the time to complete a project, T, varies inversely with the number of employees, E, if 6 employees can complete the project in 7 days, hoy long will it take 12 employees?o

Answer:

Median: 46

Mean: about 46.9

Range: 72

Step-by-step explanation:

Median:

Put them in order

11 27 33 46 50 78 83

Then find the middle value which is 46.

Mean:

Add them all together then divide by the number of values

(11+27+33+46+50+70+83)/7

about 46.8571

Range:

Highest value-lowest value

83-11

72

To solve for the median, mean, and range of the given data set, we will follow these steps:
**Step 1: Organize the Data Set**
First, we must organize the data set in ascending order to calculate the median. The given data set is: 83, 27, 11, 78, 50, 33, 46.
Arranging the numbers, we get:
11, 27, 33, 46, 50, 78, 83
**Step 2: Find the Median**
The median is the middle value of a data set when it's ordered from least to greatest. Since there are seven numbers, the middle one will be the fourth value (since there are three numbers on each side of it).
So, the median is: 46
**Step 3: Calculate the Mean**
To calculate the mean (average), we sum all the numbers and then divide by how many numbers there are.
Mean = (Sum of all numbers) / (Number of numbers)
Sum = 11 + 27 + 33 + 46 + 50 + 78 + 83 = 328
Number of numbers = 7
Mean = 328 / 7 = 46.857 (approximately)
**Step 4: Find the Range**
The range is the difference between the highest and lowest values in the data set.
Minimum value = 11
Maximum value = 83
Range = Maximum value - Minimum value
Range = 83 - 11 = 72
**Summary:**
Median: 46
Mean: Approximately 46.857
Range: 72

2x -3y = 13

4x -y = -9

Multiply the second equation by -3 to make the coefficient of Y opposite the first equation.

4x -y = -9 x -3 = -12x + 3y = 27

Now add this to the first equation:

2x -12x = -10x

-3y +3y = 0

13 +27 = 40

Now you have :

-10x = 40

Divide each side by -10:

x = 40 / -10

x = -4

Now you have a value for x, replace that into the first equation and solve for y:

2(-4) - 3y = 13

-8 - 3y = 13

Add 8 to both sides:

-3y = 21

Divide both sides by -3:

y = 21/-3

y = -7

Now you have X = -4 and y = -7

(-4,-7)

The answer is 10 as the diameter because it says to estimate pi as 3. Since we know the circumference is 30 we can reverse it to find the diameter, since Circumference is pi time diameter.

Answer:

d = 10 km

Step-by-step explanation:

Circumference is equal to pi times diameter

C = pi *d

We know the circumference is 30

30 = pi *d

Let pi = 3

30 = 3d

Divide each side by 3

30/3=3d/3

10 =d

The diameter is 30 km

Answer:

(5, −6) and R(−5, 6)

Step-by-step explanation:

Answer:

4. Q(5, -6) and R(-5, 6)

Step-by-step explanation:

In the coordinates of point P which is (-5,-6) when you reflect it on the Y axis that means that the Y would be the same but the X will change signs, thats why the point Q is (5.-6) and to reflect it on the X axis the X remains the same but the Y would change the sign this is why point R will be (-5,6).

So point Q is (5,-6) and point R is (-5,6).

Answer:

$18.66

Step-by-step explanation:

Add together the amounts Keith spent on baseball and truck:  $10.37 + $8.29 = $18.66.  We can ignore the amount he spent on the jacket.

Answer:

[tex]\$34[/tex]

Step-by-step explanation:

step 1

Avery

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=12\ years\\ P=\$2,100\\ r=7 7/8\%=7.875\%=0.07875[/tex]  

substitute in the formula above  

[tex]A=\$2,100(e)^{0.07875*12}=\$5,402.91[/tex]

step 2

Morgan

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=12\ years\\ P=\$2,100\\ r=8 1/4\%=8.25\%=0.0825\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$2,100(1+\frac{0.0825}{1})^{1*12}=\$5,436.94[/tex]  

step 3

Find the difference

[tex]\$5,436.94-\$5,402.91=\$34.03[/tex]

To the nearest dollar

[tex]\$34.03=\$34[/tex]

ANSWER

[tex] -\sqrt{3}[/tex]

EXPLANATION

The given angle is 870°.

870°-360°-360°=150°

This means that:

870° is coterminal with 150°, hence its terminal side is in the second quadrant.

It makes an acute angle of 30° with the x-axis.

Note that cotangent is negative in the second quadrant,

Hence,

[tex] \cot(870 \degree) = \cot(150 \degree) = - \cot(30 \degree) = - \frac{1}{ \tan(30 \degree) } = - \sqrt{3} [/tex]

The first option is correct.

