The human resources office at your college decided to look at how many years 3 employees had worked at the college. The employees had worked at the college for 1, 10, and 6 years. Find the standard deviation of number of years worked for the employees and round to 1 decimal place if needed.

a. The length of the arc is 6.28cm

b. The area of the sector is 25.12cm²

The arc of a circle is defined as the part or segment of the circumference of a circle. A sector is the space bounded by the arc and the radii of the circle. The smaller area is known as the minor sector and the bigger area is known as the major sector.

The length of an arc = tetha /360 ×2πr

= 45/360 × 2×3.14× 8

= 2×3.142 = 6.28cm

The area of a sector = tetha / 360 × πr²

= 45/360 × 3.14 × 8× 8

= 3.14× 8

= 25.12 cm²

Therefore, the length of the arc is 6.28cm and the area of the sector is 25.12cm²

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Jamie made 8 1/4 cups of fruit punch for a party. Her guests drank 2/3 of the punch. How much fruit punch did her guests drink Jamie made 8 1/4 cups of fruit punch for a party. A mixed number can be converted into an improper fraction by multiplying the denominator by the whole number, and then adding the numerator. Thus, we have 33/4 cups of fruit punch.

Jamie's guests drank 2/3 of the punch. If Jamie made 33/4 cups of fruit punch, then the guests drank2/3 × 33/4= 22/12 or 1 5/12 cups of fruit punch The guests drank 1 5/12 cups of fruit punch. More than 100 words: To determine how much fruit punch Jamie's guests drank, we need to calculate the amount of punch made and then multiply it by the fraction of the punch consumed by the guests. Jamie made 8 1/4 cups of fruit punch.

We'll start by converting the mixed number to an improper fraction, which is 33/4. Next, we'll multiply 33/4 by 2/3 to determine how much punch the guests drank. This is calculated as follows:2/3 × 33/4= 22/12 or 1 5/12 cups of fruit punch. Therefore, Jamie's guests drank 1 5/12 cups of fruit punch.

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Answer:

572,000 thats your answer

Answer:

572,000

Step-by-step explanation:

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

Answer:

45

Step-by-step explanation:I had that question on my test.

To prove by induction that the summation formula n∑ k=3 2^k - 1 = n^2 - 4 holds for all integers n > 2, we follow these steps:1. Base case (n=3): ∑ k=3 2^k - 1 = 2^3 - 1 = 7 n^2 - 4 = 3^2 - 4 = 9 - 4 = 5 The base case is incorrect, so the statement is false for all integer n > 2.

Prove by induction that n∑ k=3 2k −1 = n2 −4 for all integer n > 2. Proof by induction Step 1: The first thing to do is verify the base case. The base case is the first value of n, which is 3, to be verified as a true statement. When n = 3, n∑ k=3 2k −1 = 27=9n2 −4=9−4=5The above equation is true because 3∑ k=3 2k −1 = 2*3-1+2*4-1 = 5, and n2 −4 = 9-4 = 5. Therefore, the base case is verified. Step 2: Assume that the statement is true for n=k. n=k∑ k=3 2k −1 = k2 −4Now, we must prove that the statement is true for n=k+1.n=k+1∑ k=3 2k −1 = (k+1)2 −4= k2 +2k+1−4= k2 +2k−3 +1= n∑ k=3 2k −1 +2k −1The equation becomes: n∑ k=3 2k −1 +2k −1=n∑ k=3 2k+1 −1Since we have already assumed that n∑ k=3 2k −1 = n2 −4 to be true for n=k, the equation becomes :n∑ k=3 2k −1 +2k −1=n2 −4+2k −1= n2 +2k −5Since 2k+1 ≥ 5 for k ≥ 3, the following inequality holds: n2 +2k −5≤(n+1)2 −4Therefore, the equation n∑ k=3 2k −1 +2k −1=n∑ k=3 2k+1 −1 is true for n=k+1, as we have shown above. Consequently, the statement is correct for all values of n > 2. Therefore, by mathematical induction, n∑ k=3 2k −1 = n2 −4 for all integer n > 2 is proven.

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If the summation of residual equals zero for the simple linear model, then it does not imply the summation of random errors and the expectation of the summation of random errors in the model equal to zero. Because both are independent factors.

