Larry Calanan has earnings of S518 in a week. He is single and claims 2 withholding allowances. His deductions include FICA, Medicare, federal withholding, state disability insurance, state withholding, union dues of $15, and charitable contributions of $21. Find his net pay.

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

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:

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:

$13,000

Step-by-step explanation:

We have been given that the retailer earns a $25 profit each week from a customer.

The shopper visits the store all 52 weeks of the year, so number of weeks in 10 years would be 10 times 52 that is 520 weeks.

We know that the customer lifetime value stands for a prediction of the net profit attributed to the entire future relationship with a customer.

The customer lifetime value would be profit made per week times number of weeks the customer will shop.

[tex]\text{The customer lifetime value}=\$25\times 520[/tex]

[tex]\text{The customer lifetime value}=\$13,000[/tex]

Therefore, the customer lifetime value would be $13,000.

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).

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) “

Answer:

t-value = 2.441

Step-by-step explanation:

Let's assume that this is a one-tailed test to calculate the critical value, the process is this:

degrees of freedom (df)= n-1=35-1=34

From the attached table we can see:

t-value = 2.441

Final answer:

The critical value from the Studentized range distribution for the given hypothesis test can be found using the qtukey() function in R or by looking it up in the table. For n=35 and α=0.01, the critical value is approximately 4.116.

Explanation:

To find the critical value from the Studentized range distribution, we need to use the qtukey() function in R or look up the value in the Studentized range distribution table.

Since n=35 and α=0.01, we have k=5 (number of groups) and df=5*(n-1)=170.

Using R, the critical value for a 5% significance level (α=0.05) is approximately 4.116.

Answer: $1846.64

Step-by-step explanation:

Given : The average summer vacation costs $2252.

If 82% of this amount is charged on credit cards, then the amount of the vacation cost is charged will be :-

[tex]82\%\text{ of }\$2252\\\\\text{Convert percent into fraction by dividing it by 100, we get}\\\\=\$[\dfrac{82}{100}\times2252]\\\\=\$[\dfrac{184664}{100}]\\\\=\$1846.64[/tex]

Therefore the amount of the vacation cost is charged= $1846.64

Answer:

6.25 grams would be required

Step-by-step explanation:

This problem can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First step: The first step is determining how many mcg are used to make  25,000 tablets.

The problem states that each tablet contains 250 mcg of digoxin. So:

1 tablet - 250mcg

25,000 tables - x mcg

x = 25,000*250

x = 6,250,000 mcg

25,000 tables have 6,250,000mcg

Final step: Conversion of 6,250,000mcg to g

Each g has 1,000,000 mcg. How many g are in 6,250,000mcg? So:

1g - 1,000,000 mcg

xg - 6,250,000 mcg

1,000,000x = 6,250,000

[tex]x = \frac{6,250,000}{1,000,000}[/tex]

x = 6.25g

6.25 grams would be required

Answer: There will be 42 games played.

Step-by-step explanation:

The number of combination to arrange n things if r things are taken at a time:-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Similarly, the number of combination to arrange 7 teams if 2 teams are taken at a time:-

[tex]^7C_2=\dfrac{7!}{2!(7-2)!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21[/tex]

∴ Number of combination to arrange 7 teams if 2 teams are taken at a time=21

Also, each team plays each of the other teams twice.

Then, the number of  games will be played: [tex]21\times2=42[/tex]

Hence, There will be 42 games played.

Final answer:

To calculate the total number of games played in a league with 7 teams where each team plays the others twice, use the formula n(n - 1) × 2, which results in 7 * 6 * 2 = 84 games.

Explanation:

To find out the total number of games played in a baseball league with 7 teams where each team plays each of the other teams twice, we can use the formula for the number of games in a round-robin tournament: n(n - 1), where n is the number of teams. Since each team plays each other twice, the formula modifies to n(n - 1) × 2.

Substituting the number of teams (7) into the formula gives us: 7 * (7 - 1) × 2 = 7 * 6 × 2 = 42 × 2 = 84 games in total.

Answer:

a) The slope represents the change per year in the earth's surface temperature (0.02 ºC) and the T-intercept represents the average earth's surface temperature in 1900 (18.5ºC)

b) The average global surface temperature will be 22.5ºC in 2100.

Step-by-step explanation:

I think there's a "+" sign missing in the function you wrote, and that you meant to write T= 0.02t + 18.50 and I'll solve the problem for this function.

