60 POINTS, BOTH PARTS

Part A

BUSINESS: Ahmed's consulting firm began with 23 clients. The number of clients decrease at an annual rate of 0.5%.

Write a function that represents the number of clients at Ahmed's consulting firm y after x years.

A) y = 24(0.995)^x
B) y = 24(1.995)^x
C) y = 23(1.995)^x
D) y = 23(0.995)^x

Part B

After how many years will Ahmed's consulting firm have 15 clients? Round to the nearest year if necessary.

Answer:

1155

Step-by-step explanation:

165 X 7 = 1155

Answer: If Liam did 165 sit-ups a day, he would do 1155 sit-ups every week

Step-by-step explanation:

Answer:

7.50

Step-by-step explanation

Multiply 1.50 by 5 and you get 7.50.

Answer:

Step-by-step explanation:

No, this is not correct.

Step 1: Find the directional distance from every vertex on the blue image to  the center, Point C.

Point A is 1 unit left and 4 units upwards to Point C.

Point B is 4 units right and 5 units upwards to Point C.

Point C is the center of the dilation, so that point will not change.

Step 2: Apply the scale factor to the directional distances to know the distances of the new images.

The scale factor is 2 so

Point A' should be 2 units left and 8 units upwards to Point C.

Point B' should 8 units right and 10 units upwards to Point C.

Step 3:  Move the point in respect to Point C.

The new image should have the these points.

One point that is 2 units left and 8 units upwards to Point C.

Another point that is Point B' should 8 units right and 10 units upwards to Point C.

One point that coincides  with  Point C.

Answer:

(12,-7)

Step-by-step explanation:

The required ordered pair of the pre-image of D'(4, -3) is D(12, -7).

Given that,
To determine the preimage of the ordered pair of D'(4, -3) by the translation, (x, y)  to (x – 8, y+4).

Coordinate, is represented as the values on the x-axis and y-axis of the graph.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the ordered pair of the preimage be (x, y)
Now,

according to the question,
x - 8 = 4
x = 12
y + 4 = -3
y = -7

Thus, the required ordered pair of the pre-image of D'(4, -3) is D(12, -7).

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Answer:

There were 62 people on the train to begin with.

Step-by-step explanation:

Firstly,i I subtracted 21 with 18 so i got 3.

It means that the train got 3 more people from the start.

Then i subtracted 65 with 3.

And so i got 62.

Implementing a new system into an organization module by module is called a​ phased approach.

A phased approach is one of two common methods used to develop an ERP system solution. In this strategy, the system's functionalities are introduced in a certain order, gradually replacing previous systems and processes.

This frequently indicates that a business starts off with core functionality that is given top attention, and then other applications are gradually added in stages over time. An alternative implementation strategy, however, uses an all-at-once model in which the system and all apps "Go Live" simultaneously.

The optimal implementation plan for your firm will depend on the needs, goals, and strategies you have for it. This might involve a hybrid strategy where crucial functionality is added to the core ERP programs first, and then desirable features are added later on in a staged implementation. By considering all of your options, your firm can decide which will serve its interests the most effectively.

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\((x - 1)^2\) = 4|x + 1|(y + 3) This is the equation of the parabola with the given vertex (1, -3) and directrix x = -1.

To determine the equation of the parabola with the given vertex and directrix, we can use the standard form of the equation for a parabola

with a vertical axis of symmetry:

\((x - h)^2\) = 4p(y - k)

where (h, k) represents the vertex coordinates, and p is the distance between the vertex and the directrix.

In this case, the vertex is (1, -3), so h = 1 and k = -3. The directrix is x = -1, which means the distance between the vertex and the directrix is 1 unit.

Substituting the values into the standard form equation, we have:

\((x - 1)^2\)= 4p(y + 3)

To find the value of p, we can use the distance formula between a point (x, y) on the parabola and the directrix x = -1:

p = |x - (-1)|

Since the distance is 1 unit, we have:

p = |x + 1|

Now we can substitute this value back into the equation:

\((x - 1)^2\) = 4|x + 1|(y + 3)

This is the equation of the parabola with the given vertex (1, -3) and directrix x = -1.

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The Five P's technique is a problem-solving approach that involves identifying and addressing key elements to effectively solve a problem. It consists of five steps: Problem, Purpose, Plan, Process, and Product. In this explanation, I will use the example of improving customer satisfaction in a restaurant to illustrate each step of the Five P's technique.

Problem: Begin by clearly defining the problem. For instance, the problem could be that customer satisfaction ratings have been consistently low in the restaurant.

Purpose: Determine the purpose or objective of solving the problem. In this case, the purpose could be to improve customer satisfaction and increase positive reviews.

Plan: Develop a plan to address the problem. For example, the plan could involve training the staff on customer service, enhancing the menu options.

