What is the goal of inequalities is to value what from the variable

The simplest form of a^2-ab is given by 3x^3 + x^2 + 6x - 9.

We have given that,

a = x^2,

b = 3x + 2,

c = x – 3

We have to determine ab- c^2.

A fraction is in its simplest form when the numerator and the denominator have no common factors besides one.

ab- c^2

\(=x^2(3x+2) - (x-3)^2\\ =3x^3 + 2x^2 - (x^2 - 6x + 9) \\=3x^3 + 2x^2 - x^2 + 6x - 9 \\=3x^3 + x^2 + 6x - 9\\\)

The simplest form of a^2-ab is given by 3x^3 + x^2 + 6x - 9.

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Answer:

m% of n is (m/100)(n)

Step-by-step explanation:

When removing a %, you just move the period two places to the left (ex. 50% = 0.50), or just divide the number by a 100 (ex. 50% = 50/100). So then, m% of n is just the product of m/100 and n.

Answer:

Nov 1st: 2500 boxes

Dec 1st: 15% fewer boxes which is 2500 x (1- \(\frac{15}{100}\) ) = 2125

On January 1st: 20% more boxes which is 2125 x (1+ \(\frac{20}{100}\) ) = 2550 is the number of boxes

Step-by-step explanation:

Answer:

1.75 gallons of paint

Step-by-step explanation:

A student in the construction trades program has 4 1/2 gallons of paint

If the student uses 2.75 gallons in one room then the gallons of paint that are left can be calculated as follows

= 4 1/2 - 2.75

= 9/2 - 2.75

= 4.5 - 2.75

= 1.75

Hence 1.75 gallons of paint are left

The expected value of the bet is -15.693

According to the question we have been given that

If we draw a card with value 5 or less, we will be payed = 57

If failed to draws cards, we have to pay = 48

Now first we will find the probability of drawing cards with value less than or equal to 5.

Cards with value less than five are : 2,3,4,5

Total number of cards will be 16.

Probability = 16/52

Also number of cards with values greater than five is 36

Probability = 36/52

Thus the expected value of the bet will be

   = 57*(16/52) + (-48)*(36/52)    [ negative sign as we have to pay if we loose to draw the required card]

   = 17.538 - 33.231

   = -15.693

Hence the expected value is -15.693

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Answer:

x = 7

Step-by-step explanation:

The indicated angles are vertical and congruent, thus

14x + 2 = 13x + 9 ( subtract 13x from both sides )

x + 2 = 9 ( subtract 2 from both sides )

x = 7

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The probability that Ephraim gets the same number of heads that Keiko gets is (A)1/4.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Given that Keiko tosses one penny and Ephraim tosses two pennies.

We need to find  the probability Ephraim gets the same number of heads that Keiko gets;

Probability = 1/4 chance for Ephraim

Probability = 1/2 chance for Keiko

Hence, the probability that Ephraim gets the same number of heads that Keiko gets is (A)1/4.

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Answer:

\(\frac{3}{5}f = 4-2m\\ f= \frac{(4-2m) X 5}{3} \\f= \frac{20-10m}{3}\)

P.S. If u want a numerical value for 'f' , now put the value of 'm'

Let's denote the unknown quantity (amount in the account after the first week) as 'x'.

Given:

Account balance at the beginning of the month = $25

Amount spent on lunches in the first week = $10

1 - Equation: Account balance at the beginning - Amount spent = Amount in the account after the first week

x = $25 - $10

To solve the equation:

x = $15

Therefore, after the first week, there was $15 in Khalid's account.

2- Equation: Account balance after the deposit - Account balance before the deposit = Amount deposited

$30 - $15 = x

To solve the equation:

$15 = x

Therefore, Khalid deposited $15 into his account.

3- Equation: Account balance after the first transaction - Amount spent = Amount in the account after the second transaction

x = $30 - $45

To solve the equation:

x = -$15

The result is -$15, which implies that Khalid's account was overdrawn by $15 after spending $45 on lunches in the next week.

Option (c) 26.7% of the global oceans are Marine Protected Areas (MPAs). Marine Protected Areas (MPAs) are designated areas in the oceans that are set aside for conservation and management purposes.

They are intended to protect and preserve marine ecosystems, biodiversity, and various species. MPAs can have different levels of restrictions and regulations, depending on their specific objectives and conservation goals.

As of the current knowledge cutoff in September 2021, approximately 26.7% of the global oceans are designated as Marine Protected Areas. This means that a significant portion of the world's oceans has some form of protection and management in place to safeguard marine life and habitats. The establishment and expansion of MPAs have been driven by international agreements and initiatives, as well as national efforts by individual countries to conserve marine resources and promote sustainable practices.

It is worth noting that the percentage of MPAs in the global oceans may change over time as new areas are designated or existing MPAs are expanded. Therefore, it is important to refer to the most up-to-date data and reports from reputable sources to get the most accurate and current information on the extent of Marine Protected Areas worldwide.