Answer:

use math-way

Step-by-step explanation:

= - square root of 3

80 ft^3 is the answer

Answer:

200ft^3

Step-by-step explanation:

Answer:

1.732050808

Step-by-step explanation:

https : // www. desmos. com/ scientific

EDIT square root of 3

The exact value of tan240° is the same as tan60° because of the periodicity of the tangent function and the fact that 240° lies in the third quadrant of the unit circle. The value of tan60° is √3 or about 1.732.

To find the exact value of tan240°, we should recall that the tangent function is periodic with a period of 180°, meaning tan(θ) is the same as tan(θ + 180°). Also, in the unit circle, 240° lies in the third quadrant, where tangent values are positive because both sine and cosine are negative. Therefore, tan240° is the same as tan(240° - 180°), which is tan60°. The exact value of tan60° is √3) or approximately 1.732. This calculation leverages trigonometric principles and the geometric interpretation of angles on the unit circle, demonstrating how to derive accurate values for trigonometric functions in specific angular contexts.

So it's asking how many times greater is 6,000 than 600. Simply divide to find that it is 10 times greater.

Hope this helps you!

The 6 in the hundreds place is 100 and the 6 in the thousands place is 1000

Where are the answers choices

Answer:  tends to become smaller

Step-by-step explanation:

In statistics and probability , the  law of large​ numbers says that as we increase the size of the sample, then the sample mean will get closer to the true value of population mean.

Therefore, the complete statement will be :

According to the law of large​ numbers, as more observations are added to the​ sample, the difference between the sample mean and the population mean​ tends to become smaller.

Because the teacher only picked 5 students out of all the students it was a sample.

If the teacher had asked every student, it would have been a population.

Answer:

sample

Step-by-step explanation:

The teacher only asked the five students specifically so it is a sample.

Population would be if the teacher asked every student.

Answer:

[tex]|KL|=7\sqrt{2}[/tex]

Step-by-step explanation:

The given triangle is a right triangle.

The m<K=45 degrees.

This means the measure of <L is  also 45 degrees.

This implies that;

|LM|=|KM|=7 units.

From the Pythagoras Theorem;

[tex]|KL|^2=|LM|^2+|KM|^2[/tex]

[tex]|KL|^2=7^2+7^2[/tex]

[tex]|KL|^2=2(7^2)[/tex]

[tex]|KL|=\sqrt{2(7^2)}[/tex]

[tex]|KL|=7\sqrt{2}[/tex]

Option C is correct.

The answer is:

The third option,

[tex]KL=7\sqrt{2}[/tex]

Since we are working with a right triangle, we can use the following identity:

[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]

We are given:

[tex]\alpha =45\°\\LM=y=7[/tex]

[tex]hypothenuse=KL[/tex]

Then, substituting and solving we have:

[tex]Sin(45\°)=\frac{7}{hypothenuse}[/tex]

[tex]Hypothenuse=KL=\frac{y}{Sin(45\°)}=\frac{7}{\frac{\sqrt{2} }{2} } \\\\Hypothenuse=KL=7\sqrt{2}[/tex]

Hence, the answer is the third option,

[tex]KL=7\sqrt{2}[/tex]

Have a nice day!

Answer:

A  = 25√3 cm²

Step-by-step explanation:

View 5√3 cm as being the height of an equilateral triangle whose base is at the bottom of the purple figure.  To find the area of one such triangle, we use the area-of-a-triangle formula A = (1/2)(b)(h).  

                                                     opp

Using the sine function sin Ф = --------

                                                      hyp

we find the length of the hypotenuse, which is also the radius of the octagon, and because this is an equilateral triangle, is also the length of the base:

                √3       5√3 cm

sin 60° = -------- = ------------- , which produces the value of hyp:

                  2             hyp

                √3       5√3 cm

              -------- = ------------- , which produces the value of hyp:

                  2             hyp

√3·hyp = 10√3, or hyp = 10 cm

Then the area of this one triangle is A = (1/2)(b)(h), or

A = (1/2) (10 cm)(5√3 cm) = 25√3 cm²

answer for this question is (d) 3

To find the x-coordinate of the point of intersection of the two given lines, set the equations equal and solve for x, revealing that the x-coordinate is 3 (D).

The question involves finding the x-coordinate of the point of intersection of two lines represented by the equations y = –6x + 20 and y = 5x – 13. To find the point of intersection, we can set the two equations equal to each other because at the point of intersection, the y-values (and x-values) for both equations will be the same.

Setting the equations equal to each other:

–6x + 20 = 5x – 13

Adding 6x to both sides and adding 13 to both sides gives:

33 = 11x

Dividing both sides by 11:

x = 3

Therefore, the x-coordinate of the point of intersection of the two lines is 3, which corresponds to answer choice D.

Answer:

We have the following equation:

i(4-7i)

Multiplying:

4i - 7(i^2)

So we know that i = sqrt(-1), then i^2 = -1.

