters[/tex]

Complete correct question:

Steph needs to help her parents put a fence around their pool. They want the fence to be square and want each side to measure 666 meters. They already have 101010 meters of fencing. How many more meters of fencing should they buy?

Answer:

y = x + 2, assuming you need it in slope-intercept form.

Step-by-step explanation:

Isolate the y-value by dividing 2 from both sides of the equation.

Answer:I have no idea I just need points sorry lol :(

Step-by-step explanation:

Answer:

In accounting, residual value is another name for salvage value, the remaining value of an asset after it has been fully depreciated. The residual value derives its calculation from a base price, calculated after depreciation.

Answer:

290=(20+c)+(40+g)

Step-by-step explanation:

c=Gabe's children's age

g=Laura's grandchildren's age

all add up to 290

Answer:

-9.8n + 11.1

Step-by-step explanation:

1. Combine like terms

      -5.8n - 4n = -9.8n

      3.1 + 8 = 11.1

2. -9.8n +11.1

Answer:

-9.8n+11.1

Step-by-step explanation:

You have to add all like terms. That means that -5.8n and -4n have to be added together along with 3.1 and 8. That gets you -9.8n+11.1.

Answer: [tex]10m+3[/tex]

Combine Like Terms

[tex]4m+6m+3\\(4m+6m)+(3)\\10m+3[/tex]

Answer:

10m + 3

Step-by-step explanation:

You are supposed to add the like terms which are 4m and 6m to equal 10m

4m + 6m + 3

=

10m + 3

please give me brainliest

Answer:

I don’t see photo

Step-by-step explanation:

I

Don’t

See

The

Photo

Answer: Alex earned $87.5 more than Ben

Step-by-step explanation:

Last year,Alex earned a monthly salary of $250. This year, he received a pay increase of 25%. It means that the amount by which his pay was increased is

25/100 × 250 = 62.5

His new monthly salary would be

250 + 62.5 = $312.5

Last yearBen earned a monthly salary of $180. This year, he also received a pay increase of 25%. It means that the amount by which his pay was increased is

25/100 × 1800 = 45

His new monthly salary would be

180 + 45 = $225

The difference between the amount earned by Alex and Ben monthly is

312.5 - 225 = $87.5

Answer:

[tex]z(1910)=1.3429\\\\z(1230)=-0.9006\\\\z(2190)=2.2404\\\\z(1380)=-0.3558[/tex]

Step-by-step explanation:

-Given the population mean is [tex]\mu=1491[/tex]and  the standard deviation is [tex]\sigma=312[/tex], we calculate the z-scores using the formula:

[tex]z=\frac{\bar x-\mu}{\sigma}[/tex]

#The z-score for 1910 can be calculated as:

[tex]z(1910)=\frac{x-\mu}{\sigma}\\\\=\frac{1910-1491}{312}\\\\=\frac{419}{312}\\\\=1.3429[/tex]

#The z-score for 1230can be calculated as:

[tex]z(1230)=\frac{x-\mu}{\sigma}\\\\=\frac{1230-1491}{312}\\\\=\frac{-281}{312}\\\\=-0.9006[/tex]

#The z-score for 2190 is calculated as follows:

[tex]z(2190)=\frac{x-\mu}{\sigma}\\\\=\frac{2190-1491}{312}\\\\=\frac{699}{312}\\\\=2.2404[/tex]

#The z-score for 1380 is calculated as:

[tex]z(1380)=\frac{x-\mu}{\sigma}\\\\=\frac{1380-1491}{312}\\\\=\frac{-111}{312}\\\\=-0.3558[/tex]

Answer:

3/5

Step-by-step explanation:

Answer:

Your answer should be 3/5

Answer: A − 9/7

Step-by-step explanation:

Hi, to answer this question we have to convert all the numbers into decimal form.

-3 1/3 = - (3x3+1)/3 =-10/3 = - 3.3334

-4/5 = -0.8

Since he number must greater than −3 1/3 but less than − 4/5.

−3 1/3 < x < − 4/5.

- 3.3334 < x < -0.8

The correct option is A = -9/7 , because in decimal form is equal to -1.28-

- 3.3334 < -1.28 < -0.8

Answer:

81,3 ft to the nearest tenth.

Step-by-step explanation:

Tan 19 = 28 / h  where h = the horizontal distance.

h = 28 / tan 19

h = 81.3 ft.

Final answer:

To calculate the horizontal distance between the boat and the shark, the tangent of the angle of depression (19 degrees) is set equal to the vertical depth (28 ft) divided by the horizontal distance. The horizontal distance is found to be approximately 81.32 ft.

Explanation:

To determine the horizontal distance between the boat and the shark when the shark is swimming 28 ft below sea level and the angle of depression from the boat to the shark is 19 degrees, we can use trigonometry, specifically the tangent function. The angle of depression corresponds to the angle between the horizontal sightline from the boat and the line of sight to the shark.

In the right-angled triangle formed by the vertical depth of the shark, the horizontal distance to the shark, and the line of sight from the boat, the angle at the boat's position is 19 degrees and the opposite side (depth) is 28 ft. Using the formula tangent of an angle equals the opposite side divided by the adjacent side (tan(θ) = opposite/adjacent), we get:

tan(19°) = 28/horizontal distance

Therefore, the horizontal distance = 28 / tan(19°) = 28/0.3443

Calculating this, we get the horizontal distance to be approximately 81.32 ft.