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Answer: 702 cm

Step-by-step explanation:

We must first find the circumference of the circle using the circumference formula of

c=πd , or c=π2r

Substitute the given values into the formula

c=88π , or c=88*3.14

c=276.32

The circumference is 276.32 inches, but we need that measurement in centimeters.

In order to convert the inches to centimeters, we can multiply our circumference by the inch/centimeter scalar , 2.54 .

276.32 * 2.54

= 702 (rounded)

Answer:

x = 32

Step-by-step explanation:

An isosceles trapezium is one in which non-parallel sides have equal measure.

For an isosceles trapezoid, it is a rule that the two opposite angles equal 180°

∴ 2x + 20  3x = 180

solving the above equation:

2x + 3x = 180 - 20

5x = 160

x = 160 ÷ 5

x = 32

The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.

1. Identify the exact differential equation.

2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).

3. Multiply the integrating factor with the equation to make it exact.

4. Integrate both sides of the equation to obtain the general solution.

5. Check the solution by differentiating it to confirm that it satisfies the original equation.

6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.

The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.

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Answer:

(3x+2)(3x−2)

Step-by-step explanation:

The ordered pair from the scatter plot is given as follows:

(3, 14)

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

The point (Input, Output) is called an ordered pair.

From the text in this problem, the ordered pairs of the scatter plot are given as follows:

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} y=21\\ x=3 \end{cases} \\\\\\ 21=k(3)\implies \cfrac{21}{3}=k\implies 7=k\hspace{5em}\boxed{y=7x} \\\\\\ \textit{when x = -2, what is "y"?}\qquad y=7(-2)\implies y=-14\)

The best conclusion from this hypothesis test in the context of the problem is that we can reject the null hypothesis. The null hypothesis for this problem is that the errors is not greater than the population mean.

The null hypothesis for this problem is that the population mean number of errors for the ethanol group is not greater than the population mean number of errors for the placebo group.

In other words, the null hypothesis is: H₀: μe ≤ μp. The alternative hypothesis is that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group. In other words, the alternative hypothesis is: H₁: μe > μp.

The p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. In this case, the p-value is 0.0106, which is less than the significance level of 0.01. This means that the observed test statistic is significant at the 1% level, and we reject the null hypothesis.

Therefore, we conclude that there is evidence to suggest that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group.

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Given

To find the height of the tree.

Explanation:

It is given that,

From the figure, it is clear that ΔABC and ΔADE.

That implies,

Hence, the height of the tree is 100ft.

The value of P((A ∩ B) ∪ (C ∪ D ∩ E))' is approximately 0.1571. the probability that component A is not working given that the system works is approximately 0.001.

To calculate the values in Part 1 and Part 2, we'll use basic probability rules and formulas.

Given: P(A) = P(B) = 0.77, P(C) = P(D) = P(E) = 0.85

Part 1: We want to find the probability of the complement of the event (A ∩ B) ∪ (C ∪ D ∩ E), denoted as P((A ∩ B) ∪ (C ∪ D ∩ E))'.

Using De Morgan's law, the complement of a union is the intersection of complements:

P((A ∩ B) ∪ (C ∪ D ∩ E))' = P((A ∩ B)') ∩ (C ∪ D ∩ E)'

The complement of an intersection is the union of complements:

P((A ∩ B)') ∩ (C ∪ D ∩ E)' = (P(A') ∪ P(B')) ∩ (P(C') ∩ P(D') ∩ P(E'))

Substituting the given probabilities:

P((A ∩ B)') ∩ (C ∪ D ∩ E)' = (1 - P(A)) ∪ (1 - P(B)) ∩ (1 - P(C)) ∩ (1 - P(D)) ∩ (1 - P(E))

Calculating the values:

P(A') = 1 - P(A) = 1 - 0.77 = 0.23

P(B') = 1 - P(B) = 1 - 0.77 = 0.23

P(C') = 1 - P(C) = 1 - 0.85 = 0.15

P(D') = 1 - P(D) = 1 - 0.85 = 0.15

P(E') = 1 - P(E) = 1 - 0.85 = 0.15

Now, we calculate the final probability:

P((A ∩ B)') ∩ (C ∪ D ∩ E)' = (0.23 ∪ 0.23) ∩ (0.15 ∩ 0.15 ∩ 0.15)

                          = 0.23 ∩ 0.15 = 0.1571 (rounded to 4 decimal places)

Therefore, the value of P((A ∩ B) ∪ (C ∪ D ∩ E))' is approximately 0.1571.

Part 2: We want to find the probability that component A is not working given that the system works, denoted as P(A' | System Works).

