A low-strength children’s/adult chewable aspirin tablet contains 81 mg of aspirin per tablet. How many tablets may be prepared from 1 kg of aspirin?

Answer:

679.1N

Step-by-step explanation:

Assuming equation 3 is Newton's universal law of gravity:

[tex]F_g = G\frac{m_1m_2}{d^2}[/tex]

Where G is the universal gravity constant:

[tex]G=6.673 x10^{-11}\frac{Nm^2}{kg^2}[/tex]

You need to express the radius of earth in m:

[tex]3959mi*\frac{1609m}{1mi}=6.370*10^6m[/tex]

If you weight 70Kg, just replace the values in the equation:

[tex]F_g = 6.673 *10^{-11}*\frac{70*5.900*10^{24}}{(6.370*10^6)^2}= 6.673 *10^{-11}*\frac{4.13*10^{26}}{4.058*10^{13}}=\\6.673*10^{-11}*1.018*10^{13}= 679.1N[/tex]

Answer: [tex]\pm0.1706[/tex]

Step-by-step explanation:

Given : Sample size : n= 33

Critical value for significance level of [tex]\alpha:0.05[/tex] : [tex]z_{\alpha/2}= 1.96[/tex]

Sample mean : [tex]\overline{x}=2.5[/tex]

Standard deviation : [tex]\sigma= 0.5[/tex]

We assume that this is a normal distribution.

Margin of error : [tex]E=\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

i.e. [tex]E=\pm (1.96)\dfrac{0.5}{\sqrt{33}}=\pm0.170596102837\approx\pm0.1706[/tex]

Hence, the  margin of error is [tex]\pm0.1706[/tex]

Answer:

The point (10,40) is on the graph of g

Step-by-step explanation:

If the point (8,12) is on the graph of f(x) means that

f(8)=12

So, if you choose x=10, then x-2 = 8 and

g(10) = 3f(10-2)+4 = 3f(8)+4

But f(8) = 12, so

3f(8)+4 = 36+4 = 40

Hence g(10) = 40

Which means that the point (10,40) is on the graph of g

Answer: Ireland is €4.05/m

Canada is €3.26/m

Step-by-step explanation:

€4.05/m

$5.99/yd

To compare the prices, we need to transform one of them into the other. Let's transform the Canada price into Ireland price.

As $1 = €0.498

$5.99 * 0.498 = €2.983

€2.983/yd

1yd = 3ft

1ft = 0.3048m

3ft = 0.3048*3 = 0.9144 m

€2.983/yd = €2.983/3ft = €2.983/0.9144 m = €3.26/m

Ireland is €4.05/m

Canada is €3.26/m

There are 56 possible sets of five marbles where all marbles are either red or green, when selecting from a bag containing five red and three green marbles.

When considering all possible sets of five marbles where each marble is either red or green from a bag containing five red marbles and three green ones, you would use combinations to find the total number of sets.

For the red marbles alone, since there are five red marbles, the number of ways to choose five red marbles is simply C(5, 5), which equals 1. There is only one set which contains all five red marbles because you are choosing all available red marbles.

To find sets containing green marbles, we must consider all combinations of red and green marbles that add up to five. These are C(5, 4) * C(3, 1), C(5, 3) * C(3, 2), and C(5, 2) * C(3, 3). We calculate each of these combinations and then sum them to get the total possible sets that consist of only red and green marbles.

Therefore, the total number of sets composed only of red or green marbles is:

C(5, 5) = 1

C(5, 4) * C(3, 1) = 5 * 3 = 15

C(5, 3) * C(3, 2) = 10 * 3 = 30

C(5, 2) * C(3, 3) = 10 * 1 = 10

Adding these up gives us 1 + 15 + 30 + 10 = 56 possible sets.

There are 3 possible sets of five marbles in which all of them are either red or green.

To solve this problem, we need to consider the different combinations of red and green marbles that can make up a set of five marbles, where all marbles in the set are either red or green.

Firstly, let's consider the case where all five marbles are red. Since there are five red marbles in the bag, there is only one way to choose all five red marbles. This gives us one possible set.

Next, we consider the case where there are four red marbles and one green marble. There are [tex]\(\binom{5}{4}\)[/tex] ways to choose four red marbles from the five available, and [tex]\(\binom{3}{1}\)[/tex]ways to choose one green marble from the three available. Using the combination formula [tex]\(\binom{n}{r} = \frac{n!}{r!(n-r)!}\),[/tex] we calculate:

[tex]\[ \binom{5}{4} = \frac{5!}{4!(5-4)!} = \frac{5}{1} = 5 \][/tex]

and

[tex]\[ \binom{3}{1} = \frac{3!}{1!(3-1)!} = \frac{3}{1} = 3 \][/tex]

Multiplying these together gives us[tex]\(5 \times 3 = 15\)[/tex] possible sets for this case.

Now, let's consider the case where there are three red marbles and two green marbles. There are[tex]\(\binom{5}{3}\)[/tex] ways to choose three red marbles from the five available, and[tex]\(\binom{3}{2}\)[/tex]ways to choose two green marbles from the three available. Calculating the combinations:

[tex]\[ \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10 \][/tex]

and

[tex]\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3}{1} = 3 \][/tex]

Multiplying these together gives us [tex]\(10 \times 3 = 30\)[/tex] possible sets for this case.

For the case with two red marbles and three green marbles, we have \[tex](\binom{5}{2}\)[/tex] ways to choose two red marbles and [tex]\(\binom{3}{3}\)[/tex] ways to choose three green marbles. Calculating the combinations:

[tex]\[ \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \][/tex]

and

[tex]\[ \binom{3}{3} = \frac{3!}{3!(3-3)!} = \frac{1}{1} = 1 \][/tex]

Multiplying these together gives us [tex]\(10 \times 1 = 10\)[/tex] possible sets for this case.

Next, the case with one red marble and four green marbles has [tex]\(\binom{5}{1}\)[/tex]ways to choose one red marble and [tex]\(\binom{3}{4}\)[/tex] ways to choose four green marbles. However, since there are only three green marbles, it is impossible to choose four, so this case is not possible.

Finally, the case with zero red marbles and five green marbles is also not possible because we cannot choose five green marbles from only three available.

Adding up the possible sets from the cases that are possible, we have:

[tex]\[ 1 + 15 + 30 + 10 = 56 \][/tex]

However, upon reviewing the combinations, it is clear that there was an error in the calculations. The correct combinations for the case with three red marbles and two green marbles should be [tex]\(\binom{5}{3} \times \binom{3}{2} = 10 \times 3 = 30\)[/tex], and for the case with two red marbles and three green marbles, it should be [tex]\(\binom{5}{2} \times \binom{3}{3} = 10 \times 1 = 10\)[/tex]. The other cases are correct.

Therefore, the correct total number of possible sets is:

[tex]\[ 1 + 15 + 30 + 10 = 56 \][/tex]

However, the question asks for sets where all marbles are either red or green, and we have incorrectly included sets with both red and green marbles. We need to correct this by only considering the sets with all red marbles or all green marbles.

The correct sets are:

- All five marbles are red: 1 set

- All five marbles are green: This is not possible since there are only three green marbles.

Thus, there is only 1 possible set when considering all marbles must be either red or green. But since the question specifically asks for sets of five marbles, and we can't have a set of five green marbles, we are left with only the set of five red marbles.

Answer: radius = 108.75 feet

Hi!

In the drawing you can see the arch that goes from point A to B. The right line from A to B is the length L = 150 feet, across the river. The height is h = 30 feet.

There is a right triangle with hypotenuse R, and the legs are (R-h), and L/2. The Pythagorean theorem says that:

[tex]R^2 = (R-h)^2 + (\frac{L}{2}) ^2 = R^2 -2hR + h^2 + (\frac{L}{2}) ^2\\[/tex]

Then:

[tex]0 = -2hR + h^2 +(\frac{L}{2}) ^2\\R = (h^2 +(\frac{L}{2}) ^2)\frac{1}{2h}[/tex]

Plugging the values of L and h, you get R = 108.75 feet

Answer:

  108.75 ft

Step-by-step explanation:

You want the radius of a circular arc that rises 30 ft above a chord of length 150 ft.

The attached diagram shows the method we used to find the radius. The arc is symmetrical about its centerline, so we only need to find the perpendicular bisector of another chord to determine the location of the center.

Here, we have chosen a coordinate system with the ends of the arc at (±75, 0) and the center at (0, 30). The midpoint of the chord joining the two points on the right will be (75/2, 30/2) = (37.5, 15).

The slope of that chord is ...

  [tex]m=\dfrac{\text{rise}}{\text{run}}=\dfrac{-30}{75}=-\dfrac{2}{5}[/tex]

The equation of the perpendicular bisector will be the equation of a line with slope -1/m = 5/2 through the point (37.5, 15). In point-slope form, that equation is ...

  [tex]y-15=\dfrac{5}{2}(x-37.5)\\\\y=\dfrac{5}{2}x-78.75[/tex]

We note that the y-intercept is -78.75. The distance from that point to the top of the arch is ...

  30 -(-78.75) = 108.75

The radius of the circle is 108.75 ft.

__

Additional comment

We can use another relation to solve this problem even more simply. Consider the 150 ft chord divided into two pieces by a diameter that has one segment length 30, and the other equal to the diameter less 30. The products of these segment lengths are the same, so we have ...

  75·75 = 30·(d -30)
  d-30 = 187.5
  d = 217.5   ⇒   r = d/2 = 108.75

Answer:

The product of [tex]8.5 \times (-0.8) \times (-12)[/tex] is 81.6

Step-by-step explanation:

Given : [tex]8.5 \times (-0.8) \times (-12)[/tex]

To Find : Find the product

Solution:

[tex]8.5 \times (-0.8) \times (-12)[/tex]

[tex](-) \times (-) =+[/tex]

So, [tex]8.5 \times 9.6[/tex]

[tex]81.6[/tex]

Hence the product of [tex]8.5 \times (-0.8) \times (-12)[/tex] is 81.6

Step-by-step explanation:

The product of 8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12) is 81.6

Step-by-step explanation:

Given : 8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12)

To Find : Find the product

Solution:

8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12)

(-) \times (-) =+(−)×(−)=+

So, 8.5 \times 9.68.5×9.6

81.681.6

Answer:

First question: -0.577 cannot be a probability.

Second question: The number must be between 0 and 1, inclusive (D)

Third question: -0.577 cannot be a probability.

Step-by-step explanation:

A probability is a real number that is in the interval [0, 1]. Therefore, any number outside this range cannot be considered a probability. Under this premise:

First question: -0.577 cannot be a probability.

Second question: The number must be between 0 and 1, inclusive (D)

Third question: -0.577 cannot be a probability.

The number negative 0.577 cannot be a probability since it is outside the range of 0 and 1, which defines the allowed range for probabilities. Thus, the correct answer is option A (negative 0.577).

The number that could not possibly be a probability is negative 0.577. This is because the rules for a number to be considered a probability state that it must be between 0 and 1, inclusive. Therefore, option A (negative 0.577) could not be a probability, while option B (0.123) and option C (0) are both possible probabilities as they fall within the allowed range.

Probabilities must be real numbers between 0 and 1, which includes both 0 (representing an impossible event) and 1 (representing a certain event). Applying this principle, the correct answer to what must be true for a number to be a probability is option D, which states that the number must be between 0 and 1, inclusive. In conclusion, only negative 0.577 is not a possible probability.

Answer:

½ = x

Step-by-step explanation:

There is no illustration, but I can show you how to solve for x:

6x + 9 = 12

- 9 - 9

____________

6x = 3

__ __

6 6

x = ½

I am joyous to assist you anytime.

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

We are given that an equation

[tex]6x+9=12[/tex]

We have to find the equation which is equivalent to given equation.

[tex]6x+9=12[/tex]

[tex]6x=12-9[/tex]

Subtraction property of equality

[tex]6x=3[/tex]

[tex]x=\frac{3}{6}[/tex]

Division property of equality

[tex]x=\frac{1}{2}[/tex]

Answer:[tex]x=\frac{1}{2}[/tex]

Answer:

In 2003, the population was 59000 and the population has been growing by 1,700 people each year.

A.

The equation will be:

59000+1700x = (population 'x' years after 2003)

For x, you plug in the amount of years after 2003.

Like if it is the year 2003, the population is [tex]59000+1700(0)[/tex]

= 59000

when it is year 2005, the population is [tex]59000+1700(2)[/tex]

= 62400

B.

The town's population in 2007 will be :

[tex](2007-2003=4)[/tex]

[tex]59000+1700(4)[/tex]

Population = 65800

C.

[tex]59000+1700x=77700[/tex]

=> [tex]1700x=18700[/tex]

x = 11

Means [tex]2003+11=2014[/tex]

Hence, by year 2014 the population will be 77700.

To convert the car's fuel efficiency, it's necessary to convert kilometers to miles, and kilograms to gallons. Using the provided information, the car's fuel efficiency equates to approximately 24.4 miles per gallon.

To convert the car's fuel efficiency from kilometers per kilogram to miles per gallon, we will use the given conversions:

We start with the given efficiency of 7.6 km/kg and convert km to miles:

7.6 km/kg * (1 mile / 1.609 km) = 4.721 miles/kg

Now we convert kg to gallons using the density of gasoline:

4.721 miles/kg * (1 kg / 0.729 liters) * (3.785 liters / 1 gallon) = 24.4 miles/gallon.

Therefore, the car's fuel efficiency is approximately 24.4 miles per gallon.

Answer: If the solution's boiling point drops because salt is added to the soltuiton, then the reason the solution boils sooner is the addition of salt to the solution

Step-by-step explanation:

The re are two cause - consequence relations inside an other one.

I use 3 different cause - consequence connectors not to mix them up.

A --> D equals “ D because A “

A --> S equals “ the reason S happens is A “

(A --> D) --> (A --> S) Equals “ if (A --> D) then (A --> S) “

Final answer:

To find the average sale, add up all the sales ($105.78) and divide by the total number of sales (6), resulting in an average sale of $17.63.

Explanation:

To calculate the average sale made by the salesperson, we first need to add up all the sales and then divide by the total number of sales.

The sales were: $15.50, $18.98, $16.80, $14.00, $18.50, and $22.00.

First, let's find the total:

$15.50 + $18.98 + $16.80 + $14.00 + $18.50 + $22.00 = $105.78

Next, we divide this total by the number of sales to find the average. There were 6 sales in total.

Average Sale = Total Sales / Number of Sales

Average Sale = $105.78 / 6 = $17.63

Therefore, the average sale made by the salesperson was $17.63.

Answer:

Step-by-step explanation:

The first one

1                  16

2                 32

4                 64

8                128

The table that correctly relates the number of cups to the number of tablespoons is the first table.

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b

Then, their multiplication can be interpreted as:

[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]

For example,

[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]

It is specified that:

In 1 cup, there are 16 tablespoons

In 2 cups, there would be 16+16 tablespoons,

and so on,

in 'n' cups, there would be 16+16+...+16 (n times )  = 16 × n tablespoons.

Checking all the tables one by one:

Second table is incorrect because it says that 16 cups = 1 tablespoon which is wrong.

The third table is saying in 32 cups there are only 16 tablespoons, which is obviously wrong as number of tablespoon is always going to be bigger than the number of cups.

The first table is correct since:

Number of cups(n)     Number of tablespoons ( 16 × n)

1                                             16 × 1 =16

2                                            16 × 2 = 32

4                                            16 × 3 = 64

8                                             16 × 4 = 128

So it follows the formula we obtained for the number of tablespoons for given number of cups.

Learn more about multiplication here:

https://brainly.com/question/26816519

Answer:

26-7i

Step-by-step explanation:

1. expand it you will get : 20-15i+8i+6 ( notice that i^2= -1 )

2. simplify it: 26-7i

Using complex numbers, it is found that the result of the multiplication is: 26 - 7i

In this problem, the multiplication is: [tex](5 + 2i)(4 - 3i)[/tex].

Applying the distributive property:

[tex](5 + 2i)(4 - 3i) = 20 - 15i + 8i -6i^2 = 20 - 7i + 6 = 26 - 7i[/tex]

The result is: 26 - 7i

A similar problem is given at https://brainly.com/question/19392811

Check the picture below.

all we need to get the equation of the line is two points on it, in this case those would be (-3,2) and (1,1),

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}}\implies \cfrac{-1}{1+3}\implies -\cfrac{1}{4}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-\cfrac{1}{4}}[x-\stackrel{x_1}{(-3)}]\implies y-2=-\cfrac{1}{4}(x+3) \\\\\\ y-2=-\cfrac{1}{4}x-\cfrac{3}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{4}+2\implies y=-\cfrac{1}{4}x+\cfrac{5}{4}[/tex]

The equation of line is 4y + x = 4.

The slope of the line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

We have been given that Line b passes through the points  (-3,2) and (1,1),

Let

x₁ = -3, y₁ = 2

x₂ = 1, y₂ = 1

∵ (y - y₁) = {(y₂ - y₁)/(x₂ -x₁ )}(x -x₁  )

Substitute values in the formula

(y - 2) = {(1 - 2)/(1 - (-3))}(x -(-3))

(y - 2)  = {(-1)/(1+3)}(x+4)

(y - 2) = -1/4(x+4)

4y - 8 = -x - 4

4y + x = 4

Hence, the equation of line is 4y + x = 4.

Learn more about Slope of Line here:

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Answer:

1) There were 34 $3,000 investors and 26 $6,000 investors.

2) There are 26 nickels and 44 dimes in the jar.

3) 1600 sodas and 1400 hot dogs were sold.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?

x is the number of investors that contributed 3,000.

y is the number of investors that contributed 6,000.

Building the system:

There are 60 investors. So:

[tex]x + y = 60[/tex]

In all, the partnership raised $258,000. So:

[tex]3000x + 6000y = 258000[/tex]

Simplifying by 3000, we have:

[tex]x + 2y = 86[/tex]

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

[tex]1)x + y = 60[/tex]

[tex]2)x + 2y = 86[/tex]

I am going to multiply 1) by -1, then add 1) and 2), so x is canceled.

[tex]1) - x - y = -60[/tex]

[tex]2) x + 2y = 86[/tex]

[tex]-x + x -y + 2y = -60 +86[/tex]

[tex]y = 26[/tex]

Now we get back to equation 1), and find x

[tex]x + y = 60[/tex]

[tex]x = 60-y = 60-26 = 34[/tex]

There were 34 $3,000 investors and 26 $6,000 investors.

2) A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 70 coins. So:

[tex]x + y = 70[/tex]

They are worth $5.70. So:

[tex]0.05x + 0.10y = 5.70[/tex]

Solving the system:

[tex]1) x+y = 70[/tex]

[tex]2) 0.05x + 0.10y = 5.70[/tex]

I am going to divide 1) by -10, so we can add and cancel y:

[tex]1) -0.1x -0.1y = -7[/tex]

[tex]2) 0.05x + 0.1y = 5.70[/tex]

[tex] -0.1x + 0.05x -0.1y + 0.1y = -1.3[/tex]

[tex]-0.05x = -1.3[/tex] *(-100)

[tex]5x = 130[/tex]

[tex]x = \frac{130}{5}[/tex]

[tex]x = 26[/tex]

Now:

[tex]x+y = 70[/tex]

[tex]y = 70 - x = 70 - 26 = 44[/tex]

There are 26 nickels and 44 dimes in the jar.

3) The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?

x is the nuber of sodas and y is the number of hot dogs.

Building the system:

3000 items were sold. So:

[tex]x + y = 3000[/tex]

$7,4000 was the total price of these items. So:

[tex]2x + 3y = 7400[/tex]

Solving the system:

[tex]1)x + y = 3000[/tex]

[tex]2)2x + 3y = 7400[/tex]

I am going to multiply 1) by -2, so we can cancel x

[tex]1) -2x -2y = -6000[/tex]

[tex]2) 2x + 3y = 7400[/tex]

[tex]-2x + 2x -2y + 3y = -6000 + 7400[/tex]

[tex]y = 1400[/tex]

Now, going back to 1)

[tex]x + y = 3000[/tex]

[tex]x = 3000-y = 3000-1400 = 1600[/tex]

1600 sodas and 1400 hot dogs were sold.

If the weight of patient is 80 kg and the label reads 5 mg/2 mL, the administered dose will be 1.2 mL/min. Hence the correct option is B.

The order is Verapamil HCl 0.075 mg/kg IV push over 2 min.

Calculate the total amount of Verapamil needed:

0.075 mg/kg * 80 kg = 6 mg.

Find out how many mL contain 6 mg:

5 mg in 2 mL, so 6 mg will be in (6 mg * 2 mL) / 5mg = 2.4 mL.

Finally, calculate how many mL per minute:

Since the medication is to be given over 2 minutes, the rate will be 2.4 mL / 2 min = 1.2 mL/min.

Answer:

x

Step-by-step explanation:

We are given that measure of an exterior angle which are drawn at vertex M=x

We have to find the value of measurement of angle L+measurement of angle N.

Exterior angle:It is defined as that angle of triangle which is formed by the one side of triangle and the extension of an  adjacent side of triangle.  The measure of exterior angle is equal to sum of measures  of two non-adjacent interior angles of a triangle.

Angle L  and angle N are two non-adjacent angles of a given triangle LMN.

By definition of exterior angle

x=Measure of angle L+Measure of angle N

Answer:

An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem.

If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.

Answer:

[tex]a. \hspace{3} P(A\bigcap B) = \frac{3}{4}\\\\b. \hspace{3} P(A\bigcup B) = \frac{47}{50}\\\\c. \hspace{3} P(A'\bigcup B) = \frac{17}{20}\\\\[/tex]

Step-by-step explanation:

The information is configured in a double entry table in which the finishing information for the edge and surface is recorded, thus:

[tex]\begin{array}{cccc}&E&B&Total\\E&75&4&79\\B&15&6&21\\&90&10&100\\\end{array}[/tex]

Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish.

[tex]a. \hspace{3} P(A\bigcap B) = \frac{75}{100} = \frac{3}{4}\\\\b. \hspace{3} P(A\bigcup B) = P(A) + P(B) - P(A\bigcap B) = \frac{90}{100}+\frac{79}{100} - \frac{75}{100} = \frac{94}{100} =\frac{47}{50}\\\\c. \hspace{3} P(A'\bigcup B) = P(A') + P(B) - P(A'\bigcap B) = \frac{10}{100}+\frac{79}{100} - \frac{4}{100} = \frac{85}{100} =\frac{17}{20}\\\\[/tex]

Answer:

The measured weight of the water = 4.93 g

The percentage error in measured value = 1.4%

Step-by-step explanation:

Given:

Weight of the 10-mL graduate = 42.745 g

Combined weight of graduate and 5 mL water = 47.675 g

5 mL of water should weight = 5 g

thus, actual value of 5 mL water = 5 g

Now,

The measured weight of the water

= (Combined weight of graduate + 5 mL water) - Weight of the 10-mL graduate

= 47.675 g - 42.745 g

= 4.93 g

The percentage error in measured value

= [tex]\frac{\textup{Actual value-calculated value}}{\textup{Actual value}}\times100[/tex]

= [tex]\frac{\textup{5-4.93}}{\textup{5}}\times100[/tex]

or

= 1.4%

The weight of the measured water is 4.930 g, which is slightly less than the theoretical 5 g. The percentage error of the measurement is 1.4%, falling within the acceptable ±5% error range.

To calculate the weight of the measured water and the percentage error, we use the information provided. The weight of the empty graduate is 42.745 g, and the combined weight of the graduate and water is 47.675 g. Subtracting the weight of the empty graduate from the combined weight gives us the weight of the water only:

Weight of water only = 47.675 g - 42.745 g = 4.930 g

Since 5 mL of distilled water should ideally weigh 5 g, we can then calculate the percentage error:

Percentage error = [(Target amount of water - Actual volume dispensed) / Target amount of water] × 100%

Percentage error = [(5 g - 4.930 g) / 5 g] × 100%

Percentage error = [0.07 g / 5 g] × 100%

Percentage error = 1.4%

The measured water weighs slightly less than the expected 5 g, with a percentage error of 1.4%, which is within the acceptable range of ±5% error.

This is a mathematical problem where the student needs to allocate $5000 between two investments, Investment A and B, fitting certain conditions. By developing a series of equations based on the conditions given, it is possible to determine the appropriate allocations.

The subject of this question pertains to the allocation of funds in two investments, a process which involves applying principles of mathematics and financial planning. The person wants to invest $5000, with a certain percentage in Investment A (yielding 5%) and the rest in Investment B (yielding 8%), as per the stipulated conditions. To adhere to these requirements, let's denominate the investment in A as 'x' and that in B as 'y'. The restrictions provided, i.e., x needs to be at least 25% of $5000 (i.e., $1250) and y should not be more than 50% of $5000 (i.e., $2500), and x should be half the investment in y, lead us to the equation x = y/2. If you solve this system of equations, the allocations into A and B can be found. For instance, one feasible solution might be $2000 in A and $3000 in B. This ensures that A is at least 25%, B is at most 50%, and A is half of B, which abides by all the stipulations provided.

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The individual should allocate $1250 to Investment A and $3750 to Investment B.

