Find the value of x
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If a score of 17 falls one standard deviation below the mean, and a score of 25 falls one standard deviation above the mean on a test that has a normal distribution, then the mean of the test is 21.

In a normal distribution, the mean, median, and mode are all equal, and the data is symmetrically distributed around the mean. If a score of 17 falls one standard deviation below the mean, then we know that the z-score associated with this score is -1.

Similarly, if a score of 25 falls one standard deviation above the mean, then the z-score associated with this score is +1. Using the empirical rule of a normal distribution, we know that approximately 68% of the data falls within one standard deviation of the mean.

Since the two given scores are one standard deviation away from the mean, we can assume that the percentage of data between 17 and 21 is approximately 34%, and the percentage of data between 21 and 25 is also approximately 34%. Thus, the mean score is located at the midpoint of these two scores, which is 21. Therefore, the mean of this test is 21.

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Answer::

Explanation:

Let the number of lasagna cupcakes made = x

Let the number of Gorgonzola onion tarts made = y

0. It takes ,10 minutes, to assemble each pan of lasagna cupcakes.

1. It takes ,15 minutes, to roll out the Gorgonzola onion tarts and fill each pan.

2. She has a maximum of ,2 hours (120 minutes), to assemble the appetizers.

These translate to the inequality:

0. Each pan of lasagna cupcakes takes 20 minutes to bake.

1. Each pan of Gorgonzola tarts takes 6 minutes to bake.

2. She has 60 minutes to bake the appetizers.

These translate to the inequality:

Since she must bake either lasagna cupcakes or Gorgonzola tarts, we have that:

So the system of inequalities is:

The graph that bests represents this scenario is:

Step-by-step explanation:

\(2 |5 - n| - | - 3| \\ = 2 |5 - 10| - 3 \\ = 2 \times 5 - 3 \\ = 10 - 3 \\= 7\)

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Answer:

i) Area of the ring = 462cm²

ii) Perimeter of the ring = 132cm

A complete question related to this found at brainly (ID: 19152996) is stated below:

Calculate the area and perimeter of the following ring where a = 7cm, b = 14cm (i) Area of Ring (ii) The perimeter of Ring

Find attached the diagram.

Step-by-step explanation:

a= smaller radius = 7cm

b= bigger radius = 14cm

i) Area of the ring = Area of larger circle - Area of smaller circle

Area of circle = Area of a ring = πr²

π =22/7

Area of larger circle = (22/7)(14)² = 22×28

Area of larger circle = 616cm²

Area of smaller circle = (22/7)(7)² = 22×7

Area of smaller circle = 154cm²

Area of the ring = 616 - 154 = 462cm²

ii) Perimeter of ring = Perimeter of larger circle + Perimeter of smaller circle

Perimeter of circle = 2πr

When r = 7cm and π = 22/7

Perimeter of smaller circle = 2×(22/7)×7 = 2×22

Perimeter of smaller circle = 44cm

When r = 14cm and π = 22/7

Perimeter of larger circle = 2×(22/7)×14 = 4×22

Perimeter of larger circle = 88cm

Perimeter of ring = 88+44 = 132cm

Answer:

----------------------------------------

Given expression:

Evaluate the expression if a = 5 and b = - 3:

.........................

Answer:

203,549 !!!

Step-by-step explanation:

If the median of a set of data is equal to the mean, then it implies that the data has a symmetric distribution. The correct answer is option d.

This is because the mean is sensitive to extreme values and tends to be pulled in the direction of the skewness of the distribution. On the other hand, the median is not sensitive to extreme values and only depends on the order of values in the data set.

Thus, if the median and mean are equal, it suggests that the distribution is symmetric and does not have any skewness. However, one cannot infer anything about whether the distribution is normal or approximately normal based solely on the equality of the median and mean.

The correct answer is option d.

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P(x) = -2x² + 130x - 2000 when x is the price of each game to make the game profitable, the price should be at least $ 25 and no more than $ 40.

Quadratic equations are polynomial equations of degree 2 in one variable of the form f(x) = ax2 + bx + c = 0, where a, b, c, R, and a 0 are all zeros. It is the generic form of a quadratic equation in which 'a' is referred to as the leading coefficient and 'c' is referred to as the absolute term of f. (x). The roots of the quadratic equation (,) are the values of x that fulfil the quadratic equation.

There will always be two roots to the quadratic equation. Roots might be real or fictitious in nature.

p(x) = -2x² + 130x - 2000

The game will be profitable if P (x) > 0.

-2x² + 130x - 2000 > 0

-x² + 65x - 1000 > 0

x² - 65x + 1000 > 0

x(x-25) - 40(x -25) > 0

x>25 x < 40.

Therefore, price should be at least $ 25 and no more than $ 40.

The values of variables that satisfy the given quadratic equation are referred to as its roots. In other words, if f() = 0, x = is a root of the quadratic equation f(x).

The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

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Answer:

3, 108 ,1,5439984,3909t8954,9994959 etc.

Step-by-step explanation:

7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are 49.

Calculating the sum of two or more numbers is the process of multiplication. It is stated as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number.

A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation. Most word problems incorporate some type of narrative, hence they are sometimes called "story problems," and the quantity of technical jargon they employ can vary.

Given that 7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are:

Hats = (7)(7) = 49.

Hence, there are a total of 49 hats.

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Answer:

Step-by-step explanation:

The simaltaneous equation are:

● 3a + 2b = 6

● 3b - 2a = 10

Graph both equations

While graphing use x instead of a and y insread of b in the graphing tool

The solutions are the coordinates of the intetsection point between the two lines.

The intersection point coordinates are approximatively (-0.15,3.2) picture below

Wich means:

● x = a = -0.15

● y = b = 3.2

Step-by-step explanation:

3a+2b=6

3b-2a=10

3a+2b=6 multiply by 3

-2a+3b=10 multiply by 2

9a+6b=18

-4a+6b=20 (-)

13a= –2. divide b.s by 13

a= –2/13

3b-2a=10

3b-2(-2/13)=10

3b+4/13=10

3b=10-4/13

3b=126/13. divide b.s by 3

b=42/13

Answer:

true

Step-by-step explanation:

every new term is created by adding a constant to the previous term.

The length of the line segment is approximately 12.04 units. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows: d = √((x2 - x1)^2 + (y2 - y1)^2)

The length of a line segment in a two-dimensional x-y coordinate plane can be found using the distance formula. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the line segment extends from the point (2, 8) to the point (12, 2). By plugging these values into the formula, we find that:

d = √((12 - 2)^2 + (2 - 8)^2) = √(100 + 36) = √136 = 12.04

So, the length of the line segment is approximately 12.04 units. This formula is useful for finding the distance between any two points in a two-dimensional plane and can be used in various fields such as geometry, physics, and engineering. The formula is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

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Complete question:

What is the length of the line segment in the first quadrant of an x-y coordinate plane that extends from (2, 8) to (12, 2)?

Answer:

its D 136

Step-by-step explanation:

khan

Answer:

x = 3.6

Step by step explanation:

Let number of years be x

W.K.T

Simple interest is the interest calculation method that applies a constant rate of interest to the principal amount of a loan or deposit over a period of time. It is calculated as a percentage of the principal amount, multiplied by the number of periods the interest is applied for.

Simple interest is used to calculate interest on loans, deposits, and other investments. It is also used to calculate the total amount owed on a loan or the return on an investment.

I = P × R × T

Where:

I = Interest Amount

P = Principal Amount

R = Interest Rate (as a decimal)

T = Time (number of periods)

10,750 - 10000 = 10,000 x 2.1% x X

750 = 10,000 x 0.02 x X

x = 3.6

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The correct option is B. 1/11.

The probability of choosing 2 white marbles is 1/11.

A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the sequence of the selection is irrelevant.

You can choose the objects in any order in combinations. Permutations and combinations are often confused.

Now, as pet the stated question.

The total number of red marble in the bag are 5.

The total number of blue marble in the bag are 2.

The total number of white marble in the bag are 4.

The total number of yellow marble in the bag are 1.

The combination for selecting the 2 white marbles out of 4 are;

⁴C₂ = 4!/(4-2)!2!

⁴C₂ = 6

Ans, the combination for selecting the 2 marbles out of total 12 are;

¹²C₂ = 12!/(12-2)!2!

¹²C₂ = 66

Thus, the combination for selecting the 2 white marbles out of total 12 is;

= ⁴C₂ / ¹²C₂

= 6/66

= 1/11

Therefore, the the probability of outcome of the 2 white marbles out of total 12 marbles is 1/11.

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The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

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Answer:

Step-by-step explanation:

D - correct

From the table, it is seen that 191 students play sports and there are 97 students from 10 grades surveyed. Option C is correct.

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

The table provides information on the number of students who play sports, the number of 10th graders surveyed, and the total number of students. Specifically, the table shows that 191 students participate in sports and that 97 of the surveyed students are in 10th grade.

Thus, from the table, it is seen that 191 students play sports and there are 97 students from 10 grades were surveyed. Option C is correct.

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The given equation is 2cos(θ) + √3 = 0 and we have to find all its solutions. The solutions of the given equation are:θ = 30° + 360°n or θ = 330° + 360°n, where n is an integer.

The given equation is 2cos(θ) + √3 = 0 and we have to find all its solutions.

Now, to solve for cos(θ), we can use the identity:

cos30° = √3/2cos(30°) = √3/2 and sin(30°) = 1/2sin(30°) = 1/2

Now, we know that 30° is the acute angle whose cosine value is √3/2. But the given equation involves the cosine of an angle which could be positive or negative. Therefore, we will need to find all the angles whose cosine is √3/2 and also determine their quadrant.

We know that cosine is positive in the first and fourth quadrants.

Since cos30° = √3/2, the reference angle is 30°. Therefore, the corresponding angle in the fourth quadrant will be 360° - 30° = 330°.

Hence, the solutions of the given equation are:θ = 30° + 360°n or θ = 330° + 360°n, where n is an integer. This means that the general solution of the given equation is given by:θ = 30° + 360°n, θ = 330° + 360°n where n is an integer. Therefore, all the solutions of the given equation are the angles that can be expressed in either of these forms.

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The volume of the given hexagonal prism is 187.2 cm³.

A hexagonal prism is a prism with a hexagonal base and top. It is a 3D shape and thus, is a polyhedron with 8 faces, 18 edges, and 12 vertices. As it has 8 faces, it is also called an octahedron.

Given that, a hexagonal prism we need to find the volume,

So, the volume = 3 apothem × base × height

= 3 × 3 × 8 × 2.6

= 187.2

Hence, the volume of the given hexagonal prism is 187.2 cm³.

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Answer:

no solution

Step-by-step explanation:

Answer: 0.16

Step-by-step explanation:

The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

To determine this:

Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.

Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.

We know the total number of farm animal legs is 40 legs.

So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.

Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

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Answer:

10.2 units

Step-by-step explanation:

Check the attachment.

Hope this helps! :D

To represent a categorical variable with three possible levels in a regression study, you would need two dummy variables.

In general, when a categorical variable has k levels, you need to create k-1 dummy variables to represent the variable in a regression model. This is because you can represent any one level of the categorical variable as the reference category, and then use k-1 dummy variables to represent the other k-1 categories relative to the reference category.

In this case, since the categorical independent variable has three possible levels (level 1, level 2, and level 3), we would need to create two dummy variables. One dummy variable would represent the difference between level 2 and the reference level (level 1), and the other dummy variable would represent the difference between level 3 and the reference level (level 1).

For example, if we denote the dependent variable as Y, the quantitative independent variable as X, and the categorical independent variable as Z, the regression equation could be written as:

Y = β0 + β1X + β2D1 + β3D2

In this case, since the categorical independent variable has three possible levels (level 1, level 2, and level 3), we would need to create two dummy variables.

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The cost of 10 lb of rice and 50 lb of potatoes would be $99.73 using a system of linear equations.

To solve the problem, we can use a system of linear equations. Let x be the cost of 1 lb of rice and y be the cost of 1 lb of potatoes. Then we have:

20x + 30y = 21.80

30x + 12y = 17.52

To solve for x and y, we can use elimination or substitution. Here, we will use elimination. Multiplying the second equation by -2, we get:

-60x - 24y = -35.04

Adding this to the first equation, we eliminate x and get:

6y = 13.76

Dividing by 6, we get:

y = 2.2933...

Substituting this into either equation, we can solve for x:

20x + 30(2.2933...) = 21.80

20x + 68.799... = 21.80

20x = -46.999...

x = -2.3499...

Therefore, the cost of 10 lb of rice and 50 lb of potatoes would be:

10(-2.3499...) + 50(2.2933...) = $99.73 (rounded to two decimal places)

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If the correlation coefficient has a negative value, then the coefficient of determination: b. must be positive.

A regression line is a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.

A positive correlation can be defined as a terminology that is used to described a scenario (situation) in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Thus, when one variable increases, the other increases, as well.

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Complete Question:

If the correlation coefficient has a negative value, then the coefficient of determination:_________.

a. can take on either a negative or positive value.

b. must be positive.

c. will also have a negative value.

d. will equal zero.

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:

Part a) The figure a shows that AB is parallel to PR. Please see attached figure a.

Part b) The length of AB is half the length of PR

Answer:

33.333%

Step-by-step explanation:

a 6 sided die has the number 1,2,3,4,5,6. 2 are less than three so the chances of getting the of getting a number less than 3 is 2/6, simplified 1/3.