If I am wrong with the values or the + you can always substitute the values you have in your function based on the procedure I'll write down.

So, this function is T= 0.02t + 18.50.

A linear function is expressed as y = f(x) = mx + b where m is the slope of the function and b is the interception with the y-axis.

a) In this particular function, we would have that the slope of the function is 0.02 and it represents the change per year in the earth's surface temperature, since T is temperature in ºC, the change per year would be of 0.02ºC.

On the other hand, the T-intercept would be the value of the function when t=0

T(0) = 0.02(0) +18.50

T(0) = 18.50

This 18.50 represents the average surface temperature of the earth when measures started, meaning, the average surface temperature of the earth in 1900 was 18.50

b) To predict the average global surface temperature in 2100, we are going to substitute 200 in the function (since 2100 - 1900 = 200)

T(200) = 0.02 (200) + 18.50 = 4 + 18.50 = 22.5

Therefore, the average global surface temperature in 2100 will be 22.5ºC

Final answer:

The slope of the linear function represents the rate of temperature increase per year while the T-intercept represents the estimated global surface temperature in 1900. Substituting t=200 into the equation predicts an average global surface temperature of 12.50°C in 2100.

Explanation:

Understanding the Linear Model of Earth's Temperature Rise

The linear function given is T = 0.02t + 8.50, where T is the temperature in degrees Celsius and t represents the years since 1900. The slope of this function is 0.02, which indicates the average rate at which the average global surface temperature is increasing per year. The T-intercept is 8.50°C, which can be interpreted as the estimated global surface temperature in the base year, 1900.

To project the average global surface temperature in 2100, we simply substitute t = 200 into the equation (since 2100 is 200 years after 1900) and calculate:

Therefore, using this model, the predicted average global surface temperature in 2100 is 12.50°C.

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:

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.

Final answer:

The odds of winning the game with a probability of 9/10 are 9:1, which means there are 9 chances of winning for every 1 chance of losing.

Explanation:

The question asks for the odds of winning a game given a probability of winning is 9/10. To find the odds in favor of winning, we calculate the ratio of the probability of winning to the probability of not winning. There are 9 chances to win for every 10 chances, so there is 1 chance out of 10 of not winning. Therefore, the odds in favor of winning are 9:1 (9 chances to win versus 1 chance to lose).

The odds of winning the game are 9:1, meaning for every 9 times one wins, one can expect to lose approximately 1 time.

The odds of winning a game, given the probability of winning is 9/10, can be calculated by considering the definition of odds. The odds in favor of an event are given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

In this case, the probability of winning is 9/10, which means there are 9 favorable outcomes for every 10 total outcomes (including both wins and losses).

To find the odds, we subtract the probability of winning from 1 to get the probability of losing, which is 1 - 9/10 = 1/10. Now, we have 9 favorable outcomes (wins) and 1 unfavorable outcome (loss) since the total outcomes are 10.

Therefore, the odds of winning the game are 9 favorable outcomes to 1 unfavorable outcome, which is 9:1.

The correct answer is 9:1.

The probability of winning is given as 9/10.

- The probability of losing is the complement of the probability of winning, which is 1 - 9/10 = 1/10.

- Odds are calculated by comparing the number of favorable outcomes to the number of unfavorable outcomes.

- Here, there are 9 favorable outcomes (wins) and 1 unfavorable outcome (loss), so the odds of winning are 9:1.

- The odds format does not consider the total number of outcomes but rather the ratio of wins to losses. Hence, we do not include the total outcomes in the odds ratio.

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:

[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: 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:

Assuming a being a divisor of c and [tex]a,b,c \in \mathbb{Z}[/tex]

Step-by-step explanation:

We are told that [tex]a \mid c[/tex]

and that [tex]a+b =c[/tex]

which means that

[tex]\exists k \in \mathbb{N}[/tex] so that [tex]c = k.a[/tex]

so we can rewrite [tex]a+b[/tex] as

[tex]a+b = c = k.a[/tex]

[tex]b = k.a-a = (k-1).a[/tex]

and as [tex]k \in \mathbb{N}[/tex]

We have that either

Showing that [tex]a \mid c[/tex]

Answer:

[tex]n(A) = n_1A^k[/tex]

Step-by-step explanation:

