The number of hours that the employees at the grocery store worked last week is normally distributed with a mean of 24 and a standard deviation of 6. If there are 60 total employees, approximately how many worked at least 30 hours last week?

In the graph, we have four points: A=(-2,2), B=(-1,1), C=(2,0) and D=(7,-1)

At the segment AB, we have the function f(x). Its slope is (1 - 2)/[-1 -(-2)] = -1

Then, it can be expressed in the form f(x) = -x + b

Replacing x with -1, we got: 1 = 1 + b, which implies b = 0

Therefore, f(x) = -x

At the segment BC, we have the function f'(x). Its slope is (0 -1)/[2 -(-1)] = -1/3.

From this, we have: f'(x) = -x/3 + b

Replacing x with 2, we got -2/3 + b = 0, which implies b = 2/3

Therefore, function f'(x) = -x/3 + 2/3 is the function f(x) turned left with an angle of arctan(1/3) and turned up by 2/3 units.

From the segment CD, we have the function f''(x). Its slope is -1/(7-2) = -1/5

Then, it can be expressed in the form f''(x) = -x/5 + b

Replacing x with 2, we got -2/5 + b = 0, which implies b = 2/5

Therefore, the function f''(x) = -x/5 + 2/5 is the function f(x) turned left with an angle of arctan(1/

Answer:

38.25

Step-by-step explanation:

A = 1/2(8.5)(9)

Answer:

\(38.25 mm^{2}\)

Step-by-step explanation:

Area of a triangle = 1/2bh

b = 8.5

h = 9

1/2(8.5)(9) = 38.25

Answer:

Area=18ft^3 Surface Area=44ft^2

Step-by-step explanation:

The formula for area of a rectangular prism is A=lwh. So you just plus that in

Answer:

Volume = 18 cubic feet
Surface Area = 44 square feet
Double width = Double the space

Step-by-step explanation:

Please see attached explanations.

Surface area is the area (one side multiplied by another) of every side of the storage box, added together.
I have labeled each unique pair of sides as a, b, and c. That is top and bottom, left and right side, and front and back side.

Volume is the length multiplied by the width multiplied by the height.

By doubling the width, you are doubling the size of the box in that given direction. You can prove this mathematically by making the width twice of what it was and finding volume again.

The square root that could be the number shown on the number line is √17

On the number line, the position of the point is

Point = 4.1

Square both sides of the above equation

So, we have"

Point^2 = 4.1^2

This gives

Point^2 = 16.81

Approximate

Point^2 = 17

Hence, the square root that could be the number shown on the number line is √17

Read more about number line at:

https://brainly.com/question/24644930

#SPJ1

Answer:

5 five-dollar coins and 3 ten-dollar coins

Step-by-step explanation:

10x3=30

5x5=25

30+25=55

Step-by-step explanation:

The number of people to paint the bridge is inversely proportional to the number of hours it takes.

(If there are more people, it will take less time etc.)

9 people can paint the bridge in 5 hours.

=> 2 people can paint the bridge in 5 * (9/2) = 22.5 hours.

By applying the binomial distribution formula, it can be concluded that the probability of seeing at least one albino squirrel is 0.095.

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!)   where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

If n is the number of the squirrel, p is the probability of seeing albino squirrels and q is the probability of seeing non-albino squirrels, then:

n = 10000

p = 1/100000

q = 1 - 1/100000 = 99999/100000

The probability of seeing at least one albino squirrel:

= P (X ≥ 1)

= 1 - P(X< 1)

= 1 - P(X=0)

= 1 - C(10000,0) * (1/10000)⁰ * (99999/100000)¹⁰⁰⁰⁰⁻⁰

= 1 - (1 * 1 * (99999/100000)¹⁰⁰⁰⁰)

= 1 - 0.904836

= 0. 095164

≈ 0.095

Thus the probability of seeing at least one albino squirrel is 0.095.

To learn more about binomial distribution formula click here: brainly.com/question/29125646

#SPJ4

The types of graphs most appropriate for displaying categorical data are bar graphs, line graphs, pie charts, and histograms.

The graphs follows as:

To learn more about graphs refer :

https://brainly.com/question/16608196#

#SPJ11

Answer:

Is that you in your pfp?