Answer:

The amount the $20.000 will be worth in 17  years at compound interest is $65068.443

Step-by-step explanation:

Here we have the Principal, P = $20,000.00

The annual interest rate, r = 7% = 0.07

Time , t = 17 years

Number of compounding period per year, m = quarterly = 4

The compound interest can be found from the following formula;

[tex]Amount, \ A = P \left (1 + \frac{1}{r} \right )^{mt}[/tex]

Therefore, by plugging the values of the equation parameters, we have;

[tex]Amount, \ A = 20000 \left (1 + \frac{0.07}{4} \right )^{4 \times 17} = \$ 65068.443[/tex]

Therefore, the amount the $20.000 will be worth in 17  years at compound interest = $65068.443.

So, the amount of $20,000 be worth in 17 years if it is invested at 7% and compounded quarterly is $65068.443 and this can be determined by using the compound interest formula.

Given :

A newborn child receives a $20,000 gift toward college education from her grandparents.

The formula of compound interest is given by:

[tex]\rm A= P(1+\dfrac{r}{n})^{nt}[/tex]

where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest applied per time period and t is the number of periods elapsed.

Substitute the known terms in the above formula:

[tex]\rm A = 20000(1+\dfrac{0.07}{4})^{4\times 17}[/tex]

[tex]\rm A = 20000(1.0175)^{68}[/tex]

A = $65068.443

So, the amount of $20,000 be worth in 17 years if it is invested at 7% and compounded quarterly is $65068.443.

For more information, refer to the link given below:

https://brainly.com/question/22803385

Answer:

650

Step-by-step explanation:

2sf= the first two figures

so you count to the first two sf numbers so in this case

it would be 64 then you look at the next one.  But if it is 4 or below  you round or if it is 5 and above you rounded up

in this case the third digit is a 6 so you would round up to 5

answer =650

The number 646.42 can be rounded to two significant figures by increasing the second significant figure up by one because the third figure is 6 which is greater than 5. Therefore, 646.42 becomes 650.

You are requesting to round the number 646.42 to two significant figures (SF). Significant figures are the meaningful digits in a number. For example, in 646.42, there are five significant figures: 6, 4, 6, 4, 2.

To round to two significant figures, we look at the number in the third position, which is another 6. If this number is 5 or greater, we round the second significant figure up. If it is less than 5, we keep the second figure the same. Here, the next number after the two significant figure (6 and 4) is 6, which is more than 5, so you will round 4 up to 5.

Thus, rounded to two significant figures, 646.42 becomes 650.

https://brainly.com/question/19166897

#SPJ3

Answer:

2 km

Step-by-step explanation:

4π = π × r²

r² = 4

r = 2

Answer:

x=31

Step-by-step explanation:

(x-31)/4=0

multiply each side by 4 so that you have x-31=0.

x-31=0

add 31 to each side.

x=31

Answer:

No, unless you set it equal to zero.

Step-by-step explanation:

(x-31)/4=0

((x-31)/4) times 4 = 0 times 4

x-31=0

x-31 +31 =0 + 31

x=31

Answer:

(a)Sample 1

The Mean = 20

The median = 25

Sample 2

The Mean = 31

The median = 60

(b) Sample 1 has the least spread

Sample 1 has the least deviations from the mean

(c) Sample 1 align with the third sample

The least representative of the population is sample 1

Step-by-step explanation:

The mean is ∑fx/∑f

∑fx = 30 + 25 + 10 + 25 + 10 = 100

∑f = 5

Mean = 100/5 = 20

For the median, we arrange the data in increasing order;

10, 10, 25, 25, 30

The median = the middle number = 25

Sample 2

The mean is ∑fx/∑f

∑fx = 5 + 60 + 10 + 30 + 50 = 155

∑f = 5

Mean = 155/5 = 31

For the median, we arrange the data in increasing order;

5, 10, 30, 50, 60

The median = the middle number = 30

(b) Sample 1 range =$30 -$10 = $20

Sample 2 range =$65 -$5 = $60

Sample 1 has the least spread

Sample 1 standard deviation = 9.354

Sample 2 standard deviation =24.083

Sample 1 has the least deviations from the mean

(c) $30, $25, $20, $20, $25

Mean = 24

$20, $20, $25, $25, $30

Median = $25

∑fx = 120

Therefore sample 1 align with the third sample

The least representative of the population is sample 1 with ∑fx = 100.

To find the value of 6 units when 32 units are worth $2,080, calculate the per unit value by dividing $2,080 by 32 to get $65 per unit, then multiply by 6 to obtain the value of 6 units, which is $390.

The question asks to find the value of 6 units given that 32 units represent $2,080. To solve this, we first find the value of one unit by dividing the total amount of money by the number of units. So, $2,080 divided by 32 units gives us the value per unit.

Next, we multiply the value of one unit by the number of units we want to find the value for, which is 6 units. This will give us the value for 6 units. Let's go through the steps:

Therefore, the value of 6 units is $390.

Answer: 5=x

Step-by-step explanation:

Ok, so if F(x)=15, then the equation would look like this: [tex]15=5x-10[/tex]

The next step would be to add the 10 over from the right to the left side to get [tex]25=5x[/tex]

Now divide both sides by 5 to get the answer.

Answer:

70

Step-by-step explanation:

In this problem, 27 adults conduct a survey.

In the results of the survey, it is found that 35% of the adults are concerned with poverty.

If we call:

x = number of adults surveyed

y = adults concerned with poverty

This means that we can write the following relationship:

[tex]y=0.35x[/tex] (1)

where [tex]0.35[/tex] represents the percentage of adults concerned with poverty, rewritten in decimal form ([tex]0.35=\frac{35}{100}[/tex])

Later, we are told that 200 adults are surveyed, so now we have

x = 200

So substituting into eq(1) we can find how many of these adults are concerned with poverty:

[tex]y=0.35\cdot 200 =70[/tex]

Answer:

Step-by-step explanation:

Answer:

c .54 w/ bar

Step-by-step explanation: