Pure salt is made up of sodium and chloride. Each gram

of salt contains 0.393 g of sodium. About how much

sodium is in 55.7 g of pure salt?

24 g

29 g

9 g

90 g

Answer:

Step-by-step explanation:t55

An octagon has 8 sides. If each of them has a length of x, then the perimeter is 8x which is twice the perimeter of the square. (The square has a perimeter of 4x)

A dodecagon is a 12 sided regular polygon. It will have 12 sides all of which are equal to x. Since the square has a perimeter of 4x and the dodecagon has a perimeter of 12x the perimeter of the dodecagon is 3 times that of the given square.

If the  dividend of  $1.50 is expected in two months. The European put price is $3.03.

Given:

K=50, r=0.1, σ=0.3, and T=0.25

First step is to find the stock price

S0 = 50−1.50e^ -0.1667×0.1

SO=48.52

Second step is to find di and d2

d1=In(48.52/50)+(0.1+0.09/2)0.25/0.3√0.25

d1 = 0.0414

d2=d1-0.3√0.25

d2 = -0.1086

Third step is to calculate European put price

European put price=-50N(0.1086)e^ -0.1×0.25−48.52N(−0.0414)

European put price=50×0.5432e -^0.1×0.25−48.52×0.4835

European put price=$3.03

Therefore If the  dividend of  $1.50 is expected in two months. The European put price is $3.03.

The complete question is:

Calculate the price of a three-month European put option on a non-dividend-paying stock with a strike price of $50 when the current stock price is $50, the risk-free interest rate is 10% per annum, and the volatility is 30% per annum. What difference does it make to your calculations in problem 29 if a dividend of $1.50 is expected in two months?

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All of the values that m could take include the following: -3.5, -5, and -7

In Mathematics and Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

This ultimately implies that, all number lines would primarily increase in numerical value towards the right from zero (0) and decrease in numerical value towards the left from zero (0).

From the number line shown in the image attached below, we can logically deduce the inequality:

x ≤ -3

Therefore, the numerical values for x could be equal to -3.5, -5, and -7

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability that the sample contains exactly 4 minorities is 0.0577

We know that 25% of the employees of a large company are minorities. So, from any set of N employees that we ranodmly select from that large company, we can estimate that the number of minorities there is:

0.25*N

Now, we want to find the probability that the sample contains exactly 4 minorities.

Then we need to compute:

\(P = 0.25^4*0.75^3\)

We also need to count the permutations for that probability, then we need to add the factor:

\(P = 0.25^4*0.75^3*(\frac{7!}{4!*3!} )\)

Solving that we will get:

\(P = 0.25^4*0.75^3*(\frac{7!}{4!*3!} )\\\\P = 0.25^4*0.75^3*(\frac{7*6*5}{3*2} )\\\\P = 0.0577\)

That is the probability.

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Answer:

$3000

Step-by-step explanation:

The computation of the total medical bill is shown below:

Let us assume the total medical bill be $x

For plan 1,

As he pays 10% of x, So 10% of x - (1)

For plan 2 ,

As he pays 5% of x + 150, that is 0.05 of x + 150 - (2)

Now equate both the equations

0.10x = 0.05x + 150

0.05x=150

x = $3000

Total medical bill = $ 3000

Given that there are 5 red 4 green and 3 blue balls

The probability of picking a blue and a red ball with replacement is

The probability of picking a blue ball

= 3/(5 + 4 + 3)

= 3/12

The probability of picking a red ball (after replacing the blue picked earlier)

= 5/(5 + 4 + 3)

= 5/12

Hence the probability of picking a blue and a red ball with replacement is

= 3/12 * 5/12

= 15/144

= 5/48

It will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

To find out how long it will take, we can use the formula for compound interest:

A = P(1 + r)^t

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the number of years.

In this case, we want to find out how long it will take for $100 to reach $500 when it grows at 10 percent per year. So we can plug in the values and solve for t:

500 = 100(1 + 0.10)^t

5 = (1.10)^t

Taking the natural logarithm of both sides:

ln(5) = t ln(1.10)

t = ln(5) / ln(1.10)

t = 14.87 years

So it will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

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Answer:

The answer is "\(125 \ in^2\)"

Step-by-step explanation:

There is a base of five on every triangular face and a height of ten in. The field of the formulation

\(A = (\frac{1}{2})bh \\\\A = (\frac{1}{2} \times 5\ in \times 10\ in)\)

   \(= \frac{50 }{2} \ in^2\\\\=25 \ in^2\\\\\)

The base of the square has a formula area

 \(A = s^2 = (5\ in)^2 = 25 \ in^2\)

The total area consists of the sum of the four-face area and the base: \(total \ \ area = 4 \times \text{(area of 1 face) + (area of base)}\)

                   \(= 4 \times (25\ in^2 ) + 25 \ in^2 \\\\= 125 \ in^2\)

The possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

Jo flips a coin sample space for a coin = {h, t}

and rolls a 6-sided die sample space for a die = {1,2,3,4,5,6}

at a time coin is tossed and the die is rolled

the possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

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Answer:12 18

Step-by-step explanation:

6 x 2 = 12 6 x 3 = 18

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Option D is correct which is Lewie's because he surveyed people who may or may not have bought food.

a.) Kelvin's because he surveyed people leaving an area where food is sold.

b.) Kelvin's because he surveyed every other person instead of every fifth person.

c.) Lewie's because he surveyed every fifth person instead of every other person.

d.) Lewie's because he surveyed people who may or may not have bought food.