Step-by-step explanation:

Answer:

A then D then C then F thats what I see

Step-by-step explanation:

The function that describes the population of Martin is\(P(t) = 12,420 \times (1 + 0.016)^t\)

The predicted population of Martin in 2015 is 14557

The predicted  population of Martin in 2002 is 10,658

The function that describes the population of Martin as a function of the number of years t, since 2005, can be written as:

\(P(t) = 12,420 \times (1 + 0.016)^t\)

where P(t) is the population of Martin t years since 2005.

To predict the population of Martin in 2015, we need to substitute t = 10 into the equation:

P(10) = 12,420 × (1 + 0.016)¹⁰

= 14556.5

Therefore, the predicted population of Martin in 2015 is approximately 14556.5 people.

To predict the population of Martin in 2002, we need to find the number of years between 2005 and 2002, which is 3 years.

We can substitute t = -3 into the equation:

P(-3) = 12,420 × (1 + 0.016)⁻³)

= 10,658

Therefore, the predicted population of Martin in 2002 is approximately 10,658 people.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

To learn more about function click here:

brainly.com/question/30721594

#SPJ11

INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

Answer:

302

Step-by-step explanation:

Answer: = UwU

Step-by-step explanation:

Answer:

5u

Step-by-step explanation:

Simplifying

5u + -1u = u + 15

Combine like terms: 5u + -1u = 4u

4u = u + 15

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-1u' to each side of the equation.

4u + -1u = 15 + u + -1u

Combine like terms: 4u + -1u = 3u

3u = 15 + u + -1u

Combine like terms: u + -1u = 0

3u = 15 + 0

3u = 15

Divide each side by '3'.

u = 5

Simplifying

u = 5

Sylvia and Patrick gathered information on the weight of cars and the mileage they get, and then proceeded to plot the data on a graph.

For such more question on correlation

https://brainly.com/question/13879362

#SPJ8

The eigenspace associated with the eigenvalue -1 will consist of all vectors that are flipped or reversed under the reflection transformation.

In linear algebra, an eigenvalue is a scalar value that represents a special property of a square matrix. Eigenvalues are used to study the behavior of linear transformations and systems of linear equations.

In simpler terms, when we multiply the matrix A by its eigenvector v, the result is equal to the scalar multiplication of the eigenvector v by its eigenvalue λ. In other words, the matrix A only stretches or shrinks the eigenvector v without changing its direction.

The eigenvalues of a matrix A can be found by solving the characteristic equation, which is obtained by subtracting λI (λ times the identity matrix) from A and setting the determinant equal to zero. The characteristic equation helps find the eigenvalues associated with a given matrix.

To find an eigenvalue of matrix a for the linear transformation t that reflects points across some line through the origin, we can consider the following:

Since reflection across a line through the origin is an orthogonal transformation, the eigenvalues of matrix a will be ±1.

The eigenspace associated with the eigenvalue 1 will consist of all vectors that remain unchanged under the reflection transformation.

The eigenspace associated with the eigenvalue -1 will consist of all vectors that are flipped or reversed under the reflection transformation.

Please note that without additional information about the specific line of reflection, it is not possible to determine the exact eigenspace for matrix a.

To know more about eigenvalue visit:

https://brainly.com/question/31650198

#SPJ11

No, the function y=2sin(2x) is not a solution of the differential equation y'''-8y=0.

To determine whether a function is a solution to the differential equation, we have to first find the derivatives of the function. The derivatives of y=2sin(2x) are y'=4cos(2x), y''=-8sin(2x) and y'''= -16cos(2x).

Next, we have to substitute the derivatives of the given function into the differential equation. When we substitute the derivatives of y=2sin(2x) into the differential equation, we get -16cos(2x) - 8×2sin(2x) = 0. This is not equal to 0, so y=2sin(2x) is not a solution to the differential equation y'''-8y=0.

To learn more about derivatives visit:

https://brainly.com/question/23819325

#SPJ4

You can use the given data to find the 5 information box plot needs to make and use the construction rule for box plot to select the best box plot among given options.

The box plot best representing the given observations is

Option B: Box plot with minimum value 9. 1, lower quartile 9. 2, median 9. 4, upper quartile 9. 7, and maximum value 9. 8

A box plot has 5 data description.

IQR(inter quartile range)  is the difference between third and first quartile.