Taking into account that the growth rate of the number of species on the island is proportional to the density of species (number of species between area of the island), a model based on a differential equation is proposed:

[tex]\frac{dn}{dA} = k\frac{n}{A}[/tex]

This differential equation can be solved by the method of separable variables like this:

[tex]\frac{dn}{n} = k\frac{dA}{A}[/tex] with what you get:

[tex]\int\ {\frac{dn}{n}}\ = k\int\ {\frac{dA}{A}}[/tex]

[tex]ln|n| = kln|A|+C[/tex]. Taking exponentials on both sides of the equation:

[tex]e^{ln|n|} = e^{ln|A|^{k}+C}[/tex]

[tex]n(A) = e^{C}A^{k}[/tex]

how do you have to [tex]n (1) = n_1[/tex], then

[tex]n(A) = n_1A^k[/tex]

Answer:

Yes, "All isosceles triangles with congruent vertex angles are similar".

Step-by-step explanation:

Consider the provided statement.

All isosceles triangles with congruent vertex angles are similar.

As we know that the two sides of an isosceles triangle are same.

It is given that the isosceles triangles with congruent vertex angles.

If vertex angles are congruent it means the opposite side of those angles are congruent. Also the sums of the base angles are the same,

As we know the base angles of an isosceles triangle are congruent, so by the AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".

Or

let say ΔABC and ΔDEF are isosceles triangles where AB=DE and AC=DF

It means ∠B=∠E and ∠C=∠F also it is given that ∠A=∠D

Thus. from AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".

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

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:

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.

Answer:

a) $278.65 million per hour

b)  826.77 million years

Step-by-step explanation:

Given:

Total money = $53,740,394 million

Time taken to earn the money = 22 years

Now,

1 year = 365.256 days

and 1 day = 24 hours

thus,

22 years = 22 × 365.256 × 24 = 192855.168 hours

Therefore,

for a person that wants to make $53,740,394 million over exactly 22 years, will have hourly wage

= [tex]\frac{\textup{money to be earned}}{\textup{Time taken in hours}}[/tex]

= [tex]\frac{\textup{53,740,394 million}}{\textup{192855.168 hours}}[/tex]

= $278.65 million per hour

Now,

Salary of a physics professor = 65000 /year

Thus,

for physics professor to earn $53,740,394 million number of years taken will be

= [tex]\frac{\textup{$53,740,394 million}}{\textup{65000 /year}}[/tex]

= 826.77 million years

Final answer:

To earn $53,740,394 through embezzlement over 22 years equates to an "hourly wage" of $1,174.60, assuming a 40-hour workweek. It would take a physics professor making $65,000 a year approximately 827 years to earn the same amount.

Explanation:

Calculating the "hourly wage" for embezzling $53,740,394 over 22 years requires us to first determine the total hours worked over those years, assuming a standard full-time job framework of 40 hours per week. Also, to calculate how many years it would take a physics professor earning $65,000 a year to amass the same amount of money embezzled requires straightforward division.

Step 1: Calculate the Total Number of Hours Worked Over 22 years

Number of weeks in a year = 52

Hours worked per week = 40

Total hours worked in a year = 52 weeks * 40 hours/week = 2,080 hours

Total hours worked over 22 years = 2,080 hours/year * 22 years = 45,760 hours

Step 2: Calculate the Hourly "Wage" from Embezzlement

Total embezzled = $53,740,394

Hourly "wage" = Total embezzled / Total hours worked over 22 years = $53,740,394 / 45,760 hours = $1,174.60 per hour

Step 3: Calculate the Years for a Physics Professor to Earn $53,740,394

Annual salary = $65,000

Years required = Total embezzled / Annual salary = $53,740,394 / $65,000 ≈ 826.78 years

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.

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:

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:

C. Hiring part-time employees to save on costs

Step-by-step explanation:

It is good economically to not have to pay the employee full time but still have someone to help the business so they are there a shorter period of time

Though this question is not mathematics, the best example of a business economic decision is C) Hiring part-time employees to save on costs.

Economic decisions revolve around the following economic activities in the use of economic resources:

Business economic decisions are made to achieve business goals, including savings, efficiency, and effectiveness.

Thus, the best example is of a business economic decision is Option C because it involves the achievement of a business goal, savings.

Learn more about economic decisions at https://brainly.com/question/30106763.

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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:

[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.