Using the conditional probability formula:

P(A' | System Works) = P(A' ∩ System Works) / P(System Works)

To calculate the numerator:

P(A' ∩ System Works) = P(A' ∩ B' ∩ C' ∩ D' ∩ E')

                    = P(A') ∩ P(B') ∩ P(C') ∩ P(D') ∩ P(E')

                    = 0.23 ∩ 0.23 ∩ 0.15 ∩ 0.15 ∩ 0.15  = 0.0002634 (rounded to 7 decimal places)

To calculate the denominator:

P(System Works) = 1 - P(A' ∪ B' ∪ C' ∪ D' ∪ E')

= 1 - (P(A') ∪ P(B') ∪ P(C') ∪ P(D') ∪ P(E')) = 1 - (0.23 ∪ 0.23 ∪ 0.15 ∪ 0.15 ∪ 0.15) = 1 - 0.66 = 0.34

Now, we calculate the final probability:

P(A' | System Works) = P(A' ∩ System Works) / P(System Works)

= 0.0002634 / 0.34 = 0.0007735 (rounded to 7 decimal places)

Therefore, the probability that component A is not working given that the system works is approximately 0.001.

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The complete question is:<The reliability (probability of working) of each component is specified as follows and the components work or fail independently. P(A) = P(B) = 0.77 P(C) = P(D) = P(E) = 0.85 A B с DHE Part 1 What is the value of P((ANB) U(CODn E))' (Enter your answer with 3 decimal digits.) 0.1571 100% Part 2 What is the probability that the component A is not working given that the system works? (Enter your answer with 3 decimal digits.) Hint: Think of a conditional probability definition.>

Answer:

y = 3 + the square root of 2.

Step-by-step explanation:

message me if you have any other math questions

The expression that is an element of AxBxB is (1,2,3)

The given data is A= (a, b}, B = {1,2,3}

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.

\(& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\\)

\(& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\\)

\(& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}\)

The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.

The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.

Therefore, the expression that is an element of AxBxB is (1,2,3).

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Answer:

The new points after a rotation of 180 degrees is;

M’ = (-3, 1)

N’ = (-8,4)

O’ = (-6,6)

P’ = (-1 , 7)

Step-by-step explanation:

Given a point (x , y) and we rotate by 180 degrees , the new point will be (-x , -y)

So to the question;

M’ = (-3, 1)

N’ = (-8,4)

O’ = (-6,6)

P’ = (-1 , 7)

Step-by-step explanation:

Hello!

        Part A            

Peter can use the fact that 10% of 87 is 8.70 to find the amount he would save because 40% is just 4 times bigger than 10% so he can take 8.70 from to total of the coat 4 times to find out how much it cost.

        Part B            

Using the same method we know that 10% of 64 is 6.40 so we subtract that from the price of the coat 4 times to find out how much it cost

64 - 6.40 = 57.6

57.6 - 6.40 = 51.2

51.2 - 6.40 = 44.8

44.8 - 6.40 - 38.4

The price of the coat is $38.4

Hope this helps!

The area of triangle KLM is 3.5 square units.

The area of triangle KLM, we first need to determine the length of its base and height.

Since the triangle is drawn inside a rectangle, we can utilize the coordinates of its vertices to calculate these values.

The base of triangle KLM is determined by the distance between points K and L.

Using the distance formula, we can find the length of KL:

KL = √[(x2 - x1)² + (y2 - y1)²]

= √[(-5 - (-6))² + (-4 - (-5))²]

= √[1² + 1²]

= √2

Next, we need to determine the height of triangle KLM.

This can be calculated by finding the perpendicular distance between the line containing KL and point M.

To do this, we use the formula for the distance between a point and a line.

The equation of the line passing through points K and L can be found by using the slope-intercept form (y = mx + b):

m = (y2 - y1) / (x2 - x1)

= (-4 - (-5)) / (-5 - (-6))

= 1/1

= 1

Using point L, we can determine the equation of the line:

-4 = 1(-5) + b

-4 = -5 + b

b = -4 + 5

b = 1

So, the equation of the line KL is y = x + 1.

Now, we can find the perpendicular distance between line KL and point M. The formula for this distance is:

Distance = |ax + by + c| / √(a² + b²)

a = 1, b = -1 (negative reciprocal of the slope), and c = -1 (substituting the coordinates of point M into the equation of line KL). Calculating the distance:

Distance = |1(-8) + (-1)(-2) + (-1)| / √(1² + (-1)²)

= |-8 + 2 - 1| / √(1 + 1)

= |-7| / √2

= 7 / √2

Now that we have the base (KL = √2) and the height (7 / √2), we can calculate the area of triangle KLM:

Area = (1/2) × base × height

= (1/2) × √2 × (7 / √2)

= (1/2) × 7

= 7/2

= 3.5

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Answer:

the answer is 445,784

Step-by-step explanation:

The population y after x years of growth with the growth rate r and the original population C can be found using the exponential growth​ formula, . Substitute the decimal equivalent for the percent growth rate per year for r.