What is the value of x?

Answer:Force=30N

Step-by-step explanation:Torque of a force on the handle= Torque of weight on the axle.

Torque is the magnitude force that acts perpendicular.

3.5 ×180=21×Force

Force= 3.5×180 /21

Force=630/21

Force=30N

Answer:

6.74 lbs.

Step-by-step explanation:

Hope this helps.

Answer:let us compare the following pairs of power of 10,9×10^6 ÷3×10^12=3×10^-6

Step-by-step explanation:

Comparing pairs of power of 10 involve applying principle of indices.in what is known as the laws of indices

Law1 states that X^a ×X^b=X^(a+b) meaning that multiplication of indices results to addition of the indexes raise as exponenet of 10, similarly a division as in the answer above always lead to substraction of the indexes as seen in the example 9×10^6/3×10^12 will becomen9÷3×10^(6-12)=3×10^-6.

There were 20 people in the room, as each person kissed every other person once, resulting in [tex]\( \frac{20 \times 19}{2} = 190 \)[/tex] kisses.

Let's denote n as the number of people in the room. In this scenario, each person kisses every other person once, resulting in a total of [tex]\( \frac{n(n-1)}{2} \)[/tex] kisses.

Given that there were 190 kisses, we can set up the equation:

[tex]\[ \frac{n(n-1)}{2} = 190 \][/tex]

To solve for n, we multiply both sides of the equation by 2 to get rid of the fraction:

[tex]\[ n(n-1) = 380 \][/tex]

Expanding the left side:

[tex]\[ n^2 - n = 380 \][/tex]

Rearranging the equation into a quadratic form:

[tex]\[ n^2 - n - 380 = 0 \][/tex]

Now, we can solve this quadratic equation. One way is by factoring, if possible. If not, we can use the quadratic formula:

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

where [tex]\( a = 1 \), \( b = -1 \), and \( c = -380 \).[/tex]

Plugging in the values:

[tex]\[ n = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-380)}}}}{{2(1)}} \]\[ n = \frac{{1 \pm \sqrt{{1 + 1520}}}}{2} \]\[ n = \frac{{1 \pm \sqrt{{1521}}}}{2} \]\[ n = \frac{{1 \pm 39}}{{2}} \]\[ n = \frac{{1 + 39}}{{2}} \quad \text{or} \quad n = \frac{{1 - 39}}{{2}} \]\[ n = \frac{{40}}{{2}} \quad \text{or} \quad n = \frac{{-38}}{{2}} \]\[ n = 20 \quad \text{or} \quad n = -19 \][/tex]

Since the number of people cannot be negative, we discard n = -19.

Therefore, there were [tex]\( \boxed{20} \)[/tex] people in the room.

(a) The equation [tex]2h^{2} +7h+4=0[/tex] has two irrational solutions.

(b) The equation [tex]m^{2} =-40m-400[/tex] has one rational solution.

(c) The equation [tex]14r^{2} =5-7r[/tex] has two irrational solutions.

(d) The equation [tex]7w^{2} -w=-9[/tex] has two imaginary solutions.

(e) The equation [tex]3f-9f^{2} =6[/tex] has two imaginary solutions.

Explanation:

(a) Solving the equation [tex]2h^{2} +7h+4=0[/tex] , we get the solutions,

[tex]h=\frac{-7+\sqrt{17}}{4}[/tex] and [tex]h=\frac{-7-\sqrt{17}}{4}[/tex]

Thus, [tex]h=-0.719223[/tex] and [tex]h=-2.78077[/tex]

Hence, the equation [tex]2h^{2} +7h+4=0[/tex] has two irrational solutions.

(b) Solving the equation [tex]m^{2} =-40m-400[/tex] , we get the solution,

[tex]m=-20[/tex]

Hence, the equation [tex]m^{2} =-40m-400[/tex] has one rational solution.

(c) Solving the equation [tex]14r^{2} =5-7r[/tex] , we get the solutions,

[tex]r=\frac{-7+\sqrt{329}}{28}[/tex] and [tex]r=\frac{-7-\sqrt{329}}{28}[/tex]

Thus, [tex]r=-0.39779[/tex] and [tex]r=-0.89779[/tex]

Hence, the equation [tex]14r^{2} =5-7r[/tex] has two irrational solutions.

