The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays.

The expression that describe the end behavior of the expression f(x)= (3.25)^x + 6 is The curve begins infinitely close to the line y equals 6 in the second quadrant.

The behavior of the graph of a function at its "ends" on the x-axis is referred to as the end behavior of a function, f.

For example, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞), the end behavior of a function explains the trend of the graph.

The graph of the function is attached and from the graph it shows that the graph continued to tend towards towards line y = 6

Learn more about end behavior here:

https://brainly.com/question/28954897

#SPJ1

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

For more such questions on direction

https://brainly.com/question/30016405

#SPJ8

Answer:

$55.96

Step-by-step explanation:

To find 30% of $79.95, we must multiply 79.95 by .3

We get 23.985, which can be rounded to the nearest 100th to get 23.99

So, 30% of $79.95 is $23.99

Now, we can just subtract to find the sale price.

$79.95 - $23.99 = $55.96

Answer:c

Step-by-step explanation:

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

To learn more on vectors: https://brainly.com/question/31900604

#SPJ1

Notice that the polygon can be divided on 3 rectangles, as shown in the following diagram:

The 14 ft side on the original image was split on a segment of 10ft and another of 4ft.

The areas of these rectangles, are:

The total area of the polygon is the sum of the areas of the three rectangles:

Therefore, the area of the polygon is:

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

Learn more about standard deviation here :

https://brainly.com/question/12402189

#SPJ9

Answer:

x+6=40

Subtract 6

x=34

Answer:

n + 6 = 40

n = 34

Step-by-step explanation:

Sum of a number and 6. That means you got to add n and 6.

'is' means you need to put an equal sign.

n + 6 = 40

Now, lets find what n is.

Isolate the variable by subtracting 6 from both sides.

n = 34

Answer:

8 units

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

16 = 1/2 (4)*x

16 = 2x

Divide each side by 2

16/2 = 2x/2

8 =x

Answer:

8)

  a) 6,320,000

  b) 230,000

  c) 10,000,000

8)

  a) 9,300,000

  b) 5,240

  c) 28,000

The side lengths of the triangle are 12 cm, 64 cm, and 65 cm.

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let's denote the length of the shorter leg as "x". Then, according to the problem statement, the length of the longer leg is "16 cm more than four times the length of the shorter leg", which can be expressed as 4x + 16.

Also, the length of the hypotenuse is "17 cm more than four times the length of the shorter leg", which can be expressed as 4x + 17.

Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse.

So, we can write an equation as follows:

x² + (4x + 16)² = (4x + 17)²

Simplifying this equation, we get:

x² + 16x² + 128x + 256 = 16x² + 136x + 289

Bringing all the terms to one side, we get:

x² - 8x - 33 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 1, b = -8, and c = -33.

Plugging in these values, we get:

x = (8 ± √(8^2 - 4(1)(-33))) / 2(1)

x = (8 ± √(256)) / 2

x = 4 ± 8

Therefore, we have two possible values for x: x = -4 or x = 12. Since the length of a side of a triangle cannot be negative, we reject x = -4 and conclude that x = 12.

Substituting this value of x into the expressions we derived earlier, we get:

Length of shorter leg: x = 12 cm

Length of longer leg: 4x + 16 = 4(12) + 16 = 64 cm

Length of hypotenuse: 4x + 17 = 4(12) + 17 = 65 cm

Hence , the triangle is solved

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ2

Answer:

The answer is 16% I just took the test

Step-by-step explanation:

Answer:

98,000 bacteria.

Step-by-step explanation:

We are given the formula:

\(P=le^{kt}\)

Where l is the initial population, k is the rate of growth, and t is the time ( in hours).

We know that it has an initial population of 500. So, l is 500.

We also know that the population grows to 7000 after 2 hours.

And we want to find the population after 4 hours.

