What conclusion can you make about quadrilateral ABCD? Why?

The interest rate is given as follows:

5%.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

The interest accrued is given as follows:

I(t) = Prt.

For each case, the interest accrued is given as follows:

The total interest was of 13,500, hence:

I(3) + I(5) = 13500.

Meaning that the interest rate is obtained as follows:

120,000r + 150,000r = 13500

r = 13500/270000

r = 0.05.

r = 5%.

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The function would be; [tex]f(x)= x^4 + 6x^3 + 12x^2 + 8x[/tex]

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Given that a polynominal has a zero at 4 (multiplicity 2) and 0 (multiplicity 1)

Required polynomial;

[tex]= x(x + 2)^3 \\= x(x^3 + 6x^2 + 12x + 8) \\= x^4 + 6x^3 + 12x^2 + 8x[/tex]

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The value of expression  (√19+√11i)(√19-√11i) is 30.

An expression is combination of variables, numbers and operators.

The given expression is (√19+√11i)(√19-√11i)

Square root of nineteen plus square root of eleven i times to the Square root of nineteen minus square root of eleven times i

We have an algebraic property

(a+b)(a-b)=a²-b²

Take a as √19 and b as √11 i

(√19+√11i)(√19-√11i)=(√19)²-(√11i)²

=19-11(-1)

=19+11

=30

Hence, the value of  (√19+√11i)(√19-√11i) is 30.

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A linear transformation is a function from one vector space to another that preserves each vector space's underlying (linear) structure. A linear transformation can also be referred to as a linear operator or map.

The correct answers are A, D, and E.

A linear transformation from ℝ3 to ℝ3 is invertible if and only if it is bijective, meaning it is both one-to-one and onto.

The following linear transformations are invertible:

A. Identity transformation: The identity transformation maps every vector to itself and is one-to-one, so it is invertible.

D. Rotation about the x-axis: A rotation about the x-axis is a bijective linear transformation that maps each point in ℝ3 to another point in ℝ3 in a one-to-one manner, so it is invertible.

E. Dilation by a factor of 6: A dilation by a factor of 6 scales every vector by 6, and the scaling factor is nonzero, so this transformation is bijective and invertible.

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The value of x that makes the expression undefined is given as follows:

x = -4/3.

The expression for this problem is presented as follows:

(x + 8)/(3x + 4).

As it is a fractional expression, it will be undefined when the denominator assumes a value of zero.

The denominator of a fraction is the value at the bottom, hence it is given as follows:

3x + 4.

Hence the value of x that makes the expression undefined is obtained as follows:

3x + 4 = 0

3x = -4

x = -4/3.

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Answer: -81x

Step-by-step explanation:

3x times -3= -9x

-9x times -3= 27x

27x times -3= -81x

The approximate value of [tex]$\int_{0}^{2} x^4 dx$[/tex] using the trapezoidal rule is 16.

Integral : [tex]$\int_{0}^{2} x^n dx$[/tex]

n = 4

Approximation Method : Trapezoidal Rule

The trapezoidal rule is a numerical integration technique used to approximate the definite integral of a function. It works by approximating the region under the curve of the function with a series of trapezoids, and calculating the area of those trapezoids to estimate the integral.

In the given problem, we have to approximate the definite integral of [tex]$x^4$[/tex] from 0 to 2. The trapezoidal rule for approximating a definite integral is given by

[tex]$\int_{a}^{b} f(x)dx \approx \frac{h}{2} \left( f(a) + f(b) + 2 \sum_{i=1}^{n-1} f(x_i) \right)$[/tex]

where [tex]$f(x)$[/tex]  is the function, [tex]$a$[/tex]  and [tex]$b$[/tex]  are the lower and upper limits of the integral, h is the width of each trapezoid, and $n$ is the number of trapezoids.

In our case, [tex]$f(x) = x^4$, $a = 0$, $b = 2$, $h = \frac{2 - 0}{2} = 1$[/tex] and n = 2.

Substituting these values into the formula, we get

[tex]$\int_{0}^{2} x^4 dx \approx \frac{1}{2} \left( 0 + 16 + 2 \left(x_1^4 + x_2^4 \right) \right)$[/tex]

where [tex]$x_1 = \frac{2 - 0}{2} = 1$ and $x_2 = \frac{2 + 0}{2} = 1$[/tex].