Process: Execute the plan by implementing the identified strategies. This may include conducting staff training sessions, revamping the menu, and setting up a feedback mechanism for customers to share their experiences.

Product: Evaluate the outcome of the implemented strategies and assess the results. Monitor customer satisfaction ratings, review feedback from customers, and analyze any changes in positive reviews and customer loyalty. Adjust the strategies as needed to further enhance customer satisfaction.

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Based on the information, we can infer that the coordinates of point C are (8, 15). Additionally, the perimeter of the second triangle would be 64.

To find the distance of the sides of the triangle we must identify the information we know. Since the perimeter is equal to 50 and the base to 16 we can infer that each side measures 17 as shown below.

50 - 16 = 34

34 / 2 = 17

In this case we know its height and its base, so we can find the length of the side by dividing the triangle in two and finding the hypotenuse. In this formula we can replace b by 6.25 or 15, which are the two available options we have.

a² + b² = c²

8² + 15² = c²

64 + 225 = c²

289 = c²

17 = c

Then the correct answer would be option C. On the other hand, if the points of this triangle are modified, we must use the same procedure. We divide this triangle in two and there are two right triangles with a base of 12 and a height of 16, we are going to calculate the distance of the side.

So the side of these triangles is 20 and the base is 24. So, its perimeter is 64.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

option b)  x³ + x² + 3x - 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

= x³ + x - 3 + x² + 2x

= x³ + x² + 3x - 3

Answer: 4x^2

Step-by-step explanation:

Sorry I don't know how to explain I hope this helps you have a great day

Answer:

Here we want to create a histogram of:

Number of houses Vs day.

First you need to create a rectangular coordinate axis.

In the x-axis you will divide the days as:

day 1, day2, day3 etc

in the y-axis you will measure the number of houses visited.

then, for the first day our height will be 12 units

for the second day, our height will be 28 units...

and so on.

Remember that for histograms you need to use columns.

Then, our histogram will look like:

Answer:

A

C

B

Step-by-step explanation:

A) All the corners of the square touch the edge of the circle
B) Only 1 side of the square touches the circle so it forms a chord.

C) The circle is inside the square so the sides of the square form tangents (Perpendicular lines to the radius).

The data set would list each day in February with a temperature measurement, measured on an interval scale.

The data set in question would list the temperatures in Albany, NY each day in the month of February. This data set would be classified as interval data, as it would measure temperatures on a numerical scale. Interval data is composed of numerical values that are measured on an interval scale, meaning that the difference between any two values is the same, regardless of their position on the scale. Temperature is an example of an interval data type, as it is measured numerically and the difference between two temperatures is the same regardless of where they are on the scale (e.g. the difference between 50°F and 55°F is the same as the difference between 90°F and 95°F). This data set would be useful for tracking temperature trends over a period of time, and for making predictions about future temperatures in a certain area.

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Answer:

B

Step-by-step explanation:

Answer:

the answer is 32,768 hopes this helps

Step-by-step explanation:

8^5 = 8x8x8x8x8 = 64x8x8x8= 64x64x8 = 4096x8= 32,768

Answer:

Step-by-step explanation:

the dot is on the 32 and the line is the 3rd line

Answer:

irrational

Step-by-step explanation:

irrational because there will still be a 2 under the root when you simplify to 2√2

The solution for system of equation provided as per the given question will be x = -19 and y = 55 or (-19,55).

It is given that the equations are:

y = –3x – 2

Simplifying it further, we get:

y + 3x = -2 (equation 1)

5x + 2y = 15 (equation 2)

Multiplying y + 3x = -2 by 2 and subtracting from 5x + 2y = 15, we get:

2y - 2y + 5x -6x = 15 + 4

-x = 19

x = -19

Plugging the value of x in the equation y + 3x = -2, we get:

y + 3 × - 19 = -2

y - 57 = -2

y = -2 + 57

y = 55

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Your answer would be 37.5%

For the first card you picked, the probability of picking a number less than 3 is 2/4 = 1/2, because there are 2 cards that are less than 3 and a total of 4 cards.

When picking the second card, it is still out of 4 because you replaced the first one, so the probability of picking a card greater than 1 is 3/4 because there are 3 cards that are greater than 1 out of a total of 4.

Therefore the total probability would be 1/2 × 3/4 = 3/8. To find this as a percentage we just multiply by 100, and this gives us 37.5%.

I hope this helps!

Answer:

You have three card : 1, 2, 3 and 4.

You first pick one card randomly, the probability of picking a number less than 3 is:

P = 2/4  

You then pick a second card after putting the first card back, the probability of picking a number greater than 1 is:

P = 3/4

=> The probability of picking a number less than 3 and then picking a number greater than 1:

P = (2/4) x (3/4) = 3/8

Hope this helps!