(d) Solving the equation [tex]7w^{2} -w=-9[/tex] , we get the solutions,

[tex]w=\frac{1}{14}+i \frac{\sqrt{251}}{14}[/tex] and [tex]w=\frac{1}{14}-i \frac{\sqrt{251}}{14}[/tex]

Hence, the equation [tex]7w^{2} -w=-9[/tex] has two imaginary solutions.

(e)  Solving the equation [tex]3f-9f^{2} =6[/tex] , we get the solutions,

[tex]f=\frac{1}{6}-i \frac{\sqrt{23}}{6}[/tex] and [tex]f=\frac{1}{6}+i \frac{\sqrt{23}}{6}[/tex]

Hence, the equation [tex]3f-9f^{2} =6[/tex] has two imaginary solutions.

To construct a Pareto chart for the Wagenlucht Ice Cream Company, rank the flavors by preference, calculate relative frequencies, then draw a bar chart accordingly.

The first step in constructing a Pareto chart is to order your categories (in this case, ice cream flavors) from largest to smallest frequency. Therefore, we will rank them as follows: Choco-Nuts (12), Strawberry Cream (4), and Orange Mint (4).

Then, calculate the relative frequencies - the number of people who preferred a particular flavor divided by the total number of people sampled. Choco-Nuts: 12/20 = 0.6, Strawberry Cream: 4/20 = 0.2, Orange Mint: 4/20 = 0.2.

Start a vertical bar chart with the flavors on the horizontal axis. Using the relative frequencies, draw proportional vertical bars for each: Choco-Nuts would be the tallest, then Strawberry Cream and Orange Mint, which are both the same size. This is your Pareto chart.

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The correct answer is option C. The relative frequency are as Choco-Nuts: 0.6, Strawberry Cream: 0.2, Orange Mint: 0.2.

To construct a Pareto chart representing the preferences for the Wagenlucht Ice Cream Company flavors, we need to follow these steps and choose an appropriate vertical scale. Here's the process:

1. Collect the data:

Strawberry Cream: 4 preferences

Choco-Nuts: 12 preferences

Orange Mint: 4 preferences

2. Calculate the total number of preferences:

[tex]\[ \text{Total preferences} = 4 + 12 + 4 = 20 \][/tex]

3. Calculate the relative frequencies:

Strawberry Cream: [tex]\(\frac{4}{20} = 0.2\)[/tex]

Choco-Nuts: [tex]\(\frac{12}{20} = 0.6\)[/tex]

Orange Mint: [tex]\(\frac{4}{20} = 0.2\)[/tex]

4. Order the categories in descending order of frequency:

Choco-Nuts: 60%

Strawberry Cream: 20%

Orange Mint: 20%

The complete question is:

Wagenlucht Ice Cream Company is always trying to create new flavors of ice cream. They are market testing three kinds to find out which one has the best chance of becoming popular. They give small samples of each to 20 people at a grocery store. 4 ice cream tasters preferred the Strawberry Cream, 12 preferred Choco- Nuts, and 4 loved the Orange Mint. Construct a Pareto chart to represent these preferences. Choose the vertical scale so that the relative frequencies are represented.

A. Choco-Nuts: 0.6, Strawberry Cream: 0.3, Orange Mint: 0.3.

B. Choco-Nuts: 0.4, Strawberry Cream: 0.4, Orange Mint: 0.1.

C. Choco-Nuts: 0.6, Strawberry Cream: 0.2, Orange Mint: 0.2.

D. Choco-Nuts: 0.6, Strawberry Cream: 0.4, Orange Mint: 0.2.

Answer:

The youngest brother's age is 21 years.

Step-by-step explanation:

Given:

The ages of 3 brothers are consecutive integers.

If the oldest brothers age is decreased by twice the youngest brother age the result is -19

To find the age of the youngest brother.

Solution:

Let the age of youngest broth be = [tex]x[/tex]  years

The ages are consecutive integers.

So, age of the next older brother will be = [tex](x+1)[/tex] years

The age of the oldest brother will be = [tex](x+2)[/tex] years

The oldest brothers age is decreased by twice the youngest brother age.

The above statement can be represented as:

⇒ [tex](x+2)-2x[/tex]

Simplifying.

⇒ [tex]x-2x+2[/tex]

⇒[tex]-x+2[/tex]

The result for the above expression = -19.

So, we have:

[tex]-x+2=-19[/tex]

Subtracting both sides by 2.