For that reason:

4i - 7(i^2) = 4i - 7(-1) = 4i + 7

So the answer is: 4i +7

Answer for the problem is 4i-7i^2

Answer:

The correct answer is A) 1/2 pound

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

If 6 is x, then it would be (6-3)2+1. 6-3 is 3, 3 times 2 is 6, 6+1=7

The answer is 7... Just Plug 6 into x and then solve

(8, 8) and (0, 8). If the equation is y = any number, the second coordinate will always be that number. :)

Answer:

1 degree = 60 minutes

Step-by-step explanation:

The DMS method is for Degree Minutes Seconds.  That allows you to give a precise location the way it's most commonly used on paper maps.  Today, with the electronic maps we mostly use the numeric version (34.234 degrees for example).

So, in the DMS method, one degree is basically like an hour on your clock.  It can be divided into 60 minutes.  Then, those minutes can be divided into 60 seconds.  Just like an hour, a degree has 60 minutes and 3600 seconds.

Final answer:

One degree in the DMS method of angle measurement is divided into 60 minutes. To convert DMS to DD, like with 118 degrees 15 minutes, divide the minutes by 60 and add the result to the degrees, giving you 118.25.

Explanation:

In the DMS method of angle measurement, one degree is equivalent to 60 minutes of angle. This is similar to how an hour of time is divided into 60 minutes. To visualize this, if you consider a full circle being 360 degrees, each degree can be further subdivided into 60 smaller parts, each of these parts is known as a minute of angle.

For example, the conversion of 118 degrees 15 minutes to decimal degrees (DD) is a simple mathematical process. You would divide the minutes by 60 since there are 60 minutes in a degree, resulting in the equation 118 + 15/60, which equals 118.25 degrees. This conversion is an important skill in coordinate conversion activities, where positions are described in DMS format and need to be converted to DD for calculations.

Answer:  B, A, B

Step-by-step explanation:

Let's find the z-score for both companies using the formula: [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

Company A: [tex]z=\dfrac{43-38.2}{1.7}=\large\boxed{2.8}[/tex]

Company B: [tex]z=\dfrac{43-36.9}{2.4}=\large\boxed{2.5}[/tex]

The z-score from Company B is closer to 0 than the z-score of Company A so it it more likely that a package of 43 lozenges is produced by Company B

Since the z-score from Company A is closer to zero than the z-score of Company B, the company that produced a package with 43 lozenges in it is most likely Company A.

To find which company is more likely to produce a package with 43 lozenges, we'll first calculate the z-scores for each company using the formula:

[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]

Where:

- [tex]\( x \)[/tex] is the number of lozenges in the package (43)

- [tex]\( \mu \)[/tex] is the mean number of lozenges in the package for each company

- [tex]\( \sigma \)[/tex] is the standard deviation of the number of lozenges in the package for each company

For Company A:

[tex]\[ z_A = \frac{43 - 38.2}{1.7} = \frac{4.8}{1.7} \approx 2.82 \][/tex]

For Company B:

[tex]\[ z_B = \frac{43 - 36.9}{2.4} = \frac{6.1}{2.4} \approx 2.54 \][/tex]

Since the z-score for Company A (2.82) is higher than the z-score for Company B (2.54), it indicates that the value of 43 lozenges is relatively further away from the mean for Company A compared to Company B.

Thus, Company A is more likely to produce a package with 43 lozenges.

The correct question is:

Suppose Company A produces packages of throat lozenges that are normally distributed with a mean of 38.2 individual lozenges and a standard deviation of 1.7 lozenges.

Company B produces packages of throat lozenges that are normally distributed with a mean of 36.9 individual lozenges and a standard deviation of 2.4 lozenges.

Select from the drop-down menus to correctly complete the statement.

Since the [tex]$z$[/tex]-score from [tex]$\square$[/tex] is closer to zero than the [tex]$z$[/tex]-score of [tex]$\square$[/tex] , the company that produced a package with 43 lozenges in it is most likely [tex]$\square$[/tex] .

Answer:A?

Step-by-step explanation:

Answer:

x = 55.6

Step-by-step explanation:

In this triangle, the hypotenuse is the unknownj.  The sine function relates the hypotenuse, the angle and the side opposite the angle:

sin Ф = opp / hyp

Here, sin 20° = 19 / x.  This can be rearranged as x = 19 / sin 20°

This works out to x = 19 / 0.342, or 55.6.

x = 55.6

ANSWER

B) 15

EXPLANATION

The given polynomial is

[tex]23 {x}^{5} + 12 {x}^{2} + 19 { x }^{3} + 15 {x}^{6} [/tex]

We arrange this polynomial in ascending powers of x to obtain the standard form;

[tex] 15 {x}^{6} + 23 {x}^{5} + 19 { x }^{3} + 12 {x}^{2}[/tex]

The degree of this polynomial is 6.

