Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-3,9)
(0,-3) (6,-6)

Answer:  \(\bold{G(t)=356e^{-0.59413t}}\)

Step-by-step explanation:

Use the decay formula: \(P=P_oe^{kt}\)   where

Given: P = 44.5, P₀ = 356, k = unknown, t = 210 minutes (3.5 hours)

\(44.5=356e^{k(3.5)}\\\\\\\dfrac{44.5}{356}=e^{3.5k}\\\\\\0.125=e^{3.5k}\\\\\\ln(0.125)=3.5k\\\\\\\dfrac{ln(0.125)}{3.5}=k\\\\\\-0.59413=k\)

Input P₀ = 356 and k = -0.59413 into the decay formula

              \(\large\boxed{P=356e^{-0.59413t}}\)

To solve this equation, you will need to isolate the variable h on one side of the equation. To do this, you can start by adding 2 and y to both sides of the equation to get rid of the constants on the right side:

√3h² - 2 - y = 0

√3h² - 2 + 2 + y = 0 + 2 + y

√3h² = 2 + y

Next, you can square both sides of the equation to eliminate the square root on the left side:

(√3h²)² = (2 + y)²

3h² = 4 + 4y + y²

Then, you can rearrange the terms on the right side to get the equation in standard form:

3h² = 4 + 4y + y²

3h² = (4 + y)(1 + y)

Finally, you can divide both sides of the equation by 3 to isolate the variable h:

h² = (4 + y)/3

Since y is given as 5, you can substitute this value into the equation to find the value of h:

h² = (4 + 5)/3

h² = 9/3

h = √(9/3)

Since h is less than 0, the value of h must be negative.

Therefore, the value of h is -√(9/3).

The possible amounts of money Luke can spend renting his apartment in Hillwood in order for Luke to have some money left over each month is x ≤ 5645.

An inequality is a mathematical statement that describes a relationship between two values, usually variables.

Luke's monthly income is $7645 and his other monthly expenses are $2000. Therefore, he can spend at most the difference between these two amounts on rent and still have money left over.

Let's use x to represent the cost of the rent in Hillwood.

So the inequality is:

x ≤ 7645 - 2000

Simplifying,

x ≤ 5645

Therefore, the possible amounts of money Luke can spend renting his apartment in Hillwood in order for Luke to have some money left over each month is x ≤ 5645.

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The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a speed of 61 kilometers per hour.

Convert the speed into a kilometer per minute. Then we have

Speed = 61 / 60

Speed = 1.01667 kilometers per minute

Then the number of kilometers will the car travel in 20 minutes will be given as,

1.01667 = d / 20

d = 1.01667 x 20

d = 20.33 kilometers

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

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Answer:

x-2

hope it helps

The required values are;Lower limit = 54.7 Upper limit = 61.3 Mean = 58

The given data points for the sample are,Sample size (n) = 31 Sample mean (x) = 58 Sample standard deviation (s) = 6.5To find the 99% confidence interval for the population mean (μ), we need to use the formula given below;99% Confidence interval for the population mean (μ) = ( x - z (α/2) (s/√n) , x + z (α/2) (s/√n) )

Where,z (α/2) = The z-value from the standard normal distribution table for the level of confidence α/2, which is 0.5% or 0.005. (From this, we can get the value of z (α/2) as 2.576)

Let us plug the given values in the above formula.99% Confidence interval for the population mean (μ) = ( 58 - 2.576 (6.5/√31) , 58 + 2.576 (6.5/√31) )99%

Confidence interval for the population mean (μ) = ( 54.7, 61.3 )Thus, the 99% confidence interval for the population mean (μ) is (54.7, 61.3).The mean of the population (μ) is (54.7 + 61.3) / 2 = 58.Lower limit: 54.7Upper limit: 61.3Mean: 58

Therefore, the required values are;Lower limit = 54.7Upper limit = 61.3Mean = 58

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Answer:

3

Step-by-step explanation:

if you put six beside the unknown side then you will see that x =3

Answer:

16

Step-by-step explanation:

93:6=15.5 As the box can't be half so 16 boxes. In 15 she will pack in each 6 books and in other box 3 books

Answer:

She will need 16 boxes with space for 3 more books

Step-by-step explanation:

All of the statements are false except statement d. Counter-examples are given for each false statement each and explained below.

a) The statement is incorrect because there may exist elements in set B that are not included in the union of sets A and B.

Counter-example: if we take A as {1} and B as {2}, we can see that B is not part of the union of A and B, denoted as A ∪ B.

(b) The statement is incorrect because the union of sets A and B can include elements that are not in set A.

Counterexample: Let A = {1} and B = {2}. Then (A ∪ B) = {1, 2}, and {1, 2} is not a subset of A since it contains an element (2) that is not in A.

(c) The statement is false because removing set B from the union of sets A and B may result in elements that are not present in set A.

Counterexample: Let A = {1} and B = {2}. Then (A ∪ B) - B = {1} - {2} = {1}, which is not equal to A.