[tex]-x+2-2=-19-2[/tex]

[tex]-x=-21[/tex]

Multiplying both sides by -1.

∴ [tex]x=21[/tex]

Thus, the youngest brother's age is 21 years

Answer:

Option C. 16

Step-by-step explanation:

Number of differents colors = 4

Number of differents sizes = 2

Case 1: 3 notepads of the same size and the same color:

If we have a package with the same size and the same color, the number of possible packages is:

N° packages = 4(colors)*2(sizes) = 8

Case 2: 3 notepads of the same size and different colors:      

In this case, to calculate the number of possible permutations of packages without repetitions we need to use the following equation:    

[tex] C_{n}^[p} = \frac{n!}{p!(n-p)!} [/tex]

where p: is the number of colors for each package = 3, and n: is the total number of colors = 4.

[tex] C_{4}^[3} = \frac{4!}{3!(4-3)!} = \frac{4*3*2*1}{3*2*1} = 4 [/tex]

This number calculated is for one size, if the have two different sizes the number of possible packages is:

N° packages = 4(colors)*2(sizes) = 8    

Therefore, the total number of different possible packages is:

N° packages = case 1 + case 2 = 8 + 8 = 16

So, the correct answer is option C = 16.

I hope it helps you!

The value of the constants b and c in the given polynomial, p(x) = x² + bx + c are b = 2, and c = -24.

Given a polynomial:

p(x) = x² + bx + c

It is also given that:

[tex]\lim_{x \to 4} \frac{p(x)}{x-4} =10[/tex]

Since the denominator is x - 4 when the limit sets to 4, the denominator will have 0 there.

But, this can't be possible.

So, the expression inside the limit is given below:

[tex]\lim_{x \to 4}\frac{(x+a)(x-4)}{x-4}=10[/tex]

When the limit tends to 10, the expression becomes:

4 + a = 10

a = 6

So, the expression inside the limit becomes:

p(x) = (x + 6)(x - 4)

      = x² + 6x - 4x - 24

      = x² + 2x - 24

So, x² + bx + c = x² + 2x - 24

Comparing the coefficients of the polynomial expression:

b = 2

c = -24

Hence, the constants are b = 2, and c = -24.

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The constants b and c in the polynomial satisfy the equation 4b + c = 24. There are infinitely many pairs of (b, c) that can satisfy this equation, therefore they are not unique.

In this question, we are dealing with limits and polynomials. We are given that p(x) = x2 + bx + c and lim x→4 [p(x)/(x-4)] = 10.

Substituting p(x) into the equation, we get lim x→4 [(x2 + bx + c) / (x - 4)] = 10.

Using the rule lim x→a [f(x)] = f(a), we find that 42 + 4b + c = 40. This simplifies to 16 + 4b + c = 40, and further to 4b + c = 24.

So, the constants b and c must satisfy this equation. Therefore, they are not unique as there are infinitely many pairs of (b, c) that can satisfy this equation. For example, if b = 5, then c = 4. If b = 6, then c = 0. And so on.

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Answer:7980 ways

Step-by-step explanation:

When select predident:21 ways

When select secretary: 20 ways

When select treasurer: 19 ways

It is permutation

N permutation r=NPR

20permutation3=21×20×19= 7980 ways

Answer:

7980 ways

Step-by-step explanation:

Pretty simple.

we are finding variation.

Variation = N factorial/ (N-P)factorial/

N = the total number of elements we have available

P = the number of elements out of n we need to select

N = 21

P = 3

Variation = 21 factorial/(21-3)factorial = 21 factorial/ 18 factorial

Variation = 21x20x19x 18factorial/ 18 factorial

Variation = 21x20x19 = 7980 possible ways of selecting 3 positions out of a board of 21 members.

is it clear?

Answer:

The average of 12 and 40 is 26

Step-by-step explanation:

The average of the values 12 and 40

The variable of average is avg

Average of numbers is sum of all number divide by number of numbers.

Expression:-

[tex]\text{Avg}=\dfrac{12+40}{2}[/tex]

Now simplify the average

[tex]\text{Avg}=\dfrac{52}{2}[/tex]

[tex]\text{Avg}=26[/tex]

Hence, the average of 12 and 40 is 26

The average of the values 12 and 40 is calculated by adding the two numbers together and dividing by 2. This computation can be assigned to a variable named 'avg' in a Python programming context.