Substituting these values, we get

[tex]$\int_{0}^{2} x^4 dx \approx \frac{1}{2} \left( 0 + 16 + 2 \left(1^4 + 1^4 \right) \right) = 16$[/tex]So, the approximate value of [tex]$\int_{0}^{2} x^4 dx$[/tex] using the trapezoidal rule is 16.

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The solution is, The value of the 6 in 0.96 is 10 times the value of the 6 in 93.601.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

The number 42,316 is different from 61,432 because the digits are in different positions.

here, we have,

the 6s in 0.96 , is, the place value of 6 is 0.06 = 6/100

and in 93.601, the place value of 6 is 0.6 = 6/10

so, we get,

6/10 * 10 = 6/100

Hence, The solution is, The value of the 6 in 0.96 is 10 times the value of the 6 in 93.601.

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The models that represent the sum 1.2 + 0.3 are

Option 3 and Option 5

For Option 3:

The first square represents 1.2, with all 10 columns shaded in one color. The next two columns represent 0.3, shaded in a different color. The sum of 1.2 and 0.3 is 1.5, which is represented by the combination of the two squares.

For Option 5:

On the number line, the first arrow represents 1.2, starting from 0 and ending 2 marks past 1, which is equal to 1.2. The second arrow represents 0.3, starting from 2 marks past 1 and ending at 5 marks past 1, which is equal to 1.5. The sum of 1.2 and 0.3 is 1.5, which is represented by the end point of the second arrow on the number line.

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Answer: 6 (7+4n)

Step-by-step explanation: 6 is the gcf

For a matrix A, the determined matrices are

a) Matrix E₁ is [tex]E₁ = \begin{bmatrix} \frac{1}{2} & \frac{ - 3}{2} \\ -1 & 3\end{bmatrix} [/tex]

and it's inverse is equals to zero.

b) Matrix E₂ and it's inverse E₂⁻¹ are

[tex]E₂ = \begin{bmatrix} 1 & -3 \\ - 5& - 1\end{bmatrix} [/tex]

[tex]E₂⁻¹ = \begin{bmatrix} \frac{ - 1}{16} & \frac{3}{16} \\ \\ \frac{5}{16} & \frac{1}{16} \end{bmatrix}[/tex]

We have a matrix 2×2, A such that

[tex]A= \begin{bmatrix} 1 & -3 \\ -1 & 3\end{bmatrix}[/tex]

and we have to determine the matrix E₁ with their inverses. Also, matrix E₁ is generated by multiplying the first row of matrix A by 1/2. As we see elements of first row of matrix are 1 and -3.

[tex]E₁ = \begin{bmatrix} 1 \times \frac{1}{2} & -3 \times \frac{1}{2} \\ -1 & 3\end{bmatrix}

[/tex]

[tex]E₁ = \begin{bmatrix} \frac{1}{2} & \frac{ - 3}{2} \\ -1 & 3\end{bmatrix} [/tex]

The inverse of A is A⁻¹only when AA⁻¹= A⁻¹A = I.

Steps to determine the inverse of a 2x2 matrix:

Determinant of E₁ = ad - bc , here a =1/2 , b = -3/2 , c= -1 and d = 3. So, |E₁ | = 1/2× 3 - (-3/2)×(-1) = 3/2 - 3/2 = 0 . Thus, Inverse of E₁⁻¹ = 0 .

b) When we multiplies the second row of A by -4 then the elementary matrix E₂ is form. [tex]E₂ = \begin{bmatrix} 1 & -3 \\ -1 + (- 4)& 3 + ( - 4)\end{bmatrix}[/tex]

[tex]E₂ = \begin{bmatrix} 1 & -3 \\ - 5& - 1\end{bmatrix}[/tex]

Now, we have determine the Inverse of E₂. The determinant of |E₂| = -1× 1 - (-5)×(-3) = -1 - 15 = -16

So, inverse of matrix is , E₂⁻¹

[tex]E₂⁻¹ = \frac{1}{16}\begin{bmatrix} - 1 & - ( -3) \\ - ( - 5)& 1\end{bmatrix}[/tex]

[tex]E₂⁻¹ = \frac{1}{16} \begin{bmatrix} -1 & 3 \\ 5& 1\end{bmatrix}[/tex]

[tex]E₂⁻¹ = \begin{bmatrix} \frac{ - 1}{16} & \frac{3}{16} \\\\\frac{5}{16} & \frac{1}{16} \end{bmatrix}[/tex]

Hence, we get the required inverse.