As the main concern for this survey is to determine the average number of people who buy food at the mall, therefore more focus should be given to the mall entrance as people may come but may or may not purchase something from the food area.

Thus, Kelvin's survey won't give the correct result for the survey.

Hence, option D is correct which is Lewie's because he surveyed people who may or may not have bought food.

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Answer:

Lewie Survey produces less valid result.

Step-by-step explanation:

Given:

1. Kelvin surveys every other person leaving the food area.

2. Lewie surveys every fifth person leaving the mall's main entrance.

Therefore,

Kelvin will able to produce valid result as he is surveying every person who is leaving food court.

Means,

There are high chances that would have bought food from the court.

Whereas,

Lewie is surveying every fifth person leaving the the mall's entrance.

Therefore,

Here probability to produce valid result is less as they may have not buy food or they may visited other shops.

So, Lewie survey will produce less valid result

Answer with step by step explanation

First, let us find the circumference of the small circle.

The radius of the small circle is 5 cm.

So, now let us see the formula which is needed to find the circumference.

C = 2 π r

Let us find it now.

Circumference of the small circle.

C = 2 π r

C = 2 × 3.14 × 5

C = 31.4 cm

  ≈ 30 cm → nearest 10th

Now let us find the circumference of the big circle.

The radius of the big circle is 10 cm.

C = 2 π r

C =  2 × 3.14 × 10

C = 62.8 cm

   ≈  60 cm → nearest 10th

Answer: Circumference:  C = 2πr = 16.3

2(3.14)r = 16.3

r = 16.3/6.28

r = 2.5955414

Area:  A = πr2

A = 3.14(2.5955414)2

A = 21.15366242 in2

Rounded to nearest whole number the area is 21 in2

Step-by-step explanation:

* Lets revise some rules of a circle

- The circumference of a circle = 2πr , where r is the radius of it

- The area of the circle = πr²

* Lets solve the problem

∵ A circular plate has circumference 16.3 inches

∵ The circumference = 2πr

∵ π = 3.14

- Lets find the radius of the plate

∵ 16.3 = 2(3.14)r

∴ 16.3 = 6.28r

- Divide both sides by 6.28

∴ r = 16.3/6.28 = 2.5955 ≅ 2.6

∴ The radius of the plate is 2.6 inches

* Lets find the area of the plate

∵ The area = πr²

∵ π = 3.14

∵ 4 = 2.6

∴ The area = 3.14(2.6)² = 21.22 ≅ 21

* The area of the plate is 21 inches

Answer:

Step-by-step explanation:

r is the radius

Circumference = 2πr = 16.3

r = 16.3/(2π) = 8.15/π

Area = πr² = π(8.15/π)² = 8.15²/π ≈ 21.1 sq in

Answer:

12 + 15= 27/2 = 13.5 kg

Step-by-step explanation:

Answer:

36 answered correctly

Step-by-step explanation:

Hey there!

Well 90% of 40 is 36.

This is true because 90% as a fraction not simplified is 36/40 and when we do,

36 ÷ 40 we get .9.

And we move the decimal places 2 times to the right in .9 and we get 90%.

Hope this helps :)

Answer:

36

Step-by-step explanation:

Answer: Graph D

Step-by-step explanation:

The slope is 2

x goes after the slope in graph functions

The line goes through 3 on the y-axis so that’s where + 3 comes in.

2x + 3

\(x+ y =15~~...(i)\\\\x-y = 5~~...(ii)\\\\\text{(i) +(ii):}\\\\x+y+x-y = 15+5\\\\\implies 2x = 20\\\\\implies x = \dfrac{20} 2 = 10\\\\\text{(i)-(ii):}\\\\x+y -x +y = 15 -5\\\\\implies 2y = 10\\\\\implies y=\dfrac{10}2 = 5\\\\\text{Hence the numbers are 10 and 5}\)

A sample size of at least 29 is necessary to achieve a margin of error of $8 for a 90% confidence interval of the mean daily spending on all holiday spending.

The following equation may be used to calculate a confidence interval's margin of error:

Margin of error = z *  \((\frac{standard\: deviation} {\sqrt{(sample\:\: size)} }\:)\)

We want the margin of error to be $8, so we can set up the following equation:

\($8 = 1.645 * (\$26 / \sqrt{(sample\: size))\)

To solve for the sample size, we need to isolate the variable "sample size" on one side of the equation:

\(\sqrt{(sample\: size)} = 1.645 * (\$26 / \$8)\\\sqrt{(sample\: size)} = 5.365\)

sample size = \((5.365)^2\)

sample size = 28.8

We can round up to the nearest whole number to ensure that the sample size is large enough:

sample size = 29

Margin of error refers to the range of possible values that a statistical result may vary from the actual population parameter. It is a measure of the precision of a survey or poll's results and indicates how much confidence one can have in the results.

When conducting a survey or poll, researchers typically take a sample from a larger population and use statistical techniques to estimate the parameters of interest, such as the mean or proportion. The margin of error is then calculated based on the sample size, level of confidence, and the variability of the data. It's important to consider the margin of error when interpreting survey results to avoid making incorrect conclusions or assumptions.

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Therefore, the work done by the force field F is 10π given by the line integral.

The work done by the force field F along the arch of the cycloid is given by the line integral of F·dr over the curve r(t), i.e.,

W = ∫C F · dr = ∫0^2π F(r(t)) · r'(t) dt

Using the given values of F(x,y) and r(t), we can compute F(r(t)) · r'(t) as follows:

F(r(t)) · r'(t) = (t - sin(t))i + (5 - cos(t))j · (cos(t)i + sin(t)j)

= (t - sin(t))cos(t) + (5 - cos(t))sin(t)

Hence, we have:

W = ∫0^2π [(t - sin(t))cos(t) + (5 - cos(t))sin(t)] dt

integration by parts, we can evaluate this integral to get:

W = [t sin(t) + (5 - cos(t))cos(t)]|0^2π

= 10π

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Answer: the answer is  4

To determine which policy is more popular, we can conduct a hypothesis test. Let's assume that the null hypothesis is that the two policies have the same level of popularity, and the alternative hypothesis is that one policy is more popular than the other. We can calculate the p-value for each policy using a two-sample proportion test. Comparing the p-values to the significance level of 10%, we can see if either policy is significantly more popular.

To conduct a hypothesis test, we need to calculate the sample proportions for each policy. For the first policy, the sample proportion is 346/452 = 0.765. For the second policy, the sample proportion is 269/378 = 0.712.

We can then calculate the standard error for each sample proportion using the formula sqrt(p*(1-p)/n), where p is the sample proportion and n is the sample size. For the first policy, the standard error is sqrt(0.765*(1-0.765)/452) = 0.029. For the second policy, the standard error is sqrt(0.712*(1-0.712)/378) = 0.032.

We can then calculate the test statistic, which is the difference between the sample proportions divided by the standard error of the difference. This is given by (0.765 - 0.712) / sqrt((0.765*(1-0.765)/452) + (0.712*(1-0.712)/378)) = 2.13.

Finally, we can calculate the p-value for this test statistic using a normal distribution. The p-value for a two-tailed test is 0.033, which is less than the significance level of 10%. Therefore, we can conclude that the first policy is significantly more popular than the second policy at a 10% significance level.

Based on the hypothesis test, we can conclude that the first policy is more popular than the second policy at a 10% significance level. Therefore, the politician should publicly support the first policy during the reelection campaign.

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Answer: Greater than

Hope this helps :)

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The percentage of winning if 20 winning numbers are randomly selected from numbers 1 to 80 is 12.48%.

Given There are 80 numbers from which 20 numbers are selected randomly in a game of Keno by player and after selection of 20 winning numbers again 20 numbers are selected and player wins if the player has correctly selected 3,4,or 5 of the 20 winning numbers.

Probability is the chance of happening an event among all the events possible.

Probability of winning is calculated as under:

Probability=\(C(20,3)C(60,17)/C(80,20)\)

We have taken C(20,3) because player will win if 5 numbers are selected from 20 winning numbers.

We have taken C(60,17) because after selection of 20 numbers 60 numbers will left from 80 and after winning from 3 numbers 17  numbers left and from total 80, 20 numbers are taken.

=C(20,3)C(60,17)/C(80,20)

=(20!/3!17!  * 60!/17!43!)/80!/20!60!

=1140*387221678682300/35353161422121743200

=12.48%

Hence the probability of winning is 12.48%.

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Answer:

cesar is 11 1/4 years old

Step-by-step explanation:

k = kaleighs age

d = dwaynes age

3k - 2d = 5

d + k = 30

rewrite

     -k     -k

d = 30 - k

substitute

3k - 2(30 - k) = 5

3k - 60 + k = 5

4k - 60 = 5

   + 60    +60

4k = 65

/4   /4

k = 16.25

16.25 - 5 = 11.25 or 11 1/4