To compute the average of the values 12 and 40, you sum the two numbers and then divide by the count of numbers. In this case, there are two numbers, so the sum (12 + 40) is divided by 2. Thus, in the programming language Python, you could write this as:

avg = (12 + 40) / 2

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Answer:19+25+10+14+80 gives you 148

Step-by-step explanation:

Tommy earned approximately $68 altogether.

Given:

- Clothes: 19%

- Food: 25%

- Savings: 10%

- Other: 14%

To find out how much Tommy earned altogether, we need to detemine what percentage of his earnings $80 on entertainment represents.

First, we sum up these percentages to find out what portion of his earnings $80 represents:

Total percentage spent = Clothes + Food + Savings + Other

Total percentage spent = 19% + 25% + 10% + 14%

Total percentage spent = 68%

Now, we need to find out how much $80 represents as a percentage of his total earnings:

Percentage of earnings spent on entertainment = (Amount spent on entertainment / Total percentage spent) * 100%

Percentage of earnings spent on entertainment = (80 / 68) * 100%

Percentage of earnings spent on entertainment ≈ 117.65%

Now, to find out how much Tommy earned altogether, we need to determine the total amount represented by 100%, which is his total earnings. Since $80 represents approximately 117.65% of his earnings:

Total earnings = (Amount spent on entertainment / Percentage of earnings spent on entertainment) * 100%

Total earnings = (80 / 117.65%) * 100%

Total earnings ≈ $68

Therefore, Tommy earned approximately $68 altogether.

Answer:

12

Step-by-step explanation:

P=a+b+c       P=3+4+5    P=12

The perimeter of a triangle is 12 cm.

Option B is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

There are three sides to a triangle.

So,

The sides are 3 cm, 4 cm, and 5 cm.

Now,

The perimeter of a triangle.

= Sum of all the sides

= 3 + 4 + 5

= 12 cm

Thus,

The perimeter of a triangle is 12 cm.

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Answer:

The estimated number of deer in this population will be 147.

Step-by-step explanation:

Let we assume

Total number of deer = x

If we presume that this sample ratio is typical for the entire herd

Then,

The ratio of total number of the deer and initially collected, tagged and released deer will be equal to the ratio of later captured 55 deer and 9 tagged deer.

So

[tex]\frac{x}{24}=\frac{55}{9}[/tex]

[tex]x=\frac{55}{9}\times24[/tex]

[tex]x=146.66[/tex]

Hence the estimate number of deer = 147

A. Jose would be 30 feet east of the mailbox after 5 seconds.

B. A formula that expresses Jose's distance from the mailbox is,

D = 10 + 6t

C. As time increases, his distance from the mailbox increases proportionally.

Given that;

Jose is standing 10 feet east of a mailbox when he begins walking directly east of the mailbox at a constant speed of 6 feet per second.

A. In 5 seconds,

Jose would have travelled a distance equal to his speed multiplied by the time.

Since he is walking directly east, the distance travelled would be;

6 feet/second × 5 seconds = 30 feet.

Therefore, Jose would be 30 feet east of the mailbox after 5 seconds.

B. To express Jose's distance from the mailbox (D) in terms of the number of seconds (t) since he started walking, use the formula:

D = 10 + 6t

The initial distance from the mailbox which is 10 feet is added to the distance he walks 6 feet/second × t seconds to get the total distance.

C. Yes, Jose's distance from the mailbox is proportional to the time elapsed since he started walking away from the mailbox.

This is evident from the formula D = 10 + 6t

Where the coefficient of t (6) represents the constant rate at which his distance increases with time.

As time increases, his distance from the mailbox increases proportionally.

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Jose is 40 feet from the mailbox after 5 seconds. His distance from the mailbox can be expressed by the formula D=10+6t. His distance from the mailbox is proportional to the time elapsed since he started walking away from the mailbox.

A. Since Jose is moving at a speed of 6 feet per second, after 5 seconds, he would have walked 5*6=30 feet. He initially starts 10 feet east of the mailbox, so his total distance from the mailbox 5 seconds later is 10+30=40 feet.

B. The formula that expresses Jose's distance from the mailbox in terms of the number of seconds t since he started walking is D = 10 + 6t, where D is the distance and t is the time in seconds. In this formula, 10 represents his initial distance from the mailbox, and 6t represents how far he walks.