The information is about linear regression. The summation of residual equals zero in case of the simple linear model. The sum of all the residuals is the multiplcation of expected value tothe total no of data points. Subsequently the expectation of residuals is 0, the sum of all the residual terms is zero. The summation of residuals equals zero for the simple linear model. This however doesn't mean that the random error summations are zero. The summation of residuals goes to zero only because of the equivalence of negative and positive residuals, i.e., the values have residues on both negative and positive sides equally. The summation of random errors cannot be zero as the errors are present in the system and are independent, unlike the residuals. Thus, the expectation of the summation of random errors can be zero or non-zero as they are independent factors and are unknown to the observer.

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The percentage of members that voted is 70%.

The art club had an election to select a president. 42 out of the 60 members of the art club voted in the election.

Therefore, the percentage of the members that voted can be calculated as follows;

percentage that voted = number of people that voted / total number members × 100

Therefore,

number of people that voted = 42

total number members = 60

Hence,

percentage that voted = 42 / 60 ×100

percentage that voted = 4200 / 60

Therefore,

percentage that voted = 70%

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

A, B, E  

explanation:                                                                                                                                            

Answer:

A: The range of scores is 38.

B: Without the outlier, the range of scores would be 12.

C: The outlier impacts the range more than it impacts the interquartile range.

D: The interquartile range is 9.

F: Without the outlier, the interquartile range would be 9.5.

Step-by-step explanation:

edg2020

True. Marginal cost refers to the additional cost incurred by producing one more unit of output.

Since the production of one more unit requires the use of additional variable factors of production (such as labor or raw materials), marginal cost always reflects the cost of those variable factors. Fixed costs, on the other hand, do not change with changes in output and are not included in marginal cost calculations. Therefore, marginal cost only reflects the change in cost associated with variable factors of production.

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If 150 is the 15%, to find which number is the 100% we use the rule of 3

and the rule say that:

The missing number in the boxes using the concept of perfect square are;

1) 4

2) 7 and 2

3) 4

4) 3 and 9

5) 3

A perfect square is defined as a number that is the square of a whole number. For example, 36 is a perfect square being the square of 6. Other perfect squares that are between 0 and 1000 are 1, 4, 9, 16, 25, 3649, 64, e.t.c

1st box: We see it as;

___ * 2 * 2

Using the concept of perfect squares and the pattern given, we can say that the missing number is 4

2nd box: 14 * __ * ___

Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 7 and 2

3rd box: 2 * 8 * ___

Using the concept of perfect squares and the pattern given, we can say that the missing number is 4

4th box: __ * 3 * _____

Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 3 and 9

5th: 3 * ____

Using the concept of perfect squares and the pattern given, we can say that the missing number is 3

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The expression, (5 > 57 % 8), evaluates to false.

To determine if the expression (5 > 57 % 8) evaluates to true or false, we need to first calculate the value of 57 % 8.

Step 1: Calculate 57 % 8, which represents the remainder when 57 is divided by 8.
57 % 8 = 1

Step 2: Compare 5 and the result from Step 1 using the '>' operator.
5 > 1

Step 3: Determine if the comparison in Step 2 is true or false.
Since 5 is greater than 1, the expression evaluates to true.

So, the expression (5 > 57 % 8) evaluates to true.

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Answer:

20:40

Step-by-step explanation:

The required ratio of lollipops to candy bars is 1:2.

Given that,
There are 20 lollipops and 40 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Total number of lollipops = 20, in a bag

Total number of candy bars = 40, in a bag

The ratio of lollipops to a candy bar in a bag,
Ratio = number of lollipops/number of candy bars
Ratio = 20 / 40
Ratio = 1 / 2
Ratio = 1:2

Thus, the required ratio of lollipops to candy bars is 1:2.

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Answer:

Integers are 48, 49, 50

Step-by-step explanation:

x+(x+1)+(x+2) = 147

3x + 3 = 147

3x = 147-3

x = 144 / 3 = 48

Answer: 100

Step-by-step explanation:

Because 88.9% of the data falls between approximately 47.62 and Blank.

Answer:

Step-by-step explanation:

The function r(t) for the line passing through the points P(9, 5, 9) and Q(8, 4, 5) can be written as r(t) = (9-t, 5-t, 9-t).