(d) The statement is true because removing the set A from the set B minus A will result in set A itself.

(e) The statement is false because there can be cases where sets A, B, and C have overlapping elements, indicating that A is not disjoint from C.

Counterexample: Let A = {1}, B = {2}, and C = {1, 2}. Then A + B = {1, 2} and B + C = {1, 2}, but A ∩ C = {1} is not an empty set, so A and C are not disjoint.

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Answer:

A

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

\(log_{8}\) (x + 9) + 3 = 3 ( subtract 3 from both sides )

\(log_{8}\) (x + 9) = 0 , then

x + 9 = \(8^{0}\) = 1 ( subtract 9 from both sides )

x = - 8

The function (g+h)(n-4) is the sum of the function g(n-4) and h(n-4) will be written as (g+h)(n-4) = n² - 7n + 9.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

g(n) = n² + 4n

h(n) = - 3n - 3

The function (g+h)(n) is calculated as,

(g+h)(n) = g(n) + h(n)

(g+h)(n) = n² + 4n - 3n - 3

(g+h)(n) = n² + n - 3

Put n = n - 4, then we have

(g+h)(n-4) = (n - 4)² + (n - 4) - 3

(g+h)(n-4) = n² + 16 - 8n + n - 4 - 3

(g+h)(n-4) = n² - 7n + 9

The function (g+h)(n-4) will be (g+h)(n-4) = n² - 7n + 9.

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Answer: The dimensions are 10 2/3 feet by 5 1/3 feet (Ten and two-thirds and five and one third).

Step-by-step explanation: This is our system of equations:y=Lengthx=Widthy=2x2x+2y=32We can substitute the y value in the second equation by plugging in the first equation: 2x+2(2x)=322x+4x=326x=32x=16/3 or 5 1/3We can plug in this x value into the first equation to find the y value:y=2(16/3)y=32/3 or 10 2/3

(a)

Let X be the percentage of students who passed in both Nepali and English. Then the percentage of students who failed in at least one of the subjects would be:

Percentage of students who failed in Nepali = 30%

Percentage of students who failed in English = 27%

Percentage of students who failed in both subjects = 15%

Therefore, the percentage of students who failed in at least one of the subjects would be:

30% + 27% - 15% = 42%

This means that the percentage of students who passed in both subjects would be:

100% - 42% = 58%

Therefore, 58% of students passed in both Nepali and English.

    ____________

   /            \

  /              \

 /      NE        \

/                  \

/____________________\

       EN

NE: Nepali

EN: English

The left circle represents Nepali, the right circle represents English, and the overlap represents students who failed in both subjects. The percentage values can be added to each section of the Venn diagram to make it clearer.

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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Check the picture below.

so the height of the pole is "p", and the angle of depression to the foot of the pole is really "44 + a".

so let's use the 44° angle first

\(\tan(44^o )=\cfrac{\stackrel{opposite}{30-p}}{\underset{adjacent}{25}}\implies 25\tan(44^o)=30-p\implies 25\tan(44^o)+p=30 \\\\\\ p=30-25\tan(44^o)\implies \boxed{p\approx 9}\)

now, let's use the red triangle, namely the angle "44 + a"

\(\tan(44+a)=\cfrac{\stackrel{opposite}{30}}{\underset{adjacent}{25}}\implies \tan(44+a)=\cfrac{6}{5} \\\\\\ 44+a=\tan^{-1}\left( \cfrac{6}{5} \right) \implies 44+a\approx 50^o\)

Make sure your calculator is in Degree mode.

No, {{a, d, e}, {b, c}, {d, f}} is not a partition of {a, b, c, d, e, f} because it does not cover all the elements of the set, and some elements appear in multiple subsets.

We have,

A partition of a set S is a collection of non-empty subsets of S such that every element in S belongs to exactly one subset in the collection and every element in the collection is distinct.

In this case, the element "d" appears in both {{a, d, e}} and {{d, f}}, violating the condition of belonging to exactly one subset, and the element "c" is not included in any of the subsets, violating the condition of covering all elements in the set.

Thus,

No, {{a, d, e}, {b, c}, {d, f}} is not a partition of {a, b, c, d, e, f} because it does not cover all the elements of the set, and some elements appear in multiple subsets.

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Hey there! I'm happy to help!

To solve by substitution, rearrange one of the equations for one of the variables.

3x+2y=11

Subtract 2y from both sides.

3x=11-2y

Divide both sides by 3.

x=11/3-2/3y

Now we plug this value of x into the second equation to solve for y.

2(11/3-2/3y)-2y=14

We use distributive property to undo the parentheses.

22/3-4/3y-2y=14

We combine like terms.

22/3-10/3y=14

We subtract 22/3 from both sides.

-10/3y=20/3

Divide both sides by -10/3.

y=-2

We plug this value into one of the equations to solve for x.

3x+2(-2)=11

3x-4=11

Add 4 to both sides.

