What is the value of the product (3 - 2i) (3 +2i)?
O 5
9 + 4;
9 – 4;

A chi-squared statistic provides strong evidence in favor of the alternative hypothesis if its value is A.  a large positive number.

Chi-squared statistics or chi-squared test is a statistical method used to find out if there is a significant difference between the expected and observed frequencies in one or more categories of a contingency table. This test is used to determine whether the null hypothesis can be rejected or not. Chi-squared statistics are a non-parametric test that helps to determine whether the data is close to what is expected or not. This test is used when the data is ordinal or nominal.

Chisquare test is often used for: Testing if the observed frequencies of a nominal variable are significantly different from the expected frequencies Assessing if two or more distributions are the same. The chi-squared statistic provides evidence for or against the null hypothesis. A large positive value of the chi-squared statistic indicates that the null hypothesis can be rejected.

Therefore, option A. a large positive number, is the correct answer.

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Based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

Chebyshev's Theorem states that for any given number k greater than 1, at least (1 - 1/k²) of the data values in a dataset will fall within k standard deviations of the mean.

In this case, we have a sample size of 225 bags and a mean weight of 353 gm with a standard deviation of 6 gm.

To find a lower bound for the number of bags that weigh between 335 and 371 gm, we need to calculate the range within k standard deviations of the mean.

First, let's find the number of standard deviations for the given range:

Lower range: (335 - 353) / 6 = -3

Upper range: (371 - 353) / 6 = 3

Since we want to find the lower bound, we consider the lower range and use its absolute value: |-3| = 3.

Now, we can use Chebyshev's Theorem to find the lower bound:

(1 - 1/k²) ≤ (1 - 1/3²) = 1 - 1/9 = 8/9

This means that at least 8/9 of the bags will fall within 3 standard deviations of the mean.

To find the lower bound for the number of bags, we multiply this probability by the sample size:

Lower bound = (8/9) * 225 = 200

Therefore, based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

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Step-by-step explanation:

4a)

the principle of similar triangles : they have the same angles.

and we do not forget : the sum of all angles in a triangle is always 180 degrees.

a = 180 - 65 - 45 = 70 degrees

b = 65 degrees

c = 70 degrees

b)

same principles.

x = 58 degrees

y = 52 degrees

z = 180 - 58 - 52 = 70 degrees

c)

same principles.

plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.

x = 85 degrees

y = 180 - 40 - 85 = 55 degrees

z = 180 - 85 = 95 degrees

d)

again same principles.

y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).

the angle POQ is again complementary with 87 degrees,

POQ = 180 - 87 = 93 degrees

x + y + 93 = x + 2x + 93 = 180

3x = 87

x = 29 degrees

y = 2x = 2×29 = 58 degrees

Answer:

x = 149 degree

Step-by-step explanation:

First, we have to find the missing angle of the triangle

1 triangle = 180 degree

We know 2 angles, one is 63 degrees and one is 86 degrees.

63 + 86 = 149 degree

180 - 149 = 31 degree

So, the angle of the triangle is 31 degrees. Now we know that angle add with the x to get 180 degrees, so

180 - 31 = 149 degree

So, x = 149 degree

The one-way ANOVA model for the response variable is y ij = μ + τ i + ε ij

The one-way ANOVA model for the response variable in the context of an experiment assessing the effect of multiple treatments is as follows:

y ij = μ + τ i + ε ij

where:

y ij represents the jth value of the response variable for the ith treatment.

μ is the overall mean of the response variable.

τ i is the effect of the ith treatment.

ε ij is the random error term representing the variability in the response variable that is not explained by the treatments.

In this model, the treatment effect (τ_i) represents the differences in the response variable among the different treatments. The error term (ε_ij) accounts for the random variability and any other factors that may influence the response variable but are not included in the model.

The goal of performing the ANOVA is to assess whether there are significant differences in the means of the response variable across the treatments. This is done by analyzing the variation between the treatment means (sums of squares) and comparing it to the variation within each treatment group (residual sums of squares). The F-test is commonly used for this purpose.

By analyzing the model, we can estimate the treatment means, test for the significance of the treatment effects, and make inferences about the differences between the treatment means. The model provides a framework for understanding the relationship between the treatments and the response variable in the context of the experiment.

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Answer:

27,35

Step-by-step explanation:

Answer:

y=mx+b

Step-by-step explanation:

use that formula

Answer:

Leila is paid $10 plus $8 an hour

She was paid $66

Let the number of times be x

According to the problem,

10+8x=66

8x=66-10

8x=56

x=56/8

x=7

She worked for 7 hours.

Answer:

C. y - 6= 3/5(x + 4).

Step-by-step explanation:

y

=

m

x

+

c

−

6

=

(

4

×

3

5

)

+

c

c

=

−

12

5

−

6

=

−

42

5

So:

y

=

3

5

x

−

42

5

The point slope form comes from the definition of slope as a measure of the change in  

y

for a given change in  

x

in passing from point 1 to point 2, i.e.:

slope

=

m

=

Δ

y

Δ

x

=

y

2

−

y

1

x

2

−

x

1

...........(1).

The only difference here is that you do not have 2 points but only one!

So you have: the value of  

m

and the coordinates of one point, say, point 1. So we can write in (1):

3

5

=

y

−

(

−

6

)

x

−

4

where the coordinates of the other point are the unknown  

x

,

y

.

You get rearranging:

y

+

6

=

3

5

(

x

−

4

)

y

+

6

=

3

5

x

−

12

5

y

=

3

5

x

−

12

5

−

6

y

=

3

5

x

−

42

5

26. AH = w, BF = x , FC = z, DH = y 27. The opposite sides of the quadrilateral are congruent, and they are parallel because the quadrilateral is symmetric with respect to the center of the circle.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent. Tangent has an equation since it is a line.

26. We know that,

From a point out side of the circle  the two tangents to the circle are equal.

Thus, AH = AE = w

BF =BE = x

FC = CG = z

DH = DG = y

27. The opposite sides of the quadrilateral are congruent, and they are parallel because the quadrilateral is symmetric with respect to the center of the circle.

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Answer:

The answer is below

Step-by-step explanation:

From the image attached, the measurement of the roof is 5 m by 9 m on  both sides. Hence:

Area of roof = 2 (5 * 9) = 90 m²

Since solar panels cost $4.00 per square meter, therefore:

Cost of solar panels = $4.00 per square meter * 90 m² = $360

The area of the front wall of the barn = (8 m * 7 m) + (1/2 * 8 m * 3 m) - (4 m * 4 m) = 52 m²

The area of the back wall of the barn = (8 m * 7 m) + (1/2 * 8 m * 3 m) = 68 m²

Area of each side wall of barn = 9 m * 7 m = 63 m²

Total area of wall = 52 m² + 68 m² + (2 * 63 m²) = 246 m²

Cost of shingles = $2.50 for each square meter * 246 m² = $615

Total cost of project = $615 + $360 = $975

a )The equation of the new parallel line is   x - y = 3

b ) The equation of the new perpendicular line is   x + y = -1

The given line passes through the points (0, 3 ) and (-3, 0).

Here,

\((x _{1}, y _{1}) = (-3, 0)\\\\(x _{2}, y _{2}) = (0, 3)\)

The slope of the line = m

\(m =\frac{y_{2}- y _{1}}{x _{2}- x_{1}} \\\\m = \frac{3-0}{0+3} \\\\m = \frac{3}{3} = 1\)

The slope of the given line is 1

a ) The new line passes through the point (1, -2) and is parallel to the given line .

           \(y- y_{1} = m (x- x_{1}) -- (1)\)

          y + 2 = 1 (x -1 )

          y  +2 = x - 1

           x - y -1 -2 = 0

           x - y - 3 =0

           x - y = 3

The equation of the new parallel line is   x - y = 3

b ) The new line passes through the point (1, -2) and is perpendicular to the given line .

           \(y- y_{1} = m (x- x_{1}) -- (1)\)

          y + 2 = -1 (x -1 )

          y  +2 = - x + 1

           x + y -1 +2 = 0

           x + y + 1 = 0

           x + y = -1

The equation of the new perpendicular line is   x + y = -1

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The value of the account is $165,627.27.

After a certain number of years, the value of an investment account is represented by the expression 10,300(1 + 0.0412)^120. Given expression: 10,300(1 + 0.0412)^120Adding 1 to 0.0412, we get 1.0412. Now, the expression becomes:

=10,300 × 1.0412^120

Using a scientific calculator or spreadsheet software, we can evaluate this expression to get the value of the account as approximately $165,627.27. Therefore, the value of the account is $165,627.27.

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As the total number of weekly reservations remains the same. The average number of booked rooms is likely to decrease.

By offering a discount on three-bed rooms, some customers who would have originally booked a different type of room now book a three-bed room instead. This means that the number of three-bed rooms booked will increase, while the number of other room types booked will decrease.

Since the total number of weekly reservations remains the same, the increase in three-bed room bookings must be offset by a decrease in bookings for other room types. This means that the average number of booked rooms will likely decrease.

For example, suppose there were originally 50 room bookings, consisting of 20 three-bed rooms and 30 other room types. If the discount on three-bed rooms leads to 25 bookings for three-bed rooms and 25 bookings for other room types, then the average number of booked rooms would be (25 x 3 + 25 x 1) / 50 = 2, which is lower than the original average of (20 x 3 + 30 x 1) / 50 = 1.8.

Therefore, the average number of booked rooms is likely to decrease when a discount is offered on three-bed rooms, even if the total number of weekly reservations remains the same.

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the correct format for a multiple regression equation is

ŷ= \(b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}\)

multiple regression: The relationship between a single dependent or criterion variable and multiple independent or predictor variables is typically explained by multiple regression. The constant term and multiple independent variables with their corresponding coefficients are used to model a dependent variable. The term "multiple regression" refers to the fact that it requires two or more predictor variables.

because, the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; and the maximum number of passengers.

thus, ŷ=\(b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}\) is the multiple regression equation.

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The simplified form of the expression -10g - 4h² +15g -8h² -4 is -12h² +5g -4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is -10g - 4h² +15g -8h² -4. The expression will be simplified as below,

E = -10g - 4h² +15g -8h² -4

E = - 4h²-8h² -10g +15g - 4

E = -12h² + 5g - 4

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Answer:

-12h² +5g -4.

Step-by-step explanation

i just did it

Answer:

x < 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

3x + 1 < 10

Step 2: Solve for x

Here we see that any value x smaller than 3 would work as a solution to the inequality.

The number of participants that would be needed for a within-subjects experiment is 80.

An experiment simply means a research that's conducted in order to get information about a particular thing.

In this case, we want to know the number of participants that will be neeed within-subjects experiment comparing four different treatment conditions with a total of 20 scores in each treatment.

This will be:

= Number of scores × Number of treatment

= 20 × 4

= 80

The participants needed are 80.

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The scientific notation or representation of expression (2.5 X 1/10²)(4.2 X 10⁶) is equal to 10.5×10⁴.

Scientific notation is a way of writing very large or very small numbers. Numbers are written in scientific notation as a number from 1 to 10 multiplied by a power of 10.For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸. 

Scientific notation is utilized by scientists, mathematicians, and engineers whilst they may be operating with very huge or very small numbers

Solution for scientific notation according to the information given:

(2.5 X 10^-2)(4.2 X 10⁶) = 2.5 ×(1/10²) × 4.2 × 10⁶

                                        = 2.5 × 4.2 × 10⁴

                                        = 10.5 × 10⁴

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Let G = Z³ be a set with Z³ = { (k₁, k₂, k₃) | k₁, k₂, k₃ ∈ Z }. Then the operation *: G × G → G is defined by:

(k₁, k₂, k₃) * (l₁, l₂, l₃) = (k₁ + (-1)ⁿl₁, k₂l₂, k₃l₃). We must prove that G is a group. To prove that G is a group, we have to check if it satisfies a group's necessary conditions.

To do this, we must show that it has the following properties:

i. Closure

ii. Associativity

iii. Identity

iv. Inverse

i. Closure

Let (k₁, k₂, k₃), (l₁, l₂, l₃) ∈ G. Then

(k₁, k₂, k₃) * (l₁, l₂, l₃) = (k₁ + (-1)ⁿl₁, k₂l₂, k₃l₃) = (m₁, m₂, m₃) ∈ G, where m₁, m₂, m₃ ∈ Z. Therefore, G is closed under * operation.

ii. Associativity

Let (k₁, k₂, k₃), (l₁, l₂, l₃), (m₁, m₂, m₃) ∈ G. Then

((k₁, k₂, k₃) * (l₁, l₂, l₃)) * (m₁, m₂, m₃) = ((k₁ + (-1)ⁿl₁, k₂l₂, k₃l₃) * (m₁, m₂, m₃))(k₁ + (-1)ⁿl₁ + (-1)ⁿ′m₁, k₂l₂m₂, k₃l₃m₃)

= (k₁ + (-1)ⁿl₁ + (-1)ⁿ′m₁, k₂l₂m₂, k₃l₃m₃) = (k₁, k₂, k₃) * (l₁ + (-1)ⁿ′m₁, l₂m₂, l₃m₃) = (k₁, k₂, k₃) * ((l₁, l₂, l₃) * (m₁, m₂, m₃))

Therefore, the operation * is associative.

iii. Identity

Let e = (0, 1, 1) be the identity element in G. Then,

(k₁, k₂, k₃) ∈ G, (k₁, k₂, k₃) * e = (k₁ + (-1)ⁿ . 0, k₂ . 1, k₃ . 1) = (k₁, k₂, k₃) = e * (k₁, k₂, k₃)

Therefore, e is an identity element in G.

iv. Inverse

Let (k₁, k₂, k₃) ∈ G. Then, we need to find an element (l₁, l₂, l₃) ∈ G such that (k₁, k₂, k₃) * (l₁, l₂, l₃) = e

Suppose l₁ = (-1)ⁿk₁. Then, (k₁, k₂, k₃) * (l₁, l₂, l₃) = (k₁ + (-1)ⁿ(-1)ⁿk₁, k₂k₂, k₃k₃) = (0, 1, 1)

Therefore, (l₁, l₂, l₃) = (-1)ⁿk₁, (1/k₂, 1/k₃) is the inverse of (k₁, k₂, k₃) in G. Therefore, G is a group as it satisfies all the necessary conditions of a group.

In abstract algebra, a group is a mathematical object with a set and an operation. To be a group, the operation must satisfy specific properties. The properties are closure, associativity, identity, and inverse. A group must also be closed under the operation. The operation must be associative, which means that the order in which the operation is done does not matter.

The group must have an identity element, which is the element that gives the same element when the operation is performed with any other element. Finally, every component of the group must have an inverse. The inverse of an element is the element that gives the identity element when the operation is performed with the original element. In this problem, we need to show that G is a group.

The operation * on G is defined as:

(k₁, k₂, k₃) * (l₁, l₂, l₃) = (k₁ + (-1)ⁿl₁, k₂l₂, k₃l₃)

We must prove that G satisfies all the properties of a group. First, we show that G is closed under the operation *:

(k₁, k₂, k₃) * (l₁, l₂, l₃) = (k₁ + (-1)ⁿl₁, k₂l₂, k₃l₃) = (m₁, m₂, m₃) ∈ G, where m₁, m₂, m₃ ∈ Z. Therefore, G is closed under * operation.

Next, we prove that the operation is associative. We have:

((k₁, k₂, k₃) * (l₁, l₂, l₃)) * (m₁, m₂, m₃) = ((k₁ + (-1)ⁿl₁, k₂l₂, k₃l₃) * (m₁, m₂, m₃))

(k₁ + (-1)ⁿl₁ + (-1)ⁿ′m₁, k₂l₂m₂, k₃l₃m₃)= (k₁ + (-1)ⁿl₁ + (-1)ⁿ′m₁, k₂l₂m₂, k₃l₃m₃)

(k₁, k₂, k₃) * (l₁ + (-1)ⁿ′m₁, l₂m₂, l₃m₃) = (k₁, k₂, k₃) * ((l₁, l₂, l₃) * (m₁, m₂, m₃))Therefore, the operation * is associative.

Next, we show that G has an identity element. Let e = (0, 1, 1) be the identity element in G. Then,

for any (k₁, k₂, k₃) ∈ G, (k₁, k₂, k₃) * e = (k₁ + (-1)ⁿ . 0, k₂ . 1, k₃ . 1) = (k₁, k₂, k₃) = e * (k₁, k₂, k₃).

Therefore, e is an identity element in G. Finally; we show that every element in G has an inverse.

Let (k₁, k₂, k₃) ∈ G. Then, we need to find an element (l₁, l₂, l₃) ∈ G such that (k₁, k₂, k₃) * (l₁, l₂, l₃) = e. Suppose

l₁ = (-1)ⁿk₁. Then

(k₁, k₂, k₃) * (l₁, l₂, l₃) = (k₁ + (-1)ⁿ(-1)ⁿk₁, k₂k₂, k₃k₃) = (0, 1, 1).

Therefore, (l₁, l₂, l₃) = (-1)ⁿk₁, (1/k₂, 1/k₃) is the inverse of (k₁, k₂, k₃) in G. Thus, we have shown that G is a group as it satisfies all the necessary conditions of a group.

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Rachel's Coffee Shop used 33 pounds of type A coffee at a cost of $4.20 per pound, and four times as many pounds of type B coffee at a cost of $5.50 per pound, to create a blend costing a total of $864.60.

Let's use the variable "x" to represent the number of pounds of type A coffee used in the blend.

The amount of type B coffee used in the mix was four times that of type A, therefore we can write:

number of pounds of type B coffee = 4x

The total cost of the blend is given as $864.60, so we can write an equation based on the cost:

\(4.2x + 5.5(4x) = 864.60\)

Simplifying and solving for x, we get:

\(4.2x + 22x = 864.60\)

\(26.2x = 864.60\)

\(x = 33\)

As a result, the mix contained 33 pounds of type A coffee.

To check our answer, we can substitute x = 33 into the equation we used to solve for it and verify that the total cost is indeed $864.60.

\(4.2(33) + 5.5(4*33)\)

= \(138.6 + 726.0\)

= \(864.6\)

The total cost matches, so our answer is correct.

Therefore, Rachel's Coffee Shop used 33 pounds of type A coffee in the blend.

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The complete question is:

A blend made by Rachel's Coffee Shop combines two different kinds of coffee. Rachel pays $4.20 per pound for type A coffee and $5.50 for type B coffee. This month's blend cost $864.60 and included four pounds more of type B coffee than type A. How many pounds of coffee of type A were consumed?

Answer:

its positive

Step-by-step explanation:

because the line going upward

Answer:

positive

Step-by-step explanation:

Answer:

Step-by-step explanation:

The implied utilization of the resources in the process can be calculated by dividing the demand rate by the total capacity of the resources. In this case, the total capacity is 1.1 + 0.93 = 2.03 clients per hour. Therefore, the implied utilization is 0.75 / 2.03 = 0.369 (or 36.9%).

The implied utilization represents the proportion of the available capacity that is being utilized to meet the demand. In this scenario, approximately 36.9% of the total capacity is being utilized to serve the clients. This indicates that there is still some unused capacity available in the process.

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Answer:

50.28 m²

Step-by-step explanation:

Area of a circle = pi r²

= 22/7 × 4 × 4

= 50.28 m²

The property used in this is the commutative law of multiplication.

What is the commutative law of multiplication?

In mathematics, commutative law refers to either of two rules relating to the addition and multiplication of numbers that are expressed symbolically as a + b = b + a and ab = ba. These principles imply that rearranging the terms or factors of any finite sum or product has no effect on it.

Here, we have

Given:  5x1 = 5 = 1x5

We have to find which property of multiplication is applied here.

5x1 = 5

1x5 = 5

We concluded from the given statement that the commutative law of multiplication is applied here.

commutative law of multiplication: ab = ba

Hence, the property used in this is the commutative law of multiplication.

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Answer:

it's C

Step-by-step explanation:

Recall that linear (straight) equations are given in the form y = mx + b.  Looking at your options, we can see there is only one equation in this form, which is letter c, y = 12x + 17.  Therefore your answer is c.

The total number of ways to split the group of 10 people into two groups of size 3 and one group of size 4 is 120 * 35 * 1 = 4,200. To split a group of 10 people into two groups of size 3 and one group of size 4, we can use the concept of combinations.

The number of ways to split the group can be calculated by determining the number of combinations of selecting 3 people from 10 for the first group, then selecting 3 people from the remaining 7 for the second group, leaving the remaining 4 people for the third group.

To split the group of 10 people into two groups of size 3 and one group of size 4, we can calculate the number of ways using combinations. The first group of size 3 can be formed by selecting 3 people from the total of 10 people. This can be represented as C(10, 3) = 10! / (3!(10-3)!).

Evaluating this expression:

C(10, 3) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

After selecting the first group, we are left with 7 people. From these 7 people, we need to select another group of size 3, which can be represented as C(7, 3) = 7! / (3!(7-3)!).

Evaluating this expression:

C(7, 3) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35.

Lastly, we have 4 people remaining, and they will form the third group of size 4. Since there is only one group left, there is only one way to assign the remaining 4 people to this group.

Therefore, the total number of ways to split the group of 10 people into two groups of size 3 and one group of size 4 is 120 * 35 * 1 = 4,200.

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The values of x make the triangle a right triangle is 25

Given that

Legs = 15 and 20

For a right triangle, we have

x^2 = 15^2 + 20^2

So, we have

x^2 = 625

This gives

x = 25

In this case, the value of x would be less than 25 calculated above

In this case, the value of x would be greater than 25 calculated above

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