If f(x) = x³ - 10x² + 7x + 18 and x - 2 is a factor of f(x), then find all of the
zeros of f(x) algebraically.

To find the fraction of the square quilt block that is shaded, we need to count the number of shaded unit squares and divide it by the total number of unit squares in the quilt block. Let us begin by counting the number of shaded unit squares.

We notice that there are a total of 6 unit squares that are shaded. The unit squares that are shaded are the 2 squares that are completely shaded and the 4 squares that are half shaded due to the presence of triangles.

Next, we need to count the total number of unit squares in the quilt block. We notice that the quilt block is made up of 9 unit squares, each of which can be divided into 4 smaller unit squares. Thus, the total number of unit squares in the quilt block is 9 x 4 = 36.

Therefore, the fraction of the square quilt block that is shaded is 6/36 or 1/6.

To summarize, the shaded portion of the quilt block consists of 6 unit squares out of a total of 36 unit squares. Thus, the fraction of the square quilt block that is shaded is 1/6.

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The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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Answer:

135

Step-by-step explanation:

5 times 35 equals 135

Answer:

$175

Step-by-step explanation:

because that is how much she deposited

To determine the proportion of at-home games that were wins, we need to calculate the conditional probability of a win given that the game was played at home. Let's denote the proportion of at-home games that were wins as P(W|H).

We know that 60% of all games were at-home games, which means that 0.60 is the probability of an at-home game (P(H)). We also know that 40% of all games were wins, so the probability of a win (P(W)) is 0.40. Additionally, we are given that 35% of all games were at-home wins, which means P(W∩H) = 0.35.

To find P(W|H), we can use the conditional probability formula:

P(W|H) = P(W∩H) / P(H)

Substituting the given values:

P(W|H) = 0.35 / 0.60

Calculating the result:

P(W|H) ≈ 0.5833

Rounding to two decimal places, the proportion of at-home games that were wins is approximately 0.58 or 58%.

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just add all the numbers together and then divide them by how many numbers there were, and youll find the mode (average)

the lat one u just subtract 30 from 45, and find how many more scores

Answer:

the answer would be 5b as the exterior angle is subdivided with the co efficient

Step-by-step explanation:

The equivalent value of m is given by the expression m = 1

Given data ,

We can use the properties of exponents to solve this problem. Specifically, when we multiply two powers with the same base, we add their exponents.

So, we have:

(-3)^(m+1) × (-3)⁵ = (-3)⁷

Using the property of exponents, we can add the exponents on the left-hand side:

(-3)^(m+1+5) = (-3)⁷

Simplifying the exponents on the left-hand side:

(-3)^(m+6) = (-3)⁷

We know that two powers with the same base are equal if and only if their exponents are equal. So, we can set the exponents equal to each other:

m + 6 = 7

Subtracting 6 from both sides:

m = 1

Hence , m = 1 is the value that satisfies the equation

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Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Friend functions may directly modify or access the private data members. group of answer choices are true.

A friend function in C++ is a function that is not a member of a class but has access to its private and protected members. It is declared with the keyword "friend" inside the class. One of the advantages of using friend functions is that they can directly modify or access the private data members of a class, bypassing the normal access restrictions.

Friend functions are able to do this because they are granted special privileges by the class they are declared in. This means that they can access private data members and even modify them without using the usual public member functions of the class.

This feature can be useful in certain scenarios. For example, if we have a class that represents a complex number, we may want to provide a friend function to calculate the magnitude of the complex number directly using its private data members, instead of going through a getter function..

In conclusion, friend functions in C++ can indeed directly modify or access private data members. While this can be a powerful tool in certain cases, it should be used with caution to maintain the integrity of the class's encapsulation.

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Step-by-step explanation:

you're just going to switch x and y and then solve for y

Answer:

Hello,

Step-by-step explanation:

The problem is that the inverse function is not a function but

an union of 2 functions.

\(y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-\sqrt{x-1} ) * ((y+6)+\sqrt{x-1}) =0\\\\y=-6+\sqrt{x-1}-6\ or\ y=-6-\sqrt{x-1}\\\)

For the fun

,\(f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^{-1}(x)=-6-\sqrt{x-1} =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^{-1}(x)=-6+\sqrt{x-1} =0\ if\ x\geq 6\\\)

Answer:

10i - 2

Step-by-step explanation:

( 1 + 4i ) - ( 3 - 6i )

= 1 + 4i - 3 + 6i

= 1 - 3 + 4i + 6i

= - 2 + 10i

= 10i - 2

Answer:

10-10i

Step-by-step explanation:

Isolate i on one side of the equation.