The given data is

9.4, 9.2, 9.7, 9.8, 9.4, 9.7, 9.6, 9.3, 9.2, 9.1, 9.4

The sorted data in ascending order is

9.1, 9.2, 9.2, 9.3, 9.4, 9.4, 9.4, 9.6, 9.7, 9.7, 9.8

The mid value(6th here since there are 11 observations) is the median = 9.4

The minimum value is 9.1

The maximum value is 9.8

The first quartile is the average of the two mid values of the first 6 observation(it is because 6 is even, otherwise we'd've taken mid value)

It is (3rd value + 4th value)/2 =  9.25

The third quartile is the average of the two mid value of the last 6 observations.

It is (8th value + 9th value)/2 = (9.6 + 9.7)/2 = 9.65

The second option is best representing the given information compared to other options.

Thus,

The box plot best representing the given observations is

Option B: Box plot with minimum value 9. 1, lower quartile 9. 2, median 9. 4, upper quartile 9. 7, and maximum value 9. 8

Learn more about box plot here:

https://brainly.com/question/1523909

Answer:

89999

Step-by-step explanation:

The person's height can be estimated to be 12.5 feet based on the given information.

In this scenario, we can use similar triangles to find the height of the person. Let's consider the triangles formed by the person, the street light, and their respective shadows. The height of the street light is given as 30 feet, and the length of its shadow is 40 feet. Similarly, the length of the person's shadow is given as 10 feet.

Since the triangles formed are similar, we can set up a proportion to solve for the person's height. The ratio of the person's height to their shadow length is equal to the ratio of the street light's height to its shadow length.

Using the given values, we have:

(person's height) / 10 = 30 / 40

Cross-multiplying, we find:

(person's height) = (10 * 30) / 40 = 300 / 40 = 7.5 feet

Therefore, the person's estimated height is 7.5 feet.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ11

Bucket number 2 will contain 45 after sorting the data.

According to the statement, we are given that a data list is sorted using bucket sort with 4 buckets and we have to find which bucket will contain the number 45.

So, the given data list is:

76, 56, 93, 24, 45, 88, 13, 7, 37

The list of data is sorted into buckets and the data contains numbers from 0 to 100.

We know that the 100 numbers are being sorted with 4 buckets which means each bucket contains 25 numbers.

So, let us consider

BUCKET 1: 0 to 25

It contains data numbers 7, 13, and 24.

Now,

BUCKET 2: 25 to 50

It contains data numbers 37 and 45.

Now,

BUCKET 3: 50 to 75

It contains data number 56.

Now,

BUCKET 4: 75 to 100

It contains data numbers 76, 88, and 93.

From sorting, the 45 number sort in bucket 2.

So, bucket number 2 will contain 45 after the list is sorted.

To learn more about Bucket sorting or bin sorting;

https://brainly.com/question/31481690

#SPJ4

2 is the constant of proportionality for the relationship given in the table.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

By using the formula y=kx we find this

k is the constant of proportionality.

0.8=k(0.4)

Divide both sides by 0.4

k=0.8/0.4

k=2

Hence, 2 is the constant of proportionality for the relationship given in the table.

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

well, first off, hmmm let's find their slopes in the first place

\(p=\stackrel{\stackrel{m}{\downarrow }}{2}n+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad {\Large \begin{array}{llll} \boxed{x=2} \end{array}}\)

now,  to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below for BrandY\((\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 6 } \implies {\Large \begin{array}{llll} 1=Y \end{array}}\)

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above for BrandZ

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 }=Z \end{array}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{X}{2} ~~ > ~~ \stackrel{Y}{1}\hspace{5em}\stackrel{X}{2}~~ > ~~ \stackrel{Z}{\frac{3}{2}}~\hfill\)

The tangential vector, normal vector, and binormal vector are given by:

T = -7i - (7a sinh(t/a))j

N = [-7i - (7a sinh(t/a))j]/sqrt[(-7)^2 + (7a sinh(t/a))^2]

B = (-7 / √49 + 49a² sinh²(t/a)) i + (7a sinh(t/a) / √49 + 49a² sinh²(t/a)) j.

Given the space curve r(t) = -7ti - (7a cosh(t/a))j, a > 0.

Tangential vector T can be determined using the following formula:T = r'(t)

Where r'(t) is the derivative of r(t) with respect to t.Thus, we need to differentiate r(t) with respect to t.

Here's the differentiation:r(t) = -7ti - (7a cosh(t/a))j

The derivative of the first component is -7 and the derivative of the second component is -7a sinh(t/a).

