Sketch the graph of the function below, including correct signs, x-intercepts and y-
intercepts.
f(x) = (x + 5)(x + 3)(x - 2)2

Answer:

Cumulative Frequency:

The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.

The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.

Step-by-step explanation:

Answer:

819 is the old one because all the numbers are 4 each when you count them.

The number 819 is odd among all the numbers.

A positional numeral system uses a single symbol, the numerical digit, either individually or in combination to represent numbers. The term "digit" refers to the ten symbols of the conventional base-10 numeral system, or decimal digits, to which the ten digits of the hands correspond.

The given numbers are:-

67626, 28917, 14412, 819, 54372, 96131

In the given numbers above all the numbers have 5 digits like 67626, 28917, 14412, 54372, 96131 and the number 819 has only three digits.

Therefore, the number 819 is odd among all the numbers.

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The mean and standard deviation of the sampling distribution for each sample size are as follows:

(a) n = 9: Mean = 10, Standard Deviation ≈ 3.333

(b) n = 15: Mean = 10, Standard Deviation ≈ 2.582

(c) n = 36: Mean = 10, Standard Deviation = 1.667

(d) n = 50: Mean = 10, Standard Deviation ≈ 1.414

(e) n = 100: Mean = 10, Standard Deviation = 1

(f) n = 400: Mean = 10, Standard Deviation = 0.5

To determine the mean and standard deviation of the sampling distribution of the sample means (x) for each given sample size, we can use the following formulas:

Mean of sampling distribution (μx) = Population mean (μ)

Standard deviation of sampling distribution (σx) = Population standard deviation (σ) / √(sample size)

Given that the population mean (μ) is 10 and the population standard deviation (σ) is 10, we can calculate the mean and standard deviation of the sampling distribution for each sample size as follows:

(a) n = 9:

μx = μ = 10

σx = σ / √n = 10 / √9 = 10 / 3 ≈ 3.333

(b) n = 15:

μx = μ = 10

σx = σ / √n = 10 / √15 ≈ 2.582

(c) n = 36:

μx = μ = 10

σx = σ / √n = 10 / √36 = 10 / 6 = 1.667

(d) n = 50:

μx = μ = 10

σx = σ / √n = 10 / √50 ≈ 1.414

(e) n = 100:

μx = μ = 10

σx = σ / √n = 10 / √100 = 10 / 10 = 1

(f) n = 400:

μx = μ = 10

σx = σ / √n = 10 / √400 = 10 / 20 = 0.5

Therefore, the mean and standard deviation of the sampling distribution for each sample size are as follows:

(a) n = 9: Mean = 10, Standard Deviation ≈ 3.333

(b) n = 15: Mean = 10, Standard Deviation ≈ 2.582

(c) n = 36: Mean = 10, Standard Deviation = 1.667

(d) n = 50: Mean = 10, Standard Deviation ≈ 1.414

(e) n = 100: Mean = 10, Standard Deviation = 1

(f) n = 400: Mean = 10, Standard Deviation = 0.5

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Answer:

C

Step-by-step explanation:

Took the assignment before

Answer:

f(-3) = |(-3)-2| = |-5| = 5

The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

Given lines of equations:

x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.

Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.

Let `t=2`, then the point on the line is

\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T

herefore, direction vector `

\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)

For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)

Let the angle between the direction vectors `v1` and `v2` be `θ`.

Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.

Thus, we have:

(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ

=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)

Therefore,

`θ = cos⁻¹(8/(4√10))`

which is approximately `28.07°`.

Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

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Answer:

The two numbers are 7 and 11.

[711?  Is this an ad?  ← :)]

Step-by-step explanation:

Let A and B stand for the two numbers.

We are told that:

1)  A+B=18, and

2)  A-B=4

Take the first expression and rearrange to isolate A:

A+B=18

A=18-B

Use this in the second expression:

(18-B)-B=4

-2B = -14

B = 7

From (1) we find A:  

A+B=18

A+7=18

A= 11

If A=11, then B=7 (from A+B=18)

CHECK:

Does A+B=18?

  11 + 7 = 18?  YES

Does A-B=4?

    11 - 7 = 4?  YES

Answer

56.6

Explanation

To solve this, we will use one of the principles for the order of operations.