(3-4i)+(7-6i)

DISTRIBUTIVE PROPERTY:

A(B+C)=AB+AC

A(B-C)=AB-AC

(A+BI)±(C+DI)=(A±C)+(B±D)I

(3+7)+(-4-6)i (Solve.)

7+3=10

-4-6i=-10

10-10i

Therefore, the final answer is 10-10i.

Step-by-step explanation:

Answer:

Mean:6

Mad:2.29

Step-by-step explanation:

a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.

To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64

Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.

b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L

Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75

Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.

In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.

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Answer:

h=48/x

Step-by-step explanation:

The rectangular equation for the surface is either y = 2kzj or z = y/2kj, depending on how you choose to eliminate the parameters.

To eliminate the parameters from the vector-valued function r(u,v)=ui+vj+v/2k and find the rectangular equation for the surface, we need to solve for u and v in terms of x, y, and z.

Starting with the x-coordinate:

ui = x
=> u = x/i

Moving on to the y-coordinate:

vj = y
=> v = y/j

Finally, for the z-coordinate:

v/2k = z
=> v = 2kz

Substituting the expressions for u and v in terms of x, y, and z, we get the rectangular equation:

x/i = u
y/j = v
2kz = v

Simplifying, we can write this as:

x/i = u
y/j = 2kz
y = 2kzj
or
x/i = u
z = v/2k
x/i = u
z = y/2kj

So the rectangular equation for the surface is either y = 2kzj or z = y/2kj, depending on how you choose to eliminate the parameters.

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Answer:

it does verify Thays its equal too PQRS

Answer: 7.21

Step-by-step explanation: Plug points into \(\sqrt{(x^2-x^1)^2+(y^2-y^1)^2}\)

The x-component of the vector ⃗ is -9.98 and the y-component is 8.53.

We can find the x and y components of the vector ⃗ by using trigonometry. The magnitude of the vector is given as 13.1, and the direction of the vector is 50∘ counter-clockwise from the -axis. We can use the cosine and sine functions to find the x and y components, respectively.

cos(50∘) = -0.6428, sin(50∘) = 0.7660

x-component = magnitude x cos(50∘) = 13.1 x (-0.6428) = -9.98

y-component = magnitude x sin(50∘) = 13.1 x (0.7660) = 8.53

Therefore, the x-component of the vector ⃗ is -9.98, and the y-component is 8.53.

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The x-component of the vector is approximately 8.375 and the y-component is approximately 9.955.

To find the x- and y-components of the vector, we can use trigonometry.

Given that the magnitude of the vector is 13.1 and the direction is 50° counter-clockwise from the - axis, we can determine the x- and y-components as follows:

The x-component (horizontal component) can be found using the formula:

x = magnitude * cos(angle)

x = 13.1 * cos(50°)

x ≈ 8.375

The y-component (vertical component) can be found using the formula:

y = magnitude * sin(angle)

y = 13.1 * sin(50°)

y ≈ 9.955

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The length of the shorter leg is 2.5 feet and the longer leg is 4.5 feet.

It is important to note that the Pythagoras theorem states that the square of the sides are equal to the hypotenuse.

This will be:

a = First leg = x

b = Second leg = x + 4

c = Hypothenuse = 7

This will then be:

a² + b² = c²

x² + (x + 4)² = 7²

x² + x² + 8x + + 16 = 49

Collect like terms

2x² + 8x + 16 - 49

2x² + 8x - 33

Using the quadratic formula, x = 2.5.

Therefore shorter leg = 2.5 feet

Longer leg = 2.5 + 4 = 6.5 feet

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The experiment has not been repeated.

The answer to the question:1. (a) The sum of squares for the factor is 14.18.2. (b) The number of degrees of freedom for the single factor in the experiment is 1.3. (c) The number of degrees of freedom for the error is 23.4. (d) The mean square for error is 1.64.5. (e) The value of the test statistic is 8.63.6. (f) If the significance level is 0.05, the conclusion is to reject the null hypothesis. Yes.7. (g) The p-value for the test statistic is 0.0086.8. (i) Laura used how many levels of the factor in this experiment? One.9. (j) Laura replicated this experiment how many times? The experiment has not been repeated.A complete randomized design with a single factor was conducted by physics graduate student Laura van Iertia. She is hoping to solve the mystery of the unified theory and complete her dissertation with the results of this experiment. The results of this experiment are summarized in the following ANOVA display:Source df SS MS F Factor 1 14.18 14.18 8.63 Error 23 37.75 1.64 - Total 24 52.93 - The questions and answers based on this experiment are given below:(a) The sum of squares for the factor is 14.18.(b) The number of degrees of freedom for the single factor in the experiment is 1.(c) The number of degrees of freedom for the error is 23.(d) The mean square for error is 1.64.(e) The value of the test statistic is 8.63.(f) If the significance level is 0.05, the conclusion is to reject the null hypothesis. Yes.(g) The p-value for the test statistic is 0.0086.(i) Laura used how many levels of the factor in this experiment? One.(j) Laura replicated this experiment how many times? The experiment has not been repeated.