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Complete question:

Let A be a 2 x 2 matrix. Given the following descriptions, A = [ 1 -3 ; -1 3]

determine the following elementary matrices and their inverses.

a. The elementary matrix E1 multiplies the first row of A by 1/2 .

b. The elementary matrix E2 adding the second row of A by -4

The amount of sugar that Jill sprinkles on the brownies will be 1/15 cusp.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Jill has 2/5 of a cup of powdered sugar. She sprinkles 1/6 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies.

Then the amount of sugar that Jill sprinkles on the brownies is given as,

⇒ (2/5) x (1/6)

⇒ 2 / 30

⇒ 1/15

The amount of sugar that Jill sprinkles on the brownies will be 1/15 cusp.

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A pie chart can be created by representing the relative frequency distribution data as a circle, where each interval is represented as a slice with the size proportional to its relative frequency.

Frequency distribution:

O<10: 0

10<20: 8

20<30: 4

30<40: 2

40<50: 1

50<60: 1

The histogram can be created by plotting the frequency distribution data on a bar graph where the x-axis represents the intervals, and the y-axis represents the frequency count.

The frequency polygon can be created by plotting the midpoints of the intervals on the x-axis and the frequency count on the y-axis, and connecting the plotted points with line segments.

The relative frequency distribution can be calculated by dividing the frequency count of each interval by the total number of observations and multiplying by 100.

O<10: 0/20 x 100 = 0%

10<20: 8/20 x 100 = 40%

20<30: 4/20 x 100 = 20%

30<40: 2/20 x 100 = 10%

40<50: 1/20 x 100 = 5%

50<60: 1/20 x 100 = 5%

The sizes of the slices can be labeled to represent the corresponding percent of total observations.

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Answer:

B.

Step-by-step explanation:

It is B because the height of the triangle is 9 and the height of B is 9. The bottom side of the triangle is 16 and the bottom of B is 16. The other labeled side is 10 and the side parallel to that side is 10 in figure B.

The values of x in the expression are -5, -9

From the question, we have the following parameters that can be used in our computation:

|x + 7| = 2

Remove the absolute bracket

So, we have the following representation

x + 7 = -2 or x + 7 = 2

Evaluate the like terms

x = -9 or x = -5

Hence, the values are -5 and -9

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Answer:

6

Step-by-step explanation:

The radius of the base of the cone is 3 units, since the diameter is 6 units. Let's call the height of the cone "h".

We can use the formula for the volume of a cone to find h:

V = (1/3)πr^2h

72π = (1/3)π(3^2)h

72π = (1/3)π(9)h

72π = 3πh

h = 72/3

h = 24

Now we can use the Pythagorean theorem to find the length of the segment:

a^2 + h^2 = c^2

a^2 + 24^2 = 6^2

a^2 = 36

a = 6

So the segment drawn from the apex to the edge of the circular base is 6 units, rounded to the nearest tenth.

The first system points are (2,-1) and the second system points are (-2,3).

The elementary row operations can be used to solve a system of equations in an easy way and used to find the rank of a matrix.

There are three types of elementary row operations:

1) Interchanging two rows.

Interchanging the first and second rows is given by R₁ ↔ R₂.

2) Multiplying/dividing a row by a scalar.

If the first row is multiplied by some scalar, with 3, it is measured as

R₁ → 3R₁.

3) Multiplying/dividing a row by some scalar and adding/subtracting to the corresponding elements of another row.

If the first row is multiplied by 3 and added to the second row, we can write it as R₁ → 3R₁ + R₂ (or) R₂ → R₂ + 3R₁.

Now by using the elementary row operation we can find the system of equations:

The given systems are:

2x₁+x₂=3                 2x₁+x₂=-1              

4x₁+3x₂=5               4x₁+3x₂=1

and the matrix is  

[tex]\left[\begin{array}{cccc}2&1|&3&-1\\4&3|&5&-1\\\end{array}\right][/tex]

Apply elementary row operation

R₂-2R₁

[tex]\left[\begin{array}{cccc}2&1|&3&-1\\4&3|&5&-1\\\end{array}\right]--- > \left[\begin{array}{cccc}2&1|&3&-1\\0&1|&-1&3\\\end{array}\right][/tex]

Now Apply R₁-R₂

[tex]\left[\begin{array}{cccc}2&0|&4&-4\\0&1|&-1&3\\\end{array}\right][/tex]

Apply R₁/2

[tex]\left[\begin{array}{cccc}1&0|&2&-2\\0&1|&-1&3\\\end{array}\right][/tex]

The two linear systems are

x₁+0=2        x₁+0=-2    

0+x₂=-1      0+x₂=3

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The per share dividend dollar amount paid out by Langs Inc. in 2020 is $0.50.

