Simplify\left(2-\sqrt{3}\right)^2

Answer:

x = -6, -2

Step-by-step explanation:

x^2 + 9x + 18 - (x + 6)

x^2 + 9x + 18 -x - 6

x^2 + 8x + 12

(x+6)(x+2)

x = -6, -2

Answer:

Volume of the solid figure = 1131 cubic inches

Step-by-step explanation:

Volume of solid figure = Volume of half cylindrical prism + Volume of the rectangular prism

Volume of half cylindrical prism = \(\frac{1}{2}(\pi r^2h)\)

                                                     = \((\frac{1}{2})(\pi )(17-11)^2(6)\)

                                                     = 339.29 cubic inch.

Volume of the rectangular prism = (length × width × height)

                                                      = 11 × 6 × 12

                                                      = 792 cubic inches

Volume of the solid figure = 339.29 + 792

                                            = 1131.29

                                            ≈ 1131 cubic inches

The subset W = {[b], where a, b ≤ R} is not a subspace of V. To determine whether W is a subspace of it satisfies three conditions: closure under addition, closure under scalar multiplication, and containing the zero.

In W, the elements are of the form [b], where a and b are real numbers. The condition for closure under addition states that if we take two vectors [b1] and [b2] from W, their sum [b1] + [b2] must also be in W. However, in this case, the sum [b1] + [b2] does not fall into the form [b] for all possible values of a and b. Thus, W fails the closure under addition condition.

Similarly, W fails the closure under scalar multiplication condition. If we multiply a vector [b] from W by a scalar, the result may not be in the form [b] for all possible values of a and b.

Finally, W also fails to contain the zero vector [0] since there is no value of a and b that satisfies the condition a + 2b = 0.

In conclusion, W does not satisfy the three conditions necessary to be a subspace of V, making it not a subspace.

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Answer:

The answer is 17.4.

Step-by-step explanation:

Mean is the average of all the numbers. To do this, you have to add up all the numbers then divide by how many numbers there are.

First, let's add up all the numbers.

11+14+15+16+16+18+20+20+22+22 = 174!

Next, let's divide the numbers by how many numbers there are. There are 10 numbers in total.

174÷10 = 17.4

Hope this helps! :3

Answer:

17.4

Step-by-step explanation:

To find the mean of a data set, add all numbers. Then, divide the sum by how many numbers are present.

11 + 14 + 15 + 16 + 16 + 18 + 20 + 20 + 22 + 22 = 174

There are 10 numbers, so divide 174 by 10.

174 / 10 = 17.4

Therefore, 17.4 is the mean of the data set.

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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Answer:

125

Step-by-step explanation:

The height of the right circular cylinder shown below is 12 feet and its base has a radius of 3 feet.

Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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Answer:

Jun 25, 2018 — Reflection over the y -axis. Vertical stretch by a factor of two. Horizontal translation right two units. Vertical translation up two units. I hope this helps you .. ;]

Step-by-step explanation:

the answer is -7 i think

The number of ways to distribute 30 identical candies among four children, with\(C_(2) r\)eceiving at least 4 and at most 7 candies and \(C_(3)\)receiving at least 2 and at most 6 candies, is equal to 930.

To find the number of ways to distribute 30 identical candies among four children with the given conditions, we can use the concept of generating function.

Let's denote the number of candies received by \(C_(1), C_(2), C_(3),\) and \(C_(4)\)as x, y, z, and w, respectively.

The generating function for \(C_(2)\)can be expressed as \((x^4 + x^5 + x^6 + x^7)\), representing the possible number of candies they can receive (at least 4 and at most 7).

The generating function for \(C_(3)\) can be expressed as\((x^2 + x^3 + x^4 +\)\(x^5 + x^6),\)representing the possible number of candies they can receive (at least 2 and at most 6).

Now, we need to find the coefficient of the term x^30 in the expansion of the product of these generating functions.

\((x^4 + x^5 + x^6 + x^7) * (x^2 + x^3 + x^4 + x^5 + x^6) = x^6 + 2x^7 + 3x^8 +\)\(4x^9 +\)\(5x^10 + 6x^11 + 7x^12 + ...\)

By observing the pattern, we can see that the coefficients of the terms with powers less than 6 are 0. Therefore, we only need to consider the coefficients from the term\(x^6\) onwards.

Adding up the coefficients of the terms \(x^6, x^7, x^8, ..., x^30,\)we can determine the number of ways to distribute the candies:

1 + 2 + 3 + 4 + 5 + 6 + 7 + ... + 25 + 26 + 27 + 28 + 29 + 30

This sum can be calculated using the formula for the sum of an arithmetic series:

n * (n + 1) / 2

Substituting n = 30, we get:

30 * (30 + 1) / 2 = 30 * 31 / 2 = 930

Therefore, the number of ways to distribute 30 identical candies among four children, with\(C_(2)\) receiving at least 4 and at most 7 candies and \(C_(3)\)receiving at least 2 and at most 6 candies, is equal to 930.