First, since we know that the population grows to 7000 after 2 hours, let's substitute 2 for t and 7000 for P. Let's also substitute 500 for l. This yields:

\(7000=500e^{2k}\)

Divide both sides by 500:

\(e^{2k}=14\)

We can solve for the rate k here, but this is not necessary. In fact, when can find our solution with just this.

Let's go back to our original equation. We want to find the population after 4 hours. So, substitute 4 for t:

\(P=500e^{4k}\)

We want to find the total population, P. Notice that we can rewrite our exponent as:

\(P=500(e^{2k})^2\)

This is the exact same thing we acquired earlier. So, we know that the expression within the parentheses is 14. Substitute:

\(P=500(14)^2\)

Square and multiply:

\(P=500(196)=98000\)

So, after 4 hours, there will be 98,000 bacteria.

And we're done!

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer and Step-by-step explanation:

Given: diameter = 16ft                                                                                                                                             height = 5 ft.                                                                                                                                                                      Depth = 4ft

Work =?

As we know that work = force x distance

W= distance x density x volume                      

W= ʃ04 (5-y) 62.5x ∏ (d/2)2dy                   (area = ∏r2     ,    r= d/2)

      = 62.5 ʃ04 (5-y) ∏ (4y) dy

      =62.5∏ ʃ04 (5-y) 4ydy

        =62.5∏ ʃ04 20y-4y2dy

      =62.5∏ |20y2/2 – 4y3/3|04

      =62.5∏ |74.66|

       =14659ft.lbs (approximately)

The work (in ft-lb) that would be required to pump all of the water over the upper rim is :

Work =?

work = force x distance

W= distance x density x volume                      

W= ʃ04 (5-y) 62.5x ∏ (d/2)2dy        (area = ∏r2     ,    r= d/2)

W  = 62.5 ʃ04 (5-y) ∏ (4y) dy

W  =62.5∏ ʃ04 (5-y) 4ydy

W  =62.5∏ ʃ04 20y-4y2dy

W  =62.5∏ |20y2/2 – 4y3/3|04

W =62.5∏ |74.66|

W =14659ft.lbs (approximately)

The work (in ft-lb) that would be required to pump all of the water over the upper rim is 14659ft.lbs

Know more :

https://brainly.com/question/5038760?referrer=searchResults

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Step-by-step explanation:

all the pink area above the blue line (above means ">", and the blue line is -1/2 x), and not including the line.

Answer:

-1/2

Step-by-step explanation:

the slope of the first line is 2

to get the line perpendicular, you swap the numerator and denominator, then if positive make negative and the other way around

Answer:

Step-by-step explanation:

true because the sum of the squares of the legs gives the measure of the hypotenuse (Pythagoras' theorem)

Answer:

Vertical

Step-by-step explanation:

Answer:

∠1 and ∠3 = vertical

Step-by-step explanation:

vertically opposite angles are equal

The answer is D) AABC is translated 1 unit right, then rotated 90° clockwise about the origin

If you follow the steps translating triangle ABC to A"B"C" and rotating it. You will get that answer. I can envision it mentally simply by following one coordinate at a time which can help me during tests and is how the translations work.

For instance if you moved the A coordinate 2 units to the right it would sit on the y axis, and when rotated 90 degrees wouldn't 1 unit above the x axis but on it. You can simply use mental math for questions like this because they are simple enough to follow where you just pick a coordinate and do the translating and dilating based on what you are given.

Sorry if it's not a mathematical explanation but it's how I usually solve these questions! Hope I could help!!
~Neo

The Sequence of Transformation that has been applied is; D. AABC is translated 1 unit right, then rotated 90° clockwise about the origin.

From triangle translation of ABC to A"B"C" and rotation of it, we can see that;

If we moved the A coordinate 2 units to the right it would sit on the y axis, but when rotated 90°, it would be 1 unit on the x axis.

Thus, applying the principe of translation and rotation we can say that AABC is translated 1 unit right, then rotated 90° clockwise about

the origin.