55 + (12 - 4) ÷ 5

BODMAS or PEMDAS indicates that the expression in the bracket is simplified first before the multiplication or division, then, the addition or subtraction follows.

So,

55 + (12 - 4) ÷ 5

= 55 + 8 ÷ 5

= 55 + 1.6

= 56.6

Hope this Helps!!!

Answer to the first question: no, the sum is not always a monomial

Consider adding 2x and 5y. Both of which are monomials. Their sum is 2x+5y. We don't have like terms, so we can't combine them. The sum is a binomial as it has 2 terms.

======================================

Answer to the second question: yes, their product is alway a monomial

Going back to 2x and 5y. Multiply those two monomials and we get 10xy as a product. This is a monomial as it is one term. If p and q are monomials, then so is pq.

Answer:

Part A: 0

Part B: All real numbers

Step-by-step explanation:

Part A:

We have:

\((6^2)^x=1\)

First, let's evaluate the square:

\(36^x=1\)

Now, what to the xth power will equal 1?

Remember the fact that anything (except for 0) to the zeroth power is 1.

Therefore, our x is 0:

\(36^0=1\)

Part B:

We have:

\((6^0)^x=1\)

Like mentioned previously, anything to the zeroth power is 1. Thus:

\(1^x=1\)

Now, 1 is a special base because 1 to any (real) power is still going to be 1. For example:

\(1^0=1,1^1=1,1^{999},\text{ and } 1^{\pi}=1\)

Therefore, our values of x is all real numbers.

And we're done!

Answer:

The slope of the graph is -3

Step-by-step explanation:

do rise over run.

3 down, 1 right

Answer:

Step-by-step explanation:

45

Answer:

Step-by-step explanation:

12x-34

Add all the sides together

2(x+3) + 6x + 4(x – 10)

distribute:

2x+6 + 6x + 4x-40

and add:

12x-34

Answer:

number 4/the last option

Step-by-step explanation:

this is because each individual Tshirt = X. and we already know that we have 33$ to spend

Andrea arrived 5 minutes past 11:00 am, or at 11:05 am. Adding the 8 minutes indicated on her card, we get 11:13 am as the time Andrea arrived.

Let x be the number of minutes past 11:00 am that Andrea arrived. Then, Zach arrived (x + 15) minutes past 11:00 am. Two minutes ago (i.e., at 11:28 am), Andrea had been waiting for (28 - x) minutes, and Zach had been waiting for (13 + x) minutes. Three minutes from now (i.e., at 11:33 am), Andrea will have been waiting for (33 - x) minutes, and Zach will have been waiting for (18 + x) minutes. Since Andrea and Zach have waited for the same amount of time, we can set up the equation:

Solving for x, we get:

2x = 10

x = 5

Therefore, Andrea arrived 5 minutes past 11:00 am, or at 11:05 am. Adding the 8 minutes indicated on her card, we get 11:13 am as the time Andrea arrived.

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A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.

Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.

Proof: Given, AB = DE, BC = EF, AC = DF.

To prove: ΔABC ≅ ΔDEF.

We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.

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Answer:

7 x 21

Step-by-step explanation:

We can say that the dimensions are a and b. Since this is a rectangle, we know that the perimeter will be 2a + 2b. So our first equation is:

2a + 2b = 56.

They also tell us that the length is 3 times its width. So we can say this:

a = 3b.

Now we can substitute, and we can do the full problem with the given info:

2a + 2b = 56

a = 3b

2a = 6b

6b + 2b = 56

8b = 56

b = 7

Now that we know b, we can multiply it by 3 to get a:

b = 7

a = 3b

a = 21.

So our answer is:

a = 21

b = 7

Answer:

Dimensions:

7 x 21

Answer:

Width=7

Length=21

Step-by-step explanation:

p=56 feet

L=3W

P=2L + 2W

56=2(3W)+2W

56=6W+2W

56=8W

W=56/8 = 7 ⇒ Width=7

L=3W

L=3*7

L=21 feet ( length=21 feet)

check : p=2l+2w

P=2(21)+2(7)

p=42+14=56

a) The regression equation for the given data is Overhead Costs = 231,000 + 47.8 × Billable Hours

b) The coefficients of the regression model are b₀ = 231,000 and b₁ = 47.8

a. To develop a simple linear regression model between billable hours and overhead costs, we can use the following formula

Overhead Costs = b₀ + b₁ × Billable Hours

where b₀ is the intercept and b₁ is the slope of the regression line. We can use a statistical software or a spreadsheet program to obtain the regression coefficients. For these data, the regression equation is

Overhead Costs = 231,000 + 47.8 × Billable Hours

b. The coefficients of the regression model are b₀ = 231,000 and b₁ = 47.8. The fixed component of the model (b₀) represents the overhead costs that the consulting firm incurs regardless of the billable hours. This can include expenses such as rent, utilities, salaries, and other fixed costs.