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The number of ways to distribute 30 identical candies among four children C_(1),C_(2),C_(3) and C_(4) so that C_(2) receives atleast 4 and atmost 7 candies, C_(3) receives atleast 2 and atmost 6 candies, is equal to :

205

615

510

930

The percent difference equation is a formula used to calculate the relative difference between two values as a percentage of their average.

The equation uses the formula as,

                      percent difference =  \(\frac{|x_1 - x_2|}{(\frac{x_1 + x_2}{2}) } * 100\)

where,

\(x_1\) and \(x_2\) are the two values being compared.

| | denotes the absolute value of the difference between the two values.

The percent difference equation is commonly used in scientific experiments and quality control to compare the accuracy of two measurements or the performance of two instruments. It can also be used to compare the results of a measurement with a theoretical value or an accepted standard.

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Answer:

A. 49% chance

B. 9% chance

C. 21% chance

Step-by-step explanation:

A. 0.7 x 0.7 = 0.49

B. 0.3 x 0.3 = 0.09

C. 0.7 x 0.3 = 0.21

Hope this helps :)

The first derivative of a function is a mathematical tool that tells us how the function is changing at any given point. More specifically, it tells us whether the function is at that point. If the first derivative is positive, the function is increasing;

1. Calculate the first derivative of the function, which represents the slope of the tangent line at each point.
2. Identify the critical points, which are the points where the first derivative is either zero or undefined.
3. To determine if the function is increasing or decreasing, examine the sign of the first derivative in the intervals created by the critical points:
  a. If the first derivative is positive in an interval, the function is increasing in that interval, as the tangent line has a positive slope.
  b. If the first derivative is negative in an interval, the function is decreasing in that interval, as the tangent line has a negative slope.

By following these steps, you can use the first derivative to determine where the function is increasing and decreasing.

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In 1 gram if carbon there is 5 × 10²² carbon atoms,

so, in 3 grams of carbon the number of carbon atom is equal to :

Given:

The insect population function is:

\(f(x)=10(2)^x\)

Where x is the number of weeks.

To find:

The population after 4 weeks.

Solution:

The population of insect after x weeks is given by:

\(f(x)=10(2)^x\)

We need to find the population after 4 weeks.

After substituting \(x=4\), we get

\(f(4)=10(2)^4\)

\(f(4)=10(16)\)

\(f(4)=160\)

The population after 4 weeks is 160. Therefore, the correct option is C.

The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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1) H0: percentage of households with unsafe water <= 7%, Ha: percentage of households with unsafe water > 7%.

2) (a) obtained P-value suggests the percentage of households with unsafe water in Rockford is greater than 7%, (b) Reject H0, and switch to bottled water as there is evidence to suggest the water is unsafe, (c) switching to bottled water when it is not necessary could result in unnecessary expenses for the city, (d) if the water is safe, the probability of making a Type I error is 0.05.

3) (a) P-value of 0.217 suggests that there is no evidence to suggest the water is unsafe, (b) if the decision to keep the current water is wrong, it could lead to health problems for residents exposed to unsafe water.

4) The consequences of a Type II error in question 3 are more severe than those of a Type I error in question 2 as the former could result in adverse health effects.

1) The Hypotheses in the given statements are,

Null hypothesis (H0): The percentage of households in Rockford with unsafe water is less than or equal to 7%.

Alternative hypothesis (Ha): The percentage of households in Rockford with unsafe water is greater than 7%.

2) (a) The P-value of 0.025 indicates that if the null hypothesis were true (i.e., if the percentage of households with unsafe water were less than or equal to 7%), we would observe a sample proportion of 12/100 or more extreme in only 2.5% of samples.

(b) With a significance level of 0.05, we reject the null hypothesis since the P-value is less than the significance level. This means we have evidence to suggest that the percentage of households with unsafe water in Rockford is greater than 7%. Therefore, Rockford should switch to bottled water to ensure safe drinking water.

(c) If the decision to switch to bottled water is wrong, it could result in unnecessary expenses for the city and inconvenience for its residents.

(d) If the water is safe, the probability of making a Type I error (incorrectly rejecting the null hypothesis) is equal to the significance level, which is 0.05.

3) (a) With a P-value of 0.217, we fail to reject the null hypothesis since the P-value is greater than the significance level. This means we do not have sufficient evidence to suggest that the percentage of households with unsafe water in Rockford is greater than 7%, and therefore, there is no need to switch to bottled water.