Read more about Translation and Rotation at; https://brainly.com/question/5612016

#SPJ5

Answer:

1234567891011121314151617181920

The number of bacteria present after 13 hours is 5,306.

The number of bacteria present after 13 hours is calculated by applying half-life equation.

N = N₀ x 2^(t / d)

Where:

Since the bacteria population grew from 3,000 to 3,600 in 6 hours, the value of d is calculated as follows;

3,600 = 3,000 x 2^(6 / d)

3600/3000 = 2^(6 / d)

1.2 = 2^(6 / d)

log2 (1.2) = 6/d

0.38 = 6/d

d = 6/0.38

d = 15.8 hours

The number of bacteria after 13 hours is calculated as follows;

N = 3,000 x 2^(13 / 15.8)

N = 5,306.5 ≈ 5,306

Learn more about growth rate here: https://brainly.com/question/29334875

#SPJ1

The complete question is below:

A culture started with 3,000 bacteria. After 6 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present in 13 hours. round your answer to the nearest whole number.

Answer:

0.0234375

Step-by-step explanation:

You just keep dividing by 2

If I'm wrong, sorry

Answer:

0.046875 aka 3/64

Step-by-step explanation:

In a geometric sequence, each term will be related to the previous term by undergoing either multiplication or division.

In this case, each case is exactly 1/2 of the previous term. 12 is half of 24, and 6 is half of 12. By continuing this sequence, we get

1: 24

2: 12 (24 * 1/2)

3: 6 (12 * 1/2)

4: 3 (6 * 1/2)

5: 3/2 (3 * 1/2)

6: 3/4 (3/2 * 1/2)

7. 3/8 (3/4 * 1/2)

8. 3/16 (3/8 * 1/2)

9. 3/32 (3/16 * 1/2)

10. 3/64 (3/32 * 1/2)

There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.

Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.

In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.

For example, two people could own different numbers of credit cards but have the same monthly charges.

As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).

Because of this, case 3 does not represent a function.

for such more question on function

https://brainly.com/question/16332322

#SPJ8

Answer:  geometric series

Step-by-step explanation:

If it is arithmetic, the difference from each term to the next will always be the same.

4096 - 1024 = 3072; 1024 - 256 = 768

3072 ≠ 768. so not arithmetic

If it is geometric, the ratio of each term to the next will always be the same.

4096/1024 = 4

1024/256 = 4

256/64 = 4

64/16 = 4

This is a geometric series. Each term (after the first) is (1/4) of the term before.

Hope this helps.

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

he two numbers that multiply to -35 and add to get -18 are -5 and 3.

To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.

Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:

-5 + 3 = -2

So, -5 and 3 are the two numbers that multiply to -35 and add to -18.

This shows that the Probability distribution of the scores of a randomly selected senior executive is correct.

Probability distribution for the job satisfaction score of a randomly selected senior executive

A probability distribution is a table of all possible values of a variable (like scores) and the likelihood of their occurrence.

The percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives are given as:Job Satisfaction Score    IS Senior Executives (%)1 5%2 9%3 38%4 42%5 6%

To determine the probability distribution of the scores for a randomly selected senior executive, we convert the percentage distribution into a probability distribution by dividing the percentage frequency of each score by 100. Then, we add up the probabilities of all scores to verify that they sum up to 1 (or 100%).

Therefore, the probability distribution is:

Job Satisfaction Score     Probability of Occurrence1                                    

 0.052                                      0.093                              

  0.384                                      0.425                                      0.06

The sum of the probabilities of all scores is 0.05 + 0.09 + 0.38 + 0.42 + 0.06 = 1.00 or 100%.

This shows that the probability distribution of the scores of a randomly selected senior executive is correct.

For more questions on Probability .

https://brainly.com/question/25839839

#SPJ8

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

For such more questions on Cost of tile and carpet.

https://brainly.com/question/29574063

#SPJ8