In this case, the fixed component is $231,000, which represents the overhead costs that the firm has to pay even if they do not bill any hours to clients. The slope of the regression line (b₁) represents the change in overhead costs for each additional billable hour. In this case, the slope is 47.8.

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Answer:

1. non repeating

2. non repeating

3. repeating

Step-by-step explanation:

1. 5/12 = 0.41666666666667

2. 18/25 = 0.72

3. 17/22 = 0.77272727272

Given vector a= 137.0m at 40 degrees. west of north. To determine how much of vector a points due east, the following steps can be used:Step 1: Draw a diagram of the vector a and mark the direction of west and north.

The diagram would look like this: Step 2: Find the components of the vector a, that is, the horizontal component and the vertical component.

Step 3: To find the horizontal component, use the sine function: sin 40° = perpendicular / hypotenuse perpendicular

= hypotenuse x sin 40°perpendicular

= 137.0 x sin 40°perpendicular

= 88.1 m Therefore, the horizontal component of vector a is 88.1 m.

Step 4: To find the vertical component, use the cosine function:cos 40° = base/hypotenuse base

= hypotenuse x cos 40°base

= 137.0 x cos 40°base

= 104.6 m Therefore, the vertical component of vector a is 104.6 m. Step 5: Since we want to find the part of vector a that points due east, we need to use the horizontal component which is 88.1 m. Therefore, 88.1 m of vector a points due east.Thus, the long answer to the question is:88.1 m of vector a points due east.

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A' after the first transformation AND find A'' after the second transformation is:

x=(-3, -3)

A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.

The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.

Generally, the equation for is  mathematically given as

The point (5,3)  translated by the vector <2,6>

x= (-5 + 2, -3 + 6)

x=(-3, -3)

In conclusion, When you reflect it across the line y = 0, the x coordinate remains the same, and the y coordinate changes sign.  (-3, 3)

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There are 56 different ways to choose 5 books from this collection.

In this case, we have 8 subjects from which we need to choose 5 books. Since there are at least 5 copies of each book, we can assume that we have enough copies of each subject to choose from. The formula for combinations is nCr = n! / (r!(n-r)!), where n represents the total number of subjects and r represents the number of books to be chosen.  

In our case, n = 8 and r = 5.

Plugging these values into the formula, we get 8! / (5!(8-5)!) = 8! / (5!3!).

Simplifying further, we get (8 * 7 * 6) / (3 * 2 * 1) = 56.

Therefore, there are 56 different ways to choose 5 books from this collection.

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Answer:

The probability that Dominik is the goalie given that the goal attempt was blocked is 0.667 or 66.7%.

Step-by-step explanation:

To find the probability of Wayne attempting a shot on goal, we need to count the number of times Wayne appears in the data and divide it by the total number of shots taken:

Number of shots attempted by Wayne: 4

Total number of shots: 10

Probability of Wayne attempting a shot on goal: 4/10 = 0.4 or 40%

Therefore, the probability of Wayne attempting a shot on goal is 0.4 or 40%.

To find the probability of a goal given that Wayne took the shot, we need to count the number of goals scored by Wayne and divide it by the total number of shots he attempted:

Number of goals scored by Wayne: 2

Number of shots attempted by Wayne: 4

Probability of a goal given that Wayne took the shot: 2/4 = 0.5 or 50%

Therefore, the probability of a goal given that Wayne took the shot is 0.5 or 50%.