To find the function r(t) for the line passing through two points, we can use the parametric form of a line equation. The general form of a line equation is r(t) = P + t(Q - P), where P and Q are the given points and t is a parameter.

In this case, P(9, 5, 9) and Q(8, 4, 5). Plugging these values into the equation, we have:

r(t) = (9, 5, 9) + t((8, 4, 5) - (9, 5, 9))

    = (9, 5, 9) + t(-1, -1, -4)

    = (9-t, 5-t, 9-4t).

Therefore, the function r(t) for the line passing through the points P(9, 5, 9) and Q(8, 4, 5) is r(t) = (9-t, 5-t, 9-4t).

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Answer:

y = -x+5

Step-by-step explanation:

Answer:

slop is 0.5 and intercept of y is -3

Answer:

½ is the slope,-3 is the intercept

Step-by-step explanation:

now to find the slope and intercept

we use the equation,

y=mx + c

where m is the slope

and c is the y intercept

so we compare 4y=2x-12 to the equation

but we first have to make y the subject of the equation in the question – 4y is already the subject –

y=2x-12/4

y=2x/4 -3

comparing...

we see that m is 2/4=½ c= -3

Answer:

The answer is b

Step-by-step explanation:

Hope i helped ^^

By expanding and equating the real and imaginary parts of the given equation, we can show that v = u tan(3θ/2) and r = 4^2 cos^2(θ/2), where r is the modulus of the complex number u - iv.

Let's expand the equation (1 + z)(1 - i 2z^2) and equate the real and imaginary parts to establish the given results.

Expanding the equation:

(1 + z)(1 - i 2z^2) = 1 - i 2z^2 + z - iz 2z^2.

Now, equating the real and imaginary parts:

Real part: 1 + z = 1 + cosθ + i sinθ = 2cos^2(θ/2).

Imaginary part: -2z^2 - iz = -2(cos^2θ + i sin^2θ) - i(2cosθ sinθ) = -2cos^2(θ/2) - i sinθ cosθ.

Comparing the imaginary parts:

-2cos^2(θ/2) - i sinθ cosθ = -v.

We can conclude that v = 2cos^2(θ/2).

Now, comparing the real and imaginary parts of u - iv, we have:

Real part: u = 2cos^2(θ/2).

Imaginary part: -v = -2cos^2(θ/2).

Comparing the expressions for the imaginary part, we get:

v = u tan(3θ/2).

Therefore, we have shown that v = u tan(3θ/2) and r = 4^2 cos^2(θ/2), where r is the modulus of the complex number u - iv.

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The value of a and b from the given equation y = ax + b is -0.5 and -5

y = ax + b

-4 = -2a + b

-4.5 = -a + b

-4 = -2a + b

-4.5 = -a + b

-4 - (-4.5) = -2a - (-a)

-4 + 4.5 = -2a + a

0.5 = - a

a = -0.5

-4 = -2a + b

-4 = -2(-0.5) + b

-4 = 1 + b

-4 - 1 = b

-5 = b

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Answer:

Paulina is reading a book with 677pages total. If she has already read 345 and plans to read 23 pages a day, how many days, x, will she nees to read at that pace until she finishes the entire book?

Step-by-step explanation:

\(345 + 23x = 677\)

23x=677-345

x=677-345/23

x=332/23

x= 14.43 days

Answer:

14

Step-by-step explanation:

1/7*X=2

X=2/(1/7)

X=2*7

X=14

➪ Product of two rational numbers = 2

➪ One of the number = \( \frac{1}{7} \)

➪ The other number.

\(\huge{\boxed{\boxed{\tt{\purple{Solution\:⤵}}}}}\)

\(\sf\blue{The \:other \:number \:is\: 14.}\) ✅

❥ Let the other number be \(x\).

❥ As per the question, we have

\(product \: of \: two \: rational \: numbers \: = 2 \\ ⇢  \frac{1}{7} \times x = 2 \\ ⇢ x = 2 \times 7 \\ ⇢ x = 14\)

\(\sf\red{Therefore,\:the\:other\: number\: is\: 14.}\)

\( \frac{1}{7} \times 14 = 2 \\➪ \: \frac{14}{7} = 2 \\ ➪ \: 2 = 2\\ ➪ \: L. H. S. = R. H. S.\)

Hence verified.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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