Let's denote the amount invested in Investment A as[tex]\( x[/tex]  and the amount invested in Investment B as[tex]\( y \)[/tex] . The individual has a total of $5000 to invest, so we have our first equation:\[ x + y = 5000 \]The individual wants to invest at least 25% of the total amount in Investment A, which gives us the second equation[tex]:\[ x \geq 0.25 \times 5000 \][ x \geq 1250 \][/tex]. The individual also wants to invest at most 50% of the total amount in Investment B, which gives us the third equation:[tex]\[ y \leq 0.50 \times 5000 \][ y \leq 2500 \[/tex]]. Additionally, the investment in A should be at least half the investment in B, leading to the fourth equation:[tex]\[ x \geq \frac{1}{2} y \][/tex] Now, let's solve these equations. From the first equation, we can express[tex]\( y \) in terms of \( x \):[ y = 5000 - x ]Substituting \( y \) into the inequality from the third equation, we get:[ 5000 - x \leq 2500 \][ x \geq 5000 - 2500 \][ x \geq 2500 \]This satisfies the condition from the second equation \( x \geq 1250 \).Now, we substitute \( y \) into the fourth equation:\[ x \geq \frac{1}{2} (5000 - x) \] 2x \geq 5000 - x \] 3x \geq 5000 \][ x \geq \frac{5000}{3} \][ x \geq 1666.\overline{6} Since \( x \)[/tex] must be a whole number of dollars, the smallest whole number that satisfies[tex]\( x \geq 1666.\overline{6} \) is \( x = 1667 \)[/tex] . However, we must also ensure that \( y \) is within the allowed range. Let's calculate [tex]\( y \) using \( x = 1667 \):\[ y = 5000 - x \]\[ y = 5000 - 1667 \]\[ y = 3333 \][/tex]

This allocation does not satisfy the condition that[tex]\( y \)[/tex] must be at most $2500. Therefore, we need to find the maximum value of \[tex]( x[/tex]  that satisfies both [tex]\( x \geq 1666.\overline{6} \) and \( y \leq 2500 \).Since \( x \) must be at least half of \( y \), and \( y \) must be at most $2500, we can set \( x \) to half of $2500, which is $1250:\[ x = \frac{1}{2} \times 2500 x = 1250 \]Now, let's check if \( y \) is within the allowed range:[ y = 5000 - x \][ y = 5000 - 1250 \][ y = 3750 \][/tex]This allocation satisfies all the conditions:-[tex]\( x = 1250 \)[/tex]  is more than 25% of the total investment.- [tex]\( y = 3750 \[/tex] ) is less than 50% of the total investment.- [tex]\( x \)[/tex]  is half o[tex]f \( y \).[/tex] Therefore, the individual should allocate $1250 to Investment A and $3750 to Investment B.

Answer:

The cost of old ball is $120.

Step-by-step explanation:

Consider the provided information.

The cost of new ball is $300.

Which is three times the price of his old ball less $60.

Let the price of old ball is x.

Thus the above information can be written as:

[tex]3x-60=300[/tex]

[tex]3x=360[/tex]

[tex]x=120[/tex]

Hence, the cost of old ball is $120.

Answer:

[tex](p\lor q \lor r)\land s[/tex]

Step-by-step explanation:

The dual of a compound preposition is obtained by replacing

[tex]\land \;with\;\lor[/tex]

[tex]\lor \;with\;\land[/tex]

and replacing T(true) with F(false) and F with T.

So, the dual of the compound proposition

[tex](p\land q \land r)\lor s[/tex]

is

[tex](p\lor q \lor r)\land s[/tex]

Answer: (p ∨q∨r)∧s

Step-by-step explanation:

Our proposition is:

(p /\ q/\ r) v s

This means

(P and Q and R ) or S

The proposition is true if P, Q and R are true, or if S is true.

Then the dual of this is

(P or Q or R) and S

The dual of a porposition can be obtained by changing the ∧ for ∨, the ∨ for ∧, the Trues for Falses and the Falses for Trues.

Then, the dual can be writted as:

(p ∨q∨r)∧s

The proposition is true if S is true, and P or Q or R are true.

Answer:

i think it is E the last one

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

The total cost C (in dollars) to participate in a ski club is given by the literal equation :

C=85x+60C=85x+60

Where x is the number of ski trips you take.

1. When C = 315 ;substituting the value of C in the above equation.

315=85x+60315=85x+60

=> 85x=315-6085x=315−60

=> 85x=25585x=255

x = 3 trips.

2. When C = 485

485=85x+60485=85x+60

=> 85x=485-6085x=485−60

=> 85x=42585x=425

x = 5 trips.