3x=15

Divide both sides by 3.

x=5

So, the solution is x=5 and y=-2 or (5,-2).

Have a wonderful day! :D

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

U and V are mutually exclusive events. P(U) = 0.26; P(V) = 0.37. So,

a. P(U AND V) = 0

b. P(U|V) = 0

c. P(U OR V) = P(U) + P(V)

U and V cannot happen at the same time since they are mutually exclusive events. Therefore, the probability of their intersection, P(U AND V), is equal to 0.

Comparably, the conditional probability P(U|V) denotes the likelihood that event U will take place in the event that event V has already happened. U, however, is not possible if V has already happened because U and V are mutually exclusive. Consequently, P(U|V) likewise equals 0.

To find the probability of the union of U and V, P(U OR V), we add the individual probabilities of U and V because they are mutually exclusive. Therefore, P(U OR V) = P(U) + P(V) = 0.26 + 0.37 = 0.63.

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Answer:

22.96 cm

Step-by-step explanation:

Let the point of contact of the tangent with the circle be R.

Let the centre of the circle be O.

We are told that from Point P, the length of the tangent is 24 cm.

Thus, PR = 24 cm

Now, the radius will be perpendicular to the tangent at the point of contact with the circle.

Thus, ORP will form a right angle triangle where ∠R = 90°

Since radius = 7 cm, we can use pythagoras theorem to find OP which is the distance of P from the centre.

Thus;

OP = √(24² - 7²)

OP = √527

OP = 22.96 cm

The difference quotient for the function f(x) = 69x + 2 is a constant value of 69. This means that the average rate of change of the function over any interval is always 69.

To evaluate and simplify the difference quotient for the function f(x) = 69x + 2, we first need to understand what the difference quotient represents. The difference quotient is a mathematical expression that measures the average rate of change of a function over a given interval. It is defined as:

[f(x + h) - f(x)] / h,

where h represents a small change in the x-values.

Let's proceed with calculating the difference quotient for the given function:

[f(x + h) - f(x)] / h

= [(69(x + h) + 2) - (69x + 2)] / h

= [69x + 69h + 2 - 69x - 2] / h

= (69h) / h

= 69.

To simplify the expression, we used the distributive property to expand the function f(x + h). Then, we simplified the numerator by combining like terms. The constant terms 2 and -2 canceled each other out. The h term in the numerator can be factored out, which allows us to cancel it out with the h term in the denominator. Finally, we are left with the simplified expression of 69.

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Answer:

x= 251

Step-by-step explanation:

300x= 190x + 27,610

300x-190x= 27,610

110x= 27610

x= 27610/110

x= 251

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The equation Monique, Clarence, Jose and Quincy linear graph is y = (-1/2)x, y = (1/2)x, y = 1.5x + 1 and y = -1.5x - 1 respectively

An equation is an expression that shows the relationship between two or more numbers and variables.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Monique graph passes through (0, 0) and (2, -1). Hence:

y - 0 = [(-1 - 0)/(2 - 0)](x - 0)

y = (-1/2)x

Clarence graph passes through (0, 0) and (2, 1). Hence:

y - 0 = [(1 - 0)/(2 - 0)](x - 0)

y = (1/2)x

Jose graph passes through (0, 1) and (-2, -2). Hence:

y - 1 = [(-2 - 1)/(-2 - 0)](x - 0)

y = 1.5x + 1

Quincy graph passes through (0, -1) and (-2, 2). Hence:

y - (-1) = [(2 - (-1))/(-2 - 0)](x - 0)

y = -1.5x - 1

The equation Monique graph is y = (-1/2)x

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The number of ways can joey select 1 that will run on his operating system and 1 that will not = 42ways

Given that,

Joey finds video games that he would like to have = 13

Will run on his operating system = 7

Will not run on his operating system = 6

Number of ways can joey select 1 that will run on his operating system and 1 that will not,

So,

We can write,

Joey Will run on his operating system = 7 = \(7C_{1}\)

Joey Will not run on his operating system = 6 = \(6C_{1}\)

Then,

\(nC_{k}\) = n ! / k !(n-k) !

\(7C_{1}\) = 7 ! / 1  ! ( 7-1) !

\(7C_{1}\) = 7 ! / 1 ! 6 !

\(7C_{1}\) = \(\frac{1*2*3*4*5*6*7}{1*2*3*4*5*6}\)

\(7C_{1}\) = 7

Then also,

\(6C_{1}\) = 6

So,

7 * 6 = 42

Therefore,

The number of ways can joey select 1 that will run on his operating system and 1 that will not = 42ways

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Answer:

In the beginning f(x)=3x+2

Step-by-step explanation:

Because if you look at function examples, the f(x) always goes in the beginning. :)

The equation is converted into f ( x ) = 3x + 2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be y = 3x + 2

Now , the equation is of the form f ( x ) = 3x + 2

where the domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

Therefore , y = f ( x )

Hence , the equation is f ( x ) = 3x + 2

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