The coefficient of the leading term is 15

Answer:

[tex]\$806.14[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part 1)

Find the interest rate r

we have  

[tex]t=1\ years\\ P=\$575\\ r=?\\n=1\\A=\$615[/tex]  

substitute in the formula above  and solve for r

[tex]\$615=\$575(1+\frac{r}{1})^{1*1}[/tex]  

[tex]\$615=\$575(1+r)[/tex]  

[tex]r=(615/575)-1\\ \\ r=0.07[/tex]

The interest rate is 7%

Part 2)

we have  

[tex]t=4\ years\\ P=\$615\\ r=0.07\\n=1\\A=?[/tex]  

substitute in the formula

[tex]A=\$615(1+\frac{0.07}{1})^{1*4}[/tex]  

[tex]A=\$615(1.07)^{4}=\$806.14[/tex]  

Answer:

Part 1) [tex]\$250[/tex] is not enough to cover the cost of 4 tickets

Part 2) She would need to work an additional 14 hours to purchase 4 concert tickets

therefore

No, she would need to work an additional 14 hours to purchase 4 concert tickets

Step-by-step explanation:

step 1

Find the cost of 4 tickets

[tex]4*(75+12.95)=\$351.80[/tex]

so

[tex]\$351.80> \$250[/tex]

therefore

[tex]\$250[/tex] is not enough to cover the cost of 4 tickets

step 2

Find the number of hours needed to work to cover the difference

The difference is equal to

[tex]\$351.80-\$250=\$101.80[/tex]

Let

x-----> the number of hours needed to work to cover the difference

The inequality that represent the situation is

[tex]7.50x \geq 101.50[/tex]

[tex]x \geq 101.50/7.50[/tex]

[tex]x \geq 13.5\ hours[/tex]

The minimum number of hours is 14

Answer:

26 cm

Step-by-step explanation:

Tangents drawn to a circle from a point outside the circle are equal in length.

On the left side the tangents are 4/ 4 and 3/3

On the right side the tangents are 2/ 2 and 4/4

Calculating perimeter from the bottom left clockwise

perimeter = 4 + 4 + 3 + 3 +2 + 2 + 4 + 4 = 26 cm

Sounds like you have

[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(1+\frac kn\right)^2\frac1n[/tex]

which translates to the sum of the areas of [tex]n[/tex] rectangles with dimensions [tex]\left(1+\dfrac kn\right)^2[/tex] (height) and [tex]\dfrac1n[/tex] (width). This is the right-endpoint Riemann sum for approximating the area under [tex]x^2[/tex] over the interval [1, 2].

Answer:

Option C

Step-by-step explanation:

We are given that

[tex]\lim_{n\rightarrow\infty}\sum_{k=1}^{n}(1+\frac{k}{n})^2\times \frac{1}{n}[/tex]

We have to find the definite integral for the given summation.

We know that

[tex]\lim_{n\rightarrow \infty}\sum_{k=a}^{n}f(a+k\frac{b-a}{n})(\frac{b-a}{n}=\int_{a}^{b}f(x)dx[/tex]

Using the formula

a=1

[tex]\frac{b-a}{n}=\frac{b-1}{n}[/tex]

[tex]\frac{b-1}{n}=\frac{1}{n}[/tex]

[tex]b-1=1[/tex]

[tex]b=1+1=2[/tex]

[tex]\lim_{n\rightarrow\infty}\sum_{k=1}^{n}(1+\frac{k}{n})^2\times \frac{1}{n}=\int_{1}^{2}x^2 dx[/tex]

Option C is true.

Answer:

Place them in a line.

Step-by-step explanation:

Take the First cube and place it on the paper

Then place another cube behind that cube

Repeat with remaining cubes

Should end up with a line of cubes that create a rectangular prism.

Ramon cannot form a rectangular prism using exactly 5 cubes because a rectangular prism has 6 faces, which would each be formed by a cube. To create even the smallest possible rectangular prism, he would need at least 6 cubes.

No, Ramon cannot make a rectangular prism using exactly 5 cubes. A rectangular prism is a three-dimensional figure with six faces that are rectangles. It would not be possible to form a rectangular prism using only 5 cubes because to form a rectangular prism you need at least 6 cubes.

Each cube would represent one face of the rectangular prism.

This is because a rectangular prism has 3 dimensions: length, width, and height. Even if you make the smallest possible rectangular prism, you would need a minimum of 6 cubes (1 cube length, 1 cube width, and 6 cubes high). If he has only 5 cubes, at least one dimension (length, width, or height) would be incomplete.

https://brainly.com/question/31408211

#SPJ2

Answer:

its C

Step-by-step explanation:

There you go, you didn’t show the representation but I drew one.