C. Yes, as Jose walks away from the mailbox, his distance from the mailbox is proportional to the time elapsed since he started walking away from the mailbox. This can be seen from the formula D=10+6t, which is in the form y=mx+b, indicating a linear relationship in which the dependent variable (distance) is proportional to the independent variable (time). The coefficient of t, which is 6, is the constant of proportionality.

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Answer:

Tommy earned $250 altogether.

Step-by-step explanation:

Let the total earning of Tommy be 'x' dollars.

Given:

Money spent on entertainment = $80

From the circle shown below:

Percent spent on clothes = 19%

Percent spent on food = 25%

Percent spent on other things = 14%

Percent of savings = 10%

Addition of all percents = 100%

⇒ 19% + 25% + 10% + 14% + % Entertainment = 100%

⇒ 68% + % Entertainment = 100%

⇒ % Entertainment = 100% - 68% = 32%

Therefore, as per question:

[tex]32\%\ of\ x=\$80\\\\0.32x=80\\\\x=\frac{80}{0.32}\\\\x=\$250\\[/tex]

Hence, Tommy earned $250 altogether.

The correct option is option D , i.e., a cone opening along y - axis.

It is given that a set of points is there whose distance from the y-axis equals the distance from the x-z plane.

We have to find out which of the given options describe these set of points.

What is a cone ?

A cone is a series of tapering circular plates which stack over each other from a flat base to a point.

As per the question ;

Distance from y-axis = Distance from the x-z plane

y = [tex]\sqrt{x^{2} + z^{2} }[/tex]

y² = x² + z²

So , this is a cone that has its vertex at the origin and opens along y-axis.

Thus , the correct option is option D , i.e., a cone opening along y - axis.

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Answer:

as v tends to c( speed of light), the mass of the particle moves towards an infinite value

Step-by-step explanation:

The concept applied here is the theory of relativity.

what the theory entails is the measurements of events i.e things that happen, where and when they happen and to what large extend are events seperated in space and time. Albert Einstein was the first to published his findings on the theory of relativity.

When velocity of particle approaches to velocity of light . then, mass of particle approaches to infinite value.

In theory of relativity, the mass of a particle with velocity v is given as,

                      [tex]m=\frac{m_{0}}{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

where [tex]m_{0}[/tex] is the mass of the particle at rest and c is the speed of light.

When velocity v tends to velocity of light c.

                     [tex]m=\frac{m_{0}}{\sqrt{1-\frac{c^{2} }{c^{2} } } }\\\\m=\frac{m_{0}}{\sqrt{1-1} } \\\\m=\frac{m_{0}}{ 0} =\infty[/tex]

Hence, when velocity of particle approaches to velocity of light . then, mass of particle approaches to infinite value.

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The graph of the function [tex]f(x)=-\sqrt{x}[/tex] is the first graph which is attached below.

Step-by-step explanation:

The function is [tex]f(x)=-\sqrt{x}[/tex]

To graph the function, we need to know the domain and range of the function.

The domain is found by substituting the values for x.

Thus, the domain is [tex]x\geq 0[/tex]

The range of the function is determined as [tex]y\leq 0[/tex]. Since, substituting the values of x we get the corresponding y-value which lies in the interval [tex](-\infty, 0][/tex].

The graph of the function [tex]f(x)=-\sqrt{x}[/tex] is the first graph which is attached below.

Answer:

The answer to your question is letter D

Step-by-step explanation:

To demonstrate if the data are measurements of the sides of a right triangle use the pythagorean theorem.

                         c² = a² + b²

A. 25, 23, 7       25² = 23² + 7²

                        625 = 529 + 49

                        625 ≠ 578            These values are not of a right triangle

B. 9, 6,3             9² = 6² + 3²

                       81 = 36 + 9

                        81 ≠ 45                These values are not of a right triangle

c. 18, 15, 4         18² = 15² + 4²

                        324 = 225 + 16

                        324 ≠  241             These values are not of a right triangle

D. none of the above                     This is the right answer

Answer:

The answer is D. none of the above

Step-by-step explanation:

The length of the sides of a right triangle will be related according to the formula a^2 + b^2 = c^2, A,B,C will not work with this formula.

Hope this helps :)

Answer:

y = (x + 7) (x + 6) (x − 3)

Step-by-step explanation:

Using rational root theorem, possible rational roots are:

±1, ±2, ±3, ±6, ±7, ±9, ±14, ±18, ±21, ±42, ±63, ±126

Using trial and error, we find that +3 is one of the roots.