(b) If the decision to keep the current water is wrong, it could lead to health problems for the residents who are exposed to unsafe water.

4) The consequences in question 3 are more serious because if we make a Type II error (incorrectly failing to reject the null hypothesis), we are essentially allowing households to continue consuming unsafe water, which could have adverse health effects. On the other hand, if we make a Type I error in question 2, we may incur some unnecessary expenses, but it is less severe than putting people's health at risk.

Therefore, the null hypothesis is that the percentage of households with unsafe water in Rockford is less than or equal to 7%, while the alternative hypothesis is that it is greater than 7%. With a sample proportion of 12/100 households having unsafe water, a significance test is performed with a P-value of 0.025, leading to the rejection of the null hypothesis, and the recommendation to switch to bottled water. The consequences of making an incorrect decision could result in unnecessary expenses or adverse health effects.

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Answer:

x=83º

Step-by-step explanation:

The interior angle sum of a Hexagon is 720º

146+169+59+129+134+x=720

x=720-637

x=83

Answer:

the area of is

Step-by-step explanation:

Answer: The student got the wrong answer. ✅

Step-by-step explanation: When you add 364 and 728 together, you get 1092. To make it easier to understand, it is like having 3 piles of 100, 6 piles of 10, and 4 ones on one side, and 7 piles of 100, 2 piles of 10, and 8 ones on the other side, when you put them together you get 10 piles of 100, 8 piles of 10 and 12 ones.

To find the biggest number they have in common, you can divide both numbers by 2 and you get 182 and 364.

So the correct way to rewrite 364 + 728 is 364 * (3+2) ✅

Answer:

$11.61

Step-by-step explanation:

In an observational study, the statement that a cause and effect can be determined is false.

Observational studies simply establish associations between predictor and outcome variables. Observational studies cannot confirm that an association contemplates cause and effect.

In observational studies, confounding variables may explain an observed relationship between predictor and outcome variables.

In an observational study, a cause and effect cannot be determined. Observational studies are used to gather data about a particular population or phenomenon, but they do not allow for the determination of cause-and-effect relationships.

This is because observational studies do not control the variables that are being studied and, therefore, cannot determine the relationship between two variables.

In order to determine cause and effect, a controlled experiment is needed in which the variables are manipulated, and their effects are observed.

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Answer:

14

Step-by-step explanation:

How many 1/2s are in 7? Then, write a multiplication equation and a division equation that answer the question.

Let the number of 1/2s = x

Hence:

Division Equation =

7 ÷ 1/2

Multiplication Equation =

= 7 × 2/1

= 14

There are 14 1/2s in 7

Answer:

Step-by-step explanation:

The value of (f- g)(x) is  2x - 26.

This is a question of subtraction of functions.

Subtraction of functions

The subtraction of function involves the creation of a new function through the addition of two other functions.

Subtraction of one real-valued function from another.

Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.

Given that:-

f(x) = 2x + 1

g(x) = 27

We have to find the value of (f- g)(x)

We know that,

(f- g)(x) = f(x) - g(x)

Hence, we can write,

(f- g)(x) = 2x + 1 - 27 = 2x - 26

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Answer: $5 for each eraser

Step-by-step explanation:

$5 in magazines ( 1 magazine )

? in erasers ( 4 erasers total )

$25 in total

step 1.      25-5= 20

step 2.     20/4= 5

step 3.     $5 = each eraser (some expensive erasers)

Answer: Each eraser cost 5$

Step-by-step explanation: magazine for 5$ and four erasers. if you count by fives and do 5$ magazine but spent 25$ it would be 5$ because 5$x5$=25$>.

Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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The closest coordinate plane to the point (6, 2, 7) is the xy-plane.

To determine which coordinate plane is closest to a given point, we look at the value of the coordinate that is perpendicular to each plane. The xy-plane is defined by the equation z = 0, which means that the z-coordinate is always 0 on this plane.

In the given point (6, 2, 7), the z-coordinate is 7. Since it is not equal to 0, the point does not lie on the xy-plane. However, we can compare the absolute values of the z-coordinate with the absolute values of the coordinates on the other planes.

The absolute value of 7 is smaller than the absolute values of 6 and 2, indicating that the point (6, 2, 7) is closer to the xy-plane than the other coordinate planes.

Regarding the equation of the sphere with center (6, 2, 7) that just touches the xy-plane at one point, we need additional information to determine the radius of the sphere or the coordinates of the point of tangency. Without this information, we cannot provide a specific equation for the sphere.

Therefore, the xy-plane is the coordinate plane closest to the point (6, 2, 7), indicating that the z-coordinate is further away from zero compared to the other coordinates.

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