To calculate the per-share dividend dollar amount, we first need to calculate the total dividends paid out in 2020. We can find this by subtracting the retained earnings at the end of 2019 from the retained earnings at the end of 2020: $4,326,800 - $4,216,800 = $110,000. This $110,000 represents the total dividends paid out in 2020, since the company only uses retained earnings to pay dividends.

Next, we divide the total dividends by the number of shares outstanding at the end of 2020: $110,000 / 220,000 shares = $0.50. This is the per share dividend dollar amount, rounded to the nearest cent.

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Complete Question:

Given the following information for Langs, Inc., calculate per share dividend dollar amount (that is, the dividends per share), rounded to the nearest cent (i.e., $5.21843 = $5.22) that the company paid out in 2020:

The probability that point p is closer to point o than to any of the vertices is 0.3737.

The probability that point p is closer to point o than to any of the vertices can be found by considering the ratio of the area of the equilateral triangle xyz to the area of its circumscribed circle. This ratio is [tex]$\frac{3\sqrt{3}}{4\pi}$[/tex]. We can use this ratio to calculate the probability that point $p$ is closer to point o than to any of the vertices:

[tex]$P(op < xp, yp, zp) = \frac{3\sqrt{3}}{4\pi} = 0.3737$[/tex]

Therefore, the probability that point $p$ is closer to point $o$ than to any of the vertices is 0.3737.

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False. It is not reasonable to assume all groups have equal variances in this case.

The standard deviation is a measure of variability or spread of the data. If the standard deviations of different groups are significantly different, then it suggests that the spread of the data within each group is also different. When comparing multiple groups, equal variances are typically assumed so that a valid statistical test can be performed.

If the variances are unequal, then a different type of test, such as Welch's ANOVA, should be used. In this case, the large difference in the standard deviations of the four groups (4974, 6585, 3288, 5488) suggests that it is not reasonable to assume equal variances and a different test should be used.

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The volume of the given cylinder would be = 1.33mm³

The formula that can be used to calculate the volume of the cylinder = v = πr²h

Where,

π = 3.14

r= 0.5mm

h= 1.7 mm

V = 3.14×0.5²×1.7

V= 3.14× 0.25×1.7

V= 1.3345

V= 1.33mm³ ( to the nearest tenth)

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What does the problem asks for:

 --> mean and median

Let's calculate the mean:

 [tex]\text{Mean}=\dfrac{\text{sum of all the numbers}}{\text{number of numbers given}}[/tex]

   --> the sum of all the numbers = 21 + 40 + 48 + 26+ 32 + 31 = 198

   --> number of numbers given: 6

       ==> let's calculate

            [tex]\text{Mean}=\dfrac{198}{6} =33[/tex]

Let's calculate the median

 --> Median definition: middle number in an ordered sequence

   ==> let's order the sequence: 21, 26, 31, 32, 40, 48

      --> since there are an even number of numbers, there isn't an exact

            middle number

           --> thus, we must find the mean of the two numbers closest to the

               middle

                         [tex]\text{Median} = \dfrac{31+32}{2} =\dfrac{63}{2} =31.5[/tex]

Answer: 31.5

Step-by-step explanation:

21, 26, 31, 32, 40, 48

Median

31+32= 63

63÷2= 31.5

Mean

21+26+31+32+40+48=198

198÷6=33

By using trigonometry formula, The height of the hot-air balloon is 3,497.47 ft.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

Given that, the angle of depression from the hot-air balloon to the car is 32°.

the hypotenuse of balloon and car is 6600ft.

from the formula Sin A = height/ hypotenuse

⇒ Sin32° = height / 6600

⇒ height = 6600 * Sin32°

⇒ height = 6600 * 0.5299

⇒ height = 3,497.4671 ft

The height of the hot-air balloon is 3,497.47 ft.