Hence, the tangential vector T is given by:T = r'(t) = -7i - (7a sinh(t/a))j

The magnitude of the tangential vector is given by:|T| = sqrt[(-7)^2 + (7a sinh(t/a))^2]

The normal vector N can be found by the formula:N = T/|T|

That is: N = [-7i - (7a sinh(t/a))j]/sqrt[(-7)^2 + (7a sinh(t/a))^2]

Finally, the binormal vector is given by the cross product of T and N. B = T x N = i j k - 7 0 - 7a sinh(t/a) / √49 + 49a² sinh²(t/a) i - 7 0 - 7 / √49 + 49a² sinh²(t/a) j 0 0 0 k

B = (-7 / √49 + 49a² sinh²(t/a)) i + (7a sinh(t/a) / √49 + 49a² sinh²(t/a)) j

Therefore, tangential vector, normal vector, and binormal vector are given by:

T = -7i - (7a sinh(t/a))j

N = [-7i - (7a sinh(t/a))j]/sqrt[(-7)^2 + (7a sinh(t/a))^2]

B = (-7 / √49 + 49a² sinh²(t/a)) i + (7a sinh(t/a) / √49 + 49a² sinh²(t/a)) j.

To learn more about tangential vector, normal vector, and binormal vector visit: brainly.com/question/30895285

#SPJ11

Answer:

141,600,000 miles

Step-by-step explanation:

If you provide the desired standard error value, I can help you calculate the corresponding population standard deviation.

The standard error is a measure of the variability or uncertainty of a sample mean. It is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, if we want the standard error to be smaller, the population standard deviation should be larger.

To determine how large the population standard deviation needs to be, we need to specify a desired standard error value. Without that information, it is not possible to provide a specific answer. The relationship between the population standard deviation and the standard error is inversely proportional, so as the population standard deviation increases, the standard error decreases.

Know more about standard deviation here:

https://brainly.com/question/23907081

#SPJ11

Answer:

Answer B, Dogs, cats, fish, birds, reptiles, hamsters

12% for birds, 20% for cats, 40% for dogs, 15% for fish, 3% for hamsters, and 10% for reptiles

Step-by-step explanation:

For the first you simply have to order the votes in desending order, from the most popular choice to the least, that being the order in option B

For the second, because there are 200 people who voted and percentages are out of 100%, you simply have to divide the number of votes for each kind of pet by 2 to get the percentage of people who voted for it.

The relative size of each category from largest to smallest is option B. Dogs, cats, fish, birds, reptiles, hamsters.

Percentage is defined as the parts of a number per fraction of 100. So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Given,

Total students surveyed = 200

Students who preferred dogs = 80

Students who preferred reptiles = 20

Students who preferred birds  = 24

Students who preferred cats = 40

Students who preferred fish = 30

Students who preferred hamsters = 6

(a) So most of the students preferred dogs, then cats, then fish, then birds, reptiles and hamsters.

So the relative size of each category from smallest to largest is Dogs, cats, fish, birds, reptiles, hamsters.

(b) Percentage of dogs = (80 / 200) × 100 = 40%

Percentage of reptiles = (20 / 200) × 100 = 10%

Percentage of birds = (24 / 200) × 100 = 12%

Percentage of cats = (40 / 200) × 100 = 20%

Percentage of fish = (30 / 200) × 100 = 15%

Percentage of hamsters = (6 / 200) × 100 = 3%

(c) Number of degrees for dogs = 40% × 360° = 144°

Number of degrees for reptiles = 10% × 360° = 36°

Number of degrees for birds = 12% × 360° = 43.2°

Number of degrees for cats = 20% × 360° = 72°

Number of degrees for fish = 15% × 360° = 54°

Number of degrees for hamsters = 3% × 360° = 10.8°

Hence the percentage and degree of each category is found.

Learn more about Percentage here :

https://brainly.com/question/626448

#SPJ2

The graph of the given inequality y ≥ x² + 1 is a shaded region above the downward-facing parabola -x² + 1.

Hence, graph A represents the given inequality.

The inequality  y ≥ x² + 1 represents a region in the coordinate plane where y is greater than or equal to the value of the function -x² + 1 for any given x. The graph of this inequality is a shaded region above the downward-facing parabola -x² + 1. The vertex of this parabola is located at the point (0,1), and as x moves away from 0, the value of the function becomes more negative.

Therefore, the shaded region includes all points (x, y) where y is greater than or equal to the y-value of the parabola at that x-value. The resulting graph is a curve that opens downward and flattens out at y=1 as x moves further away from 0.

Hence, the correct option is A.

To know more about inequality here

https://brainly.com/question/31434121

#SPJ1