There are 3 ways to continue from here: continue using trial and error to look for other rational roots; use long division to factor; or use grouping.

Using grouping:

y = x³ + 10x² + 3x − 126

y = x³ + 10x² − 39x + 42x − 126

y = x (x² + 10x − 39) + 42 (x − 3)

y = x (x + 13) (x − 3) + 42 (x − 3)

y = (x (x + 13) + 42) (x − 3)

y = (x² + 13x + 42) (x − 3)

y = (x + 7) (x + 6) (x − 3)

Answer:

There are 198 children at the circus show.

Step-by-step explanation:

Let the total number of spectators be 'x'.

Given:

Number of men = [tex]\frac{1}{4}[/tex] of the total number

Number of women = [tex]\frac{2}{5}[/tex] of the remaining number.

Also, number of women = 132

Number of men = [tex]\frac{1}{4}\ of\ x=\frac{x}{4}[/tex]

Now, spectators remaining = Total number - Number of men

Spectators remaining = [tex]x-\frac{x}{4}=\frac{4x-x}{4}=\frac{3x}{4}[/tex]

Now, number of women = [tex]\frac{2}{5}\times \frac{3x}{4}=\frac{6x}{20}[/tex]

Now, as per question:

Number of women = 132. Therefore,

[tex]\frac{6x}{20}=132[/tex]

[tex]6x=132\times 20[/tex]

[tex]x=\frac{2640}{6}=440[/tex]

Therefore, the total number of spectators = 440

Also, number of men = [tex]\frac{x}{4}=\frac{440}{4}=110[/tex]

Now, total number of spectators is the sum of the number of men, women and children.

Let the number of children be 'c'.

Total number = Men + Women + Children

[tex]440=110+132+c\\440=242+c\\c=440-242=198[/tex]

Therefore, there are 198 children at the circus show.

Answer:

5

Step-by-step explanation:

a+b=-1

x+y+z=2

7a+7b+6z+6x+6y=7(a+b)+6(z+x+y)=7(-1)+6(2)=-7+12=5

Answer:

a) Decrease

b) New mean = 78.43

c) Decrease                        

Step-by-step explanation:

We are given the following in the question:

Total number of students in class = 28

Average of 27 students = 79

Standard Deviation of 27 students = 6.5

New student's score = 63

a) The new student's score will decrease the average.

b) New mean

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean = \dfrac{\displaystyle\sum x_i}{27} = 79\\\\\sum x_i = 27\times 79 = 2133[/tex]

New mean =

[tex]\text{ New mean} =\dfrac{ \displaystyle\sum x_i +63}{28}\\\\ =\dfrac{2133+63}{28}= \dfrac{2196}{28} = 78.43[/tex]

Thus, the new mean is 78.43

c) Since the new mean decreases, standard deviation for new scores will decrease.

This is because the new value is within the usual values i.e. within two standard deviations of the mean. So, this wont cause a lot of variation as this value will be closer to already available data values. Also number of observations (n) in the denominator is increasing. Based on both these points we can conclude that standard deviation will decrease

Formula for Standard Deviation:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

Answer:

Cashew 12.5lb

Peanuts 37.5lb

Step-by-step explanation:

Let the number of pounds of cashewnuts and peanuts be c and p respectively.

Firstly, the total mass of the nuts is 50.

This means:

c + p = 50

Now let’s work with the money

4p + 7c = 4.75(50)

From the first equation, let c = 50 - p

Substitute this into the second equation.

4p + 7(50 - p) = 237.5

4p + 350 - 7p = 237.5

3p = 112.5

P = 112.5/3 = 37.5lb

For Cashew c = 50 - p = 50 - 37.5 = 12.5lb

Answer: the number of ducks in the field is 25

the number of pigs in the field is 9

Step-by-step explanation:

Let x represent the number of ducks in the field.

Let y represent the number of pigs in the field.

A duck has one head and a pig also has one head.

The number of ducks and pigs in a field totals 34. This means that

x + y = 34

The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, it means that

2x + 4y = 86 - - - - - - - - - - -- - 1

Substituting x = 34 - y into equation 1, it becomes

2(34 - y) + 4y = 86

68 - 2y + 4y = 86

- 2y + 4y = 86 - 68

2y = 18

y = 18/2 = 9

Substituting y = 9 into x = 34 - y, it becomes

x = 34 - 9 = 25

To find the number of ducks and pigs in the field, we can set up a system of equations and solve them. Using the given information and the equations x + y = 34 and 2x + 4y = 86, we can find that there are 25 ducks and 9 pigs in the field.