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Answer: x = 3

Step-by-step explanation:

6x + 5 = 3x + 14

subtract 5 from both sides:

6x + 5 - 5 = 3x + 14 - 5

6x = 3x + 9

subtract 3x from both sides:

6x - 3x = 3x + 9 - 3x

3x = 9

divide both sides by 3:

3x/3 = 9/3

x = 3

Answer:

x=

Step-by-step explanation:

collect like terms

6x-3x =14x-5

3x=9

x=

a. The family pays $336.

b. The family's payment when the dental charge is $4500 is  $2375.

c. The model that relates payment and charges are,

250 + 0.2x, x < 1500 and 250 + 0.5x, x > 1500.

A function that is piecewise defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.

Piecewise definition is more of an expression of the function than it is a property of the function.

a. Determining the family's payment if the dental charge is $680.

$650 falls in the category of the first $250 paid by the family and the rest 80% paid by the insurance company.

So, $(680 - 250) = $430.

Therefore, The family pays 250 + 0.2x (when x < 1500).

= 250 + 0.2(430).

= 250 + 86.

= $336.

b. The family's payment when the dental charge is $4500 is,

= 4500 - 250.

= $4250.

So, 250 + 0.5(4250)   (when x > 1500).

= 250 + 2125.

= $2375.

c. The model that relates payment and charges are,

250 + 0.2x. (x < 1500) and 250 + 0.5x (x > 1500).

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Answer: 32/243

Step-by-step Explanation: multiply 16/81 by 2/3                                              

Answer:

a) 90

b) 46

c) 111

d) -45

Step-by-step explanation:

78 is greater than -12 by 90 (78 + (-12) = 66)

-23 is less than 23 by 46 (23 + (-23) = 0)

To give 105, 111 must be added to -6 (105 + (-6) = 99)

To give -30, -45 must be added to 15 (-30 + 15 = -15)

True, Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

What does a response variable in an experiment mean?

Response Continuum In an experimental investigation, this is the result that is assessed after manipulating the explanatory variable; it is also referred to as the dependent or outcome variable.

                                Its value is expected or its variation is explained by the explanatory variable.

What other name would you give the answer variable?

The term "dependent variable" is one more typical moniker for the response variable. The response variable is frequently referred to as just "the response" for short.

                        There are several more terms for the predictor variables, including "explanatory variables," "independent variables," "predictors," and "regressors."

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Negating a statement in terms of quantifiers means expressing the opposite of the statement using quantifiers such as "for all" (∀) and "there exists" (∃) instead of using negation symbols like "not". The key to negating a statement using quantifiers is to switch the quantifiers and negate the predicate.

For example, the negation of the statement "For all x, P(x)" is "There exists x such that not P(x)" because we have switched the universal quantifier "for all" to the existential quantifier "there exists" and negated the predicate P(x). On the other hand, the negation of the statement "There exists x such that P(x)" is "For all x, not P(x)" because we have switched the existential quantifier to the universal quantifier and negated the predicate.

Similarly, the negation of a statement involving "and" or "or" can be found by negating each component and switching the connective. For example, the negation of "P(x) and Q(x)" is "P(x) or not Q(x)" or "not P(x) or Q(x)".

In this context, the negation statements are:

a) There exists x such that x <= 1

b) There exists x such that x > 2

c) For all x, x < 4

d) For all x, x >= 0

e) There exists x such that x >= -1 and x <= 2

f) For all x, x >= 4 and x <= 7

The complete question is given below:

"

Express the negation of each of these statements in terms of quantifiers without using the negation symbol.

a) ∀x(x>1)

b) ∀x(x≤2)

c) ∃x(x≥4)

d) ∃x(x<0)

e) ∀x((x<−1)∨(x>2))

f) ∃x((x<4)∨(x>7))

"

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a) The combined number of $3 carwashes for cars, c, and $5 carwashes for trucks or SUVs, t, needed can be represented by the equation y = c + t.

b) If only 5 cars are washed, the number of trucks or SUVs needed to be washed to raise the full $915 is 180.

An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent.

Equations use the equation symbol (=) to show the equality of expressions.

The total amount needed for the new equipment = $915

The charge for a car wash per car = $3

The charge for cash wash per truck or SUV = $5

Let the number of cars = c

Let the number of trucks or SUVs = t

c + t = y... Equation 1

3c + 5t = 915... Equation 2

If the number of cars, c = 5

From equation 2:

3c + 5t = 915

3(5) + 5t = 915

15 + 5t = 915

5t = 900

t = 180

Thus, from equation 2, we can determine that if cars are 5, the trucks or SUVs must be 180 to meet the target.

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