Answer:

10,932,240

Step-by-step explanation:

According to the Naspa World list American english have 16,564 6-letters words. Now about the special characters we have the next list  !"#$%&'()*+,-./:;<=>?@[\]^_`{|}~ and considering the space as a special character we have a total of 33 special characters. For numbers we have a total of 10 digits.

Then to know how many possibles exists we have to find how many possibles are for the last two characters then.

[tex]33\cdot10=330[/tex]

That is the amount os possibles if always the special character go before de number, but as the number could be before the special character we have to multiply this quantity by 2.

Then we have 16,564 words for the first 6 characters and 660 options for the last two. To know the total amount of possibilities we just need to multiply this numbers, then:

[tex]16,564\cdot660=10,932,240[/tex]

Final answer:

To find the number of possible passwords, calculate the number of 6-letter words possible with 26 letters, then multiply by the number of digits (10), the number of special characters (32), and account for the two possible orders of digit and special character, leading to the formula 26⁶ * 10 * 32 * 2.

Explanation:

The question involves calculating the number of possible passwords that can be formed by using an English word of exactly 6 letters, followed by a digit and a special character in any order. To calculate this, we consider that there are 26 letters in the English alphabet, 10 possible digits (0-9), and assuming a common set of 32 possible special characters (for example, punctuation marks, symbols, etc.).

First, calculate the number of 6-letter English words that can be formed. Since the question mentions the word is not case-sensitive, each position in the word can be filled by any of the 26 letters. Therefore, the number of 6-letter words is 26⁶.

Then, for each of these words, a digit (10 choices) and a special character (32 choices) can be added in either order. Since the order matters, there are 2 different ways of arranging these two additional characters (digit-special character or special character-digit).

Therefore, the total number of possible passwords is calculated as 26⁶ * 10 * 32 * 2.

This approach highlights the significant number of combinations possible even with seemingly simple password creation rules, underlining the importance of complex passwords for enhancing security.

Answer:

8 degrees

Step-by-step explanation:

6° - (-2°) = 8°

The probability that the mean weight of 4 randomly selected men is between 160 lb and 180 lb is approximately 0.5025 (up to four decimal places).

To find the probability that the mean weight of 4 randomly selected men falls between 160 lb and 180 lb, you can use the Central Limit Theorem.

According to the Central Limit Theorem, the distribution of sample means will be approximately normally distributed, regardless of the distribution of the population, as long as the sample size is sufficiently large.

The formula for the standard error of the mean [tex](\(SE\))[/tex] is given by:

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} \][/tex]

where:

- [tex]\(\sigma\)[/tex] is the population standard deviation,

- [tex]\(n\)[/tex] is the sample size.

In this case, [tex]\(\sigma = 29\)[/tex] lb (population standard deviation) and [tex]\(n = 4\)[/tex] (sample size).

[tex]\[ SE = \frac{29}{\sqrt{4}} = \frac{29}{2} = 14.5 \][/tex]

Now, you can find the z-scores for the values 160 lb and 180 lb using the formula:

[tex]\[ z = \frac{X - \mu}{SE} \][/tex]

where:

- [tex]\(X\)[/tex] is the value you're interested in,

- [tex]\(\mu\)[/tex] is the population mean,

- [tex]\(SE\)[/tex] is the standard error of the mean.

For [tex]\(X = 160\)[/tex] lb:

[tex]\[ z_{160} = \frac{160 - 172}{14.5} \approx -0.8276 \][/tex]

For [tex]\(X = 180\)[/tex] lb:

[tex]\[ z_{180} = \frac{180 - 172}{14.5} \approx 0.5517 \][/tex]

Now, you can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores.

The probability that the mean weight is between 160 lb and 180 lb is given by the difference in these probabilities:

[tex]\[ P(160 < \text{mean} < 180) = P(z_{180}) - P(z_{160}) \][/tex]

Substitute the z-scores:

[tex]\[ P(160 < \text{mean} < 180) = P(0.5517) - P(-0.8276) \][/tex]

Using a standard normal distribution table or calculator, you can find these probabilities. Once you find the probabilities, subtract the smaller from the larger to get the probability in the specified range.

[tex]\[ P(160 < \text{mean} < 180) \approx 0.7082 - 0.2057 \][/tex]

[tex]\[ P(160 < \text{mean} < 180) \approx 0.5025 \][/tex]

So, the probability that the mean weight of 4 randomly selected men is between 160 lb and 180 lb is approximately 0.5025 (up to four decimal places).