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ANSWER:

A. 2.2%

STEP-BY-STEP EXPLANATION:

We can calculate the probability using the quotient of the area of the small circle and the area of the entire rectangular sector, like this:

In the circle the radius is 6 inches and in the rectangle the length is 84 inches and the width is 60 inches.

Therefore we replace and we have:

The function takes a vector called "data" and a midpoint "m" as inputs and centers the data around the midpoint. It ensures that the midpoint becomes the new zero or center point of the data.

To center the data around the midpoint, we need to calculate the difference between each element of the data vector and the midpoint. This can be done by subtracting the midpoint from each element in the data vector. By doing so, the midpoint becomes the new zero or center point of the data.

Here is an example implementation of the function in Python:

def center_data(data, m):

   centered_data = [x - m for x in data]

   return centered_data

In this function, we iterate over each element in the data vector and subtract the midpoint "m" from it. The result is stored in a new vector called "centered_data" which represents the centered version of the original data vector. This ensures that the midpoint becomes the new zero or center point of the data. The centered_data vector can be further used for analysis or visualization purposes.

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Answer:2.25 m/s^2

Step-by-step explanation:

a = (v-u)/t = 27/12 = 2.25 m/s^2

Kim stands in a line of people, being the 25th person counting from the front and the 12th person counting from the rear, there are total 34 people in the line.

To find the total number of people in the line, we can add the number of people in front of Kim and the number of people behind Kim, then subtract one to account for Kim herself.
At the front of the line, there are 24 people in front of Kim (since she is the 25th person counting from the front). From the rear of the line, there are 11 people behind Kim (since she is the 12th person counting from the rear).
To find the total number of people in the line, we can add these two numbers:
24 (people in front of Kim) + 11 (people behind Kim) = 35
However, we need to subtract one to account for Kim herself. Therefore, the total number of people in the line is 35 - 1 = 34.

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The interquartile range for the given data is 1 quesadilla.

The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.

To get the interquartile range, we must know the first and third quartiles. To find those, we need to know the median of the data.

There are 11 data points, so we can cross out 5 numbers on the left and cross out 5 numbers on the right. That leaves a median of 1.

Since we know the median is 1, we can find the first quartile by finding the median of the following numbers:

0, 0, 1/4, 1/2, 1/2  (any number less than 1).

There are five numbers, so cross out two numbers from the left and cross out two numbers from the right. We are left with the first quartile of 1/4.

Now that we have the first quartile, we need to find the third quartile. Since the median was actually the first "1" in the data set, the third quartile will be the median of the numbers to the right of that "

1: 1, 1, 5/4, 2, 2.

Cross out the leftmost two numbers, and cross out the rightmost two numbers. We are left with the third quartile of 5/4.

Now that we have both the third and first quartiles, we can find the interquartile range! The IQR is calculated by finding the third quartile minus the first quartile.

5/4 - 1/4 = 4/4 = 1.

Therefore, the interquartile range is 1 quesadilla.

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The difference between AIC and BIC penalty lies in their approach to model selection.

AIC (Akaike Information Criterion) is a measure of the goodness of fit of a statistical model. It is used to compare different models and select the one that fits the data best. AIC is based on the principle of maximum likelihood, which means it is more focused on finding the model that fits the data best.

On the other hand, BIC (Bayesian Information Criterion) is a criterion for model selection based on the Bayesian approach. It is also used to compare different models, but it takes into account the complexity of the model. BIC tends to favor simpler models, and it is more focused on finding the model that is most likely to be true given the data.

In summary, AIC is more focused on finding the model that fits the data best, while BIC is more focused on finding the model that is most likely to be true given the data.

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Possible length of the third side of the Triangle must be between 11 and 23.

As the third side of the triangle is between the sum of the sides and difference of the sides excluding both the numbers.

As triangle consist of three sides and it should must be in between two extreme values.

As by the property of Triangle

Third side should be less than sum of the sides and,

it should be greater than difference of the sides.

Sum of the sides = AB + BC = 6 + 17 = 23

Difference of the sides = 17 - 6 = 11

Then the third side will be between 11 and 23 excluding 11 and 23.

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Answer:

B - Spider-Man

Step-by-step explanation:

Answer:

15-9z

Step-by-step explanation:

combine like terms,, the like terms we have are the terms (z) and the whole numbers so we combine 6,8, and 1-- and combine -5z and -4z to get the solution.