:)

Based on a survey of 400 non-fatal accidents, where 173 involved faulty equipment, the point estimate for the population proportion (p) of accidents that involved faulty equipment is 173/400 = 0.4325.

To calculate the point estimate for the population proportion, we divide the number of accidents involving faulty equipment (173) by the total number of accidents surveyed (400).

This gives us a ratio of 0.4325, which represents the estimated proportion of accidents involving faulty equipment in the population.

A point estimate is a single value that serves as an approximation or best guess for an unknown population parameter.

In this case, the population proportion (p) represents the proportion of all accidents that involved faulty equipment. The point estimate of 0.4325 suggests that approximately 43.25% of non-fatal accidents may involve faulty equipment based on the sample data.

It's important to note that this point estimate is subject to sampling variability and may not perfectly reflect the true population proportion. To obtain a more precise estimate with a measure of uncertainty, one would need to consider confidence intervals or conduct hypothesis testing using statistical methods.

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Arden's crate has dimensions of 3 feet by 2 feet by 1 foot (since it's open-topped and turned upside down). To cover all five faces with square tiles that measure 1 foot by 1 foot, we need to find the total surface area of the crate. As each tile measures 1 sq ft, Arden will need 126 square tiles to cover the five faces of the open-faced crate.

The surface area of each of the two shorter sides is 3 feet by 1 foot = 3 square feet. The surface area of the bottom (which is now the top) is 2 feet by 3 feet = 6 square feet. The surface area of the longer sides is 2 feet by 1 foot = 2 square feet each, for a total of 4 square feet. So the total surface area is:

2(3 square feet) + 6 square feet + 4(2 square feet) = 20 square feet

Since each square tile is 1 foot by 1 foot, each tile covers 1 square foot. Therefore, Arden will need 20 square tiles to cover all five faces of her crate.

Note: The number "833" given in the question is not related to the crate and tiles problem, so it can be ignored.

To determine the number of 1 ft by 1 ft square tiles Arden needs to cover the five faces of the open-faced crate, first, we need to calculate the surface area of each face. The crate has the following dimensions: 3 ft (length), 2 ft (width), and 12 ft (height).

There are two side faces, two front/back faces, and one bottom face. Calculate the area of each face as follows:

1. Side face: length x height = 3 ft x 12 ft = 36 sq ft (there are two of these faces)
2. Front/Back face: width x height = 2 ft x 12 ft = 24 sq ft (there are two of these faces)
3. Bottom face: length x width = 3 ft x 2 ft = 6 sq ft

Now, sum up the surface area of all the faces:
(36 sq ft x 2) + (24 sq ft x 2) + 6 sq ft = 72 sq ft + 48 sq ft + 6 sq ft = 126 sq ft

As each tile measures 1 sq ft, Arden will need 126 square tiles to cover the five faces of the open-faced crate.

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The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

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The slopes of the secant lines do not appear to be approaching a limit.

For each value of x, calculate y and then use the slope formula to find the slope of P Q for the given limit.

x = 2 → y = 0 : Q(2, 0) ⇒ m =0 − 0 / 2 − 1 = 0

x = 1.5 → y ≈ 0.866 : Q(1.5, 0.866) ⇒ m = 0.866 − 0/ 1.5 − 1 ≈ 1.73

x = 1.4 → y ≈ −0.434 : Q(1.4, −0.434) ⇒ m =−0.434 − 0 / 1.4 − 1 = −1.08

x = 1.3 → y ≈ −0.823 : Q(1.3, −0.823) ⇒ m = −0.823 − 0/1.3 − 1 = −2.74

x = 1.2 → y ≈ 0.866 : Q(1.2, 0.866) ⇒ m = 0.866 − 0 / 1.2 − 1 = 4.33

x = 1.1 → y ≈ −0.282 : Q(1.1, −0.282) ⇒ m = −0.282 − 0/1.1 − 1 = −2.82

x = 0.9 → y ≈ −0.342 : Q(0.9, −0.342) ⇒ m = −0.342 − 0/0.9 − 1 = 3.42

x = 0.8 → y = 1 : Q(0.8, 1) ⇒ m = 1 − 0/ 0.8 − 1 = −5

x = 0.7 → y ≈ 0.782 : Q(0.7, 0.782) ⇒ m = 0.782 − 0/0.7 − 1 = −2.61

x = 0.6 → y ≈ 0.866 : Q(0.6, 0.866) ⇒ m = 0.866 − 0 / 0.6 − 1 = −2.17

x = 0.5 → y = 0 : Q(0.5, 0) ⇒ m = 0 − 0 / 0.5 − 1 = 0

Hence, The slopes of the secant lines do not appear to be approaching a limit.

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Answer:

1a 2a

Step-by-step explanation:

n × (−2+5 ) = −8+20

n × 3 = 12

n = 4

2 + (n+6) = −1+6

n + 8 = 5

n = -3