To solve this problem, we can use a system of equations. Let x represent the number of ducks and y represent the number of pigs. From the given information, we can set up two equations:

x + y = 34  (equation 1)

2x + 4y = 86  (equation 2)

Now, we can solve the system of equations. We can start by multiplying equation 1 by 2 to eliminate the x variable:

2(x + y) = 2(34)

2x + 2y = 68

Next, we can subtract equation 2 from this new equation:

(2x + 2y) - (2x + 4y) = 68 - 86

-2y = -18

Dividing both sides of the equation by -2 gives us:

y = 9

Substituting this value back into equation 1:

x + 9 = 34

x = 34 - 9

x = 25

Therefore, there are 25 ducks and 9 pigs in the field.

Answer:

The given statement describe inferential statistics.    

Step-by-step explanation:

Descriptive Statistic:

Inferential Statistic:

Given Scenario:

"Based on a sample of 170 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company-hired truck drivers."

Thus, this is an example of a inferential statistics as a sample was used to estimate the population.

Here,

Sample:

Sample of 170 truck drivers

Population:

All truck drivers.

With the help of a sample, we approximated the population, thus, this statement describe inferential statistics.

The statement is an example of inferential statistics, as it makes a general conclusion about a population (all truck drivers) based on a sample.

The statement "Based on a sample of 170 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company-hired truck drivers" describes the use of inferential statistics. This type of statistics is used when analysts want to make predictions or inferences about a population based on the data collected from a sample. In contrast, descriptive statistics are used simply to describe what the data show, such as calculating averages, medians, ranges, and so on. Since the statement indicates a broader conclusion about the earnings of independent versus company-hired truck drivers in general, based on a sample, it utilizes inferential statistics.

Answer:

A) True

Step-by-step explanation:

A basic variable is a variable that corresponds to a pivot column. A variable that does not corresponds to a pivot column is known as a free variable. It is required to row reduce the augmented matrix into echelon form so as to determine which of the variables are free and which of them are basic.

The statement is true. A basic variable in a linear system corresponds to a pivot column in the coefficient matrix. Basic variables have the leading ones in the matrix, while the rest are free variables.

The statement 'A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix.' is true. In a linear system, the basic variables are indeed those that correspond to the pivot column in the coefficient matrix. For example, if we have a linear system represented by a coefficient matrix, the basic variables would be the variables associated with the columns that have a leading one (also known as the pivot). The rest of the variables are known as free variables.

Consider a matrix with three columns representing three variables: x, y, and z. If x and y have leading ones and z does not, x and y would be the basic variables, whilst z would be a free variable. Therefore, understanding the relationship between the basic variables and the pivot column in a system's coefficient matrix is crucial in solving linear systems.

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In Physics, accuracy and precision are terms used to discuss the validity of measurements. Accuracy refers to how close a measured value is to its true value, while precision discusses the consistency or reproducibility of measurements. Good precision can reduce errors but does not necessarily improve accuracy.

In the field of Physics, accuracy and precision are used to discuss the reliability of measurements taken during experiments. Accuracy refers to how closely the measured value of a quantity corresponds to its 'true' value. For example, if we aim to measure a length of 10 meters, an accurate measurement would be as close to 10 meters as possible.

On the other hand, precision represents the degree of similarity, or reproducibility, between repeated measurements. If we measure the same length of 10 meters multiple times and get results like 9.9m, 10.1m, 10.0m, 9.9m, the measurements would be considered precise because they are closely clustered together, even if they are not necessarily 'accurate' (exact 10m).

It's important to understand that better precision does not always ensure better accuracy. The more measurements you make and the better the precision, the smaller the error will be, but accuracy requires measurements to be close to the actual value.

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Answer:

Step-by-step explanation:

total number of marbles=3+6+5+4+2=20

favorable events=3+4=7

P=(7/20)^{100}

Answer:

3.25

Step-by-step explanation:

36:24 = 2:3

6x-6 = (2/3)3x+7

x=3.25

Answer:

11=x

Step-by-step explanation:

AB   AC

    =

ED   EC

36:24=6x−6:3x+7

108x+252=144x−144

396=36x

11=x