To find the probability that Dominik is the goalie given that the goal attempt was blocked, we need to count the number of times Dominik appears as the goalie when a shot was blocked and divide it by the total number of blocked shots:

Number of blocked shots where Dominik was the goalie: 2

Total number of blocked shots: 3

Probability that Dominik is the goalie given that the goal attempt was blocked: 2/3 = 0.667 or 66.7%

Therefore, the probability that Dominik is the goalie given that the goal attempt was blocked is 0.667 or 66.7%.

You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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The tanker has been filling the reservoir for 4 minutes given that it fills at a rate of 10 1/4 gallons per minute.

Rate refers to the relationship of two quantities of different units. Usually, it is a measure or quantity of something per unit time.

rate = amount / time

If a tank truck fills the gas station's reservoir at the rate of 10 1/4 gallons per minute, and if the reservoir is empty at the start and become 41 gallons full, we can determine how long the tanker has been filling the reservoir by dividing the final amount by the rate.

time = amount / rate

where amount = 41 gallons

rate = 10 1/4 gallons per minute

time = 41 gallons / 10 1/4 gallons per minute

time = 4 minutes

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a. The total frictional losses (EF) in the system, including the suction and discharge lines and the elevation difference, are calculated to be 122.8 J/kg. b. The calculated value of  mechanical energy balance Ws is -186.9 J/kg. c. the mass flow rate is \(m_dot = 0.0040 m^3/s\) *

The frictional losses in the suction and discharge lines are determined using the Darcy-Weisbach equation and assuming a friction factor. The elevation difference is considered as the static head difference.

The work done by the pump (Ws) is determined through the mechanical energy balance equation. The equation takes into account the pressure at the pump suction, the density of water, the velocity head, and the elevation difference. The calculated value of Ws is -186.9 J/kg. Assumptions made in the calculations include the friction factor and neglecting minor losses.

Finally, to determine the pump power, we need to know the flow rate. If the flow rate is not provided, we cannot calculate the pump power. However, if the flow rate is known, and assuming an efficiency of 80%, we can calculate the pump power using the equation Power = (Ws * \(m_dot\)) / efficiency, where \(m_dot\)is the mass flow rate of water.

b) The mechanical energy balance equation for the pump can be written as:

\(Ws = ΔH + Ef + Ep\)

where Ws is the work done by the pump per unit mass, ΔH is the change in elevation head, Ef is the frictional losses, and Ep is the pressure head.

Since the water discharges to the atmosphere, the pressure head can be neglected (Ep = 0). Also, there is no change in elevation head (ΔH = 0). Therefore, the equation simplifies to:

\(Ws = Ef\)

From part a), we have already calculated Ef. Thus, Ws is -186.9 J/kg.

c) The pump power (P) can be calculated using the equation:

\(P = Ws * m_dot / η\)

where m_dot is the mass flow rate and η is the efficiency of the pump.

Given that the efficiency is 80% (η = 0.80), and the mass flow rate is \(m_dot = 0.0040 m^3/s *\)

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Answer:

The directional derivative of f at (0, 1) in the direction of theta = pi/3 is sqrt(3)/2.

Step-by-step explanation:

To find the directional derivative of f at (0, 1) in the direction of theta = pi/3, we need to compute the dot product of the gradient of f at (0, 1) and the unit vector u in the direction of theta.

First, we need to find the gradient of f:

∇f(x, y) = <∂f/∂x, ∂f/∂y>

= <-y sin(xy), cos(xy) - xy sin(xy)>

Evaluating at (0, 1), we get:

∇f(0, 1) = <0, 1>

Next, we need to find the unit vector u in the direction of theta = pi/3:

u = <cos(pi/3), sin(pi/3)>

= <1/2, sqrt(3)/2>

Now we can compute the directional derivative:

D_u f(0, 1) = ∇f(0, 1) · u

= <0, 1> · <1/2, sqrt(3)/2>

= sqrt(3)/2

Therefore, The directional derivative of f at (0, 1) in the direction of theta = pi/3 is sqrt(3)/2.

of f at (0, 1) in the direction of theta = pi/3 is sqrt(3)/2.

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Answer:

Step-by-step explanation:

Let 'x' represent the actual salary.

|x - 25,000| <= 1800

- 1,800 <= x - 25,000 <= 1,800

25,000 - 1,800 <= x <= 25,000 + 1,800

23,200 <= x <= 26,800

The range of the salary is the closed interval [23,200, 26,800].